Details

Time bar (total: 5.3s)

sample94.0ms

Algorithm
intervals
Results
44.0ms127×body1280valid
21.0ms25×body2560valid
13.0ms62×body640valid
4.0ms29×body320valid
1.0ms9×body160valid
0.0ms4×body80valid

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: 38.8b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.9b
(- (cos (+ x eps)) (cos x))
2.0b
(cos (+ x eps))

rewrite18.0ms

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 cos-sum add-cbrt-cube log1p-expm1-u
1×associate--l- sub-neg flip3-- diff-log flip-- diff-cos distribute-lft-out-- difference-of-squares
Counts
2 → 40
Calls
2 calls:
7.0ms
(- (cos (+ x eps)) (cos x))
9.0ms
(cos (+ x eps))

series64.0ms

Counts
2 → 6
Calls
2 calls:
48.0ms
(- (cos (+ x eps)) (cos x))
16.0ms
(cos (+ x eps))

simplify75.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (70.0ms)

IterNodesCost
0192385
1523285
22519275
35001220

prune115.0ms

Filtered
46 candidates to 31 candidates (67.4%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New331346
Fresh000
Picked101
Done000
Total341347

Merged error: 16.0b

Counts
47 → 13

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos x) (cos eps))
0.1b
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b
(* (sin x) (sin eps))
2.9b
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
17×*-un-lft-identity
15×add-cube-cbrt
11×prod-diff add-log-exp
8×pow1 add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u fma-neg diff-log log1p-expm1-u
3×sub-neg associate--l+ cos-mult sin-mult
2×flip3-- pow-prod-down prod-exp *-commutative flip-- cbrt-unprod unswap-sqr
1×associate--l- frac-sub distribute-lft-out-- sub-div difference-of-squares
Counts
4 → 93
Calls
4 calls:
7.0ms
(* (cos x) (cos eps))
5.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
5.0ms
(* (sin x) (sin eps))
10.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series292.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (cos x) (cos eps))
77.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
48.0ms
(* (sin x) (sin eps))
124.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify50.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0381988
11342837
25002822

prune278.0ms

Filtered
105 candidates to 72 candidates (68.6%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New9411105
Fresh8412
Picked101
Done000
Total10315118

Merged error: 15.9b

Counts
118 → 15

localize14.0ms

Local error

Found 2 expressions with local error:

0.1b
(fma (sin x) (sin eps) (cos x))
2.9b
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
2×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
2 → 20
Calls
2 calls:
1.0ms
(fma (sin x) (sin eps) (cos x))
1.0ms
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

series194.0ms

Counts
2 → 6
Calls
2 calls:
54.0ms
(fma (sin x) (sin eps) (cos x))
140.0ms
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify117.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
087209
1240182
2795182
33587180
45001180

prune134.0ms

Filtered
26 candidates to 21 candidates (80.8%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New19726
Fresh21214
Picked101
Done000
Total221941

Merged error: 15.8b

Counts
41 → 19

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (sin x) (sin eps) (cos x))
0.2b
(log1p (expm1 (fma (sin x) (sin eps) (cos x))))
0.6b
(expm1 (fma (sin x) (sin eps) (cos x)))
6.1b
(fma (cos eps) (cos x) (- (log1p (expm1 (fma (sin x) (sin eps) (cos x))))))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
5×log1p-expm1-u
4×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
2×fma-udef
1×log1p-udef expm1-log1p log1p-expm1 expm1-udef
Counts
4 → 42
Calls
4 calls:
1.0ms
(fma (sin x) (sin eps) (cos x))
1.0ms
(log1p (expm1 (fma (sin x) (sin eps) (cos x))))
1.0ms
(expm1 (fma (sin x) (sin eps) (cos x)))
1.0ms
(fma (cos eps) (cos x) (- (log1p (expm1 (fma (sin x) (sin eps) (cos x))))))

series403.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(fma (sin x) (sin eps) (cos x))
88.0ms
(log1p (expm1 (fma (sin x) (sin eps) (cos x))))
83.0ms
(expm1 (fma (sin x) (sin eps) (cos x)))
181.0ms
(fma (cos eps) (cos x) (- (log1p (expm1 (fma (sin x) (sin eps) (cos x))))))

simplify44.0ms

Algorithm
egg-herbie
Counts
54 → 54
Iterations

Useful iterations: 3 (38.0ms)

IterNodesCost
0143404
1377348
21274346
35001343

prune146.0ms

Filtered
54 candidates to 37 candidates (68.5%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New52254
Fresh21618
Picked101
Done000
Total551873

Merged error: 15.8b

Counts
73 → 18

regimes195.0ms

Accuracy

83.4% (1.7b remaining)

Error of 16.0b against oracle of 14.4b and baseline of 24.3b

bsearch98.0ms

Steps
ItersRangePoint
5
8.302285036860256e-12
2.488528676647712e-11
2.4528526892709564e-11
8
-5.019434032731091e-23
-7.911591592415915e-28
-4.937039226618903e-23

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03944
13944

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.6s4445×body1280valid
562.0ms623×body2560valid
427.0ms1867×body640valid
108.0ms711×body320valid
29.0ms270×body160valid
5.0ms84×body80valid