Details

Time bar (total: 26.7s)

sample441.0ms

Algorithm
intervals
Results
142.0ms113×body1280valid
69.0ms75×body640valid
63.0ms47×body1280nan
51.0ms52×body640nan
35.0ms136×body80overflowed
24.0ms36×body320valid
14.0ms20×body320nan
12.0ms26×body160valid
5.0ms11×body80nan
3.0ms7×body160nan
2.0ms8×body80valid

simplify72.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
013348
145348
2276947
3500247

prune16.0ms

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: 62.2b

Counts
2 → 2

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b
(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))
7.8b
(+ (- z 1.0) 1.0)

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
20×add-log-exp
17×distribute-lft-out
16×exp-prod
15×add-sqr-sqrt
11×associate-*r*
10×add-cube-cbrt
9×add-exp-log
7×pow1 unpow-prod-down sum-log
6×distribute-lft-neg-in distribute-rgt-neg-in add-cbrt-cube
5×rem-exp-log
4×associate-*l* neg-log distribute-lft-out--
3×prod-exp unswap-sqr
2×associate-+l- associate-+l+ sqrt-pow1 diff-log sqrt-prod sqr-pow
1×unpow-prod-up +-commutative neg-sub0 exp-neg pow-to-exp neg-mul-1 sub-neg distribute-neg-in flip3-+ pow1/2 exp-diff associate-*r/ exp-sum pow-prod-down pow-exp *-commutative cbrt-unprod flip-+ pow-sub
Counts
4 → 90
Calls
4 calls:
11.0ms
(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
19.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
2.0ms
(sqrt (* PI 2.0))
7.0ms
(+ (- z 1.0) 1.0)

series25.0ms

Counts
4 → 10
Calls
4 calls:
6.0ms
(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)

simplify57.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0552704
12036643
25001638

prune507.0ms

Filtered
68 candidates to 100 candidates (-47.1%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New955100
Fresh101
Picked101
Done000
Total975102

Merged error: 0.6b

Counts
102 → 5

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
0.6b
(* (* (* (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))

rewrite206.0ms

Algorithm
rewrite-expression-head
Rules
392×frac-add
130×frac-times
102×associate-*r/
82×*-un-lft-identity
56×flip3-+ flip-+
52×exp-neg associate-+l- pow-sub
51×distribute-lft-out
35×neg-sub0 exp-diff
23×associate-*l/
22×associate-*r*
21×add-exp-log
17×un-div-inv
16×add-sqr-sqrt exp-prod
15×prod-exp add-cbrt-cube add-log-exp
12×pow1
11×add-cube-cbrt
7×unpow-prod-down cbrt-unprod
6×distribute-lft-neg-in distribute-rgt-neg-in
5×associate-*l* sum-log rem-exp-log
4×pow-prod-down neg-log
3×distribute-lft-out-- unswap-sqr
2×pow-to-exp sqrt-pow1 pow-exp sqrt-prod *-commutative sqr-pow
1×unpow-prod-up distribute-rgt-in neg-mul-1 distribute-neg-in distribute-lft-in pow1/2 diff-log exp-sum
Counts
4 → 223
Calls
4 calls:
11.0ms
(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
153.0ms
(* (* (* (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))))
19.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
2.0ms
(sqrt (* PI 2.0))

series66.0ms

Counts
4 → 10
Calls
4 calls:
2.0ms
(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
46.0ms
(* (* (* (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))

simplify287.0ms

Algorithm
egg-herbie
Counts
233 → 233
Iterations

Useful iterations: 1 (61.0ms)

IterNodesCost
0374523930
1500223816

prune5.0s

Filtered
140 candidates to 233 candidates (-66.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2258233
Fresh404
Picked101
Done000
Total2308238

