Details

sample920.0ms

Algorithm

intervals

Results

355.0ms	126×	body	10240	exit
217.0ms	107×	body	1280	valid
79.0ms	78×	body	640	valid
51.0ms	43×	body	1280	nan
36.0ms	45×	body	320	valid
35.0ms	40×	body	640	nan
15.0ms	23×	body	320	nan
9.0ms	16×	body	160	valid
7.0ms	15×	body	160	nan
2.0ms	11×	body	80	valid
1.0ms	6×	body	80	nan

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5032
3	2323
2	422
1	140
0	55

prune41.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize142.0ms

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))))
0.5b	(* (/ (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))

rewrite1.8m

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`
9×	`pow1` `exp-sum`
7×	`cbrt-unprod`
6×	`difference-of-squares`
5×	`unpow-prod-down` `div-exp`
4×	`expm1-log1p-u` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l` `distribute-lft-out--` `add-log-exp`
3×	`pow-to-exp` `cbrt-undiv` `pow-exp`
2×	`associate-+r-` `sqrt-pow1` `exp-diff` `pow-prod-down` `associate-/r/` `*-commutative` `div-inv` `unswap-sqr`
1×	`distribute-rgt-in` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `pow1/2` `associate--r-` `sqr-pow`

Counts

4 → 622

Calls

4 calls:

57.8s	(* (* (/ (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))))
50.1s	(* (/ (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))))
80.0ms	(/ (sqrt (* PI 2)) (exp (+ 0.5 (- z -6))))
15.0ms	(sqrt (* PI 2))

series1.3s

Counts

4 → 10

Calls

4 calls:

760.0ms	(* (* (/ (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))))
325.0ms	(* (/ (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))))
167.0ms	(/ (sqrt (* PI 2)) (exp (+ 0.5 (- z -6))))
0.0ms	(sqrt (* PI 2))

simplify8.7s

Counts

632 → 632

Iterations

Iter	Nodes
done	5001
0	1809

prune17.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize176.0ms

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))) (pow (+ 0.5 (- z -6)) 0.5))
0.5b	(* (/ (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))

rewrite2.5m

Algorithm

rewrite-expression-head

Rules

1848×	`frac-add`
510×	`flip3-+` `flip-+`
451×	`associate-*l/`
371×	`frac-times`
223×	`associate-*r/`
162×	`*-un-lft-identity`
150×	`pow-sub`
111×	`distribute-lft-out`
95×	`add-exp-log`
77×	`prod-exp`
34×	`associate-r`
33×	`times-frac`
31×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`add-cbrt-cube`
22×	`associate-l`
19×	`pow-to-exp` `pow-exp`
11×	`div-exp` `cbrt-unprod`
10×	`sqrt-prod`
9×	`pow1` `exp-sum`
5×	`unpow-prod-down`
4×	`expm1-log1p-u` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`cbrt-undiv`
2×	`associate-+r-` `sqrt-pow1` `exp-diff` `pow-prod-down` `associate-/r/` `*-commutative` `div-inv` `unswap-sqr`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `pow1/2` `distribute-lft-out--` `sqr-pow`

Counts

4 → 623

Calls

4 calls:

1.9m	(* (* (* (/ (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))) (pow (+ 0.5 (- z -6)) 0.5))
33.0s	(* (/ (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))))
69.0ms	(/ (sqrt (* PI 2)) (exp (+ 0.5 (- z -6))))
4.0ms	(sqrt (* PI 2))

series973.0ms

Counts

4 → 10

Calls

4 calls:

