Details

sample1.0s

Algorithm

intervals

Results

293.0ms	111×	body	10240	exit
231.0ms	95×	body	1280	valid
171.0ms	90×	body	640	valid
83.0ms	46×	body	320	valid
71.0ms	48×	body	1280	nan
38.0ms	34×	body	640	nan
15.0ms	11×	body	160	nan
14.0ms	16×	body	160	valid
14.0ms	16×	body	320	nan
2.0ms	9×	body	80	nan
2.0ms	10×	body	80	valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 3 (476.0ms)

Iter	Nodes	Cost
0	55	94
1	133	94
2	447	92
3	2857	89
done	5001	89

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize96.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
1.0b	(/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
1.0b	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
1.0b	(sqrt (* PI 2.0))

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

74×	`*-un-lft-identity`
27×	`distribute-lft-out`
22×	`times-frac`
15×	`add-exp-log`
14×	`add-sqr-sqrt`
11×	`associate-l` `add-cbrt-cube`
9×	`add-cube-cbrt`
7×	`pow1` `unpow-prod-down` `distribute-lft-out--`
6×	`prod-exp` `add-log-exp`
4×	`associate-+l-` `div-exp` `associate-r` `associate-/r*`
3×	`unswap-sqr`
2×	`cbrt-undiv` `pow-to-exp` `sqrt-pow1` `exp-sum` `associate-*l/` `pow-exp` `sqrt-prod` `cbrt-unprod` `pow-sub` `sqr-pow`
1×	`unpow-prod-up` `+-commutative` `frac-2neg` `flip3-+` `pow1/2` `exp-diff` `pow-prod-down` `frac-add` `clear-num` `sum-log` `associate-/r/` `-commutative` `flip-+` `div-inv` `associate-/l/` `associate-/l`

Counts

4 → 91

Calls

4 calls:

317.0ms	(+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
925.0ms	(/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
956.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
7.0ms	(sqrt (* PI 2.0))

series1.1s

Counts

4 → 10

Calls

4 calls:

123.0ms	(+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
618.0ms	(/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
405.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
0.0ms	(sqrt (* PI 2.0))

simplify1.8s

Counts

101 → 101

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	281	2677
1	785	2589
2	3605	2304
done	5000	2293

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize93.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp z)) (exp (- (- 1.0 7.0) 0.5))) (+ (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -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	(+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
1.0b	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
1.0b	(sqrt (* PI 2.0))

rewrite1.2m

Algorithm

rewrite-expression-head

Rules

1689×	`frac-add`
557×	`flip3-+` `flip-+`
441×	`frac-times`
244×	`*-un-lft-identity`
222×	`exp-diff`
221×	`associate-*r/`
168×	`distribute-lft-out`
115×	`associate-*l/`
37×	`associate-r`
23×	`add-exp-log`
20×	`add-cbrt-cube`
18×	`times-frac`
17×	`prod-exp`
13×	`add-sqr-sqrt`
12×	`pow1` `associate-l`
9×	`cbrt-unprod`
8×	`add-cube-cbrt`
7×	`unpow-prod-down` `distribute-lft-out--`
6×	`add-log-exp`
4×	`div-exp` `pow-prod-down`
3×	`unswap-sqr`
2×	`cbrt-undiv` `pow-to-exp` `sqrt-pow1` `pow-exp` `sqrt-prod` `*-commutative` `sqr-pow`
1×	`unpow-prod-up` `+-commutative` `distribute-rgt-in` `associate-+l-` `distribute-lft-in` `pow1/2` `sum-log` `pow-sub`

Counts

4 → 563

Calls

4 calls:

1.2m	(* (* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp z)) (exp (- (- 1.0 7.0) 0.5))) (+ (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -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))))))
278.0ms	(+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
924.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
4.0ms	(sqrt (* PI 2.0))

series1.5s

Counts

4 → 10

Calls

4 calls:

974.0ms	(* (* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp z)) (exp (- (- 1.0 7.0) 0.5))) (+ (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -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))))))
99.0ms	(+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
404.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
0.0ms	(sqrt (* PI 2.0))

simplify1.4s

Counts

573 → 573

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	1739	179417
done	5001	179142

prune16.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize113.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (- 1.0 7.0))) (+ (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -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	(+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
1.0b	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
1.0b	(sqrt (* PI 2.0))

rewrite59.3s

Algorithm

rewrite-expression-head

Rules

1689×	`frac-add`
557×	`flip3-+` `flip-+`
441×	`frac-times`
337×	`associate-*l/`
244×	`*-un-lft-identity`
223×	`associate-+l-` `pow-sub`
222×	`exp-diff`
221×	`associate-*r/`
168×	`distribute-lft-out`
37×	`associate-r`
21×	`add-exp-log`
18×	`times-frac`
15×	`prod-exp` `add-cbrt-cube`
13×	`add-sqr-sqrt`
12×	`pow1` `associate-l`
8×	`add-cube-cbrt`
7×	`unpow-prod-down` `cbrt-unprod` `distribute-lft-out--`
6×	`add-log-exp`
4×	`pow-prod-down`
3×	`unswap-sqr`
2×	`pow-to-exp` `sqrt-pow1` `pow-exp` `sqrt-prod` `*-commutative` `sqr-pow`
1×	`unpow-prod-up` `+-commutative` `distribute-rgt-in` `distribute-lft-in` `pow1/2` `sum-log`

Counts

4 → 561

Calls

4 calls:

57.8s	(* (* (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (- 1.0 7.0))) (+ (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -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))))))
314.0ms	(+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
1.1s	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
7.0ms	(sqrt (* PI 2.0))

series961.0ms

Counts

4 → 10

Calls

4 calls:

610.0ms	(* (* (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (- 1.0 7.0))) (+ (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -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))))))
74.0ms	(+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
276.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
0.0ms	(sqrt (* PI 2.0))

simplify1.1s

Counts

571 → 571

Iterations

Useful iterations: done (913.0ms)

Iter	Nodes	Cost
0	1718	178330
done	5001	178165

prune11.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize95.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
1.0b	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
1.0b	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
1.0b	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

216×	`add-sqr-sqrt`
208×	`unpow-prod-down`
132×	`times-frac`
116×	`associate-l`
96×	`add-exp-log` `*-un-lft-identity`
72×	`add-cube-cbrt` `unswap-sqr`
52×	`pow-exp`
48×	`prod-exp` `sqrt-prod`
40×	`sqr-pow`
24×	`div-exp` `associate-r`
16×	`pow-to-exp`
12×	`rec-exp` `1-exp` `add-cbrt-cube`
4×	`pow1` `*-commutative` `cbrt-unprod` `div-inv` `add-log-exp`

Counts

4 → 296

Calls

4 calls:

49.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
48.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
50.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
51.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
0.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
0.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
0.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

simplify632.0ms

Counts

300 → 300

Iterations

Useful iterations: done (616.0ms)

Iter	Nodes	Cost
0	190	5200
1	433	4952
2	1454	4708
done	5001	4568

prune3.0s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes179.0ms

Accuracy

0% (0.8b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	57	90
1	78	90
done	78	90

end0.0ms

sample25.3s

Algorithm

intervals

Results

9.3s	3905×	body	10240	exit
6.6s	3353×	body	1280	valid
2.8s	2538×	body	640	valid
2.4s	1509×	body	1280	nan
1.2s	1234×	body	320	valid
1.2s	1231×	body	640	nan
799.0ms	623×	body	320	nan
266.0ms	620×	body	160	valid
140.0ms	306×	body	160	nan
64.0ms	335×	body	80	valid
51.0ms	309×	body	80	nan