Details

Time bar (total: 26.4s)

sample619.0ms

Algorithm
intervals
Results
109.0ms102×body1280valid
62.0ms80×body640valid
54.0ms42×body1280nan
31.0ms36×body640nan
24.0ms41×body320valid
23.0ms124×body80overflowed
22.0ms36×body320nan
9.0ms24×body160valid
3.0msbody160nan
2.0ms10×body80valid
1.0msbody80nan

simplify75.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
013348
145348
2276947
3500247

prune34.0ms

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: 62.1b

Counts
2 → 2

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (neg (+ (+ (- z 1.0) 7.0) 0.5))))
1.0b
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
1.0b
(sqrt (* PI 2.0))
8.4b
(+ (- z 1.0) 1.0)

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
15×add-exp-log associate-*r*
13×add-sqr-sqrt
11×add-cbrt-cube
10×prod-exp
pow1 add-log-exp
add-cube-cbrt
unpow-prod-down distribute-lft-out
associate-*r/
associate-+l- associate-*l*
cbrt-unprod pow-sub
exp-neg unswap-sqr
neg-sub0 frac-times pow-to-exp associate-+l+ sqrt-pow1 exp-diff pow-prod-down pow-exp sum-log sqrt-prod *-commutative distribute-lft-out-- sqr-pow
unpow-prod-up +-commutative sub-neg distribute-neg-in flip3-+ pow1/2 diff-log exp-sum associate-*l/ un-div-inv flip-+
Counts
4 → 85
Calls
4 calls:
31.0ms
(* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (neg (+ (+ (- z 1.0) 7.0) 0.5))))
18.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
2.0ms
(sqrt (* PI 2.0))
8.0ms
(+ (- z 1.0) 1.0)

series46.0ms

Counts
4 → 10
Calls
4 calls:
26.0ms
(* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (neg (+ (+ (- z 1.0) 7.0) 0.5))))
18.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms
(sqrt (* PI 2.0))
2.0ms
(+ (- z 1.0) 1.0)

simplify91.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
07081125
13058989
25002983

prune1.0s

Filtered
95 candidates to 65 candidates (31.6%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New90595
Fresh101
Picked101
Done000
Total92597

Merged error: 0.6b

Counts
97 → 5

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (neg (+ (+ (- z 1.0) 7.0) 0.5))))
0.3b
(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
1.0b
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
1.0b
(sqrt (* PI 2.0))

rewrite223.0ms

Algorithm
rewrite-expression-head
Rules
392×frac-add
132×frac-times
107×associate-*r/
62×*-un-lft-identity
56×flip3-+ flip-+
55×associate-+l- pow-sub
54×exp-neg
41×distribute-lft-out
36×neg-sub0 exp-diff
27×add-exp-log
26×associate-*r*
24×associate-*l/
22×prod-exp
20×add-cbrt-cube
18×un-div-inv
14×pow1 add-sqr-sqrt
10×cbrt-unprod
add-cube-cbrt
unpow-prod-down
associate-*l*
pow-prod-down
add-log-exp
pow-to-exp pow-exp *-commutative unswap-sqr
sqrt-pow1 sqrt-prod sqr-pow
unpow-prod-up distribute-rgt-in distribute-neg-in distribute-lft-in pow1/2 exp-sum distribute-lft-out--
Counts
4 → 218
Calls
4 calls:
30.0ms
(* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (neg (+ (+ (- z 1.0) 7.0) 0.5))))
146.0ms
(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
18.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
2.0ms
(sqrt (* PI 2.0))

series85.0ms

Counts
4 → 10
Calls
4 calls:
27.0ms
(* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (neg (+ (+ (- z 1.0) 7.0) 0.5))))
40.0ms
(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
18.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms
(sqrt (* PI 2.0))

simplify300.0ms

Algorithm
egg-herbie
Counts
228 → 228
Iterations

Useful iterations: 1 (66.0ms)

IterNodesCost
0379624353
1500324219

prune3.9s

Filtered
228 candidates to 139 candidates (39.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New2199228
Fresh314
Picked101
Done000
Total22310233

