Details

Time bar (total: 40.8s)

sample880.0ms

Algorithm
intervals
Results
297.0ms123×body1280valid
189.0ms82×body640valid
120.0ms44×body1280nan
79.0ms38×body640nan
57.0ms123×body80overflowed
38.0ms23×body320nan
36.0ms30×body320valid
12.0ms15×body160valid
10.0ms13×body160nan
3.0ms9×body80valid
1.0ms4×body80nan

simplify116.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
013348
145348
2276947
3500247

prune32.0ms

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: 62.0b

Counts
2 → 2

localize96.0ms

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))
3.9b
(+ (- z 1.0) 1.0)

rewrite69.0ms

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:
16.0ms
(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
30.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
4.0ms
(sqrt (* PI 2.0))
15.0ms
(+ (- z 1.0) 1.0)

series35.0ms

Counts
4 → 10
Calls
4 calls:
3.0ms
(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
29.0ms
(* (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)

simplify97.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
0552704
12036643
25001638

prune876.0ms

Filtered
100 candidates to 68 candidates (32.0%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New964100
Fresh101
Picked101
Done000
Total984102

Merged error: 0.8b

Counts
102 → 4

localize86.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
0.8b
(* (* (* (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))

rewrite365.0ms

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:
18.0ms
(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
275.0ms
(* (* (* (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))))
31.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
4.0ms
(sqrt (* PI 2.0))

series114.0ms

Counts
4 → 10
Calls
4 calls:
4.0ms
(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
79.0ms
(* (* (* (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))))
31.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms
(sqrt (* PI 2.0))

simplify607.0ms

Algorithm
egg-herbie
Counts
233 → 233
Iterations

Useful iterations: 1 (110.0ms)

IterNodesCost
0374523930
1500223816

prune5.4s

Filtered
233 candidates to 140 candidates (39.9%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2258233
Fresh303
Picked101
Done000
Total2298237

Merged error: 0b

Counts
237 → 8

localize83.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
1.0b
(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
1.0b
(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
1.0b
(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
216×add-sqr-sqrt
208×unpow-prod-down
132×times-frac
116×associate-*l*
96×add-exp-log *-un-lft-identity
72×add-cube-cbrt unswap-sqr
52×pow-exp
48×prod-exp sqrt-prod
40×sqr-pow
24×div-exp associate-*r*
16×pow-to-exp
12×rec-exp 1-exp add-cbrt-cube
4×pow1 *-commutative cbrt-unprod div-inv add-log-exp
Counts
4 → 296
Calls
4 calls:
14.0ms
(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
17.0ms
(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
14.0ms
(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
14.0ms
(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
0.0ms
(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
0.0ms
(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
0.0ms
(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

simplify82.0ms

Algorithm
egg-herbie
Counts
300 → 300
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04352848
115332748
250012604

prune8.1s

Filtered
300 candidates to 177 candidates (41.0%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2991300
Fresh167
Picked011
Done000
Total3008308

Merged error: 0b

Counts
308 → 8

localize70.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
0.8b
(* (* (* (* (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)

rewrite273.0ms

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)))
209.0ms
(* (* (* (* (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))))
21.0ms
(* (* (pow (+ z 6.5) (- z 0.5)) (sqrt 2.0)) (sqrt PI))
2.0ms
(sqrt PI)

series87.0ms

Counts
4 → 10
Calls
4 calls:
2.0ms
(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
66.0ms
(* (* (* (* (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))))
18.0ms
(* (* (pow (+ z 6.5) (- z 0.5)) (sqrt 2.0)) (sqrt PI))
0.0ms
(sqrt PI)

simplify428.0ms

Algorithm
egg-herbie
Counts
230 → 230
Iterations

Useful iterations: 1 (78.0ms)

IterNodesCost
0375623599
1500223498

prune5.3s

Filtered
230 candidates to 135 candidates (41.3%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2282230
Fresh246
Picked011
Done011
Total2308238

Merged error: 0b

Counts
238 → 8

regimes191.0ms

Accuracy

0% (1.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08894
19294
29294

end0.0ms

sample17.3s

Algorithm
intervals
Results
5.7s3302×body1280valid
3.1s2518×body640valid
2.6s1508×body1280nan
1.7s1275×body640nan
1.2s1277×body320valid
1.1s3865×body80overflowed
578.0ms592×body320nan
370.0ms639×body160valid
194.0ms308×body160nan
103.0ms350×body80valid
81.0ms313×body80nan

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