Details

Time bar (total: 22.8s)

sample356.0ms

Algorithm
intervals
Results
117.0ms118×body1280valid
59.0ms70×body640valid
48.0ms47×body1280nan
26.0ms33×body640nan
20.0ms122×body80overflowed
19.0ms35×body320valid
8.0ms14×body320nan
6.0ms19×body160valid
3.0ms16×body80valid
3.0ms7×body160nan
2.0ms12×body80nan

simplify73.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
013348
145348
2276947
3500247

prune31.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 60.1b

Counts
2 → 2

localize47.0ms

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))
5.7b
(+ (- z 1.0) 1.0)

rewrite43.0ms

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)

series298.0ms

Counts
4 → 10
Calls
4 calls:
16.0ms
(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
272.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms
(sqrt (* PI 2.0))
9.0ms
(+ (- z 1.0) 1.0)

simplify58.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0552704
12036643
25001638

prune746.0ms

Filtered
100 candidates to 68 candidates (68.0%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New955100
Fresh101
Picked101
Done000
Total975102

Merged error: 0.6b

Counts
102 → 5

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite213.0ms

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)))
154.0ms
(* (* (* (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))

series901.0ms

Counts
4 → 10
Calls
4 calls:
17.0ms
(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
603.0ms
(* (* (* (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))))
281.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms
(sqrt (* PI 2.0))

simplify294.0ms

Algorithm
egg-herbie
Counts
233 → 233
Iterations

Useful iterations: 1 (63.0ms)

IterNodesCost
0374523936
1500123816

prune1.9s

Filtered
233 candidates to 140 candidates (60.1%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New22211233
Fresh404
Picked101
Done000
Total22711238

Merged error: 0.0b

Counts
238 → 11

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
0.5b
(* (* (* (* (sqrt 2.0) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (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
(* (* (sqrt 2.0) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (sqrt PI))
1.0b
(sqrt PI)

rewrite207.0ms

Algorithm
rewrite-expression-head
Rules
560×frac-add
212×frac-times
173×exp-neg
147×associate-*l/
104×mul-1-neg
102×associate-*r/
80×flip3-+ flip-+
73×*-un-lft-identity
69×un-div-inv
52×neg-sub0 exp-diff
46×distribute-lft-out
24×pow1
23×add-cbrt-cube
18×add-exp-log
17×associate-*r*
16×exp-prod
15×add-log-exp
13×pow-prod-down prod-exp cbrt-unprod
12×add-sqr-sqrt
11×add-cube-cbrt
6×distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod
5×sum-log rem-exp-log
4×neg-log
2×associate-*l* *-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 → 270
Calls
4 calls:
16.0ms
(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
147.0ms
(* (* (* (* (sqrt 2.0) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (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))))
12.0ms
(* (* (sqrt 2.0) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (sqrt PI))
1.0ms
(sqrt PI)

series941.0ms

Counts
4 → 10
Calls
4 calls:
22.0ms
(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
628.0ms
(* (* (* (* (sqrt 2.0) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (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))))
291.0ms
(* (* (sqrt 2.0) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (sqrt PI))
0.0ms
(sqrt PI)

simplify377.0ms

Algorithm
egg-herbie
Counts
280 → 280
Iterations

Useful iterations: 1 (64.0ms)

IterNodesCost
0415533219
1500333106

prune2.0s

Filtered
280 candidates to 135 candidates (48.2%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2791280
Fresh2810
Picked011
Done000
Total28110291

Merged error: 0.0b

Counts
291 → 10

localize52.0ms

Local error

Found 4 expressions with local error:

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)))))
0.6b
(* (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))

rewrite527.0ms

Algorithm
rewrite-expression-head
Rules
504×frac-add
150×associate-*r/
146×frac-times
72×flip3-+ flip-+
62×*-un-lft-identity
52×associate-+l- pow-sub
51×neg-sub0 exp-neg exp-diff
41×distribute-lft-out
30×add-exp-log
23×associate-*r*
22×prod-exp
20×add-cbrt-cube
16×add-sqr-sqrt
14×pow1
10×cbrt-unprod
9×add-cube-cbrt associate-*l*
7×unpow-prod-down associate-*l/
5×distribute-rgt-in distribute-lft-in pow-prod-down
4×add-log-exp unswap-sqr
3×pow-to-exp pow-exp *-commutative
2×sqrt-pow1 sqrt-prod sqr-pow
1×unpow-prod-up distribute-neg-in pow1/2 exp-sum distribute-lft-out--
Counts
4 → 250
Calls
4 calls:
156.0ms
(* (* (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)))))
325.0ms
(* (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))

series1.0s

Counts
4 → 10
Calls
4 calls:
577.0ms
(* (* (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)))))
189.0ms
(* (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))))
275.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms
(sqrt (* PI 2.0))

simplify342.0ms

Algorithm
egg-herbie
Counts
260 → 260
Iterations

Useful iterations: 1 (62.0ms)

IterNodesCost
0355828660
1500128457

prune2.0s

Filtered
260 candidates to 170 candidates (65.4%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New2591260
Fresh088
Picked011
Done011
Total25911270

Merged error: 0.0b

Counts
270 → 11

regimes198.0ms

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
08847
19947
29947

end0.0ms

sample10.1s

Algorithm
intervals
Results
3.4s3383×body1280valid
1.8s2455×body640valid
1.6s1511×body1280nan
952.0ms1216×body640nan
641.0ms1257×body320valid
628.0ms3854×body80overflowed
345.0ms611×body320nan
220.0ms659×body160valid
111.0ms315×body160nan
57.0ms333×body80valid
42.0ms291×body80nan

Profiling

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