Details

Time bar (total: 7.5s)

sample136.0ms

Algorithm
intervals
Results
71.0ms57×body2560valid
40.0ms102×body1280valid
10.0ms48×body640valid
4.0ms26×body320valid
1.0ms11×body160valid
1.0ms12×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: 30.2b

localize12.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
1.5b
(- 1.0 (cos x))

rewrite24.0ms

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:
16.0ms
(/ (- 1.0 (cos x)) (sin x))
6.0ms
(- 1.0 (cos x))

series54.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(/ (- 1.0 (cos x)) (sin x))
17.0ms
(- 1.0 (cos x))

simplify78.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0233396
1673373
22654373
35001373

prune142.0ms

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)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) (sin x))
0.4b
(pow (cos x) 3)
0.4b
(+ (cos x) 1.0)
1.3b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
543×times-frac
517×add-sqr-sqrt
337×*-un-lft-identity
208×difference-of-squares
205×add-cube-cbrt
159×unpow-prod-down cube-prod
105×sqr-pow
81×associate-/l*
65×distribute-lft-out--
13×difference-cubes
10×add-exp-log add-cbrt-cube
8×associate-/r/ add-log-exp
5×pow1 flip3-+ flip-+ div-inv
3×cbrt-undiv pow-unpow div-exp associate-/r*
2×div-sub
1×+-commutative cube-mult pow-to-exp sub-neg flip3-- pow-pow frac-2neg diff-log unpow3 pow-exp clear-num sum-log flip-- associate-/l/ distribute-lft-out rem-cube-cbrt
Counts
4 → 412
Calls
4 calls:
101.0ms
(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) (sin x))
3.0ms
(pow (cos x) 3)
6.0ms
(+ (cos x) 1.0)
26.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series241.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) (sin x))
25.0ms
(pow (cos x) 3)
9.0ms
(+ (cos x) 1.0)
50.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify104.0ms

Algorithm
egg-herbie
Counts
424 → 424
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
014279452
150029346

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
56×unpow-prod-down cube-prod
44×difference-of-squares
40×cbrt-prod
27×sqr-pow
18×*-un-lft-identity
14×add-cube-cbrt
8×add-log-exp
7×add-exp-log
6×pow-unpow add-cbrt-cube
5×pow1 pow-exp
4×cube-mult unpow3
3×pow-to-exp
2×pow-pow rem-cube-cbrt
1×+-commutative sub-neg flip3-- flip3-+ diff-log sum-log flip-- flip-+ distribute-lft-out distribute-lft-out--
Counts
4 → 135
Calls
4 calls:
3.0ms
(pow (cos x) 3)
6.0ms
(+ (cos x) 1.0)
6.0ms
(pow (pow (cos x) 3) 3)
44.0ms
(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

series137.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(pow (cos x) 3)
9.0ms
(+ (cos x) 1.0)
55.0ms
(pow (pow (cos x) 3) 3)
47.0ms
(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

simplify62.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04211014
11553953
25002916

prune300.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos x) 3)
0.4b
(+ (cos x) 1.0)
1.3b
(- (pow 1.0 3) (pow (cos x) 3))
1.4b
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

rewrite102.0ms

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
(pow (cos x) 3)
6.0ms
(+ (cos x) 1.0)
23.0ms
(- (pow 1.0 3) (pow (cos x) 3))
66.0ms
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

series126.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(pow (cos x) 3)
9.0ms
(+ (cos x) 1.0)
48.0ms
(- (pow 1.0 3) (pow (cos x) 3))
43.0ms
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

simplify46.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0348673
11242636
25001608

prune290.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

regimes87.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.4b

bsearch76.0ms

Steps
ItersRangePoint
9
1.3330246063773173e-09
3.618674152218468
0.021299805520742916
7
-0.23317146499959118
-0.002309702793432406
-0.024219913715803645

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05228
15228

end0.0ms

sample4.2s

Algorithm
intervals
Results
2.1s1592×body2560valid
1.2s2800×body1280valid
437.0ms1866×body640valid
152.0ms892×body320valid
51.0ms475×body160valid
24.0ms372×body80valid
16.0ms3×body5120valid