Details

Time bar (total: 56.7s)

sample1.6s

Algorithm
intervals
Results
1.3s126×body5120exit
126.0ms61×body1280nan
84.0ms257×body80valid
62.0ms43×body640nan
19.0ms18×body320nan
13.0ms14×body160nan
2.0msbody80nan

simplify27.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
0517487

prune21.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 1.2b

Counts
2 → 2

localize57.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ PI (sin (* PI z)))
0.9b
(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
1.0b
(* (exp (- z (+ 7.0 0.5))) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (+ 2.0 (neg z))) (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))))) (+ (/ 12.507343278686905 (+ (neg z) 5.0)) (+ (/ -0.13857109526572012 (+ (neg z) 6.0)) (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))))))))
1.0b
(sqrt (* PI 2.0))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
162×*-un-lft-identity
103×distribute-lft-out
27×times-frac
20×associate-*r*
16×add-sqr-sqrt
14×add-cube-cbrt
pow1
add-cbrt-cube
add-exp-log
distribute-rgt-neg-in add-log-exp
associate-*l*
flip3-+ exp-diff associate-/r* flip-+ associate-/l*
frac-times sqrt-pow1 associate-*r/ exp-sum pow-prod-down
cbrt-undiv +-commutative distribute-rgt-in sub-neg frac-2neg distribute-lft-in pow1/2 div-exp associate-*l/ frac-add prod-exp clear-num sum-log sqrt-prod *-commutative cbrt-unprod div-inv unswap-sqr
Counts
4 → 104
Calls
4 calls:
4.0ms
(/ PI (sin (* PI z)))
32.0ms
(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
1.2s
(* (exp (- z (+ 7.0 0.5))) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (+ 2.0 (neg z))) (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))))) (+ (/ 12.507343278686905 (+ (neg z) 5.0)) (+ (/ -0.13857109526572012 (+ (neg z) 6.0)) (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))))))))
3.0ms
(sqrt (* PI 2.0))

series33.0ms

Counts
4 → 10
Calls
4 calls:
7.0ms
(/ PI (sin (* PI z)))
5.0ms
(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
20.0ms
(* (exp (- z (+ 7.0 0.5))) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (+ 2.0 (neg z))) (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))))) (+ (/ 12.507343278686905 (+ (neg z) 5.0)) (+ (/ -0.13857109526572012 (+ (neg z) 6.0)) (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))))))))
0.0ms
(sqrt (* PI 2.0))

simplify35.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 0 (19.0ms)

IterNodesCost
050572798

prune511.0ms

Filtered
73 candidates to 114 candidates (-56.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New10311114
Fresh101
Picked101
Done000
Total10511116

Merged error: 0b

Counts
116 → 11

localize58.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ PI (sin (* PI z)))
1.0b
(/ (* (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))))) (exp z)) (exp (+ 7.0 0.5)))
1.0b
(+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))
1.0b
(sqrt (* PI 2.0))

rewrite532.0ms

Algorithm
rewrite-expression-head
Rules
994×*-un-lft-identity
397×times-frac
335×distribute-lft-out
192×distribute-lft-out--
25×frac-add
24×add-log-exp
15×sum-log
14×add-sqr-sqrt add-cube-cbrt
11×add-cbrt-cube
add-exp-log
pow1 associate-/r*
flip3-+ flip-+
associate-/l*
cbrt-undiv div-exp
frac-2neg sqrt-pow1 exp-sum associate-*l/ clear-num div-inv associate-/l/
+-commutative associate-+r+ pow1/2 pow-prod-down prod-exp sqrt-prod cbrt-unprod
Counts
4 → 157
Calls
4 calls:
4.0ms
(/ PI (sin (* PI z)))
362.0ms
(/ (* (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))))) (exp z)) (exp (+ 7.0 0.5)))
137.0ms
(+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))
3.0ms
(sqrt (* PI 2.0))

series44.0ms

Counts
4 → 10
Calls
4 calls:
7.0ms
(/ PI (sin (* PI z)))
23.0ms
(/ (* (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))))) (exp z)) (exp (+ 7.0 0.5)))
14.0ms
(+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))
0.0ms
(sqrt (* PI 2.0))

simplify56.0ms

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 0 (14.0ms)

IterNodesCost
050966634

prune605.0ms

Filtered
80 candidates to 167 candidates (-108.8%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1652167
Fresh3710
Picked011
Done000
Total16810178

