Details

sample1.9s

Algorithm

intervals

Results

890.0ms	137×	body	10240	exit
343.0ms	107×	body	1280	valid
166.0ms	75×	body	640	valid
141.0ms	48×	body	1280	nan
71.0ms	35×	body	640	nan
68.0ms	49×	body	320	valid
51.0ms	18×	body	160	valid
29.0ms	18×	body	320	nan
11.0ms	12×	body	160	nan
5.0ms	11×	body	80	valid
4.0ms	9×	body	80	nan

simplify940.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	2155
2	413
1	140
0	55

prune56.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize147.0ms

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:

519.0ms	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
538.0ms	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
10.0ms	(sqrt (* PI 2))
4.0ms	(sqrt (* PI 2))

series859.0ms

Counts

4 → 8

Calls

4 calls:

472.0ms	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
387.0ms	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
0.0ms	(sqrt (* PI 2))
0.0ms	(sqrt (* PI 2))

simplify3.0s

Counts

104 → 104

Iterations

Iter	Nodes
3	6551
2	1312
1	400
0	162

prune4.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize213.0ms

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))

rewrite972.0ms

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:

433.0ms	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
529.0ms	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
4.0ms	(sqrt (* PI 2))
5.0ms	(sqrt (* PI 2))

series850.0ms

Counts

4 → 8

Calls

4 calls:

402.0ms	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
448.0ms	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
0.0ms	(sqrt (* PI 2))
0.0ms	(sqrt (* PI 2))

simplify1.9s

Counts

104 → 104

Iterations

Iter	Nodes
3	4972
2	1093
1	328
0	126

prune3.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize175.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (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))))))
0.6b	(/ (* (* (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:

1.1m	(* (* (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))))))
22.9s	(/ (* (* (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))))
119.0ms	(* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5))))
5.0ms	(sqrt (* PI 2))

series1.8s

Counts

4 → 10

Calls

4 calls:

592.0ms	(* (* (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))))))
838.0ms	(/ (* (* (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))))
396.0ms	(* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5))))
0.0ms	(sqrt (* PI 2))

simplify4.0s

Counts

195 → 195

Iterations

Iter	Nodes
1	3322
0	787

prune8.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize139.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5)))) (/ (exp (+ 0.5 (+ z 6))) (+ (/ -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)))))))
0.5b	(/ (exp (+ 0.5 (+ z 6))) (+ (/ -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))))))
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

1414×	`*-un-lft-identity`
1108×	`distribute-lft-out`
360×	`frac-add`
358×	`times-frac`
138×	`associate-/r*`
103×	`associate-/r/`
99×	`flip3-+` `flip-+`
88×	`add-sqr-sqrt`
83×	`add-cube-cbrt`
61×	`exp-sum`
30×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`div-exp`
10×	`associate-r`
9×	`prod-exp`
7×	`pow1` `cbrt-undiv`
6×	`unpow-prod-down`
5×	`associate-/l*`
4×	`expm1-log1p-u` `associate-l` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-to-exp` `pow-exp` `cbrt-unprod` `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 → 462

Calls

4 calls:

42.0s	(/ (* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5)))) (/ (exp (+ 0.5 (+ z 6))) (+ (/ -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)))))))
43.4s	(/ (exp (+ 0.5 (+ z 6))) (+ (/ -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))))))
139.0ms	(* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5))))
4.0ms	(sqrt (* PI 2))

series1.5s

Counts

4 → 10

Calls

4 calls:

887.0ms	(/ (* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5)))) (/ (exp (+ 0.5 (+ z 6))) (+ (/ -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)))))))
291.0ms	(/ (exp (+ 0.5 (+ z 6))) (+ (/ -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))))))
361.0ms	(* (sqrt (* PI 2)) (pow (+ 0.5 (+ z 6)) (+ z (+ -1 0.5))))
0.0ms	(sqrt (* PI 2))

simplify4.7s

Counts

472 → 472

Iterations

Iter	Nodes
1	3299
0	902

prune18.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes167.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 0.9b

bsearch0.0ms

simplify17.0ms

Iterations

Iter	Nodes
2	74
1	74
0	53

end0.0ms

sample49.4s

Algorithm

intervals

Results

17.4s	3880×	body	10240	exit
11.2s	3450×	body	1280	valid
7.7s	2431×	body	640	valid
4.2s	1487×	body	1280	nan
3.1s	1246×	body	640	nan
2.6s	1260×	body	320	valid
1.1s	695×	body	320	nan
1.0s	601×	body	160	valid
406.0ms	348×	body	160	nan
149.0ms	343×	body	80	valid
117.0ms	292×	body	80	nan