Details

Time bar (total: 27.7s)

sample625.0ms

Algorithm
intervals
Results
249.0ms116×body5120exit
139.0ms110×body1280valid
72.0ms76×body640valid
59.0ms44×body1280nan
34.0ms34×body640nan
28.0ms42×body320valid
10.0ms14×body320nan
8.0ms19×body160valid
3.0msbody160nan
2.0ms11×body80valid
2.0msbody80nan

simplify19.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (16.0ms)

IterNodesCost
0537289

prune15.0ms

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: 0.7b

Counts
2 → 2

localize55.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (* PI 2.0)) (* (pow (+ z (- 7.0 (- 1.0 0.5))) (+ z (- 0.5 1.0))) (/ (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 z) (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (/ 771.3234287776531 (+ z (- 3.0 1.0))) (/ -176.6150291621406 (+ z (- 4.0 1.0)))))) (+ (/ 12.507343278686905 (+ z (- 5.0 1.0))) (+ (/ -0.13857109526572012 (+ z (- 6.0 1.0))) (+ (/ 9.984369578019572e-06 (+ z (- 7.0 1.0))) (/ 1.5056327351493116e-07 (+ z (- 8.0 1.0)))))))) (exp (+ z (- 7.0 (- 1.0 0.5)))))))
0.6b
(/ (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 z) (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (/ 771.3234287776531 (+ z (- 3.0 1.0))) (/ -176.6150291621406 (+ z (- 4.0 1.0)))))) (+ (/ 12.507343278686905 (+ z (- 5.0 1.0))) (+ (/ -0.13857109526572012 (+ z (- 6.0 1.0))) (+ (/ 9.984369578019572e-06 (+ z (- 7.0 1.0))) (/ 1.5056327351493116e-07 (+ z (- 8.0 1.0)))))))) (exp (+ z (- 7.0 (- 1.0 0.5)))))
0.9b
(+ (/ -0.13857109526572012 (+ z (- 6.0 1.0))) (+ (/ 9.984369578019572e-06 (+ z (- 7.0 1.0))) (/ 1.5056327351493116e-07 (+ z (- 8.0 1.0)))))
1.0b
(sqrt (* PI 2.0))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
769×*-un-lft-identity
516×distribute-lft-out
161×times-frac
31×add-sqr-sqrt add-cube-cbrt
27×distribute-lft-out--
23×add-exp-log
21×exp-sum
20×associate-/l*
15×add-cbrt-cube
13×prod-exp
pow1 add-log-exp
cbrt-unprod
associate-*r/ div-exp associate-*l* frac-add associate-/r*
associate-+r- flip3-+ sum-log flip-+
cbrt-undiv pow-to-exp sqrt-pow1 pow-prod-down pow-exp sqrt-prod associate-/l/ pow-sub
+-commutative frac-times associate-+r+ frac-2neg pow1/2 exp-diff associate-*r* associate-*l/ clear-num associate-/r/ *-commutative div-inv
Counts
4 → 202
Calls
4 calls:
657.0ms
(* (sqrt (* PI 2.0)) (* (pow (+ z (- 7.0 (- 1.0 0.5))) (+ z (- 0.5 1.0))) (/ (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 z) (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (/ 771.3234287776531 (+ z (- 3.0 1.0))) (/ -176.6150291621406 (+ z (- 4.0 1.0)))))) (+ (/ 12.507343278686905 (+ z (- 5.0 1.0))) (+ (/ -0.13857109526572012 (+ z (- 6.0 1.0))) (+ (/ 9.984369578019572e-06 (+ z (- 7.0 1.0))) (/ 1.5056327351493116e-07 (+ z (- 8.0 1.0)))))))) (exp (+ z (- 7.0 (- 1.0 0.5)))))))
614.0ms
(/ (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 z) (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (/ 771.3234287776531 (+ z (- 3.0 1.0))) (/ -176.6150291621406 (+ z (- 4.0 1.0)))))) (+ (/ 12.507343278686905 (+ z (- 5.0 1.0))) (+ (/ -0.13857109526572012 (+ z (- 6.0 1.0))) (+ (/ 9.984369578019572e-06 (+ z (- 7.0 1.0))) (/ 1.5056327351493116e-07 (+ z (- 8.0 1.0)))))))) (exp (+ z (- 7.0 (- 1.0 0.5)))))
49.0ms
(+ (/ -0.13857109526572012 (+ z (- 6.0 1.0))) (+ (/ 9.984369578019572e-06 (+ z (- 7.0 1.0))) (/ 1.5056327351493116e-07 (+ z (- 8.0 1.0)))))
2.0ms
(sqrt (* PI 2.0))

