Details

Time bar (total: 4.9s)

sample91.0ms

Algorithm
intervals
Results
44.0ms112×body1280valid
18.0ms21×body2560valid
14.0ms59×body640valid
3.0ms18×body320valid
2.0ms35×body80valid
1.0ms11×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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 37.5b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.8b
(- (sin (+ x eps)) (sin x))
3.8b
(sin (+ x eps))

rewrite12.0ms

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:
7.0ms
(- (sin (+ x eps)) (sin x))
4.0ms
(sin (+ x eps))

series64.0ms

Counts
2 → 6
Calls
2 calls:
46.0ms
(- (sin (+ x eps)) (sin x))
18.0ms
(sin (+ x eps))

simplify74.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (70.0ms)

IterNodesCost
0192386
1538285
22616275
35002220

prune106.0ms

Filtered
46 candidates to 31 candidates (67.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New351146
Fresh000
Picked101
Done000
Total361147

Merged error: 14.7b

Counts
47 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.2b
(* (sin x) (cos eps))
0.2b
(* (cos x) (sin eps))
2.3b
(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite26.0ms

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:
6.0ms
(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
4.0ms
(* (sin x) (cos eps))
4.0ms
(* (cos x) (sin eps))
9.0ms
(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series310.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
42.0ms
(* (sin x) (cos eps))
46.0ms
(* (cos x) (sin eps))
110.0ms
(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify51.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0373918
11424763
25001741

prune248.0ms

Filtered
97 candidates to 67 candidates (69.1%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New861197
Fresh10010
Picked101
Done000
Total9711108

Merged error: 0.3b

Counts
108 → 11

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b
(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
0.2b
(* (cos x) (sin eps))
1.7b
(- (cos eps) 1)

rewrite11.0ms

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:
1.0ms
(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
4.0ms
(* (cos x) (sin eps))
5.0ms
(- (cos eps) 1)

series173.0ms

Counts
3 → 9
Calls
3 calls:
108.0ms
(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
43.0ms
(* (cos x) (sin eps))
22.0ms
(- (cos eps) 1)

simplify96.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (90.0ms)

IterNodesCost
0276442
1932347
23460325
35001303

prune190.0ms

Filtered
70 candidates to 44 candidates (62.9%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New63770
Fresh5510
Picked101
Done000
Total691281

Merged error: 0.1b

Counts
81 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos x) (sin eps))
0.4b
(pow (cos eps) 3)
0.4b
(+ (cos eps) 1)
1.6b
(- (pow (cos eps) 3) 1)

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
49×add-sqr-sqrt
42×*-un-lft-identity
36×prod-diff
34×add-cube-cbrt
18×unpow-prod-down cube-prod
12×fma-neg
9×add-exp-log
8×add-log-exp difference-of-squares sqr-pow
7×pow1 add-cbrt-cube
5×cube-mult unpow3
4×expm1-log1p-u difference-of-sqr-1 log1p-expm1-u
3×pow-unpow expm1-def fma-def associate-*r* associate-*l*
2×pow-to-exp pow-exp
1×+-commutative sub-neg flip3-- pow-pow flip3-+ diff-log pow-prod-down prod-exp sum-log *-commutative flip-- cbrt-unprod flip-+ distribute-lft-out distribute-lft-out-- rem-cube-cbrt unswap-sqr
Counts
4 → 140
Calls
4 calls:
4.0ms
(* (cos x) (sin eps))
2.0ms
(pow (cos eps) 3)
4.0ms
(+ (cos eps) 1)
9.0ms
(- (pow (cos eps) 3) 1)

series137.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (cos x) (sin eps))
29.0ms
(pow (cos eps) 3)
10.0ms
(+ (cos eps) 1)
52.0ms
(- (pow (cos eps) 3) 1)

simplify59.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0411902
11750601
25002579

prune288.0ms

Filtered
152 candidates to 74 candidates (48.7%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1520152
Fresh01111
Picked011
Done000
Total15212164

Merged error: 0.1b

Counts
164 → 12

regimes107.0ms

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
01913
11913

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.3s3232×body1280valid
547.0ms620×body2560valid
453.0ms1872×body640valid
136.0ms779×body320valid
57.0ms1134×body80valid
37.0ms363×body160valid