2tan (problem 3.3.2)

Time bar (total: 18.6s)

analyze62.0ms (0.3%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%50.6%49.4%0%0%0%0
0%0%50.6%49.4%0%0%0%1
0%0%50.6%49.4%0%0%0%2
0%0%25.3%74.7%0%0%0%3
0%0%25.3%74.7%0%0%0%4
0%0%19%81%0%0%0%5
0%0%15.8%84.2%0%0%0%6
0%0%11.1%88.9%0%0%0%7
0%0%8.7%91.3%0%0%0%8
0%0%5.9%94.1%0%0%0%9
0%0%4.5%95.5%0%0%0%10
0%0%3.1%96.9%0%0%0%11
0%0%2.7%97.3%0%0%0%12
Compiler

Compiled 28 to 18 computations (35.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 33.0ms
ival-tan: 8.0ms (23.9% of total)
...c/correct-round.rkt:119:19: 8.0ms (23.9% of total)
ival-mult: 3.0ms (9% of total)
ival-and: 3.0ms (9% of total)
ival-<=: 3.0ms (9% of total)
ival-add: 2.0ms (6% of total)
ival-fabs: 2.0ms (6% of total)
ival-sub: 2.0ms (6% of total)
ival-<: 2.0ms (6% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

sample7.8s (41.9%)

Results
4.2s26519×0precondition
1.2s4505×1valid
717.0ms3751×0valid
Precisions
Click to see histograms. Total time spent on operations: 4.5s
...c/correct-round.rkt:119:19: 1.5s (33.9% of total)
ival-tan: 651.0ms (14.5% of total)
ival-mult: 396.0ms (8.8% of total)
ival-add: 364.0ms (8.1% of total)
ival-sub: 310.0ms (6.9% of total)
ival-fabs: 305.0ms (6.8% of total)
ival-<: 277.0ms (6.2% of total)
ival-<=: 260.0ms (5.8% of total)
ival-and: 189.0ms (4.2% of total)
backward-pass: 162.0ms (3.6% of total)
const: 48.0ms (1.1% of total)
Bogosity

preprocess49.0ms (0.3%)

Algorithm
2×egg-herbie
Rules
376×fnmadd-define
344×fnmsub-define
344×fmsub-define
320×sum3-define
308×fmm-def
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02146
14342
29442
319842
450742
591742
6128542
7154842
8168442
9171142
067
197
2147
3217
4317
5637
61227
72107
82957
94017
104797
114857
04857
Stop Event
1×iter limit
1×saturated
1×saturated
Calls
Call 1
Inputs
(- (tan (+ x eps)) (tan x))
Outputs
(- (tan (+ x eps)) (tan x))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Call 2
Inputs
(- (tan (+ x eps)) (tan x))
(- (tan (+ (neg x) eps)) (tan (neg x)))
(- (tan (+ x (neg eps))) (tan x))
(neg (- (tan (+ (neg x) eps)) (tan (neg x))))
(neg (- (tan (+ x (neg eps))) (tan x)))
(- (tan (+ eps x)) (tan eps))
Outputs
(- (tan (+ x eps)) (tan x))
(- (tan (+ (neg x) eps)) (tan (neg x)))
(+ (tan x) (tan (- eps x)))
(- (tan (+ x (neg eps))) (tan x))
(- (tan (- x eps)) (tan x))
(neg (- (tan (+ (neg x) eps)) (tan (neg x))))
(- (tan (- x eps)) (tan x))
(neg (- (tan (+ x (neg eps))) (tan x)))
(+ (tan x) (tan (- eps x)))
(- (tan (+ eps x)) (tan eps))
(- (tan (+ x eps)) (tan eps))

explain134.0ms (0.7%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2156(-5.873652495899441e-120 1.6599195452804653e-122)2(-3.0317712604842883e-143 3.680345174714297e-145)(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
20-0-(tan.f64 (+.f64 x eps))
00-0-x
00-0-(+.f64 x eps)
00-0-(tan.f64 x)
00-0-eps
Results
64.0ms264×1valid
20.0ms242×0valid
1.0ms4×2valid
1.0ms2×3valid
Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 33.0ms
ival-tan: 12.0ms (36.7% of total)
ival-add: 9.0ms (27.5% of total)
backward-pass: 7.0ms (21.4% of total)
ival-sub: 4.0ms (12.2% of total)
const: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler

Compiled 9 to 6 computations (33.3% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶65.0%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify13.0ms (0.1%)

Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(tan.f64 x)
✓cost-diff0
(+.f64 x eps)
✓cost-diff0
(tan.f64 (+.f64 x eps))
✓cost-diff0
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Rules
124×fnmadd-define
122×sum3-define
80×fma-lowering-fma.f32
80×fnmsub-define
80×fmsub-define
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0618
1918
21418
32118
43118
56318
612218
721018
829518
940118
1047918
1148518
048518
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(- (tan (+ x eps)) (tan x))
(tan (+ x eps))
(+ x eps)
x
eps
(tan x)
Outputs
(- (tan (+ x eps)) (tan x))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(tan (+ x eps))
(tan.f64 (+.f64 x eps))
(+ x eps)
(+.f64 x eps)
x
eps
(tan x)
(tan.f64 x)

localize64.0ms (0.3%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(+.f64 x eps)
✓accuracy100.0%
(tan.f64 x)
✓accuracy99.8%
(tan.f64 (+.f64 x eps))
✓accuracy65.2%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
44.0ms132×1valid
10.0ms121×0valid
1.0ms2×2valid
1.0ms1×3valid
Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 21.0ms
ival-tan: 13.0ms (61.3% of total)
ival-add: 3.0ms (14.1% of total)
backward-pass: 3.0ms (14.1% of total)
ival-sub: 2.0ms (9.4% of total)
const: 0.0ms (0% of total)

series11.0ms (0.1%)

Counts
4 → 84
Calls
Call 1
Inputs
#<alt (- (tan (+ x eps)) (tan x))>
#<alt (tan (+ x eps))>
#<alt (+ x eps)>
#<alt (tan x)>
Outputs
#<alt (/ (sin eps) (cos eps))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))>
#<alt (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (/ (sin eps) (cos eps))>
#<alt (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))>
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))>
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))>
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))>
#<alt (/ (sin x) (cos x))>
#<alt (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))>
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))>
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))>
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
Calls

21 calls:

TimeVariablePointExpression
2.0ms
eps
@0
(- (tan (+ x eps)) (tan x))
2.0ms
eps
@inf
(- (tan (+ x eps)) (tan x))
1.0ms
x
@inf
(- (tan (+ x eps)) (tan x))
1.0ms
x
@0
(- (tan (+ x eps)) (tan x))
1.0ms
x
@-inf
(- (tan (+ x eps)) (tan x))

rewrite352.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
3856×*-lowering-*.f32
3856×*-lowering-*.f64
3276×/-lowering-/.f32
3276×/-lowering-/.f64
1940×fma-lowering-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0616
14616
242316
3659116
0869816
Stop Event
1×iter limit
1×node limit
Counts
4 → 239
Calls
Call 1
Inputs
(- (tan (+ x eps)) (tan x))
(tan (+ x eps))
(+ x eps)
(tan x)
Outputs
(+.f64 (tan.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(+.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x) (tan.f64 x)))
(+.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (tan.f64 (+.f64 x eps)))
(+.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))))
(+.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 #s(literal 0 binary64) (-.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))))
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))))
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
(-.f64 (/.f64 (*.f64 (cos.f64 x) (sin.f64 (+.f64 x eps))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) (/.f64 (*.f64 (sin.f64 x) (cos.f64 (+.f64 x eps))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
(-.f64 (/.f64 (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (*.f64 (cos.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (*.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (*.f64 (cos.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))))
(-.f64 (+.f64 (tan.f64 (+.f64 x eps)) #s(literal 0 binary64)) (tan.f64 x))
(fma.f64 (tan.f64 (+.f64 x eps)) (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))))
(fma.f64 (tan.f64 (+.f64 x eps)) (/.f64 (tan.f64 (+.f64 x eps)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))
(fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(fma.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(fma.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))))
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(/.f64 (*.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))))))
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x x) (*.f64 eps eps)))))
(/.f64 (*.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (+.f64 (*.f64 x x) (*.f64 eps eps)))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal -1 binary64))
(*.f64 (+.f64 x eps) (*.f64 (-.f64 x eps) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))
(*.f64 (+.f64 x eps) (/.f64 (-.f64 x eps) (-.f64 x eps)))
(*.f64 #s(literal 1 binary64) (+.f64 x eps))
(*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))
(*.f64 (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))) (*.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))))
(*.f64 (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))) (/.f64 (+.f64 x eps) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))
(*.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))
(*.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))))
(*.f64 (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 x eps))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (-.f64 (*.f64 x x) (*.f64 eps eps)))
(*.f64 (-.f64 (*.f64 eps eps) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x)))
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 (*.f64 x x) (*.f64 eps eps))) (+.f64 x eps))
(*.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (-.f64 eps x)) (*.f64 eps (*.f64 (-.f64 eps x) (*.f64 eps (-.f64 eps x))))))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (-.f64 eps x)) (-.f64 (*.f64 eps (-.f64 eps x)) (*.f64 x x)))))
(*.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (*.f64 (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (+.f64 (*.f64 x x) (*.f64 eps (+.f64 x eps))))
(tan.f64 x)
(neg.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(/.f64 (sin.f64 x) (cos.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(/.f64 (*.f64 (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x))) (neg.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal -1 binary64))
(*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 #s(literal 1 binary64) (tan.f64 x))
(*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

simplify330.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
3412×*-lowering-*.f32
3412×*-lowering-*.f64
2990×fma-lowering-fma.f32
2990×fma-lowering-fma.f64
2652×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01571381
14941186
218961117
377621117
086191117
Stop Event
1×iter limit
1×node limit
Counts
84 → 84
Calls
Call 1
Inputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin eps) (cos eps))
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin x) (cos x))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
x
(* x (+ 1 (* 1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
Outputs
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (*.f64 x (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 x (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (*.f64 (sin.f64 eps) x) (cos.f64 eps))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 x (+.f64 (*.f64 x (-.f64 (*.f64 (sin.f64 eps) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (cos.f64 eps))) (*.f64 x (+.f64 (-.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1/6 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (-.f64 (-.f64 (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1/6 binary64)) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (*.f64 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1/6 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (cos.f64 x)) (*.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))))
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (*.f64 (sin.f64 eps) x) (cos.f64 eps))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))))
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (*.f64 x (-.f64 (*.f64 (sin.f64 eps) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (cos.f64 eps))) (*.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (-.f64 #s(literal 1/6 binary64) (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))))))))))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1/6 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
eps
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
x
(* x (+ 1 (/ eps x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
(* x (+ 1 (/ eps x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
(* x (+ 1 (/ eps x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
x
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
eps
(* eps (+ 1 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
(* eps (+ 1 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
(* eps (+ 1 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
x
(* x (+ 1 (* 1/3 (pow x 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64)))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 x #s(literal 2/15 binary64)))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))

eval40.0ms (0.2%)

Compiler

Compiled 8811 to 993 computations (88.7% saved)

prune55.0ms (0.3%)

Pruning

19 alts after pruning (18 fresh and 1 done)

PrunedKeptTotal
New30518323
Fresh000
Picked011
Done000
Total30519324
Accuracy
100.0%
Counts
324 → 19
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶65.2%
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
▶65.0%
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
35.6%
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
63.8%
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (sin.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (cos.f64 x)))
▶98.3%
(/.f64 (sin.f64 eps) (cos.f64 eps))
65.0%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
65.2%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
65.2%
(-.f64 (*.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
65.0%
(-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps))) (tan.f64 x))
64.1%
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64))))))))))
64.0%
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 x #s(literal 2/15 binary64))))))))
63.8%
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64))))))
✓65.0%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶63.5%
(-.f64 (tan.f64 (+.f64 x eps)) x)
98.6%
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 x (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (*.f64 (sin.f64 eps) x) (cos.f64 eps))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))))
98.8%
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
99.3%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
99.7%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1/6 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
▶99.8%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (-.f64 (-.f64 (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1/6 binary64)) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (*.f64 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1/6 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (cos.f64 x)) (*.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
Compiler

Compiled 1189 to 526 computations (55.8% saved)

simplify279.0ms (1.5%)

