2tan (problem 3.3.2)

Time bar (total: 18.3s)

analyze62.0ms (0.3%)

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

Compiled 28 to 18 computations (35.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 33.0ms
ival-tan: 8.0ms (24% of total)
...c/correct-round.rkt:119:19: 7.0ms (21% of total)
ival-fabs: 4.0ms (12% of total)
ival-mult: 3.0ms (9% of total)
ival-<=: 3.0ms (9% of total)
ival-<: 3.0ms (9% of total)
ival-add: 2.0ms (6% of total)
ival-sub: 2.0ms (6% of total)
ival-and: 2.0ms (6% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

sample8.0s (43.8%)

Results
4.1s26658×0precondition
1.5s4460×1valid
536.0ms3796×0valid
Precisions
Click to see histograms. Total time spent on operations: 4.1s
...c/correct-round.rkt:119:19: 927.0ms (22.6% of total)
ival-tan: 799.0ms (19.5% of total)
ival-<: 383.0ms (9.4% of total)
ival-add: 359.0ms (8.8% of total)
ival-mult: 356.0ms (8.7% of total)
ival-fabs: 326.0ms (8% of total)
ival-<=: 274.0ms (6.7% of total)
ival-sub: 225.0ms (5.5% of total)
backward-pass: 209.0ms (5.1% of total)
ival-and: 188.0ms (4.6% of total)
const: 50.0ms (1.2% of total)
Bogosity

preprocess59.0ms (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))

explain120.0ms (0.7%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2161(-9.184010098225329e-117 1.4956578685835446e-119)3(8.01705359178264e-18 2.0918227997823182e-19)(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
30-2(50.40595539445659 0.45081442814641726)(tan.f64 (+.f64 x eps))
00-0-x
00-0-(+.f64 x eps)
00-0-(tan.f64 x)
00-0-eps
Results
61.0ms260×1valid
21.0ms252×0valid
Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 28.0ms
ival-tan: 12.0ms (43% of total)
backward-pass: 6.0ms (21.5% of total)
ival-add: 5.0ms (17.9% of total)
ival-sub: 4.0ms (14.3% of total)
const: 1.0ms (3.6% 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
▶63.8%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify14.0ms (0.1%)

Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

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

Useful iterations: 0 (0.0ms)

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

localize58.0ms (0.3%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(+.f64 x eps)
✓accuracy100.0%
(tan.f64 x)
✓accuracy99.9%
(tan.f64 (+.f64 x eps))
✓accuracy64.0%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
30.0ms130×1valid
11.0ms126×0valid
Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 14.0ms
ival-tan: 6.0ms (44.1% of total)
ival-add: 3.0ms (22% of total)
backward-pass: 3.0ms (22% of total)
ival-sub: 2.0ms (14.7% of total)
const: 0.0ms (0% of total)

series11.0ms (0.1%)

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

21 calls:

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

rewrite218.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
1772×/-lowering-/.f32
1772×/-lowering-/.f64
1682×*-lowering-*.f32
1682×*-lowering-*.f64
1288×sum4-define
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0616
12116
28516
359416
4543416
0806516
Stop Event
1×iter limit
1×node limit
Counts
4 → 358
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 (tan.f64 (+.f64 x eps)) (+.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (+.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (tan.f64 x))))
(+.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (tan.f64 (+.f64 x eps)))
(+.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (+.f64 (tan.f64 (+.f64 x eps)) (+.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (tan.f64 x))))
(+.f64 #s(literal 0 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))
(+.f64 (+.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (tan.f64 x)) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))
(+.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (+.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (tan.f64 x)))
(+.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (-.f64 (*.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (tan.f64 x))))
(+.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (+.f64 (+.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (tan.f64 x)) (+.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (tan.f64 x))))
(+.f64 (*.f64 (tan.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (cos.f64 x))) (neg.f64 (*.f64 (tan.f64 x) (/.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))))))
(+.f64 (*.f64 (tan.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (cos.f64 x))) (neg.f64 (*.f64 (tan.f64 x) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (-.f64 (tan.f64 x) (+.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (tan.f64 x))))
(-.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (neg.f64 (tan.f64 (+.f64 x eps))))
(-.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (*.f64 #s(literal 1 binary64) (neg.f64 (tan.f64 (+.f64 x eps)))))
(-.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))))
(-.f64 #s(literal 0 binary64) (-.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))))
(-.f64 #s(literal 0 binary64) (-.f64 (-.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))) (+.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (tan.f64 x))))
(-.f64 (*.f64 (tan.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (cos.f64 x))) (*.f64 (tan.f64 x) (/.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))))
(-.f64 (*.f64 (tan.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (cos.f64 x))) (*.f64 (tan.f64 x) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))))
(-.f64 (*.f64 (tan.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (cos.f64 x))) (-.f64 (*.f64 (tan.f64 x) (/.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))) (+.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (tan.f64 x))))
(-.f64 (*.f64 (tan.f64 (+.f64 x eps)) (/.f64 (cos.f64 x) (cos.f64 x))) (-.f64 (*.f64 (tan.f64 x) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))) (+.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (tan.f64 x))))
(-.f64 (/.f64 (/.f64 (sin.f64 (+.f64 x eps)) (tan.f64 x)) (/.f64 (cos.f64 (+.f64 x eps)) (tan.f64 x))) (/.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 (+.f64 x eps)) (tan.f64 x))))
(-.f64 (/.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (tan.f64 x)) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (tan.f64 x))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (tan.f64 x))))
(-.f64 (/.f64 (cos.f64 x) (/.f64 (cos.f64 x) (tan.f64 (+.f64 x eps)))) (/.f64 (/.f64 (sin.f64 x) (tan.f64 (+.f64 x eps))) (/.f64 (cos.f64 x) (tan.f64 (+.f64 x eps)))))
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(+.f64 x eps)
(+.f64 eps x)
(+.f64 #s(literal 0 binary64) (tan.f64 x))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 x))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(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 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(/.f64 (*.f64 #s(literal 1 binary64) (-.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)) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) #s(literal -1 binary64)) (cos.f64 x))
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal -1 binary64))
(*.f64 (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) (tan.f64 x)) #s(literal -1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (/.f64 #s(literal -1 binary64) (cos.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(*.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (/.f64 #s(literal -1 binary64) (cos.f64 x)))

simplify306.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
3400×*-lowering-*.f32
3400×*-lowering-*.f64
2990×fma-lowering-fma.f32
2990×fma-lowering-fma.f64
2652×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01571381
14941186
218961117
377521117
086071117
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 x (*.f64 (sin.f64 eps) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (cos.f64 eps)))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 x (+.f64 (*.f64 x (-.f64 (*.f64 (sin.f64 eps) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (cos.f64 eps))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 eps (-.f64 #s(literal -1/6 binary64) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.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 (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 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.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 (sin.f64 x) (/.f64 (+.f64 #s(literal 1/6 binary64) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.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 x (*.f64 (sin.f64 eps) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (cos.f64 eps)))) (/.f64 (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 #s(literal 1 binary64) (+.f64 (*.f64 x (-.f64 (*.f64 (sin.f64 eps) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (cos.f64 eps))) (*.f64 x (+.f64 #s(literal 1/6 binary64) (-.f64 (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 eps (-.f64 #s(literal -1/6 binary64) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.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 (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 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64))))))))))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))

eval60.0ms (0.3%)

Compiler

Compiled 10029 to 956 computations (90.5% saved)

prune59.0ms (0.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New42814442
Fresh000
Picked011
Done000
Total42815443
Accuracy
100.0%
Counts
443 → 15
Alt Table
Click to see full alt table
StatusAccuracyProgram
63.8%
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 x eps)))
63.8%
(/.f64 (/.f64 (-.f64 (neg.f64 (neg.f64 (*.f64 (cos.f64 x) (sin.f64 (+.f64 x eps))))) (*.f64 (sin.f64 x) (cos.f64 (+.f64 x eps)))) (-.f64 #s(literal 0 binary64) (cos.f64 (+.f64 x eps)))) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
63.8%
(/.f64 (/.f64 (sin.f64 (+.f64 x (-.f64 eps x))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
96.9%
(/.f64 (sin.f64 eps) (cos.f64 eps))
64.0%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
▶63.8%
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x))
63.8%
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)))
62.4%
(-.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 (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))))
62.0%
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64))))))
✓63.8%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶61.8%
(-.f64 (tan.f64 (+.f64 x 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)))))
98.7%
(*.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))))))
▶98.9%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 eps (-.f64 #s(literal -1/6 binary64) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
Compiler

Compiled 657 to 358 computations (45.5% saved)

simplify191.0ms (1%)

Algorithm
1×egg-herbie
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
✓cost-diff0
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
✓cost-diff0
(+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
✓cost-diff0
(*.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)))))
✓cost-diff0
(+.f64 x eps)
✓cost-diff0
(sin.f64 (+.f64 x eps))
✓cost-diff0
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
✓cost-diff0
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x))
✓cost-diff0
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64))))))))))
✓cost-diff0
(+.f64 x eps)
✓cost-diff0
(tan.f64 (+.f64 x eps))
✓cost-diff0
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))))
✓cost-diff0
(+.f64 x eps)
✓cost-diff0
(tan.f64 (+.f64 x eps))
✓cost-diff0
(-.f64 (tan.f64 (+.f64 x eps)) x)
✓cost-diff6592
(*.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)))))
✓cost-diff6592
(*.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))))
✓cost-diff19648
(+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.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))))))
✓cost-diff25856
(-.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)))))
Rules
3572×*-lowering-*.f32
3572×*-lowering-*.f64
3062×+-lowering-+.f64
3062×+-lowering-+.f32
1660×sum4-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
053914
1158696
2571574
32280574
08330574
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(* eps (+ 1 (+ (* eps (+ (* 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))))))) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
eps
(+ 1 (+ (* eps (+ (* 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))))))) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
1
(+ (* eps (+ (* 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))))))) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* eps (+ (* 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))))))) (* (/ (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))))))) (* (/ (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)))))))
(- -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)))
-1/2
(/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))
(* -1/2 (pow (sin x) 2))
(pow (sin x) 2)
(sin x)
x
2
(pow (cos x) 2)
(cos x)
(- (/ (* 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)))
(+ 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))))
(/ (sin x) (cos x))
(- (tan (+ x eps)) x)
(tan (+ x eps))
(+ x eps)
x
eps
(- (tan (+ x eps)) (* x (+ 1 (* x (* x (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315))))))))))
(tan (+ x eps))
(+ x eps)
x
eps
(* x (+ 1 (* x (* x (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315)))))))))
(+ 1 (* x (* x (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315))))))))
1
(* x (* x (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315)))))))
(* x (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315))))))
(+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315)))))
1/3
(* (* x x) (+ 2/15 (* x (* x 17/315))))
(* x x)
(+ 2/15 (* x (* x 17/315)))
2/15
(* x (* x 17/315))
(* x 17/315)
17/315
(- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x))
(/ (sin (+ x eps)) (cos (+ x eps)))
(sin (+ x eps))
(+ x eps)
x
eps
(cos (+ x eps))
(tan x)
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
eps
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
1
(/ (pow (sin x) 2) (pow (cos x) 2))
(pow (sin x) 2)
(sin x)
x
2
(pow (cos x) 2)
(cos x)
Outputs
(* eps (+ 1 (+ (* eps (+ (* 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))))))) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.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))) (+.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)))) #s(literal -1/3 binary64)))) (*.f64 eps eps)) (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (*.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 (sin.f64 x) (cos.f64 x)))) #s(literal 1 binary64))))
eps
(+ 1 (+ (* eps (+ (* 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))))))) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+.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))) (+.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)))) #s(literal -1/3 binary64)))) (*.f64 eps eps)) (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (*.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 (sin.f64 x) (cos.f64 x)))) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ (* eps (+ (* 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))))))) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+.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))) (+.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)))) #s(literal -1/3 binary64)))) (*.f64 eps eps)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (*.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 (sin.f64 x) (cos.f64 x)))))
(* eps (+ (* 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))))))) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(*.f64 eps (+.f64 (*.f64 eps (-.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 (-.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 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 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))))))) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+.f64 (*.f64 eps (-.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 (-.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 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 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)))))))
(*.f64 eps (-.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 (-.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)))))
(- -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 #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 (-.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))))
-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 #s(literal -1/2 binary64) (*.f64 (/.f64 (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)))) #s(literal -1/3 binary64))))
(+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))
(/.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)))
(* -1/2 (pow (sin x) 2))
(*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(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)
(- (/ (* 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 -5/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 0 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)))
(+ 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)))
(* (/ (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))
(- (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
(- (tan (+ x eps)) (* x (+ 1 (* x (* x (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315))))))))))
(+.f64 (tan.f64 (+.f64 eps x)) (*.f64 x (-.f64 #s(literal -1 binary64) (*.f64 x (*.f64 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))))))))))
(tan (+ x eps))
(tan.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(* x (+ 1 (* x (* x (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315)))))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 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)))))))))
(+ 1 (* x (* x (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315))))))))
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 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))))))))
1
#s(literal 1 binary64)
(* x (* x (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315)))))))
(*.f64 x (*.f64 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)))))))
(* x (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315))))))
(*.f64 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))))))
(+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315)))))
(+.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)))))
1/3
#s(literal 1/3 binary64)
(* (* x x) (+ 2/15 (* x (* x 17/315))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 x x) #s(literal 17/315 binary64))))
(* x x)
(*.f64 x x)
(+ 2/15 (* x (* x 17/315)))
(+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 x x) #s(literal 17/315 binary64)))
2/15
#s(literal 2/15 binary64)
(* x (* x 17/315))
(*.f64 (*.f64 x x) #s(literal 17/315 binary64))
(* x 17/315)
(*.f64 x #s(literal 17/315 binary64))
17/315
#s(literal 17/315 binary64)
(- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x))
(/ (sin (+ x eps)) (cos (+ x eps)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(sin (+ x eps))
(sin.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(cos (+ x eps))
(cos.f64 (+.f64 eps x))
(tan x)
(tan.f64 x)
(* 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 (/ (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))))
1
#s(literal 1 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))
(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)

localize558.0ms (3%)

Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(cos.f64 x)
✓accuracy100.0%
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
✓accuracy100.0%
(*.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)))))
✓accuracy100.0%
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
✓accuracy99.9%
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))
✓accuracy99.9%
(sin.f64 (+.f64 x eps))
✓accuracy99.9%
(cos.f64 (+.f64 x eps))
✓accuracy64.0%
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x))
✓accuracy99.8%
(*.f64 x (*.f64 x #s(literal 17/315 binary64)))
✓accuracy99.6%
(*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))
✓accuracy99.5%
(*.f64 x #s(literal 17/315 binary64))
✓accuracy64.5%
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))))
✓accuracy100.0%
(+.f64 x eps)
✓accuracy99.9%
(tan.f64 (+.f64 x eps))
✓accuracy65.2%
(-.f64 (tan.f64 (+.f64 x eps)) x)
✓accuracy99.7%
(-.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)))))
✓accuracy99.7%
(*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
✓accuracy99.5%
(*.f64 eps (-.f64 #s(literal -1/6 binary64) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.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 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.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
238.0ms134×1valid
108.0ms119×0valid
37.0ms3×3valid
Compiler

Compiled 954 to 54 computations (94.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 194.0ms
ival-mult: 37.0ms (19.1% of total)
ival-tan: 33.0ms (17% of total)
...c/correct-round.rkt:119:19: 32.0ms (16.5% of total)
backward-pass: 25.0ms (12.9% of total)
ival-add: 18.0ms (9.3% of total)
ival-div: 13.0ms (6.7% of total)
ival-sub: 12.0ms (6.2% of total)
ival-pow: 9.0ms (4.6% of total)
ival-cos: 8.0ms (4.1% of total)
ival-sin: 8.0ms (4.1% of total)
const: 1.0ms (0.5% of total)

series43.0ms (0.2%)

