Details

Time bar (total: 5.7s)

sample96.0ms

Algorithm
intervals
Results
46.0ms136×body1280valid
25.0ms29×body2560valid
12.0ms59×body640valid
3.0ms20×body320valid
1.0ms9×body160valid
1.0ms3×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: 40.4b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.5b
(- (cos (+ x eps)) (cos x))
2.8b
(cos (+ 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 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))
4.0ms
(cos (+ x eps))

series70.0ms

Counts
2 → 6
Calls
2 calls:
55.0ms
(- (cos (+ x eps)) (cos x))
15.0ms
(cos (+ x eps))

simplify76.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (71.0ms)

IterNodesCost
0192385
1523285
22519275
35001220

prune120.0ms

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: 17.6b

Counts
47 → 13

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (cos x) (cos eps))
0.1b
(fma (sin x) (sin eps) (cos x))
2.4b
(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×add-cube-cbrt *-un-lft-identity
5×pow1 add-exp-log add-cbrt-cube add-log-exp
3×expm1-log1p-u associate-*r* associate-*l* prod-diff log1p-expm1-u
2×fma-udef
1×sub-neg flip3-- fma-neg diff-log pow-prod-down prod-exp cos-mult *-commutative flip-- cbrt-unprod associate--r+ unswap-sqr
Counts
3 → 50
Calls
3 calls:
4.0ms
(* (cos x) (cos eps))
1.0ms
(fma (sin x) (sin eps) (cos x))
5.0ms
(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

series226.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(* (cos x) (cos eps))
49.0ms
(fma (sin x) (sin eps) (cos x))
133.0ms
(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

simplify116.0ms

Algorithm
egg-herbie
Counts
59 → 59
Iterations

Useful iterations: 3 (110.0ms)

IterNodesCost
0235486
1832409
24494406
35001404

prune197.0ms

Filtered
59 candidates to 43 candidates (72.9%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New481159
Fresh3912
Picked101
Done000
Total522072

Merged error: 17.5b

Counts
72 → 20

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))
2.3b
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite25.0ms

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:
4.0ms
(* (cos x) (cos eps))
5.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
5.0ms
(* (sin x) (sin eps))
9.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series297.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (cos x) (cos eps))
82.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
43.0ms
(* (sin x) (sin eps))
129.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify48.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0381989
11342838
25002822

prune275.0ms

Filtered
105 candidates to 73 candidates (69.5%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New996105
Fresh51419
Picked101
Done000
Total10520125

Merged error: 17.4b

Counts
125 → 20

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin x) (sin eps))
0.3b
(* (fma (cos x) (cos eps) (* (sin x) (sin eps))) (- (* (cos x) (cos eps)) (* (sin x) (sin eps))))
0.4b
(/ (* (fma (cos x) (cos eps) (* (sin x) (sin eps))) (- (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (fma (cos x) (cos eps) (* (sin x) (sin eps))))
3.5b
(- (/ (* (fma (cos x) (cos eps) (* (sin x) (sin eps))) (- (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (fma (cos x) (cos eps) (* (sin x) (sin eps)))) (cos x))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
27×*-un-lft-identity
25×add-cube-cbrt
23×prod-diff
15×times-frac
13×add-exp-log add-cbrt-cube
8×pow1 associate-*r/
7×fma-neg
6×associate-*r* associate-*l* add-log-exp
5×div-inv sin-mult
4×expm1-log1p-u cos-mult log1p-expm1-u associate-/l/
3×distribute-rgt-in sub-neg flip3-- distribute-lft-in prod-exp associate-/r* flip-- cbrt-unprod
2×cbrt-undiv div-exp pow-prod-down *-commutative frac-sub sub-div unswap-sqr
1×frac-2neg diff-log clear-num associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 122
Calls
4 calls:
5.0ms
(* (sin x) (sin eps))
8.0ms
(* (fma (cos x) (cos eps) (* (sin x) (sin eps))) (- (* (cos x) (cos eps)) (* (sin x) (sin eps))))
10.0ms
(/ (* (fma (cos x) (cos eps) (* (sin x) (sin eps))) (- (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (fma (cos x) (cos eps) (* (sin x) (sin eps))))
10.0ms
(- (/ (* (fma (cos x) (cos eps) (* (sin x) (sin eps))) (- (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (fma (cos x) (cos eps) (* (sin x) (sin eps)))) (cos x))

series423.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (sin x) (sin eps))
168.0ms
(* (fma (cos x) (cos eps) (* (sin x) (sin eps))) (- (* (cos x) (cos eps)) (* (sin x) (sin eps))))
82.0ms
(/ (* (fma (cos x) (cos eps) (* (sin x) (sin eps))) (- (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (fma (cos x) (cos eps) (* (sin x) (sin eps))))
129.0ms
(- (/ (* (fma (cos x) (cos eps) (* (sin x) (sin eps))) (- (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (fma (cos x) (cos eps) (* (sin x) (sin eps)))) (cos x))

simplify94.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
05353033
125402567
250012218

prune329.0ms

Filtered
134 candidates to 90 candidates (67.2%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New1295134
Fresh51419
Picked101
Done000
Total13519154

Merged error: 17.4b

Counts
154 → 19

regimes208.0ms

Accuracy

79.3% (2.1b remaining)

Error of 16.7b against oracle of 14.6b and baseline of 24.6b

bsearch97.0ms

Steps
ItersRangePoint
3
2.731921632534707e-06
3.410959855244386e-06
2.774361521454062e-06
9
-7.380054493915698e-30
-9.003243692419012e-36
-7.258807214549238e-30

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04130
14130

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.6s4426×body1280valid
576.0ms654×body2560valid
426.0ms1894×body640valid
105.0ms664×body320valid
28.0ms274×body160valid
5.0ms88×body80valid