Algorithm
1×egg-herbie
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 (tan.f64 x) (tan.f64 eps))
✓cost-diff0
(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
✓cost-diff6528
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
✓cost-diff0
(+.f64 x eps)
✓cost-diff0
(cos.f64 (+.f64 x eps))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
✓cost-diff6528
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
✓cost-diff0
(cos.f64 eps)
✓cost-diff0
(sin.f64 eps)
✓cost-diff0
(/.f64 (sin.f64 eps) (cos.f64 eps))
✓cost-diff0
(+.f64 x eps)
✓cost-diff0
(tan.f64 (+.f64 x eps))
✓cost-diff0
(-.f64 (tan.f64 (+.f64 x eps)) x)
✓cost-diff130688
(*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (-.f64 (-.f64 (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1/6 binary64)) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (*.f64 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1/6 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (cos.f64 x)) (*.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64))))))))
✓cost-diff143360
(+.f64 (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (-.f64 (-.f64 (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1/6 binary64)) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (*.f64 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1/6 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (cos.f64 x)) (*.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
✓cost-diff149952
(+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (-.f64 (-.f64 (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1/6 binary64)) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (*.f64 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1/6 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (cos.f64 x)) (*.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
✓cost-diff149952
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (-.f64 (-.f64 (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1/6 binary64)) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (*.f64 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1/6 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (cos.f64 x)) (*.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
Rules
3310×--lowering--.f32
3310×--lowering--.f64
2838×*-lowering-*.f32
2838×*-lowering-*.f64
2378×+-lowering-+.f64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0621745
11911270
27321058
33705919
08254919
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
eps
(+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
1
(+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))))
(+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))
(* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(/ (sin x) (cos x))
(sin x)
x
(cos x)
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(pow (sin x) 2)
2
(pow (cos x) 2)
(* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))
(- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))
(- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)))))
(+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6)
(* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))
-1/6
(+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))
-1/2
(+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)))
(/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))
(* -1/2 (pow (sin x) 2))
(/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))
(* 1/6 (pow (sin x) 2))
1/6
(* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))
(+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))
(/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x))
(* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
(+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))
(+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)))
(+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)
-1/3
(- (tan (+ x eps)) x)
(tan (+ x eps))
(+ x eps)
x
eps
(/ (sin eps) (cos eps))
(sin eps)
eps
(cos eps)
(+ (* (/ 1 (cos (+ x eps))) (sin (+ x eps))) (- 0 (tan x)))
(/ 1 (cos (+ x eps)))
1
(cos (+ x eps))
(+ x eps)
x
eps
(sin (+ x eps))
(- 0 (tan x))
0
(tan x)
(+ (* (/ 1 (- 1 (* (tan x) (tan eps)))) (+ (tan x) (tan eps))) (- 0 (tan x)))
(/ 1 (- 1 (* (tan x) (tan eps))))
1
(- 1 (* (tan x) (tan eps)))
(* (tan x) (tan eps))
(tan x)
x
(tan eps)
eps
(+ (tan x) (tan eps))
(- 0 (tan x))
0
Outputs
(* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 (*.f64 (-.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))))) (*.f64 eps eps)) (*.f64 (+.f64 (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
eps
(+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+.f64 (*.f64 (-.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))))) (*.f64 eps eps)) (*.f64 (+.f64 (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
1
#s(literal 1 binary64)
(+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+.f64 (*.f64 (-.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))))) (*.f64 eps eps)) (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps)) (*.f64 eps (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))))
(* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))))
(*.f64 eps (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (*.f64 eps (-.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))))))))
(+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))
(+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (*.f64 eps (-.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))))))))
(* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(sin x)
(sin.f64 x)
x
(cos x)
(cos.f64 x)
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow (sin x) 2)
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
2
#s(literal 2 binary64)
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))
(*.f64 eps (-.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))))))
(- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))
(-.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))))))
(- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)))))
(-.f64 #s(literal 0 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6)
(+.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/6 binary64))
(* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64)))
-1/6
#s(literal -1/6 binary64)
(+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))
(+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
-1/2
#s(literal -1/2 binary64)
(+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* -1/2 (pow (sin x) 2))
(*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))
(/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* 1/6 (pow (sin x) 2))
(*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)
(* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))
(*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))))
(+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))
(+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64))) (*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))))
(/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x))
(/.f64 (*.f64 (sin.f64 x) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (cos.f64 x))
(* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
(*.f64 (sin.f64 x) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)))
(+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64)) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 5/6 binary64))))
(- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(-.f64 #s(literal 1/6 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))))
(* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)
(*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) #s(literal -1/3 binary64))
-1/3
#s(literal -1/3 binary64)
(- (tan (+ x eps)) x)
(-.f64 (tan.f64 (+.f64 eps x)) x)
(tan (+ x eps))
(tan.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(sin eps)
(sin.f64 eps)
eps
(cos eps)
(cos.f64 eps)
(+ (* (/ 1 (cos (+ x eps))) (sin (+ x eps))) (- 0 (tan x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(/ 1 (cos (+ x eps)))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x)))
1
#s(literal 1 binary64)
(cos (+ x eps))
(cos.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(sin (+ x eps))
(sin.f64 (+.f64 eps x))
(- 0 (tan x))
(-.f64 #s(literal 0 binary64) (tan.f64 x))
0
#s(literal 0 binary64)
(tan x)
(tan.f64 x)
(+ (* (/ 1 (- 1 (* (tan x) (tan eps)))) (+ (tan x) (tan eps))) (- 0 (tan x)))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(/ 1 (- 1 (* (tan x) (tan eps))))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
1
#s(literal 1 binary64)
(- 1 (* (tan x) (tan eps)))
(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))
(* (tan x) (tan eps))
(*.f64 (tan.f64 x) (tan.f64 eps))
(tan x)
(tan.f64 x)
x
(tan eps)
(tan.f64 eps)
eps
(+ (tan x) (tan eps))
(+.f64 (tan.f64 x) (tan.f64 eps))
(- 0 (tan x))
(-.f64 #s(literal 0 binary64) (tan.f64 x))
0
#s(literal 0 binary64)

localize902.0ms (4.9%)

Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 (tan.f64 x) (tan.f64 eps))
✓accuracy100.0%
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
✓accuracy100.0%
(+.f64 (tan.f64 x) (tan.f64 eps))
✓accuracy92.8%
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
✓accuracy100.0%
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
✓accuracy99.9%
(sin.f64 (+.f64 x eps))
✓accuracy99.8%
(cos.f64 (+.f64 x eps))
✓accuracy92.7%
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
✓accuracy100.0%
(sin.f64 eps)
✓accuracy100.0%
(cos.f64 eps)
✓accuracy100.0%
(/.f64 (sin.f64 eps) (cos.f64 eps))
✓accuracy100.0%
(+.f64 x eps)
✓accuracy99.8%
(tan.f64 (+.f64 x eps))
✓accuracy93.1%
(-.f64 (tan.f64 (+.f64 x eps)) x)
✓accuracy99.7%
(*.f64 eps (-.f64 (-.f64 (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1/6 binary64)) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (*.f64 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1/6 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (cos.f64 x)) (*.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64))))))
✓accuracy99.7%
(+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
✓accuracy99.3%
(-.f64 (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1/6 binary64)) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
✓accuracy99.2%
(+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1/6 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
Results
571.0ms130×5exit
93.0ms111×0valid
23.0ms5×3valid
16.0ms4×2valid
11.0ms6×1valid
Compiler

Compiled 1797 to 61 computations (96.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 330.0ms
backward-pass: 134.0ms (40.6% of total)
ival-mult: 34.0ms (10.3% of total)
ival-add: 28.0ms (8.5% of total)
ival-sub: 25.0ms (7.6% of total)
...c/correct-round.rkt:119:19: 25.0ms (7.6% of total)
ival-div: 22.0ms (6.7% of total)
ival-tan: 18.0ms (5.5% of total)
compiled-spec: 14.0ms (4.2% of total)
ival-sin: 11.0ms (3.3% of total)
ival-cos: 9.0ms (2.7% of total)
ival-pow: 9.0ms (2.7% of total)
const: 1.0ms (0.3% of total)

series100.0ms (0.5%)

Counts
23 → 480
Calls
Call 1
Inputs
#<alt (* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))))>
#<alt (- (tan (+ x eps)) x)>
#<alt (tan (+ x eps))>
#<alt (+ x eps)>
#<alt (/ (sin eps) (cos eps))>
#<alt (sin eps)>
#<alt (cos eps)>
#<alt (+ (* (/ 1 (cos (+ x eps))) (sin (+ x eps))) (- 0 (tan x)))>
#<alt (/ 1 (cos (+ x eps)))>
#<alt (cos (+ x eps))>
#<alt (+ (* (/ 1 (- 1 (* (tan x) (tan eps)))) (+ (tan x) (tan eps))) (- 0 (tan x)))>
#<alt (/ 1 (- 1 (* (tan x) (tan eps))))>
#<alt (- 1 (* (tan x) (tan eps)))>
#<alt (* (tan x) (tan eps))>
#<alt (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))>
#<alt (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)))))>
#<alt (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)))>
#<alt (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))>
#<alt (sin (+ x eps))>
#<alt (+ (tan x) (tan eps))>
Outputs
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* -1 (* (pow eps 4) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))>
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* -1 (* (pow eps 4) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))>
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
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#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))>
#<alt (* 1/3 (pow eps 2))>
#<alt (+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))>
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#<alt (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))>
#<alt (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))>
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#<alt (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))>
#<alt (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))>
#<alt (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))>
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#<alt (sin eps)>
#<alt (sin eps)>
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#<alt (cos eps)>
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#<alt (cos eps)>
#<alt (cos eps)>
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#<alt (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))>
#<alt (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))>
#<alt (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))>
#<alt (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))>
#<alt (* -1 (* (pow eps 2) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* -1 (* (pow eps 2) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* 1/3 eps)>
#<alt (+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x)))>
#<alt (+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x)))))>
#<alt (+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x)))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (cos eps)))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin x)>
#<alt (+ (sin x) (* eps (cos x)))>
#<alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))>
#<alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (/ (sin eps) (cos eps))>
#<alt (+ x (/ (sin eps) (cos eps)))>
#<alt (+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps)))>
#<alt (+ (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (sin eps) (cos eps)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (/ (sin x) (cos x))>
#<alt (+ eps (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
Calls

120 calls:

TimeVariablePointExpression
17.0ms
eps
@0
(+ (* (/ 1 (- 1 (* (tan x) (tan eps)))) (+ (tan x) (tan eps))) (- 0 (tan x)))
11.0ms
x
@inf
(* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
7.0ms
x
@-inf
(* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
5.0ms
eps
@-inf
(* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
4.0ms
eps
@0
(* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))

rewrite325.0ms (1.8%)

Algorithm
1×batch-egg-rewrite
Rules
3800×*-lowering-*.f32
3800×*-lowering-*.f64
2764×/-lowering-/.f32
2764×/-lowering-/.f64
1796×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
062913
1505410
26725404
08745404
Stop Event
1×iter limit
1×node limit
Counts
23 → 494
Calls
Call 1
Inputs
(* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))))
(- (tan (+ x eps)) x)
(tan (+ x eps))
(+ x eps)
(/ (sin eps) (cos eps))
(sin eps)
(cos eps)
(+ (* (/ 1 (cos (+ x eps))) (sin (+ x eps))) (- 0 (tan x)))
(/ 1 (cos (+ x eps)))
(cos (+ x eps))
(+ (* (/ 1 (- 1 (* (tan x) (tan eps)))) (+ (tan x) (tan eps))) (- 0 (tan x)))
(/ 1 (- 1 (* (tan x) (tan eps))))
(- 1 (* (tan x) (tan eps)))
(* (tan x) (tan eps))
(+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))
(- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)))))
(+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)))
(* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))
(sin (+ x eps))
(+ (tan x) (tan eps))
Outputs
(+.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) (*.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))) eps) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps))
(fma.f64 eps #s(literal 1 binary64) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))))
(fma.f64 #s(literal 1 binary64) eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))))
(/.f64 (+.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) #s(literal 3 binary64))) (+.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))))) (*.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))))))))
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(/.f64 (*.f64 (-.f64 (pow.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))) #s(literal 2 binary64))) eps) (+.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))
(*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))
(*.f64 (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))) eps)
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps)))
(+.f64 (*.f64 #s(literal 1 binary64) (*.f64 (sin.f64 x) (cos.f64 eps))) (*.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (sin.f64 eps))))
(+.f64 (*.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 1 binary64)) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 1 binary64)))
(sin.f64 (+.f64 eps x))
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps)))
(/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps))) (-.f64 (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (*.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))))))
(/.f64 (-.f64 (*.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps))) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))))
(*.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))
(*.f64 (sin.f64 (+.f64 eps x)) #s(literal 1 binary64))
(+.f64 (tan.f64 x) (tan.f64 eps))
(+.f64 (tan.f64 x) (*.f64 (tan.f64 eps) #s(literal 1 binary64)))
(+.f64 (tan.f64 eps) (tan.f64 x))
(+.f64 (*.f64 (tan.f64 eps) #s(literal 1 binary64)) (tan.f64 x))
(-.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (-.f64 (tan.f64 x) (tan.f64 eps))))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x)) (tan.f64 eps))
(fma.f64 (sin.f64 eps) (/.f64 #s(literal 1 binary64) (cos.f64 eps)) (tan.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)))) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))))
(/.f64 (sin.f64 (+.f64 eps x)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/.f64 (+.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)))))
(/.f64 (+.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (tan.f64 eps)))))
(/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (-.f64 (tan.f64 x) (tan.f64 eps)))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 eps))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 eps))))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (cos.f64 eps)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (sin.f64 eps))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (cos.f64 eps)))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 eps))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (-.f64 #s(literal 0 binary64) (sin.f64 eps)))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 eps))))
(/.f64 (+.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (tan.f64 eps))) (*.f64 (cos.f64 x) #s(literal 1 binary64))) (*.f64 (cos.f64 x) (/.f64 #s(literal 1 binary64) (tan.f64 eps))))
(/.f64 (+.f64 (*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (cos.f64 eps))) (*.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps)))) (*.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) (cos.f64 eps))))
(/.f64 (+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 eps))) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 eps))))
(/.f64 (+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (cos.f64 eps)) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (sin.f64 eps))) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (cos.f64 eps)))
(/.f64 (+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 eps))) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (-.f64 #s(literal 0 binary64) (sin.f64 eps)))) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 eps))))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 eps)) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 eps)) (sin.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 eps)) (cos.f64 x)))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (sin.f64 x)))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(/.f64 (+.f64 (*.f64 (sin.f64 eps) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (cos.f64 eps) #s(literal 1 binary64))) (*.f64 (cos.f64 eps) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(/.f64 (+.f64 (*.f64 (sin.f64 eps) (-.f64 #s(literal 0 binary64) (cos.f64 x))) (*.f64 (cos.f64 eps) (-.f64 #s(literal 0 binary64) (sin.f64 x)))) (*.f64 (cos.f64 eps) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(/.f64 (+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 eps)) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(/.f64 (+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) (cos.f64 x)) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 eps)) (sin.f64 x))) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 eps)) (cos.f64 x)))
(/.f64 (+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) (-.f64 #s(literal 0 binary64) (cos.f64 x))) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 eps)) (-.f64 #s(literal 0 binary64) (sin.f64 x)))) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 eps)) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)))))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (-.f64 (tan.f64 x) (tan.f64 eps)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (neg.f64 (-.f64 (tan.f64 x) (tan.f64 eps))))
(/.f64 (-.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 (tan.f64 eps) (tan.f64 x)))
(*.f64 #s(literal 1 binary64) (+.f64 (tan.f64 x) (tan.f64 eps)))
(*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 1 binary64))
(*.f64 (+.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x))))))
(*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 x) (tan.f64 eps))))

simplify396.0ms (2.1%)