Counts
25 → 420
Calls
Call 1
Inputs
#<alt (- (/ (* 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 (+ (+ -1/2 (/ (* -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 (/ (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))))>
#<alt (- (tan (+ x eps)) x)>
#<alt (tan (+ x eps))>
#<alt (+ x eps)>
#<alt (- (tan (+ x eps)) (* x (+ 1 (* x (* x (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315))))))))))>
#<alt (* x (+ 1 (* x (* x (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315)))))))))>
#<alt (- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x))>
#<alt (/ (sin (+ x eps)) (cos (+ x eps)))>
#<alt (sin (+ x eps))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))>
#<alt (pow (sin 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 (* 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)))))))>
#<alt (* 1/6 (pow (sin x) 2))>
#<alt (* x 17/315)>
#<alt (* x (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315))))))>
#<alt (* x (* x 17/315))>
#<alt (cos (+ x eps))>
#<alt (pow (cos x) 2)>
#<alt (cos x)>
Outputs
#<alt (* -5/6 (pow x 2))>
#<alt (* (pow x 2) (- (* -14/9 (pow x 2)) 5/6))>
#<alt (* (pow x 2) (- (* (pow x 2) (- (* -89/54 (pow x 2)) 14/9)) 5/6))>
#<alt (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -1289/945 (pow x 2)) 89/54)) 14/9)) 5/6))>
#<alt (- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt -1/2>
#<alt (- (* -4/3 (pow x 2)) 1/2)>
#<alt (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)>
#<alt (- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)>
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 5/3 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2))))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2))))))))>
#<alt (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))>
#<alt (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))>
#<alt (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))>
#<alt (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))>
#<alt (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))>
#<alt (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))>
#<alt (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))>
#<alt (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))>
#<alt x>
#<alt (* x (+ 1 (* 4/3 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<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 (+ 1/6 (+ (* -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 (* -1 x)>
#<alt (* x (- (/ (sin (+ eps x)) (* x (cos (+ eps x)))) 1))>
#<alt (* x (- (/ (sin (+ eps x)) (* x (cos (+ eps x)))) 1))>
#<alt (* x (- (/ (sin (+ eps x)) (* x (cos (+ eps x)))) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) (* x (cos (- eps (* -1 x)))))))))>
#<alt (* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) (* x (cos (- eps (* -1 x)))))))))>
#<alt (* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) (* x (cos (- eps (* -1 x)))))))))>
#<alt (- (/ (sin x) (cos x)) x)>
#<alt (- (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) 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))) 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))) x)>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) x)>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) x)>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) x)>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) x)>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) x)>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) x)>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) x)>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) 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 (/ (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 (* -17/315 (pow x 7))>
#<alt (* -1 (* (pow x 7) (+ 17/315 (* 2/15 (/ 1 (pow x 2))))))>
#<alt (* (pow x 7) (- (* -1 (/ (+ 2/15 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 17/315))>
#<alt (* (pow x 7) (- (* -1 (/ (+ 1/3 (/ 1 (pow x 2))) (pow x 4))) (+ 17/315 (* 2/15 (/ 1 (pow x 2))))))>
#<alt (* -17/315 (pow x 7))>
#<alt (* -1 (* (pow x 7) (+ 17/315 (* 2/15 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 7) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2)))))))>
#<alt (* -1 (* (pow x 7) (+ 17/315 (+ (/ 1/3 (pow x 4)) (+ (* 2/15 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))))>
#<alt (- (/ (sin x) (cos x)) (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))))>
#<alt (- (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow 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))))) (/ (sin x) (cos x))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow 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))))) (/ (sin x) (cos x))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))))>
#<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 (* 17/315 (pow x 7))>
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#<alt (* x (+ 1/3 (* 2/15 (pow x 2))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))>
#<alt (* 17/315 (pow x 5))>
#<alt (* (pow x 5) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2))))))>
#<alt (* (pow x 5) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2))))))>
#<alt (* 17/315 (pow x 5))>
#<alt (* (pow x 5) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 2/15 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 17/315)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 2/15 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 17/315)))>
#<alt (* 17/315 (pow x 2))>
#<alt (* 17/315 (pow x 2))>
#<alt (* 17/315 (pow x 2))>
#<alt (* 17/315 (pow x 2))>
#<alt (* 17/315 (pow x 2))>
#<alt (* 17/315 (pow x 2))>
#<alt (* 17/315 (pow x 2))>
#<alt (* 17/315 (pow x 2))>
#<alt (* 17/315 (pow x 2))>
#<alt (* 17/315 (pow x 2))>
#<alt (* 17/315 (pow x 2))>
#<alt (* 17/315 (pow x 2))>
#<alt (cos eps)>
#<alt (+ (cos eps) (* -1 (* x (sin eps))))>
#<alt (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))>
#<alt (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<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)>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
Calls

105 calls:

TimeVariablePointExpression
8.0ms
eps
@0
(* 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)))))))
3.0ms
x
@-inf
(- (tan (+ x eps)) (* x (+ 1 (* x (* x (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315))))))))))
2.0ms
x
@inf
(- (/ (* 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))))
2.0ms
x
@-inf
(- (/ (* 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))))
2.0ms
x
@0
(- (/ (* 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))))

rewrite419.0ms (2.3%)

Algorithm
1×batch-egg-rewrite
Rules
5094×*-lowering-*.f32
5094×*-lowering-*.f64
4414×/-lowering-/.f32
4414×/-lowering-/.f64
2052×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
048354
1187231
21019191
08249191
Stop Event
1×iter limit
1×node limit
Counts
25 → 1444
Calls
Call 1
Inputs
(- (/ (* 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 (/ (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))))
(- (tan (+ x eps)) x)
(tan (+ x eps))
(+ x eps)
(- (tan (+ x eps)) (* x (+ 1 (* x (* x (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315))))))))))
(* x (+ 1 (* x (* x (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315)))))))))
(- (/ (sin (+ x eps)) (cos (+ x eps))) (tan x))
(/ (sin (+ x eps)) (cos (+ x eps)))
(sin (+ x eps))
(* eps (+ 1 (/ (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))
(pow (sin 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))))))
(* 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 (pow (sin x) 2))
(* x 17/315)
(* x (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315))))))
(* x (* x 17/315))
(cos (+ x eps))
(pow (cos x) 2)
(cos x)
Outputs
(+.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/6 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/6 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (fma.f64 (neg.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (cos.f64 x))) (/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (cos.f64 x)) (*.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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(+.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (neg.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (fma.f64 (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))
(+.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))))
(+.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 #s(literal 1/6 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (neg.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (fma.f64 (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))
(+.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 #s(literal 1/6 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))))
(+.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (neg.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (fma.f64 (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))
(+.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))))
(+.f64 (fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (neg.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (fma.f64 (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))
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(fma.f64 (*.f64 x (+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 x x) #s(literal 17/315 binary64)))) (*.f64 x x) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 x x) #s(literal 17/315 binary64))) (*.f64 x #s(literal 1/3 binary64)))
(*.f64 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 (+.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))))) x)
(*.f64 x (*.f64 x #s(literal 17/315 binary64)))
(*.f64 (*.f64 x x) #s(literal 17/315 binary64))
(*.f64 #s(literal 17/315 binary64) (*.f64 x x))
(*.f64 (*.f64 x #s(literal 17/315 binary64)) x)
(+.f64 (cos.f64 (+.f64 x eps)) (+.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))
(+.f64 (cos.f64 (+.f64 x eps)) (fma.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 eps) (*.f64 (sin.f64 x) (sin.f64 eps))))
(+.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps))))
(+.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 eps)))
(cos.f64 (+.f64 x eps))
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps))))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 eps)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps))))
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 eps)))
(/.f64 (-.f64 (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (-.f64 x eps))) (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 x eps)))) #s(literal 2 binary64))
(/.f64 (-.f64 (*.f64 (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (-.f64 x eps))) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 x eps))))) #s(literal 4 binary64))
(+.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 (cos.f64 x)) (log.f64 (cos.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) (cos.f64 (-.f64 x x)))))
(/.f64 (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) (cos.f64 (-.f64 x x))) #s(literal 2 binary64))
(/.f64 (neg.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 (exp.f64 #s(literal 2 binary64)) (log.f64 (cos.f64 x)))
(*.f64 (cos.f64 x) (cos.f64 x))
(*.f64 (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) (cos.f64 (-.f64 x x))) #s(literal 1/2 binary64))
(exp.f64 (log.f64 (cos.f64 x)))
(cos.f64 x)

simplify327.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
4450×*-lowering-*.f32
4450×*-lowering-*.f64
2240×+-lowering-+.f64
2240×+-lowering-+.f32
1430×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
05016761
115885614
254865282
081885282
Stop Event
1×iter limit
1×node limit
Counts
420 → 420
Calls
Call 1
Inputs
(* -5/6 (pow x 2))
(* (pow x 2) (- (* -14/9 (pow x 2)) 5/6))
(* (pow x 2) (- (* (pow x 2) (- (* -89/54 (pow x 2)) 14/9)) 5/6))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -1289/945 (pow x 2)) 89/54)) 14/9)) 5/6))
(- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
-1/2
(- (* -4/3 (pow x 2)) 1/2)
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (/ (* (pow (sin x) 2) (+ 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)))) (+ 1/2 (/ (* (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)))) (+ 1/2 (/ (* (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)))) (+ 1/2 (/ (* (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)))) (+ 1/2 (/ (* (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)))) (+ 1/2 (/ (* (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)))) (+ 1/2 (/ (* (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)))) (+ 1/2 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(pow x 2)
(* (pow x 2) (+ 1 (* 5/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2))))))))
(/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))
(/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))
(/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))
(/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))
(/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))
(/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))
(/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))
(/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))
x
(* x (+ 1 (* 4/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (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 (+ 1/6 (+ (* -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)))
(* -1 x)
(* x (- (/ (sin (+ eps x)) (* x (cos (+ eps x)))) 1))
(* x (- (/ (sin (+ eps x)) (* x (cos (+ eps x)))) 1))
(* x (- (/ (sin (+ eps x)) (* x (cos (+ eps x)))) 1))
(* -1 x)
(* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) (* x (cos (- eps (* -1 x)))))))))
(* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) (* x (cos (- eps (* -1 x)))))))))
(* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) (* x (cos (- eps (* -1 x)))))))))
(- (/ (sin x) (cos x)) x)
(- (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) 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))) 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))) x)
(- (/ (sin (+ eps x)) (cos (+ eps x))) x)
(- (/ (sin (+ eps x)) (cos (+ eps x))) x)
(- (/ (sin (+ eps x)) (cos (+ eps x))) x)
(- (/ (sin (+ eps x)) (cos (+ eps x))) x)
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) x)
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) x)
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) x)
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) 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)))
(/ (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)))
(* -17/315 (pow x 7))
(* -1 (* (pow x 7) (+ 17/315 (* 2/15 (/ 1 (pow x 2))))))
(* (pow x 7) (- (* -1 (/ (+ 2/15 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 17/315))
(* (pow x 7) (- (* -1 (/ (+ 1/3 (/ 1 (pow x 2))) (pow x 4))) (+ 17/315 (* 2/15 (/ 1 (pow x 2))))))
(* -17/315 (pow x 7))
(* -1 (* (pow x 7) (+ 17/315 (* 2/15 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2)))))))
(* -1 (* (pow x 7) (+ 17/315 (+ (/ 1/3 (pow x 4)) (+ (* 2/15 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))))
(- (/ (sin x) (cos x)) (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))))
(- (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow 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))))) (/ (sin x) (cos x))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow 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))))) (/ (sin x) (cos x))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))))
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))))))))
(* 17/315 (pow x 7))
(* (pow x 7) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 17/315 (+ (/ 1/3 (pow x 4)) (+ (* 2/15 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 17/315 (pow x 7))
(* (pow x 7) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 2/15 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 17/315)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/3 (/ 1 (pow x 2))) (pow x 4))) (+ 17/315 (* 2/15 (/ 1 (pow x 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)))
(/ (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))))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(* 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))))
(* 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
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps))))))
(* 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
(+ 1 (pow x 2))
(+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(pow x 2)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/ (pow (sin x) 2) (pow (cos 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
(+ 1/3 (* 4/3 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* 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 (/ (* (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 (/ (* (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 (/ (* (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 (/ (* (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 (/ (* (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 (/ (* (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 (/ (* (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 (/ (* (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 (/ (* (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 (/ (* (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 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* 1/3 eps)
(+ (* 1/3 eps) (* 4/3 (* eps (pow x 2))))
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* 17/9 (* eps (pow x 2))))))
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* (pow x 2) (+ (* 248/135 (* eps (pow x 2))) (* 17/9 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 (/ (* (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 (/ (* (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 (/ (* (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 (/ (* (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 (/ (* (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 (/ (* (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 (/ (* (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))))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* -1/18 (pow x 2))))
(* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/135 (pow x 2)) 1/18))))
(* (pow x 2) (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/135 (* -1/1890 (pow x 2)))) 1/18))))
(* 1/6 (pow (sin x) 2))
(* 1/6 (pow (sin x) 2))
(* 1/6 (pow (sin x) 2))
(* 1/6 (pow (sin x) 2))
(* 1/6 (pow (sin x) 2))
(* 1/6 (pow (sin x) 2))
(* 1/6 (pow (sin x) 2))
(* 1/6 (pow (sin x) 2))
(* 17/315 x)
(* 17/315 x)
(* 17/315 x)
(* 17/315 x)
(* 17/315 x)
(* 17/315 x)
(* 17/315 x)
(* 17/315 x)
(* 17/315 x)
(* 17/315 x)
(* 17/315 x)
(* 17/315 x)
(* 1/3 x)
(* x (+ 1/3 (* 2/15 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))
(* 17/315 (pow x 5))
(* (pow x 5) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2))))))
(* (pow x 5) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2))))))
(* 17/315 (pow x 5))
(* (pow x 5) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 2/15 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 17/315)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 2/15 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 17/315)))
(* 17/315 (pow x 2))
(* 17/315 (pow x 2))
(* 17/315 (pow x 2))
(* 17/315 (pow x 2))
(* 17/315 (pow x 2))
(* 17/315 (pow x 2))
(* 17/315 (pow x 2))
(* 17/315 (pow x 2))
(* 17/315 (pow x 2))
(* 17/315 (pow x 2))
(* 17/315 (pow x 2))
(* 17/315 (pow x 2))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
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)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
Outputs
(* -5/6 (pow x 2))
(*.f64 #s(literal -5/6 binary64) (*.f64 x x))
(* (pow x 2) (- (* -14/9 (pow x 2)) 5/6))
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(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* (pow x 2) (+ (* 248/135 (* eps (pow x 2))) (* 17/9 eps))))))
(+.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 4/3 binary64) eps) (*.f64 (*.f64 x x) (+.f64 (*.f64 eps (*.f64 (*.f64 x x) #s(literal 248/135 binary64))) (*.f64 #s(literal 17/9 binary64) 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))))))
(*.f64 eps (+.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(*.f64 eps (+.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(*.f64 eps (+.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(*.f64 eps (+.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(*.f64 eps (+.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(*.f64 eps (+.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(*.f64 eps (+.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(*.f64 eps (+.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(* 1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* -1/18 (pow x 2))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal -1/18 binary64))))
(* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/135 (pow x 2)) 1/18))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/18 binary64) (*.f64 x (*.f64 x #s(literal 1/135 binary64)))))))
(* (pow x 2) (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/135 (* -1/1890 (pow x 2)))) 1/18))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/18 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/135 binary64) (*.f64 (*.f64 x x) #s(literal -1/1890 binary64)))))))))
(* 1/6 (pow (sin x) 2))
(*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(* 1/6 (pow (sin x) 2))
(*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(* 1/6 (pow (sin x) 2))
(*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(* 1/6 (pow (sin x) 2))
(*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(* 1/6 (pow (sin x) 2))
(*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(* 1/6 (pow (sin x) 2))
(*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(* 1/6 (pow (sin x) 2))
(*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(* 1/6 (pow (sin x) 2))
(*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(* 17/315 x)
(*.f64 x #s(literal 17/315 binary64))
(* 17/315 x)
(*.f64 x #s(literal 17/315 binary64))
(* 17/315 x)
(*.f64 x #s(literal 17/315 binary64))
(* 17/315 x)
(*.f64 x #s(literal 17/315 binary64))
(* 17/315 x)
(*.f64 x #s(literal 17/315 binary64))
(* 17/315 x)
(*.f64 x #s(literal 17/315 binary64))
(* 17/315 x)
(*.f64 x #s(literal 17/315 binary64))
(* 17/315 x)
(*.f64 x #s(literal 17/315 binary64))
(* 17/315 x)
(*.f64 x #s(literal 17/315 binary64))
(* 17/315 x)
(*.f64 x #s(literal 17/315 binary64))
(* 17/315 x)
(*.f64 x #s(literal 17/315 binary64))
(* 17/315 x)
(*.f64 x #s(literal 17/315 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 2/15 (pow x 2))))
(*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) #s(literal 2/15 binary64))))
(* x (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))
(*.f64 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))))))
(* x (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))
(*.f64 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))))))
(* 17/315 (pow x 5))
(*.f64 #s(literal 17/315 binary64) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(*.f64 (+.f64 #s(literal 17/315 binary64) (/.f64 #s(literal 2/15 binary64) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2))))))
(*.f64 (+.f64 (+.f64 #s(literal 17/315 binary64) (/.f64 #s(literal 2/15 binary64) (*.f64 x x))) (/.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2))))))
(*.f64 (+.f64 (+.f64 #s(literal 17/315 binary64) (/.f64 #s(literal 2/15 binary64) (*.f64 x x))) (/.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 5 binary64)))
(* 17/315 (pow x 5))
(*.f64 #s(literal 17/315 binary64) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(*.f64 (+.f64 #s(literal 17/315 binary64) (/.f64 #s(literal 2/15 binary64) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 2/15 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 17/315)))
(*.f64 (-.f64 #s(literal -17/315 binary64) (/.f64 (+.f64 #s(literal 2/15 binary64) (/.f64 #s(literal 1/3 binary64) (*.f64 x x))) (*.f64 x x))) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 5 binary64))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 2/15 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 17/315)))
(*.f64 (-.f64 #s(literal -17/315 binary64) (/.f64 (+.f64 #s(literal 2/15 binary64) (/.f64 #s(literal 1/3 binary64) (*.f64 x x))) (*.f64 x x))) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 5 binary64))))
(* 17/315 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 17/315 binary64))
(* 17/315 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 17/315 binary64))
(* 17/315 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 17/315 binary64))
(* 17/315 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 17/315 binary64))
(* 17/315 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 17/315 binary64))
(* 17/315 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 17/315 binary64))
(* 17/315 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 17/315 binary64))
(* 17/315 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 17/315 binary64))
(* 17/315 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 17/315 binary64))
(* 17/315 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 17/315 binary64))
(* 17/315 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 17/315 binary64))
(* 17/315 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 17/315 binary64))
(cos eps)
(cos.f64 eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(-.f64 (cos.f64 eps) (*.f64 x (sin.f64 eps)))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x (cos.f64 eps))) (sin.f64 eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 eps)) (*.f64 #s(literal 1/6 binary64) (*.f64 x (sin.f64 eps))))) (sin.f64 eps))))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1 (* eps (sin x))))
(-.f64 (cos.f64 x) (*.f64 (sin.f64 x) eps))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+.f64 (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) (sin.f64 x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(+.f64 (cos.f64 x) (*.f64 eps (-.f64 (*.f64 eps (+.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)))) (sin.f64 x))))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 x eps))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 x eps))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 x eps))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 x eps))
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 x x) (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64))))))
(+ 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 #s(literal -1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) #s(literal -2/45 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))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) #s(literal 1/24 binary64))))))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)

eval800.0ms (4.4%)

