Details

sample1.9s

Algorithm

intervals

Results

594.0ms	83×	body	640	valid
535.0ms	136×	body	10240	exit
289.0ms	100×	body	1280	valid
194.0ms	70×	body	1280	nan
71.0ms	39×	body	640	nan
60.0ms	44×	body	320	valid
53.0ms	24×	body	320	nan
17.0ms	18×	body	160	valid
5.0ms	11×	body	80	valid
4.0ms	5×	body	160	nan
4.0ms	9×	body	80	nan

simplify820.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	2155
2	413
1	140
0	55

prune62.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.0b

localize183.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
1.0b	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
1.0b	(sqrt (* PI 2))
1.0b	(sqrt (* PI 2))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
22×	`associate-l`
20×	`add-sqr-sqrt`
14×	`unpow-prod-down` `add-exp-log`
10×	`pow1` `add-cube-cbrt` `distribute-lft-out`
8×	`add-cbrt-cube` `associate-r`
6×	`prod-exp` `unswap-sqr`
4×	`expm1-log1p-u` `sqrt-pow1` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `unpow-prod-up` `pow1/2` `pow-prod-down` `associate-l/` `pow-exp` `-commutative` `associate-+l-` `cbrt-unprod` `distribute-lft-out--` `pow-sub`

Counts

4 → 96

Calls

4 calls:

561.0ms	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
555.0ms	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
8.0ms	(sqrt (* PI 2))
8.0ms	(sqrt (* PI 2))

series750.0ms

Counts

4 → 8

Calls

4 calls:

389.0ms	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
361.0ms	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
0.0ms	(sqrt (* PI 2))
0.0ms	(sqrt (* PI 2))

simplify3.1s

Counts

104 → 104

Iterations

Iter	Nodes
3	6551
2	1312
1	400
0	162

prune3.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize207.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (* PI 2))
1.0b	(sqrt (* PI 2))
1.0b	(sqrt (* PI 2))
1.0b	(sqrt (* PI 2))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
8×	`sqrt-pow1`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cbrt-cube` `pow1/2` `pow-prod-down` `add-exp-log` `add-cube-cbrt` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 56

Calls

4 calls:

4.0ms	(sqrt (* PI 2))
4.0ms	(sqrt (* PI 2))
4.0ms	(sqrt (* PI 2))
8.0ms	(sqrt (* PI 2))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(sqrt (* PI 2))
0.0ms	(sqrt (* PI 2))
0.0ms	(sqrt (* PI 2))
0.0ms	(sqrt (* PI 2))

simplify7.6s

Counts

60 → 60

Iterations

Iter	Nodes
7	5842
6	1977
5	821
4	374
3	186
2	95
1	49
0	29

prune2.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.5b

localize153.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5)))) (+ (/ -0.13857109526572012 (- z -5)) (+ (+ (/ 12.507343278686905 (+ z 4)) (+ (+ (+ (/ -1259.1392167224028 (+ 1 z)) (/ 771.3234287776531 (+ z 2))) 0.9999999999998099) (+ (/ 676.5203681218851 z) (/ -176.6150291621406 (+ z 3))))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))))))
0.7b	(/ (* (* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5)))) (+ (/ -0.13857109526572012 (- z -5)) (+ (+ (/ 12.507343278686905 (+ z 4)) (+ (+ (+ (/ -1259.1392167224028 (+ 1 z)) (/ 771.3234287776531 (+ z 2))) 0.9999999999998099) (+ (/ 676.5203681218851 z) (/ -176.6150291621406 (+ z 3))))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7)))))) (exp (+ 0.5 (+ z 6))))
1.0b	(* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5))))
1.0b	(sqrt (* PI 2))