Merged error: 0.2b

Counts
233 → 10

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (sqrt PI) (* (sqrt 2.0) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))) (exp (neg (+ (+ (- z 1.0) 7.0) 0.5))))
0.3b
(* (* (* (sqrt PI) (* (sqrt 2.0) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))) (exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
1.0b
(* (sqrt PI) (* (sqrt 2.0) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))))
1.0b
(sqrt PI)

rewrite232.0ms

Algorithm
rewrite-expression-head
Rules
392×frac-add
162×associate-*r/
132×frac-times
56×flip3-+ flip-+
55×associate-+l- pow-sub
54×exp-neg
53×*-un-lft-identity
43×add-exp-log
37×prod-exp
36×neg-sub0 exp-diff distribute-lft-out
32×add-cbrt-cube
24×associate-*l/
21×pow1
19×cbrt-unprod
18×un-div-inv
16×associate-*r*
10×add-sqr-sqrt pow-prod-down
add-cube-cbrt
associate-*l*
sqrt-prod
add-log-exp
pow-to-exp pow-exp *-commutative
distribute-rgt-in rem-sqrt-square distribute-neg-in distribute-lft-in sqrt-pow1 pow1/2 exp-sum
Counts
4 → 218
Calls
4 calls:
40.0ms
(* (* (sqrt PI) (* (sqrt 2.0) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))) (exp (neg (+ (+ (- z 1.0) 7.0) 0.5))))
153.0ms
(* (* (* (sqrt PI) (* (sqrt 2.0) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))) (exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
18.0ms
(* (sqrt PI) (* (sqrt 2.0) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))))
2.0ms
(sqrt PI)

series89.0ms

Counts
4 → 10
Calls
4 calls:
26.0ms
(* (* (sqrt PI) (* (sqrt 2.0) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))) (exp (neg (+ (+ (- z 1.0) 7.0) 0.5))))
46.0ms
(* (* (* (sqrt PI) (* (sqrt 2.0) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))) (exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
18.0ms
(* (sqrt PI) (* (sqrt 2.0) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))))
0.0ms
(sqrt PI)

simplify293.0ms

Algorithm
egg-herbie
Counts
228 → 228
Iterations

Useful iterations: 1 (64.0ms)

IterNodesCost
0382324784
1500124651

prune3.8s

Filtered
228 candidates to 136 candidates (40.4%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2271228
Fresh369
Picked011
Done000
Total2308238

Merged error: 0.2b

Counts
238 → 8

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite316.0ms

Algorithm
rewrite-expression-head
Rules
112×frac-add
75×add-exp-log
61×*-un-lft-identity
53×prod-exp
41×distribute-lft-out
34×associate-*l/
32×add-cbrt-cube
23×associate-*l*
20×div-exp
16×flip3-+ flip-+ associate-/l/
13×add-sqr-sqrt cbrt-unprod
11×pow-to-exp pow-exp
pow1
add-cube-cbrt associate-+l-
unpow-prod-down
cbrt-undiv
associate-*r*
exp-diff pow-sub add-log-exp
associate-/r/ unswap-sqr
unpow-prod-up frac-times sqrt-pow1 associate-*r/ pow-prod-down *-commutative sqr-pow
sub-neg frac-2neg times-frac pow1/2 exp-sum clear-num associate-/r* sqrt-prod div-inv associate-/l* distribute-lft-out--
Counts
4 → 146
Calls
4 calls:
151.0ms
(/ (* (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z))) (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5))))
130.0ms
(* (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z)))
24.0ms
(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
2.0ms
(sqrt (* PI 2.0))

series114.0ms

Counts
4 → 10
Calls
4 calls:
65.0ms
(/ (* (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z))) (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5))))
32.0ms
(* (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z)))
16.0ms
(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
0.0ms
(sqrt (* PI 2.0))

simplify121.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 1 (49.0ms)

IterNodesCost
028898099
150037502

prune3.6s

Filtered
156 candidates to 110 candidates (29.5%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1533156
Fresh246
Picked011
Done101
Total1568164

Merged error: 0.2b

Counts
164 → 8

regimes186.0ms

Accuracy

0% (1.0b remaining)

Error of 1.0b against oracle of 0.1b and baseline of 1.0b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07549
17549

end0.0ms

sample11.0s

Algorithm
intervals
Results
3.6s3360×body1280valid
1.9s2461×body640valid
1.8s1531×body1280nan
1.0s1210×body640nan
718.0ms1295×body320valid
679.0ms3818×body80overflowed
396.0ms631×body320nan
227.0ms629×body160valid
119.0ms315×body160nan
64.0ms340×body80valid
50.0ms306×body80nan

Profiling

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