Details

Time bar (total: 9.1s)

sample159.0ms

Algorithm
intervals
Results
75.0ms56×body2560valid
50.0ms93×body1280valid
17.0ms54×body640valid
6.0ms27×body320valid
2.0ms11×body160valid
1.0ms15×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0114
1144
2164
3164

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize12.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (- 1.0 (cos x)) (sin x))
1.4b
(- 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))

series10.0ms

Counts
2 → 6
Calls
2 calls:
7.0ms
(/ (- 1.0 (cos x)) (sin x))
2.0ms
(- 1.0 (cos x))

simplify34.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0292569
1965460
25002460

prune394.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x))
0.3b
(pow (cos x) 3)
0.3b
(fma (cos x) (cos x) (* 1.0 (cos x)))
1.3b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
144×prod-diff
110×add-sqr-sqrt
94×*-un-lft-identity
90×unpow-prod-down cube-prod
84×add-cube-cbrt
34×sqr-pow
26×cube-mult unpow3
16×difference-of-squares
12×fma-neg
7×pow1 add-exp-log add-cbrt-cube
6×add-log-exp
5×distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow associate-*r* associate-*l*
1×difference-cubes pow-to-exp sub-neg flip3-- pow-pow diff-log pow-prod-down pow-exp prod-exp *-commutative flip-- cbrt-unprod fma-udef rem-cube-cbrt unswap-sqr
Counts
4 → 247
Calls
4 calls:
3.0ms
(* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x))
1.0ms
(pow (cos x) 3)
0.0ms
(fma (cos x) (cos x) (* 1.0 (cos x)))
21.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series38.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x))
5.0ms
(pow (cos x) 3)
11.0ms
(fma (cos x) (cos x) (* 1.0 (cos x)))
8.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify104.0ms

Algorithm
egg-herbie
Counts
259 → 259
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
06162913
121531995
250021966

prune932.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (cos x) 3)
0.3b
(fma (cos x) (cos x) (* 1.0 (cos x)))
0.6b
(expm1 (pow (cos x) 3))
1.3b
(- (pow 1.0 3) (log1p (expm1 (pow (cos x) 3))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
36×prod-diff
33×*-un-lft-identity
31×add-cube-cbrt
16×unpow-prod-down cube-prod
12×fma-neg
7×add-log-exp
6×sqr-pow
5×pow1 add-exp-log cube-mult unpow3 add-cbrt-cube log1p-expm1-u
4×expm1-log1p-u difference-of-squares
3×pow-unpow
2×diff-log
1×pow-to-exp sub-neg log1p-udef expm1-log1p flip3-- pow-pow pow-exp flip-- fma-udef distribute-lft-out-- expm1-udef rem-cube-cbrt
Counts
4 → 114
Calls
4 calls:
1.0ms
(pow (cos x) 3)
0.0ms
(fma (cos x) (cos x) (* 1.0 (cos x)))
0.0ms
(expm1 (pow (cos x) 3))
13.0ms
(- (pow 1.0 3) (log1p (expm1 (pow (cos x) 3))))

series50.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(pow (cos x) 3)
7.0ms
(fma (cos x) (cos x) (* 1.0 (cos x)))
10.0ms
(expm1 (pow (cos x) 3))
28.0ms
(- (pow 1.0 3) (log1p (expm1 (pow (cos x) 3))))

simplify67.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
03771164
11523743
25002735

prune860.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma (cos x) (cos x) (* 1.0 (cos x)))
0.6b
(expm1 (pow (cos x) 3))
1.2b
(log (- (pow 1.0 3) (log1p (expm1 (pow (cos x) 3)))))
1.3b
(- (pow 1.0 3) (log1p (expm1 (pow (cos x) 3))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
36×prod-diff
33×*-un-lft-identity
29×add-cube-cbrt
14×unpow-prod-down cube-prod
12×fma-neg
8×log-prod difference-of-squares
7×add-log-exp
6×sqr-pow
5×pow1 add-exp-log log1p-expm1-u
4×expm1-log1p-u cube-mult unpow3 add-cbrt-cube
2×log-div flip3-- diff-log flip-- distribute-lft-out--
1×sub-neg log1p-udef expm1-log1p rem-log-exp log-pow fma-udef expm1-udef
Counts
4 → 110
Calls
4 calls:
0.0ms
(fma (cos x) (cos x) (* 1.0 (cos x)))
0.0ms
(expm1 (pow (cos x) 3))
11.0ms
(log (- (pow 1.0 3) (log1p (expm1 (pow (cos x) 3)))))
13.0ms
(- (pow 1.0 3) (log1p (expm1 (pow (cos x) 3))))

series79.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(fma (cos x) (cos x) (* 1.0 (cos x)))
10.0ms
(expm1 (pow (cos x) 3))
37.0ms
(log (- (pow 1.0 3) (log1p (expm1 (pow (cos x) 3)))))
25.0ms
(- (pow 1.0 3) (log1p (expm1 (pow (cos x) 3))))

simplify58.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
03651826
11265954
25002931

prune899.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

regimes383.0ms

Accuracy

97.4% (0.8b remaining)

Error of 1.0b against oracle of 0.2b and baseline of 29.5b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04345
14345

end0.0ms

sample4.8s

Algorithm
intervals
Results
2.2s1540×body2560valid
1.6s2807×body1280valid
596.0ms1881×body640valid
217.0ms926×body320valid
73.0ms473×body160valid
33.0ms370×body80valid
13.0ms3×body5120valid