Details

Time bar (total: 4.5m)

sample1.4s

Algorithm
intervals
Results
451.0ms111×body10240exit
293.0ms104×body1280valid
205.0ms74×body640valid
116.0ms47×body640nan
74.0ms34×body1280nan
73.0ms49×body320valid
21.0ms16×body320nan
17.0ms19×body160valid
7.0ms15×body80valid
6.0msbody160nan
3.0msbody80nan

simplify3.2s

Counts
1 → 1
Iterations
IterNodes
done5032
32323
2422
1140
055

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize185.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (/ (sqrt (* PI 2)) (exp (+ 0.5 (- z -6)))) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z)))) (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))))
0.7b
(* (/ (sqrt (* PI 2)) (exp (+ 0.5 (- z -6)))) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z))))
1.0b
(/ (sqrt (* PI 2)) (exp (+ 0.5 (- z -6))))
1.0b
(sqrt (* PI 2))

rewrite51.4s

Algorithm
rewrite-expression-head
Rules
1848×frac-add
510×flip3-+ flip-+
371×frac-times
223×associate-*r/
180×*-un-lft-identity
152×associate-*l/
150×pow-sub
111×distribute-lft-out
55×associate-*r*
49×add-sqr-sqrt
35×add-cube-cbrt
33×times-frac
30×add-exp-log
22×associate-*l*
21×unpow-prod-up
20×add-cbrt-cube
18×prod-diff
17×prod-exp
10×sqrt-prod
pow1 exp-sum
cbrt-unprod
difference-of-squares
unpow-prod-down div-exp
expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u associate-/l* distribute-lft-out-- add-log-exp
pow-to-exp cbrt-undiv pow-exp
associate-+r- sqrt-pow1 exp-diff pow-prod-down associate-/r/ *-commutative div-inv unswap-sqr
distribute-rgt-in clear-num sub-neg frac-2neg distribute-lft-in pow1/2 associate--r- sqr-pow
Counts
4 → 622
Calls
4 calls:
27.7s
(* (* (/ (sqrt (* PI 2)) (exp (+ 0.5 (- z -6)))) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z)))) (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))))
23.6s
(* (/ (sqrt (* PI 2)) (exp (+ 0.5 (- z -6)))) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z))))
72.0ms
(/ (sqrt (* PI 2)) (exp (+ 0.5 (- z -6))))
5.0ms
(sqrt (* PI 2))

series1.2s

Counts
4 → 10
Calls
4 calls:
755.0ms
(* (* (/ (sqrt (* PI 2)) (exp (+ 0.5 (- z -6)))) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z)))) (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))))
352.0ms
(* (/ (sqrt (* PI 2)) (exp (+ 0.5 (- z -6)))) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z))))
134.0ms
(/ (sqrt (* PI 2)) (exp (+ 0.5 (- z -6))))
0.0ms
(sqrt (* PI 2))

simplify8.9s

Counts
632 → 632
Iterations
IterNodes
done5001
01809

prune17.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize146.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (* (/ (sqrt (* PI 2)) (exp (+ 0.5 z))) (exp -6)) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z)))) (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))))
0.7b
(* (* (/ (sqrt (* PI 2)) (exp (+ 0.5 z))) (exp -6)) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z))))
1.0b
(* (/ (sqrt (* PI 2)) (exp (+ 0.5 z))) (exp -6))
1.0b
(sqrt (* PI 2))

rewrite46.7s

Algorithm
rewrite-expression-head
Rules
1848×frac-add
510×flip3-+ flip-+
378×associate-*l/
371×frac-times
223×associate-*r/
171×*-un-lft-identity
150×pow-sub
111×distribute-lft-out
58×associate-*r*
41×add-exp-log
40×add-sqr-sqrt
34×prod-exp
32×add-cbrt-cube
26×add-cube-cbrt
22×associate-*l*
21×unpow-prod-up
18×prod-diff
17×times-frac
16×cbrt-unprod
14×pow1
difference-of-squares
unpow-prod-down div-exp pow-prod-down sqrt-prod
expm1-log1p-u pow-to-exp exp-sum pow-exp insert-posit16 log1p-expm1-u distribute-lft-out-- add-log-exp
cbrt-undiv *-commutative
sqrt-pow1 unswap-sqr
distribute-rgt-in sub-neg distribute-lft-in pow1/2 div-inv associate--r- sqr-pow
Counts
4 → 609
Calls
4 calls:
27.5s
(* (* (* (/ (sqrt (* PI 2)) (exp (+ 0.5 z))) (exp -6)) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z)))) (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))))
19.1s
(* (* (/ (sqrt (* PI 2)) (exp (+ 0.5 z))) (exp -6)) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z))))
82.0ms
(* (/ (sqrt (* PI 2)) (exp (+ 0.5 z))) (exp -6))
7.0ms
(sqrt (* PI 2))

series2.1s

Counts
4 → 10
Calls
4 calls:
1.1s
(* (* (* (/ (sqrt (* PI 2)) (exp (+ 0.5 z))) (exp -6)) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z)))) (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))))
796.0ms
(* (* (/ (sqrt (* PI 2)) (exp (+ 0.5 z))) (exp -6)) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z))))
241.0ms
(* (/ (sqrt (* PI 2)) (exp (+ 0.5 z))) (exp -6))
0.0ms
(sqrt (* PI 2))

