Details

Time bar (total: 6.9s)

sample125.0ms

Algorithm
intervals
Results
59.0ms46×body2560valid
36.0ms89×body1280valid
13.0ms56×body640valid
6.0ms38×body320valid
2.0ms15×body160valid
1.0ms12×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: 27.4b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
2.2b
(- 1.0 (cos x))

rewrite11.0ms

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))
4.0ms
(- 1.0 (cos x))

series61.0ms

Counts
2 → 6
Calls
2 calls:
42.0ms
(/ (- 1.0 (cos x)) (sin x))
19.0ms
(- 1.0 (cos x))

simplify81.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0233396
1673373
22640373
35002373

prune158.0ms

Filtered
58 candidates to 42 candidates (72.4%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New421658
Fresh000
Picked101
Done000
Total431659

Merged error: 0.3b

Counts
59 → 16

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.3b
(log (- 1.0 (cos x)))
0.4b
(exp (log (- 1.0 (cos x))))
2.2b
(- 1.0 (cos x))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt *-un-lft-identity
30×log-prod
25×exp-sum
24×add-cube-cbrt times-frac
8×associate-/l*
7×distribute-lft-out-- difference-of-squares
6×pow1 add-exp-log log-div add-cbrt-cube add-log-exp
4×exp-prod flip3-- exp-diff flip--
3×associate-/r*
2×log-pow associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp rem-log-exp clear-num div-inv rem-exp-log
Counts
4 → 98
Calls
4 calls:
8.0ms
(/ (exp (log (- 1.0 (cos x)))) (sin x))
3.0ms
(log (- 1.0 (cos x)))
5.0ms
(exp (log (- 1.0 (cos x))))
4.0ms
(- 1.0 (cos x))

series154.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(/ (exp (log (- 1.0 (cos x)))) (sin x))
76.0ms
(log (- 1.0 (cos x)))
18.0ms
(exp (log (- 1.0 (cos x))))
19.0ms
(- 1.0 (cos x))

simplify83.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 3 (73.0ms)

IterNodesCost
0289829
1791761
22667734
35001708

prune225.0ms

Filtered
110 candidates to 67 candidates (60.9%)
Pruning

18 alts after pruning (17 fresh and 1 done)

PrunedKeptTotal
New1019110
Fresh7815
Picked011
Done000
Total10818126

Merged error: 0.3b

Counts
126 → 18

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (cos x) 1.0)
0.4b
(pow (cos x) 3)
1.1b
(log (- (pow 1.0 3) (pow (cos x) 3)))
2.0b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt
32×difference-of-squares
30×*-un-lft-identity
27×unpow-prod-down cube-prod
25×log-prod
17×sqr-pow
10×distribute-lft-out--
8×add-cube-cbrt add-log-exp
6×pow1 add-exp-log
5×add-cbrt-cube
3×pow-unpow
2×difference-cubes log-div flip3-- flip--
1×+-commutative cube-mult pow-to-exp sub-neg pow-pow flip3-+ diff-log unpow3 rem-log-exp pow-exp sum-log log-pow flip-+ distribute-lft-out rem-cube-cbrt
Counts
4 → 105
Calls
4 calls:
4.0ms
(+ (cos x) 1.0)
5.0ms
(pow (cos x) 3)
12.0ms
(log (- (pow 1.0 3) (pow (cos x) 3)))
12.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series204.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(+ (cos x) 1.0)
34.0ms
(pow (cos x) 3)
111.0ms
(log (- (pow 1.0 3) (pow (cos x) 3)))
48.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify49.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0338848
11210805
25001769

prune326.0ms

Filtered
117 candidates to 63 candidates (53.8%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New1107117
Fresh31316
Picked101
Done101
Total11520135

Merged error: 0.2b

Counts
135 → 20

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (pow (cos x) 3) 3)
0.4b
(pow (cos x) 3)
1.1b
(log (- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3))))
2.0b
(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
145×add-sqr-sqrt
91×unpow-prod-down cube-prod
88×difference-of-squares
80×cbrt-prod
50×sqr-pow
48×log-prod
19×*-un-lft-identity
15×add-cube-cbrt
8×add-exp-log
6×pow1 pow-unpow add-cbrt-cube add-log-exp
5×pow-exp
4×cube-mult unpow3
3×pow-to-exp
2×log-div flip3-- pow-pow flip-- distribute-lft-out-- rem-cube-cbrt
1×sub-neg diff-log rem-log-exp log-pow
Counts
4 → 182
Calls
4 calls:
5.0ms
(pow (pow (cos x) 3) 3)
3.0ms
(pow (cos x) 3)
30.0ms
(log (- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3))))
25.0ms
(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

series256.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(pow (pow (cos x) 3) 3)
28.0ms
(pow (cos x) 3)
113.0ms
(log (- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3))))
54.0ms
(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

simplify71.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04361907
114321827
250011734

prune340.0ms

Filtered
194 candidates to 72 candidates (37.1%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New1904194
Fresh31619
Picked101
Done000
Total19420214

Merged error: 0.2b

Counts
214 → 20

regimes106.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.3b

bsearch92.0ms

Steps
ItersRangePoint
10
2.7173623733142798e-14
0.17152303280385153
0.021343474190141223
6
-0.06221852409423964
-0.011085094476318487
-0.02444188556502387

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04827
14827

end0.0ms

sample4.3s

Algorithm
intervals
Results
2.2s1615×body2560valid
1.2s2688×body1280valid
471.0ms1912×body640valid
174.0ms946×body320valid
56.0ms480×body160valid
26.0ms7×body5120valid
24.0ms352×body80valid

Profiling

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