Details

Time bar (total: 8.0s)

sample130.0ms

Algorithm
intervals
Results
60.0ms51×body2560valid
43.0ms102×body1280valid
12.0ms53×body640valid
3.0ms21×body320valid
2.0ms16×body160valid
1.0ms13×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0114
1144
2164
3164

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
1.7b
(- 1.0 (cos x))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt *-un-lft-identity
19×add-cube-cbrt
15×times-frac
9×prod-diff
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-exp-log add-cbrt-cube add-log-exp
3×fma-neg associate-/r*
2×pow1 expm1-log1p-u flip3-- flip-- log1p-expm1-u associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
2 → 68
Calls
2 calls:
9.0ms
(/ (- 1.0 (cos x)) (sin x))
3.0ms
(- 1.0 (cos x))

series61.0ms

Counts
2 → 6
Calls
2 calls:
35.0ms
(/ (- 1.0 (cos x)) (sin x))
26.0ms
(- 1.0 (cos x))

simplify37.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0292569
1965460
25002460

prune180.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
0.2b
(exp (/ (- 1.0 (cos x)) (sin x)))
1.3b
(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.7b
(- 1.0 (cos x))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt *-un-lft-identity
45×times-frac
40×add-cube-cbrt
38×exp-prod
20×log-pow
11×distribute-lft-out-- difference-of-squares
9×prod-diff
7×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×log-prod fma-neg div-sub associate-/r* div-inv
2×flip3-- exp-diff flip-- associate-/l/
1×cbrt-undiv sub-neg log-div frac-2neg diff-log div-exp rem-log-exp clear-num rem-exp-log
Counts
4 → 132
Calls
4 calls:
9.0ms
(/ (- 1.0 (cos x)) (sin x))
11.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
12.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
6.0ms
(- 1.0 (cos x))

series137.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(/ (- 1.0 (cos x)) (sin x))
42.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
38.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
18.0ms
(- 1.0 (cos x))

simplify42.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
03681009
11099873
25002871

prune351.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x))
0.3b
(pow (cos x) 3)
0.3b
(+ 1.0 (cos x))
1.5b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
591×add-sqr-sqrt
537×times-frac
411×*-un-lft-identity
279×add-cube-cbrt
234×unpow-prod-down cube-prod
208×difference-of-squares
144×prod-diff
130×sqr-pow
79×associate-/l*
65×distribute-lft-out--
26×cube-mult unpow3
13×difference-cubes
12×fma-neg
10×add-exp-log add-cbrt-cube
8×add-log-exp
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv pow-unpow fma-def div-exp associate-/r*
2×div-sub
1×+-commutative pow-to-exp sub-neg flip3-- pow-pow frac-2neg flip3-+ diff-log pow-exp clear-num sum-log flip-- flip-+ associate-/l/ distribute-lft-out rem-cube-cbrt
Counts
4 → 571
Calls
4 calls:
61.0ms
(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x))
1.0ms
(pow (cos x) 3)
3.0ms
(+ 1.0 (cos x))
25.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series243.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x))
33.0ms
(pow (cos x) 3)
10.0ms
(+ 1.0 (cos x))
47.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify129.0ms

Algorithm
egg-herbie
Counts
583 → 583
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
0160710864
150019904

prune1.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(expm1 (- (pow 1.0 3) (pow (cos x) 3)))
0.3b
(pow (cos x) 3)
0.3b
(+ 1.0 (cos x))
1.5b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
144×prod-diff
107×add-sqr-sqrt
95×*-un-lft-identity
90×unpow-prod-down cube-prod
83×add-cube-cbrt
34×sqr-pow
26×cube-mult unpow3
16×difference-of-squares
12×fma-neg
8×add-log-exp
5×pow1 add-exp-log add-cbrt-cube log1p-expm1-u distribute-lft-out--
4×expm1-log1p-u
3×pow-unpow fma-def
1×difference-cubes +-commutative pow-to-exp sub-neg expm1-log1p flip3-- pow-pow flip3-+ diff-log pow-exp sum-log flip-- flip-+ distribute-lft-out expm1-udef rem-cube-cbrt
Counts
4 → 245
Calls
4 calls:
0.0ms
(expm1 (- (pow 1.0 3) (pow (cos x) 3)))
1.0ms
(pow (cos x) 3)
3.0ms
(+ 1.0 (cos x))
25.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series192.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(expm1 (- (pow 1.0 3) (pow (cos x) 3)))
28.0ms
(pow (cos x) 3)
16.0ms
(+ 1.0 (cos x))
48.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify101.0ms

Algorithm
egg-herbie
Counts
257 → 257
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
05732743
119841853
250011824

prune338.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

regimes204.0ms

Accuracy

97.8% (0.7b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 30.1b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04749
14749

end0.0ms

sample4.4s

Algorithm
intervals
Results
2.1s1561×body2560valid
1.5s2856×body1280valid
446.0ms1831×body640valid
143.0ms916×body320valid
50.0ms454×body160valid
25.0ms380×body80valid
8.0ms2×body5120valid