2tan (problem 3.3.2)

Time bar (total: 16.5s)

analyze57.0ms (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: 34.0ms
ival-tan: 8.0ms (23.8% of total)
...c/correct-round.rkt:119:19: 7.0ms (20.8% of total)
ival-<=: 4.0ms (11.9% of total)
ival-add: 3.0ms (8.9% of total)
ival-mult: 3.0ms (8.9% of total)
ival-fabs: 3.0ms (8.9% of total)
ival-<: 3.0ms (8.9% of total)
ival-sub: 2.0ms (5.9% of total)
ival-and: 1.0ms (3% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

sample7.3s (44.2%)

Results
4.0s26201×0precondition
1.2s4434×1valid
541.0ms3822×0valid
Precisions
Click to see histograms. Total time spent on operations: 4.3s
...c/correct-round.rkt:119:19: 877.0ms (20.4% of total)
ival-tan: 708.0ms (16.4% of total)
ival-sub: 471.0ms (10.9% of total)
ival-<=: 450.0ms (10.5% of total)
ival-mult: 405.0ms (9.4% of total)
ival-<: 390.0ms (9.1% of total)
ival-fabs: 345.0ms (8% of total)
ival-add: 321.0ms (7.5% of total)
ival-and: 147.0ms (3.4% of total)
backward-pass: 139.0ms (3.2% of total)
const: 52.0ms (1.2% of total)
Bogosity

preprocess51.0ms (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))

explain92.0ms (0.6%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2202(-1.9527437492280147e-131 1.107869717900018e-133)5(7.906697221524028e-285 2.0647855124499167e-286)(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
61(-187.4627652821368 1.7615816217441026e-10)2(68.43922430872213 4.970146358281208e-7)(tan.f64 (+.f64 x eps))
00-0-x
00-0-(+.f64 x eps)
00-0-(tan.f64 x)
00-0-eps
Results
45.0ms268×1valid
16.0ms242×0valid
1.0ms2×3valid
Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 30.0ms
ival-tan: 16.0ms (52.9% of total)
ival-add: 5.0ms (16.5% of total)
backward-pass: 4.0ms (13.2% of total)
ival-sub: 4.0ms (13.2% of total)
const: 1.0ms (3.3% 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
▶64.3%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify37.0ms (0.2%)

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)

localize40.0ms (0.2%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(+.f64 x eps)
✓accuracy100.0%
(tan.f64 x)
✓accuracy99.7%
(tan.f64 (+.f64 x eps))
✓accuracy64.7%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
19.0ms134×1valid
10.0ms121×0valid
0.0ms1×3valid
Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 16.0ms
ival-tan: 7.0ms (44.8% of total)
ival-sub: 4.0ms (25.6% of total)
ival-add: 3.0ms (19.2% of total)
backward-pass: 2.0ms (12.8% of total)
const: 0.0ms (0% of total)

series12.0ms (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
3.0ms
eps
@inf
(- (tan (+ x eps)) (tan x))
2.0ms
eps
@0
(- (tan (+ x eps)) (tan x))
1.0ms
x
@0
(- (tan (+ x eps)) (tan x))
1.0ms
x
@inf
(- (tan (+ x eps)) (tan x))
1.0ms
x
@-inf
(- (tan (+ x eps)) (tan x))

rewrite314.0ms (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
241916
3655516
0850716
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 (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 (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 (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 (+.f64 x eps) (-.f64 #s(literal 0 binary64) (-.f64 x 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 (*.f64 eps (-.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 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (-.f64 eps 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))

simplify268.0ms (1.6%)

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
14941286
218911261
377211261
085671261
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 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.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 #s(literal 1/2 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)))) #s(literal -1/2 binary64)) (-.f64 (/.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 (+.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 (pow.f64 (sin.f64 eps) #s(literal 2 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 (+.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 -1/6 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 (*.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 (+.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 (/.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)))))))))
(* 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 #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 (*.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 (+.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 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #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 (*.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 (+.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 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.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 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) #s(literal -1/2 binary64)) (-.f64 #s(literal 1/6 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 (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)) #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 (+.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 -1/6 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 (*.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 (+.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 (/.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))))))))))
(/ (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 (*.f64 x 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))

eval37.0ms (0.2%)

Compiler

Compiled 8812 to 983 computations (88.8% saved)

prune51.0ms (0.3%)

Pruning

23 alts after pruning (22 fresh and 1 done)

PrunedKeptTotal
New30122323
Fresh000
Picked011
Done000
Total30123324
Accuracy
100.0%
Counts
324 → 23
Alt Table
Click to see full alt table
StatusAccuracyProgram
64.7%
(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)))
64.7%
(/.f64 (/.f64 (-.f64 (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (*.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (cos.f64 x))
64.7%
(/.f64 (-.f64 (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (*.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)))))
▶97.0%
(/.f64 (sin.f64 eps) (cos.f64 eps))
64.7%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
63.7%
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) (tan.f64 x))
▶64.7%
(-.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))
64.7%
(-.f64 (*.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))) (tan.f64 x))
26.2%
(-.f64 (tan.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (tan.f64 x))
63.7%
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) (tan.f64 x))
63.8%
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
▶64.3%
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)))
62.7%
(-.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 (*.f64 x x) #s(literal 17/315 binary64)))))))))
62.6%
(-.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))))))))
62.6%
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64))))))
✓64.3%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶62.3%
(-.f64 (tan.f64 (+.f64 x eps)) x)
8.0%
(-.f64 (tan.f64 eps) (tan.f64 x))
97.2%
(+.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))))))
99.2%
(*.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 -1/6 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 (*.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 (+.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 (/.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)))))))))
98.4%
(*.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 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))))))
▶99.3%
(*.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 -1/6 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 (*.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 (+.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 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #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 (*.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 (+.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 1329 to 600 computations (54.9% saved)

simplify269.0ms (1.6%)

Algorithm
1×egg-herbie
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(+.f64 (tan.f64 x) (tan.f64 eps))
✓cost-diff0
(/.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))))
✓cost-diff0
(*.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))))
✓cost-diff0
(-.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))
✓cost-diff0
(+.f64 x eps)
✓cost-diff0
(tan.f64 (+.f64 x eps))
✓cost-diff128
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
✓cost-diff128
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.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-diff143744
(*.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 -1/6 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 (*.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 (+.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 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #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 (*.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 (+.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-diff156416
(+.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 -1/6 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 (*.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 (+.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 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #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 (*.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 (+.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-diff163008
(+.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 -1/6 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 (*.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 (+.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 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #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 (*.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 (+.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-diff163008
(*.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 -1/6 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 (*.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 (+.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 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #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 (*.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 (+.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
3376×*-lowering-*.f32
3376×*-lowering-*.f64
2354×--lowering--.f32
2354×--lowering--.f64
2338×+-lowering-+.f64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0571767
11771480
26831175
333461062
081761062
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 (- (- -1/6 (+ -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))))))) (* eps (+ (/ (* (sin x) (+ 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)))))))) (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 (- (- -1/6 (+ -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))))))) (* eps (+ (/ (* (sin x) (+ 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)))))))) (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 (- (- -1/6 (+ -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))))))) (* eps (+ (/ (* (sin x) (+ 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)))))))) (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 (- (- -1/6 (+ -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))))))) (* eps (+ (/ (* (sin x) (+ 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)))))))) (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 (- (- -1/6 (+ -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))))))) (* eps (+ (/ (* (sin x) (+ 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)))))))) (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 (- (- -1/6 (+ -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))))))) (* eps (+ (/ (* (sin x) (+ 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)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))
(- (- -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))))))) (* eps (+ (/ (* (sin x) (+ 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)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))
(- -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
(+ -1/2 (+ (/ (* -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))))))
-1/2
(+ (/ (* -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)))))
(/ (* -1/2 (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 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))
(* 1/6 (pow (sin x) 2))
1/6
(* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* eps (+ (/ (* (sin x) (+ 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)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))
(+ (/ (* (sin x) (+ 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)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))
(/ (* (sin x) (+ 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)))))))) (cos x))
(* (sin x) (+ 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 (+ -1/2 (+ (/ (* -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)))))))
(* (* (/ (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)
(- (tan (+ x eps)) (* (/ 1 (cos x)) (sin x)))
(tan (+ x eps))
(+ x eps)
x
eps
(* (/ 1 (cos x)) (sin x))
(/ 1 (cos x))
1
(cos x)
(sin x)
(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ 1 (* (tan x) (tan eps)))) (tan x))
(* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ 1 (* (tan x) (tan eps))))
(/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2)))
(+ (tan x) (tan eps))
(tan x)
x
(tan eps)
eps
(- 1 (pow (* (tan x) (tan eps)) 2))
1
(pow (* (tan x) (tan eps)) 2)
(* (tan x) (tan eps))
2
(+ 1 (* (tan x) (tan eps)))
Outputs
(* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -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))))))) (* eps (+ (/ (* (sin x) (+ 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)))))))) (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 (-.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 -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (+.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 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 (- (- -1/6 (+ -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))))))) (* eps (+ (/ (* (sin x) (+ 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)))))))) (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 (-.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 -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (+.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 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 (- (- -1/6 (+ -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))))))) (* eps (+ (/ (* (sin x) (+ 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)))))))) (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 (-.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 -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (+.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 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 (- (- -1/6 (+ -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))))))) (* eps (+ (/ (* (sin x) (+ 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)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))))
(*.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (*.f64 eps (-.f64 (+.f64 (-.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 -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (+.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 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))))))) (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 (- (- -1/6 (+ -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))))))) (* eps (+ (/ (* (sin x) (+ 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)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (*.f64 eps (-.f64 (+.f64 (-.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 -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (+.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 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))))))) (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 (- (- -1/6 (+ -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))))))) (* eps (+ (/ (* (sin x) (+ 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)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))
(*.f64 eps (-.f64 (+.f64 (-.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 -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (+.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 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)))))))
(- (- -1/6 (+ -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))))))) (* eps (+ (/ (* (sin x) (+ 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)))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))
(-.f64 (+.f64 (-.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 -4/3 binary64))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) (*.f64 eps (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (+.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 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))))))
(- -1/6 (+ -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)))))))
(+.f64 (-.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 -4/3 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)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))
(-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64)) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64)) #s(literal 1/2 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)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 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)) (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(-.f64 (*.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)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 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)
(* (+ 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)))
(* eps (+ (/ (* (sin x) (+ 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)))))))) (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 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 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) (+ 1/6 (+ -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)))))))) (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 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 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) (+ 1/6 (+ -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)))))))) (cos x))
(/.f64 (*.f64 (sin.f64 x) (+.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 binary64))) (cos.f64 x))
(* (sin x) (+ 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))))))))
(*.f64 (sin.f64 x) (+.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 binary64)))
(+ 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)))))))
(+.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 4 binary64))) #s(literal -1/3 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)
(- (tan (+ x eps)) (* (/ 1 (cos x)) (sin x)))
(-.f64 (tan.f64 (+.f64 eps x)) (/.f64 (sin.f64 x) (cos.f64 x)))
(tan (+ x eps))
(tan.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(* (/ 1 (cos x)) (sin x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ 1 (cos x))
(/.f64 #s(literal 1 binary64) (cos.f64 x))
1
#s(literal 1 binary64)
(cos x)
(cos.f64 x)
(sin x)
(sin.f64 x)
(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ 1 (* (tan x) (tan eps)))) (tan x))
(-.f64 (/.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 #s(literal 1 binary64) (*.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)))) (tan.f64 x))
(* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ 1 (* (tan x) (tan eps))))
(/.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 #s(literal 1 binary64) (*.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))))
(/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2)))
(/.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))))
(+ (tan x) (tan eps))
(+.f64 (tan.f64 x) (tan.f64 eps))
(tan x)
(tan.f64 x)
x
(tan eps)
(tan.f64 eps)
eps
(- 1 (pow (* (tan x) (tan eps)) 2))
(-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))
1
#s(literal 1 binary64)
(pow (* (tan x) (tan eps)) 2)
(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64))
(* (tan x) (tan eps))
(*.f64 (tan.f64 x) (tan.f64 eps))
2
#s(literal 2 binary64)
(+ 1 (* (tan x) (tan eps)))
(+.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))

localize441.0ms (2.7%)

Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(+.f64 (tan.f64 x) (tan.f64 eps))
✓accuracy100.0%
(*.f64 (tan.f64 x) (tan.f64 eps))
✓accuracy99.8%
(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64))
✓accuracy64.7%
(-.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))
✓accuracy100.0%
(/.f64 #s(literal 1 binary64) (cos.f64 x))
✓accuracy100.0%
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
✓accuracy99.7%
(tan.f64 (+.f64 x eps))
✓accuracy64.7%
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.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)
✓accuracy99.7%
(tan.f64 (+.f64 x eps))
✓accuracy65.7%
(-.f64 (tan.f64 (+.f64 x eps)) x)
✓accuracy99.5%
(*.f64 (sin.f64 x) (+.f64 #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 (*.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 (+.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)))))))))
✓accuracy99.5%
(*.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))
✓accuracy98.5%
(-.f64 #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 (*.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 (+.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))))))))
✓accuracy98.5%
(+.f64 #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 (*.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 (+.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
196.0ms137×1valid
76.0ms115×0valid
17.0ms3×3valid
3.0ms1×2valid
Compiler