Compiler

Compiled 210904 to 16532 computations (92.2% saved)

prune360.0ms (2%)

Pruning

28 alts after pruning (25 fresh and 3 done)

PrunedKeptTotal
New2951202971
Fresh459
Picked325
Done011
Total2958282986
Accuracy
100.0%
Counts
2986 → 28
Alt Table
Click to see full alt table
StatusAccuracyProgram
63.8%
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 x eps)))
63.8%
(/.f64 (/.f64 (sin.f64 (+.f64 x (-.f64 eps x))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
63.8%
(/.f64 (-.f64 (*.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) (*.f64 (cos.f64 (+.f64 x eps)) (sin.f64 x))) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
▶96.9%
(/.f64 (sin.f64 eps) (cos.f64 eps))
▶64.0%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
62.5%
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (-.f64 (cos.f64 x) (*.f64 (sin.f64 x) eps))) (tan.f64 x))
✓63.8%
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x))
63.4%
(-.f64 (/.f64 (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (cos.f64 (+.f64 x eps))) (tan.f64 x))
62.6%
(-.f64 (-.f64 (tan.f64 (+.f64 x eps)) x) (*.f64 x (*.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))))))))
62.4%
(-.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)))))))
✓62.6%
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))))
62.0%
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64))))))
✓63.8%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
62.0%
(-.f64 (tan.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))))
5.6%
(-.f64 (tan.f64 x) x)
98.4%
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
97.7%
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 17/45 binary64)) (*.f64 eps #s(literal 2/3 binary64)))))))
97.5%
(+.f64 eps (*.f64 x (*.f64 x (+.f64 eps (*.f64 eps (*.f64 (*.f64 x x) #s(literal 2/3 binary64)))))))
97.2%
(*.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) eps)
98.7%
(*.f64 eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x))))))
98.9%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/6 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps) (*.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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
98.9%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 eps (-.f64 #s(literal -1/6 binary64) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))
▶98.9%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 eps (-.f64 #s(literal -1/6 binary64) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.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 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
98.8%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) #s(literal 1/3 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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
97.6%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))))))))
▶97.7%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) #s(literal 62/315 binary64)))))))))))
97.5%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 2/3 binary64))))))
▶96.9%
eps
Compiler

Compiled 1393 to 743 computations (46.7% saved)

simplify251.0ms (1.4%)

Algorithm
1×egg-herbie
Localize:

Found 15 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(tan.f64 x)
✓cost-diff0
(+.f64 (tan.f64 x) (tan.f64 eps))
✓cost-diff0
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
✓cost-diff0
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓cost-diff0
(cos.f64 eps)
✓cost-diff0
(sin.f64 eps)
✓cost-diff0
(/.f64 (sin.f64 eps) (cos.f64 eps))
✓cost-diff0
(*.f64 x x)
✓cost-diff0
(*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) #s(literal 62/315 binary64)))))))))
✓cost-diff0
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) #s(literal 62/315 binary64))))))))))
✓cost-diff0
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) #s(literal 62/315 binary64)))))))))))
✓cost-diff6592
(*.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)))))
✓cost-diff6592
(*.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))))
✓cost-diff19648
(+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.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))))))
✓cost-diff25856
(-.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)))))
Rules
4112×*-lowering-*.f32
4112×*-lowering-*.f64
3672×+-lowering-+.f64
3672×+-lowering-+.f32
1642×sum3-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
060932
1177720
2657597
32664597
08567597
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(* eps (+ 1 (+ (* eps (+ (* 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))))))) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow (cos x) 2)))))
eps
(+ 1 (+ (* eps (+ (* 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))))))) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow (cos x) 2))))
1
(+ (* eps (+ (* 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))))))) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow (cos x) 2)))
(* eps (+ (* 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))))))) (* (/ (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))))))) (* (/ (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)))))))
(- -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)))
-1/2
(/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))
(* -1/2 (pow (sin x) 2))
(pow (sin x) 2)
(sin x)
x
2
(pow (cos x) 2)
(cos x)
(- (/ (* 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)))
(+ 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))))
(/ (sin x) (cos x))
(/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow (cos x) 2))
(- 1/2 (* 1/2 (cos (* 2 x))))
1/2
(* 1/2 (cos (* 2 x)))
(cos (* 2 x))
(* 2 x)
eps
(* eps (+ 1 (* (* x x) (+ 1 (* (* x x) (+ 2/3 (* x (* x (+ 17/45 (* (* x x) 62/315))))))))))
eps
(+ 1 (* (* x x) (+ 1 (* (* x x) (+ 2/3 (* x (* x (+ 17/45 (* (* x x) 62/315)))))))))
1
(* (* x x) (+ 1 (* (* x x) (+ 2/3 (* x (* x (+ 17/45 (* (* x x) 62/315))))))))
(* x x)
x
(+ 1 (* (* x x) (+ 2/3 (* x (* x (+ 17/45 (* (* x x) 62/315)))))))
(* (* x x) (+ 2/3 (* x (* x (+ 17/45 (* (* x x) 62/315))))))
(+ 2/3 (* x (* x (+ 17/45 (* (* x x) 62/315)))))
2/3
(* x (* x (+ 17/45 (* (* x x) 62/315))))
(* x (+ 17/45 (* (* x x) 62/315)))
(+ 17/45 (* (* x x) 62/315))
17/45
(* (* x x) 62/315)
62/315
(/ (sin eps) (cos eps))
(sin eps)
eps
(cos eps)
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
(+ (tan x) (tan eps))
(tan x)
x
(tan eps)
eps
(- 1 (* (tan x) (tan eps)))
1
(* (tan x) (tan eps))
Outputs
(* eps (+ 1 (+ (* eps (+ (* 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))))))) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow (cos x) 2)))))
(*.f64 eps (+.f64 (*.f64 eps (+.f64 (*.f64 eps (-.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 #s(literal -1/2 binary64) (-.f64 #s(literal -5/6 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)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))))) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
eps
(+ 1 (+ (* eps (+ (* 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))))))) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow (cos x) 2))))
(+.f64 (*.f64 eps (+.f64 (*.f64 eps (-.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 #s(literal -1/2 binary64) (-.f64 #s(literal -5/6 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)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))))) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
1
#s(literal 1 binary64)
(+ (* eps (+ (* 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))))))) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow (cos x) 2)))
(+.f64 (*.f64 eps (+.f64 (*.f64 eps (-.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 #s(literal -1/2 binary64) (-.f64 #s(literal -5/6 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)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))))) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(* eps (+ (* 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))))))) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(*.f64 eps (+.f64 (*.f64 eps (-.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 #s(literal -1/2 binary64) (-.f64 #s(literal -5/6 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)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 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))))))) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+.f64 (*.f64 eps (-.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 #s(literal -1/2 binary64) (-.f64 #s(literal -5/6 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)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 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)))))))
(*.f64 eps (-.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 #s(literal -1/2 binary64) (-.f64 #s(literal -5/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 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 #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 #s(literal -1/2 binary64) (-.f64 #s(literal -5/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 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 #s(literal -1/2 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -5/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
(+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)))
(+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
-1/2
#s(literal -1/2 binary64)
(/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))
(*.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(* -1/2 (pow (sin x) 2))
(*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(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)
(- (/ (* 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)) (-.f64 #s(literal 0 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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #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)))
(+ 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)))
(* (/ (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))
(/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow (cos x) 2))
(/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(- 1/2 (* 1/2 (cos (* 2 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))
1/2
#s(literal 1/2 binary64)
(* 1/2 (cos (* 2 x)))
(*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))
(cos (* 2 x))
(cos.f64 (*.f64 x #s(literal 2 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
eps
(* eps (+ 1 (* (* x x) (+ 1 (* (* x x) (+ 2/3 (* x (* x (+ 17/45 (* (* x x) 62/315))))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) #s(literal 62/315 binary64)))))))))))
eps
(+ 1 (* (* x x) (+ 1 (* (* x x) (+ 2/3 (* x (* x (+ 17/45 (* (* x x) 62/315)))))))))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) #s(literal 62/315 binary64))))))))))
1
#s(literal 1 binary64)
(* (* x x) (+ 1 (* (* x x) (+ 2/3 (* x (* x (+ 17/45 (* (* x x) 62/315))))))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) #s(literal 62/315 binary64)))))))))
(* x x)
(*.f64 x x)
x
(+ 1 (* (* x x) (+ 2/3 (* x (* x (+ 17/45 (* (* x x) 62/315)))))))
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) #s(literal 62/315 binary64))))))))
(* (* x x) (+ 2/3 (* x (* x (+ 17/45 (* (* x x) 62/315))))))
(*.f64 x (*.f64 x (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) #s(literal 62/315 binary64)))))))
(+ 2/3 (* x (* x (+ 17/45 (* (* x x) 62/315)))))
(+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) #s(literal 62/315 binary64)))))
2/3
#s(literal 2/3 binary64)
(* x (* x (+ 17/45 (* (* x x) 62/315))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) #s(literal 62/315 binary64))))
(* x (+ 17/45 (* (* x x) 62/315)))
(*.f64 x (+.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) #s(literal 62/315 binary64))))
(+ 17/45 (* (* x x) 62/315))
(+.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) #s(literal 62/315 binary64)))
17/45
#s(literal 17/45 binary64)
(* (* x x) 62/315)
(*.f64 (*.f64 x x) #s(literal 62/315 binary64))
62/315
#s(literal 62/315 binary64)
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(sin eps)
(sin.f64 eps)
eps
(cos eps)
(cos.f64 eps)
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
(+ (tan x) (tan eps))
(+.f64 (tan.f64 x) (tan.f64 eps))
(tan x)
(tan.f64 x)
x
(tan eps)
(tan.f64 eps)
eps
(- 1 (* (tan x) (tan eps)))
(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))
1
#s(literal 1 binary64)
(* (tan x) (tan eps))
(*.f64 (tan.f64 x) (tan.f64 eps))

localize768.0ms (4.2%)

Localize:

Found 15 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
✓accuracy100.0%
(+.f64 (tan.f64 x) (tan.f64 eps))
✓accuracy100.0%
(*.f64 (tan.f64 x) (tan.f64 eps))
✓accuracy64.0%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓accuracy100.0%
(sin.f64 eps)
✓accuracy100.0%
(cos.f64 eps)
✓accuracy100.0%
(/.f64 (sin.f64 eps) (cos.f64 eps))
✓accuracy99.8%
(*.f64 x (*.f64 x (+.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) #s(literal 62/315 binary64)))))
✓accuracy99.8%
(*.f64 (*.f64 x x) #s(literal 62/315 binary64))
✓accuracy99.7%
(*.f64 x (+.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) #s(literal 62/315 binary64))))
✓accuracy99.7%
(*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) #s(literal 62/315 binary64)))))))
✓accuracy99.7%
(*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
✓accuracy99.5%
(*.f64 eps (-.f64 #s(literal -1/6 binary64) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.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 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.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)))))))
✓accuracy55.3%
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))
Results
567.0ms248×1valid
19.0ms2×3valid
5.0ms6×0valid
Compiler

Compiled 977 to 61 computations (93.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 359.0ms
ival-cos: 78.0ms (21.7% of total)
ival-mult: 55.0ms (15.3% of total)
backward-pass: 54.0ms (15% of total)
...c/correct-round.rkt:119:19: 44.0ms (12.2% of total)
ival-div: 33.0ms (9.2% of total)
ival-add: 32.0ms (8.9% of total)
ival-tan: 23.0ms (6.4% of total)
ival-pow: 15.0ms (4.2% of total)
ival-sub: 12.0ms (3.3% of total)
ival-sin: 12.0ms (3.3% of total)
const: 2.0ms (0.6% of total)

series50.0ms (0.3%)

Counts
24 → 360
Calls
Call 1
Inputs
#<alt (- (/ (* 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 (+ (+ -1/2 (/ (* -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 (/ (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))))>
#<alt (* eps (+ 1 (* (* x x) (+ 1 (* (* x x) (+ 2/3 (* x (* x (+ 17/45 (* (* x x) 62/315))))))))))>
#<alt (+ 1 (* (* x x) (+ 1 (* (* x x) (+ 2/3 (* x (* x (+ 17/45 (* (* x x) 62/315)))))))))>
#<alt (* (* x x) (+ 1 (* (* x x) (+ 2/3 (* x (* x (+ 17/45 (* (* x x) 62/315))))))))>
#<alt (* x x)>
#<alt (/ (sin eps) (cos eps))>
#<alt (sin eps)>
#<alt (cos eps)>
#<alt (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))>
#<alt (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))>
#<alt (+ (tan x) (tan eps))>
#<alt (tan x)>
#<alt (- 1/2 (* 1/2 (cos (* 2 x))))>
#<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 (* 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)))))))>
#<alt (* 1/6 (pow (sin x) 2))>
#<alt (* (* x x) (+ 2/3 (* x (* x (+ 17/45 (* (* x x) 62/315))))))>
#<alt (* x (+ 17/45 (* (* x x) 62/315)))>
#<alt (* (* x x) 62/315)>
#<alt (* x (* x (+ 17/45 (* (* x x) 62/315))))>
#<alt (* (tan x) (tan eps))>
Outputs
#<alt (* -5/6 (pow x 2))>
#<alt (* (pow x 2) (- (* -14/9 (pow x 2)) 5/6))>
#<alt (* (pow x 2) (- (* (pow x 2) (- (* -89/54 (pow x 2)) 14/9)) 5/6))>
#<alt (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -1289/945 (pow x 2)) 89/54)) 14/9)) 5/6))>
#<alt (- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt -1/2>
#<alt (- (* -4/3 (pow x 2)) 1/2)>
#<alt (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)>
#<alt (- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)>
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 5/3 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2))))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2))))))))>
#<alt (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))>
#<alt (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))>
#<alt (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))>
#<alt (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))>
#<alt (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))>
#<alt (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))>
#<alt (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))>
#<alt (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))>
#<alt x>
#<alt (* x (+ 1 (* 4/3 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))>
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))>
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))>
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))>
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))>
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))>
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))>
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))>
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))>
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))>
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))>
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))>
#<alt eps>
#<alt (+ eps (* eps (pow x 2)))>
#<alt (+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))>
#<alt (+ eps (* (pow x 2) (+ eps (* (pow x 2) (+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps))))))>
#<alt (* 62/315 (* eps (pow x 8)))>
#<alt (* (pow x 8) (+ (* 62/315 eps) (* 17/45 (/ eps (pow x 2)))))>
#<alt (* (pow x 8) (+ (* 62/315 eps) (+ (* 17/45 (/ eps (pow x 2))) (* 2/3 (/ eps (pow x 4))))))>
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#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))>
#<alt (* 1/3 eps)>
#<alt (+ (* 1/3 eps) (* 4/3 (* eps (pow x 2))))>
#<alt (+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* 17/9 (* eps (pow x 2))))))>
#<alt (+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* (pow x 2) (+ (* 248/135 (* eps (pow x 2))) (* 17/9 eps))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* -1/18 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/135 (pow x 2)) 1/18))))>
#<alt (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/135 (* -1/1890 (pow x 2)))) 1/18))))>
#<alt (* 1/6 (pow (sin x) 2))>
#<alt (* 1/6 (pow (sin x) 2))>
#<alt (* 1/6 (pow (sin x) 2))>
#<alt (* 1/6 (pow (sin x) 2))>
#<alt (* 1/6 (pow (sin x) 2))>
#<alt (* 1/6 (pow (sin x) 2))>
#<alt (* 1/6 (pow (sin x) 2))>
#<alt (* 1/6 (pow (sin x) 2))>
#<alt (* 2/3 (pow x 2))>
#<alt (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))>
#<alt (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))>
#<alt (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))>
#<alt (* 62/315 (pow x 6))>
#<alt (* (pow x 6) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2))))))>
#<alt (* 62/315 (pow x 6))>
#<alt (* (pow x 6) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2))))))>
#<alt (* 17/45 x)>
#<alt (* x (+ 17/45 (* 62/315 (pow x 2))))>
#<alt (* x (+ 17/45 (* 62/315 (pow x 2))))>
#<alt (* x (+ 17/45 (* 62/315 (pow x 2))))>
#<alt (* 62/315 (pow x 3))>
#<alt (* (pow x 3) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))>
#<alt (* 62/315 (pow x 3))>
#<alt (* (pow x 3) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))>
#<alt (* 62/315 (pow x 2))>
#<alt (* 62/315 (pow x 2))>
#<alt (* 62/315 (pow x 2))>
#<alt (* 62/315 (pow x 2))>
#<alt (* 62/315 (pow x 2))>
#<alt (* 62/315 (pow x 2))>
#<alt (* 62/315 (pow x 2))>
#<alt (* 62/315 (pow x 2))>
#<alt (* 62/315 (pow x 2))>
#<alt (* 62/315 (pow x 2))>
#<alt (* 62/315 (pow x 2))>
#<alt (* 62/315 (pow x 2))>
#<alt (* 17/45 (pow x 2))>
#<alt (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))>
#<alt (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))>
#<alt (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))>
#<alt (* 62/315 (pow x 4))>
#<alt (* (pow x 4) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))>
#<alt (* 62/315 (pow x 4))>
#<alt (* (pow x 4) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 62/315 (* 17/45 (/ 1 (pow 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