Algorithm
1×egg-herbie
Rules
5418×+-lowering-+.f64
5418×+-lowering-+.f32
4382×*-lowering-*.f32
4382×*-lowering-*.f64
1912×fma-lowering-fma.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
078416834
1276614333
0840714333
Stop Event
1×iter limit
1×node limit
Counts
480 → 480
Calls
Call 1
Inputs
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* -1 (* (pow eps 4) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2)))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* -1 (* (pow eps 4) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 4) (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))))) eps))))
(* (pow eps 4) (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps))) eps))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* -1 (* (pow eps 3) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* -1 (* (pow eps 3) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(+ 1 (* 1/3 (pow eps 2)))
(+ 1 (+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2))))))))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))))
(+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))
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(/ (pow (sin x) 2) (pow (cos x) 2))
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(* 1/3 (pow eps 2))
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(/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
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(/ 1 (cos (+ eps x)))
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(cos eps)
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(cos (+ eps x))
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(cos x)
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(cos (+ eps x))
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(/ (sin eps) (cos eps))
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(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* -1 (/ (pow (sin eps) 4) (pow (cos eps) 4))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
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(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* -1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/3 (/ (sin x) (cos x))) (+ (* -1/3 (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
1
(+ 1 (/ (* x (sin eps)) (cos eps)))
(+ 1 (* x (- (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)) (* -1 (/ (sin eps) (cos eps))))))
(+ 1 (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/3 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* -1 (/ (sin eps) (cos eps))))))
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
1
(+ 1 (/ (* eps (sin x)) (cos x)))
(+ 1 (* eps (- (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)) (* -1 (/ (sin x) (cos x))))))
(+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))) (* -1/3 (/ (sin x) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (sin x) (cos x))))))
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
1
(+ 1 (* -1 (/ (* x (sin eps)) (cos eps))))
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(+ 1 (* x (- (* (pow x 2) (- (* -2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))))
(- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))
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(- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))
(- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))
1
(+ 1 (* -1 (/ (* eps (sin x)) (cos x))))
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(- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))
(- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))
(/ (* x (sin eps)) (cos eps))
(* x (+ (* 1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps))))
(* x (+ (* (pow x 2) (+ (* 2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps))))
(* x (+ (* (pow x 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* 17/315 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 2/15 (/ (sin eps) (cos eps))))))) (/ (sin eps) (cos eps))))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* eps (sin x)) (cos x))
(* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x))))
(* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x))))
(* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x))))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
-1/3
(- (* -4/3 (pow x 2)) 1/3)
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3)
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
1/3
(+ 1/3 (* 4/3 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* -1/3 (pow x 2))
(* (pow x 2) (- (* -2/9 (pow x 2)) 1/3))
(* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/945 (pow x 2)) 17/135)) 2/9)) 1/3))
(+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* -1 (* (pow eps 2) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* -1 (* (pow eps 2) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* 1/3 eps)
(+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x)))
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x)))))
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(/ (sin eps) (cos eps))
(+ x (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps)))
(+ (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (sin eps) (cos eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(/ (sin x) (cos x))
(+ eps (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
Outputs
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 (*.f64 eps (sin.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 (*.f64 eps (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (+.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (cos.f64 x)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))))))
(* -1 (* (pow eps 4) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(*.f64 (+.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (cos.f64 x)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (*.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 4 binary64))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* eps (+ 1 (* 1/3 (pow eps 2))))
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(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
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(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* -1 (* (pow eps 3) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* -1 (* (pow eps 2) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* 1/3 eps)
(*.f64 eps #s(literal 1/3 binary64))
(+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x)))
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(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x)))))
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(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x)))))))
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(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))
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(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x)))

eval182.0ms (1%)

Compiler

Compiled 66670 to 3959 computations (94.1% saved)

prune123.0ms (0.7%)

Pruning

23 alts after pruning (20 fresh and 3 done)

PrunedKeptTotal
New1034141048
Fresh7613
Picked325
Done011
Total1044231067
Accuracy
100.0%
Counts
1067 → 23
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓65.2%
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
64.8%
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 eps (/.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
✓65.0%
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
▶23.6%
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
35.6%
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
65.0%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
65.2%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
▶65.0%
(-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps))) (tan.f64 x))
64.1%
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64))))))))))
✓65.0%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
65.2%
(+.f64 (/.f64 (tan.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (/.f64 (tan.f64 eps) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (-.f64 #s(literal 0 binary64) (tan.f64 x))))
▶99.8%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)
98.6%
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))
99.4%
(*.f64 eps (+.f64 (*.f64 eps (*.f64 #s(literal 1 binary64) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
▶98.6%
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))))
98.8%
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
99.0%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
98.9%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
99.5%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps #s(literal 1/3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
98.3%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))
98.3%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/15 binary64))))))
98.3%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
▶98.3%
eps
Compiler

Compiled 1191 to 663 computations (44.3% saved)

simplify211.0ms (1.1%)

Algorithm
1×egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
✓cost-diff128
(*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))
✓cost-diff128
(sin.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))))
✓cost-diff6656
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
✓cost-diff0
(cos.f64 (+.f64 x eps))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
✓cost-diff128
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)))
✓cost-diff128
(-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps))) (tan.f64 x))
✓cost-diff256
(*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))
✓cost-diff256
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))
✓cost-diff256
(+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))
✓cost-diff256
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))))
✓cost-diff45440
(*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))
✓cost-diff45440
(+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))
✓cost-diff45440
(*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))))
✓cost-diff45440
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)
Rules
2474×--lowering--.f32
2474×--lowering--.f64
2416×*-lowering-*.f32
2416×*-lowering-*.f64
2312×+-lowering-+.f64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0671011
1222880
2810812
33542754
47716754
08116754
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
(* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))))
eps
(+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))
(pow (tan x) 2)
(tan x)
x
2
(* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))
(+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))
(+ (tan x) (pow (tan x) 3))
(pow (tan x) 3)
3
(* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))
(- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))
(+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3)))
(* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))
(+ 1 (pow (tan x) 2))
1
(- 1/3 (* (pow (tan x) 2) -1/3))
1/3
(* (pow (tan x) 2) -1/3)
-1/3
(* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))
(+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))
(* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x))
(+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))))
-1/2
(+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))
(- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))
1/6
(* (+ (tan x) (pow (tan x) 3)) -1/3)
eps
(* eps (+ (* 1/3 (* eps eps)) (+ 1 (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))))))
eps
(+ (* 1/3 (* eps eps)) (+ 1 (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3)))))))
(* 1/3 (* eps eps))
1/3
(* eps eps)
(+ 1 (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))))
1
(* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3)))))
x
(+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))
(* x (+ 1 (* (* eps eps) 4/3)))
(+ 1 (* (* eps eps) 4/3))
(* (* eps eps) 4/3)
4/3
(* eps (+ 1 (* (* eps eps) 2/3)))
(+ 1 (* (* eps eps) 2/3))
(* (* eps eps) 2/3)
2/3
(- (* (/ 1 (cos (+ x eps))) (sin (+ x eps))) (tan x))
(* (/ 1 (cos (+ x eps))) (sin (+ x eps)))
(/ 1 (cos (+ x eps)))
1
(cos (+ x eps))
(+ x eps)
x
eps
(sin (+ x eps))
(tan x)
(+ (* (/ 1 (cos (+ x eps))) (sin (* (+ (* x (* x x)) (* eps (* eps eps))) (/ 1 (+ (* x x) (* eps (- eps x))))))) (- 0 (tan x)))
(/ 1 (cos (+ x eps)))
1
(cos (+ x eps))
(+ x eps)
x
eps
(sin (* (+ (* x (* x x)) (* eps (* eps eps))) (/ 1 (+ (* x x) (* eps (- eps x))))))
(* (+ (* x (* x x)) (* eps (* eps eps))) (/ 1 (+ (* x x) (* eps (- eps x)))))
(+ (* x (* x x)) (* eps (* eps eps)))
(* x (* x x))
(* x x)
(* eps (* eps eps))
(* eps eps)
(/ 1 (+ (* x x) (* eps (- eps x))))
(+ (* x x) (* eps (- eps x)))
(* eps (- eps x))
(- eps x)
(- 0 (tan x))
0
(tan x)
Outputs
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
(*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 (*.f64 eps (+.f64 (*.f64 eps (*.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64)))))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1/3 binary64) (*.f64 (tan.f64 x) (*.f64 eps #s(literal -1/3 binary64))))))) (*.f64 (+.f64 (*.f64 eps (tan.f64 x)) #s(literal 1 binary64)) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))))
(* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))))
(*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (*.f64 eps (+.f64 (*.f64 eps (*.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64)))))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1/3 binary64) (*.f64 (tan.f64 x) (*.f64 eps #s(literal -1/3 binary64))))))) (*.f64 (+.f64 (*.f64 eps (tan.f64 x)) #s(literal 1 binary64)) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))
eps
(+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))
(+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (*.f64 eps (+.f64 (*.f64 eps (*.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64)))))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1/3 binary64) (*.f64 (tan.f64 x) (*.f64 eps #s(literal -1/3 binary64))))))) (*.f64 (+.f64 (*.f64 eps (tan.f64 x)) #s(literal 1 binary64)) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))
(pow (tan x) 2)
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(tan x)
(tan.f64 x)
x
2
#s(literal 2 binary64)
(* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))
(*.f64 eps (+.f64 (*.f64 eps (+.f64 (*.f64 eps (*.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64)))))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1/3 binary64) (*.f64 (tan.f64 x) (*.f64 eps #s(literal -1/3 binary64))))))) (*.f64 (+.f64 (*.f64 eps (tan.f64 x)) #s(literal 1 binary64)) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))
(+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))
(+.f64 (*.f64 eps (+.f64 (*.f64 eps (*.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64)))))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1/3 binary64) (*.f64 (tan.f64 x) (*.f64 eps #s(literal -1/3 binary64))))))) (*.f64 (+.f64 (*.f64 eps (tan.f64 x)) #s(literal 1 binary64)) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))
(+ (tan x) (pow (tan x) 3))
(+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))
(pow (tan x) 3)
(pow.f64 (tan.f64 x) #s(literal 3 binary64))
3
#s(literal 3 binary64)
(* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))
(*.f64 eps (+.f64 #s(literal 1/3 binary64) (-.f64 (*.f64 (tan.f64 x) (-.f64 (*.f64 (tan.f64 x) #s(literal 1/3 binary64)) (*.f64 eps (-.f64 (-.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (-.f64 (*.f64 eps #s(literal -1/3 binary64)) (tan.f64 x))))))
(- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))
(+.f64 #s(literal 1/3 binary64) (-.f64 (*.f64 (tan.f64 x) (-.f64 (*.f64 (tan.f64 x) #s(literal 1/3 binary64)) (*.f64 eps (-.f64 (-.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (-.f64 (*.f64 eps #s(literal -1/3 binary64)) (tan.f64 x)))))
(+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3)))
(+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64))))
(* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))
(+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))
(+ 1 (pow (tan x) 2))
(+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(- 1/3 (* (pow (tan x) 2) -1/3))
(+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)))
1/3
#s(literal 1/3 binary64)
(* (pow (tan x) 2) -1/3)
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))
-1/3
#s(literal -1/3 binary64)
(* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))
(*.f64 eps (*.f64 (tan.f64 x) (+.f64 (-.f64 (-.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64))) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))))
(+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))
(*.f64 (tan.f64 x) (+.f64 (-.f64 (-.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64))) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))))
(* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x))
(*.f64 (tan.f64 x) (-.f64 (-.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64))))
(+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))))
(-.f64 (-.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64)))
-1/2
#s(literal -1/2 binary64)
(+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))
(+.f64 #s(literal 1/6 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))
(- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))
(-.f64 (-.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
1/6
#s(literal 1/6 binary64)
(* (+ (tan x) (pow (tan x) 3)) -1/3)
(*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))
eps
(* eps (+ (* 1/3 (* eps eps)) (+ 1 (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 x (+.f64 eps (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps #s(literal 2/3 binary64))))))))))
eps
(+ (* 1/3 (* eps eps)) (+ 1 (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3)))))))
(+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 x (+.f64 x (+.f64 eps (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps #s(literal 2/3 binary64)))))))))
(* 1/3 (* eps eps))
(*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))
1/3
#s(literal 1/3 binary64)
(* eps eps)
(*.f64 eps eps)
(+ 1 (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x (+.f64 eps (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps #s(literal 2/3 binary64))))))))
1
#s(literal 1 binary64)
(* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3)))))
(*.f64 x (+.f64 x (+.f64 eps (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps #s(literal 2/3 binary64)))))))
x
(+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))
(+.f64 x (+.f64 eps (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x #s(literal 4/3 binary64)) (*.f64 eps #s(literal 2/3 binary64))))))
(* x (+ 1 (* (* eps eps) 4/3)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))
(+ 1 (* (* eps eps) 4/3))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))
(* (* eps eps) 4/3)
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
4/3
#s(literal 4/3 binary64)
(* eps (+ 1 (* (* eps eps) 2/3)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal 2/3 binary64)))))
(+ 1 (* (* eps eps) 2/3))
(+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal 2/3 binary64))))
(* (* eps eps) 2/3)
(*.f64 eps (*.f64 eps #s(literal 2/3 binary64)))
2/3
#s(literal 2/3 binary64)
(- (* (/ 1 (cos (+ x eps))) (sin (+ x eps))) (tan x))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(* (/ 1 (cos (+ x eps))) (sin (+ x eps)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ 1 (cos (+ x eps)))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x)))
1
#s(literal 1 binary64)
(cos (+ x eps))
(cos.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(sin (+ x eps))
(sin.f64 (+.f64 eps x))
(tan x)
(tan.f64 x)
(+ (* (/ 1 (cos (+ x eps))) (sin (* (+ (* x (* x x)) (* eps (* eps eps))) (/ 1 (+ (* x x) (* eps (- eps x))))))) (- 0 (tan x)))
(-.f64 (/.f64 (sin.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(/ 1 (cos (+ x eps)))
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x)))
1
#s(literal 1 binary64)
(cos (+ x eps))
(cos.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(sin (* (+ (* x (* x x)) (* eps (* eps eps))) (/ 1 (+ (* x x) (* eps (- eps x))))))
(sin.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))
(* (+ (* x (* x x)) (* eps (* eps eps))) (/ 1 (+ (* x x) (* eps (- eps x)))))
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))
(+ (* x (* x x)) (* eps (* eps eps)))
(+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))
(* x (* x x))
(*.f64 x (*.f64 x x))
(* x x)
(*.f64 x x)
(* eps (* eps eps))
(*.f64 eps (*.f64 eps eps))
(* eps eps)
(*.f64 eps eps)
(/ 1 (+ (* x x) (* eps (- eps x))))
(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))
(+ (* x x) (* eps (- eps x)))
(+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))
(* eps (- eps x))
(*.f64 eps (-.f64 eps x))
(- eps x)
(-.f64 eps x)
(- 0 (tan x))
(-.f64 #s(literal 0 binary64) (tan.f64 x))
0
#s(literal 0 binary64)
(tan x)
(tan.f64 x)

localize974.0ms (5.2%)

Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓accuracy99.9%
(sin.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))))
✓accuracy99.8%
(cos.f64 (+.f64 x eps))
✓accuracy93.3%
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
✓accuracy71.0%
(*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))
✓accuracy100.0%
(/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
✓accuracy99.9%
(sin.f64 (+.f64 x eps))
✓accuracy99.8%
(cos.f64 (+.f64 x eps))
✓accuracy93.4%
(-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps))) (tan.f64 x))
✓accuracy99.9%
(*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))
✓accuracy99.9%
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
✓accuracy99.9%
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
✓accuracy99.9%
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
✓accuracy99.8%
(*.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (tan.f64 x))
✓accuracy99.8%
(*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))
✓accuracy99.7%
(*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))
✓accuracy99.3%
(+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))))
Results
659.0ms140×5exit
120.0ms111×0valid
8.0ms3×1valid
6.0ms2×2valid
Compiler