rewrite1.4m

Algorithm

rewrite-expression-head

Rules

240×	`frac-add`
117×	`*-un-lft-identity`
88×	`distribute-lft-out`
68×	`associate-*r/`
66×	`flip3-+` `flip-+`
34×	`associate-/l/`
30×	`associate-r` `add-exp-log`
20×	`add-cbrt-cube`
17×	`prod-exp`
15×	`add-sqr-sqrt`
10×	`add-cube-cbrt`
9×	`pow1`
7×	`cbrt-unprod`
6×	`unpow-prod-down`
5×	`div-exp` `associate-l`
4×	`expm1-log1p-u` `associate-/r*` `times-frac` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `cbrt-undiv` `pow-exp` `unswap-sqr`
2×	`sqrt-pow1` `exp-sum` `pow-prod-down` `*-commutative` `sqrt-prod` `sqr-pow`
1×	`distribute-rgt-in` `unpow-prod-up` `clear-num` `frac-2neg` `distribute-lft-in` `pow1/2` `div-inv` `associate-/l*`

Counts

4 → 185

Calls

4 calls:

1.0m	(* (* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5)))) (+ (/ -0.13857109526572012 (- z -5)) (+ (+ (/ 12.507343278686905 (+ z 4)) (+ (+ (+ (/ -1259.1392167224028 (+ 1 z)) (/ 771.3234287776531 (+ z 2))) 0.9999999999998099) (+ (/ 676.5203681218851 z) (/ -176.6150291621406 (+ z 3))))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))))))
21.1s	(/ (* (* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5)))) (+ (/ -0.13857109526572012 (- z -5)) (+ (+ (/ 12.507343278686905 (+ z 4)) (+ (+ (+ (/ -1259.1392167224028 (+ 1 z)) (/ 771.3234287776531 (+ z 2))) 0.9999999999998099) (+ (/ 676.5203681218851 z) (/ -176.6150291621406 (+ z 3))))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7)))))) (exp (+ 0.5 (+ z 6))))
160.0ms	(* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5))))
4.0ms	(sqrt (* PI 2))

series1.9s

Counts

4 → 10

Calls

4 calls:

640.0ms	(* (* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5)))) (+ (/ -0.13857109526572012 (- z -5)) (+ (+ (/ 12.507343278686905 (+ z 4)) (+ (+ (+ (/ -1259.1392167224028 (+ 1 z)) (/ 771.3234287776531 (+ z 2))) 0.9999999999998099) (+ (/ 676.5203681218851 z) (/ -176.6150291621406 (+ z 3))))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))))))
861.0ms	(/ (* (* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5)))) (+ (/ -0.13857109526572012 (- z -5)) (+ (+ (/ 12.507343278686905 (+ z 4)) (+ (+ (+ (/ -1259.1392167224028 (+ 1 z)) (/ 771.3234287776531 (+ z 2))) 0.9999999999998099) (+ (/ 676.5203681218851 z) (/ -176.6150291621406 (+ z 3))))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7)))))) (exp (+ 0.5 (+ z 6))))
378.0ms	(* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5))))
0.0ms	(sqrt (* PI 2))

simplify4.2s

Counts

195 → 195

Iterations

Iter	Nodes
1	3322
0	787

prune8.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize156.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5)))) (+ (/ -0.13857109526572012 (- z -5)) (+ (+ (/ 12.507343278686905 (+ z 4)) (+ (+ (+ (/ -1259.1392167224028 (+ 1 z)) (/ 771.3234287776531 (+ z 2))) 0.9999999999998099) (+ (/ 676.5203681218851 z) (/ -176.6150291621406 (+ z 3))))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7)))))) (exp 0.5))
0.7b	(/ (/ (* (* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5)))) (+ (/ -0.13857109526572012 (- z -5)) (+ (+ (/ 12.507343278686905 (+ z 4)) (+ (+ (+ (/ -1259.1392167224028 (+ 1 z)) (/ 771.3234287776531 (+ z 2))) 0.9999999999998099) (+ (/ 676.5203681218851 z) (/ -176.6150291621406 (+ z 3))))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7)))))) (exp 0.5)) (exp (+ z 6)))
1.0b	(* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5))))
1.0b	(sqrt (* PI 2))