Compiled 1823 to 58 computations (96.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 194.0ms
ival-mult: 46.0ms (23.7% of total)
backward-pass: 25.0ms (12.9% of total)
ival-div: 23.0ms (11.9% of total)
ival-add: 20.0ms (10.3% of total)
...c/correct-round.rkt:119:19: 17.0ms (8.8% of total)
ival-tan: 16.0ms (8.2% of total)
ival-sub: 13.0ms (6.7% of total)
ival-pow: 13.0ms (6.7% of total)
ival-sin: 10.0ms (5.2% of total)
ival-cos: 9.0ms (4.6% of total)
const: 1.0ms (0.5% of total)

series96.0ms (0.6%)

Counts
23 → 444
Calls
Call 1
Inputs
#<alt (* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -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))))))) (* eps (+ (/ (* (sin x) (+ 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)))))))) (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 (- (- -1/6 (+ -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))))))) (* eps (+ (/ (* (sin x) (+ 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)))))))) (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 (- (- -1/6 (+ -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))))))) (* eps (+ (/ (* (sin x) (+ 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)))))))) (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 (- (- -1/6 (+ -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))))))) (* eps (+ (/ (* (sin x) (+ 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)))))))) (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 (- (tan (+ x eps)) (* (/ 1 (cos x)) (sin x)))>
#<alt (* (/ 1 (cos x)) (sin x))>
#<alt (- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ 1 (* (tan x) (tan eps)))) (tan x))>
#<alt (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ 1 (* (tan x) (tan eps))))>
#<alt (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2)))>
#<alt (+ (tan x) (tan eps))>
#<alt (+ 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)))))))>
#<alt (- -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)))))))>
#<alt (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)>
#<alt (* (sin x) (+ 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))))))))>
#<alt (/ 1 (cos x))>
#<alt (pow (* (tan x) (tan eps)) 2)>
#<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)))))))>
#<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 (/ (+ (* -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))))>
#<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 (/ (+ (* -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))))>
#<alt (* eps (+ 1 (* 1/3 (pow eps 2))))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))>
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#<alt (* (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)))))>
#<alt (* (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)))))>
#<alt (* (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)))))>
#<alt (* (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)))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (+ 1/2 (* 5/24 (pow x 2)))))>
#<alt (+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 5/24 (* 61/720 (pow x 2)))))))>
#<alt (/ 1 (cos x))>
#<alt (/ 1 (cos x))>
#<alt (/ 1 (cos x))>
#<alt (/ 1 (cos x))>
#<alt (/ 1 (cos x))>
#<alt (/ 1 (cos x))>
#<alt (/ 1 (cos x))>
#<alt (/ 1 (cos x))>
#<alt (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))>
#<alt (* (pow x 2) (+ (* 2/3 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))>
#<alt (* (pow x 2) (+ (* (pow x 2) (+ (* 17/45 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))>
#<alt (* (pow x 2) (+ (* (pow x 2) (+ (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* (pow x 2) (+ (* 62/315 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 17/45 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))>
#<alt (* (pow eps 2) (+ (* 2/3 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* (pow eps 2) (+ (* (pow eps 2) (+ (* 17/45 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* (pow eps 2) (+ (* (pow eps 2) (+ (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* (pow eps 2) (+ (* 62/315 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 17/45 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<alt (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))>
#<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

111 calls:

TimeVariablePointExpression
13.0ms
x
@-inf
(* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -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))))))) (* eps (+ (/ (* (sin x) (+ 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)))))))) (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)))))
11.0ms
eps
@inf
(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ 1 (* (tan x) (tan eps)))) (tan x))
8.0ms
x
@inf
(* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -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))))))) (* eps (+ (/ (* (sin x) (+ 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)))))))) (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)))))
6.0ms
eps
@inf
(* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -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))))))) (* eps (+ (/ (* (sin x) (+ 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)))))))) (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 (- (- -1/6 (+ -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))))))) (* eps (+ (/ (* (sin x) (+ 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)))))))) (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)))))

rewrite476.0ms (2.9%)

Algorithm
1×batch-egg-rewrite
Rules
3312×*-lowering-*.f32
3312×*-lowering-*.f64
2394×/-lowering-/.f32
2394×/-lowering-/.f64
1936×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
057856
1460463
25606448
08006448
Stop Event
1×iter limit
1×node limit
Counts
23 → 446
Calls
Call 1
Inputs
(* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- -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))))))) (* eps (+ (/ (* (sin x) (+ 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)))))))) (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 (- (- -1/6 (+ -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))))))) (* eps (+ (/ (* (sin x) (+ 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)))))))) (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 (- (- -1/6 (+ -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))))))) (* eps (+ (/ (* (sin x) (+ 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)))))))) (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 (- (- -1/6 (+ -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))))))) (* eps (+ (/ (* (sin x) (+ 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)))))))) (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)
(- (tan (+ x eps)) (* (/ 1 (cos x)) (sin x)))
(* (/ 1 (cos x)) (sin x))
(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ 1 (* (tan x) (tan eps)))) (tan x))
(* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2))) (+ 1 (* (tan x) (tan eps))))
(/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 2)))
(+ (tan x) (tan eps))
(+ 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 (+ -1/2 (+ (/ (* -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)))))))
(* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)
(* (sin x) (+ 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 (cos x))
(pow (* (tan x) (tan eps)) 2)
(* (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 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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))))) #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)))))))))))
(+.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 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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))))) #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 #s(literal 1 binary64) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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))))) #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)))))))))) (*.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
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(/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) (-.f64 (*.f64 (*.f64 (sin.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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (*.f64 (sin.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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))))) (*.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) (*.f64 (sin.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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))))))))
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(/.f64 (*.f64 (sin.f64 x) (-.f64 #s(literal 1/36 binary64) (pow.f64 (+.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) #s(literal 2 binary64)))) (-.f64 #s(literal 2/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))))
(/.f64 (*.f64 (+.f64 #s(literal 1/216 binary64) (pow.f64 (+.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) #s(literal 3 binary64))) (sin.f64 x)) (+.f64 #s(literal 1/36 binary64) (*.f64 (+.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (+.f64 #s(literal -2/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))))))
(/.f64 (*.f64 (-.f64 #s(literal 1/36 binary64) (pow.f64 (+.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) #s(literal 2 binary64))) (sin.f64 x)) (-.f64 #s(literal 2/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))))
(*.f64 (sin.f64 x) (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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))))) #s(literal -1/3 binary64)))
(*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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))))) #s(literal -1/3 binary64)) (sin.f64 x))
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)))
(/.f64 #s(literal 1 binary64) (cos.f64 x))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(pow.f64 (cos.f64 x) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 x)))
(*.f64 (pow.f64 (cos.f64 x) #s(literal -1/2 binary64)) (pow.f64 (cos.f64 x) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 (*.f64 (tan.f64 x) (tan.f64 eps)))))
(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 (*.f64 (tan.f64 x) (tan.f64 eps)))) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))
(*.f64 (tan.f64 x) (*.f64 (tan.f64 eps) (*.f64 (tan.f64 x) (tan.f64 eps))))
(*.f64 (tan.f64 eps) (*.f64 (tan.f64 x) (*.f64 (tan.f64 x) (tan.f64 eps))))
(*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
(*.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(*.f64 (exp.f64 (log.f64 (*.f64 (tan.f64 x) (tan.f64 eps)))) (exp.f64 (log.f64 (*.f64 (tan.f64 x) (tan.f64 eps)))))
(*.f64 (*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (tan.f64 x)) (tan.f64 eps))
(*.f64 (*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (tan.f64 eps)) (tan.f64 x))
(exp.f64 (*.f64 (log.f64 (*.f64 (tan.f64 x) (tan.f64 eps))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 eps))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(/.f64 (sin.f64 x) (*.f64 (cos.f64 x) (/.f64 #s(literal 1 binary64) (tan.f64 eps))))
(/.f64 (sin.f64 x) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 eps)) (cos.f64 x)))
(/.f64 (tan.f64 x) (/.f64 #s(literal 1 binary64) (tan.f64 eps)))
(/.f64 (tan.f64 eps) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.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 #s(literal 1 binary64) (sin.f64 eps)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (cos.f64 eps)))
(/.f64 (*.f64 #s(literal 1 binary64) (-.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 (sin.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 #s(literal 0 binary64) (sin.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 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 eps)) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (cos.f64 eps)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.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 #s(literal 1 binary64) (-.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 (sin.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 eps) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(/.f64 (*.f64 (sin.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 #s(literal 0 binary64) (sin.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 #s(literal 0 binary64) (sin.f64 eps)) (sin.f64 x)) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 eps)) (cos.f64 x)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.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 (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 (tan.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (-.f64 #s(literal 0 binary64) (cos.f64 eps)))
(/.f64 (*.f64 (tan.f64 eps) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 (*.f64 (tan.f64 eps) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(/.f64 (*.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) (tan.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 eps)))
(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))
(*.f64 (sin.f64 x) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (tan.f64 eps)))
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(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (sin.f64 x) (tan.f64 eps)))
(*.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 (pow.f64 (tan.f64 x) #s(literal 1 binary64)) (pow.f64 (tan.f64 eps) #s(literal 1 binary64)))
(*.f64 (pow.f64 (tan.f64 eps) #s(literal 1 binary64)) (pow.f64 (tan.f64 x) #s(literal 1 binary64)))
(*.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 1/2 binary64)))
(*.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (/.f64 #s(literal 1 binary64) (cos.f64 eps)))
(*.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 (*.f64 (tan.f64 eps) (/.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x))

simplify402.0ms (2.4%)

Algorithm
1×egg-herbie
Rules
5128×+-lowering-+.f64
5128×+-lowering-+.f32
5024×*-lowering-*.f32
5024×*-lowering-*.f64
1608×fma-lowering-fma.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
071816473
1252715853
0882215853
Stop Event
1×iter limit
1×node limit
Counts
444 → 444
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))))
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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)))) (+ (* -1/2 (/ (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))))))
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(+ 1 (* 1/3 (pow eps 2)))
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(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2))))))))
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(/ (pow (sin x) 2) (pow (cos x) 2))
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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))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -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)))) (+ (* -1/2 (/ (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))))))
(* 1/3 (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)))))))))))
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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)))) (/ (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))) (+ (* -1/2 (/ (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 (+ (* 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 (+ (* 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 (+ (* 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 (+ (* 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 (+ (* 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 (* (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))))
(* -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 (+ (* -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 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)))))))
(* (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 (/ (- (+ 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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(* (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)))))
(* (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)))))
(* (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)))))
(* (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)))))
(* (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)))))
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* 5/24 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 5/24 (* 61/720 (pow x 2)))))))
(/ 1 (cos x))
(/ 1 (cos x))
(/ 1 (cos x))
(/ 1 (cos x))
(/ 1 (cos x))
(/ 1 (cos x))
(/ 1 (cos x))
(/ 1 (cos x))
(/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))
(* (pow x 2) (+ (* 2/3 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))
(* (pow x 2) (+ (* (pow x 2) (+ (* 17/45 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))
(* (pow x 2) (+ (* (pow x 2) (+ (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* (pow x 2) (+ (* 62/315 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 17/45 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))
(* (pow eps 2) (+ (* 2/3 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 17/45 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* (pow eps 2) (+ (* 62/315 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 17/45 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/ (* 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) (+ 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 eps (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)))) (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 #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 #s(literal 1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (*.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)))) (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 (*.f64 #s(literal -1/3 binary64) (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 (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) (/.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 #s(literal 1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (*.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)))) (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 (*.f64 #s(literal -1/3 binary64) (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 (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) (/.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)))))))
(*.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 #s(literal -1/3 binary64) (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 (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) (/.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)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/3 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)) (+ (/ (* (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)))))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (-.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 (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))))) (*.f64 (cos.f64 x) (*.f64 eps eps))))) (+.f64 (/.f64 (*.f64 (*.f64 #s(literal -1/3 binary64) (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 (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) (/.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)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/3 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)) (+ (/ 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)))))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (-.f64 (+.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 (*.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))))) (*.f64 (cos.f64 x) (*.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 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1/3 binary64) eps))) (+.f64 (/.f64 (*.f64 (*.f64 #s(literal -1/3 binary64) (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 (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) (/.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)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/3 binary64))))
(* -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 (*.f64 #s(literal -1/3 binary64) (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 (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) (/.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))))
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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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(* 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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(* 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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(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps eps)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* (pow eps 2) (+ (* 2/3 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 17/45 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 (*.f64 #s(literal 17/45 binary64) (*.f64 eps eps)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* (pow eps 2) (+ (* 62/315 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 17/45 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 (*.f64 #s(literal 62/315 binary64) (*.f64 eps eps)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 17/45 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2)))
(/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(/ (* x (sin eps)) (cos eps))
(/.f64 (*.f64 x (sin.f64 eps)) (cos.f64 eps))
(* x (+ (* 1/3 (/ (* (pow x 2) (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 1/3 binary64) (sin.f64 eps)) (cos.f64 eps)))))
(* 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 (*.f64 x x) (/.f64 (*.f64 #s(literal 2/15 binary64) (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 (*.f64 (*.f64 #s(literal 17/315 binary64) (*.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 (*.f64 eps eps) (/.f64 (*.f64 #s(literal 1/3 binary64) (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 (*.f64 #s(literal 1/3 binary64) (sin.f64 x)) (cos.f64 x)) (/.f64 (*.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 eps (sin.f64 x)) eps)) (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 (*.f64 #s(literal 17/315 binary64) (*.f64 (*.f64 eps (sin.f64 x)) eps)) (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)))

eval211.0ms (1.3%)