90 calls:

TimeVariablePointExpression
14.0ms
eps
@inf
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
7.0ms
eps
@-inf
(/ (sin eps) (cos eps))
3.0ms
x
@inf
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
2.0ms
eps
@-inf
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
2.0ms
eps
@0
(* eps (+ 1 (* (* x x) (+ 1 (* (* x x) (+ 2/3 (* x (* x (+ 17/45 (* (* x x) 62/315))))))))))

rewrite324.0ms (1.8%)

Algorithm
1×batch-egg-rewrite
Rules
4728×*-lowering-*.f32
4728×*-lowering-*.f64
2498×/-lowering-/.f32
2498×/-lowering-/.f64
1840×frac-times
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
054373
1197252
21171201
08737201
Stop Event
1×iter limit
1×node limit
Counts
24 → 890
Calls
Call 1
Inputs
(- (/ (* 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 (/ (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))))
(* eps (+ 1 (* (* x x) (+ 1 (* (* x x) (+ 2/3 (* x (* x (+ 17/45 (* (* x x) 62/315))))))))))
(+ 1 (* (* x x) (+ 1 (* (* x x) (+ 2/3 (* x (* x (+ 17/45 (* (* x x) 62/315)))))))))
(* (* x x) (+ 1 (* (* x x) (+ 2/3 (* x (* x (+ 17/45 (* (* x x) 62/315))))))))
(* x x)
(/ (sin eps) (cos eps))
(sin eps)
(cos eps)
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
(+ (tan x) (tan eps))
(tan x)
(- 1/2 (* 1/2 (cos (* 2 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))))))
(* 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 (pow (sin x) 2))
(* (* x x) (+ 2/3 (* x (* x (+ 17/45 (* (* x x) 62/315))))))
(* x (+ 17/45 (* (* x x) 62/315)))
(* (* x x) 62/315)
(* x (* x (+ 17/45 (* (* x x) 62/315))))
(* (tan x) (tan eps))
Outputs
(+.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 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 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 (*.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 (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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -5/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 (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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -5/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -5/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (fma.f64 (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (cos.f64 x))) (/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (cos.f64 x)) (*.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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -5/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 (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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 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 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))))
(+.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (neg.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))))) (fma.f64 (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))))))
(+.f64 (fma.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (/.f64 #s(literal -1/6 binary64) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (neg.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))))) (fma.f64 (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))))))
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(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) (cos.f64 x)) (/.f64 (/.f64 #s(literal -1 binary64) (cos.f64 eps)) (/.f64 #s(literal 1 binary64) (sin.f64 x))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 eps)) (cos.f64 x)) (/.f64 (sin.f64 eps) (/.f64 #s(literal 1 binary64) (sin.f64 x))))
(*.f64 (/.f64 (tan.f64 eps) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x))))
(*.f64 (/.f64 (tan.f64 eps) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) #s(literal -1 binary64)) (/.f64 (tan.f64 x) (cos.f64 eps)))
(*.f64 (*.f64 (tan.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 eps))) (sin.f64 eps))
(*.f64 (*.f64 (tan.f64 eps) (/.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x))
(*.f64 (*.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (cos.f64 eps)))
(*.f64 (*.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (cos.f64 x)))

simplify321.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
4828×*-lowering-*.f32
4828×*-lowering-*.f64
2380×+-lowering-+.f64
2380×+-lowering-+.f32
1630×sum3-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
05146359
116915471
259695222
080195222
Stop Event
1×iter limit
1×node limit
Counts
360 → 360
Calls
Call 1
Inputs
(* -5/6 (pow x 2))
(* (pow x 2) (- (* -14/9 (pow x 2)) 5/6))
(* (pow x 2) (- (* (pow x 2) (- (* -89/54 (pow x 2)) 14/9)) 5/6))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -1289/945 (pow x 2)) 89/54)) 14/9)) 5/6))
(- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
-1/2
(- (* -4/3 (pow x 2)) 1/2)
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/2 (/ (* (pow (sin x) 2) (+ 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)))) (+ 1/2 (/ (* (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)))) (+ 1/2 (/ (* (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)))) (+ 1/2 (/ (* (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)))) (+ 1/2 (/ (* (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)))) (+ 1/2 (/ (* (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)))) (+ 1/2 (/ (* (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)))) (+ 1/2 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(pow x 2)
(* (pow x 2) (+ 1 (* 5/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2))))))))
(/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))
(/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))
(/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))
(/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))
(/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))
(/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))
(/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))
(/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))
x
(* x (+ 1 (* 4/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps))))))
(* 62/315 (* eps (pow x 8)))
(* (pow x 8) (+ (* 62/315 eps) (* 17/45 (/ eps (pow x 2)))))
(* (pow x 8) (+ (* 62/315 eps) (+ (* 17/45 (/ eps (pow x 2))) (* 2/3 (/ eps (pow x 4))))))
(* (pow x 8) (+ (* 62/315 eps) (+ (* 17/45 (/ eps (pow x 2))) (+ (* 2/3 (/ eps (pow x 4))) (/ eps (pow x 6))))))
(* 62/315 (* eps (pow x 8)))
(* (pow x 8) (+ (* 62/315 eps) (* 17/45 (/ eps (pow x 2)))))
(* (pow x 8) (+ (* 62/315 eps) (+ (* 17/45 (/ eps (pow x 2))) (* 2/3 (/ eps (pow x 4))))))
(* (pow x 8) (+ (* 62/315 eps) (+ (* 17/45 (/ eps (pow x 2))) (+ (* 2/3 (/ eps (pow x 4))) (/ eps (pow x 6))))))
1
(+ 1 (pow x 2))
(+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))
(* 62/315 (pow x 8))
(* (pow x 8) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2))))))
(* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (+ (* 17/45 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 62/315 (pow x 8))
(* (pow x 8) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2))))))
(* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (+ (* 17/45 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))
(* 62/315 (pow x 8))
(* (pow x 8) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2))))))
(* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (+ (* 17/45 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 62/315 (pow x 8))
(* (pow x 8) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2))))))
(* (pow x 8) (+ 62/315 (+ (/ 2/3 (pow x 4)) (+ (* 17/45 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
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))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
1
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* -1 (/ (pow (sin eps) 4) (pow (cos eps) 4))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* -1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/3 (/ (sin x) (cos x))) (+ (* -1/3 (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))
(/ (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 (- (* x (- 1/3 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ (sin x) (cos x))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (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 (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (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)))
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))
(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))))
(- 1/2 (* 1/2 (cos (* 2 x))))
(- 1/2 (* 1/2 (cos (* 2 x))))
(- 1/2 (* 1/2 (cos (* 2 x))))
(- 1/2 (* 1/2 (cos (* 2 x))))
(- 1/2 (* 1/2 (cos (* 2 x))))
(- 1/2 (* 1/2 (cos (* 2 x))))
(- 1/2 (* 1/2 (cos (* 2 x))))
(- 1/2 (* 1/2 (cos (* 2 x))))
1/3
(+ 1/3 (* 4/3 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* 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 (/ (* (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 (/ (* (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 (/ (* (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 (/ (* (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 (/ (* (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 (/ (* (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 (/ (* (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 (/ (* (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 (/ (* (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 (/ (* (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 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* 1/3 eps)
(+ (* 1/3 eps) (* 4/3 (* eps (pow x 2))))
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* 17/9 (* eps (pow x 2))))))
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* (pow x 2) (+ (* 248/135 (* eps (pow x 2))) (* 17/9 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 (/ (* (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 (/ (* (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 (/ (* (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 (/ (* (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 (/ (* (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 (/ (* (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 (/ (* (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))))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* -1/18 (pow x 2))))
(* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/135 (pow x 2)) 1/18))))
(* (pow x 2) (+ 1/6 (* (pow x 2) (- (* (pow x 2) (+ 1/135 (* -1/1890 (pow x 2)))) 1/18))))
(* 1/6 (pow (sin x) 2))
(* 1/6 (pow (sin x) 2))
(* 1/6 (pow (sin x) 2))
(* 1/6 (pow (sin x) 2))
(* 1/6 (pow (sin x) 2))
(* 1/6 (pow (sin x) 2))
(* 1/6 (pow (sin x) 2))
(* 1/6 (pow (sin x) 2))
(* 2/3 (pow x 2))
(* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))
(* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))
(* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))
(* 62/315 (pow x 6))
(* (pow x 6) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2))))))
(* 62/315 (pow x 6))
(* (pow x 6) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 62/315 (+ (/ 2/3 (pow x 4)) (* 17/45 (/ 1 (pow x 2))))))
(* 17/45 x)
(* x (+ 17/45 (* 62/315 (pow x 2))))
(* x (+ 17/45 (* 62/315 (pow x 2))))
(* x (+ 17/45 (* 62/315 (pow x 2))))
(* 62/315 (pow x 3))
(* (pow x 3) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(* 62/315 (pow x 3))
(* (pow x 3) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(* 62/315 (pow x 2))
(* 62/315 (pow x 2))
(* 62/315 (pow x 2))
(* 62/315 (pow x 2))
(* 62/315 (pow x 2))
(* 62/315 (pow x 2))
(* 62/315 (pow x 2))
(* 62/315 (pow x 2))
(* 62/315 (pow x 2))
(* 62/315 (pow x 2))
(* 62/315 (pow x 2))
(* 62/315 (pow x 2))
(* 17/45 (pow x 2))
(* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))
(* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))
(* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))
(* 62/315 (pow x 4))
(* (pow x 4) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(* 62/315 (pow x 4))
(* (pow x 4) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 62/315 (* 17/45 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 62/315 (* 17/45 (/ 1 (pow 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
(* -5/6 (pow x 2))
(*.f64 #s(literal -5/6 binary64) (*.f64 x x))
(* (pow x 2) (- (* -14/9 (pow x 2)) 5/6))
(*.f64 x (*.f64 x (+.f64 #s(literal -5/6 binary64) (*.f64 (*.f64 x x) #s(literal -14/9 binary64)))))
(* (pow x 2) (- (* (pow x 2) (- (* -89/54 (pow x 2)) 14/9)) 5/6))
(*.f64 (*.f64 x x) (+.f64 #s(literal -5/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -14/9 binary64) (*.f64 (*.f64 x x) #s(literal -89/54 binary64))))))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -1289/945 (pow x 2)) 89/54)) 14/9)) 5/6))
(*.f64 (*.f64 x x) (+.f64 #s(literal -5/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -14/9 binary64) (*.f64 (*.f64 (+.f64 #s(literal -89/54 binary64) (*.f64 (*.f64 x x) #s(literal -1289/945 binary64))) x) x)))))
(- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(-.f64 (*.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(-.f64 (*.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(-.f64 (*.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(-.f64 (*.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(-.f64 (*.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(-.f64 (*.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(-.f64 (*.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(- (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
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(pow x 2)
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x
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eps
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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)))
(/ (* eps (sin x)) (cos x))
(/.f64 (*.f64 (sin.f64 x) eps) (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 (*.f64 eps (*.f64 eps #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 (*.f64 (*.f64 eps eps) #s(literal 2/15 binary64)) (sin.f64 x)) (cos.f64 x)) (/.f64 (*.f64 (sin.f64 x) #s(literal 1/3 binary64)) (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 eps (*.f64 eps (+.f64 (/.f64 (*.f64 (sin.f64 x) #s(literal 1/3 binary64)) (cos.f64 x)) (*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps #s(literal 17/315 binary64))) (sin.f64 x)) (cos.f64 x)) (/.f64 (*.f64 (sin.f64 x) #s(literal 2/15 binary64)) (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)))

eval235.0ms (1.3%)

Compiler

Compiled 60641 to 6300 computations (89.6% saved)

prune175.0ms (1%)

Pruning

33 alts after pruning (28 fresh and 5 done)

PrunedKeptTotal
New1339111350
Fresh31720
Picked325
Done033
Total1345331378
Accuracy
100.0%
Counts
1378 → 33
Alt Table
Click to see full alt table
StatusAccuracyProgram
63.8%
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 x eps)))
▶63.8%
(/.f64 (/.f64 (sin.f64 (+.f64 x (-.f64 eps x))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
63.8%
(/.f64 (-.f64 (*.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) (*.f64 (cos.f64 (+.f64 x eps)) (sin.f64 x))) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
▶96.9%
(/.f64 eps (cos.f64 eps))
✓64.0%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
62.5%
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (-.f64 (cos.f64 x) (*.f64 (sin.f64 x) eps))) (tan.f64 x))
✓63.8%
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x))
63.4%
(-.f64 (/.f64 (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (cos.f64 (+.f64 x eps))) (tan.f64 x))
62.6%
(-.f64 (-.f64 (tan.f64 (+.f64 x eps)) x) (*.f64 x (*.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))))))))
62.4%
(-.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)))))))
✓62.6%
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))))
62.0%
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64))))))
✓63.8%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
62.0%
(-.f64 (tan.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))))
5.6%
(-.f64 (tan.f64 x) x)
98.4%
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
97.7%
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 x (*.f64 x #s(literal 62/315 binary64))))))))) (*.f64 (*.f64 x x) eps)) eps)
97.7%
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 17/45 binary64)) (*.f64 eps #s(literal 2/3 binary64)))))))
97.5%
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 x (*.f64 x (*.f64 eps #s(literal 2/3 binary64)))))))
▶97.2%
(*.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) eps)
98.7%
(*.f64 eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 eps (-.f64 (/.f64 (*.f64 (sin.f64 x) #s(literal -1 binary64)) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))))))
97.7%
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 x (*.f64 x #s(literal 62/315 binary64)))))) (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 x x)))
▶98.9%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (-.f64 #s(literal -5/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) eps) (*.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 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
98.9%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 eps (-.f64 #s(literal -1/6 binary64) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))
98.8%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) #s(literal 1/3 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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
98.8%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) #s(literal 1/3 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 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
▶97.6%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))))))))
97.5%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 2/3 binary64))))))
96.9%
(*.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))))))
96.9%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 2/15 binary64) (*.f64 eps (*.f64 eps #s(literal 17/315 binary64))))))))))
96.9%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3 binary64)))))
96.9%
(tan.f64 eps)
✓96.9%
eps
Compiler

Compiled 1452 to 841 computations (42.1% saved)

simplify198.0ms (1.1%)