Compiled 1115 to 67 computations (94% saved)

Precisions
Click to see histograms. Total time spent on operations: 358.0ms
backward-pass: 153.0ms (42.7% of total)
ival-mult: 67.0ms (18.7% of total)
ival-add: 34.0ms (9.5% of total)
...c/correct-round.rkt:119:19: 33.0ms (9.2% of total)
ival-sub: 16.0ms (4.5% of total)
ival-pow: 15.0ms (4.2% of total)
ival-sin: 13.0ms (3.6% of total)
compiled-spec: 8.0ms (2.2% of total)
ival-tan: 6.0ms (1.7% of total)
ival-div: 6.0ms (1.7% of total)
ival-cos: 5.0ms (1.4% of total)
const: 2.0ms (0.6% of total)

series96.0ms (0.5%)

Counts
23 → 480
Calls
Call 1
Inputs
#<alt (+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)>
#<alt (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))))>
#<alt (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))>
#<alt (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))>
#<alt (* eps (+ (* 1/3 (* eps eps)) (+ 1 (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))))))>
#<alt (+ (* 1/3 (* eps eps)) (+ 1 (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3)))))))>
#<alt (+ 1 (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))))>
#<alt (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3)))))>
#<alt (- (* (/ 1 (cos (+ x eps))) (sin (+ x eps))) (tan x))>
#<alt (* (/ 1 (cos (+ x eps))) (sin (+ x eps)))>
#<alt (/ 1 (cos (+ x eps)))>
#<alt (cos (+ x eps))>
#<alt (+ (* (/ 1 (cos (+ x eps))) (sin (* (+ (* x (* x x)) (* eps (* eps eps))) (/ 1 (+ (* x x) (* eps (- eps x))))))) (- 0 (tan x)))>
#<alt (sin (* (+ (* x (* x x)) (* eps (* eps eps))) (/ 1 (+ (* x x) (* eps (- eps x))))))>
#<alt (* (+ (* x (* x x)) (* eps (* eps eps))) (/ 1 (+ (* x x) (* eps (- eps x)))))>
#<alt (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))))>
#<alt (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))>
#<alt (* (+ (tan x) (pow (tan x) 3)) -1/3)>
#<alt (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x))>
#<alt (* 1/3 (* eps eps))>
#<alt (* (* eps eps) 2/3)>
#<alt (* (* eps eps) 4/3)>
#<alt (sin (+ x eps))>
Outputs
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))>
#<alt (* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))>
#<alt (* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))>
#<alt (* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))>
#<alt (* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))>
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps))))>
#<alt (* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps))))>
#<alt (+ eps (* 1/3 (pow eps 3)))>
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))))>
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))>
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))>
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))>
#<alt (* eps (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))>
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))>
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps))))>
#<alt (* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps))))>
#<alt (* 1/3 (pow eps 3))>
#<alt (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))>
#<alt (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))>
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#<alt (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
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#<alt (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
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#<alt (- (/ (sin (/ (- (pow x 3) (* -1 (pow eps 3))) (+ (* -1 (* eps x)) (+ (pow eps 2) (pow x 2))))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
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#<alt (sin eps)>
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#<alt eps>
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#<alt x>
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#<alt x>
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#<alt eps>
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#<alt -1/3>
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#<alt (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* 1/3 eps)>
#<alt (+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x)))>
#<alt (+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x)))))>
#<alt (+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x)))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))>
#<alt (* -1/3 x)>
#<alt (* x (- (* -4/9 (pow x 2)) 1/3))>
#<alt (* x (- (* (pow x 2) (- (* -17/45 (pow x 2)) 4/9)) 1/3))>
#<alt (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/945 (pow x 2)) 17/45)) 4/9)) 1/3))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 x)>
#<alt (* x (- (* -13/9 (pow x 2)) 1/3))>
#<alt (* x (- (* (pow x 2) (- (* -107/45 (pow x 2)) 13/9)) 1/3))>
#<alt (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2516/945 (pow x 2)) 107/45)) 13/9)) 1/3))>
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))>
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))>
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))>
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))>
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))>
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))>
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))>
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (* 4/3 (pow eps 2))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (cos eps)))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin x)>
#<alt (+ (sin x) (* eps (cos x)))>
#<alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))>
#<alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
Calls

120 calls:

TimeVariablePointExpression
21.0ms
x
@0
(* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x))
14.0ms
x
@inf
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
5.0ms
x
@-inf
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
4.0ms
x
@0
(* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3)))))
3.0ms
eps
@0
(* eps (+ (* 1/3 (* eps eps)) (+ 1 (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))))))

rewrite329.0ms (1.8%)

Algorithm
1×batch-egg-rewrite
Rules
2980×*-lowering-*.f32
2980×*-lowering-*.f64
1904×+-lowering-+.f64
1904×+-lowering-+.f32
1716×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
067588
1526478
25874473
08008473
Stop Event
1×iter limit
1×node limit
Counts
23 → 365
Calls
Call 1
Inputs
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
(* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))))
(+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))
(* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))
(* eps (+ (* 1/3 (* eps eps)) (+ 1 (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))))))
(+ (* 1/3 (* eps eps)) (+ 1 (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3)))))))
(+ 1 (* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3))))))
(* x (+ (* x (+ 1 (* (* eps eps) 4/3))) (* eps (+ 1 (* (* eps eps) 2/3)))))
(- (* (/ 1 (cos (+ x eps))) (sin (+ x eps))) (tan x))
(* (/ 1 (cos (+ x eps))) (sin (+ x eps)))
(/ 1 (cos (+ x eps)))
(cos (+ x eps))
(+ (* (/ 1 (cos (+ x eps))) (sin (* (+ (* x (* x x)) (* eps (* eps eps))) (/ 1 (+ (* x x) (* eps (- eps x))))))) (- 0 (tan x)))
(sin (* (+ (* x (* x x)) (* eps (* eps eps))) (/ 1 (+ (* x x) (* eps (- eps x))))))
(* (+ (* x (* x x)) (* eps (* eps eps))) (/ 1 (+ (* x x) (* eps (- eps x)))))
(+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))))
(* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))
(* (+ (tan x) (pow (tan x) 3)) -1/3)
(* (+ -1/2 (+ (* (pow (tan x) 2) -1/3) (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))) (tan x))
(* 1/3 (* eps eps))
(* (* eps eps) 2/3)
(* (* eps eps) 4/3)
(sin (+ x eps))
Outputs
(+.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)
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(sin.f64 (+.f64 eps x))
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps)))
(/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps))) (-.f64 (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (*.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))))))
(/.f64 (-.f64 (*.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps))) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))))
(*.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))
(*.f64 (sin.f64 (+.f64 eps x)) #s(literal 1 binary64))

simplify440.0ms (2.4%)