Compiler

Compiled 60901 to 3677 computations (94% saved)

prune116.0ms (0.7%)

Pruning

29 alts after pruning (26 fresh and 3 done)

PrunedKeptTotal
New1015151030
Fresh61117
Picked325
Done011
Total1024291053
Accuracy
100.0%
Counts
1053 → 29
Alt Table
Click to see full alt table
StatusAccuracyProgram
64.7%
(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)))
64.7%
(/.f64 (/.f64 (-.f64 (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (*.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (cos.f64 x))
64.7%
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
97.0%
(/.f64 eps (cos.f64 eps))
26.4%
(-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 #s(literal 1 binary64) (*.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)))) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 #s(literal 1 binary64) (*.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)))) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) (/.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 #s(literal 1 binary64) (*.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 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 #s(literal 1 binary64) (*.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)))) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) (/.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 #s(literal 1 binary64) (*.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)))))))))
64.7%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
63.7%
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) (tan.f64 x))
✓64.7%
(-.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))
▶64.7%
(-.f64 (*.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))) (tan.f64 x))
63.7%
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) (tan.f64 x))
▶63.8%
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
✓64.3%
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)))
62.7%
(-.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 (*.f64 x x) #s(literal 17/315 binary64)))))))))
62.6%
(-.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))))))))
✓64.3%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
8.0%
(-.f64 (tan.f64 eps) (tan.f64 x))
▶99.4%
(+.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 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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))))) #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)
▶97.2%
(+.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)))))))
99.0%
(*.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)))))))
97.2%
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.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))))))))
98.4%
(*.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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (*.f64 eps (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)))) (cos.f64 x))))))
98.1%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 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))))))
96.9%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))
97.0%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/315 binary64))))))))
97.0%
(*.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))))))
97.0%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
97.0%
(tan.f64 eps)
▶97.0%
eps
Compiler

Compiled 1481 to 710 computations (52.1% saved)

simplify251.0ms (1.5%)

Algorithm
1×egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓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-diff128
(*.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)))
✓cost-diff128
(-.f64 (*.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))) (tan.f64 x))
✓cost-diff0
(+.f64 x eps)
✓cost-diff0
(tan.f64 (+.f64 x eps))
✓cost-diff256
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
✓cost-diff256
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
✓cost-diff0
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
✓cost-diff256
(+.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)))))
✓cost-diff256
(*.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))))))
✓cost-diff384
(+.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)))))))
✓cost-diff38976
(*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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))))) #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-diff45312
(+.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 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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))))) #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-diff45312
(*.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 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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))))) #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-diff45312
(+.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 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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))))) #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
3902×+-lowering-+.f64
3902×+-lowering-+.f32
2632×*-lowering-*.f32
2632×*-lowering-*.f64
2062×sum3-define
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
056808
1204728
2810704
33548702
08603702
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 (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -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 (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -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 (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -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 (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))
(+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))
(+ (tan x) (pow (tan x) 3))
(pow (tan x) 3)
3
(* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))
(- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))
(- 1/3 (- (* (pow (tan x) 2) -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))))
(* (pow (tan x) 2) -1/3)
-1/3
(* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))
(+ 1 (pow (tan x) 2))
1
(* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))
(+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))
(* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x))
(+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3)
(* (+ (tan x) (pow (tan x) 3)) -1/3)
eps
(+ (* eps (+ 1 (* 1/3 (* eps eps)))) (* x (+ (* (* eps x) (+ 1 (* (* eps eps) 4/3))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3))))))
(* eps (+ 1 (* 1/3 (* eps eps))))
eps
(+ 1 (* 1/3 (* eps eps)))
1
(* 1/3 (* eps eps))
1/3
(* eps eps)
(* x (+ (* (* eps x) (+ 1 (* (* eps eps) 4/3))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3)))))
x
(+ (* (* eps x) (+ 1 (* (* eps eps) 4/3))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3))))
(* (* eps x) (+ 1 (* (* eps eps) 4/3)))
(* eps x)
(+ 1 (* (* eps eps) 4/3))
(* (* eps eps) 4/3)
4/3
(* (* eps eps) (+ 1 (* (* eps eps) 2/3)))
(+ 1 (* (* eps eps) 2/3))
(* (* eps eps) 2/3)
2/3
(- (tan (+ x eps)) (/ 1 (/ 1 (tan x))))
(tan (+ x eps))
(+ x eps)
x
eps
(/ 1 (/ 1 (tan x)))
1
(/ 1 (tan x))
(tan x)
(- (* (/ 1 (- 1 (* (tan x) (tan eps)))) (+ (tan x) (tan eps))) (tan x))
(* (/ 1 (- 1 (* (tan x) (tan eps)))) (+ (tan x) (tan eps)))
(/ 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))
Outputs
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) eps)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (*.f64 (tan.f64 x) (+.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 eps #s(literal -1/3 binary64))) (+.f64 (*.f64 (tan.f64 x) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 #s(literal -1/3 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)))))))))))))))
(* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))))
(*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) eps)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (*.f64 (tan.f64 x) (+.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 eps #s(literal -1/3 binary64))) (+.f64 (*.f64 (tan.f64 x) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 #s(literal -1/3 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))))))))))))))
eps
(+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))
(+.f64 (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) eps)) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (*.f64 (tan.f64 x) (+.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 eps #s(literal -1/3 binary64))) (+.f64 (*.f64 (tan.f64 x) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 #s(literal -1/3 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)))))))))))))
(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 (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))
(*.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (*.f64 (tan.f64 x) (+.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 eps #s(literal -1/3 binary64))) (+.f64 (*.f64 (tan.f64 x) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 #s(literal -1/3 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)))))))))))))
(+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))
(+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (*.f64 (tan.f64 x) (+.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 eps #s(literal -1/3 binary64))) (+.f64 (*.f64 (tan.f64 x) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 #s(literal -1/3 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))))))))))))
(+ (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 (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))
(*.f64 eps (-.f64 #s(literal 1/3 binary64) (*.f64 (tan.f64 x) (+.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 eps #s(literal -1/3 binary64))) (+.f64 (*.f64 (tan.f64 x) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 #s(literal -1/3 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))))))))))
(- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))
(-.f64 #s(literal 1/3 binary64) (*.f64 (tan.f64 x) (+.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 eps #s(literal -1/3 binary64))) (+.f64 (*.f64 (tan.f64 x) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 eps (+.f64 #s(literal -1/3 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)))))))))
(- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))
(+.f64 #s(literal 1/3 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))))
1/3
#s(literal 1/3 binary64)
(- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))
(-.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)))
(* (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)
(* (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)
(* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))
(*.f64 eps (*.f64 (tan.f64 x) (+.f64 (+.f64 #s(literal -1/3 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)))) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))))
(+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))
(*.f64 (tan.f64 x) (+.f64 (+.f64 #s(literal -1/3 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)))) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))))
(* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x))
(*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 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)))))
(+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3)
(+.f64 #s(literal -1/3 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))))
(* (+ (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 (* 1/3 (* eps eps)))) (* x (+ (* (* eps x) (+ 1 (* (* eps eps) 4/3))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3))))))
(*.f64 eps (+.f64 (*.f64 (+.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 eps x) #s(literal 4/3 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))) x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))))
(* eps (+ 1 (* 1/3 (* eps eps))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))))
eps
(+ 1 (* 1/3 (* eps eps)))
(+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))
1
#s(literal 1 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)
(* x (+ (* (* eps x) (+ 1 (* (* eps eps) 4/3))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3)))))
(*.f64 x (*.f64 eps (+.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 eps x) #s(literal 4/3 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))
x
(+ (* (* eps x) (+ 1 (* (* eps eps) 4/3))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3))))
(*.f64 eps (+.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 eps x) #s(literal 4/3 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))))))
(* (* eps x) (+ 1 (* (* eps eps) 4/3)))
(*.f64 (*.f64 eps x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))))
(* eps x)
(*.f64 eps x)
(+ 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 eps) (+ 1 (* (* eps eps) 2/3)))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))
(+ 1 (* (* eps eps) 2/3))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)))
(* (* eps eps) 2/3)
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
2/3
#s(literal 2/3 binary64)
(- (tan (+ x eps)) (/ 1 (/ 1 (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
(/ 1 (/ 1 (tan x)))
(tan.f64 x)
1
#s(literal 1 binary64)
(/ 1 (tan x))
(/.f64 #s(literal 1 binary64) (tan.f64 x))
(tan x)
(tan.f64 x)
(- (* (/ 1 (- 1 (* (tan x) (tan eps)))) (+ (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))
(* (/ 1 (- 1 (* (tan x) (tan eps)))) (+ (tan x) (tan eps)))
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
(/ 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))

localize505.0ms (3.1%)

Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓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))
✓accuracy100.0%
(*.f64 (tan.f64 x) (tan.f64 eps))
✓accuracy64.7%
(-.f64 (*.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))) (tan.f64 x))
✓accuracy100.0%
(/.f64 #s(literal 1 binary64) (tan.f64 x))
✓accuracy99.7%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
✓accuracy99.7%
(tan.f64 (+.f64 x eps))
✓accuracy64.7%
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
✓accuracy99.8%
(+.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)))))
✓accuracy99.7%
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))
✓accuracy99.6%
(*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))
✓accuracy99.6%
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64))
✓accuracy99.6%
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))
✓accuracy99.5%
(*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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))))) #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))))))
✓accuracy99.5%
(*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))
✓accuracy99.4%
(*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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))))) #s(literal -1/3 binary64)) (tan.f64 x))
Results
251.0ms136×1valid
76.0ms116×0valid
17.0ms3×3valid
3.0ms1×2valid
Compiler

Compiled 943 to 57 computations (94% saved)

Precisions
Click to see histograms. Total time spent on operations: 251.0ms
ival-mult: 131.0ms (52.1% of total)
ival-add: 26.0ms (10.3% of total)
ival-tan: 22.0ms (8.8% of total)
...c/correct-round.rkt:119:19: 22.0ms (8.8% of total)
backward-pass: 17.0ms (6.8% of total)
ival-pow: 14.0ms (5.6% of total)
ival-sub: 11.0ms (4.4% of total)
ival-div: 8.0ms (3.2% of total)
const: 1.0ms (0.4% of total)

series108.0ms (0.7%)

Counts
26 → 516
Calls
Call 1
Inputs
#<alt (+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -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 (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -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 (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))>
#<alt (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))>
#<alt (+ (* eps (+ 1 (* 1/3 (* eps eps)))) (* x (+ (* (* eps x) (+ 1 (* (* eps eps) 4/3))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3))))))>
#<alt (* x (+ (* (* eps x) (+ 1 (* (* eps eps) 4/3))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3)))))>
#<alt (+ (* (* eps x) (+ 1 (* (* eps eps) 4/3))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3))))>
#<alt (* eps (+ 1 (* 1/3 (* eps eps))))>
#<alt (- (tan (+ x eps)) (/ 1 (/ 1 (tan x))))>
#<alt (/ 1 (/ 1 (tan x)))>
#<alt (tan (+ x eps))>
#<alt (+ x eps)>
#<alt (- (* (/ 1 (- 1 (* (tan x) (tan eps)))) (+ (tan x) (tan eps))) (tan x))>
#<alt (* (/ 1 (- 1 (* (tan x) (tan eps)))) (+ (tan x) (tan eps)))>
#<alt (/ 1 (- 1 (* (tan x) (tan eps))))>
#<alt (- 1 (* (tan x) (tan eps)))>
#<alt (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x))>
#<alt (* (+ (tan x) (pow (tan x) 3)) -1/3)>
#<alt (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))>
#<alt (* (pow (tan x) 2) -1/3)>
#<alt (* (* eps eps) 4/3)>
#<alt (* (* eps eps) 2/3)>
#<alt (* 1/3 (* eps eps))>
#<alt (/ 1 (tan x))>
#<alt (* (tan x) (tan 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)))) (/ (* (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)))))>
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#<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) (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

129 calls:

TimeVariablePointExpression
24.0ms
eps
@0
(- 1 (* (tan x) (tan eps)))
16.0ms
x
@inf
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (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 (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
4.0ms
x
@0
(- (tan (+ x eps)) (/ 1 (/ 1 (tan x))))
3.0ms
x
@-inf
(+ (* eps (+ 1 (* 1/3 (* eps eps)))) (* x (+ (* (* eps x) (+ 1 (* (* eps eps) 4/3))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3))))))

rewrite342.0ms (2.1%)

