Details

Time bar (total: 8.3s)

sample158.0ms

Algorithm
intervals
Results
74.0ms56×body2560valid
52.0ms93×body1280valid
16.0ms54×body640valid
5.0ms27×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

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity
15×times-frac
12×add-cube-cbrt
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r*
2×pow1 flip3-- flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
2 → 52
Calls
2 calls:
8.0ms
(/ (- 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))
3.0ms
(- 1.0 (cos x))

simplify79.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0233396
1673373
22654373
35001373

prune331.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
23×*-un-lft-identity
16×difference-of-squares
15×unpow-prod-down cube-prod
9×add-cube-cbrt sqr-pow
8×add-log-exp
7×pow1 add-exp-log add-cbrt-cube
5×distribute-lft-out--
4×associate-*r*
3×pow-unpow associate-*l*
2×flip3-+ associate-*r/ flip-+ distribute-lft-out
1×difference-cubes +-commutative distribute-rgt-in cube-mult pow-to-exp sub-neg flip3-- pow-pow distribute-lft-in diff-log unpow3 pow-prod-down pow-exp prod-exp sum-log *-commutative flip-- cbrt-unprod rem-cube-cbrt unswap-sqr
Counts
4 → 92
Calls
4 calls:
11.0ms
(* (cos x) (+ (cos x) 1.0))
3.0ms
(+ (cos x) 1.0)
1.0ms
(pow (cos x) 3)
15.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series19.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(* (cos x) (+ (cos x) 1.0))
2.0ms
(+ (cos x) 1.0)
5.0ms
(pow (cos x) 3)
7.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify67.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
0353593
11734555
25001535

prune742.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (cos x) 1.0)
0.3b
(pow (cos x) 3)
1.3b
(- (pow 1.0 3) (pow (cos x) 3))
1.3b
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt
32×difference-of-squares
31×*-un-lft-identity
27×unpow-prod-down cube-prod
26×log-pow
25×exp-prod
17×sqr-pow
10×distribute-lft-out--
9×add-cube-cbrt
8×add-log-exp
6×pow1
5×add-exp-log log-prod add-cbrt-cube
3×pow-unpow
2×difference-cubes sub-neg exp-sum
1×+-commutative cube-mult pow-to-exp log-div flip3-- pow-pow flip3-+ exp-diff diff-log unpow3 rem-log-exp pow-exp sum-log flip-- flip-+ distribute-lft-out rem-cube-cbrt
Counts
4 → 109
Calls
4 calls:
3.0ms
(+ (cos x) 1.0)
1.0ms
(pow (cos x) 3)
15.0ms
(- (pow 1.0 3) (pow (cos x) 3))
52.0ms
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

series22.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(+ (cos x) 1.0)
6.0ms
(pow (cos x) 3)
7.0ms
(- (pow 1.0 3) (pow (cos x) 3))
8.0ms
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

simplify48.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0348673
11242636
25001608

prune866.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (cos x) 3)
0.3b
(cbrt (pow (pow (cos x) 3) 3))
0.4b
(pow (pow (cos x) 3) 3)
1.3b
(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
86×add-sqr-sqrt
74×unpow-prod-down cube-prod
70×cbrt-prod
44×difference-of-squares
30×sqr-pow
23×*-un-lft-identity
21×add-cube-cbrt
7×add-exp-log cube-mult unpow3
6×pow-unpow add-cbrt-cube add-log-exp
5×pow1 pow-exp
3×pow-to-exp
2×pow-pow rem-cube-cbrt
1×sub-neg flip3-- pow1/3 diff-log flip-- rem-cbrt-cube distribute-lft-out--
Counts
4 → 162
Calls
4 calls:
1.0ms
(pow (cos x) 3)
4.0ms
(cbrt (pow (pow (cos x) 3) 3))
4.0ms
(pow (pow (cos x) 3) 3)
33.0ms
(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

series30.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(pow (cos x) 3)
6.0ms
(cbrt (pow (pow (cos x) 3) 3))
11.0ms
(pow (pow (cos x) 3) 3)
7.0ms
(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

simplify58.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
03741174
113021092
250021051

prune686.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes324.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 29.5b

bsearch46.0ms

Steps
ItersRangePoint
9
0.006665254470786589
7065.8830381017015
0.02381899285814825
9
-14674.600957416102
-0.00012459925560949148
-0.024626500594623808

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04521
14521

end0.0ms

sample4.6s

Algorithm
intervals
Results
2.1s1540×body2560valid
1.5s2807×body1280valid
570.0ms1881×body640valid
185.0ms926×body320valid
79.0ms473×body160valid
30.0ms370×body80valid
13.0ms3×body5120valid