Algorithm
1×egg-herbie
Rules
6422×+-lowering-+.f64
6422×+-lowering-+.f32
4640×*-lowering-*.f32
4640×*-lowering-*.f64
1358×distribute-lft-in
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
084016757
1299514572
0893314572
Stop Event
1×iter limit
1×node limit
Counts
480 → 480
Calls
Call 1
Inputs
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps))))
(* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps))))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(* eps (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps))))
(* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps))))
(* 1/3 (pow eps 3))
(+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2)))))))))))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (+ (* eps x) (pow x 2))))
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(* 2/3 (* (pow eps 4) x))
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(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2))))))
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(* eps (+ 1 (* 1/3 (pow eps 2))))
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1
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(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (+ eps x)))
(/ 1 (cos (- x (* -1 eps))))
(/ 1 (cos (- x (* -1 eps))))
(/ 1 (cos (- x (* -1 eps))))
(/ 1 (cos (- x (* -1 eps))))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos x)
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(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(- (/ (sin (/ (+ (pow eps 3) (pow x 3)) (+ (* eps (- eps x)) (pow x 2)))) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (/ (+ (pow eps 3) (pow x 3)) (+ (* eps (- eps x)) (pow x 2)))) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (/ (+ (pow eps 3) (pow x 3)) (+ (* eps (- eps x)) (pow x 2)))) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (/ (+ (pow eps 3) (pow x 3)) (+ (* eps (- eps x)) (pow x 2)))) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (/ (- (pow eps 3) (* -1 (pow x 3))) (+ (* eps (+ eps (* -1 x))) (pow x 2)))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (/ (- (pow eps 3) (* -1 (pow x 3))) (+ (* eps (+ eps (* -1 x))) (pow x 2)))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (/ (- (pow eps 3) (* -1 (pow x 3))) (+ (* eps (+ eps (* -1 x))) (pow x 2)))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (/ (- (pow eps 3) (* -1 (pow x 3))) (+ (* eps (+ eps (* -1 x))) (pow x 2)))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (/ (+ (pow eps 3) (pow x 3)) (- (+ (pow eps 2) (pow x 2)) (* eps x)))) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (/ (+ (pow eps 3) (pow x 3)) (- (+ (pow eps 2) (pow x 2)) (* eps x)))) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (/ (+ (pow eps 3) (pow x 3)) (- (+ (pow eps 2) (pow x 2)) (* eps x)))) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (/ (+ (pow eps 3) (pow x 3)) (- (+ (pow eps 2) (pow x 2)) (* eps x)))) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (/ (- (pow x 3) (* -1 (pow eps 3))) (+ (* -1 (* eps x)) (+ (pow eps 2) (pow x 2))))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (/ (- (pow x 3) (* -1 (pow eps 3))) (+ (* -1 (* eps x)) (+ (pow eps 2) (pow x 2))))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (/ (- (pow x 3) (* -1 (pow eps 3))) (+ (* -1 (* eps x)) (+ (pow eps 2) (pow x 2))))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (/ (- (pow x 3) (* -1 (pow eps 3))) (+ (* -1 (* eps x)) (+ (pow eps 2) (pow x 2))))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(sin (/ (+ (pow eps 3) (pow x 3)) (+ (* eps (- eps x)) (pow x 2))))
(sin (/ (+ (pow eps 3) (pow x 3)) (+ (* eps (- eps x)) (pow x 2))))
(sin (/ (+ (pow eps 3) (pow x 3)) (+ (* eps (- eps x)) (pow x 2))))
(sin (/ (+ (pow eps 3) (pow x 3)) (+ (* eps (- eps x)) (pow x 2))))
(sin (/ (- (pow eps 3) (* -1 (pow x 3))) (+ (* eps (+ eps (* -1 x))) (pow x 2))))
(sin (/ (- (pow eps 3) (* -1 (pow x 3))) (+ (* eps (+ eps (* -1 x))) (pow x 2))))
(sin (/ (- (pow eps 3) (* -1 (pow x 3))) (+ (* eps (+ eps (* -1 x))) (pow x 2))))
(sin (/ (- (pow eps 3) (* -1 (pow x 3))) (+ (* eps (+ eps (* -1 x))) (pow x 2))))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(sin (/ (+ (pow eps 3) (pow x 3)) (- (+ (pow eps 2) (pow x 2)) (* eps x))))
(sin (/ (+ (pow eps 3) (pow x 3)) (- (+ (pow eps 2) (pow x 2)) (* eps x))))
(sin (/ (+ (pow eps 3) (pow x 3)) (- (+ (pow eps 2) (pow x 2)) (* eps x))))
(sin (/ (+ (pow eps 3) (pow x 3)) (- (+ (pow eps 2) (pow x 2)) (* eps x))))
(sin (/ (- (pow x 3) (* -1 (pow eps 3))) (+ (* -1 (* eps x)) (+ (pow eps 2) (pow x 2)))))
(sin (/ (- (pow x 3) (* -1 (pow eps 3))) (+ (* -1 (* eps x)) (+ (pow eps 2) (pow x 2)))))
(sin (/ (- (pow x 3) (* -1 (pow eps 3))) (+ (* -1 (* eps x)) (+ (pow eps 2) (pow x 2)))))
(sin (/ (- (pow x 3) (* -1 (pow eps 3))) (+ (* -1 (* eps x)) (+ (pow eps 2) (pow x 2)))))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (- (+ 1 (* -1 (/ (+ (* -1 (pow eps 2)) (pow eps 2)) (pow x 2)))) (* -1 (/ eps x))))
(* x (- (+ 1 (* -1 (/ (* eps (+ (* -1 (pow eps 2)) (pow eps 2))) (pow x 3)))) (+ (* -1 (/ eps x)) (+ (* -1 (/ (pow eps 2) (pow x 2))) (/ (pow eps 2) (pow x 2))))))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ (- (+ (* -1 (/ (pow eps 2) x)) (/ (pow eps 2) x)) (* -1 eps)) x)) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (* eps (+ (* -1 (pow eps 2)) (pow eps 2))) x)) (+ (* -1 (pow eps 2)) (pow eps 2))) x)) (* -1 eps)) x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (- (+ 1 (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow eps 2)))) (* -1 (/ x eps))))
(* eps (- (+ 1 (* -1 (/ (* x (+ (* -1 (pow x 2)) (pow x 2))) (pow eps 3)))) (+ (* -1 (/ x eps)) (+ (* -1 (/ (pow x 2) (pow eps 2))) (/ (pow x 2) (pow eps 2))))))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ (- (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps)) (* -1 x)) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (* x (+ (* -1 (pow x 2)) (pow x 2))) eps)) (+ (* -1 (pow x 2)) (pow x 2))) eps)) (* -1 x)) eps)) 1)))
-1/3
(- (* -4/3 (pow x 2)) 1/3)
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3)
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3)
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* 1/3 eps)
(+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x)))
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x)))))
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* -1/3 x)
(* x (- (* -4/9 (pow x 2)) 1/3))
(* x (- (* (pow x 2) (- (* -17/45 (pow x 2)) 4/9)) 1/3))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/945 (pow x 2)) 17/45)) 4/9)) 1/3))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 x)
(* x (- (* -13/9 (pow x 2)) 1/3))
(* x (- (* (pow x 2) (- (* -107/45 (pow x 2)) 13/9)) 1/3))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2516/945 (pow x 2)) 107/45)) 13/9)) 1/3))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(* 4/3 (pow eps 2))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
Outputs
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (*.f64 eps (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 eps (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))))))) #s(literal 1 binary64))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 eps (+.f64 (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (+.f64 (*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1/3 binary64)) (*.f64 (sin.f64 x) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))))) (+.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)))))))))
(* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(*.f64 (+.f64 (*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1/3 binary64)) (*.f64 (sin.f64 x) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) (*.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 4 binary64))))
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (*.f64 #s(literal -1/3 binary64) (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (*.f64 (sin.f64 x) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))))))
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (*.f64 eps eps))) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) (*.f64 eps eps)))))) (+.f64 (*.f64 #s(literal -1/3 binary64) (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (*.f64 (sin.f64 x) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))))))
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) (*.f64 eps eps)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (*.f64 eps eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 eps (*.f64 eps eps)))))) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (+.f64 (*.f64 #s(literal -1/3 binary64) (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (*.f64 (sin.f64 x) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))))))
(* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(*.f64 (+.f64 (*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1/3 binary64)) (*.f64 (sin.f64 x) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) (*.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 4 binary64))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (+.f64 (*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1/3 binary64)) (*.f64 (sin.f64 x) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))))) (*.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
(* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps))))
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(* 1/3 (pow eps 3))
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(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))
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(* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
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(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
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(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
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(* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
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(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* 1/3 (pow eps 2))
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
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(* eps (+ 1 (pow x 2)))
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(* eps (+ 1 (+ (* eps x) (pow x 2))))
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(* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))))
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(* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (+ (* 2/3 (* eps x)) (* 4/3 (pow x 2))))))) (pow x 2))))
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(* 2/3 (* (pow eps 4) x))
(*.f64 (*.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 4 binary64))) x)
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (* 1/3 (/ 1 eps)))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (*.f64 x #s(literal 2/3 binary64)) (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (/.f64 (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) eps))))
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2))))))
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(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ x (pow eps 2)) (/ (pow x 2) (pow eps 3))))))))
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(* 2/3 (* (pow eps 4) x))
(*.f64 (*.f64 #s(literal 2/3 binary64) (pow.f64 eps #s(literal 4 binary64))) x)
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (* 1/3 (/ 1 eps)))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (*.f64 x #s(literal 2/3 binary64)) (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (/.f64 (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) eps))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (* -1 (/ x eps))) eps)) (* 2/3 x)))
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(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (+ 1/3 (* 4/3 (pow x 2)))) (* -1 (/ (+ x (+ (/ 1 eps) (/ (pow x 2) eps))) eps))) eps)) (* 2/3 x)))
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(* eps (+ 1 (* 1/3 (pow eps 2))))
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(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
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(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
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(* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))))
(*.f64 (*.f64 eps (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))
(*.f64 (*.f64 x x) (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (/.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) x)))
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (+ (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (pow x 2)) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))))
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(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (+ (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (pow x 2)) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 x x)))) (/.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) x)))
(* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))))
(*.f64 (*.f64 eps (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))
(*.f64 (*.f64 x x) (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (/.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) x)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) (* -1 (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) x))) x)) (* eps (+ 1 (* 4/3 (pow eps 2))))))
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(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) (* -1 (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) x))) x)) (* eps (+ 1 (* 4/3 (pow eps 2))))))
(*.f64 (*.f64 x x) (-.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 eps eps))) (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) x)) x)))
(+ 1 (pow x 2))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (+ (* eps x) (pow x 2)))
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(sin eps)
(sin.f64 eps)
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(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
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(sin (/ (+ (pow eps 3) (pow x 3)) (+ (* eps (- eps x)) (pow x 2))))
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(sin (/ (+ (pow eps 3) (pow x 3)) (+ (* eps (- eps x)) (pow x 2))))
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(sin (/ (+ (pow eps 3) (pow x 3)) (+ (* eps (- eps x)) (pow x 2))))
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(sin (/ (+ (pow eps 3) (pow x 3)) (+ (* eps (- eps x)) (pow x 2))))
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(sin (/ (- (pow eps 3) (* -1 (pow x 3))) (+ (* eps (+ eps (* -1 x))) (pow x 2))))
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(sin (/ (- (pow eps 3) (* -1 (pow x 3))) (+ (* eps (+ eps (* -1 x))) (pow x 2))))
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(sin (/ (- (pow eps 3) (* -1 (pow x 3))) (+ (* eps (+ eps (* -1 x))) (pow x 2))))
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(sin (/ (- (pow eps 3) (* -1 (pow x 3))) (+ (* eps (+ eps (* -1 x))) (pow x 2))))
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(sin x)
(sin.f64 x)
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(sin (/ (+ (pow eps 3) (pow x 3)) (- (+ (pow eps 2) (pow x 2)) (* eps x))))
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(sin (/ (+ (pow eps 3) (pow x 3)) (- (+ (pow eps 2) (pow x 2)) (* eps x))))
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(sin (/ (+ (pow eps 3) (pow x 3)) (- (+ (pow eps 2) (pow x 2)) (* eps x))))
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(sin (/ (+ (pow eps 3) (pow x 3)) (- (+ (pow eps 2) (pow x 2)) (* eps x))))
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(sin (/ (- (pow x 3) (* -1 (pow eps 3))) (+ (* -1 (* eps x)) (+ (pow eps 2) (pow x 2)))))
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(sin (/ (- (pow x 3) (* -1 (pow eps 3))) (+ (* -1 (* eps x)) (+ (pow eps 2) (pow x 2)))))
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(sin (/ (- (pow x 3) (* -1 (pow eps 3))) (+ (* -1 (* eps x)) (+ (pow eps 2) (pow x 2)))))
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eps
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
x
(* x (+ 1 (/ eps x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
(* x (- (+ 1 (* -1 (/ (+ (* -1 (pow eps 2)) (pow eps 2)) (pow x 2)))) (* -1 (/ eps x))))
(*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 0 binary64) (*.f64 x x)) (/.f64 eps x))))
(* x (- (+ 1 (* -1 (/ (* eps (+ (* -1 (pow eps 2)) (pow eps 2))) (pow x 3)))) (+ (* -1 (/ eps x)) (+ (* -1 (/ (pow eps 2) (pow x 2))) (/ (pow eps 2) (pow x 2))))))
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x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 (/.f64 eps (-.f64 #s(literal 0 binary64) x)) #s(literal -1 binary64))))
(* -1 (* x (- (* -1 (/ (- (+ (* -1 (/ (pow eps 2) x)) (/ (pow eps 2) x)) (* -1 eps)) x)) 1)))
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(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (* eps (+ (* -1 (pow eps 2)) (pow eps 2))) x)) (+ (* -1 (pow eps 2)) (pow eps 2))) x)) (* -1 eps)) x)) 1)))
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x
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
eps
(* eps (+ 1 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
(* eps (- (+ 1 (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow eps 2)))) (* -1 (/ x eps))))
(*.f64 eps (+.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (/.f64 x eps))))
(* eps (- (+ 1 (* -1 (/ (* x (+ (* -1 (pow x 2)) (pow x 2))) (pow eps 3)))) (+ (* -1 (/ x eps)) (+ (* -1 (/ (pow x 2) (pow eps 2))) (/ (pow x 2) (pow eps 2))))))
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eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 (-.f64 #s(literal 0 binary64) eps) (+.f64 (/.f64 x (-.f64 #s(literal 0 binary64) eps)) #s(literal -1 binary64)))
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-1/3
#s(literal -1/3 binary64)
(- (* -4/3 (pow x 2)) 1/3)
(+.f64 (*.f64 (*.f64 x x) #s(literal -4/3 binary64)) #s(literal -1/3 binary64))
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3)
(+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -17/9 binary64)) #s(literal -4/3 binary64))) #s(literal -1/3 binary64))
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3)
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(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
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(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
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(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
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(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
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(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
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(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
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(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(-.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)))))
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* 1/3 eps)
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(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(*.f64 (sin.f64 x) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(*.f64 (sin.f64 x) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(*.f64 (sin.f64 x) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(*.f64 (sin.f64 x) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(*.f64 (sin.f64 x) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))
(* 1/3 (pow eps 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(* 1/3 (pow eps 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(* 1/3 (pow eps 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(* 1/3 (pow eps 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(* 1/3 (pow eps 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(* 1/3 (pow eps 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(* 1/3 (pow eps 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(* 1/3 (pow eps 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(* 1/3 (pow eps 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(* 1/3 (pow eps 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(* 1/3 (pow eps 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(* 1/3 (pow eps 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(* 2/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
(* 2/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
(* 2/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
(* 2/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
(* 2/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
(* 2/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
(* 2/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
(* 2/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
(* 2/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
(* 2/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
(* 2/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
(* 2/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
(* 4/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
(* 4/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
(* 4/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
(* 4/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
(* 4/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
(* 4/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
(* 4/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
(* 4/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
(* 4/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
(* 4/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
(* 4/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
(* 4/3 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (cos eps)))
(+.f64 (sin.f64 eps) (*.f64 x (cos.f64 eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) (*.f64 #s(literal -1/2 binary64) (*.f64 x (sin.f64 eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) (*.f64 x (+.f64 (*.f64 (sin.f64 eps) #s(literal -1/2 binary64)) (*.f64 (*.f64 x (cos.f64 eps)) #s(literal -1/6 binary64)))))))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin x)
(sin.f64 x)
(+ (sin x) (* eps (cos x)))
(+.f64 (sin.f64 x) (*.f64 eps (cos.f64 x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+.f64 (sin.f64 x) (*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(+.f64 (sin.f64 x) (*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64)))))))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))

eval178.0ms (1%)

Compiler

Compiled 51912 to 2954 computations (94.3% saved)

prune111.0ms (0.6%)

Pruning

32 alts after pruning (26 fresh and 6 done)

PrunedKeptTotal
New89521916
Fresh10515
Picked235
Done033
Total90732939
Accuracy
100.0%
Counts
939 → 32
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓65.2%
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
64.8%
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 eps (/.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
✓65.0%
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
✓23.6%
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
▶65.0%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
▶65.2%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
64.5%
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x)))) (tan.f64 x))
✓65.0%
(-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps))) (tan.f64 x))
64.1%
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64))))))))))
✓65.0%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
98.9%
(+.f64 (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
65.2%
(+.f64 (/.f64 (tan.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (/.f64 (tan.f64 eps) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (-.f64 #s(literal 0 binary64) (tan.f64 x))))
99.0%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps)
98.9%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))))) eps)
99.3%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) (*.f64 #s(literal 4/3 binary64) (*.f64 eps x))))))))) eps)
99.5%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 eps eps)))))))) eps)
99.7%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)
▶99.8%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 #s(literal -1/3 binary64) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)
99.5%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))) eps)
98.9%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)
98.3%
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))) eps)
98.6%
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps)
98.3%
(+.f64 (*.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)
6.3%
(*.f64 (*.f64 eps (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))
96.3%
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 (-.f64 (*.f64 x #s(literal -2/3 binary64)) (/.f64 (+.f64 (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) (/.f64 x eps)) eps)) (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps eps)))))))
98.5%
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 x x)))))
98.6%
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))))
98.5%
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x x))))
▶98.3%
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 eps (*.f64 eps eps)))))))
98.5%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x))))
▶98.5%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
✓98.3%
eps
Compiler

Compiled 1421 to 838 computations (41% saved)

simplify265.0ms (1.4%)

Algorithm
1×egg-herbie
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(tan.f64 x)
✓cost-diff0
(+.f64 (tan.f64 x) (tan.f64 eps))
✓cost-diff0
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
✓cost-diff0
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓cost-diff0
(tan.f64 (+.f64 x eps))
✓cost-diff0
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))
✓cost-diff256
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
✓cost-diff0
(*.f64 eps eps)
✓cost-diff0
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
✓cost-diff256
(+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 eps (*.f64 eps eps))))))
✓cost-diff256
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 eps (*.f64 eps eps)))))))
✓cost-diff0
(*.f64 x x)
✓cost-diff0
(+.f64 #s(literal 1 binary64) (*.f64 x x))
✓cost-diff0
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
✓cost-diff32192
(*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 #s(literal -1/3 binary64) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))
✓cost-diff32384
(+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 #s(literal -1/3 binary64) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))
✓cost-diff32384
(*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 #s(literal -1/3 binary64) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))))
✓cost-diff32384
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 #s(literal -1/3 binary64) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)
Rules
5700×+-lowering-+.f64
5700×+-lowering-+.f32
2884×*-lowering-*.f32
2884×*-lowering-*.f64
1488×sum3-define
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
050600
1160535
2541506
32193480
08174480
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
(* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))))
eps
(+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))
(pow (tan x) 2)
(tan x)
x
2
(* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))
(+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))
(+ (tan x) (pow (tan x) 3))
(pow (tan x) 3)
3
(* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))
(- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))
(+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3)))
(* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))
(+ 1 (pow (tan x) 2))
1
(- 1/3 (* (pow (tan x) 2) -1/3))
1/3
(* (pow (tan x) 2) -1/3)
-1/3
(* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))
(+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))
(* -1/3 (tan x))
(* (+ (tan x) (pow (tan x) 3)) -1/3)
(* eps (+ 1 (* x x)))
eps
(+ 1 (* x x))
1
(* x x)
x
(* eps (+ (* 1/3 (* eps eps)) (+ 1 (* 2/3 (* x (* eps (* eps eps)))))))
eps
(+ (* 1/3 (* eps eps)) (+ 1 (* 2/3 (* x (* eps (* eps eps))))))
(* 1/3 (* eps eps))
1/3
(* eps eps)
(+ 1 (* 2/3 (* x (* eps (* eps eps)))))
1
(* 2/3 (* x (* eps (* eps eps))))
2/3
(* x (* eps (* eps eps)))
x
(* eps (* eps eps))
(/ 1 (/ 1 (- (tan (+ x eps)) (tan x))))
1
(/ 1 (- (tan (+ x eps)) (tan x)))
(- (tan (+ x eps)) (tan x))
(tan (+ x eps))
(+ x eps)
x
eps
(tan x)
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
(+ (tan x) (tan eps))
(tan x)
x
(tan eps)
eps
(- 1 (* (tan x) (tan eps)))
1
(* (tan x) (tan eps))
Outputs
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) eps))) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 (tan.f64 x) #s(literal -1/3 binary64)) (+.f64 (tan.f64 x) eps))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (tan.f64 x) (*.f64 eps #s(literal 1/3 binary64))))))))))
(* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))))
(*.f64 eps (+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 (tan.f64 x) #s(literal -1/3 binary64)) (+.f64 (tan.f64 x) eps))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (tan.f64 x) (*.f64 eps #s(literal 1/3 binary64)))))))) (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) eps))))
eps
(+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 (tan.f64 x) #s(literal -1/3 binary64)) (+.f64 (tan.f64 x) eps))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (tan.f64 x) (*.f64 eps #s(literal 1/3 binary64)))))))) (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) eps)))
(pow (tan x) 2)
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(tan x)
(tan.f64 x)
x
2
#s(literal 2 binary64)
(* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))
(*.f64 eps (+.f64 (*.f64 eps (+.f64 (*.f64 eps (*.f64 (tan.f64 x) #s(literal 1/3 binary64))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 eps (*.f64 (tan.f64 x) #s(literal 1/3 binary64))))))) (*.f64 (+.f64 (*.f64 eps (tan.f64 x)) #s(literal 1 binary64)) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))
(+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))
(+.f64 (*.f64 eps (+.f64 (*.f64 eps (*.f64 (tan.f64 x) #s(literal 1/3 binary64))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 eps (*.f64 (tan.f64 x) #s(literal 1/3 binary64))))))) (*.f64 (+.f64 (*.f64 eps (tan.f64 x)) #s(literal 1 binary64)) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))
(+ (tan x) (pow (tan x) 3))
(+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))
(pow (tan x) 3)
(pow.f64 (tan.f64 x) #s(literal 3 binary64))
3
#s(literal 3 binary64)
(* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))
(*.f64 eps (+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 (tan.f64 x) #s(literal -1/3 binary64)) (+.f64 (tan.f64 x) eps))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (tan.f64 x) (*.f64 eps #s(literal 1/3 binary64))))))
(- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))
(+.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 (tan.f64 x) #s(literal -1/3 binary64)) (+.f64 (tan.f64 x) eps))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (tan.f64 x) (*.f64 eps #s(literal 1/3 binary64)))))
(+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3)))
(+.f64 (+.f64 #s(literal 1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64)))
(* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))
(+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))
(+ 1 (pow (tan x) 2))
(+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(- 1/3 (* (pow (tan x) 2) -1/3))
(-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))
1/3
#s(literal 1/3 binary64)
(* (pow (tan x) 2) -1/3)
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))
-1/3
#s(literal -1/3 binary64)
(* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))
(*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 (tan.f64 x) #s(literal 2 binary64))))
(+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))
(*.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 (tan.f64 x) #s(literal 2 binary64))))
(* -1/3 (tan x))
(*.f64 (tan.f64 x) #s(literal -1/3 binary64))
(* (+ (tan x) (pow (tan x) 3)) -1/3)
(*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))
(* eps (+ 1 (* x x)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
eps
(+ 1 (* x x))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
1
#s(literal 1 binary64)
(* x x)
(*.f64 x x)
x
(* eps (+ (* 1/3 (* eps eps)) (+ 1 (* 2/3 (* x (* eps (* eps eps)))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 eps (*.f64 x #s(literal 2/3 binary64)))))))
eps
(+ (* 1/3 (* eps eps)) (+ 1 (* 2/3 (* x (* eps (* eps eps))))))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 eps (*.f64 x #s(literal 2/3 binary64))))))
(* 1/3 (* eps eps))
(*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))
1/3
#s(literal 1/3 binary64)
(* eps eps)
(*.f64 eps eps)
(+ 1 (* 2/3 (* x (* eps (* eps eps)))))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x #s(literal 2/3 binary64))))
1
#s(literal 1 binary64)
(* 2/3 (* x (* eps (* eps eps))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x #s(literal 2/3 binary64)))
2/3
#s(literal 2/3 binary64)
(* x (* eps (* eps eps)))
(*.f64 eps (*.f64 eps (*.f64 eps x)))
x
(* eps (* eps eps))
(*.f64 eps (*.f64 eps eps))
(/ 1 (/ 1 (- (tan (+ x eps)) (tan x))))
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
1
#s(literal 1 binary64)
(/ 1 (- (tan (+ x eps)) (tan x)))
(/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
(- (tan (+ x eps)) (tan x))
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
(tan (+ x eps))
(tan.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(tan x)
(tan.f64 x)
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
(+ (tan x) (tan eps))
(+.f64 (tan.f64 x) (tan.f64 eps))
(tan x)
(tan.f64 x)
x
(tan eps)
(tan.f64 eps)
eps
(- 1 (* (tan x) (tan eps)))
(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))
1
#s(literal 1 binary64)
(* (tan x) (tan eps))
(*.f64 (tan.f64 x) (tan.f64 eps))