Algorithm
1×batch-egg-rewrite
Rules
2850×*-lowering-*.f32
2850×*-lowering-*.f64
2208×fma-lowering-fma.f32
2208×fma-lowering-fma.f64
1958×fmm-def
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
056482
1475433
25401433
08199433
Stop Event
1×iter limit
1×node limit
Counts
26 → 464
Calls
Call 1
Inputs
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -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 (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))))
(+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))
(* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))
(+ (* eps (+ 1 (* 1/3 (* eps eps)))) (* x (+ (* (* eps x) (+ 1 (* (* eps eps) 4/3))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3))))))
(* x (+ (* (* eps x) (+ 1 (* (* eps eps) 4/3))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3)))))
(+ (* (* eps x) (+ 1 (* (* eps eps) 4/3))) (* (* eps eps) (+ 1 (* (* eps eps) 2/3))))
(* eps (+ 1 (* 1/3 (* eps eps))))
(- (tan (+ x eps)) (/ 1 (/ 1 (tan x))))
(/ 1 (/ 1 (tan x)))
(tan (+ x eps))
(+ x eps)
(- (* (/ 1 (- 1 (* (tan x) (tan eps)))) (+ (tan x) (tan eps))) (tan x))
(* (/ 1 (- 1 (* (tan x) (tan eps)))) (+ (tan x) (tan eps)))
(/ 1 (- 1 (* (tan x) (tan eps))))
(- 1 (* (tan x) (tan eps)))
(* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x))
(* (+ (tan x) (pow (tan x) 3)) -1/3)
(* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* (+ (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) -1/3) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))
(* (pow (tan x) 2) -1/3)
(* (* eps eps) 4/3)
(* (* eps eps) 2/3)
(* 1/3 (* eps eps))
(/ 1 (tan x))
(* (tan x) (tan 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 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 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 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)
(+.f64 (*.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (*.f64 (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))) (*.f64 eps eps)) eps))
(+.f64 (+.f64 eps (*.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))) (*.f64 eps eps)))
(-.f64 (/.f64 (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 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) #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 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)) (/.f64 (*.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 (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) eps)))
(fma.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 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))) eps)
(fma.f64 (+.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 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 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 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) #s(literal 2 binary64)) (*.f64 eps (-.f64 eps (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))))))))))) (+.f64 (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 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 #s(literal -1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)))))))))) #s(literal 3 binary64)) (*.f64 eps (*.f64 eps eps)))))
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(/.f64 (*.f64 #s(literal -1 binary64) (tan.f64 eps)) (/.f64 #s(literal -1 binary64) (tan.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 eps)) (tan.f64 x))
(*.f64 (*.f64 (tan.f64 eps) #s(literal 1 binary64)) (tan.f64 x))
(+.f64 (tan.f64 x) (tan.f64 eps))
(+.f64 (tan.f64 x) (*.f64 #s(literal 1 binary64) (tan.f64 eps)))
(+.f64 (tan.f64 x) (*.f64 (tan.f64 eps) #s(literal 1 binary64)))
(+.f64 (tan.f64 eps) (tan.f64 x))
(+.f64 (*.f64 #s(literal 1 binary64) (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 #s(literal 1 binary64) (tan.f64 x) (tan.f64 eps))
(/.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 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #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 eps) (cos.f64 x)))
(/.f64 (sin.f64 (+.f64 eps x)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(/.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #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 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #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) (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) (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 (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 -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 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #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 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #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 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 eps) #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))))

simplify467.0ms (2.8%)

Algorithm
1×egg-herbie
Rules
6406×+-lowering-+.f64
6406×+-lowering-+.f32
4644×*-lowering-*.f32
4644×*-lowering-*.f64
1378×distribute-lft-in
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
084517484
1300517148
0860417148
Stop Event
1×iter limit
1×node limit
Counts
516 → 516
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))))
(* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))))
(* eps (+ 1 (+ (* eps (+ x (* eps (+ 1/3 (+ (* 2/3 (* eps x)) (* 4/3 (pow x 2))))))) (pow x 2))))
(* 2/3 (* (pow eps 4) x))
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (* 1/3 (/ 1 eps)))))
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2))))))
(* (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))))))))
(* 2/3 (* (pow eps 4) x))
(* (pow eps 4) (+ (* -1 (/ (- (* -4/3 (pow x 2)) 1/3) eps)) (* 2/3 x)))
(* (pow eps 4) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ x eps))) 1/3) eps)) (* 2/3 x)))
(* (pow eps 4) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ (+ x (* -1 (/ (- (* -1 (pow x 2)) 1) eps))) eps))) 1/3) eps)) (* 2/3 x)))
(* 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 (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
(* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))))
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) 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))))
(* (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))))
(* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))))
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) 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))))))
(* (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))))))
(* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))
(* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))
(* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))
(* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))
(* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))))
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))
(* eps (* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))))
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))
(* (pow x 2) (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))
(* eps (pow x 2))
(* eps (+ (* eps x) (pow x 2)))
(* eps (+ (* eps (+ x (* 4/3 (* eps (pow x 2))))) (pow x 2)))
(* eps (+ (* eps (+ x (* eps (+ (* 2/3 (* eps x)) (* 4/3 (pow x 2)))))) (pow x 2)))
(* 2/3 (* (pow eps 4) x))
(* (pow eps 4) (+ (* 2/3 x) (* 4/3 (/ (pow x 2) eps))))
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (/ x (pow eps 2)))))
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ x (pow eps 2)) (/ (pow x 2) (pow eps 3))))))
(* 2/3 (* (pow eps 4) x))
(* (pow eps 4) (+ (* 2/3 x) (* 4/3 (/ (pow x 2) eps))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -4/3 (pow x 2)) (* -1 (/ x eps))) eps)) (* 2/3 x)))
(* (pow eps 4) (+ (* -1 (/ (+ (* -4/3 (pow x 2)) (* -1 (/ (+ x (/ (pow x 2) eps)) eps))) eps)) (* 2/3 x)))
(* eps x)
(* eps (+ eps x))
(* eps (+ x (* eps (+ 1 (* 4/3 (* eps x))))))
(* eps (+ x (* eps (+ 1 (* eps (+ (* 2/3 eps) (* 4/3 x)))))))
(* 2/3 (pow eps 4))
(* (pow eps 4) (+ 2/3 (* 4/3 (/ x eps))))
(* (pow eps 4) (+ 2/3 (+ (* 4/3 (/ x eps)) (/ 1 (pow eps 2)))))
(* (pow eps 4) (+ 2/3 (+ (* 4/3 (/ x eps)) (+ (/ 1 (pow eps 2)) (/ x (pow eps 3))))))
(* 2/3 (pow eps 4))
(* (pow eps 4) (+ 2/3 (* 4/3 (/ x eps))))
(* (pow eps 4) (+ 2/3 (* -1 (/ (- (* -4/3 x) (/ 1 eps)) eps))))
(* (pow eps 4) (+ 2/3 (* -1 (/ (+ (* -4/3 x) (* -1 (/ (+ 1 (/ x eps)) eps))) eps))))
(* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))
(+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))
(+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))
(+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))
(* eps (* x (+ 1 (* 4/3 (pow eps 2)))))
(* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))
(* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))
(* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))
(* eps (* x (+ 1 (* 4/3 (pow eps 2)))))
(* -1 (* x (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))))
(* -1 (* x (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))))
(* -1 (* x (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) x)))))
eps
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* 1/3 (pow eps 3))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* 1/3 (pow eps 3))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(/ (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)))
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))
(/ (sin eps) (cos eps))
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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)))))
(* (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 (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)))
(* 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))
(* 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))
(* 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))
(/ 1 x)
(/ (+ 1 (* -1/3 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) 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) (sin 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)))
(/ (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) (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 (/.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 (+ (* 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 (*.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 1/3 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 (*.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) (- (+ (* 1/3 (/ 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 (/.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 #s(literal -1/3 binary64) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.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 (*.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)))))
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(* (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))))))
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(* -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)))))
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(* (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))))))
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(* (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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(* 1/3 (pow eps 2))
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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 (/ (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))))))
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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 (/ (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))))))
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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 (/ (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))))))
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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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(* (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 (* (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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(* 1/3 (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 (+ (* 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 (+ (* 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 (pow.f64 eps #s(literal 4 binary64)) #s(literal 2/3 binary64)) x)
(* (pow eps 4) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (* 1/3 (/ 1 eps)))))
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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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(* (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 (pow.f64 eps #s(literal 4 binary64)) #s(literal 2/3 binary64)) x)
(* (pow eps 4) (+ (* -1 (/ (- (* -4/3 (pow x 2)) 1/3) eps)) (* 2/3 x)))
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(* (pow eps 4) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ x eps))) 1/3) eps)) (* 2/3 x)))
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(* (pow eps 4) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ (+ x (* -1 (/ (- (* -1 (pow x 2)) 1) eps))) eps))) 1/3) eps)) (* 2/3 x)))
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(* eps (+ 1 (* 1/3 (pow eps 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))))))
(*.f64 (*.f64 eps eps) (+.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 (*.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 1/3 binary64) (/.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)))) (/ (* (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)
(*.f64 eps #s(literal 1/3 binary64))
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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))) (+ (* -1/3 (/ (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 (- (+ 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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(* 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)))))))
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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)))) (/ (* (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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(/ (* (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) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ x (/ (sin eps) (cos eps)))
(+.f64 x (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.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)))))) (/ (sin eps) (cos eps)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) #s(literal 2/15 binary64)))))))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(+ eps (/ (sin x) (cos x)))
(+.f64 eps (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))
(+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 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)))))))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps)))

eval137.0ms (0.8%)

Compiler

Compiled 50151 to 3177 computations (93.7% saved)

prune111.0ms (0.7%)

Pruning

34 alts after pruning (29 fresh and 5 done)

PrunedKeptTotal
New98214996
Fresh61521
Picked235
Done123
Total991341025
Accuracy
100.0%
Counts
1025 → 34
Alt Table
Click to see full alt table
StatusAccuracyProgram
64.7%
(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)))
64.7%
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
97.0%
(/.f64 eps (cos.f64 eps))
26.4%
(-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 #s(literal 1 binary64) (*.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)))) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 #s(literal 1 binary64) (*.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)))) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) (/.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 #s(literal 1 binary64) (*.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 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 #s(literal 1 binary64) (*.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)))) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) (/.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 #s(literal 1 binary64) (*.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)))))))))
64.7%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
63.7%
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) (tan.f64 x))
✓64.7%
(-.f64 (*.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))) (tan.f64 x))
63.7%
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) (tan.f64 x))
▶62.2%
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x)))
62.1%
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -1/45 binary64)) #s(literal -1/3 binary64)))) x)))
✓63.8%
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
✓64.3%
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)))
62.7%
(-.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 (*.f64 x x) #s(literal 17/315 binary64)))))))))
62.6%
(-.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) #s(literal 2/15 binary64)))))))
✓64.3%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
8.0%
(-.f64 (tan.f64 eps) (tan.f64 x))
▶98.4%
(+.f64 (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
98.1%
(+.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 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)
▶99.2%
(+.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 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.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)
99.1%
(+.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)
98.4%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)
48.9%
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 2/3 binary64) (/.f64 (+.f64 (*.f64 x #s(literal -4/3 binary64)) (/.f64 #s(literal -1 binary64) eps)) eps)))))
97.0%
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 2/3 binary64) (/.f64 (*.f64 x #s(literal 4/3 binary64)) eps)))))
97.2%
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps x)))
98.4%
(*.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)))))
96.9%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))
97.0%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/315 binary64))))))))
97.0%
(*.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))))))
97.2%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x))))
▶97.2%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
97.0%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
▶97.0%
(tan.f64 eps)
✓97.0%
eps
Compiler

Compiled 1503 to 798 computations (46.9% saved)

simplify219.0ms (1.3%)

