Details

Time bar (total: 5.3s)

sample87.0ms

Algorithm
intervals
Results
44.0ms113×body1280valid
15.0ms18×body2560valid
11.0ms47×body640valid
4.0ms25×body320valid
2.0ms37×body80valid
2.0ms16×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.7b

localize8.0ms

Local error

Found 2 expressions with local error:

2.1b
(- (sin (+ x eps)) (sin x))
2.6b
(sin (+ x eps))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt prod-diff
4×add-log-exp
3×fma-neg
2×pow1 add-exp-log expm1-log1p-u sin-sum add-cbrt-cube log1p-expm1-u
1×sub-neg flip3-- diff-log diff-sin associate--l+ flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 40
Calls
2 calls:
24.0ms
(- (sin (+ x eps)) (sin x))
4.0ms
(sin (+ x eps))

series63.0ms

Counts
2 → 6
Calls
2 calls:
39.0ms
(- (sin (+ x eps)) (sin x))
24.0ms
(sin (+ x eps))

simplify74.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (70.0ms)

IterNodesCost
0192386
1538285
22616275
35002220

prune112.0ms

Filtered
46 candidates to 31 candidates (67.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.2b
(* (cos x) (sin eps))
0.2b
(* (sin x) (cos eps))
4.0b
(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
17×*-un-lft-identity
15×add-cube-cbrt
11×add-log-exp
9×prod-diff
8×pow1 add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u
3×fma-neg
2×diff-log pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
1×+-commutative sub-neg flip3-- fma-def flip3-+ associate--l+ sin-cos-mult flip-- flip-+ distribute-lft-out-- difference-of-squares
Counts
4 → 85
Calls
4 calls:
4.0ms
(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
7.0ms
(* (cos x) (sin eps))
4.0ms
(* (sin x) (cos eps))
21.0ms
(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series294.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
47.0ms
(* (cos x) (sin eps))
44.0ms
(* (sin x) (cos eps))
114.0ms
(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify50.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0373918
11424763
25001741

prune281.0ms

Filtered
97 candidates to 68 candidates (70.1%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b
(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
0.2b
(* (cos x) (sin eps))
2.3b
(- (cos eps) 1)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×*-un-lft-identity
12×add-cube-cbrt
9×prod-diff
6×add-exp-log
5×pow1 add-cbrt-cube add-log-exp
3×expm1-log1p-u fma-neg associate-*r* associate-*l* log1p-expm1-u
2×difference-of-squares
1×sub-neg expm1-def flip3-- diff-log difference-of-sqr-1 pow-prod-down prod-exp *-commutative flip-- cbrt-unprod fma-udef distribute-lft-out-- unswap-sqr
Counts
3 → 61
Calls
3 calls:
0.0ms
(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
4.0ms
(* (cos x) (sin eps))
4.0ms
(- (cos eps) 1)

series178.0ms

Counts
3 → 9
Calls
3 calls:
110.0ms
(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
49.0ms
(* (cos x) (sin eps))
19.0ms
(- (cos eps) 1)

simplify97.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (92.0ms)

IterNodesCost
0276442
1932347
23460325
35001303

prune224.0ms

Filtered
70 candidates to 45 candidates (64.3%)
Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (pow (cos eps) 3) 1) (fma (cos eps) (+ (cos eps) 1) 1))
0.3b
(+ (cos eps) 1)
0.4b
(pow (cos eps) 3)
2.1b
(- (pow (cos eps) 3) 1)

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
118×add-sqr-sqrt
85×*-un-lft-identity
53×add-cube-cbrt
48×times-frac
40×difference-of-squares
36×prod-diff
30×unpow-prod-down cube-prod
20×difference-of-sqr-1 sqr-pow
16×associate-/l*
12×fma-neg
9×add-exp-log
8×add-log-exp
7×add-cbrt-cube
5×pow1 cube-mult unpow3 distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow expm1-def fma-def associate-/r*
2×pow-to-exp flip3-- pow-exp flip-- associate-/l/
1×cbrt-undiv +-commutative sub-neg pow-pow frac-2neg flip3-+ diff-log div-sub div-exp clear-num sum-log flip-+ div-inv distribute-lft-out rem-cube-cbrt
Counts
4 → 204
Calls
4 calls:
28.0ms
(/ (- (pow (cos eps) 3) 1) (fma (cos eps) (+ (cos eps) 1) 1))
3.0ms
(+ (cos eps) 1)
1.0ms
(pow (cos eps) 3)
13.0ms
(- (pow (cos eps) 3) 1)

series199.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ (- (pow (cos eps) 3) 1) (fma (cos eps) (+ (cos eps) 1) 1))
10.0ms
(+ (cos eps) 1)
36.0ms
(pow (cos eps) 3)
47.0ms
(- (pow (cos eps) 3) 1)

simplify83.0ms

Algorithm
egg-herbie
Counts
216 → 216
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
05442069
123491758
250011700

prune499.0ms

Filtered
216 candidates to 97 candidates (44.9%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes117.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02014
12014

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.4s3322×body1280valid
526.0ms601×body2560valid
450.0ms1836×body640valid
114.0ms748×body320valid
55.0ms1129×body80valid
51.0ms364×body160valid