rewrite41.9s

Algorithm

rewrite-expression-head

Rules

120×	`frac-add`
46×	`times-frac`
35×	`associate-/l/`
34×	`associate-*r/`
33×	`flip3-+` `flip-+`
32×	`add-sqr-sqrt` `*-un-lft-identity` `add-exp-log`
29×	`add-cbrt-cube`
27×	`add-cube-cbrt`
17×	`prod-exp`
16×	`div-exp`
10×	`cbrt-undiv` `associate-r`
8×	`exp-sum` `associate-/l*`
7×	`pow1` `associate-/r*` `cbrt-unprod` `div-inv`
6×	`unpow-prod-down`
4×	`expm1-log1p-u` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-exp` `distribute-lft-out` `unswap-sqr`
2×	`clear-num` `frac-2neg` `sqrt-pow1` `sqrt-prod` `sqr-pow`
1×	`unpow-prod-up` `pow1/2` `pow-prod-down` `*-commutative`

Counts

4 → 171

Calls

4 calls:

21.0s	(/ (* (* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5)))) (+ (/ -0.13857109526572012 (- z -5)) (+ (+ (/ 12.507343278686905 (+ z 4)) (+ (+ (+ (/ -1259.1392167224028 (+ 1 z)) (/ 771.3234287776531 (+ z 2))) 0.9999999999998099) (+ (/ 676.5203681218851 z) (/ -176.6150291621406 (+ z 3))))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7)))))) (exp 0.5))
20.7s	(/ (/ (* (* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5)))) (+ (/ -0.13857109526572012 (- z -5)) (+ (+ (/ 12.507343278686905 (+ z 4)) (+ (+ (+ (/ -1259.1392167224028 (+ 1 z)) (/ 771.3234287776531 (+ z 2))) 0.9999999999998099) (+ (/ 676.5203681218851 z) (/ -176.6150291621406 (+ z 3))))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7)))))) (exp 0.5)) (exp (+ z 6)))
141.0ms	(* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5))))
8.0ms	(sqrt (* PI 2))

series2.4s

Counts

4 → 10

Calls

4 calls:

871.0ms	(/ (* (* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5)))) (+ (/ -0.13857109526572012 (- z -5)) (+ (+ (/ 12.507343278686905 (+ z 4)) (+ (+ (+ (/ -1259.1392167224028 (+ 1 z)) (/ 771.3234287776531 (+ z 2))) 0.9999999999998099) (+ (/ 676.5203681218851 z) (/ -176.6150291621406 (+ z 3))))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7)))))) (exp 0.5))
1.2s	(/ (/ (* (* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5)))) (+ (/ -0.13857109526572012 (- z -5)) (+ (+ (/ 12.507343278686905 (+ z 4)) (+ (+ (+ (/ -1259.1392167224028 (+ 1 z)) (/ 771.3234287776531 (+ z 2))) 0.9999999999998099) (+ (/ 676.5203681218851 z) (/ -176.6150291621406 (+ z 3))))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7)))))) (exp 0.5)) (exp (+ z 6)))
395.0ms	(* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5))))
0.0ms	(sqrt (* PI 2))

simplify7.5s

Counts

181 → 181

Iterations

Iter	Nodes
2	10576
1	1973
0	585

prune8.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes164.0ms

Accuracy

0% (0.8b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 0.8b

bsearch0.0ms

simplify25.0ms

Iterations

Iter	Nodes
2	74
1	74
0	54

end0.0ms

sample47.8s

Algorithm

intervals

Results

16.4s	3726×	body	10240	exit
10.9s	3446×	body	1280	valid
6.3s	2425×	body	640	valid
4.3s	1491×	body	1280	nan
3.8s	1257×	body	640	nan
2.8s	1241×	body	320	valid
1.5s	629×	body	320	nan
665.0ms	629×	body	160	valid
263.0ms	300×	body	160	nan
195.0ms	344×	body	80	valid
157.0ms	305×	body	80	nan