Details

Time bar (total: 7.2s)

sample144.0ms

Algorithm
intervals
Results
77.0ms62×body2560valid
35.0ms77×body1280valid
16.0ms55×body640valid
4.0ms25×body320valid
2.0ms18×body160valid
2.0ms19×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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.2b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
2.0b
(- 1.0 (cos x))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt *-un-lft-identity
19×add-cube-cbrt
15×times-frac
9×prod-diff
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-exp-log add-cbrt-cube add-log-exp
3×fma-neg associate-/r*
2×pow1 expm1-log1p-u flip3-- flip-- log1p-expm1-u associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
2 → 68
Calls
2 calls:
7.0ms
(/ (- 1.0 (cos x)) (sin x))
5.0ms
(- 1.0 (cos x))

series64.0ms

Counts
2 → 6
Calls
2 calls:
45.0ms
(/ (- 1.0 (cos x)) (sin x))
19.0ms
(- 1.0 (cos x))

simplify38.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0292569
1965460
25002460

prune186.0ms

Filtered
74 candidates to 51 candidates (68.9%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New591574
Fresh000
Picked101
Done000
Total601575

Merged error: 0.2b

Counts
75 → 15

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
0.1b
(fma 1/240 (pow x 5) (* 1/2 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 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
1.0ms
(fma 1/240 (pow x 5) (* 1/2 x))

series182.0ms

Counts
2 → 6
Calls
2 calls:
60.0ms
(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
123.0ms
(fma 1/240 (pow x 5) (* 1/2 x))

simplify36.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
061148
1188130
21009130
35002130

prune93.0ms

Filtered
26 candidates to 21 candidates (80.8%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New26026
Fresh01414
Picked011
Done000
Total261541

Merged error: 0.2b

Counts
41 → 15

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.1b
(/ (sin x) (- 1.0 (cos x)))
2.0b
(- 1.0 (cos x))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
112×add-sqr-sqrt *-un-lft-identity
78×add-cube-cbrt
26×associate-/r*
17×distribute-lft-out-- difference-of-squares
16×add-exp-log
11×associate-/r/
10×add-cbrt-cube
9×prod-diff
8×div-exp
6×flip3-- flip-- div-inv associate-/l*
5×add-log-exp
4×pow1 cbrt-undiv
3×expm1-log1p-u fma-neg log1p-expm1-u
2×rec-exp frac-2neg 1-exp clear-num
1×sub-neg pow-flip diff-log inv-pow
Counts
3 → 177
Calls
3 calls:
9.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
7.0ms
(/ (sin x) (- 1.0 (cos x)))
4.0ms
(- 1.0 (cos x))

series95.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
41.0ms
(/ (sin x) (- 1.0 (cos x)))
19.0ms
(- 1.0 (cos x))

simplify73.0ms

Algorithm
egg-herbie
Counts
186 → 186
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
05721779
126361549
250011441

prune266.0ms

Filtered
186 candidates to 96 candidates (51.6%)
Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New1806186
Fresh6713
Picked011
Done011
Total18615201

Merged error: 0.2b

Counts
201 → 15

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x))
0.3b
(pow (cos x) 3)
0.4b
(+ 1.0 (cos x))
1.8b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
591×add-sqr-sqrt
537×times-frac
411×*-un-lft-identity
279×add-cube-cbrt
234×unpow-prod-down cube-prod
208×difference-of-squares
144×prod-diff
130×sqr-pow
79×associate-/l*
65×distribute-lft-out--
26×cube-mult unpow3
13×difference-cubes
12×fma-neg
10×add-exp-log add-cbrt-cube
8×add-log-exp
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv pow-unpow fma-def div-exp associate-/r*
2×div-sub
1×+-commutative pow-to-exp sub-neg flip3-- pow-pow frac-2neg flip3-+ diff-log pow-exp clear-num sum-log flip-- flip-+ associate-/l/ distribute-lft-out rem-cube-cbrt
Counts
4 → 571
Calls
4 calls:
32.0ms
(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x))
2.0ms
(pow (cos x) 3)
4.0ms
(+ 1.0 (cos x))
17.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series252.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (sin x))
35.0ms
(pow (cos x) 3)
10.0ms
(+ 1.0 (cos x))
49.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify139.0ms

Algorithm
egg-herbie
Counts
583 → 583
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
0160710864
150019904

prune982.0ms

Filtered
583 candidates to 254 candidates (43.6%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New5776583
Fresh4812
Picked101
Done112
Total58315598

Merged error: 0.1b

Counts
598 → 15

regimes149.0ms

Accuracy

98.2% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 31.7b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04145
14145

end0.0ms

sample4.3s

Algorithm
intervals
Results
2.2s1627×body2560valid
1.2s2716×body1280valid
460.0ms1897×body640valid
146.0ms920×body320valid
62.0ms496×body160valid
25.0ms341×body80valid
11.0ms3×body5120valid