634.0ms	(* (* (* (/ (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))) (pow (+ 0.5 (- z -6)) 0.5))
238.0ms	(* (/ (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))))
100.0ms	(/ (sqrt (* PI 2)) (exp (+ 0.5 (- z -6))))
0.0ms	(sqrt (* PI 2))

simplify6.7s

Counts

633 → 633

Iterations

Iter	Nodes
done	5000
0	1934

prune11.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize108.0ms

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))) (pow (+ 0.5 (- z -6)) 0.5))
0.5b	(* (* (/ (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))

rewrite2.4m

Algorithm

rewrite-expression-head

Rules

1848×	`frac-add`
677×	`associate-*l/`
510×	`flip3-+` `flip-+`
371×	`frac-times`
223×	`associate-*r/`
153×	`*-un-lft-identity`
150×	`pow-sub`
128×	`add-exp-log`
127×	`prod-exp`
111×	`distribute-lft-out`
38×	`add-cbrt-cube`
37×	`associate-r`
25×	`pow-to-exp` `pow-exp`
22×	`add-sqr-sqrt` `associate-l`
21×	`cbrt-unprod`
17×	`times-frac` `add-cube-cbrt`
14×	`pow1`
11×	`div-exp`
5×	`unpow-prod-down` `pow-prod-down` `sqrt-prod`
4×	`expm1-log1p-u` `exp-sum` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `*-commutative`
2×	`sqrt-pow1` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `pow1/2` `div-inv` `distribute-lft-out--` `sqr-pow`

Counts

4 → 616

Calls

4 calls:

1.9m	(* (* (* (* (/ (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))) (pow (+ 0.5 (- z -6)) 0.5))
24.1s	(* (* (/ (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))))
77.0ms	(* (/ (sqrt (* PI 2)) (exp (+ 0.5 z))) (exp -6))
4.0ms	(sqrt (* PI 2))

series1.3s

Counts

4 → 10

Calls

4 calls:

763.0ms	(* (* (* (* (/ (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)))) (pow (+ 0.5 (- z -6)) (- z 1))) (pow (+ 0.5 (- z -6)) 0.5))
318.0ms	(* (* (/ (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))))
171.0ms	(* (/ (sqrt (* PI 2)) (exp (+ 0.5 z))) (exp -6))
0.0ms	(sqrt (* PI 2))

simplify6.5s

Counts

626 → 626

Iterations

Iter	Nodes
done	5000
0	1945

prune12.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize106.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (sqrt (* PI 2)) (exp (+ 0.5 (- z -6))))
1.0b	(/ (sqrt (* PI 2)) (exp (+ 0.5 (- z -6))))
1.0b	(sqrt (* PI 2))
1.0b	(sqrt (* PI 2))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

32×	`times-frac`
24×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
12×	`sqrt-prod`
10×	`pow1` `exp-sum`
8×	`associate-/r` `add-cbrt-cube` `associate-/l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `sqrt-pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `clear-num` `associate-+r-` `frac-2neg` `pow1/2` `exp-diff` `div-exp` `pow-prod-down` `associate-/r/` `div-inv`

Counts

4 → 108

Calls

4 calls:

61.0ms	(/ (sqrt (* PI 2)) (exp (+ 0.5 (- z -6))))
61.0ms	(/ (sqrt (* PI 2)) (exp (+ 0.5 (- z -6))))
4.0ms	(sqrt (* PI 2))
4.0ms	(sqrt (* PI 2))

series189.0ms

Counts

4 → 8

Calls

4 calls:

96.0ms	(/ (sqrt (* PI 2)) (exp (+ 0.5 (- z -6))))
92.0ms	(/ (sqrt (* PI 2)) (exp (+ 0.5 (- z -6))))
0.0ms	(sqrt (* PI 2))
0.0ms	(sqrt (* PI 2))

simplify1.2s

Counts

116 → 116

Iterations

Iter	Nodes
done	5104
3	2207
2	597
1	201
0	106

prune1.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes133.0ms

Accuracy

0% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch0.0ms

simplify14.0ms

Iterations

Iter	Nodes
done	81
1	81
0	58

end0.0ms

sample21.7s

Algorithm

intervals

Results

8.1s	3699×	body	10240	exit
5.2s	3331×	body	1280	valid
2.8s	2531×	body	640	valid
1.9s	1468×	body	1280	nan
1.4s	1196×	body	640	nan
1.0s	1251×	body	320	valid
392.0ms	598×	body	320	nan
285.0ms	637×	body	160	valid
141.0ms	370×	body	160	nan
113.0ms	339×	body	80	valid
75.0ms	275×	body	80	nan