Details

Time bar (total: 5.7s)

sample149.0ms

Algorithm
intervals
Results
82.0ms62×body2560valid
37.0ms78×body1280valid
14.0ms62×body640valid
4.0ms29×body320valid
2.0ms17×body160valid
1.0ms8×body80valid

simplify5.0ms

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 (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.6b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
1.4b
(- 1.0 (cos x))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity
15×times-frac
12×add-cube-cbrt
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r*
2×pow1 flip3-- flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
2 → 52
Calls
2 calls:
6.0ms
(/ (- 1.0 (cos x)) (sin x))
3.0ms
(- 1.0 (cos x))

series12.0ms

Counts
2 → 6
Calls
2 calls:
8.0ms
(/ (- 1.0 (cos x)) (sin x))
4.0ms
(- 1.0 (cos x))

simplify78.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0233396
1673373
22640373
35002373

prune136.0ms

Filtered
58 candidates to 42 candidates (27.6%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New401858
Fresh000
Picked101
Done000
Total411859

Merged error: 0.2b

Counts
59 → 18

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
0.1b
(* 1/240 (pow x 5))
0.1b
(* 1/24 (pow x 3))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×associate-*r*
13×add-exp-log
10×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down add-log-exp
7×add-cbrt-cube unswap-sqr
6×associate-*l* prod-exp
4×cube-prod sqr-pow
3×pow1 sum-log
2×pow-to-exp pow-exp *-commutative cbrt-unprod
1×+-commutative cube-mult associate-+r+ flip3-+ unpow3 flip-+
Counts
3 → 69
Calls
3 calls:
7.0ms
(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
5.0ms
(* 1/240 (pow x 5))
6.0ms
(* 1/24 (pow x 3))

series14.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
4.0ms
(* 1/240 (pow x 5))
4.0ms
(* 1/24 (pow x 3))

simplify44.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0301375
11301346
25002346

prune150.0ms

Filtered
78 candidates to 49 candidates (37.2%)
Pruning

18 alts after pruning (17 fresh and 1 done)

PrunedKeptTotal
New77178
Fresh11617
Picked011
Done000
Total781896

Merged error: 0.2b

Counts
96 → 18

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 1/240 (pow x 5))
0.1b
(* 1/24 (pow x 3))
0.4b
(log (exp (* 1/24 (pow x 3))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×associate-*r*
13×add-exp-log
11×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down
7×add-cbrt-cube unswap-sqr
6×associate-*l* prod-exp
4×pow1 cube-prod add-log-exp sqr-pow
3×log-prod log-pow
2×pow-to-exp pow-exp *-commutative cbrt-unprod
1×cube-mult exp-prod exp-to-pow unpow3 rem-log-exp
Counts
3 → 70
Calls
3 calls:
5.0ms
(* 1/240 (pow x 5))
6.0ms
(* 1/24 (pow x 3))
2.0ms
(log (exp (* 1/24 (pow x 3))))

series12.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(* 1/240 (pow x 5))
4.0ms
(* 1/24 (pow x 3))
4.0ms
(log (exp (* 1/24 (pow x 3))))

simplify188.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0226274
1897249
24689249
35001249

prune160.0ms

Filtered
79 candidates to 49 candidates (38.0%)
Pruning

18 alts after pruning (16 fresh and 2 done)

PrunedKeptTotal
New79079
Fresh01616
Picked011
Done011
Total791897

Merged error: 0.2b

Counts
97 → 18

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b
(/ (sin x) (- 1.0 (cos x)))
1.4b
(- 1.0 (cos x))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
105×add-sqr-sqrt *-un-lft-identity
71×add-cube-cbrt
26×associate-/r*
17×distribute-lft-out-- difference-of-squares
16×add-exp-log
11×associate-/r/
10×add-cbrt-cube
8×div-exp
6×flip3-- flip-- div-inv associate-/l*
5×add-log-exp
4×pow1 cbrt-undiv
2×rec-exp frac-2neg 1-exp clear-num
1×sub-neg pow-flip diff-log inv-pow
Counts
3 → 159
Calls
3 calls:
11.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
6.0ms
(/ (sin x) (- 1.0 (cos x)))
3.0ms
(- 1.0 (cos x))

series18.0ms

Counts
3 → 9
Calls
3 calls:
7.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
8.0ms
(/ (sin x) (- 1.0 (cos x)))
3.0ms
(- 1.0 (cos x))

simplify60.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05101595
123961450
250011337

prune112.0ms

Filtered
168 candidates to 84 candidates (50.0%)
Pruning

17 alts after pruning (15 fresh and 2 done)

PrunedKeptTotal
New1653168
Fresh31215
Picked101
Done022
Total16917186

Merged error: 0.1b

Counts
186 → 17

regimes222.0ms

Accuracy

97.9% (0.7b remaining)

Error of 0.9b against oracle of 0.2b and baseline of 32.0b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04735
14735

end0.0ms

sample4.2s

Algorithm
intervals
Results
2.1s1598×body2560valid
1.2s2743×body1280valid
438.0ms1851×body640valid
169.0ms981×body320valid
54.0ms477×body160valid
22.0ms346×body80valid
11.0ms4×body5120valid

Profiling

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