simplify8.5s

Counts
619 → 619
Iterations
IterNodes
done5001
01816

prune18.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize223.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (* (* (sqrt (* PI 2)) (exp -6)) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z)))) (pow (+ 0.5 (- z -6)) z)) (* (exp (+ 0.5 z)) (pow (+ 0.5 (- z -6)) (- 1 0.5))))
0.8b
(* (* (sqrt (* PI 2)) (exp -6)) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z))))
1.0b
(sqrt (* PI 2))
1.0b
(* (sqrt (* PI 2)) (exp -6))

rewrite32.9s

Algorithm
rewrite-expression-head
Rules
616×frac-add
170×flip3-+ flip-+
149×associate-*r/
138×*-un-lft-identity
127×add-exp-log
109×distribute-lft-out
106×prod-exp
74×associate-*l/ associate-/l/
43×add-cbrt-cube
40×div-exp
28×associate-*r*
22×pow-to-exp pow-exp
20×cbrt-unprod
14×pow1
add-sqr-sqrt
cbrt-undiv
add-cube-cbrt
associate-*l* pow-prod-down
expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
sqrt-pow1 *-commutative sqrt-prod
distribute-rgt-in clear-num associate-/r* frac-2neg distribute-lft-in times-frac pow1/2 associate-/r/ div-inv associate-/l* pow-sub unswap-sqr
Counts
4 → 294
Calls
4 calls:
17.3s
(/ (* (* (* (sqrt (* PI 2)) (exp -6)) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z)))) (pow (+ 0.5 (- z -6)) z)) (* (exp (+ 0.5 z)) (pow (+ 0.5 (- z -6)) (- 1 0.5))))
15.5s
(* (* (sqrt (* PI 2)) (exp -6)) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z))))
8.0ms
(sqrt (* PI 2))
35.0ms
(* (sqrt (* PI 2)) (exp -6))

series1.2s

Counts
4 → 8
Calls
4 calls:
897.0ms
(/ (* (* (* (sqrt (* PI 2)) (exp -6)) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z)))) (pow (+ 0.5 (- z -6)) z)) (* (exp (+ 0.5 z)) (pow (+ 0.5 (- z -6)) (- 1 0.5))))
283.0ms
(* (* (sqrt (* PI 2)) (exp -6)) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z))))
0.0ms
(sqrt (* PI 2))
0.0ms
(* (sqrt (* PI 2)) (exp -6))

simplify5.2s

Counts
302 → 302
Iterations
IterNodes
done5001
01221

prune4.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize121.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (exp (+ 0.5 z)) (pow (+ 0.5 (- z -6)) (- 1 0.5))) (* (* (* (sqrt (* PI 2)) (exp -6)) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z)))) (pow (+ 0.5 (- z -6)) z)))
0.8b
(* (* (sqrt (* PI 2)) (exp -6)) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z))))
1.0b
(sqrt (* PI 2))
1.0b
(* (sqrt (* PI 2)) (exp -6))

rewrite25.6s

Algorithm
rewrite-expression-head
Rules
616×frac-add
170×flip3-+ flip-+
149×associate-*r/
138×*-un-lft-identity
127×add-exp-log
109×distribute-lft-out
106×prod-exp
74×associate-*l/ associate-/r/
43×add-cbrt-cube
40×div-exp
28×associate-*r*
22×pow-to-exp pow-exp
20×cbrt-unprod
14×pow1
add-sqr-sqrt
cbrt-undiv
add-cube-cbrt
associate-*l* pow-prod-down
expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
sqrt-pow1 *-commutative sqrt-prod
distribute-rgt-in clear-num associate-/r* frac-2neg distribute-lft-in times-frac pow1/2 div-inv associate-/l* pow-sub unswap-sqr associate-/l/
Counts
4 → 294
Calls
4 calls:
13.4s
(/ (* (exp (+ 0.5 z)) (pow (+ 0.5 (- z -6)) (- 1 0.5))) (* (* (* (sqrt (* PI 2)) (exp -6)) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z)))) (pow (+ 0.5 (- z -6)) z)))
12.2s
(* (* (sqrt (* PI 2)) (exp -6)) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z))))
4.0ms
(sqrt (* PI 2))
17.0ms
(* (sqrt (* PI 2)) (exp -6))

series1.1s

Counts
4 → 8
Calls
4 calls:
800.0ms
(/ (* (exp (+ 0.5 z)) (pow (+ 0.5 (- z -6)) (- 1 0.5))) (* (* (* (sqrt (* PI 2)) (exp -6)) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z)))) (pow (+ 0.5 (- z -6)) z)))
286.0ms
(* (* (sqrt (* PI 2)) (exp -6)) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ 1 z))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ 3 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (/ 1.5056327351493116e-07 (+ 7 z)))) (/ 9.984369578019572e-06 (+ 6 z))))
0.0ms
(sqrt (* PI 2))
0.0ms
(* (sqrt (* PI 2)) (exp -6))

simplify5.8s

Counts
302 → 302
Iterations
IterNodes
done5000
01214

prune5.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes99.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

bsearch0.0ms

simplify15.0ms

Iterations
IterNodes
done81
181
058

end0.0ms

sample31.2s

Algorithm
intervals
Results
10.6s3700×body10240exit
9.1s3375×body1280valid
3.7s2446×body640valid
2.8s1425×body1280nan
2.0s1151×body640nan
1.3s1259×body320valid
566.0ms596×body320nan
516.0ms666×body160valid
236.0ms306×body160nan
124.0ms342×body80valid
104.0ms303×body80nan