series75.0ms

Counts
4 → 10
Calls
4 calls:
44.0ms
(* (sqrt (* PI 2.0)) (* (pow (+ z (- 7.0 (- 1.0 0.5))) (+ z (- 0.5 1.0))) (/ (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 z) (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (/ 771.3234287776531 (+ z (- 3.0 1.0))) (/ -176.6150291621406 (+ z (- 4.0 1.0)))))) (+ (/ 12.507343278686905 (+ z (- 5.0 1.0))) (+ (/ -0.13857109526572012 (+ z (- 6.0 1.0))) (+ (/ 9.984369578019572e-06 (+ z (- 7.0 1.0))) (/ 1.5056327351493116e-07 (+ z (- 8.0 1.0)))))))) (exp (+ z (- 7.0 (- 1.0 0.5)))))))
24.0ms
(/ (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 z) (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (/ 771.3234287776531 (+ z (- 3.0 1.0))) (/ -176.6150291621406 (+ z (- 4.0 1.0)))))) (+ (/ 12.507343278686905 (+ z (- 5.0 1.0))) (+ (/ -0.13857109526572012 (+ z (- 6.0 1.0))) (+ (/ 9.984369578019572e-06 (+ z (- 7.0 1.0))) (/ 1.5056327351493116e-07 (+ z (- 8.0 1.0)))))))) (exp (+ z (- 7.0 (- 1.0 0.5)))))
7.0ms
(+ (/ -0.13857109526572012 (+ z (- 6.0 1.0))) (+ (/ 9.984369578019572e-06 (+ z (- 7.0 1.0))) (/ 1.5056327351493116e-07 (+ z (- 8.0 1.0)))))
0.0ms
(sqrt (* PI 2.0))

simplify105.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
0524614034

prune794.0ms

Filtered
81 candidates to 212 candidates (-161.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New20210212
Fresh101
Picked101
Done000
Total20410214

Merged error: 0.0b

Counts
214 → 10

localize63.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (sqrt (* PI 2.0)) (* (+ 0.9999999999998099 (+ (+ (/ -0.13857109526572012 (+ z (- 6.0 1.0))) (+ (/ 9.984369578019572e-06 (+ z (- 7.0 1.0))) (/ 1.5056327351493116e-07 (+ z (- 8.0 1.0))))) (+ (/ 676.5203681218851 z) (+ (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (/ 771.3234287776531 (+ z (- 3.0 1.0))) (/ -176.6150291621406 (+ z (- 4.0 1.0))))) (/ 12.507343278686905 (+ z (- 5.0 1.0))))))) (pow (+ z (+ 7.0 (- 0.5 1.0))) (+ z (- 0.5 1.0)))))
0.9b
(+ (/ -0.13857109526572012 (+ z (- 6.0 1.0))) (+ (/ 9.984369578019572e-06 (+ z (- 7.0 1.0))) (/ 1.5056327351493116e-07 (+ z (- 8.0 1.0)))))
1.0b
(+ (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (/ 771.3234287776531 (+ z (- 3.0 1.0))) (/ -176.6150291621406 (+ z (- 4.0 1.0))))) (/ 12.507343278686905 (+ z (- 5.0 1.0))))
1.0b
(sqrt (* PI 2.0))

rewrite813.0ms

Algorithm
rewrite-expression-head
Rules
1234×*-un-lft-identity
576×distribute-lft-out
405×times-frac
135×distribute-lft-out--
18×add-log-exp
14×add-exp-log
13×frac-add
pow1 sum-log add-cbrt-cube
flip3-+ prod-exp flip-+
associate-*r/
add-sqr-sqrt add-cube-cbrt
associate-*l*
associate-+r- cbrt-unprod pow-sub
+-commutative frac-times sqrt-pow1 pow-prod-down associate-*l/ sqrt-prod
pow-to-exp associate-+l+ associate-+r+ pow1/2 associate-*r* pow-exp *-commutative
Counts
4 → 184
Calls
4 calls:
640.0ms
(* (sqrt (* PI 2.0)) (* (+ 0.9999999999998099 (+ (+ (/ -0.13857109526572012 (+ z (- 6.0 1.0))) (+ (/ 9.984369578019572e-06 (+ z (- 7.0 1.0))) (/ 1.5056327351493116e-07 (+ z (- 8.0 1.0))))) (+ (/ 676.5203681218851 z) (+ (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (/ 771.3234287776531 (+ z (- 3.0 1.0))) (/ -176.6150291621406 (+ z (- 4.0 1.0))))) (/ 12.507343278686905 (+ z (- 5.0 1.0))))))) (pow (+ z (+ 7.0 (- 0.5 1.0))) (+ z (- 0.5 1.0)))))
49.0ms
(+ (/ -0.13857109526572012 (+ z (- 6.0 1.0))) (+ (/ 9.984369578019572e-06 (+ z (- 7.0 1.0))) (/ 1.5056327351493116e-07 (+ z (- 8.0 1.0)))))
93.0ms
(+ (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (/ 771.3234287776531 (+ z (- 3.0 1.0))) (/ -176.6150291621406 (+ z (- 4.0 1.0))))) (/ 12.507343278686905 (+ z (- 5.0 1.0))))
4.0ms
(sqrt (* PI 2.0))