Merged error: 0b

Counts
238 → 8

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (+ (+ (+ (+ (+ (+ (+ 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 1.0) 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 1.0) 0.5)))) (exp (+ (+ (- 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))

rewrite324.0ms

Algorithm
rewrite-expression-head
Rules
224×frac-add
63×*-un-lft-identity
41×distribute-lft-out
37×associate-+l- associate-*r/
35×pow-sub
33×associate-/l/
32×frac-times flip3-+ associate-*l/ flip-+
30×add-exp-log
20×add-cbrt-cube
17×prod-exp
15×add-sqr-sqrt associate-*l*
12×associate-*r*
10×add-cube-cbrt
9×pow1
7×unpow-prod-down cbrt-unprod
5×div-exp
4×times-frac associate-/r* add-log-exp
3×cbrt-undiv pow-to-exp pow-exp unswap-sqr
2×sqrt-pow1 exp-sum pow-prod-down sqrt-prod *-commutative sqr-pow
1×unpow-prod-up frac-2neg pow1/2 exp-diff clear-num associate-/r/ div-inv associate-/l* distribute-lft-out--
Counts
4 → 163
Calls
4 calls:
135.0ms
(* (+ (+ (+ (+ (+ (+ (+ (+ 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 1.0) 0.5))))
149.0ms
(/ (* (+ (+ (+ (+ (+ (+ (+ (+ 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 1.0) 0.5)))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
20.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
2.0ms
(sqrt (* PI 2.0))

series97.0ms

Counts
4 → 10
Calls
4 calls:
36.0ms
(* (+ (+ (+ (+ (+ (+ (+ (+ 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 1.0) 0.5))))
42.0ms
(/ (* (+ (+ (+ (+ (+ (+ (+ (+ 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 1.0) 0.5)))) (exp (+ (+ (- 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))

simplify151.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 1 (48.0ms)

IterNodesCost
0283010823
1500110412

prune4.3s

Filtered
139 candidates to 173 candidates (-24.5%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1721173
Fresh167
Picked101
Done000
Total1747181

Merged error: 0b

Counts
181 → 7

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b
(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))) (/ (exp (+ (+ (- z 1.0) 7.0) 0.5)) (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 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))

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
500×*-un-lft-identity
370×distribute-lft-out
147×times-frac
56×frac-add
47×add-sqr-sqrt
42×add-cube-cbrt
21×add-exp-log
16×associate-/l/
15×associate-+l- add-cbrt-cube
14×add-log-exp
13×associate-*r/ exp-sum associate-/r/ div-inv pow-sub
11×associate-*r* associate-/l*
9×div-exp associate-/r*
8×flip3-+ flip-+
7×pow1 unpow-prod-down
6×exp-prod prod-exp
5×cbrt-undiv sum-log
4×associate-*l* rem-exp-log
3×unswap-sqr
2×pow-to-exp sqrt-pow1 pow-exp sqrt-prod cbrt-unprod distribute-lft-out-- sqr-pow
1×unpow-prod-up frac-2neg pow1/2 exp-diff diff-log pow-prod-down clear-num *-commutative
Counts
4 → 215
Calls
4 calls:
10.0ms
(exp (+ (+ (- z 1.0) 7.0) 0.5))
148.0ms
(/ (+ (+ (+ (+ (+ (+ (+ (+ 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))) (/ (exp (+ (+ (- z 1.0) 7.0) 0.5)) (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 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))

series68.0ms

Counts
4 → 10
Calls
4 calls:
2.0ms
(exp (+ (+ (- z 1.0) 7.0) 0.5))
49.0ms
(/ (+ (+ (+ (+ (+ (+ (+ (+ 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))) (/ (exp (+ (+ (- z 1.0) 7.0) 0.5)) (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 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))

simplify123.0ms

Algorithm
egg-herbie
Counts
225 → 225
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
017839862
150019567

prune1.7s

Filtered
116 candidates to 225 candidates (-94.0%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2241225
Fresh156
Picked011
Done000
Total2257232

Merged error: 0b

Counts
232 → 7

regimes102.0ms

Accuracy

0% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 0.9b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07245
17245

end0.0ms

sample12.8s

Algorithm
intervals
Results
4.3s3339×body1280valid
2.3s2472×body640valid
2.0s1499×body1280nan
1.2s1222×body640nan
867.0ms1297×body320valid
842.0ms3886×body80overflowed
419.0ms595×body320nan
277.0ms629×body160valid
133.0ms302×body160nan
77.0ms356×body80valid
53.0ms285×body80nan

Profiling

Loading profile data...