Details

Time bar (total: 6.9s)

sample136.0ms

Algorithm
intervals
Results
67.0ms53×body2560valid
39.0ms87×body1280valid
13.0ms54×body640valid
6.0ms36×body320valid
2.0ms17×body160valid
1.0ms9×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: 29.3b

Counts
2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
1.8b
(- 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))

series53.0ms

Counts
2 → 6
Calls
2 calls:
34.0ms
(/ (- 1.0 (cos x)) (sin x))
19.0ms
(- 1.0 (cos x))

simplify82.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0233396
1673373
22654373
35001373

prune161.0ms

Filtered
58 candidates to 42 candidates (72.4%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New461258
Fresh000
Picked101
Done000
Total471259

Merged error: 0.2b

Counts
59 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.3b
(exp (log (- 1.0 (cos x))))
0.3b
(log (- 1.0 (cos x)))
1.8b
(- 1.0 (cos x))

rewrite23.0ms

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))
5.0ms
(exp (log (- 1.0 (cos x))))
3.0ms
(log (- 1.0 (cos x)))
4.0ms
(- 1.0 (cos x))

series149.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(/ (exp (log (- 1.0 (cos x)))) (sin x))
18.0ms
(exp (log (- 1.0 (cos x))))
73.0ms
(log (- 1.0 (cos x)))
18.0ms
(- 1.0 (cos x))

simplify84.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 3 (74.0ms)

IterNodesCost
0289829
1791761
22667734
35001708

prune247.0ms

Filtered
110 candidates to 70 candidates (63.6%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New1028110
Fresh3811
Picked101
Done000
Total10616122

Merged error: 0.2b

Counts
122 → 16

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(log (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))))
0.4b
(pow (cos x) 3)
0.5b
(+ (cos x) 1.0)
1.6b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
132×add-sqr-sqrt
81×log-prod
78×*-un-lft-identity
75×times-frac
64×difference-of-squares
51×unpow-prod-down cube-prod
36×add-cube-cbrt
33×sqr-pow
20×distribute-lft-out--
8×add-exp-log add-log-exp
6×pow1
5×add-cbrt-cube
4×difference-cubes
3×pow-unpow
2×flip3-+ rem-log-exp associate-/r/ flip-+
1×+-commutative cube-mult pow-to-exp sub-neg log-div flip3-- pow-pow diff-log unpow3 div-exp pow-exp sum-log log-pow flip-- div-inv distribute-lft-out rem-cube-cbrt
Counts
4 → 161
Calls
4 calls:
23.0ms
(log (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))))
3.0ms
(pow (cos x) 3)
4.0ms
(+ (cos x) 1.0)
12.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series316.0ms

Counts
4 → 12
Calls
4 calls:
226.0ms
(log (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))))
28.0ms
(pow (cos x) 3)
10.0ms
(+ (cos x) 1.0)
52.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify90.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
07842810
126522748
250022680

prune443.0ms

Filtered
173 candidates to 88 candidates (50.9%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New1685173
Fresh31215
Picked101
Done000
Total17217189

Merged error: 0.2b

Counts
189 → 17

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (pow (cos x) 3) 3)
0.4b
(pow (cos x) 3)
0.5b
(+ (cos x) 1.0)
1.6b
(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
56×unpow-prod-down cube-prod
44×difference-of-squares
40×cbrt-prod
27×sqr-pow
18×*-un-lft-identity
14×add-cube-cbrt
8×add-log-exp
7×add-exp-log
6×pow-unpow add-cbrt-cube
5×pow1 pow-exp
4×cube-mult unpow3
3×pow-to-exp
2×pow-pow rem-cube-cbrt
1×+-commutative sub-neg flip3-- flip3-+ diff-log sum-log flip-- flip-+ distribute-lft-out distribute-lft-out--
Counts
4 → 135
Calls
4 calls:
5.0ms
(pow (pow (cos x) 3) 3)
3.0ms
(pow (cos x) 3)
4.0ms
(+ (cos x) 1.0)
26.0ms
(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

series147.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(pow (pow (cos x) 3) 3)
28.0ms
(pow (cos x) 3)
10.0ms
(+ (cos x) 1.0)
52.0ms
(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

simplify66.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
04211014
11553953
25002916

prune294.0ms

Filtered
147 candidates to 61 candidates (41.5%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New1461147
Fresh01616
Picked101
Done000
Total14717164

Merged error: 0.2b

Counts
164 → 17

regimes173.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.4b

bsearch97.0ms

Steps
ItersRangePoint
10
0.005370866090842012
4.21737757242384e+15
0.025186331199138896
10
-3.4402871636077537
-5.738045557766166e-18
-0.023141644690732637

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04832
14832

end0.0ms

sample4.2s

Algorithm
intervals
Results
2.1s1586×body2560valid
1.3s2776×body1280valid
445.0ms1838×body640valid
155.0ms959×body320valid
54.0ms471×body160valid
25.0ms368×body80valid
5.0ms2×body5120valid