Algorithm
1×egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
✓cost-diff0
(*.f64 eps (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
✓cost-diff0
(/.f64 (*.f64 eps (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
✓cost-diff0
(+.f64 (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
✓cost-diff0
(+.f64 x eps)
✓cost-diff0
(tan.f64 (+.f64 x eps))
✓cost-diff128
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x))
✓cost-diff128
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x)))
✓cost-diff0
(tan.f64 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-diff19456
(*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.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))))))))
✓cost-diff25792
(+.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 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.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)))))))))
✓cost-diff25792
(*.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 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.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))))))))))
✓cost-diff25792
(+.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 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.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)
Rules
4582×+-lowering-+.f64
4582×+-lowering-+.f32
3402×*-lowering-*.f32
3402×*-lowering-*.f64
1602×sum3-define
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
051599
1166562
2603543
32513542
08183542
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 (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
(* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))))
eps
(+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))
(pow (tan x) 2)
(tan x)
x
2
(* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))
(+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))
(+ (tan x) (pow (tan x) 3))
(pow (tan x) 3)
3
(* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))
(- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))
(- 1/3 (- (* (pow (tan x) 2) -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))))
(* (pow (tan x) 2) -1/3)
-1/3
(* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))
(+ 1 (pow (tan x) 2))
1
(* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))
(+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))
(* x -1/3)
(* (+ (tan x) (pow (tan x) 3)) -1/3)
(* eps (+ 1 (* x x)))
eps
(+ 1 (* x x))
1
(* x x)
x
(tan eps)
eps
(- (tan (+ x eps)) (/ 1 (/ (+ 1 (* (* x x) (+ (* (* x x) (+ (* (* x x) -2/945) -1/45)) -1/3))) x)))
(tan (+ x eps))
(+ x eps)
x
eps
(/ 1 (/ (+ 1 (* (* x x) (+ (* (* x x) (+ (* (* x x) -2/945) -1/45)) -1/3))) x))
1
(/ (+ 1 (* (* x x) (+ (* (* x x) (+ (* (* x x) -2/945) -1/45)) -1/3))) x)
(+ 1 (* (* x x) (+ (* (* x x) (+ (* (* x x) -2/945) -1/45)) -1/3)))
(* (* x x) (+ (* (* x x) (+ (* (* x x) -2/945) -1/45)) -1/3))
(* x x)
(+ (* (* x x) (+ (* (* x x) -2/945) -1/45)) -1/3)
(* (* x x) (+ (* (* x x) -2/945) -1/45))
(+ (* (* x x) -2/945) -1/45)
(* (* x x) -2/945)
-2/945
-1/45
-1/3
(+ (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)) eps)
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(* eps (pow (sin x) 2))
eps
(pow (sin x) 2)
(sin x)
x
2
(pow (cos x) 2)
(cos x)
Outputs
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* x -1/3) (* (+ (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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))) (+.f64 (*.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 eps (*.f64 x #s(literal 1/3 binary64))))))))))
(* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))))
(*.f64 eps (+.f64 (*.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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))) (+.f64 (*.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 eps (*.f64 x #s(literal 1/3 binary64))))))))))
eps
(+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))
(+.f64 (*.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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))) (+.f64 (*.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 eps (*.f64 x #s(literal 1/3 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 (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))
(*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (+.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))) (+.f64 (*.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 eps (*.f64 x #s(literal 1/3 binary64))))))))
(+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))
(+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (+.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))) (+.f64 (*.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 eps (*.f64 x #s(literal 1/3 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 (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))) (+.f64 (*.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 eps (*.f64 x #s(literal 1/3 binary64))))))
(- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))
(+.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64))) (+.f64 (*.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 eps (*.f64 x #s(literal 1/3 binary64)))))
(- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))))
(+.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))))
1/3
#s(literal 1/3 binary64)
(- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))
(-.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)))
(* (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)
(* (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)
(* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))
(*.f64 #s(literal -1/3 binary64) (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 x (tan.f64 x)))))
(+ (* x -1/3) (* (+ (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 x (tan.f64 x))))
(* x -1/3)
(*.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
(tan eps)
(tan.f64 eps)
eps
(- (tan (+ x eps)) (/ 1 (/ (+ 1 (* (* x x) (+ (* (* x x) (+ (* (* x x) -2/945) -1/45)) -1/3))) x)))
(-.f64 (tan.f64 (+.f64 eps x)) (/.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/3 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))))))))
(tan (+ x eps))
(tan.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(/ 1 (/ (+ 1 (* (* x x) (+ (* (* x x) (+ (* (* x x) -2/945) -1/45)) -1/3))) x))
(/.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/3 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64)))))))
1
#s(literal 1 binary64)
(/ (+ 1 (* (* x x) (+ (* (* x x) (+ (* (* x x) -2/945) -1/45)) -1/3))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/3 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64)))))) x)
(+ 1 (* (* x x) (+ (* (* x x) (+ (* (* x x) -2/945) -1/45)) -1/3)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/3 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))))))
(* (* x x) (+ (* (* x x) (+ (* (* x x) -2/945) -1/45)) -1/3))
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/3 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64)))))
(* x x)
(*.f64 x x)
(+ (* (* x x) (+ (* (* x x) -2/945) -1/45)) -1/3)
(+.f64 #s(literal -1/3 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))))
(* (* x x) (+ (* (* x x) -2/945) -1/45))
(*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64)))
(+ (* (* x x) -2/945) -1/45)
(+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))
(* (* x x) -2/945)
(*.f64 (*.f64 x x) #s(literal -2/945 binary64))
-2/945
#s(literal -2/945 binary64)
-1/45
#s(literal -1/45 binary64)
-1/3
#s(literal -1/3 binary64)
(+ (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)) eps)
(*.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 (pow (sin x) 2)) (pow (cos x) 2))
(/.f64 (*.f64 eps (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* eps (pow (sin x) 2))
(*.f64 eps (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
eps
(pow (sin x) 2)
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(sin x)
(sin.f64 x)
x
2
#s(literal 2 binary64)
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos x)
(cos.f64 x)

localize372.0ms (2.3%)

Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(/.f64 (*.f64 eps (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
✓accuracy100.0%
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
✓accuracy100.0%
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
✓accuracy99.9%
(*.f64 eps (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
✓accuracy99.7%
(tan.f64 (+.f64 x eps))
✓accuracy99.7%
(*.f64 (*.f64 x x) #s(literal -2/945 binary64))
✓accuracy99.6%
(*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))
✓accuracy65.5%
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x)))
✓accuracy100.0%
(tan.f64 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)))
✓accuracy99.6%
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))
✓accuracy99.5%
(*.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.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))))))
✓accuracy99.5%
(*.f64 x #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))
Results
182.0ms134×1valid
74.0ms118×0valid
13.0ms3×3valid
2.0ms1×2valid
Compiler

Compiled 687 to 52 computations (92.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 187.0ms
ival-pow: 48.0ms (25.7% of total)
ival-mult: 37.0ms (19.8% of total)
ival-add: 24.0ms (12.9% of total)
...c/correct-round.rkt:119:19: 22.0ms (11.8% of total)
backward-pass: 16.0ms (8.6% of total)
ival-tan: 15.0ms (8% of total)
ival-div: 10.0ms (5.4% of total)
ival-sub: 7.0ms (3.8% of total)
ival-cos: 3.0ms (1.6% of total)
ival-sin: 3.0ms (1.6% of total)
const: 1.0ms (0.5% of total)

series40.0ms (0.2%)

Counts
23 → 420
Calls
Call 1
Inputs
#<alt (+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)>
#<alt (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))))>
#<alt (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))>
#<alt (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))>
#<alt (* eps (+ 1 (* x x)))>
#<alt (+ 1 (* x x))>
#<alt (* x x)>
#<alt (tan eps)>
#<alt (- (tan (+ x eps)) (/ 1 (/ (+ 1 (* (* x x) (+ (* (* x x) (+ (* (* x x) -2/945) -1/45)) -1/3))) x)))>
#<alt (/ 1 (/ (+ 1 (* (* x x) (+ (* (* x x) (+ (* (* x x) -2/945) -1/45)) -1/3))) x))>
#<alt (tan (+ x eps))>
#<alt (+ x eps)>
#<alt (+ (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)) eps)>
#<alt (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))>
#<alt (* eps (pow (sin x) 2))>
#<alt (pow (sin x) 2)>
#<alt (* (+ (tan x) (pow (tan x) 3)) -1/3)>
#<alt (* x -1/3)>
#<alt (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))>
#<alt (* (pow (tan x) 2) -1/3)>
#<alt (* (* x x) (+ (* (* x x) (+ (* (* x x) -2/945) -1/45)) -1/3))>
#<alt (* (* x x) -2/945)>
#<alt (pow (cos x) 2)>
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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))>
#<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 x) (+ (* -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))))))))>
#<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 x) (+ (* -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))))))))>
#<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 x) (+ (* -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))))))))>
#<alt (* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))>
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#<alt (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))>
#<alt (* (pow eps 3) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 3) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 3) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
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#<alt (* -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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))))>
#<alt (* -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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))))>
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#<alt (* 1/3 (* (pow eps 3) x))>
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#<alt (* 1/3 (* (pow eps 3) x))>
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#<alt (* -1 (* x (+ (* -1 (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x)) (* -1/3 (pow eps 3)))))>
#<alt (* -1 (* x (+ (* -1 (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x)) (* -1/3 (pow eps 3)))))>
#<alt (* eps (+ 1 (pow x 2)))>
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#<alt eps>
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#<alt 1>
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#<alt (pow x 2)>
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#<alt (pow x 2)>
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#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
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#<alt (pow x 2)>
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#<alt eps>
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#<alt (/ (sin eps) (cos eps))>
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#<alt (/ (sin eps) (cos eps))>
#<alt (/ (sin eps) (cos eps))>
#<alt (/ (sin eps) (cos eps))>
#<alt (/ (sin eps) (cos eps))>
#<alt (/ (sin eps) (cos eps))>
#<alt (/ (sin eps) (cos eps))>
#<alt (/ (sin eps) (cos eps))>
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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)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
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#<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))) (/ x (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3)))))>
#<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))) (/ x (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3)))))>
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#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ x (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3)))))>
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#<alt x>
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#<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)))>
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#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))>
#<alt (/ (sin x) (cos x))>
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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))))) (/ (sin x) (cos x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
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#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
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#<alt eps>
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#<alt x>
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#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
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#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
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#<alt (* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))>
#<alt eps>
#<alt (+ eps (* eps (pow x 2)))>
#<alt (+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps))))))>
#<alt (+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps))))))>
#<alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))>
#<alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))>
#<alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))>
#<alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))>
#<alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))>
#<alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))>
#<alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))>
#<alt (+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))>
#<alt (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))>
#<alt (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))>
#<alt (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))>
#<alt (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))>
#<alt (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))>
#<alt (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))>
#<alt (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))>
#<alt (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))>
#<alt (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))>
#<alt (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))>
#<alt (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))>
#<alt (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))>
#<alt (* eps (pow x 2))>
#<alt (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps)))))>
#<alt (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps)))))>
#<alt (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (+ (* 2/45 eps) (* (pow x 2) (- (* -1/315 eps) (+ (* -1 (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps)))) (+ (* -2/45 eps) (* 1/3 (- (* -1/3 eps) (* -1 eps)))))))) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps)))))>
#<alt (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))>
#<alt (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))>
#<alt (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))>
#<alt (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))>
#<alt (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))>
#<alt (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))>
#<alt (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))>
#<alt (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))>
#<alt (* eps (pow (sin x) 2))>
#<alt (* eps (pow (sin x) 2))>
#<alt (* eps (pow (sin x) 2))>
#<alt (* eps (pow (sin x) 2))>
#<alt (* eps (pow (sin x) 2))>
#<alt (* eps (pow (sin x) 2))>
#<alt (* eps (pow (sin x) 2))>
#<alt (* eps (pow (sin x) 2))>
#<alt (* eps (pow (sin x) 2))>
#<alt (* eps (pow (sin x) 2))>
#<alt (* eps (pow (sin x) 2))>
#<alt (* eps (pow (sin x) 2))>
#<alt (* eps (pow x 2))>
#<alt (* (pow x 2) (+ eps (* -1/3 (* eps (pow x 2)))))>
#<alt (* (pow x 2) (+ eps (* (pow x 2) (+ (* -1/3 eps) (* 2/45 (* eps (pow x 2)))))))>
#<alt (* (pow x 2) (+ eps (* (pow x 2) (+ (* -1/3 eps) (* (pow x 2) (+ (* -1/315 (* eps (pow x 2))) (* 2/45 eps)))))))>
#<alt (* eps (pow (sin x) 2))>
#<alt (* eps (pow (sin x) 2))>
#<alt (* eps (pow (sin x) 2))>
#<alt (* eps (pow (sin x) 2))>
#<alt (* eps (pow (sin x) 2))>
#<alt (* eps (pow (sin x) 2))>
#<alt (* eps (pow (sin x) 2))>
#<alt (* eps (pow (sin x) 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))>
#<alt (pow (sin x) 2)>
#<alt (pow (sin x) 2)>
#<alt (pow (sin x) 2)>
#<alt (pow (sin x) 2)>
#<alt (pow (sin x) 2)>
#<alt (pow (sin x) 2)>
#<alt (pow (sin x) 2)>
#<alt (pow (sin x) 2)>
#<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 (* -1/3 x)>
#<alt (* -1/3 x)>
#<alt (* -1/3 x)>
#<alt (* -1/3 x)>
#<alt (* -1/3 x)>
#<alt (* -1/3 x)>
#<alt (* -1/3 x)>
#<alt (* -1/3 x)>
#<alt (* -1/3 x)>
#<alt (* -1/3 x)>
#<alt (* -1/3 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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (* -1 (* (pow eps 2) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* -1 (* (pow eps 2) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (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 (+ (* 4/9 (* (pow eps 2) x)) (* 4/3 eps))))))>
#<alt (* 1/3 (* (pow eps 2) x))>
#<alt (* x (+ (* 1/3 (pow eps 2)) (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)))>
#<alt (* x (+ (* 1/3 (pow eps 2)) (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)))>
#<alt (* x (+ (* 1/3 (pow eps 2)) (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)))>
#<alt (* 1/3 (* (pow eps 2) x))>
#<alt (* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 2)))))>
#<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 (* -1/3 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))>
#<alt (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))>
#<alt (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))>
#<alt (* -2/945 (pow x 6))>
#<alt (* -1 (* (pow x 6) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945))>
#<alt (* (pow x 6) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945))>
#<alt (* -2/945 (pow x 6))>
#<alt (* -1 (* (pow x 6) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945))>
#<alt (* (pow x 6) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt 1>
#<alt (+ 1 (* -1 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))>
#<alt (pow (cos x) 2)>
#<alt (pow (cos x) 2)>
#<alt (pow (cos x) 2)>
#<alt (pow (cos x) 2)>
#<alt (pow (cos x) 2)>
#<alt (pow (cos x) 2)>
#<alt (pow (cos x) 2)>
#<alt (pow (cos x) 2)>
Calls

105 calls:

TimeVariablePointExpression
4.0ms
eps
@0
(- (tan (+ x eps)) (/ 1 (/ (+ 1 (* (* x x) (+ (* (* x x) (+ (* (* x x) -2/945) -1/45)) -1/3))) x)))
2.0ms
x
@inf
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
2.0ms
x
@-inf
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
1.0ms
eps
@inf
(- (tan (+ x eps)) (/ 1 (/ (+ 1 (* (* x x) (+ (* (* x x) (+ (* (* x x) -2/945) -1/45)) -1/3))) x)))
1.0ms
eps
@0
(+ (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)) eps)

rewrite320.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
2760×*-lowering-*.f32
2760×*-lowering-*.f64
1738×fma-lowering-fma.f32
1738×fma-lowering-fma.f64
1560×fmsub-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
051356
1411321
24217311
08288311
Stop Event
1×iter limit
1×node limit
Counts
23 → 289
Calls
Call 1
Inputs
(+ (* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))) eps)
(* eps (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))))
(+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3))))))))
(* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))))
(* eps (+ 1 (* x x)))
(+ 1 (* x x))
(* x x)
(tan eps)
(- (tan (+ x eps)) (/ 1 (/ (+ 1 (* (* x x) (+ (* (* x x) (+ (* (* x x) -2/945) -1/45)) -1/3))) x)))
(/ 1 (/ (+ 1 (* (* x x) (+ (* (* x x) (+ (* (* x x) -2/945) -1/45)) -1/3))) x))
(tan (+ x eps))
(+ x eps)
(+ (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)) eps)
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(* eps (pow (sin x) 2))
(pow (sin x) 2)
(* (+ (tan x) (pow (tan x) 3)) -1/3)
(* x -1/3)
(* eps (- (- 1/3 (- (* (pow (tan x) 2) -1/3) (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))) (* eps (+ (* x -1/3) (* (+ (tan x) (pow (tan x) 3)) -1/3)))))
(* (pow (tan x) 2) -1/3)
(* (* x x) (+ (* (* x x) (+ (* (* x x) -2/945) -1/45)) -1/3))
(* (* x x) -2/945)
(pow (cos x) 2)
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 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (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 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (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 eps (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))))) eps))
(+.f64 (+.f64 eps (*.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 eps (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (-.f64 #s(literal 1/3 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 (*.f64 eps #s(literal -1/3 binary64)) (+.f64 (+.f64 x (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))))))
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(/.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 (*.f64 x (+.f64 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64))) (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64))))) #s(literal -1/9 binary64))) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64))) #s(literal 1/3 binary64)))
(/.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64))) (*.f64 x (*.f64 (*.f64 x (+.f64 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64))) (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64)))))) #s(literal -1/27 binary64)) (*.f64 x x)) (+.f64 (*.f64 x (*.f64 (*.f64 x (+.f64 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64))) (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64))))) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64)))))))
(/.f64 (*.f64 (+.f64 (*.f64 x (*.f64 (*.f64 x (+.f64 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64))) (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64))))) #s(literal -1/9 binary64)) (*.f64 x x)) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64))) #s(literal 1/3 binary64)))
(*.f64 x (*.f64 x (+.f64 #s(literal -1/3 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64))))))
(*.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/3 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64))))))
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/3 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64)))))
(*.f64 (+.f64 #s(literal -1/3 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64)))) (*.f64 x x))
(*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal -1/3 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64))))) #s(literal 1 binary64))
(*.f64 (*.f64 x (+.f64 #s(literal -1/3 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64))))) x)
(*.f64 (*.f64 #s(literal 1 binary64) x) (*.f64 x (+.f64 #s(literal -1/3 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64))))))
(*.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/3 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64))))) (*.f64 x x))
(*.f64 x (*.f64 x #s(literal -2/945 binary64)))
(*.f64 (*.f64 x x) #s(literal -2/945 binary64))
(*.f64 #s(literal -2/945 binary64) (*.f64 x x))
(*.f64 (*.f64 x #s(literal -2/945 binary64)) x)
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 (cos.f64 x))))
(exp.f64 (*.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 (cos.f64 x)))) #s(literal 2 binary64)))
(/.f64 (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) (cos.f64 (-.f64 x x))) #s(literal 2 binary64))
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 (cos.f64 x))) #s(literal 2 binary64))
(*.f64 (cos.f64 x) (cos.f64 x))
(*.f64 (exp.f64 (log.f64 (cos.f64 x))) (exp.f64 (log.f64 (cos.f64 x))))

simplify350.0ms (2.1%)

Algorithm
1×egg-herbie
Rules
5384×*-lowering-*.f32
5384×*-lowering-*.f64
4376×+-lowering-+.f64
4376×+-lowering-+.f32
1514×fma-lowering-fma.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
064910076
122379628
084339628
Stop Event
1×iter limit
1×node limit
Counts
420 → 420
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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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)))))
(* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(* (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 x) (+ (* -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))))))))
(* (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 x) (+ (* -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))))))))
(* (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 x) (+ (* -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))))))))
(* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 4) (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -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 (* 4/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))))
(* 1/3 (* (pow eps 4) x))
(* x (+ (* 1/3 (pow eps 4)) (+ (/ eps x) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -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)))) x))))
(* x (+ (* 1/3 (pow eps 4)) (+ (/ eps x) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -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)))) x))))
(* x (+ (* 1/3 (pow eps 4)) (+ (/ eps x) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -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)))) x))))
(* 1/3 (* (pow eps 4) x))
(* -1 (* x (+ (* -1 (/ (+ 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 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -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))))) x)) (* -1/3 (pow eps 4)))))
(* -1 (* x (+ (* -1 (/ (+ 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 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -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))))) x)) (* -1/3 (pow eps 4)))))
(* -1 (* x (+ (* -1 (/ (+ 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 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -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))))) x)) (* -1/3 (pow eps 4)))))
(/ (* 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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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))))
(* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 4) (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -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 (* 4/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
(* 1/3 (* (pow eps 4) x))
(* x (+ (* 1/3 (pow eps 4)) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -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)))) x)))
(* x (+ (* 1/3 (pow eps 4)) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -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)))) x)))
(* x (+ (* 1/3 (pow eps 4)) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -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)))) x)))
(* 1/3 (* (pow eps 4) x))
(* -1 (* x (+ (* -1 (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -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)))) x)) (* -1/3 (pow eps 4)))))
(* -1 (* x (+ (* -1 (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -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)))) x)) (* -1/3 (pow eps 4)))))
(* -1 (* x (+ (* -1 (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -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)))) x)) (* -1/3 (pow eps 4)))))
(* 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 (* 4/9 (pow eps 2)))))))))))
(* 1/3 (* (pow eps 3) x))
(* x (+ (* 1/3 (pow eps 3)) (+ (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x) (/ (pow (sin x) 2) (* x (pow (cos x) 2))))))
(* x (+ (* 1/3 (pow eps 3)) (+ (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x) (/ (pow (sin x) 2) (* x (pow (cos x) 2))))))
(* x (+ (* 1/3 (pow eps 3)) (+ (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x) (/ (pow (sin x) 2) (* x (pow (cos x) 2))))))
(* 1/3 (* (pow eps 3) x))
(* -1 (* x (+ (* -1 (/ (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -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))) x)) (* -1/3 (pow eps 3)))))
(* -1 (* x (+ (* -1 (/ (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -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))) x)) (* -1/3 (pow eps 3)))))
(* -1 (* x (+ (* -1 (/ (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -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))) x)) (* -1/3 (pow eps 3)))))
(/ (pow (sin x) 2) (pow (cos x) 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))))) (+ (/ (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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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)))
(* -1 (* (pow eps 3) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(* (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 x) (+ (* -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))))))))
(* (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 x) (+ (* -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))))))))
(* (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 x) (+ (* -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))))))))
(* -1 (* (pow eps 3) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(* -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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))))
(* -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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))))
(* -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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))))
(* 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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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)))))
(* -1 (* (pow eps 3) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* -1 (* (pow eps 3) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(* -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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))))
(* -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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))))
(* -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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))))
(* 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 (* 4/9 (pow eps 2))))))))))
(* 1/3 (* (pow eps 3) x))
(* x (+ (* 1/3 (pow eps 3)) (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x)))
(* x (+ (* 1/3 (pow eps 3)) (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x)))
(* x (+ (* 1/3 (pow eps 3)) (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x)))
(* 1/3 (* (pow eps 3) x))
(* -1 (* x (+ (* -1 (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x)) (* -1/3 (pow eps 3)))))
(* -1 (* x (+ (* -1 (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x)) (* -1/3 (pow eps 3)))))
(* -1 (* x (+ (* -1 (/ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) x)) (* -1/3 (pow eps 3)))))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
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(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
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(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
eps
(+ eps (* eps (pow x 2)))
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(* eps (pow x 2))
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(* (pow x 2) (+ eps (/ eps (pow x 2))))
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(* (pow x 2) (+ eps (/ eps (pow x 2))))
1
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(+ 1 (pow x 2))
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(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
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(pow x 2)
(pow x 2)
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eps
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
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(/ (sin eps) (cos eps))
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(+ (* 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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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))))))))
(/ -945/2 (pow x 5))
(/ (- (* 19845/4 (/ 1 (pow x 2))) 945/2) (pow x 5))
(/ (- (+ (* 19845/4 (/ 1 (pow x 2))) (/ 178605/8 (pow x 4))) 945/2) (pow x 5))
(/ (- (+ (* 19845/4 (/ 1 (pow x 2))) (/ 178605/8 (pow x 4))) (+ 945/2 (* 19825155/16 (/ 1 (pow x 6))))) (pow x 5))
(/ -945/2 (pow x 5))
(* -1 (/ (- 945/2 (* 19845/4 (/ 1 (pow x 2)))) (pow x 5)))
(* -1 (/ (+ 945/2 (* -1 (/ (+ 19845/4 (* 178605/8 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 5)))
(* -1 (/ (- (+ 945/2 (* 19825155/16 (/ 1 (pow x 6)))) (+ (* 19845/4 (/ 1 (pow x 2))) (/ 178605/8 (pow x 4)))) (pow x 5)))
(/ (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)))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1)))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps))))))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps))))))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2)))
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(* eps (pow x 2))
(* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps)))))
(* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps)))))
(* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (+ (* 2/45 eps) (* (pow x 2) (- (* -1/315 eps) (+ (* -1 (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps)))) (+ (* -2/45 eps) (* 1/3 (- (* -1/3 eps) (* -1 eps)))))))) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps)))))
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(* eps (pow (sin x) 2))
(* eps (pow (sin x) 2))
(* eps (pow (sin x) 2))
(* eps (pow (sin x) 2))
(* eps (pow (sin x) 2))
(* eps (pow (sin x) 2))
(* eps (pow (sin x) 2))
(* eps (pow (sin x) 2))
(* eps (pow (sin x) 2))
(* eps (pow (sin x) 2))
(* eps (pow (sin x) 2))
(* eps (pow (sin x) 2))
(* eps (pow x 2))
(* (pow x 2) (+ eps (* -1/3 (* eps (pow x 2)))))
(* (pow x 2) (+ eps (* (pow x 2) (+ (* -1/3 eps) (* 2/45 (* eps (pow x 2)))))))
(* (pow x 2) (+ eps (* (pow x 2) (+ (* -1/3 eps) (* (pow x 2) (+ (* -1/315 (* eps (pow x 2))) (* 2/45 eps)))))))
(* eps (pow (sin x) 2))
(* eps (pow (sin x) 2))
(* eps (pow (sin x) 2))
(* eps (pow (sin x) 2))
(* eps (pow (sin x) 2))
(* eps (pow (sin x) 2))
(* eps (pow (sin x) 2))
(* eps (pow (sin x) 2))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 2)
(pow (sin x) 2)
(* -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)
(* -1/3 x)
(* -1/3 x)
(* -1/3 x)
(* -1/3 x)
(* -1/3 x)
(* -1/3 x)
(* -1/3 x)
(* -1/3 x)
(* -1/3 x)
(* -1/3 x)
(* -1/3 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 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (* (pow eps 2) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* -1 (* (pow eps 2) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (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 (+ (* 4/9 (* (pow eps 2) x)) (* 4/3 eps))))))
(* 1/3 (* (pow eps 2) x))
(* x (+ (* 1/3 (pow eps 2)) (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)))
(* x (+ (* 1/3 (pow eps 2)) (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)))
(* x (+ (* 1/3 (pow eps 2)) (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)))
(* 1/3 (* (pow eps 2) x))
(* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 2)))))
(* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 2)))))
(* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 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))
(* -1/3 (/ (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)))
(* -1/3 (pow x 2))
(* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))
(* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))
(* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))
(* -2/945 (pow x 6))
(* -1 (* (pow x 6) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 6) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945))
(* (pow x 6) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945))
(* -2/945 (pow x 6))
(* -1 (* (pow x 6) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 6) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945))
(* (pow x 6) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
(pow (cos x) 2)
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 (+.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 #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 #s(literal 1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))))
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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)))))
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(* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
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(* (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 x) (+ (* -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))))))))
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(* (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 x) (+ (* -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))))))))
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(* (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 x) (+ (* -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))))))))
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(* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
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(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 4) (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -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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(+ eps (* 1/3 (pow eps 3)))
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(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))))
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(* 1/3 (* (pow eps 4) x))
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(* x (+ (* 1/3 (pow eps 4)) (+ (/ eps x) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -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)))) x))))
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(* x (+ (* 1/3 (pow eps 4)) (+ (/ eps x) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -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)))) x))))
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(* 1/3 (* (pow eps 4) x))
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(/ (* eps (pow (sin x) 2)) (pow (cos x) 2))
(/.f64 (*.f64 eps (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(* eps (+ (* eps (+ (/ (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))))) (+ (/ (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 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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))))
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(* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
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(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 4) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* -1 (* (pow eps 4) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 #s(literal 1/3 binary64) (+.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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 4) (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))) (* -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))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (*.f64 #s(literal 1/3 binary64) (+.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 #s(literal 0 binary64) (+.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 #s(literal 1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (/.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps)) eps)))
(* 1/3 (pow eps 3))
(*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))))
(+ (* 1/3 (pow eps 3)) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))
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(+ (* 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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(+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 4/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
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(* 1/3 (* (pow eps 4) x))
(*.f64 x (*.f64 #s(literal 1/3 binary64) (pow.f64 eps #s(literal 4 binary64))))
(* x (+ (* 1/3 (pow eps 4)) (/ (* eps (+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -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)))) x)))
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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 x) (+ (* -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))))))))
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(* -1 (* (pow eps 3) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
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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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))))
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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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))))))
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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 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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)))))
(*.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 #s(literal 1/3 binary64) (*.f64 eps (*.f64 #s(literal 1/3 binary64) (+.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 (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 #s(literal 1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))
(* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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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(* -1 (* (pow eps 3) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 #s(literal 1/3 binary64) (+.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 3) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.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 #s(literal -1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (+.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 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (*.f64 eps (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))) (+.f64 (/.f64 (sin.f64 x) (*.f64 eps (*.f64 eps (cos.f64 x)))) (/.f64 #s(literal 1/3 binary64) eps))) (*.f64 #s(literal -1/3 binary64) (+.f64 x (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))
(* (pow eps 3) (- (+ (* -1 (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 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 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* -1 (* (pow eps 3) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
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(* -1 (* (pow eps 2) (+ (* -1/3 x) (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))))))
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(* 1/3 eps)
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(* 1/3 (* (pow eps 2) x))
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(* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 2)))))
(*.f64 x (*.f64 #s(literal -1 binary64) (-.f64 (*.f64 eps (*.f64 eps #s(literal -1/3 binary64))) (/.f64 (*.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 #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))) (*.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)))))))))) x))))
(* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 2)))))
(*.f64 x (*.f64 #s(literal -1 binary64) (-.f64 (*.f64 eps (*.f64 eps #s(literal -1/3 binary64))) (/.f64 (*.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 #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))) (*.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)))))))))) x))))
(* -1 (* x (+ (* -1 (/ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (* eps (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) x)) (* -1/3 (pow eps 2)))))
(*.f64 x (*.f64 #s(literal -1 binary64) (-.f64 (*.f64 eps (*.f64 eps #s(literal -1/3 binary64))) (/.f64 (*.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 #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))) (*.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)))))))))) x))))
(* -1/3 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/3 binary64)))
(* (pow x 2) (- (* -2/9 (pow x 2)) 1/3))
(*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/9 binary64)) #s(literal -1/3 binary64)))
(* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3))
(*.f64 x (*.f64 x (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x #s(literal -17/135 binary64))) #s(literal -2/9 binary64))) #s(literal -1/3 binary64))))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/945 (pow x 2)) 17/135)) 2/9)) 1/3))
(*.f64 x (*.f64 x (+.f64 (*.f64 x (*.f64 x (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -62/945 binary64)) #s(literal -17/135 binary64))) #s(literal -2/9 binary64)))) #s(literal -1/3 binary64))))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/.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)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/.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)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/.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)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/.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)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/.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)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/.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)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/.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)))
(* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/.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)))
(* -1/3 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/3 binary64)))
(* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))
(*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -1/45 binary64)) #s(literal -1/3 binary64)))
(* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))
(*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))
(* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))
(*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))
(* -2/945 (pow x 6))
(*.f64 #s(literal -2/945 binary64) (pow.f64 x #s(literal 6 binary64)))
(* -1 (* (pow x 6) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(*.f64 (+.f64 #s(literal 2/945 binary64) (/.f64 #s(literal 1/45 binary64) (*.f64 x x))) (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))))
(* (pow x 6) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (/.f64 (+.f64 #s(literal 1/45 binary64) (/.f64 #s(literal 1/3 binary64) (*.f64 x x))) (-.f64 #s(literal 0 binary64) (*.f64 x x))) #s(literal -2/945 binary64)))
(* (pow x 6) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (/.f64 (+.f64 #s(literal 1/45 binary64) (/.f64 #s(literal 1/3 binary64) (*.f64 x x))) (-.f64 #s(literal 0 binary64) (*.f64 x x))) #s(literal -2/945 binary64)))
(* -2/945 (pow x 6))
(*.f64 #s(literal -2/945 binary64) (pow.f64 x #s(literal 6 binary64)))
(* -1 (* (pow x 6) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(*.f64 (+.f64 #s(literal 2/945 binary64) (/.f64 #s(literal 1/45 binary64) (*.f64 x x))) (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))))
(* (pow x 6) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (/.f64 (+.f64 #s(literal 1/45 binary64) (/.f64 #s(literal 1/3 binary64) (*.f64 x x))) (-.f64 #s(literal 0 binary64) (*.f64 x x))) #s(literal -2/945 binary64)))
(* (pow x 6) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (/.f64 (+.f64 #s(literal 1/45 binary64) (/.f64 #s(literal 1/3 binary64) (*.f64 x x))) (-.f64 #s(literal 0 binary64) (*.f64 x x))) #s(literal -2/945 binary64)))
(* -2/945 (pow x 2))
(*.f64 x (*.f64 x #s(literal -2/945 binary64)))
(* -2/945 (pow x 2))
(*.f64 x (*.f64 x #s(literal -2/945 binary64)))
(* -2/945 (pow x 2))
(*.f64 x (*.f64 x #s(literal -2/945 binary64)))
(* -2/945 (pow x 2))
(*.f64 x (*.f64 x #s(literal -2/945 binary64)))
(* -2/945 (pow x 2))
(*.f64 x (*.f64 x #s(literal -2/945 binary64)))
(* -2/945 (pow x 2))
(*.f64 x (*.f64 x #s(literal -2/945 binary64)))
(* -2/945 (pow x 2))
(*.f64 x (*.f64 x #s(literal -2/945 binary64)))
(* -2/945 (pow x 2))
(*.f64 x (*.f64 x #s(literal -2/945 binary64)))
(* -2/945 (pow x 2))
(*.f64 x (*.f64 x #s(literal -2/945 binary64)))
(* -2/945 (pow x 2))
(*.f64 x (*.f64 x #s(literal -2/945 binary64)))
(* -2/945 (pow x 2))
(*.f64 x (*.f64 x #s(literal -2/945 binary64)))
(* -2/945 (pow x 2))
(*.f64 x (*.f64 x #s(literal -2/945 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 x x)) #s(literal -1 binary64)) x) x))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) #s(literal -2/45 binary64))))) #s(literal -1 binary64))))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))

