Details

Time bar (total: 8.0s)

sample134.0ms

Algorithm
intervals
Results
61.0ms52×body2560valid
48.0ms104×body1280valid
10.0ms48×body640valid
5.0ms32×body320valid
1.0ms13×body160valid
0.0ms7×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: 29.9b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
0.9b
(- 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:
42.0ms
(/ (- 1.0 (cos x)) (sin x))
19.0ms
(- 1.0 (cos x))

simplify36.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0292569
1965460
25002460

prune187.0ms

Pruning

14 alts after pruning (14 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)))
0.4b
(pow (cos x) 3)
0.4b
(+ 1.0 (cos x))
0.8b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
233×add-sqr-sqrt
165×*-un-lft-identity
144×prod-diff
138×unpow-prod-down cube-prod
113×add-cube-cbrt
80×difference-of-squares
75×times-frac
66×sqr-pow
26×cube-mult unpow3
25×associate-/l* distribute-lft-out--
12×fma-neg
8×add-log-exp
7×add-exp-log add-cbrt-cube
5×pow1 difference-cubes
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow fma-def associate-/r*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv +-commutative pow-to-exp sub-neg pow-pow frac-2neg flip3-+ diff-log div-sub div-exp pow-exp clear-num sum-log flip-+ div-inv distribute-lft-out rem-cube-cbrt
Counts
4 → 354
Calls
4 calls:
59.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
1.0ms
(pow (cos x) 3)
3.0ms
(+ 1.0 (cos x))
26.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series212.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
28.0ms
(pow (cos x) 3)
17.0ms
(+ 1.0 (cos x))
48.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify154.0ms

Algorithm
egg-herbie
Counts
366 → 366
Iterations

Useful iterations: 2 (104.0ms)

IterNodesCost
08284951
132444033
250023940

prune539.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(log (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))))
0.4b
(pow (cos x) 3)
0.4b
(+ 1.0 (cos x))
0.8b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
208×add-sqr-sqrt
154×*-un-lft-identity
144×prod-diff
126×unpow-prod-down cube-prod
112×add-cube-cbrt
79×log-prod
75×times-frac
64×difference-of-squares
58×sqr-pow
26×cube-mult unpow3
20×distribute-lft-out--
12×fma-neg
8×add-exp-log add-log-exp
6×pow1
5×add-cbrt-cube
4×difference-cubes expm1-log1p-u log1p-expm1-u
3×pow-unpow fma-def
2×rem-log-exp
1×+-commutative pow-to-exp sub-neg log-div flip3-- pow-pow flip3-+ diff-log div-exp pow-exp sum-log log-pow flip-- flip-+ div-inv distribute-lft-out rem-cube-cbrt
Counts
4 → 326
Calls
4 calls:
17.0ms
(log (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))))
1.0ms
(pow (cos x) 3)
3.0ms
(+ 1.0 (cos x))
21.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series304.0ms

Counts
4 → 12
Calls
4 calls:
212.0ms
(log (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))))
34.0ms
(pow (cos x) 3)
10.0ms
(+ 1.0 (cos x))
48.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify139.0ms

Algorithm
egg-herbie
Counts
338 → 338
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
010084873
132593955
250023933

prune558.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ 1.0 (cos x))
0.6b
(log (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
0.8b
(- (pow 1.0 3) (pow (cos x) 3))
1.2b
(log (- (pow 1.0 3) (pow (cos x) 3)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
144×prod-diff
130×add-sqr-sqrt
104×*-un-lft-identity
99×unpow-prod-down cube-prod
82×add-cube-cbrt
41×sqr-pow
32×difference-of-squares
28×log-prod
25×cube-mult unpow3
12×fma-neg
10×distribute-lft-out--
8×add-log-exp
6×pow1 add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×fma-def
2×difference-cubes log-div flip3-- rem-log-exp log-pow flip--
1×+-commutative sub-neg flip3-+ diff-log sum-log flip-+ distribute-lft-out
Counts
4 → 261
Calls
4 calls:
3.0ms
(+ 1.0 (cos x))
1.0ms
(log (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
21.0ms
(- (pow 1.0 3) (pow (cos x) 3))
24.0ms
(log (- (pow 1.0 3) (pow (cos x) 3)))

series301.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(+ 1.0 (cos x))
129.0ms
(log (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
46.0ms
(- (pow 1.0 3) (pow (cos x) 3))
116.0ms
(log (- (pow 1.0 3) (pow (cos x) 3)))

simplify97.0ms

Algorithm
egg-herbie
Counts
273 → 273
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
06383166
120082253
250012238

prune635.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.1b

regimes84.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.5b

bsearch81.0ms

Steps
ItersRangePoint
8
0.003342748024832997
13.582308112339199
0.015121154527709535
9
-118.89002763209811
-0.00028315217264546786
-0.020520125187230325

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04339
14339

end0.0ms

sample4.1s

Algorithm
intervals
Results
2.1s1585×body2560valid
1.2s2776×body1280valid
436.0ms1876×body640valid
164.0ms933×body320valid
50.0ms465×body160valid
23.0ms360×body80valid
22.0ms5×body5120valid