Algorithm
1×egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(sin.f64 (+.f64 x (-.f64 eps x)))
✓cost-diff0
(/.f64 (sin.f64 (+.f64 x (-.f64 eps x))) (cos.f64 (+.f64 x eps)))
✓cost-diff0
(/.f64 (/.f64 (sin.f64 (+.f64 x (-.f64 eps x))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
✓cost-diff256
(+.f64 x (-.f64 eps x))
✓cost-diff0
(cos.f64 eps)
✓cost-diff0
(/.f64 eps (cos.f64 eps))
✓cost-diff0
(*.f64 x x)
✓cost-diff0
(*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))))))
✓cost-diff0
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))))))
✓cost-diff0
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))))))))
✓cost-diff0
(*.f64 x x)
✓cost-diff0
(+.f64 (*.f64 x x) #s(literal 1 binary64))
✓cost-diff0
(*.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) eps)
✓cost-diff0
(+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (-.f64 #s(literal -5/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) eps) (*.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 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
✓cost-diff0
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (-.f64 #s(literal -5/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) eps) (*.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 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
✓cost-diff128
(+.f64 (-.f64 #s(literal -5/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))
✓cost-diff6592
(*.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)))))
Rules
2660×+-lowering-+.f64
2660×+-lowering-+.f32
2518×*-lowering-*.f32
2518×*-lowering-*.f64
1368×fnmadd-define
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
054537
1157466
2548430
32017424
46884424
08170424
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(* eps (+ 1 (+ (* eps (+ (* (- 1/3 (* (pow (tan x) 2) (+ (- -5/6 (pow (tan x) 2)) -1/2))) eps) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow (cos x) 2)))))
eps
(+ 1 (+ (* eps (+ (* (- 1/3 (* (pow (tan x) 2) (+ (- -5/6 (pow (tan x) 2)) -1/2))) eps) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow (cos x) 2))))
1
(+ (* eps (+ (* (- 1/3 (* (pow (tan x) 2) (+ (- -5/6 (pow (tan x) 2)) -1/2))) eps) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow (cos x) 2)))
(* eps (+ (* (- 1/3 (* (pow (tan x) 2) (+ (- -5/6 (pow (tan x) 2)) -1/2))) eps) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(+ (* (- 1/3 (* (pow (tan x) 2) (+ (- -5/6 (pow (tan x) 2)) -1/2))) eps) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* (- 1/3 (* (pow (tan x) 2) (+ (- -5/6 (pow (tan x) 2)) -1/2))) eps)
(- 1/3 (* (pow (tan x) 2) (+ (- -5/6 (pow (tan x) 2)) -1/2)))
1/3
(* (pow (tan x) 2) (+ (- -5/6 (pow (tan x) 2)) -1/2))
(pow (tan x) 2)
(tan x)
x
2
(+ (- -5/6 (pow (tan x) 2)) -1/2)
(- -5/6 (pow (tan x) 2))
-5/6
-1/2
(* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(/ (sin x) (cos x))
(sin x)
(cos x)
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(pow (sin x) 2)
(pow (cos x) 2)
(/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow (cos x) 2))
(- 1/2 (* 1/2 (cos (* 2 x))))
1/2
(* 1/2 (cos (* 2 x)))
(cos (* 2 x))
(* 2 x)
(* (+ (* x x) 1) eps)
(+ (* x x) 1)
(* x x)
x
1
eps
(* eps (+ 1 (* (* x x) (+ 1 (* (* x x) (+ 2/3 (* (* x x) 17/45)))))))
eps
(+ 1 (* (* x x) (+ 1 (* (* x x) (+ 2/3 (* (* x x) 17/45))))))
1
(* (* x x) (+ 1 (* (* x x) (+ 2/3 (* (* x x) 17/45)))))
(* x x)
x
(+ 1 (* (* x x) (+ 2/3 (* (* x x) 17/45))))
(* (* x x) (+ 2/3 (* (* x x) 17/45)))
(+ 2/3 (* (* x x) 17/45))
2/3
(* (* x x) 17/45)
17/45
(/ eps (cos eps))
eps
(cos eps)
(/ (/ (sin (+ x (- eps x))) (cos (+ x eps))) (cos x))
(/ (sin (+ x (- eps x))) (cos (+ x eps)))
(sin (+ x (- eps x)))
(+ x (- eps x))
x
(- eps x)
eps
(cos (+ x eps))
(+ x eps)
(cos x)
Outputs
(* eps (+ 1 (+ (* eps (+ (* (- 1/3 (* (pow (tan x) 2) (+ (- -5/6 (pow (tan x) 2)) -1/2))) eps) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow (cos x) 2)))))
(*.f64 eps (+.f64 (*.f64 eps (+.f64 (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))))) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
eps
(+ 1 (+ (* eps (+ (* (- 1/3 (* (pow (tan x) 2) (+ (- -5/6 (pow (tan x) 2)) -1/2))) eps) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow (cos x) 2))))
(+.f64 (*.f64 eps (+.f64 (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))))) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
1
#s(literal 1 binary64)
(+ (* eps (+ (* (- 1/3 (* (pow (tan x) 2) (+ (- -5/6 (pow (tan x) 2)) -1/2))) eps) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow (cos x) 2)))
(+.f64 (*.f64 eps (+.f64 (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))))) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(* eps (+ (* (- 1/3 (* (pow (tan x) 2) (+ (- -5/6 (pow (tan x) 2)) -1/2))) eps) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(*.f64 eps (+.f64 (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))))
(+ (* (- 1/3 (* (pow (tan x) 2) (+ (- -5/6 (pow (tan x) 2)) -1/2))) eps) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64))))) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))))
(* (- 1/3 (* (pow (tan x) 2) (+ (- -5/6 (pow (tan x) 2)) -1/2))) eps)
(*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 4/3 binary64)))))
(- 1/3 (* (pow (tan x) 2) (+ (- -5/6 (pow (tan x) 2)) -1/2)))
(+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 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) (+ (- -5/6 (pow (tan x) 2)) -1/2))
(*.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))))
(pow (tan x) 2)
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(tan x)
(tan.f64 x)
x
2
#s(literal 2 binary64)
(+ (- -5/6 (pow (tan x) 2)) -1/2)
(-.f64 #s(literal -4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(- -5/6 (pow (tan x) 2))
(-.f64 #s(literal -5/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
-5/6
#s(literal -5/6 binary64)
-1/2
#s(literal -1/2 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)
(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))
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow (cos x) 2))
(/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(- 1/2 (* 1/2 (cos (* 2 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))
1/2
#s(literal 1/2 binary64)
(* 1/2 (cos (* 2 x)))
(*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))
(cos (* 2 x))
(cos.f64 (*.f64 x #s(literal 2 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* (+ (* x x) 1) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(+ (* x x) 1)
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(* x x)
(*.f64 x x)
x
1
#s(literal 1 binary64)
eps
(* eps (+ 1 (* (* x x) (+ 1 (* (* x x) (+ 2/3 (* (* x x) 17/45)))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))))))))
eps
(+ 1 (* (* x x) (+ 1 (* (* x x) (+ 2/3 (* (* x x) 17/45))))))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))))))
1
#s(literal 1 binary64)
(* (* x x) (+ 1 (* (* x x) (+ 2/3 (* (* x x) 17/45)))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))))))
(* x x)
(*.f64 x x)
x
(+ 1 (* (* x x) (+ 2/3 (* (* x x) 17/45))))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))))
(* (* x x) (+ 2/3 (* (* x x) 17/45)))
(*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))))
(+ 2/3 (* (* x x) 17/45))
(+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))
2/3
#s(literal 2/3 binary64)
(* (* x x) 17/45)
(*.f64 (*.f64 x x) #s(literal 17/45 binary64))
17/45
#s(literal 17/45 binary64)
(/ eps (cos eps))
(/.f64 eps (cos.f64 eps))
eps
(cos eps)
(cos.f64 eps)
(/ (/ (sin (+ x (- eps x))) (cos (+ x eps))) (cos x))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ x (- eps x))) (cos (+ x eps)))
(/.f64 (sin.f64 eps) (cos.f64 (+.f64 eps x)))
(sin (+ x (- eps x)))
(sin.f64 eps)
(+ x (- eps x))
eps
x
(- eps x)
(-.f64 eps x)
eps
(cos (+ x eps))
(cos.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
(cos x)
(cos.f64 x)

localize774.0ms (4.2%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(/.f64 (/.f64 (sin.f64 (+.f64 x (-.f64 eps x))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
✓accuracy100.0%
(/.f64 (sin.f64 (+.f64 x (-.f64 eps x))) (cos.f64 (+.f64 x eps)))
✓accuracy99.9%
(cos.f64 (+.f64 x eps))
✓accuracy63.8%
(+.f64 x (-.f64 eps x))
✓accuracy100.0%
(/.f64 eps (cos.f64 eps))
✓accuracy100.0%
(cos.f64 eps)
✓accuracy100.0%
(+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))
✓accuracy100.0%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))))))))
✓accuracy99.8%
(*.f64 (*.f64 x x) #s(literal 17/45 binary64))
✓accuracy99.7%
(*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))))
✓accuracy100.0%
(+.f64 (*.f64 x x) #s(literal 1 binary64))
✓accuracy100.0%
(*.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) eps)
✓accuracy100.0%
(*.f64 x x)
✓accuracy99.7%
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (-.f64 #s(literal -5/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))
✓accuracy99.5%
(*.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (-.f64 #s(literal -5/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) eps)
✓accuracy98.5%
(+.f64 (-.f64 #s(literal -5/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64))
✓accuracy55.3%
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))
Results
656.0ms248×1valid
6.0ms7×0valid
5.0ms1×3valid
Compiler

Compiled 571 to 55 computations (90.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 443.0ms
ival-cos: 167.0ms (37.7% of total)
ival-pow: 84.0ms (19% of total)
backward-pass: 43.0ms (9.7% of total)
ival-mult: 41.0ms (9.3% of total)
...c/correct-round.rkt:119:19: 32.0ms (7.2% of total)
ival-add: 26.0ms (5.9% of total)
ival-div: 23.0ms (5.2% of total)
ival-sub: 10.0ms (2.3% of total)
ival-sin: 9.0ms (2% of total)
ival-tan: 7.0ms (1.6% of total)
const: 2.0ms (0.5% of total)

series84.0ms (0.5%)

Counts
23 → 396
Calls
Call 1
Inputs
#<alt (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (+ (- -5/6 (pow (tan x) 2)) -1/2)>
#<alt (* eps (+ 1 (+ (* eps (+ (* (- 1/3 (* (pow (tan x) 2) (+ (- -5/6 (pow (tan x) 2)) -1/2))) eps) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow (cos x) 2)))))>
#<alt (+ 1 (+ (* eps (+ (* (- 1/3 (* (pow (tan x) 2) (+ (- -5/6 (pow (tan x) 2)) -1/2))) eps) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow (cos x) 2))))>
#<alt (* (+ (* x x) 1) eps)>
#<alt (+ (* x x) 1)>
#<alt (* x x)>
#<alt (* eps (+ 1 (* (* x x) (+ 1 (* (* x x) (+ 2/3 (* (* x x) 17/45)))))))>
#<alt (+ 1 (* (* x x) (+ 1 (* (* x x) (+ 2/3 (* (* x x) 17/45))))))>
#<alt (* (* x x) (+ 1 (* (* x x) (+ 2/3 (* (* x x) 17/45)))))>
#<alt (/ eps (cos eps))>
#<alt (cos eps)>
#<alt (+ x (- eps x))>
#<alt (/ (/ (sin (+ x (- eps x))) (cos (+ x eps))) (cos x))>
#<alt (/ (sin (+ x (- eps x))) (cos (+ x eps)))>
#<alt (sin (+ x (- eps x)))>
#<alt (- 1/2 (* 1/2 (cos (* 2 x))))>
#<alt (* (- 1/3 (* (pow (tan x) 2) (+ (- -5/6 (pow (tan x) 2)) -1/2))) eps)>
#<alt (* (pow (tan x) 2) (+ (- -5/6 (pow (tan x) 2)) -1/2))>
#<alt (* (* x x) (+ 2/3 (* (* x x) 17/45)))>
#<alt (* (* x x) 17/45)>
#<alt (+ 2/3 (* (* x x) 17/45))>
#<alt (cos (+ x eps))>
Outputs
#<alt x>
#<alt (* x (+ 1 (* 4/3 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))>
#<alt -4/3>
#<alt (- (* -1 (pow x 2)) 4/3)>
#<alt (- (* (pow x 2) (- (* -2/3 (pow x 2)) 1)) 4/3)>
#<alt (- (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1)) 4/3)>
#<alt (* -1 (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* -1 (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* -1 (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* -1 (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* -1 (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* -1 (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* -1 (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* -1 (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (- (+ 1 (* 1/2 (/ 1 (pow (cos x) 2)))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))>
#<alt (* (pow eps 3) (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* (pow eps 3) (- (+ 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* (pow eps 3) (- (+ 1/3 (+ (* 1/2 (/ 1 (* (pow eps 2) (pow (cos x) 2)))) (+ (/ 1 (pow eps 2)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))))) (+ (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (* (pow eps 2) (pow (cos x) 2)))))))>
#<alt (* (pow eps 3) (- (+ 1/3 (+ (* 1/2 (/ 1 (* (pow eps 2) (pow (cos x) 2)))) (+ (/ 1 (pow eps 2)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))))) (+ (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (* (pow eps 2) (pow (cos x) 2)))))))>
#<alt (* (pow eps 3) (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (* -1 (/ (- (+ (/ 1/2 (* eps (pow (cos x) 2))) (+ (/ 1 eps) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (* 1/2 (/ (cos (* 2 x)) (* eps (pow (cos x) 2))))) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (* -1 (/ (- (+ (/ 1/2 (* eps (pow (cos x) 2))) (+ (/ 1 eps) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (* 1/2 (/ (cos (* 2 x)) (* eps (pow (cos x) 2))))) eps)))))>
#<alt (* eps (+ 1 (* 1/3 (pow eps 2))))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) x))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2))))>
#<alt (* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))>
#<alt (- (+ 1 (* 1/2 (/ 1 (pow (cos x) 2)))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))>
#<alt (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))>
#<alt (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))>
#<alt (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))>
#<alt (* (pow eps 2) (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* (pow eps 2) (- (+ 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (* (pow eps 2) (pow (cos x) 2)))) (+ (/ 1 (pow eps 2)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))))) (+ (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (* (pow eps 2) (pow (cos x) 2)))))))>
#<alt (* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (* (pow eps 2) (pow (cos x) 2)))) (+ (/ 1 (pow eps 2)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))))) (+ (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (* (pow eps 2) (pow (cos x) 2)))))))>
#<alt (* (pow eps 2) (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* (pow eps 2) (- (+ 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* (pow eps 2) (- (+ 1/3 (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (- (+ 1 (* 1/2 (/ 1 (pow (cos x) 2)))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))) eps))) eps))) (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* (pow eps 2) (- (+ 1/3 (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (- (+ 1 (* 1/2 (/ 1 (pow (cos x) 2)))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))) eps))) eps))) (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (+ 1 (* 1/3 (pow eps 2)))>
#<alt (+ 1 (+ (* 1/3 (pow eps 2)) (* eps x)))>
#<alt (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))))>
#<alt (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))))))))>
#<alt (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))>
#<alt (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))>
#<alt (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))>
#<alt (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))>
#<alt (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))>
#<alt (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))>
#<alt (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))>
#<alt (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))>
#<alt eps>
#<alt (+ eps (* eps (pow x 2)))>
#<alt (+ eps (* eps (pow x 2)))>
#<alt (+ eps (* eps (pow x 2)))>
#<alt (* eps (pow x 2))>
#<alt (* (pow x 2) (+ eps (/ eps (pow x 2))))>
#<alt (* (pow x 2) (+ eps (/ eps (pow x 2))))>
#<alt (* (pow x 2) (+ eps (/ eps (pow x 2))))>
#<alt (* eps (pow x 2))>
#<alt (* (pow x 2) (+ eps (/ eps (pow x 2))))>
#<alt (* (pow x 2) (+ eps (/ eps (pow x 2))))>
#<alt (* (pow x 2) (+ eps (/ eps (pow x 2))))>
#<alt (* eps (+ 1 (pow x 2)))>
#<alt (* eps (+ 1 (pow x 2)))>
#<alt (* eps (+ 1 (pow x 2)))>
#<alt (* eps (+ 1 (pow x 2)))>
#<alt (* eps (+ 1 (pow x 2)))>
#<alt (* eps (+ 1 (pow x 2)))>
#<alt (* eps (+ 1 (pow x 2)))>
#<alt (* eps (+ 1 (pow x 2)))>
#<alt (* eps (+ 1 (pow x 2)))>
#<alt (* eps (+ 1 (pow x 2)))>
#<alt (* eps (+ 1 (pow x 2)))>
#<alt (* eps (+ 1 (pow x 2)))>
#<alt 1>
#<alt (+ 1 (pow x 2))>
#<alt (+ 1 (pow x 2))>
#<alt (+ 1 (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<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)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))>
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))>
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))>
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))>
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))>
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))>
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))>
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))>
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))>
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))>
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))>
#<alt (* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))>
#<alt eps>
#<alt (+ eps (* eps (pow x 2)))>
#<alt (+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))>
#<alt (+ eps (* (pow x 2) (+ eps (* (pow x 2) (+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps))))))>
#<alt (* 17/45 (* eps (pow x 6)))>
#<alt (* (pow x 6) (+ (* 17/45 eps) (* 2/3 (/ eps (pow x 2)))))>
#<alt (* (pow x 6) (+ (* 17/45 eps) (+ (* 2/3 (/ eps (pow x 2))) (/ eps (pow x 4)))))>
#<alt (* (pow x 6) (+ (* 17/45 eps) (+ (* 2/3 (/ eps (pow x 2))) (+ (/ eps (pow x 4)) (/ eps (pow x 6))))))>
#<alt (* 17/45 (* eps (pow x 6)))>
#<alt (* (pow x 6) (+ (* 17/45 eps) (* 2/3 (/ eps (pow x 2)))))>
#<alt (* (pow x 6) (+ (* 17/45 eps) (+ (* 2/3 (/ eps (pow x 2))) (/ eps (pow x 4)))))>
#<alt (* (pow x 6) (+ (* 17/45 eps) (+ (* 2/3 (/ eps (pow x 2))) (+ (/ eps (pow x 4)) (/ eps (pow x 6))))))>
#<alt 1>
#<alt (+ 1 (pow x 2))>
#<alt (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))>
#<alt (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))>
#<alt (* 17/45 (pow x 6))>
#<alt (* (pow x 6) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* (pow x 6) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))))>
#<alt (* 17/45 (pow x 6))>
#<alt (* (pow x 6) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* (pow x 6) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))>
#<alt (* 17/45 (pow x 6))>
#<alt (* (pow x 6) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* (pow x 6) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* 17/45 (pow x 6))>
#<alt (* (pow x 6) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* (pow x 6) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt eps>
#<alt (* eps (+ 1 (* 1/2 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (+ 1/2 (* 5/24 (pow eps 2))))))>
#<alt (* eps (+ 1 (* (pow eps 2) (+ 1/2 (* (pow eps 2) (+ 5/24 (* 61/720 (pow eps 2))))))))>
#<alt (/ eps (cos eps))>
#<alt (/ eps (cos eps))>
#<alt (/ eps (cos eps))>
#<alt (/ eps (cos eps))>
#<alt (/ eps (cos eps))>
#<alt (/ eps (cos eps))>
#<alt (/ eps (cos eps))>
#<alt (/ eps (cos eps))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow eps 2)))>
#<alt (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (/ (sin eps) (cos eps))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))>
#<alt (+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ eps (pow (cos x) 2))>
#<alt (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))>
#<alt (* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))>
#<alt (* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin eps) (* (cos x) (cos (+ eps x))))>
#<alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (sin eps) (cos eps))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))>
#<alt (+ (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (/ (sin eps) (cos (+ eps x)))>
#<alt (/ (sin eps) (cos (+ eps x)))>
#<alt (/ (sin eps) (cos (+ eps x)))>
#<alt (/ (sin eps) (cos (+ eps x)))>
#<alt (/ (sin eps) (cos (- eps (* -1 x))))>
#<alt (/ (sin eps) (cos (- eps (* -1 x))))>
#<alt (/ (sin eps) (cos (- eps (* -1 x))))>
#<alt (/ (sin eps) (cos (- eps (* -1 x))))>
#<alt (/ eps (cos x))>
#<alt (* eps (+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2))))>
#<alt (* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))>
#<alt (* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))>
#<alt (/ (sin eps) (cos (+ eps x)))>
#<alt (/ (sin eps) (cos (+ eps x)))>
#<alt (/ (sin eps) (cos (+ eps x)))>
#<alt (/ (sin eps) (cos (+ eps x)))>
#<alt (/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps))))>
#<alt (/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps))))>
#<alt (/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps))))>
#<alt (/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps))))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin (neg (* -1 eps)))>
#<alt (sin (neg (* -1 eps)))>
#<alt (sin (neg (* -1 eps)))>
#<alt (sin (neg (* -1 eps)))>
#<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 (- 1/2 (* 1/2 (cos (* 2 x))))>
#<alt (- 1/2 (* 1/2 (cos (* 2 x))))>
#<alt (- 1/2 (* 1/2 (cos (* 2 x))))>
#<alt (- 1/2 (* 1/2 (cos (* 2 x))))>
#<alt (- 1/2 (* 1/2 (cos (* 2 x))))>
#<alt (- 1/2 (* 1/2 (cos (* 2 x))))>
#<alt (- 1/2 (* 1/2 (cos (* 2 x))))>
#<alt (- 1/2 (* 1/2 (cos (* 2 x))))>
#<alt (* 1/3 eps)>
#<alt (+ (* 1/3 eps) (* 4/3 (* eps (pow x 2))))>
#<alt (+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* 17/9 (* eps (pow x 2))))))>
#<alt (+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* (pow x 2) (+ (* 248/135 (* eps (pow x 2))) (* 17/9 eps))))))>
#<alt (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))>
#<alt (* -4/3 (pow x 2))>
#<alt (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3))>
#<alt (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3))>
#<alt (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -1382/945 (pow x 2)) 248/135)) 17/9)) 4/3))>
#<alt (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (* 2/3 (pow x 2))>
#<alt (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))>
#<alt (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))>
#<alt (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))>
#<alt (* 17/45 (pow x 4))>
#<alt (* (pow x 4) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))>
#<alt (* 17/45 (pow x 4))>
#<alt (* (pow x 4) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))>
#<alt (* 17/45 (pow x 2))>
#<alt (* 17/45 (pow x 2))>
#<alt (* 17/45 (pow x 2))>
#<alt (* 17/45 (pow x 2))>
#<alt (* 17/45 (pow x 2))>
#<alt (* 17/45 (pow x 2))>
#<alt (* 17/45 (pow x 2))>
#<alt (* 17/45 (pow x 2))>
#<alt (* 17/45 (pow x 2))>
#<alt (* 17/45 (pow x 2))>
#<alt (* 17/45 (pow x 2))>
#<alt (* 17/45 (pow x 2))>
#<alt 2/3>
#<alt (+ 2/3 (* 17/45 (pow x 2)))>
#<alt (+ 2/3 (* 17/45 (pow x 2)))>
#<alt (+ 2/3 (* 17/45 (pow x 2)))>
#<alt (* 17/45 (pow x 2))>
#<alt (* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))>
#<alt (* 17/45 (pow x 2))>
#<alt (* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))>
#<alt (cos eps)>
#<alt (+ (cos eps) (* -1 (* x (sin eps))))>
#<alt (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))>
#<alt (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
Calls