localize491.0ms (2.6%)

Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 (tan.f64 x) (tan.f64 eps))
✓accuracy100.0%
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
✓accuracy100.0%
(+.f64 (tan.f64 x) (tan.f64 eps))
✓accuracy65.2%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓accuracy100.0%
(/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))
✓accuracy99.8%
(tan.f64 (+.f64 x eps))
✓accuracy99.8%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
✓accuracy65.2%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓accuracy99.9%
(*.f64 eps (*.f64 eps eps))
✓accuracy99.9%
(*.f64 x (*.f64 eps (*.f64 eps eps)))
✓accuracy99.8%
(*.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 eps (*.f64 eps eps))))
✓accuracy99.7%
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
✓accuracy100.0%
(+.f64 #s(literal 1 binary64) (*.f64 x x))
✓accuracy100.0%
(*.f64 x x)
✓accuracy100.0%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
✓accuracy99.8%
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))
✓accuracy99.5%
(*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))
✓accuracy99.5%
(*.f64 #s(literal -1/3 binary64) (tan.f64 x))
✓accuracy99.5%
(*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 #s(literal -1/3 binary64) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))
Results
247.0ms134×1valid
101.0ms118×0valid
9.0ms3×2valid
6.0ms1×3valid
Compiler

Compiled 652 to 51 computations (92.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 170.0ms
ival-mult: 54.0ms (31.8% of total)
...c/correct-round.rkt:119:19: 27.0ms (15.9% of total)
backward-pass: 23.0ms (13.5% of total)
ival-add: 21.0ms (12.4% of total)
ival-tan: 14.0ms (8.2% of total)
ival-pow: 11.0ms (6.5% of total)
ival-sub: 10.0ms (5.9% of total)
ival-div: 8.0ms (4.7% of total)
const: 1.0ms (0.6% of total)

series54.0ms (0.3%)

Counts
27 → 540
Calls
Call 1
Inputs
#<alt (+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)>
#<alt (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))))>
#<alt (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))>
#<alt (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))>
#<alt (* eps (+ 1 (* x x)))>
#<alt (+ 1 (* x x))>
#<alt (* x x)>
#<alt (* eps (+ (* 1/3 (* eps eps)) (+ 1 (* 2/3 (* x (* eps (* eps eps)))))))>
#<alt (+ (* 1/3 (* eps eps)) (+ 1 (* 2/3 (* x (* eps (* eps eps))))))>
#<alt (* 1/3 (* eps eps))>
#<alt (* eps eps)>
#<alt (/ 1 (/ 1 (- (tan (+ x eps)) (tan x))))>
#<alt (/ 1 (- (tan (+ x eps)) (tan x)))>
#<alt (- (tan (+ x eps)) (tan x))>
#<alt (tan (+ x eps))>
#<alt (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))>
#<alt (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))>
#<alt (+ (tan x) (tan eps))>
#<alt (tan x)>
#<alt (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))>
#<alt (* -1/3 (tan x))>
#<alt (* (+ (tan x) (pow (tan x) 3)) -1/3)>
#<alt (* (pow (tan x) 2) -1/3)>
#<alt (* 2/3 (* x (* eps (* eps eps))))>
#<alt (* x (* eps (* eps eps)))>
#<alt (* eps (* eps eps))>
#<alt (* (tan x) (tan eps))>
Outputs
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))>
#<alt (* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (sin x) (cos x))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))>
#<alt (* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (sin x) (cos x))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))>
#<alt (* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (sin x) (cos x))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))>
#<alt (* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))>
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps))))>
#<alt (* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps))))>
#<alt (+ eps (* 1/3 (pow eps 3)))>
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))))>
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))>
#<alt (+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 5/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))>
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))>
#<alt (* eps (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))>
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))>
#<alt (* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps))))>
#<alt (* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps))))>
#<alt (* 1/3 (pow eps 3))>
#<alt (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))>
#<alt (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))>
#<alt (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 5/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))>
#<alt (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* 1/3 (pow eps 2))>
#<alt (+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))>
#<alt (+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2)))))))>
#<alt (+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 5/9 (pow eps 2)))))))))))>
#<alt (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
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#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))>
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))>
#<alt (- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))>
#<alt (/ (sin eps) (cos eps))>
#<alt (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (+ (* x (- (+ 1 (* x (- (* x (- 1/3 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (sin x) (cos x))>
#<alt (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))>
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (sin eps) (cos eps))>
#<alt (+ x (/ (sin eps) (cos eps)))>
#<alt (+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps)))>
#<alt (+ (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (sin eps) (cos eps)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (/ (sin x) (cos x))>
#<alt (+ eps (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* 1/3 eps)>
#<alt (+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x)))>
#<alt (+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x)))))>
#<alt (+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 5/9 (* (pow eps 2) x)) (* 4/3 eps))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))))>
#<alt (* -1/3 x)>
#<alt (* x (- (* -1/9 (pow x 2)) 1/3))>
#<alt (* x (- (* (pow x 2) (- (* -2/45 (pow x 2)) 1/9)) 1/3))>
#<alt (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -17/945 (pow x 2)) 2/45)) 1/9)) 1/3))>
#<alt (* -1/3 (/ (sin x) (cos x)))>
#<alt (* -1/3 (/ (sin x) (cos x)))>
#<alt (* -1/3 (/ (sin x) (cos x)))>
#<alt (* -1/3 (/ (sin x) (cos x)))>
#<alt (* -1/3 (/ (sin x) (cos x)))>
#<alt (* -1/3 (/ (sin x) (cos x)))>
#<alt (* -1/3 (/ (sin x) (cos x)))>
#<alt (* -1/3 (/ (sin x) (cos x)))>
#<alt (* -1/3 x)>
#<alt (* x (- (* -4/9 (pow x 2)) 1/3))>
#<alt (* x (- (* (pow x 2) (- (* -17/45 (pow x 2)) 4/9)) 1/3))>
#<alt (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/945 (pow x 2)) 17/45)) 4/9)) 1/3))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (pow x 2))>
#<alt (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3))>
#<alt (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3))>
#<alt (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/945 (pow x 2)) 17/135)) 2/9)) 1/3))>
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* (pow eps 3) x)>
#<alt (* (pow eps 3) x)>
#<alt (* (pow eps 3) x)>
#<alt (* (pow eps 3) x)>
#<alt (* (pow eps 3) x)>
#<alt (* (pow eps 3) x)>
#<alt (* (pow eps 3) x)>
#<alt (* (pow eps 3) x)>
#<alt (* (pow eps 3) x)>
#<alt (* (pow eps 3) x)>
#<alt (* (pow eps 3) x)>
#<alt (* (pow eps 3) x)>
#<alt (* (pow eps 3) x)>
#<alt (* (pow eps 3) x)>
#<alt (* (pow eps 3) x)>
#<alt (* (pow eps 3) x)>
#<alt (* (pow eps 3) x)>
#<alt (* (pow eps 3) x)>
#<alt (* (pow eps 3) x)>
#<alt (* (pow eps 3) x)>
#<alt (* (pow eps 3) x)>
#<alt (* (pow eps 3) x)>
#<alt (* (pow eps 3) x)>
#<alt (* (pow eps 3) x)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (/ (* x (sin eps)) (cos eps))>
#<alt (* x (+ (* 1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps))))>
#<alt (* x (+ (* (pow x 2) (+ (* 2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps))))>
#<alt (* x (+ (* (pow x 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* 17/315 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 2/15 (/ (sin eps) (cos eps))))))) (/ (sin eps) (cos eps))))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* eps (sin x)) (cos x))>
#<alt (* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x))))>
#<alt (* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x))))>
#<alt (* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x))))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
#<alt (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))>
Calls

135 calls:

TimeVariablePointExpression
8.0ms
x
@inf
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
4.0ms
eps
@inf
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
4.0ms
x
@-inf
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
2.0ms
eps
@0
(/ 1 (- (tan (+ x eps)) (tan x)))
1.0ms
eps
@-inf
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)

rewrite460.0ms (2.5%)