series58.0ms

Counts
4 → 10
Calls
4 calls:
33.0ms
(* (sqrt (* PI 2.0)) (* (+ 0.9999999999998099 (+ (+ (/ -0.13857109526572012 (+ z (- 6.0 1.0))) (+ (/ 9.984369578019572e-06 (+ z (- 7.0 1.0))) (/ 1.5056327351493116e-07 (+ z (- 8.0 1.0))))) (+ (/ 676.5203681218851 z) (+ (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (/ 771.3234287776531 (+ z (- 3.0 1.0))) (/ -176.6150291621406 (+ z (- 4.0 1.0))))) (/ 12.507343278686905 (+ z (- 5.0 1.0))))))) (pow (+ z (+ 7.0 (- 0.5 1.0))) (+ z (- 0.5 1.0)))))
6.0ms
(+ (/ -0.13857109526572012 (+ z (- 6.0 1.0))) (+ (/ 9.984369578019572e-06 (+ z (- 7.0 1.0))) (/ 1.5056327351493116e-07 (+ z (- 8.0 1.0)))))
18.0ms
(+ (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (/ 771.3234287776531 (+ z (- 3.0 1.0))) (/ -176.6150291621406 (+ z (- 4.0 1.0))))) (/ 12.507343278686905 (+ z (- 5.0 1.0))))
0.0ms
(sqrt (* PI 2.0))

simplify73.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
050337701

prune593.0ms

Filtered
69 candidates to 194 candidates (-181.2%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1940194
Fresh099
Picked011
Done000
Total19410204

Merged error: 0.0b

Counts
204 → 10

localize53.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 z) (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (/ 771.3234287776531 (+ z (- 3.0 1.0))) (/ -176.6150291621406 (+ z (- 4.0 1.0)))))) (+ (/ 12.507343278686905 (+ z (- 5.0 1.0))) (+ (/ -0.13857109526572012 (+ z (- 6.0 1.0))) (+ (/ 9.984369578019572e-06 (+ z (- 7.0 1.0))) (/ 1.5056327351493116e-07 (+ z (- 8.0 1.0)))))))) (exp (+ z (- 7.0 (- 1.0 0.5)))))
0.9b
(+ (/ -0.13857109526572012 (+ z (- 6.0 1.0))) (+ (/ 9.984369578019572e-06 (+ z (- 7.0 1.0))) (/ 1.5056327351493116e-07 (+ z (- 8.0 1.0)))))
1.0b
(* (sqrt (* PI 2.0)) (pow (+ z (+ 7.0 (- 0.5 1.0))) (+ z (- 0.5 1.0))))
1.0b
(sqrt (* PI 2.0))

rewrite696.0ms

Algorithm
rewrite-expression-head
Rules
780×*-un-lft-identity
521×distribute-lft-out
161×times-frac
38×add-sqr-sqrt
33×add-cube-cbrt
28×distribute-lft-out--
21×exp-sum
20×associate-/l*
11×associate-*r*
10×add-exp-log
add-log-exp
add-cbrt-cube
pow1 unpow-prod-down
associate-*l* frac-add associate-/r*
flip3-+ prod-exp sum-log flip-+ unswap-sqr
associate-+r- sqrt-pow1 sqrt-prod associate-/l/ sqr-pow
cbrt-undiv unpow-prod-up +-commutative pow-to-exp associate-+r+ frac-2neg pow1/2 exp-diff associate-*r/ div-exp pow-prod-down pow-exp clear-num associate-/r/ *-commutative cbrt-unprod div-inv pow-sub
Counts
4 → 206
Calls
4 calls:
615.0ms
(/ (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 z) (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (/ 771.3234287776531 (+ z (- 3.0 1.0))) (/ -176.6150291621406 (+ z (- 4.0 1.0)))))) (+ (/ 12.507343278686905 (+ z (- 5.0 1.0))) (+ (/ -0.13857109526572012 (+ z (- 6.0 1.0))) (+ (/ 9.984369578019572e-06 (+ z (- 7.0 1.0))) (/ 1.5056327351493116e-07 (+ z (- 8.0 1.0)))))))) (exp (+ z (- 7.0 (- 1.0 0.5)))))
46.0ms
(+ (/ -0.13857109526572012 (+ z (- 6.0 1.0))) (+ (/ 9.984369578019572e-06 (+ z (- 7.0 1.0))) (/ 1.5056327351493116e-07 (+ z (- 8.0 1.0)))))
15.0ms
(* (sqrt (* PI 2.0)) (pow (+ z (+ 7.0 (- 0.5 1.0))) (+ z (- 0.5 1.0))))
2.0ms
(sqrt (* PI 2.0))