99 calls:

TimeVariablePointExpression
24.0ms
x
@0
(- 1/2 (* 1/2 (cos (* 2 x))))
17.0ms
eps
@-inf
(/ (/ (sin (+ x (- eps x))) (cos (+ x eps))) (cos x))
6.0ms
x
@inf
(* eps (+ 1 (+ (* eps (+ (* (- 1/3 (* (pow (tan x) 2) (+ (- -5/6 (pow (tan x) 2)) -1/2))) eps) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow (cos x) 2)))))
4.0ms
x
@-inf
(/ (/ (sin (+ x (- eps x))) (cos (+ x eps))) (cos x))
4.0ms
x
@-inf
(* eps (+ 1 (+ (* eps (+ (* (- 1/3 (* (pow (tan x) 2) (+ (- -5/6 (pow (tan x) 2)) -1/2))) eps) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow (cos x) 2)))))

rewrite224.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
3730×*-lowering-*.f32
3730×*-lowering-*.f64
1894×/-lowering-/.f32
1894×/-lowering-/.f64
1610×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
054283
1217211
21097193
08923193
Stop Event
1×iter limit
1×node limit
Counts
23 → 618
Calls
Call 1
Inputs
(* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ (- -5/6 (pow (tan x) 2)) -1/2)
(* eps (+ 1 (+ (* eps (+ (* (- 1/3 (* (pow (tan x) 2) (+ (- -5/6 (pow (tan x) 2)) -1/2))) eps) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow (cos x) 2)))))
(+ 1 (+ (* eps (+ (* (- 1/3 (* (pow (tan x) 2) (+ (- -5/6 (pow (tan x) 2)) -1/2))) eps) (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (pow (cos x) 2))))
(* (+ (* x x) 1) eps)
(+ (* x x) 1)
(* x x)
(* eps (+ 1 (* (* x x) (+ 1 (* (* x x) (+ 2/3 (* (* x x) 17/45)))))))
(+ 1 (* (* x x) (+ 1 (* (* x x) (+ 2/3 (* (* x x) 17/45))))))
(* (* x x) (+ 1 (* (* x x) (+ 2/3 (* (* x x) 17/45)))))
(/ eps (cos eps))
(cos eps)
(+ x (- eps x))
(/ (/ (sin (+ x (- eps x))) (cos (+ x eps))) (cos x))
(/ (sin (+ x (- eps x))) (cos (+ x eps)))
(sin (+ x (- eps x)))
(- 1/2 (* 1/2 (cos (* 2 x))))
(* (- 1/3 (* (pow (tan x) 2) (+ (- -5/6 (pow (tan x) 2)) -1/2))) eps)
(* (pow (tan x) 2) (+ (- -5/6 (pow (tan x) 2)) -1/2))
(* (* x x) (+ 2/3 (* (* x x) 17/45)))
(* (* x x) 17/45)
(+ 2/3 (* (* x x) 17/45))
(cos (+ x eps))
Outputs
(+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))
(+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x))
(-.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))
(fma.f64 (sin.f64 x) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (tan.f64 x))
(fma.f64 #s(literal 1 binary64) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))
(fma.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (/.f64 (tan.f64 x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (tan.f64 x))
(fma.f64 (tan.f64 x) #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))
(fma.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (tan.f64 x))
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (tan.f64 x) (tan.f64 x))
(fma.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (/.f64 #s(literal -1 binary64) (cos.f64 x)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))
(fma.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 x)) (tan.f64 x))
(fma.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (tan.f64 x)) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (tan.f64 x))
(neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (tan.f64 x))))
(neg.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(neg.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (cos.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (cos.f64 x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(/.f64 (+.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (cos.f64 x)) (*.f64 (cos.f64 x) (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))
(/.f64 (+.f64 (*.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (*.f64 (cos.f64 x) (tan.f64 x))) (/.f64 (cos.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(/.f64 (+.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (cos.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (/.f64 (cos.f64 x) (tan.f64 x)))
(/.f64 (+.f64 (*.f64 (sin.f64 x) (/.f64 (cos.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 (cos.f64 x) (sin.f64 x))) (*.f64 (cos.f64 x) (/.f64 (cos.f64 x) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(/.f64 (+.f64 (*.f64 (sin.f64 x) (*.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (cos.f64 x))) (*.f64 (cos.f64 x) (sin.f64 x))) (*.f64 (cos.f64 x) (*.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (cos.f64 x))))
(/.f64 (+.f64 (*.f64 (sin.f64 x) (*.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))) (*.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 x)))) (*.f64 (cos.f64 x) (*.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))))
(/.f64 (+.f64 (*.f64 (sin.f64 x) (/.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 x)))) (*.f64 (cos.f64 x) (/.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(/.f64 (+.f64 (*.f64 (sin.f64 x) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))))) (*.f64 (cos.f64 x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))))) (*.f64 (cos.f64 x) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))))))
(/.f64 (+.f64 (*.f64 (sin.f64 x) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))))) (*.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))))) (*.f64 (cos.f64 x) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))))))
(/.f64 (+.f64 (*.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (tan.f64 x))) (*.f64 (cos.f64 x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))))) (*.f64 (cos.f64 x) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (tan.f64 x))))
(/.f64 (+.f64 (*.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (tan.f64 x))) (*.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))))) (*.f64 (cos.f64 x) (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (tan.f64 x))))
(/.f64 (+.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (*.f64 (cos.f64 x) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (tan.f64 x)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))
(/.f64 (+.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (*.f64 (cos.f64 x) (*.f64 (tan.f64 x) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64))))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))
(/.f64 (+.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))
(/.f64 (+.f64 (cos.f64 x) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 (sin.f64 x) (pow.f64 (tan.f64 x) #s(literal -2 binary64))))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (cos.f64 x)))
(/.f64 (+.f64 (cos.f64 x) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (sin.f64 x)))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (cos.f64 x)))
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(fma.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 17/45 binary64))) (*.f64 x (*.f64 x #s(literal 2/3 binary64))))
(fma.f64 (*.f64 x x) #s(literal 2/3 binary64) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))))
(fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x (*.f64 x #s(literal 2/3 binary64))))
(fma.f64 #s(literal 2/3 binary64) (*.f64 x x) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))))
(fma.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x (*.f64 x #s(literal 2/3 binary64))))
(fma.f64 (*.f64 (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) (*.f64 x (*.f64 x #s(literal 2/3 binary64))))
(fma.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 17/45 binary64))) x (*.f64 x (*.f64 x #s(literal 2/3 binary64))))
(fma.f64 (*.f64 #s(literal 2/3 binary64) x) x (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))))
(fma.f64 (*.f64 (*.f64 x x) x) (*.f64 x #s(literal 17/45 binary64)) (*.f64 x (*.f64 x #s(literal 2/3 binary64))))
(fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 17/45 binary64) (*.f64 x (*.f64 x #s(literal 2/3 binary64))))
(*.f64 x (*.f64 x (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))))
(*.f64 (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))) (*.f64 x x))
(*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))) #s(literal 1 binary64))
(*.f64 (*.f64 x (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))) x)
(*.f64 (*.f64 (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))) #s(literal 1 binary64)) (*.f64 x x))
(*.f64 x (*.f64 x #s(literal 17/45 binary64)))
(*.f64 (*.f64 x x) #s(literal 17/45 binary64))
(*.f64 #s(literal 17/45 binary64) (*.f64 x x))
(*.f64 (*.f64 (*.f64 x x) #s(literal 17/45 binary64)) #s(literal 1 binary64))
(*.f64 (*.f64 x #s(literal 17/45 binary64)) x)
(+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))
(+.f64 (*.f64 (*.f64 x x) #s(literal 17/45 binary64)) #s(literal 2/3 binary64))
(fma.f64 x (*.f64 x #s(literal 17/45 binary64)) #s(literal 2/3 binary64))
(fma.f64 (*.f64 x x) #s(literal 17/45 binary64) #s(literal 2/3 binary64))
(fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64))
(fma.f64 (*.f64 x #s(literal 17/45 binary64)) x #s(literal 2/3 binary64))
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(+.f64 (cos.f64 (+.f64 x eps)) (fma.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 eps) (*.f64 (sin.f64 x) (sin.f64 eps))))
(+.f64 (cos.f64 (+.f64 x eps)) (+.f64 (+.f64 (*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (sin.f64 x) (sin.f64 eps))) (+.f64 (*.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (*.f64 (sin.f64 x) (sin.f64 eps)))))
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(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps)))
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(*.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps)))
(*.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 (+.f64 x eps))))

