Details

Time bar (total: 6.2s)

sample121.0ms

Algorithm
intervals
Results
51.0ms43×body2560valid
39.0ms86×body1280valid
16.0ms69×body640valid
4.0ms24×body320valid
2.0ms19×body160valid
1.0ms15×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: 30.7b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
2.8b
(- 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:
7.0ms
(/ (- 1.0 (cos x)) (sin x))
3.0ms
(- 1.0 (cos x))

series58.0ms

Counts
2 → 6
Calls
2 calls:
39.0ms
(/ (- 1.0 (cos x)) (sin x))
18.0ms
(- 1.0 (cos x))

simplify82.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0233396
1673373
22654373
35001373

prune149.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos x) (+ (cos x) 1.0))
0.4b
(pow (cos x) 3)
0.5b
(+ (cos x) 1.0)
2.5b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite31.0ms

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:
10.0ms
(* (cos x) (+ (cos x) 1.0))
1.0ms
(pow (cos x) 3)
3.0ms
(+ (cos x) 1.0)
15.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series114.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (cos x) (+ (cos x) 1.0))
28.0ms
(pow (cos x) 3)
10.0ms
(+ (cos x) 1.0)
49.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify70.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
0353593
11734555
25001535

prune266.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos x) 3)
0.5b
(+ (cos x) 1.0)
2.5b
(- (pow 1.0 3) (pow (cos x) 3))
2.7b
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

rewrite73.0ms

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:
1.0ms
(pow (cos x) 3)
3.0ms
(+ (cos x) 1.0)
15.0ms
(- (pow 1.0 3) (pow (cos x) 3))
49.0ms
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

series134.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(pow (cos x) 3)
9.0ms
(+ (cos x) 1.0)
45.0ms
(- (pow 1.0 3) (pow (cos x) 3))
49.0ms
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

simplify49.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0348673
11242636
25001608

prune332.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos x) 3)
0.5b
(+ (cos x) 1.0)
1.0b
(log (exp (pow (cos x) 3)))
2.5b
(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
17×*-un-lft-identity
14×log-pow
12×add-cube-cbrt exp-prod
7×pow1 unpow-prod-down cube-prod add-log-exp
6×log-prod
5×add-exp-log add-cbrt-cube
4×difference-of-squares
3×pow-unpow associate--r+ sqr-pow
2×cube-mult unpow3 distribute-lft-out--
1×+-commutative pow-to-exp sub-neg flip3-- pow-pow flip3-+ diff-log rem-log-exp pow-exp sum-log flip-- flip-+ distribute-lft-out rem-cube-cbrt
Counts
4 → 80
Calls
4 calls:
1.0ms
(pow (cos x) 3)
3.0ms
(+ (cos x) 1.0)
4.0ms
(log (exp (pow (cos x) 3)))
26.0ms
(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

series115.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(pow (cos x) 3)
10.0ms
(+ (cos x) 1.0)
31.0ms
(log (exp (pow (cos x) 3)))
47.0ms
(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

simplify43.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0296446
11109381
25001373

prune244.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 0.2b

regimes173.0ms

Accuracy

98.3% (0.5b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 29.8b

bsearch4.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04841
14841

end0.0ms

sample4.0s

Algorithm
intervals
Results
2.0s1537×body2560valid
1.2s2824×body1280valid
446.0ms1931×body640valid
151.0ms923×body320valid
47.0ms451×body160valid
21.0ms329×body80valid
20.0ms5×body5120valid