Algorithm
1×batch-egg-rewrite
Rules
3622×*-lowering-*.f32
3622×*-lowering-*.f64
1656×fma-lowering-fma.f32
1656×fma-lowering-fma.f64
1510×fmsub-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
050370
1374331
23928321
08720321
Stop Event
1×iter limit
1×node limit
Counts
27 → 498
Calls
Call 1
Inputs
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
(* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))))
(+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))
(* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))
(* eps (+ 1 (* x x)))
(+ 1 (* x x))
(* x x)
(* eps (+ (* 1/3 (* eps eps)) (+ 1 (* 2/3 (* x (* eps (* eps eps)))))))
(+ (* 1/3 (* eps eps)) (+ 1 (* 2/3 (* x (* eps (* eps eps))))))
(* 1/3 (* eps eps))
(* eps eps)
(/ 1 (/ 1 (- (tan (+ x eps)) (tan x))))
(/ 1 (- (tan (+ x eps)) (tan x)))
(- (tan (+ x eps)) (tan x))
(tan (+ x eps))
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
(+ (tan x) (tan eps))
(tan x)
(* eps (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* -1/3 (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))
(* -1/3 (tan x))
(* (+ (tan x) (pow (tan x) 3)) -1/3)
(* (pow (tan x) 2) -1/3)
(* 2/3 (* x (* eps (* eps eps))))
(* x (* eps (* eps eps)))
(* eps (* eps eps))
(* (tan x) (tan eps))
Outputs
(+.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))) eps)
(+.f64 (*.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (*.f64 (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))))) (*.f64 eps eps)) eps))
(+.f64 (+.f64 eps (*.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))))) (*.f64 eps eps)))
(-.f64 (/.f64 (pow.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))) #s(literal 2 binary64)) (-.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))) eps)) (/.f64 (*.f64 eps eps) (-.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))) eps)))
(fma.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))))))) eps)
(fma.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))))))) eps eps)
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))) #s(literal 2 binary64)) (*.f64 eps (-.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))))))))))) (+.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))) eps) (-.f64 (pow.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))) #s(literal 2 binary64)) (*.f64 eps eps))))
(/.f64 (+.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))) #s(literal 2 binary64)) (*.f64 eps (-.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))))))))))))
(/.f64 (+.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))) #s(literal 3 binary64))) (+.f64 (*.f64 eps eps) (-.f64 (pow.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))) #s(literal 2 binary64)) (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))))))) (*.f64 eps eps)))))
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(+.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) eps) (*.f64 (-.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))) eps))
(+.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) eps) (*.f64 (*.f64 (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))) (-.f64 #s(literal 0 binary64) eps)) eps))
(/.f64 (*.f64 eps (-.f64 (pow.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) #s(literal 3 binary64)) (pow.f64 (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))) #s(literal 3 binary64)))) (+.f64 (pow.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) #s(literal 2 binary64)) (*.f64 (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))) (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))
(/.f64 (*.f64 eps (-.f64 (pow.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) #s(literal 2 binary64)) (pow.f64 (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))) #s(literal 2 binary64)))) (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))
(/.f64 (*.f64 (-.f64 (pow.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) #s(literal 3 binary64)) (pow.f64 (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))) #s(literal 3 binary64))) eps) (+.f64 (pow.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) #s(literal 2 binary64)) (*.f64 (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))) (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))
(/.f64 (*.f64 (-.f64 (pow.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) #s(literal 2 binary64)) (pow.f64 (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))) #s(literal 2 binary64))) eps) (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))
(*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))
(*.f64 (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))) eps)
(/.f64 (*.f64 #s(literal -1/3 binary64) (sin.f64 x)) (cos.f64 x))
(/.f64 (*.f64 (sin.f64 x) #s(literal -1/3 binary64)) (cos.f64 x))
(*.f64 (tan.f64 x) #s(literal -1/3 binary64))
(*.f64 #s(literal -1/3 binary64) (tan.f64 x))
(+.f64 (*.f64 (tan.f64 x) #s(literal -1/3 binary64)) (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))
(+.f64 (*.f64 (tan.f64 x) #s(literal -1/3 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal -1/3 binary64)))
(+.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 (tan.f64 x) #s(literal -1/3 binary64)))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal -1/3 binary64)) (*.f64 (tan.f64 x) #s(literal -1/3 binary64)))
(/.f64 (*.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 9 binary64)))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))
(/.f64 (*.f64 #s(literal -1/3 binary64) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 6 binary64)))) (-.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))
(/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 9 binary64))) #s(literal -1/3 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))
(/.f64 (*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 6 binary64))) #s(literal -1/3 binary64)) (-.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))
(*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))
(*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))
(*.f64 (tan.f64 x) (*.f64 (tan.f64 x) #s(literal -1/3 binary64)))
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))
(*.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(*.f64 (*.f64 (tan.f64 x) #s(literal -1/3 binary64)) (tan.f64 x))
(*.f64 x (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 2/3 binary64)))
(*.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 2/3 binary64))))
(*.f64 #s(literal 2/3 binary64) (*.f64 eps (*.f64 (*.f64 eps eps) x)))
(*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x #s(literal 2/3 binary64)))
(*.f64 (*.f64 eps (*.f64 (*.f64 eps eps) x)) #s(literal 2/3 binary64))
(*.f64 (*.f64 x (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 2/3 binary64))) #s(literal 1 binary64))
(*.f64 (*.f64 eps x) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))
(*.f64 (*.f64 x #s(literal 2/3 binary64)) (*.f64 eps (*.f64 eps eps)))
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 (*.f64 eps eps) x))) #s(literal 2/3 binary64))
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 x #s(literal 2/3 binary64))) (*.f64 eps (*.f64 eps eps)))
(*.f64 (*.f64 #s(literal 2/3 binary64) (*.f64 eps (*.f64 eps eps))) x)
(*.f64 (*.f64 #s(literal 2/3 binary64) (*.f64 eps x)) (*.f64 eps eps))
(*.f64 (*.f64 (*.f64 x #s(literal 2/3 binary64)) eps) (*.f64 eps eps))
(*.f64 (*.f64 (*.f64 x #s(literal 2/3 binary64)) (*.f64 eps eps)) eps)
(*.f64 eps (*.f64 (*.f64 eps eps) x))
(*.f64 x (*.f64 eps (*.f64 eps eps)))
(*.f64 (*.f64 eps eps) (*.f64 eps x))
(*.f64 (*.f64 eps (*.f64 eps eps)) x)
(*.f64 (*.f64 eps x) (*.f64 eps eps))
(*.f64 (*.f64 x (*.f64 eps eps)) eps)
(*.f64 (*.f64 (*.f64 eps x) eps) eps)
(exp.f64 (*.f64 (log.f64 eps) #s(literal 3 binary64)))
(pow.f64 eps #s(literal 3 binary64))
(*.f64 eps (*.f64 eps eps))
(*.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))
(*.f64 (*.f64 eps eps) eps)
(*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1 binary64))
(*.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 eps #s(literal 3/2 binary64)))
(/.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps))
(/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))
(/.f64 (*.f64 (sin.f64 x) (tan.f64 eps)) (cos.f64 x))
(/.f64 (*.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps))
(*.f64 (tan.f64 x) (tan.f64 eps))
(*.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))
(*.f64 (tan.f64 eps) (tan.f64 x))
(*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 1 binary64))
(*.f64 (*.f64 #s(literal 1 binary64) (tan.f64 x)) (tan.f64 eps))
(*.f64 (*.f64 #s(literal 1 binary64) (tan.f64 eps)) (tan.f64 x))

simplify421.0ms (2.3%)

Algorithm
1×egg-herbie
Rules
5386×+-lowering-+.f64
5386×+-lowering-+.f32
4412×*-lowering-*.f32
4412×*-lowering-*.f64
1698×fma-lowering-fma.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
072314710
1256012925
0821412925
Stop Event
1×iter limit
1×node limit
Counts
540 → 540
Calls
Call 1
Inputs
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (sin x) (cos x))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (sin x) (cos x))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (sin x) (cos x))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
(* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps))))
(* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps))))
(+ eps (* 1/3 (pow eps 3)))
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 5/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ eps (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(* eps (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps))))
(* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps))))
(* 1/3 (pow eps 3))
(+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 5/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 5/9 (pow eps 2)))))))))))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (sin x) (cos x))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (sin x) (cos x))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (sin x) (cos x))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
(* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))
(* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))
(* 1/3 (pow eps 2))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2)))))))
(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 5/9 (pow eps 2))))))))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(* eps (+ 1 (pow x 2)))
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x
(* x (+ 1 (* 1/3 (pow x 2))))
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(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(/ (sin x) (cos x))
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(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
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(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))
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(* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* 1/3 eps)
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(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))))
(* -1/3 x)
(* x (- (* -1/9 (pow x 2)) 1/3))
(* x (- (* (pow x 2) (- (* -2/45 (pow x 2)) 1/9)) 1/3))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -17/945 (pow x 2)) 2/45)) 1/9)) 1/3))
(* -1/3 (/ (sin x) (cos x)))
(* -1/3 (/ (sin x) (cos x)))
(* -1/3 (/ (sin x) (cos x)))
(* -1/3 (/ (sin x) (cos x)))
(* -1/3 (/ (sin x) (cos x)))
(* -1/3 (/ (sin x) (cos x)))
(* -1/3 (/ (sin x) (cos x)))
(* -1/3 (/ (sin x) (cos x)))
(* -1/3 x)
(* x (- (* -4/9 (pow x 2)) 1/3))
(* x (- (* (pow x 2) (- (* -17/45 (pow x 2)) 4/9)) 1/3))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/945 (pow x 2)) 17/45)) 4/9)) 1/3))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (pow x 2))
(* (pow x 2) (- (* -2/9 (pow x 2)) 1/3))
(* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/945 (pow x 2)) 17/135)) 2/9)) 1/3))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(* 2/3 (* (pow eps 3) x))
(* 2/3 (* (pow eps 3) x))
(* 2/3 (* (pow eps 3) x))
(* 2/3 (* (pow eps 3) x))
(* 2/3 (* (pow eps 3) x))
(* 2/3 (* (pow eps 3) x))
(* 2/3 (* (pow eps 3) x))
(* 2/3 (* (pow eps 3) x))
(* 2/3 (* (pow eps 3) x))
(* 2/3 (* (pow eps 3) x))
(* 2/3 (* (pow eps 3) x))
(* 2/3 (* (pow eps 3) x))
(* 2/3 (* (pow eps 3) x))
(* 2/3 (* (pow eps 3) x))
(* 2/3 (* (pow eps 3) x))
(* 2/3 (* (pow eps 3) x))
(* 2/3 (* (pow eps 3) x))
(* 2/3 (* (pow eps 3) x))
(* 2/3 (* (pow eps 3) x))
(* 2/3 (* (pow eps 3) x))
(* 2/3 (* (pow eps 3) x))
(* 2/3 (* (pow eps 3) x))
(* 2/3 (* (pow eps 3) x))
(* 2/3 (* (pow eps 3) x))
(* (pow eps 3) x)
(* (pow eps 3) x)
(* (pow eps 3) x)
(* (pow eps 3) x)
(* (pow eps 3) x)
(* (pow eps 3) x)
(* (pow eps 3) x)
(* (pow eps 3) x)
(* (pow eps 3) x)
(* (pow eps 3) x)
(* (pow eps 3) x)
(* (pow eps 3) x)
(* (pow eps 3) x)
(* (pow eps 3) x)
(* (pow eps 3) x)
(* (pow eps 3) x)
(* (pow eps 3) x)
(* (pow eps 3) x)
(* (pow eps 3) x)
(* (pow eps 3) x)
(* (pow eps 3) x)
(* (pow eps 3) x)
(* (pow eps 3) x)
(* (pow eps 3) x)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(/ (* x (sin eps)) (cos eps))
(* x (+ (* 1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps))))
(* x (+ (* (pow x 2) (+ (* 2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps))))
(* x (+ (* (pow x 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* 17/315 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 2/15 (/ (sin eps) (cos eps))))))) (/ (sin eps) (cos eps))))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* eps (sin x)) (cos x))
(* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x))))
(* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x))))
(* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x))))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
Outputs
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(* eps (+ 1 (+ (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))))))))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 (*.f64 eps (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 eps (+.f64 (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (*.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))) (+.f64 #s(literal 1/3 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))))))) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (sin x) (cos x))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (sin x) (cos x))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (*.f64 eps eps))) (/.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) (cos.f64 x)))) (*.f64 #s(literal -1/3 binary64) (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))))
(* (pow eps 4) (- (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (sin x) (cos x))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps))) (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (+.f64 (+.f64 (/.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) (cos.f64 x)) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (*.f64 eps eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 eps (*.f64 eps eps)))))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))
(* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))
(* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (*.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))) (/.f64 (-.f64 (/.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (-.f64 #s(literal 0 binary64) eps)) (+.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))))) eps)))
(* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1) eps)) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps))))
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(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* -1 (* (pow eps 4) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))
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(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) eps))) eps))))
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(* (pow eps 4) (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (* -1 (/ (+ (* -1 (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (+ (/ (sin x) (cos x)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (pow (cos x) 3)))) eps))) eps))))
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(* 1/3 (pow eps 3))
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(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))
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(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (sin x) (cos x))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
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(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3)))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (sin x) (cos x))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
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(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (sin x) (cos x))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))))
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(* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))
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(* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
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(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
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(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
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(* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))
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(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (+ (/ (sin x) (* (pow eps 2) (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))) (/ (pow (sin x) 3) (* (pow eps 2) (pow (cos x) 3))))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* -1 (* (pow eps 3) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))
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(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (/ (sin x) (* eps (cos x))) (+ (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)) (/ (pow (sin x) 3) (* eps (pow (cos x) 3)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))
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(* 1/3 (pow eps 2))
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
(+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))
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(+ (* 1/3 (pow eps 2)) (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2)))))))
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(+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 5/9 (pow eps 2))))))))))
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(*.f64 eps (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))))))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
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(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(*.f64 eps (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))))))))
(* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))
(*.f64 eps (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 eps (+.f64 #s(literal 1/3 binary64) (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))))))))
(* eps (+ 1 (pow x 2)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(* eps (+ 1 (pow x 2)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(* eps (+ 1 (pow x 2)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(* eps (+ 1 (pow x 2)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(* eps (+ 1 (pow x 2)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(* eps (+ 1 (pow x 2)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(* eps (+ 1 (pow x 2)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(* eps (+ 1 (pow x 2)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(* eps (+ 1 (pow x 2)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(* eps (+ 1 (pow x 2)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(* eps (+ 1 (pow x 2)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(* eps (+ 1 (pow x 2)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
eps
(+ eps (* eps (pow x 2)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(+ eps (* eps (pow x 2)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
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(/ (sin x) (cos x))
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x
(* x (+ 1 (* 1/3 (pow x 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 x x))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
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(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
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(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
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(/ (sin x) (cos x))
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(/ (sin x) (cos x))
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(/ (sin x) (cos x))
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(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x)))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))
(*.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(*.f64 (*.f64 eps eps) (-.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(*.f64 (*.f64 eps eps) (-.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))
(* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))
(*.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(*.f64 (*.f64 eps eps) (-.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(*.f64 (*.f64 eps eps) (-.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(*.f64 (*.f64 eps eps) (-.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))
(* 1/3 eps)
(*.f64 eps #s(literal 1/3 binary64))
(+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x)))
(+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 eps eps))))
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x)))))
(+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) (*.f64 #s(literal 4/3 binary64) (*.f64 eps x)))))
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 5/9 (* (pow eps 2) x)) (* 4/3 eps))))))
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(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))))
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(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))))
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(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))))
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(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (* -1/3 (/ (sin x) (cos x))))))))
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(* x (+ (* (pow x 2) (+ (* 2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps))))
(*.f64 x (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 2/15 binary64) (/.f64 (*.f64 (*.f64 x x) (sin.f64 eps)) (cos.f64 eps))) (/.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 eps)) (cos.f64 eps))))))
(* x (+ (* (pow x 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* 17/315 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 2/15 (/ (sin eps) (cos eps))))))) (/ (sin eps) (cos eps))))
(*.f64 x (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 eps)) (cos.f64 eps)) (*.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 17/315 binary64) (/.f64 (*.f64 (*.f64 x x) (sin.f64 eps)) (cos.f64 eps))) (/.f64 (*.f64 #s(literal 2/15 binary64) (sin.f64 eps)) (cos.f64 eps))))))))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* eps (sin x)) (cos x))
(/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x))
(* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x))))
(*.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (/.f64 (sin.f64 x) (cos.f64 x))))))
(* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x))))
(*.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 eps eps) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 x)) (cos.f64 x))))))
(* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x))))
(*.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 x)) (cos.f64 x)) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 #s(literal 17/315 binary64) (*.f64 (*.f64 eps eps) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (*.f64 #s(literal 2/15 binary64) (sin.f64 x)) (cos.f64 x))))))))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))

eval208.0ms (1.1%)

Compiler

Compiled 53241 to 3747 computations (93% saved)

prune142.0ms (0.8%)

Pruning

33 alts after pruning (25 fresh and 8 done)