simplify335.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
4274×*-lowering-*.f32
4274×*-lowering-*.f64
2372×+-lowering-+.f64
2372×+-lowering-+.f32
2042×sum3-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
05126232
117165197
261125006
081765006
Stop Event
1×iter limit
1×node limit
Counts
396 → 396
Calls
Call 1
Inputs
x
(* x (+ 1 (* 4/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
-4/3
(- (* -1 (pow x 2)) 4/3)
(- (* (pow x 2) (- (* -2/3 (pow x 2)) 1)) 4/3)
(- (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1)) 4/3)
(* -1 (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* -1 (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* -1 (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* -1 (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* -1 (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* -1 (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* -1 (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* -1 (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* eps (- (+ 1 (* 1/2 (/ 1 (pow (cos x) 2)))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))
(* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))
(* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))
(* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))
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(* (pow eps 3) (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* -1 (* (pow eps 3) (+ (* -1 (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))))))
(* -1 (* (pow eps 3) (+ (* -1 (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (* -1 (/ (- (+ (/ 1/2 (* eps (pow (cos x) 2))) (+ (/ 1 eps) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (* 1/2 (/ (cos (* 2 x)) (* eps (pow (cos x) 2))))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (* -1 (/ (- (+ (/ 1/2 (* eps (pow (cos x) 2))) (+ (/ 1 eps) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (* 1/2 (/ (cos (* 2 x)) (* eps (pow (cos x) 2))))) eps)))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) x))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2))))
(* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))
(* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))
(* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))
(* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))
(* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))
(* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))
(* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))
(* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))
(- (+ 1 (* 1/2 (/ 1 (pow (cos x) 2)))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))
(- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))
(- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))
(- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))
(* (pow eps 2) (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* (pow eps 2) (- (+ 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (* (pow eps 2) (pow (cos x) 2)))) (+ (/ 1 (pow eps 2)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))))) (+ (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (* (pow eps 2) (pow (cos x) 2)))))))
(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (* (pow eps 2) (pow (cos x) 2)))) (+ (/ 1 (pow eps 2)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))))) (+ (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (* (pow eps 2) (pow (cos x) 2)))))))
(* (pow eps 2) (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* (pow eps 2) (- (+ 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* (pow eps 2) (- (+ 1/3 (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (- (+ 1 (* 1/2 (/ 1 (pow (cos x) 2)))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))) eps))) eps))) (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* (pow eps 2) (- (+ 1/3 (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (- (+ 1 (* 1/2 (/ 1 (pow (cos x) 2)))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))) eps))) eps))) (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(+ 1 (* 1/3 (pow eps 2)))
(+ 1 (+ (* 1/3 (pow eps 2)) (* eps x)))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))))
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))))))))
(- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))
(- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))
(- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))
(- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))
(- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))
(- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))
(- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))
(- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* eps (pow x 2)))
(+ eps (* eps (pow x 2)))
(* eps (pow x 2))
(* (pow x 2) (+ eps (/ eps (pow x 2))))
(* (pow x 2) (+ eps (/ eps (pow x 2))))
(* (pow x 2) (+ eps (/ eps (pow x 2))))
(* eps (pow x 2))
(* (pow x 2) (+ eps (/ eps (pow x 2))))
(* (pow x 2) (+ eps (/ eps (pow x 2))))
(* (pow x 2) (+ eps (/ eps (pow x 2))))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
(* eps (+ 1 (pow x 2)))
1
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
(* eps (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
eps
(+ eps (* eps (pow x 2)))
(+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps))))))
(* 17/45 (* eps (pow x 6)))
(* (pow x 6) (+ (* 17/45 eps) (* 2/3 (/ eps (pow x 2)))))
(* (pow x 6) (+ (* 17/45 eps) (+ (* 2/3 (/ eps (pow x 2))) (/ eps (pow x 4)))))
(* (pow x 6) (+ (* 17/45 eps) (+ (* 2/3 (/ eps (pow x 2))) (+ (/ eps (pow x 4)) (/ eps (pow x 6))))))
(* 17/45 (* eps (pow x 6)))
(* (pow x 6) (+ (* 17/45 eps) (* 2/3 (/ eps (pow x 2)))))
(* (pow x 6) (+ (* 17/45 eps) (+ (* 2/3 (/ eps (pow x 2))) (/ eps (pow x 4)))))
(* (pow x 6) (+ (* 17/45 eps) (+ (* 2/3 (/ eps (pow x 2))) (+ (/ eps (pow x 4)) (/ eps (pow x 6))))))
1
(+ 1 (pow x 2))
(+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))
(* 17/45 (pow x 6))
(* (pow x 6) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* (pow x 6) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))))
(* 17/45 (pow x 6))
(* (pow x 6) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* (pow x 6) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2/3 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))
(* 17/45 (pow x 6))
(* (pow x 6) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* (pow x 6) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* 17/45 (pow x 6))
(* (pow x 6) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* (pow x 6) (+ 17/45 (+ (* 2/3 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
eps
(* eps (+ 1 (* 1/2 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (+ 1/2 (* 5/24 (pow eps 2))))))
(* eps (+ 1 (* (pow eps 2) (+ 1/2 (* (pow eps 2) (+ 5/24 (* 61/720 (pow eps 2))))))))
(/ eps (cos eps))
(/ eps (cos eps))
(/ eps (cos eps))
(/ eps (cos eps))
(/ eps (cos eps))
(/ eps (cos eps))
(/ eps (cos eps))
(/ eps (cos eps))
1
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x)))))
(/ eps (pow (cos x) 2))
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin eps) (* (cos x) (cos (+ eps x))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(/ (sin eps) (cos (+ eps x)))
(/ (sin eps) (cos (+ eps x)))
(/ (sin eps) (cos (+ eps x)))
(/ (sin eps) (cos (+ eps x)))
(/ (sin eps) (cos (- eps (* -1 x))))
(/ (sin eps) (cos (- eps (* -1 x))))
(/ (sin eps) (cos (- eps (* -1 x))))
(/ (sin eps) (cos (- eps (* -1 x))))
(/ eps (cos x))
(* eps (+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2))))
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))))
(/ (sin eps) (cos (+ eps x)))
(/ (sin eps) (cos (+ eps x)))
(/ (sin eps) (cos (+ eps x)))
(/ (sin eps) (cos (+ eps x)))
(/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
(sin (neg (* -1 eps)))
(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))))
(- 1/2 (* 1/2 (cos (* 2 x))))
(- 1/2 (* 1/2 (cos (* 2 x))))
(- 1/2 (* 1/2 (cos (* 2 x))))
(- 1/2 (* 1/2 (cos (* 2 x))))
(- 1/2 (* 1/2 (cos (* 2 x))))
(- 1/2 (* 1/2 (cos (* 2 x))))
(- 1/2 (* 1/2 (cos (* 2 x))))
(- 1/2 (* 1/2 (cos (* 2 x))))
(* 1/3 eps)
(+ (* 1/3 eps) (* 4/3 (* eps (pow x 2))))
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* 17/9 (* eps (pow x 2))))))
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* (pow x 2) (+ (* 248/135 (* eps (pow x 2))) (* 17/9 eps))))))
(* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(* -4/3 (pow x 2))
(* (pow x 2) (- (* -17/9 (pow x 2)) 4/3))
(* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -1382/945 (pow x 2)) 248/135)) 17/9)) 4/3))
(* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(* 2/3 (pow x 2))
(* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))
(* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))
(* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))
(* 17/45 (pow x 4))
(* (pow x 4) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(* 17/45 (pow x 4))
(* (pow x 4) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(* 17/45 (pow x 2))
(* 17/45 (pow x 2))
(* 17/45 (pow x 2))
(* 17/45 (pow x 2))
(* 17/45 (pow x 2))
(* 17/45 (pow x 2))
(* 17/45 (pow x 2))
(* 17/45 (pow x 2))
(* 17/45 (pow x 2))
(* 17/45 (pow x 2))
(* 17/45 (pow x 2))
(* 17/45 (pow x 2))
2/3
(+ 2/3 (* 17/45 (pow x 2)))
(+ 2/3 (* 17/45 (pow x 2)))
(+ 2/3 (* 17/45 (pow x 2)))
(* 17/45 (pow x 2))
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(* 17/45 (pow x 2))
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
Outputs
x
(* x (+ 1 (* 4/3 (pow x 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))
(* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x (*.f64 x #s(literal 17/15 binary64))))))))
(* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/15 binary64) (*.f64 (*.f64 x x) #s(literal 248/315 binary64)))))))))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))
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(* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))
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(* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))
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(* (pow eps 3) (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
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(* eps (+ 1 (* 1/3 (pow eps 2))))
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(* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))
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(* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))
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(* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))
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(* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))
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(* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))
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(* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))
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(* eps (- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))))
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(- (+ 1 (* 1/2 (/ 1 (pow (cos x) 2)))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))
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(- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))
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(- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))
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(- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))
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(* (pow eps 2) (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
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(* (pow eps 2) (- (+ 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
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(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (* (pow eps 2) (pow (cos x) 2)))) (+ (/ 1 (pow eps 2)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))))) (+ (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (* (pow eps 2) (pow (cos x) 2)))))))
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(* (pow eps 2) (- (+ 1/3 (+ (* 1/2 (/ 1 (* (pow eps 2) (pow (cos x) 2)))) (+ (/ 1 (pow eps 2)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))))) (+ (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* 1/2 (/ (cos (* 2 x)) (* (pow eps 2) (pow (cos x) 2)))))))
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(* (pow eps 2) (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(*.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 (+.f64 #s(literal 4/3 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 eps))
(* (pow eps 2) (- (+ 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
(*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 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 (sin.f64 x) (*.f64 (cos.f64 x) eps))) (*.f64 (+.f64 #s(literal 4/3 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))))))))
(* (pow eps 2) (- (+ 1/3 (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (- (+ 1 (* 1/2 (/ 1 (pow (cos x) 2)))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))) eps))) eps))) (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
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(* (pow eps 2) (- (+ 1/3 (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (- (+ 1 (* 1/2 (/ 1 (pow (cos x) 2)))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2)))) eps))) eps))) (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))))
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(+ 1 (* 1/3 (pow eps 2)))
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(+ 1 (+ (* 1/3 (pow eps 2)) (* eps x)))
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(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2))))))))
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(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))))))))
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(- (+ 1 (+ (* 1/2 (/ 1 (pow (cos x) 2))) (* eps (+ (* eps (- 1/3 (* -1 (/ (* (pow (sin x) 2) (+ 4/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))))) (* 1/2 (/ (cos (* 2 x)) (pow (cos x) 2))))
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(*.f64 (*.f64 x x) #s(literal 17/45 binary64))
(* 17/45 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 17/45 binary64))
(* 17/45 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 17/45 binary64))
(* 17/45 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 17/45 binary64))
(* 17/45 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 17/45 binary64))
(* 17/45 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 17/45 binary64))
(* 17/45 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 17/45 binary64))
(* 17/45 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 17/45 binary64))
(* 17/45 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 17/45 binary64))
(* 17/45 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 17/45 binary64))
(* 17/45 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 17/45 binary64))
(* 17/45 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 17/45 binary64))
2/3
#s(literal 2/3 binary64)
(+ 2/3 (* 17/45 (pow x 2)))
(+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))
(+ 2/3 (* 17/45 (pow x 2)))
(+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))
(+ 2/3 (* 17/45 (pow x 2)))
(+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))
(* 17/45 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 17/45 binary64))
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))
(* 17/45 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 17/45 binary64))
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))
(* (pow x 2) (+ 17/45 (* 2/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))
(cos eps)
(cos.f64 eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(-.f64 (cos.f64 eps) (*.f64 x (sin.f64 eps)))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (*.f64 (cos.f64 eps) #s(literal -1/2 binary64))) (sin.f64 eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (+.f64 (*.f64 (cos.f64 eps) #s(literal -1/2 binary64)) (*.f64 x (*.f64 (sin.f64 eps) #s(literal 1/6 binary64))))) (sin.f64 eps))))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 x eps))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1 (* eps (sin x))))
(-.f64 (cos.f64 x) (*.f64 (sin.f64 x) eps))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+.f64 (cos.f64 x) (*.f64 eps (-.f64 (*.f64 (cos.f64 x) (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(+.f64 (cos.f64 x) (*.f64 eps (-.f64 (*.f64 eps (+.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps)))) (sin.f64 x))))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (+ eps x))
(cos.f64 (+.f64 x eps))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 x eps))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 x eps))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 x eps))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 x eps))

eval136.0ms (0.7%)

Compiler

Compiled 37162 to 4067 computations (89.1% saved)

prune163.0ms (0.9%)

Pruning

35 alts after pruning (30 fresh and 5 done)

PrunedKeptTotal
New1051201071
Fresh131023
Picked415
Done145
Total1069351104
Accuracy
100.0%
Counts
1104 → 35
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.5%
(/.f64 (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/120 binary64)))))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
99.7%
(/.f64 (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/5040 binary64)))))))))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
99.1%
(/.f64 (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
99.9%
(/.f64 (/.f64 (sin.f64 (+.f64 eps #s(literal 0 binary64))) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
99.9%
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
98.7%
(/.f64 (/.f64 eps (cos.f64 (+.f64 x eps))) (cos.f64 x))
98.7%
(/.f64 (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 (*.f64 (sin.f64 x) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))
98.4%
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
96.9%
(/.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
99.7%
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 (cos.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (sin.f64 (+.f64 eps #s(literal 0 binary64))))) (cos.f64 x)))
✓64.0%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
62.6%
(-.f64 (-.f64 (tan.f64 (+.f64 x eps)) x) (*.f64 x (*.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))))))))
62.4%
(-.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)))))))
✓62.6%
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))))
62.0%
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/3 binary64))))))
✓63.8%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
62.0%
(-.f64 (tan.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))))
5.6%
(-.f64 (tan.f64 x) x)
98.4%
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
97.7%
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 x (*.f64 x #s(literal 62/315 binary64))))))))) (*.f64 (*.f64 x x) eps)) eps)
97.4%
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps (+.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps))))))))
97.7%
(+.f64 (*.f64 eps (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))))))) eps)
97.5%
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 x (*.f64 x (*.f64 eps #s(literal 2/3 binary64)))))))
✓97.2%
(*.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) eps)
98.9%
(*.f64 (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (tan.f64 x) #s(literal -2 binary64)))) (*.f64 eps eps)) (*.f64 (tan.f64 x) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) (tan.f64 x))))) eps)
49.5%
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x))))
6.7%
(*.f64 (*.f64 x x) eps)
98.6%
(*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 (sin.f64 x) eps) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))
97.7%
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 x (*.f64 x #s(literal 62/315 binary64)))))) (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 x x)))
97.4%
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)))))))))
97.4%
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps)))))))))
98.9%
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (-.f64 #s(literal -5/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) eps) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x)))) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
97.5%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 2/3 binary64))))))
90.9%
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 eps #s(literal 0 binary64))))) #s(literal -1 binary64)))
✓96.9%
eps
Compiler

Compiled 2186 to 830 computations (62% saved)

regimes57.0ms (0.3%)

Counts
66 → 1
Calls
Call 1
Inputs
eps
(*.f64 (*.f64 x x) eps)
(*.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) 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 eps (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/15 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 2/3 binary64))))))
(+.f64 eps (*.f64 x (*.f64 x (+.f64 eps (*.f64 eps (*.f64 (*.f64 x x) #s(literal 2/3 binary64)))))))
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 x (*.f64 x (*.f64 eps #s(literal 2/3 binary64)))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 2/15 binary64) (*.f64 eps (*.f64 eps #s(literal 17/315 binary64))))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))))))))
(+.f64 (*.f64 eps (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))))))) eps)
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps)))))))))
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 17/45 binary64)) (*.f64 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 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)))))))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps (+.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) #s(literal 62/315 binary64)))))))))))
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 x (*.f64 x #s(literal 62/315 binary64))))))))) (*.f64 (*.f64 x x) eps)) eps)
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 x (*.f64 x #s(literal 62/315 binary64)))))) (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 x x)))
(tan.f64 eps)
(-.f64 (tan.f64 x) x)
(/.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 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))))
(-.f64 (-.f64 (tan.f64 (+.f64 x eps)) x) (*.f64 x (*.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 (+.f64 #s(literal 1 binary64) (/.f64 eps x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
(/.f64 (/.f64 eps (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/120 binary64)))))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/5040 binary64)))))))))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (tan.f64 x))
(/.f64 (/.f64 (sin.f64 (+.f64 eps #s(literal 0 binary64))) (cos.f64 x)) (cos.f64 (+.f64 x eps)))
(/.f64 (/.f64 (sin.f64 (+.f64 x (-.f64 eps x))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(-.f64 (/.f64 (sin.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) (cos.f64 (+.f64 x eps))) (tan.f64 x))
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 (cos.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (sin.f64 (+.f64 eps #s(literal 0 binary64))))) (cos.f64 x)))
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x) (tan.f64 (+.f64 x 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)))))
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (-.f64 (cos.f64 x) (*.f64 (sin.f64 x) eps))) (tan.f64 x))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 eps #s(literal 0 binary64))))) #s(literal -1 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 eps (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 (sin.f64 x) eps) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))
(/.f64 (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 (*.f64 (sin.f64 x) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))
(/.f64 (-.f64 (*.f64 (sin.f64 (+.f64 x eps)) (cos.f64 x)) (*.f64 (cos.f64 (+.f64 x eps)) (sin.f64 x))) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(/.f64 (/.f64 (-.f64 (neg.f64 (neg.f64 (*.f64 (cos.f64 x) (sin.f64 (+.f64 x eps))))) (*.f64 (sin.f64 x) (cos.f64 (+.f64 x eps)))) (-.f64 #s(literal 0 binary64) (cos.f64 (+.f64 x eps)))) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(*.f64 (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (tan.f64 x) #s(literal -2 binary64)))) (*.f64 eps eps)) (*.f64 (tan.f64 x) (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps) (tan.f64 x))))) eps)
(*.f64 eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 eps (-.f64 (/.f64 (*.f64 (sin.f64 x) #s(literal -1 binary64)) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) #s(literal 1/3 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 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(*.f64 eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (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))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 4/3 binary64)) #s(literal 1/3 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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (-.f64 #s(literal -5/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) eps) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x)))) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (-.f64 #s(literal -5/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) eps) (*.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 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1/6 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) eps) (*.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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 eps (-.f64 #s(literal -1/6 binary64) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.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 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 eps (-.f64 #s(literal -1/6 binary64) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 eps (-.f64 #s(literal -1/6 binary64) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (+.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 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
Outputs
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
Calls

3 calls:

18.0ms
eps
18.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
16.0ms
x
Results
AccuracySegmentsBranch
99.9%1x
99.9%1eps
99.9%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes34.0ms (0.2%)

Counts
38 → 1
Calls
Call 1
Inputs
eps
(*.f64 (*.f64 x x) eps)
(*.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) 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 eps (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/15 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 2/3 binary64))))))
(+.f64 eps (*.f64 x (*.f64 x (+.f64 eps (*.f64 eps (*.f64 (*.f64 x x) #s(literal 2/3 binary64)))))))
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 x (*.f64 x (*.f64 eps #s(literal 2/3 binary64)))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 2/15 binary64) (*.f64 eps (*.f64 eps #s(literal 17/315 binary64))))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))))))))
(+.f64 (*.f64 eps (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))))))) eps)
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps)))))))))
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 17/45 binary64)) (*.f64 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 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)))))))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps (+.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) #s(literal 62/315 binary64)))))))))))
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 x (*.f64 x #s(literal 62/315 binary64))))))))) (*.f64 (*.f64 x x) eps)) eps)
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 x (*.f64 x #s(literal 62/315 binary64)))))) (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 x x)))
(tan.f64 eps)
(-.f64 (tan.f64 x) x)
(/.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 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))))
(-.f64 (-.f64 (tan.f64 (+.f64 x eps)) x) (*.f64 x (*.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 (+.f64 #s(literal 1 binary64) (/.f64 eps x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
(/.f64 (/.f64 eps (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/120 binary64)))))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/5040 binary64)))))))))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
Outputs
(/.f64 (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/5040 binary64)))))))))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
Calls

