Details

Time bar (total: 33.7s)

sample432.0ms

Algorithm
intervals
Results
149.0ms117×body1280valid
78.0ms77×body640valid
64.0ms50×body1280nan
30.0ms31×body640nan
30.0ms42×body320valid
26.0ms126×body80overflowed
20.0ms22×body320nan
7.0ms16×body160valid
5.0ms11×body160nan
3.0ms13×body80nan
2.0ms8×body80valid

simplify71.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
013348
145348
2276947
3500247

prune18.0ms

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: 62.3b

Counts
2 → 2

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b
(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))
4.3b
(+ (- 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)))
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))
7.0ms
(+ (- z 1.0) 1.0)

series21.0ms

Counts
4 → 10
Calls
4 calls:
2.0ms
(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
17.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms
(sqrt (* PI 2.0))
1.0ms
(+ (- z 1.0) 1.0)

simplify55.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0552704
12036643
25001638

prune490.0ms

Filtered
100 candidates to 68 candidates (32.0%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New973100
Fresh101
Picked101
Done000
Total993102

Merged error: 0.4b

Counts
102 → 3

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b
(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))

rewrite199.0ms

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:
10.0ms
(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
144.0ms
(* (* (* (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))

series58.0ms

Counts
4 → 10
Calls
4 calls:
2.0ms
(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
39.0ms
(* (* (* (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))))
17.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms
(sqrt (* PI 2.0))

simplify285.0ms

Algorithm
egg-herbie
Counts
233 → 233
Iterations

Useful iterations: 1 (61.0ms)

IterNodesCost
0374523936
1500123816

prune4.7s

Filtered
233 candidates to 140 candidates (39.9%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2267233
Fresh112
Picked101
Done000
Total2288236

Merged error: 0b

Counts
236 → 8

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
0.3b
(* (* (* (* (pow (+ z 6.5) (- z 0.5)) (sqrt 2.0)) (sqrt PI)) (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
(* (* (pow (+ z 6.5) (- z 0.5)) (sqrt 2.0)) (sqrt PI))
1.0b
(sqrt PI)

rewrite188.0ms

Algorithm
rewrite-expression-head
Rules
392×frac-add
130×frac-times
127×associate-*l/
73×*-un-lft-identity
56×flip3-+ flip-+
52×exp-neg pow-sub
50×associate-*r/
46×distribute-lft-out
35×neg-sub0 exp-diff
32×add-exp-log
25×prod-exp
23×add-cbrt-cube
17×associate-*r* un-div-inv
16×pow1 exp-prod
15×add-log-exp
13×cbrt-unprod
12×add-sqr-sqrt
11×add-cube-cbrt
7×pow-prod-down
6×distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod
5×sum-log rem-exp-log
4×neg-log
2×pow-to-exp associate-*l* pow-exp *-commutative distribute-lft-out--
1×distribute-rgt-in neg-mul-1 rem-sqrt-square distribute-neg-in distribute-lft-in sqrt-pow1 pow1/2 diff-log exp-sum
Counts
4 → 220
Calls
4 calls:
10.0ms
(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
142.0ms
(* (* (* (* (pow (+ z 6.5) (- z 0.5)) (sqrt 2.0)) (sqrt PI)) (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))))
10.0ms
(* (* (pow (+ z 6.5) (- z 0.5)) (sqrt 2.0)) (sqrt PI))
1.0ms
(sqrt PI)

series59.0ms

Counts
4 → 10
Calls
4 calls:
2.0ms
(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
39.0ms
(* (* (* (* (pow (+ z 6.5) (- z 0.5)) (sqrt 2.0)) (sqrt PI)) (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))))
17.0ms
(* (* (pow (+ z 6.5) (- z 0.5)) (sqrt 2.0)) (sqrt PI))
0.0ms
(sqrt PI)

simplify287.0ms

Algorithm
egg-herbie
Counts
230 → 230
Iterations

Useful iterations: 1 (61.0ms)

IterNodesCost
0375623599
1500223498

prune4.3s

Filtered
230 candidates to 135 candidates (41.3%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New2282230
Fresh257
Picked101
Done000
Total2317238

Merged error: 0b

Counts
238 → 7

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
0.3b
(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z)) (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))))
0.4b
(/ (* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z)) (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)))) (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)))
1.0b
(sqrt (* PI 2.0))

rewrite336.0ms

Algorithm
rewrite-expression-head
Rules
448×frac-add
100×associate-*r/
96×frac-times
92×*-un-lft-identity
69×exp-neg
67×add-exp-log associate-/l/
64×flip3-+ flip-+
56×distribute-lft-out
48×prod-exp
35×neg-sub0 exp-diff
34×un-div-inv
27×add-cbrt-cube
18×div-exp
16×exp-prod
15×add-log-exp
12×pow1 add-sqr-sqrt add-cube-cbrt unpow-prod-down times-frac associate-/r* cbrt-unprod
11×associate-*r*
10×pow-to-exp pow-exp
6×distribute-lft-neg-in distribute-rgt-neg-in associate-*l/
5×sum-log rem-exp-log
4×cbrt-undiv unpow-prod-up pow-prod-down neg-log distribute-lft-out--
2×sub-neg sqrt-pow1 sqr-pow
1×distribute-rgt-in neg-mul-1 distribute-neg-in frac-2neg distribute-lft-in pow1/2 diff-log associate-*l* exp-sum clear-num sqrt-prod associate-/r/ *-commutative div-inv associate-/l* pow-sub
Counts
4 → 266
Calls
4 calls:
10.0ms
(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
142.0ms
(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z)) (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))))
154.0ms
(/ (* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z)) (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)))) (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)))
2.0ms
(sqrt (* PI 2.0))

series94.0ms

Counts
4 → 10
Calls
4 calls:
2.0ms
(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
34.0ms
(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z)) (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))))
58.0ms
(/ (* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z)) (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)))) (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)))
0.0ms
(sqrt (* PI 2.0))

simplify251.0ms

Algorithm
egg-herbie
Counts
276 → 276
Iterations

Useful iterations: 1 (58.0ms)

IterNodesCost
0343720629
1500220137

prune8.7s

Filtered
276 candidates to 179 candidates (35.1%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2760276
Fresh066
Picked011
Done000
Total2767283

Merged error: 0b

Counts
283 → 7

regimes88.0ms

Accuracy

0% (1.0b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 1.1b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07950
18450
28450

end0.0ms

sample12.9s

Algorithm
intervals
Results
4.3s3370×body1280valid
2.3s2417×body640valid
2.0s1507×body1280nan
1.2s1224×body640nan
898.0ms1316×body320valid
832.0ms3854×body80overflowed
441.0ms609×body320nan
288.0ms650×body160valid
146.0ms311×body160nan
71.0ms323×body80valid
61.0ms307×body80nan

Profiling

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