eval99.0ms (0.6%)

Compiler

Compiled 30975 to 2212 computations (92.9% saved)

prune110.0ms (0.7%)

Pruning

35 alts after pruning (28 fresh and 7 done)

PrunedKeptTotal
New75511766
Fresh71724
Picked325
Done055
Total76535800
Accuracy
100.0%
Counts
800 → 35
Alt Table
Click to see full alt table
StatusAccuracyProgram
64.7%
(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)))
64.7%
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
97.0%
(/.f64 eps (cos.f64 eps))
26.4%
(-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 #s(literal 1 binary64) (*.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)))) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 #s(literal 1 binary64) (*.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)))) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) (/.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 #s(literal 1 binary64) (*.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 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 #s(literal 1 binary64) (*.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)))) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) (/.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 #s(literal 1 binary64) (*.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)))))))))
64.7%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓64.7%
(-.f64 (*.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))) (tan.f64 x))
37.4%
(-.f64 (tan.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x)))
62.7%
(-.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 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64))))))))
✓62.2%
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x)))
62.1%
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -1/45 binary64)) #s(literal -1/3 binary64)))) x)))
✓63.8%
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
✓64.3%
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)))
62.6%
(-.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) #s(literal 2/15 binary64)))))))
✓64.3%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
8.1%
(-.f64 (tan.f64 eps) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x)))
8.0%
(-.f64 (tan.f64 eps) (tan.f64 x))
98.4%
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
97.2%
(+.f64 (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 eps #s(literal -1/315 binary64)) (-.f64 (+.f64 (*.f64 eps #s(literal -2/45 binary64)) (*.f64 eps #s(literal 2/9 binary64))) (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64)))))) (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64))))) (*.f64 eps #s(literal 2/3 binary64)))))) eps)
97.2%
(+.f64 (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 eps (*.f64 x x)) #s(literal 2/3 binary64)))) eps)
97.2%
(+.f64 (*.f64 (*.f64 x x) (+.f64 eps (*.f64 x (*.f64 x (+.f64 (*.f64 x (*.f64 x (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64))))) (*.f64 eps #s(literal 2/3 binary64))))))) eps)
98.1%
(+.f64 (*.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal 2/3 binary64)))) (*.f64 eps x))))) eps)
98.9%
(+.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)
99.2%
(+.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 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 x #s(literal -1/3 binary64)))))))))) eps)
99.1%
(+.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)
48.9%
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 2/3 binary64) (/.f64 (+.f64 (*.f64 x #s(literal -4/3 binary64)) (/.f64 #s(literal -1 binary64) eps)) eps)))))
97.0%
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 2/3 binary64) (/.f64 (*.f64 x #s(literal 4/3 binary64)) eps)))))
97.2%
(+.f64 (*.f64 eps (*.f64 x x)) eps)
98.4%
(*.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)))))
96.9%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))
97.0%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/315 binary64))))))))
97.0%
(*.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))))))
97.2%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x))))
97.0%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))))
✓97.0%
(tan.f64 eps)
✓97.0%
eps
Compiler

Compiled 2609 to 865 computations (66.8% saved)

regimes58.0ms (0.4%)

Counts
63 → 1
Calls
Call 1
Inputs
eps
(*.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 eps (*.f64 eps #s(literal 1/3 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.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 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps x)))
(+.f64 (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 eps (*.f64 x x)) #s(literal 2/3 binary64)))) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/315 binary64))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.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))))))))
(+.f64 (*.f64 (*.f64 x x) (+.f64 eps (*.f64 x (*.f64 x (+.f64 (*.f64 x (*.f64 x (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64))))) (*.f64 eps #s(literal 2/3 binary64))))))) 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 (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 eps #s(literal -1/315 binary64)) (-.f64 (+.f64 (*.f64 eps #s(literal -2/45 binary64)) (*.f64 eps #s(literal 2/9 binary64))) (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64)))))) (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64))))) (*.f64 eps #s(literal 2/3 binary64)))))) eps)
(tan.f64 eps)
(/.f64 eps (cos.f64 eps))
(-.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) #s(literal 2/15 binary64)))))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -1/45 binary64)) #s(literal -1/3 binary64)))) x)))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 2/3 binary64) (/.f64 (*.f64 x #s(literal 4/3 binary64)) eps)))))
(-.f64 (tan.f64 eps) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x)))
(-.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 (*.f64 x x) #s(literal 17/315 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 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64))))))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 2/3 binary64) (/.f64 (+.f64 (*.f64 x #s(literal -4/3 binary64)) (/.f64 #s(literal -1 binary64) eps)) eps)))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x)))
(-.f64 (tan.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x)))
(-.f64 (tan.f64 eps) (tan.f64 x))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) (tan.f64 x))
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (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 (tan.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (tan.f64 x))
(+.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 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal 2/3 binary64)))) (*.f64 eps x))))) eps)
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.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)))))
(+.f64 (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 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))))))
(-.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 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.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 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)))
(-.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 (-.f64 (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (*.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 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(/.f64 (/.f64 (-.f64 (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (*.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (cos.f64 x))
(*.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)))))))
(*.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 #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 eps (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)))) (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 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 x #s(literal -1/3 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 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.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 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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))))) #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 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 -1/6 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 (*.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 (+.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 (/.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 (/.f64 (pow.f64 (/.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 #s(literal 1 binary64) (*.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)))) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 #s(literal 1 binary64) (*.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)))) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) (/.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 #s(literal 1 binary64) (*.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 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 #s(literal 1 binary64) (*.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)))) #s(literal 2 binary64)) (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) (/.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 #s(literal 1 binary64) (*.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 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 -1/6 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 (*.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 (+.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 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #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 (*.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 (+.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))))))
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 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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))))) #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)
Calls

3 calls:

18.0ms
x
16.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
15.0ms
eps
Results
AccuracySegmentsBranch
99.4%1x
99.4%1eps
99.4%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes101.0ms (0.6%)

Counts
59 → 1
Calls
Call 1
Inputs
eps
(*.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 eps (*.f64 eps #s(literal 1/3 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.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 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps x)))
(+.f64 (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 eps (*.f64 x x)) #s(literal 2/3 binary64)))) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/315 binary64))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.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))))))))
(+.f64 (*.f64 (*.f64 x x) (+.f64 eps (*.f64 x (*.f64 x (+.f64 (*.f64 x (*.f64 x (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64))))) (*.f64 eps #s(literal 2/3 binary64))))))) 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 (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 eps #s(literal -1/315 binary64)) (-.f64 (+.f64 (*.f64 eps #s(literal -2/45 binary64)) (*.f64 eps #s(literal 2/9 binary64))) (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64)))))) (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64))))) (*.f64 eps #s(literal 2/3 binary64)))))) eps)
(tan.f64 eps)
(/.f64 eps (cos.f64 eps))
(-.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) #s(literal 2/15 binary64)))))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -1/45 binary64)) #s(literal -1/3 binary64)))) x)))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 2/3 binary64) (/.f64 (*.f64 x #s(literal 4/3 binary64)) eps)))))
(-.f64 (tan.f64 eps) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x)))
(-.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 (*.f64 x x) #s(literal 17/315 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 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64))))))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 2/3 binary64) (/.f64 (+.f64 (*.f64 x #s(literal -4/3 binary64)) (/.f64 #s(literal -1 binary64) eps)) eps)))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x)))
(-.f64 (tan.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x)))
(-.f64 (tan.f64 eps) (tan.f64 x))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) (tan.f64 x))
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (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 (tan.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (tan.f64 x))
(+.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 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal 2/3 binary64)))) (*.f64 eps x))))) eps)
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.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)))))
(+.f64 (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 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))))))
(-.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 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.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 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)))
(-.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 (-.f64 (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (*.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 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(/.f64 (/.f64 (-.f64 (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (*.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (cos.f64 x))
(*.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)))))))
(*.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 #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 eps (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)))) (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 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 x #s(literal -1/3 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 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.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 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.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:

16.0ms
eps
15.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
14.0ms
x
Results
AccuracySegmentsBranch
99.2%1x
99.2%1eps
99.2%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes51.0ms (0.3%)

Counts
58 → 1
Calls
Call 1
Inputs
eps
(*.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 eps (*.f64 eps #s(literal 1/3 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.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 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps x)))
(+.f64 (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 eps (*.f64 x x)) #s(literal 2/3 binary64)))) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/315 binary64))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.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))))))))
(+.f64 (*.f64 (*.f64 x x) (+.f64 eps (*.f64 x (*.f64 x (+.f64 (*.f64 x (*.f64 x (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64))))) (*.f64 eps #s(literal 2/3 binary64))))))) 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 (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 eps #s(literal -1/315 binary64)) (-.f64 (+.f64 (*.f64 eps #s(literal -2/45 binary64)) (*.f64 eps #s(literal 2/9 binary64))) (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64)))))) (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64))))) (*.f64 eps #s(literal 2/3 binary64)))))) eps)
(tan.f64 eps)
(/.f64 eps (cos.f64 eps))
(-.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) #s(literal 2/15 binary64)))))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -1/45 binary64)) #s(literal -1/3 binary64)))) x)))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 2/3 binary64) (/.f64 (*.f64 x #s(literal 4/3 binary64)) eps)))))
(-.f64 (tan.f64 eps) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x)))
(-.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 (*.f64 x x) #s(literal 17/315 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 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64))))))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 2/3 binary64) (/.f64 (+.f64 (*.f64 x #s(literal -4/3 binary64)) (/.f64 #s(literal -1 binary64) eps)) eps)))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x)))
(-.f64 (tan.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x)))
(-.f64 (tan.f64 eps) (tan.f64 x))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) (tan.f64 x))
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (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 (tan.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (tan.f64 x))
(+.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 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal 2/3 binary64)))) (*.f64 eps x))))) eps)
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.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)))))
(+.f64 (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 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))))))
(-.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 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.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 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)))
(-.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 (-.f64 (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (*.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 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(/.f64 (/.f64 (-.f64 (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (*.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (cos.f64 x))
(*.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)))))))
(*.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 #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 eps (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)))) (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 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 x #s(literal -1/3 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))))))
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 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.f64 x #s(literal -1/3 binary64)))))))))) eps)
Calls

3 calls:

16.0ms
x
14.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
14.0ms
eps
Results
AccuracySegmentsBranch
99.2%1x
99.2%1eps
99.2%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes49.0ms (0.3%)

Counts
56 → 1
Calls
Call 1
Inputs
eps
(*.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 eps (*.f64 eps #s(literal 1/3 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.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 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps x)))
(+.f64 (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 eps (*.f64 x x)) #s(literal 2/3 binary64)))) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/315 binary64))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.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))))))))
(+.f64 (*.f64 (*.f64 x x) (+.f64 eps (*.f64 x (*.f64 x (+.f64 (*.f64 x (*.f64 x (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64))))) (*.f64 eps #s(literal 2/3 binary64))))))) 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 (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 eps #s(literal -1/315 binary64)) (-.f64 (+.f64 (*.f64 eps #s(literal -2/45 binary64)) (*.f64 eps #s(literal 2/9 binary64))) (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64)))))) (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64))))) (*.f64 eps #s(literal 2/3 binary64)))))) eps)
(tan.f64 eps)
(/.f64 eps (cos.f64 eps))
(-.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) #s(literal 2/15 binary64)))))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -1/45 binary64)) #s(literal -1/3 binary64)))) x)))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 2/3 binary64) (/.f64 (*.f64 x #s(literal 4/3 binary64)) eps)))))
(-.f64 (tan.f64 eps) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x)))
(-.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 (*.f64 x x) #s(literal 17/315 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 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64))))))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 2/3 binary64) (/.f64 (+.f64 (*.f64 x #s(literal -4/3 binary64)) (/.f64 #s(literal -1 binary64) eps)) eps)))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x)))
(-.f64 (tan.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x)))
(-.f64 (tan.f64 eps) (tan.f64 x))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) (tan.f64 x))
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (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 (tan.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (tan.f64 x))
(+.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 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal 2/3 binary64)))) (*.f64 eps x))))) eps)
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.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)))))
(+.f64 (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 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))))))
(-.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 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.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 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)))
(-.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 (-.f64 (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (*.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 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(/.f64 (/.f64 (-.f64 (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (*.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (cos.f64 x))
(*.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)))))))
(*.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 #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 eps (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)))) (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:

15.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
15.0ms
x
14.0ms
eps
Results
AccuracySegmentsBranch
99.1%1x
99.1%1eps
99.1%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes42.0ms (0.3%)

Counts
46 → 1
Calls
Call 1
Inputs
eps
(*.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 eps (*.f64 eps #s(literal 1/3 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.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 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps x)))
(+.f64 (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 eps (*.f64 x x)) #s(literal 2/3 binary64)))) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/315 binary64))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.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))))))))
(+.f64 (*.f64 (*.f64 x x) (+.f64 eps (*.f64 x (*.f64 x (+.f64 (*.f64 x (*.f64 x (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64))))) (*.f64 eps #s(literal 2/3 binary64))))))) 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 (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 eps #s(literal -1/315 binary64)) (-.f64 (+.f64 (*.f64 eps #s(literal -2/45 binary64)) (*.f64 eps #s(literal 2/9 binary64))) (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64)))))) (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64))))) (*.f64 eps #s(literal 2/3 binary64)))))) eps)
(tan.f64 eps)
(/.f64 eps (cos.f64 eps))
(-.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) #s(literal 2/15 binary64)))))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -1/45 binary64)) #s(literal -1/3 binary64)))) x)))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 2/3 binary64) (/.f64 (*.f64 x #s(literal 4/3 binary64)) eps)))))
(-.f64 (tan.f64 eps) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x)))
(-.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 (*.f64 x x) #s(literal 17/315 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 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64))))))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 2/3 binary64) (/.f64 (+.f64 (*.f64 x #s(literal -4/3 binary64)) (/.f64 #s(literal -1 binary64) eps)) eps)))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x)))
(-.f64 (tan.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x)))
(-.f64 (tan.f64 eps) (tan.f64 x))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(-.f64 (tan.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) (tan.f64 x))
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (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 (tan.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (tan.f64 x))
(+.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 eps (*.f64 eps #s(literal 1/3 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal 2/3 binary64)))) (*.f64 eps x))))) eps)
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.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)))))
(+.f64 (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 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))))))
(-.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 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps))) (tan.f64 x))
Outputs
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
Calls

3 calls:

13.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
12.0ms
x
11.0ms
eps
Results
AccuracySegmentsBranch
98.4%1x
98.4%1eps
98.4%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes31.0ms (0.2%)

Counts
32 → 1
Calls
Call 1
Inputs
eps
(*.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 eps (*.f64 eps #s(literal 1/3 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.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 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps x)))
(+.f64 (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 eps (*.f64 x x)) #s(literal 2/3 binary64)))) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/315 binary64))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.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))))))))
(+.f64 (*.f64 (*.f64 x x) (+.f64 eps (*.f64 x (*.f64 x (+.f64 (*.f64 x (*.f64 x (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64))))) (*.f64 eps #s(literal 2/3 binary64))))))) 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 (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 eps #s(literal -1/315 binary64)) (-.f64 (+.f64 (*.f64 eps #s(literal -2/45 binary64)) (*.f64 eps #s(literal 2/9 binary64))) (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64)))))) (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64))))) (*.f64 eps #s(literal 2/3 binary64)))))) eps)
(tan.f64 eps)
(/.f64 eps (cos.f64 eps))
(-.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) #s(literal 2/15 binary64)))))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -1/45 binary64)) #s(literal -1/3 binary64)))) x)))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 2/3 binary64) (/.f64 (*.f64 x #s(literal 4/3 binary64)) eps)))))
(-.f64 (tan.f64 eps) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x)))
(-.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 (*.f64 x x) #s(literal 17/315 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 (*.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal -1/45 binary64))))))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 2/3 binary64) (/.f64 (+.f64 (*.f64 x #s(literal -4/3 binary64)) (/.f64 #s(literal -1 binary64) eps)) eps)))))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x)))
(-.f64 (tan.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))) x)))
(-.f64 (tan.f64 eps) (tan.f64 x))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Outputs
(+.f64 (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 eps #s(literal -1/315 binary64)) (-.f64 (+.f64 (*.f64 eps #s(literal -2/45 binary64)) (*.f64 eps #s(literal 2/9 binary64))) (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64)))))) (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64))))) (*.f64 eps #s(literal 2/3 binary64)))))) eps)
Calls

3 calls:

12.0ms
x
9.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
8.0ms
eps
Results
AccuracySegmentsBranch
97.2%1x
97.2%1eps
97.2%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes9.0ms (0.1%)

Counts
14 → 1
Calls
Call 1
Inputs
eps
(*.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 eps (*.f64 eps #s(literal 1/3 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.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 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps x)))
(+.f64 (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 eps (*.f64 x x)) #s(literal 2/3 binary64)))) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 eps eps) #s(literal 17/315 binary64))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.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))))))))
(+.f64 (*.f64 (*.f64 x x) (+.f64 eps (*.f64 x (*.f64 x (+.f64 (*.f64 x (*.f64 x (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64))))) (*.f64 eps #s(literal 2/3 binary64))))))) 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)))))))
Outputs
(+.f64 (*.f64 eps (*.f64 x x)) eps)
Calls

2 calls:

4.0ms
eps
4.0ms
x
Results
AccuracySegmentsBranch
97.2%1x
97.2%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

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

2 calls:

1.0ms
x
1.0ms
eps
Results
AccuracySegmentsBranch
97.2%1x
97.2%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
eps
Outputs
eps
Calls

2 calls:

5.0ms
eps
1.0ms
x
Results
AccuracySegmentsBranch
97.0%1x
97.0%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify136.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
988×unsub-neg_binary64
806×distribute-lft-neg-in_binary64
598×neg-mul-1_binary64
422×neg-sub0_binary64
356×distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
086289
1177289
2241289
3334289
4502289
5674289
6953289
71514289
81983289
92361289
102595289
112773289
122854289
132891289
142914289
152925289
162926289
172926289
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 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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))))) #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 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.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 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.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 #s(literal 1/3 binary64)))))) eps)
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
(+.f64 (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 eps #s(literal -1/315 binary64)) (-.f64 (+.f64 (*.f64 eps #s(literal -2/45 binary64)) (*.f64 eps #s(literal 2/9 binary64))) (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64)))))) (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64))))) (*.f64 eps #s(literal 2/3 binary64)))))) eps)
(+.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 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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))))) #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 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 #s(literal 1/3 binary64) (-.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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (*.f64 eps (-.f64 (*.f64 (tan.f64 x) (-.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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) #s(literal -1/3 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 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.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 #s(literal 1/3 binary64) (-.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 (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 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 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)))))) (*.f64 eps (+.f64 (*.f64 x #s(literal -1/3 binary64)) (*.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 #s(literal 1/3 binary64) (-.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 (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 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 #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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
(+.f64 eps (*.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(+.f64 (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 eps #s(literal -1/315 binary64)) (-.f64 (+.f64 (*.f64 eps #s(literal -2/45 binary64)) (*.f64 eps #s(literal 2/9 binary64))) (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64)))))) (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64))))) (*.f64 eps #s(literal 2/3 binary64)))))) eps)
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) (+.f64 (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64))) (*.f64 (*.f64 x x) (+.f64 (*.f64 eps #s(literal -1/315 binary64)) (-.f64 (+.f64 (-.f64 (*.f64 eps #s(literal 2/45 binary64)) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 eps #s(literal -1/3 binary64))) (+.f64 (*.f64 eps #s(literal -2/45 binary64)) (*.f64 eps #s(literal 2/9 binary64)))))))) (*.f64 eps #s(literal 2/3 binary64)))))))
(+.f64 (*.f64 eps (*.f64 x x)) eps)
(+.f64 eps (*.f64 eps (*.f64 x x)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 eps (+.f64 (*.f64 x x) #s(literal 1 binary64)))
eps

soundness2.2s (13.6%)

Rules
6406×+-lowering-+.f64
6406×+-lowering-+.f32
5384×*-lowering-*.f32
5384×*-lowering-*.f64
5128×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
064910076
122379628
084339628
084517484
1300517148
0860417148
051356
1411321
24217311
08288311
071816473
1252715853
0882215853
057856
1460463
25606448
08006448
01571381
14941286
218911261
377211261
085671261
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 567 to 236 computations (58.4% saved)

preprocess69.0ms (0.4%)

Compiler

Compiled 624 to 200 computations (67.9% saved)

end0.0ms (0%)

Profiling

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