series49.0ms

Counts
4 → 10
Calls
4 calls:
18.0ms
(/ (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 z) (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (/ 771.3234287776531 (+ z (- 3.0 1.0))) (/ -176.6150291621406 (+ z (- 4.0 1.0)))))) (+ (/ 12.507343278686905 (+ z (- 5.0 1.0))) (+ (/ -0.13857109526572012 (+ z (- 6.0 1.0))) (+ (/ 9.984369578019572e-06 (+ z (- 7.0 1.0))) (/ 1.5056327351493116e-07 (+ z (- 8.0 1.0)))))))) (exp (+ z (- 7.0 (- 1.0 0.5)))))
7.0ms
(+ (/ -0.13857109526572012 (+ z (- 6.0 1.0))) (+ (/ 9.984369578019572e-06 (+ z (- 7.0 1.0))) (/ 1.5056327351493116e-07 (+ z (- 8.0 1.0)))))
24.0ms
(* (sqrt (* PI 2.0)) (pow (+ z (+ 7.0 (- 0.5 1.0))) (+ z (- 0.5 1.0))))
0.0ms
(sqrt (* PI 2.0))

simplify95.0ms

Algorithm
egg-herbie
Counts
216 → 216
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
0576112119

prune827.0ms

Filtered
85 candidates to 216 candidates (-154.1%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2142216
Fresh358
Picked101
Done011
Total2188226

Merged error: 0b

Counts
226 → 8

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
1245×*-un-lft-identity
581×distribute-lft-out
405×times-frac
136×distribute-lft-out--
18×add-log-exp
13×frac-add
12×add-sqr-sqrt
11×associate-*r*
add-exp-log sum-log
pow1 add-cube-cbrt unpow-prod-down
add-cbrt-cube
flip3-+ flip-+
associate-*l*
prod-exp unswap-sqr
+-commutative sqrt-pow1 sqrt-prod sqr-pow
unpow-prod-up pow-to-exp associate-+r- associate-+l+ associate-+r+ pow1/2 associate-*r/ pow-prod-down pow-exp *-commutative cbrt-unprod pow-sub
Counts
4 → 190
Calls
4 calls:
45.0ms
(+ (/ -0.13857109526572012 (+ z (- 6.0 1.0))) (+ (/ 9.984369578019572e-06 (+ z (- 7.0 1.0))) (/ 1.5056327351493116e-07 (+ z (- 8.0 1.0)))))
85.0ms
(+ (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (/ 771.3234287776531 (+ z (- 3.0 1.0))) (/ -176.6150291621406 (+ z (- 4.0 1.0))))) (/ 12.507343278686905 (+ z (- 5.0 1.0))))
14.0ms
(* (sqrt (* PI 2.0)) (pow (+ z (+ 7.0 (- 0.5 1.0))) (+ z (- 0.5 1.0))))
2.0ms
(sqrt (* PI 2.0))

series34.0ms

Counts
4 → 10
Calls
4 calls:
7.0ms
(+ (/ -0.13857109526572012 (+ z (- 6.0 1.0))) (+ (/ 9.984369578019572e-06 (+ z (- 7.0 1.0))) (/ 1.5056327351493116e-07 (+ z (- 8.0 1.0)))))
9.0ms
(+ (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (/ 771.3234287776531 (+ z (- 3.0 1.0))) (/ -176.6150291621406 (+ z (- 4.0 1.0))))) (/ 12.507343278686905 (+ z (- 5.0 1.0))))
19.0ms
(* (sqrt (* PI 2.0)) (pow (+ z (+ 7.0 (- 0.5 1.0))) (+ z (- 0.5 1.0))))
0.0ms
(sqrt (* PI 2.0))

simplify80.0ms

Algorithm
egg-herbie
Counts
200 → 200
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
049496085
149496085

prune529.0ms

Filtered
71 candidates to 200 candidates (-181.7%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1991200
Fresh336
Picked011
Done011
Total2026208

Merged error: 0b

Counts
208 → 6

regimes62.0ms

Accuracy

0% (1.0b remaining)

Error of 1.0b against oracle of 0.0b and baseline of 1.0b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
08690
18690

end0.0ms

sample20.4s

Algorithm
intervals
Results
8.3s3951×body5120exit
4.2s3325×body1280valid
2.4s2509×body640valid
2.0s1536×body1280nan
1.2s1211×body640nan
867.0ms1273×body320valid
431.0ms596×body320nan
291.0ms642×body160valid
145.0ms317×body160nan
76.0ms341×body80valid
60.0ms306×body80nan

Profiling

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