PrunedKeptTotal
New132391332
Fresh51621
Picked325
Done066
Total1331331364
Accuracy
100.0%
Counts
1364 → 33
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓65.2%
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
✓65.0%
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
✓23.6%
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
99.2%
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps))
✓65.0%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
✓65.2%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
64.8%
(-.f64 (/.f64 (+.f64 eps (/.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
64.5%
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x)))) (tan.f64 x))
✓65.0%
(-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps))) (tan.f64 x))
64.1%
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64))))))))))
✓65.0%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
98.9%
(+.f64 (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
99.8%
(+.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))))))) eps) eps)
99.0%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps)
98.9%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))))) eps)
99.3%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) (*.f64 #s(literal 4/3 binary64) (*.f64 eps x))))))))) eps)
99.7%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 #s(literal -1/3 binary64) (tan.f64 x)) (*.f64 x #s(literal -1/3 binary64)))))))))) eps)
99.5%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))) eps)
98.9%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)
98.3%
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))) eps)
98.6%
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps)
98.5%
(+.f64 (*.f64 eps (*.f64 x x)) eps)
98.3%
(+.f64 (*.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)
51.1%
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x))))
96.3%
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 (-.f64 (*.f64 x #s(literal -2/3 binary64)) (/.f64 (+.f64 (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) (/.f64 x eps)) eps)) (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps eps)))))))
98.5%
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 x x)))))
98.6%
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))))
98.5%
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x x))))
98.3%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))))))
98.5%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x))))
6.3%
(*.f64 eps (*.f64 x x))
64.1%
(exp.f64 (*.f64 (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 1 binary64)))
✓98.3%
eps
Compiler

Compiled 2448 to 819 computations (66.5% saved)

regimes58.0ms (0.3%)

Counts
63 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 x x))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 (*.f64 eps (*.f64 x x)) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x))))
(+.f64 (*.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x x))))
(*.f64 (*.f64 eps (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/15 binary64))))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 eps (*.f64 eps eps)))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 x x)))))
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))) eps)
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))))
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps)
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 (-.f64 (*.f64 x #s(literal -2/3 binary64)) (/.f64 (+.f64 (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) (/.f64 x eps)) eps)) (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps eps)))))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))
(-.f64 (tan.f64 (+.f64 x eps)) x)
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64))))))
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 x #s(literal 2/15 binary64))))))))
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64))))))))))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))))) eps)
(-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps))) (tan.f64 x))
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x)))) (tan.f64 x))
(exp.f64 (*.f64 (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 1 binary64)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(+.f64 (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
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(-.f64 (*.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
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(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 x (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (*.f64 (sin.f64 eps) x) (cos.f64 eps))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 #s(literal -1/3 binary64) (tan.f64 x)) (*.f64 x #s(literal -1/3 binary64)))))))))) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)
(+.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))))))) eps) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 #s(literal -1/3 binary64) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1/6 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
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Outputs
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)
Calls

3 calls:

17.0ms
eps
16.0ms
x
15.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
AccuracySegmentsBranch
99.8%1x
99.8%1eps
99.8%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes77.0ms (0.4%)

Counts
60 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 x x))
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(-.f64 (tan.f64 (+.f64 x eps)) x)
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(/.f64 (sin.f64 eps) (cos.f64 eps))
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(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x)))) (tan.f64 x))
(exp.f64 (*.f64 (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 1 binary64)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(+.f64 (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(-.f64 (/.f64 (+.f64 eps (/.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))) eps)
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (sin.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (cos.f64 x)))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 eps eps)))))))) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) (*.f64 #s(literal 4/3 binary64) (*.f64 eps x))))))))) eps)
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 eps (/.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(+.f64 (/.f64 (tan.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (/.f64 (tan.f64 eps) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (-.f64 #s(literal 0 binary64) (tan.f64 x))))
(-.f64 (*.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(*.f64 eps (+.f64 (*.f64 eps (*.f64 #s(literal 1 binary64) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps #s(literal 1/3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 x (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (*.f64 (sin.f64 eps) x) (cos.f64 eps))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 #s(literal -1/3 binary64) (tan.f64 x)) (*.f64 x #s(literal -1/3 binary64)))))))))) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)
(+.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))))))) eps) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 #s(literal -1/3 binary64) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)
Outputs
(+.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))))))) eps) eps)
Calls

3 calls:

23.0ms
eps
16.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
15.0ms
x
Results
AccuracySegmentsBranch
99.8%1x
99.8%1eps
99.8%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes57.0ms (0.3%)

Counts
58 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 x x))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 (*.f64 eps (*.f64 x x)) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x))))
(+.f64 (*.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x x))))
(*.f64 (*.f64 eps (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))
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(-.f64 (tan.f64 (+.f64 x eps)) x)
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(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) (*.f64 #s(literal 4/3 binary64) (*.f64 eps x))))))))) eps)
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 eps (/.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(+.f64 (/.f64 (tan.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (/.f64 (tan.f64 eps) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (-.f64 #s(literal 0 binary64) (tan.f64 x))))
(-.f64 (*.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(*.f64 eps (+.f64 (*.f64 eps (*.f64 #s(literal 1 binary64) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps #s(literal 1/3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 x (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (*.f64 (sin.f64 eps) x) (cos.f64 eps))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 #s(literal -1/3 binary64) (tan.f64 x)) (*.f64 x #s(literal -1/3 binary64)))))))))) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)
Outputs
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)
Calls

3 calls:

21.0ms
eps
14.0ms
x
14.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
AccuracySegmentsBranch
99.7%1x
99.7%1eps
99.7%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes59.0ms (0.3%)

Counts
57 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 x x))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 (*.f64 eps (*.f64 x x)) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x))))
(+.f64 (*.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x x))))
(*.f64 (*.f64 eps (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/15 binary64))))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 eps (*.f64 eps eps)))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 x x)))))
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))) eps)
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))))
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps)
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 (-.f64 (*.f64 x #s(literal -2/3 binary64)) (/.f64 (+.f64 (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) (/.f64 x eps)) eps)) (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps eps)))))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))
(-.f64 (tan.f64 (+.f64 x eps)) x)
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64))))))
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 x #s(literal 2/15 binary64))))))))
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64))))))))))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))))) eps)
(-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps))) (tan.f64 x))
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x)))) (tan.f64 x))
(exp.f64 (*.f64 (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 1 binary64)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(+.f64 (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(-.f64 (/.f64 (+.f64 eps (/.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))) eps)
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (sin.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (cos.f64 x)))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 eps eps)))))))) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) (*.f64 #s(literal 4/3 binary64) (*.f64 eps x))))))))) eps)
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 eps (/.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(+.f64 (/.f64 (tan.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (/.f64 (tan.f64 eps) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (-.f64 #s(literal 0 binary64) (tan.f64 x))))
(-.f64 (*.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(*.f64 eps (+.f64 (*.f64 eps (*.f64 #s(literal 1 binary64) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps #s(literal 1/3 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 x (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (*.f64 (sin.f64 eps) x) (cos.f64 eps))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 #s(literal -1/3 binary64) (tan.f64 x)) (*.f64 x #s(literal -1/3 binary64)))))))))) eps)
Outputs
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 #s(literal -1/3 binary64) (tan.f64 x)) (*.f64 x #s(literal -1/3 binary64)))))))))) eps)
Calls

3 calls:

15.0ms
eps
14.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
14.0ms
x
Results
AccuracySegmentsBranch
99.7%1x
99.7%1eps
99.7%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes50.0ms (0.3%)

Counts
56 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 x x))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 (*.f64 eps (*.f64 x x)) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
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(-.f64 (tan.f64 (+.f64 x eps)) x)
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64))))))
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 x #s(literal 2/15 binary64))))))))
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64))))))))))
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(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
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(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps)
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(-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps))) (tan.f64 x))
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x)))) (tan.f64 x))
(exp.f64 (*.f64 (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 1 binary64)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(+.f64 (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
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(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
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(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(-.f64 (/.f64 (+.f64 eps (/.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))) eps)
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Outputs
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 eps eps)))))))) eps)
Calls

3 calls:

15.0ms
x
15.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
14.0ms
eps
Results
AccuracySegmentsBranch
99.5%1x
99.5%1eps
99.5%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes115.0ms (0.6%)

Counts
45 → 1
Calls
Call 1
Inputs
eps
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(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(-.f64 (/.f64 (+.f64 eps (/.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))) eps)
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (sin.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (cos.f64 x)))
Outputs
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))) eps)
Calls

3 calls:

86.0ms
x
12.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
11.0ms
eps
Results
AccuracySegmentsBranch
99.5%1x
99.5%1eps
99.5%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes62.0ms (0.3%)

Counts
43 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 x x))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 (*.f64 eps (*.f64 x x)) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x))))
(+.f64 (*.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x x))))
(*.f64 (*.f64 eps (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/15 binary64))))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 eps (*.f64 eps eps)))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 x x)))))
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))) eps)
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))))
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps)
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 (-.f64 (*.f64 x #s(literal -2/3 binary64)) (/.f64 (+.f64 (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) (/.f64 x eps)) eps)) (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps eps)))))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))
(-.f64 (tan.f64 (+.f64 x eps)) x)
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64))))))
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 x #s(literal 2/15 binary64))))))))
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64))))))))))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))))) eps)
(-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps))) (tan.f64 x))
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x)))) (tan.f64 x))
(exp.f64 (*.f64 (log.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal 1 binary64)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(+.f64 (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/9 binary64))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(-.f64 (/.f64 (+.f64 eps (/.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
Outputs
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps)
Calls

3 calls:

37.0ms
x
11.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
11.0ms
eps
Results
AccuracySegmentsBranch
99.0%1x
99.0%1eps
99.0%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes28.0ms (0.1%)

Counts
29 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 x x))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 (*.f64 eps (*.f64 x x)) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x))))
(+.f64 (*.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x x))))
(*.f64 (*.f64 eps (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/15 binary64))))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 eps (*.f64 eps eps)))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 x x)))))
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))) eps)
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))))
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps)
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 (-.f64 (*.f64 x #s(literal -2/3 binary64)) (/.f64 (+.f64 (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) (/.f64 x eps)) eps)) (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps eps)))))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))
(-.f64 (tan.f64 (+.f64 x eps)) x)
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64))))))
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 x #s(literal 2/15 binary64))))))))
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64))))))))))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)
Outputs
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)
Calls

3 calls:

8.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
7.0ms
x
7.0ms
eps
Results
AccuracySegmentsBranch
98.9%1x
98.9%1eps
98.9%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes24.0ms (0.1%)

Counts
28 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 x x))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 (*.f64 eps (*.f64 x x)) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x))))
(+.f64 (*.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x x))))
(*.f64 (*.f64 eps (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/15 binary64))))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 eps (*.f64 eps eps)))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 x x)))))
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))) eps)
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))))
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps)
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 (-.f64 (*.f64 x #s(literal -2/3 binary64)) (/.f64 (+.f64 (*.f64 #s(literal 4/3 binary64) (*.f64 x x)) (/.f64 x eps)) eps)) (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps eps)))))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))
(-.f64 (tan.f64 (+.f64 x eps)) x)
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64))))))
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 x #s(literal 2/15 binary64))))))))
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64))))))))))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
Outputs
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps)
Calls

3 calls:

7.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
7.0ms
eps
7.0ms
x
Results
AccuracySegmentsBranch
98.6%1x
98.6%1eps
98.6%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes16.0ms (0.1%)

Counts
18 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 x x))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 (*.f64 eps (*.f64 x x)) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x))))
(+.f64 (*.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x x))))
(*.f64 (*.f64 eps (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/15 binary64))))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 eps (*.f64 eps eps)))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))) (*.f64 x x)))))
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))) eps)
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))))
Outputs
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))))
Calls

2 calls:

5.0ms
x
5.0ms
eps
Results
AccuracySegmentsBranch
98.6%1x
98.6%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes8.0ms (0%)

Counts
12 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 x x))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 (*.f64 eps (*.f64 x x)) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x))))
(+.f64 (*.f64 eps (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x x))))
(*.f64 (*.f64 eps (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/15 binary64))))))
Outputs
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x))))
Calls

2 calls:

4.0ms
eps
4.0ms
x
Results
AccuracySegmentsBranch
98.5%1x
98.5%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

Counts
5 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 x x))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 (*.f64 eps (*.f64 x x)) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
Outputs
(+.f64 (*.f64 eps (*.f64 x x)) eps)
Calls

2 calls:

2.0ms
x
2.0ms
eps
Results
AccuracySegmentsBranch
98.5%1x
98.5%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

Counts
3 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 x x))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
Outputs
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
Calls

2 calls:

3.0ms
x
2.0ms
eps
Results
AccuracySegmentsBranch
98.5%1eps
98.5%1x
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

Accuracy

Total -58.8b remaining (-5286.8%)

Threshold costs -58.8b (-5286.8%)

Counts
2 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 x x))
Outputs
eps
Calls

2 calls:

1.0ms
x
1.0ms
eps
Results
AccuracySegmentsBranch
98.3%1eps
98.3%1x
Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify53.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
546×unsub-neg_binary64
284×neg-mul-1_binary64
182×*-commutative_binary64
174×+-commutative_binary64
142×distribute-lft-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0118404
1241404
2294404
3340404
4402404
5441404
6554404
7746404
8806404
9847404
10898404
111053404
121225404
131238404
141248404
151257404
161258404
Stop Event
1×saturated
Calls
Call 1
Inputs
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)
(+.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))))))) eps) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 #s(literal -1/3 binary64) (tan.f64 x)) (*.f64 x #s(literal -1/3 binary64)))))))))) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 eps eps)))))))) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps)
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps)
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x))))
(+.f64 (*.f64 eps (*.f64 x x)) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
eps
Outputs
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)
(+.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (+.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (-.f64 (*.f64 (tan.f64 x) (-.f64 (-.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) #s(literal 1/6 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) #s(literal -1/2 binary64))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))))
(+.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))))))) eps) eps)
(+.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))))) (*.f64 eps (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)
(+.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)) (*.f64 x #s(literal -1/3 binary64)))))))))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 #s(literal -1/3 binary64) (tan.f64 x)) (*.f64 x #s(literal -1/3 binary64)))))))))) eps)
(+.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 (tan.f64 x) #s(literal -1/3 binary64)))))))))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 eps eps)))))))) eps)
(+.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 eps eps)))))))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))) eps)
(+.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))) eps)
(+.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps))))))))
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)
(+.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))) eps)
(+.f64 eps (*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)))))))))
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x))))
(+.f64 (*.f64 eps (*.f64 x x)) eps)
(+.f64 eps (*.f64 eps (*.f64 x x)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
eps

soundness2.3s (12.3%)

Rules
6422×+-lowering-+.f64
6422×+-lowering-+.f32
5418×+-lowering-+.f64
5418×+-lowering-+.f32
5386×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
072314710
1256012925
0821412925
062913
1505410
26725404
08745404
050370
1374331
23928321
08720321
084016757
1299514572
0893314572
01571381
14941186
218961117
377621117
086191117
078416834
1276614333
0840714333
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 845 to 359 computations (57.5% saved)

preprocess82.0ms (0.4%)

Compiler

Compiled 854 to 264 computations (69.1% saved)

end0.0ms (0%)

Profiling

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