Merged error: 0b

Counts
178 → 10

localize64.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ (* (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (exp (log (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))))))) (exp z)) (exp (+ 7.0 0.5)))
1.0b
(+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))
1.0b
(sqrt (* PI 2.0))
1.0b
(exp (log (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))))

rewrite565.0ms

Algorithm
rewrite-expression-head
Rules
1968×*-un-lft-identity
772×times-frac
670×distribute-lft-out
384×distribute-lft-out--
74×exp-sum
72×log-prod
50×frac-add
24×add-log-exp
15×sum-log
11×log-div flip3-+ exp-diff flip-+
add-cbrt-cube
pow1 add-sqr-sqrt add-cube-cbrt
add-exp-log
exp-prod associate-/r*
cbrt-undiv sqrt-pow1 div-exp associate-*l/ associate-/l/
+-commutative associate-+r+ frac-2neg pow1/2 pow-prod-down prod-exp clear-num sqrt-prod log-pow cbrt-unprod div-inv rem-exp-log associate-/l*
Counts
4 → 225
Calls
4 calls:
227.0ms
(/ (* (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (exp (log (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))))))) (exp z)) (exp (+ 7.0 0.5)))
137.0ms
(+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))
3.0ms
(sqrt (* PI 2.0))
139.0ms
(exp (log (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))))

series62.0ms

Counts
4 → 10
Calls
4 calls:
24.0ms
(/ (* (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (exp (log (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))))))) (exp z)) (exp (+ 7.0 0.5)))
24.0ms
(+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))
0.0ms
(sqrt (* PI 2.0))
14.0ms
(exp (log (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))))

simplify93.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
0518011076

prune736.0ms

Filtered
79 candidates to 235 candidates (-197.5%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New2350235
Fresh088
Picked011
Done011
Total23510245

Merged error: 0b

Counts
245 → 10

localize57.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (* PI 2.0)) (* (* (exp (- z (+ 7.0 0.5))) (* (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))))) (pow (+ 7.0 (- 0.5 z)) (- 0.5 z)))) (/ PI (sin (* PI z)))))
1.0b
(* (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))))) (pow (+ 7.0 (- 0.5 z)) (- 0.5 z)))
1.0b
(+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))
1.0b
(sqrt (* PI 2.0))

rewrite924.0ms

Algorithm
rewrite-expression-head
Rules
1037×*-un-lft-identity
384×times-frac
373×distribute-lft-out
193×distribute-lft-out--
50×add-exp-log
39×associate-*r/
38×prod-exp
35×add-cbrt-cube
31×frac-times
25×frac-add
24×add-log-exp
23×associate-*l/
20×cbrt-unprod
16×pow1
15×flip3-+ associate-*l* sum-log flip-+ pow-sub
13×add-sqr-sqrt
12×exp-diff associate-*r*
add-cube-cbrt
pow-prod-down
unpow-prod-down
div-exp
cbrt-undiv pow-to-exp pow-exp unswap-sqr
unpow-prod-up sqrt-pow1 sqrt-prod *-commutative sqr-pow
+-commutative sub-neg associate-+r+ pow1/2
Counts
4 → 204
Calls
4 calls:
384.0ms
(* (sqrt (* PI 2.0)) (* (* (exp (- z (+ 7.0 0.5))) (* (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))))) (pow (+ 7.0 (- 0.5 z)) (- 0.5 z)))) (/ PI (sin (* PI z)))))
364.0ms
(* (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))))) (pow (+ 7.0 (- 0.5 z)) (- 0.5 z)))
136.0ms
(+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))
2.0ms
(sqrt (* PI 2.0))

series109.0ms

Counts
4 → 10
Calls
4 calls:
69.0ms
(* (sqrt (* PI 2.0)) (* (* (exp (- z (+ 7.0 0.5))) (* (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))))) (pow (+ 7.0 (- 0.5 z)) (- 0.5 z)))) (/ PI (sin (* PI z)))))
26.0ms
(* (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))))) (pow (+ 7.0 (- 0.5 z)) (- 0.5 z)))
14.0ms
(+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z)))))))
0.0ms
(sqrt (* PI 2.0))

simplify122.0ms

Algorithm
egg-herbie
Counts
214 → 214
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
0498413020
1498413020

prune1.2s

Filtered
107 candidates to 214 candidates (-100.0%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2122214
Fresh347
Picked101
Done022
Total2168224

Merged error: 0b

Counts
224 → 8

regimes92.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07881
17881

end0.0ms

sample47.9s

Algorithm
intervals
Results
39.2s3930×body5120exit
3.0s1509×body1280nan
2.5s8095×body80valid
1.8s1210×body640nan
651.0ms622×body320nan
211.0ms306×body160nan
85.0ms285×body80nan

Profiling

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