3 calls:

11.0ms
x
10.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
10.0ms
eps
Results
AccuracySegmentsBranch
99.7%1x
99.7%1eps
99.7%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes33.0ms (0.2%)

Counts
37 → 1
Calls
Call 1
Inputs
eps
(*.f64 (*.f64 x x) eps)
(*.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) 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 eps (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/15 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 2/3 binary64))))))
(+.f64 eps (*.f64 x (*.f64 x (+.f64 eps (*.f64 eps (*.f64 (*.f64 x x) #s(literal 2/3 binary64)))))))
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 x (*.f64 x (*.f64 eps #s(literal 2/3 binary64)))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 2/15 binary64) (*.f64 eps (*.f64 eps #s(literal 17/315 binary64))))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))))))))
(+.f64 (*.f64 eps (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))))))) eps)
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps)))))))))
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 17/45 binary64)) (*.f64 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 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)))))))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps (+.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) #s(literal 62/315 binary64)))))))))))
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 x (*.f64 x #s(literal 62/315 binary64))))))))) (*.f64 (*.f64 x x) eps)) eps)
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 x (*.f64 x #s(literal 62/315 binary64)))))) (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 x x)))
(tan.f64 eps)
(-.f64 (tan.f64 x) x)
(/.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 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))))
(-.f64 (-.f64 (tan.f64 (+.f64 x eps)) x) (*.f64 x (*.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 (+.f64 #s(literal 1 binary64) (/.f64 eps x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
(/.f64 (/.f64 eps (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/120 binary64)))))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
Outputs
(/.f64 (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/120 binary64)))))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
Calls

3 calls:

10.0ms
eps
9.0ms
x
9.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
AccuracySegmentsBranch
99.5%1x
99.5%1eps
99.5%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes33.0ms (0.2%)

Counts
36 → 1
Calls
Call 1
Inputs
eps
(*.f64 (*.f64 x x) eps)
(*.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) 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 eps (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/15 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 2/3 binary64))))))
(+.f64 eps (*.f64 x (*.f64 x (+.f64 eps (*.f64 eps (*.f64 (*.f64 x x) #s(literal 2/3 binary64)))))))
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 x (*.f64 x (*.f64 eps #s(literal 2/3 binary64)))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 2/15 binary64) (*.f64 eps (*.f64 eps #s(literal 17/315 binary64))))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))))))))
(+.f64 (*.f64 eps (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))))))) eps)
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps)))))))))
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 17/45 binary64)) (*.f64 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 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)))))))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps (+.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) #s(literal 62/315 binary64)))))))))))
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 x (*.f64 x #s(literal 62/315 binary64))))))))) (*.f64 (*.f64 x x) eps)) eps)
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 x (*.f64 x #s(literal 62/315 binary64)))))) (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 x x)))
(tan.f64 eps)
(-.f64 (tan.f64 x) x)
(/.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 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))))
(-.f64 (-.f64 (tan.f64 (+.f64 x eps)) x) (*.f64 x (*.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 (+.f64 #s(literal 1 binary64) (/.f64 eps x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
(/.f64 (/.f64 eps (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
Outputs
(/.f64 (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
Calls

3 calls:

11.0ms
eps
10.0ms
x
9.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
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)

regimes31.0ms (0.2%)

Counts
35 → 1
Calls
Call 1
Inputs
eps
(*.f64 (*.f64 x x) eps)
(*.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) 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 eps (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/15 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 2/3 binary64))))))
(+.f64 eps (*.f64 x (*.f64 x (+.f64 eps (*.f64 eps (*.f64 (*.f64 x x) #s(literal 2/3 binary64)))))))
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 x (*.f64 x (*.f64 eps #s(literal 2/3 binary64)))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 2/15 binary64) (*.f64 eps (*.f64 eps #s(literal 17/315 binary64))))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))))))))
(+.f64 (*.f64 eps (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))))))) eps)
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps)))))))))
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 17/45 binary64)) (*.f64 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 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)))))))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps (+.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) #s(literal 62/315 binary64)))))))))))
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 x (*.f64 x #s(literal 62/315 binary64))))))))) (*.f64 (*.f64 x x) eps)) eps)
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 x (*.f64 x #s(literal 62/315 binary64)))))) (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 x x)))
(tan.f64 eps)
(-.f64 (tan.f64 x) x)
(/.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 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))))
(-.f64 (-.f64 (tan.f64 (+.f64 x eps)) x) (*.f64 x (*.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 (+.f64 #s(literal 1 binary64) (/.f64 eps x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
(/.f64 (/.f64 eps (cos.f64 (+.f64 x eps))) (cos.f64 x))
Outputs
(/.f64 (/.f64 eps (cos.f64 (+.f64 x eps))) (cos.f64 x))
Calls

3 calls:

10.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
9.0ms
x
9.0ms
eps
Results
AccuracySegmentsBranch
98.7%1eps
98.7%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
98.7%1x
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes31.0ms (0.2%)

Counts
34 → 1
Calls
Call 1
Inputs
eps
(*.f64 (*.f64 x x) eps)
(*.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) 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 eps (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/15 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 2/3 binary64))))))
(+.f64 eps (*.f64 x (*.f64 x (+.f64 eps (*.f64 eps (*.f64 (*.f64 x x) #s(literal 2/3 binary64)))))))
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 x (*.f64 x (*.f64 eps #s(literal 2/3 binary64)))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 2/15 binary64) (*.f64 eps (*.f64 eps #s(literal 17/315 binary64))))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))))))))
(+.f64 (*.f64 eps (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))))))) eps)
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps)))))))))
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 17/45 binary64)) (*.f64 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 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)))))))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps (+.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) #s(literal 62/315 binary64)))))))))))
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 x (*.f64 x #s(literal 62/315 binary64))))))))) (*.f64 (*.f64 x x) eps)) eps)
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 x (*.f64 x #s(literal 62/315 binary64)))))) (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 x x)))
(tan.f64 eps)
(-.f64 (tan.f64 x) x)
(/.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 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))))
(-.f64 (-.f64 (tan.f64 (+.f64 x eps)) x) (*.f64 x (*.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 (+.f64 #s(literal 1 binary64) (/.f64 eps x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
Outputs
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
Calls

3 calls:

10.0ms
eps
9.0ms
x
9.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
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)

regimes33.0ms (0.2%)

Counts
33 → 1
Calls
Call 1
Inputs
eps
(*.f64 (*.f64 x x) eps)
(*.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) 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 eps (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/15 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 2/3 binary64))))))
(+.f64 eps (*.f64 x (*.f64 x (+.f64 eps (*.f64 eps (*.f64 (*.f64 x x) #s(literal 2/3 binary64)))))))
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 x (*.f64 x (*.f64 eps #s(literal 2/3 binary64)))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 2/15 binary64) (*.f64 eps (*.f64 eps #s(literal 17/315 binary64))))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))))))))
(+.f64 (*.f64 eps (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))))))) eps)
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps)))))))))
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 17/45 binary64)) (*.f64 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 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)))))))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps (+.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) #s(literal 62/315 binary64)))))))))))
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 x (*.f64 x #s(literal 62/315 binary64))))))))) (*.f64 (*.f64 x x) eps)) eps)
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 x (*.f64 x #s(literal 62/315 binary64)))))) (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 x x)))
(tan.f64 eps)
(-.f64 (tan.f64 x) x)
(/.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 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))))
(-.f64 (-.f64 (tan.f64 (+.f64 x eps)) x) (*.f64 x (*.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 (+.f64 #s(literal 1 binary64) (/.f64 eps x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Outputs
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
Calls

3 calls:

11.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
9.0ms
x
8.0ms
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)

regimes18.0ms (0.1%)

Counts
31 → 1
Calls
Call 1
Inputs
eps
(*.f64 (*.f64 x x) eps)
(*.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) 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 eps (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/15 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 2/3 binary64))))))
(+.f64 eps (*.f64 x (*.f64 x (+.f64 eps (*.f64 eps (*.f64 (*.f64 x x) #s(literal 2/3 binary64)))))))
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 x (*.f64 x (*.f64 eps #s(literal 2/3 binary64)))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 2/15 binary64) (*.f64 eps (*.f64 eps #s(literal 17/315 binary64))))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))))))))
(+.f64 (*.f64 eps (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))))))) eps)
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps)))))))))
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 17/45 binary64)) (*.f64 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 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)))))))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps (+.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) #s(literal 62/315 binary64)))))))))))
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 x (*.f64 x #s(literal 62/315 binary64))))))))) (*.f64 (*.f64 x x) eps)) eps)
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 x (*.f64 x #s(literal 62/315 binary64)))))) (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 x x)))
(tan.f64 eps)
(-.f64 (tan.f64 x) x)
(/.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 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))))
(-.f64 (-.f64 (tan.f64 (+.f64 x eps)) x) (*.f64 x (*.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 (+.f64 #s(literal 1 binary64) (/.f64 eps x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/15 binary64) (*.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))))
(/.f64 (sin.f64 eps) (cos.f64 eps))
Outputs
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 x (*.f64 x #s(literal 62/315 binary64))))))))) (*.f64 (*.f64 x x) eps)) eps)
Calls

2 calls:

8.0ms
x
8.0ms
eps
Results
AccuracySegmentsBranch
97.7%1x
97.7%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes13.0ms (0.1%)

Counts
18 → 1
Calls
Call 1
Inputs
eps
(*.f64 (*.f64 x x) eps)
(*.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) 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 eps (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/15 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 2/3 binary64))))))
(+.f64 eps (*.f64 x (*.f64 x (+.f64 eps (*.f64 eps (*.f64 (*.f64 x x) #s(literal 2/3 binary64)))))))
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 x (*.f64 x (*.f64 eps #s(literal 2/3 binary64)))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 2/15 binary64) (*.f64 eps (*.f64 eps #s(literal 17/315 binary64))))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))))))))
(+.f64 (*.f64 eps (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))))))) eps)
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps)))))))))
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 17/45 binary64)) (*.f64 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 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps (+.f64 x eps)))))))))
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 eps (+.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) #s(literal 62/315 binary64)))))))))))
Outputs
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 17/45 binary64)) (*.f64 eps #s(literal 2/3 binary64)))))))
Calls

2 calls:

6.0ms
eps
5.0ms
x
Results
AccuracySegmentsBranch
97.7%1x
97.7%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes9.0ms (0.1%)

Counts
14 → 1
Calls
Call 1
Inputs
eps
(*.f64 (*.f64 x x) eps)
(*.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) 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 eps (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/15 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 2/3 binary64))))))
(+.f64 eps (*.f64 x (*.f64 x (+.f64 eps (*.f64 eps (*.f64 (*.f64 x x) #s(literal 2/3 binary64)))))))
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 x (*.f64 x (*.f64 eps #s(literal 2/3 binary64)))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 2/15 binary64) (*.f64 eps (*.f64 eps #s(literal 17/315 binary64))))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))))))))
(+.f64 (*.f64 eps (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))))))) eps)
(*.f64 eps (+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps)))))))))
Outputs
(+.f64 (*.f64 eps (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))))))) eps)
Calls

2 calls:

4.0ms
eps
4.0ms
x
Results
AccuracySegmentsBranch
97.7%1x
97.7%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes10.0ms (0.1%)

Counts
12 → 1
Calls
Call 1
Inputs
eps
(*.f64 (*.f64 x x) eps)
(*.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) 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 eps (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/15 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 2/3 binary64))))))
(+.f64 eps (*.f64 x (*.f64 x (+.f64 eps (*.f64 eps (*.f64 (*.f64 x x) #s(literal 2/3 binary64)))))))
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 x (*.f64 x (*.f64 eps #s(literal 2/3 binary64)))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 2/15 binary64) (*.f64 eps (*.f64 eps #s(literal 17/315 binary64))))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))))))))
Outputs
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))))))))
Calls

2 calls:

5.0ms
eps
4.0ms
x
Results
AccuracySegmentsBranch
97.6%1x
97.6%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes8.0ms (0%)

Counts
11 → 1
Calls
Call 1
Inputs
eps
(*.f64 (*.f64 x x) eps)
(*.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) 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 eps (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/15 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 2/3 binary64))))))
(+.f64 eps (*.f64 x (*.f64 x (+.f64 eps (*.f64 eps (*.f64 (*.f64 x x) #s(literal 2/3 binary64)))))))
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 x (*.f64 x (*.f64 eps #s(literal 2/3 binary64)))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 2/15 binary64) (*.f64 eps (*.f64 eps #s(literal 17/315 binary64))))))))))
Outputs
(+.f64 eps (*.f64 x (*.f64 x (+.f64 eps (*.f64 eps (*.f64 (*.f64 x x) #s(literal 2/3 binary64)))))))
Calls

2 calls:

4.0ms
x
3.0ms
eps
Results
AccuracySegmentsBranch
97.5%1x
97.5%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0%)

Counts
8 → 1
Calls
Call 1
Inputs
eps
(*.f64 (*.f64 x x) eps)
(*.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) 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 eps (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/15 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 2/3 binary64))))))
Outputs
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 2/3 binary64))))))
Calls

2 calls:

3.0ms
eps
3.0ms
x
Results
AccuracySegmentsBranch
97.5%1x
97.5%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes19.0ms (0.1%)

Counts
7 → 1
Calls
Call 1
Inputs
eps
(*.f64 (*.f64 x x) eps)
(*.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) 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 eps (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 (*.f64 x x) (+.f64 eps (/.f64 eps (*.f64 x x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 2/15 binary64))))))
Outputs
(*.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) eps)
Calls

2 calls:

16.0ms
eps
3.0ms
x
Results
AccuracySegmentsBranch
97.2%1x
97.2%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

Accuracy

Total -57.7b remaining (-2896.8%)

Threshold costs -57.7b (-2896.8%)

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

2 calls:

1.0ms
x
1.0ms
eps
Results
AccuracySegmentsBranch
96.9%1x
96.9%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify10.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
76×*-commutative_binary64
48×+-commutative_binary64
2×1-exp_binary64
2×1-exp_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
091232
1156232
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/5040 binary64)))))))))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/120 binary64)))))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (/.f64 eps (cos.f64 (+.f64 x eps))) (cos.f64 x))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 x (*.f64 x #s(literal 62/315 binary64))))))))) (*.f64 (*.f64 x x) eps)) eps)
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 17/45 binary64)) (*.f64 eps #s(literal 2/3 binary64)))))))
(+.f64 (*.f64 eps (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))))))) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))))))))
(+.f64 eps (*.f64 x (*.f64 x (+.f64 eps (*.f64 eps (*.f64 (*.f64 x x) #s(literal 2/3 binary64)))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 2/3 binary64))))))
(*.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) eps)
eps
Outputs
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/5040 binary64)))))))))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/5040 binary64)))))))))) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/120 binary64)))))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (*.f64 #s(literal 1/120 binary64) (*.f64 eps eps)))))) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (cos.f64 (+.f64 eps x))) (cos.f64 x))
(/.f64 (/.f64 eps (cos.f64 (+.f64 x eps))) (cos.f64 x))
(/.f64 (/.f64 eps (cos.f64 (+.f64 eps x))) (cos.f64 x))
(+.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 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 x (*.f64 x #s(literal 62/315 binary64))))))))) (*.f64 (*.f64 x x) eps)) eps)
(+.f64 eps (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 17/45 binary64) (*.f64 x (*.f64 x #s(literal 62/315 binary64))))))))) (*.f64 eps (*.f64 x x))))
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 17/45 binary64)) (*.f64 eps #s(literal 2/3 binary64)))))))
(+.f64 eps (*.f64 (*.f64 x x) (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 17/45 binary64) (*.f64 eps (*.f64 x x))) (*.f64 eps #s(literal 2/3 binary64)))))))
(+.f64 (*.f64 eps (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))))))) eps)
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64)))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 x x) #s(literal 17/45 binary64))))))))
(+.f64 eps (*.f64 x (*.f64 x (+.f64 eps (*.f64 eps (*.f64 (*.f64 x x) #s(literal 2/3 binary64)))))))
(+.f64 eps (*.f64 x (*.f64 x (+.f64 eps (*.f64 eps (*.f64 #s(literal 2/3 binary64) (*.f64 x x)))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 2/3 binary64))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2/3 binary64) (*.f64 x x))))))
(*.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x)))
eps

soundness2.2s (11.8%)

Rules
5094×*-lowering-*.f32
5094×*-lowering-*.f64
4728×*-lowering-*.f32
4728×*-lowering-*.f64
4450×*-lowering-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
054373
1197252
21171201
08737201
054283
1217211
21097193
08923193
048354
1187231
21019191
08249191
01571381
14941186
218961117
377521117
086071117
0616
12116
28516
359416
4543416
0806516
05016761
115885614
254865282
081885282
05126232
117165197
261125006
081765006
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
1×iter limit
1×node limit
Compiler

Compiled 731 to 416 computations (43.1% saved)

preprocess82.0ms (0.4%)

Compiler

Compiled 510 to 210 computations (58.8% saved)

end0.0ms (0%)

Profiling

Loading profile data...