Details

Time bar (total: 7.2s)

sample150.0ms

Algorithm
intervals
Results
92.0ms62×body2560valid
31.0ms78×body1280valid
12.0ms55×body640valid
4.0ms26×body320valid
2.0ms18×body160valid
1.0ms17×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0114
1144
2164
3164

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize13.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
0.9b
(- 1.0 (cos x))

rewrite13.0ms

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))
4.0ms
(- 1.0 (cos x))

series55.0ms

Counts
2 → 6
Calls
2 calls:
35.0ms
(/ (- 1.0 (cos x)) (sin x))
20.0ms
(- 1.0 (cos x))

simplify80.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0233396
1673373
22654373
35001373

prune156.0ms

Filtered
58 candidates to 42 candidates (72.4%)
Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
0.3b
(exp (/ (- 1.0 (cos x)) (sin x)))
0.6b
(log (exp (/ (- 1.0 (cos x)) (sin x))))
0.9b
(- 1.0 (cos x))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt *-un-lft-identity
45×times-frac
38×exp-prod
33×add-cube-cbrt
20×log-pow
11×distribute-lft-out-- difference-of-squares
7×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
3×log-prod div-sub associate-/r* div-inv
2×flip3-- exp-diff flip-- associate-/l/
1×cbrt-undiv sub-neg log-div frac-2neg diff-log div-exp rem-log-exp clear-num rem-exp-log
Counts
4 → 112
Calls
4 calls:
8.0ms
(/ (- 1.0 (cos x)) (sin x))
15.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
12.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms
(- 1.0 (cos x))

series136.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ (- 1.0 (cos x)) (sin x))
48.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
35.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
19.0ms
(- 1.0 (cos x))

simplify88.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0303818
1799768
22970766
35001766

prune313.0ms

Filtered
124 candidates to 89 candidates (71.8%)
Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

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)))
0.3b
(pow (cos x) 3)
0.4b
(+ (cos x) 1.0)
0.8b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
157×add-sqr-sqrt
89×*-un-lft-identity
80×difference-of-squares
75×times-frac
63×unpow-prod-down cube-prod
41×sqr-pow
37×add-cube-cbrt
25×associate-/l* distribute-lft-out--
8×add-log-exp
7×add-exp-log add-cbrt-cube
5×pow1 difference-cubes
3×pow-unpow associate-/r*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative cube-mult pow-to-exp sub-neg pow-pow frac-2neg diff-log unpow3 div-sub div-exp pow-exp clear-num sum-log div-inv distribute-lft-out rem-cube-cbrt
Counts
4 → 189
Calls
4 calls:
51.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
1.0ms
(pow (cos x) 3)
3.0ms
(+ (cos x) 1.0)
19.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series222.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
34.0ms
(pow (cos x) 3)
10.0ms
(+ (cos x) 1.0)
48.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify101.0ms

Algorithm
egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
06172953
126992889
250012810

prune458.0ms

Filtered
201 candidates to 105 candidates (52.2%)
Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
132×add-sqr-sqrt
81×log-prod
78×*-un-lft-identity
75×times-frac
64×difference-of-squares
51×unpow-prod-down cube-prod
36×add-cube-cbrt
33×sqr-pow
20×distribute-lft-out--
8×add-exp-log add-log-exp
6×pow1
5×add-cbrt-cube
4×difference-cubes
3×pow-unpow
2×flip3-+ rem-log-exp associate-/r/ flip-+
1×+-commutative cube-mult pow-to-exp sub-neg log-div flip3-- pow-pow diff-log unpow3 div-exp pow-exp sum-log log-pow flip-- div-inv distribute-lft-out rem-cube-cbrt
Counts
4 → 161
Calls
4 calls:
21.0ms
(log (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))))
2.0ms
(pow (cos x) 3)
3.0ms
(+ (cos x) 1.0)
15.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series321.0ms

Counts
4 → 12
Calls
4 calls:
229.0ms
(log (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))))
35.0ms
(pow (cos x) 3)
10.0ms
(+ (cos x) 1.0)
48.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify93.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
07842876
126482812
250012808

prune411.0ms

Filtered
173 candidates to 88 candidates (50.9%)
Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

regimes177.0ms

Accuracy

98.3% (0.5b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 30.2b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04649
14649

end0.0ms

sample4.2s

Algorithm
intervals
Results
2.1s1605×body2560valid
1.2s2781×body1280valid
440.0ms1894×body640valid
144.0ms900×body320valid
49.0ms455×body160valid
37.0ms7×body5120valid
23.0ms358×body80valid