Details

sample1.4s

Algorithm

intervals

Results

1.2s	114×	body	10240	exit
50.0ms	258×	body	80	valid
49.0ms	47×	body	1280	nan
29.0ms	41×	body	640	nan
4.0ms	8×	body	320	nan
2.0ms	12×	body	80	nan
2.0ms	5×	body	160	nan

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	60	123
1	148	123
2	592	121
3	3622	98
done	5000	83

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize58.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ -0.13857109526572012 (- 6.0 z))) (+ (+ (+ (+ (/ -1259.1392167224028 (+ 2.0 (- z))) (+ (/ 771.3234287776531 (+ 3.0 (- z))) 0.9999999999998099)) (+ (/ 12.507343278686905 (- 5.0 z)) (/ 676.5203681218851 (- 1.0 z)))) (/ 9.984369578019572e-06 (+ 7.0 (- z)))) (/ -176.6150291621406 (+ 4.0 (- z)))))
0.9b	(+ (/ 771.3234287776531 (+ 3.0 (- z))) 0.9999999999998099)
1.0b	(/ (pow (+ 7.0 (- 0.5 z)) (- 0.5 z)) (exp (+ 7.0 (- 0.5 z))))
1.0b	(sqrt (* PI 2.0))

rewrite35.4s

Algorithm

rewrite-expression-head

Rules

228×	`frac-add`
158×	`*-un-lft-identity`
111×	`add-log-exp`
98×	`distribute-lft-out`
88×	`sum-log`
59×	`flip3-+` `flip-+`
44×	`times-frac`
26×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`unpow-prod-down`
12×	`exp-sum`
11×	`associate-/l*`
10×	`unpow-prod-up`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
5×	`sub-neg` `distribute-lft-out--` `sqr-pow`
4×	`associate-/r*`
3×	`div-exp`
2×	`+-commutative` `sqrt-pow1`
1×	`cbrt-undiv` `pow-to-exp` `associate-+r-` `associate-+l+` `associate-+r+` `frac-2neg` `pow1/2` `exp-diff` `pow-prod-down` `pow-exp` `clear-num` `sqrt-prod` `associate-/r/` `div-inv` `associate-/l/` `pow-sub`

Counts

4 → 200

Calls

4 calls:

35.3s	(+ (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ -0.13857109526572012 (- 6.0 z))) (+ (+ (+ (+ (/ -1259.1392167224028 (+ 2.0 (- z))) (+ (/ 771.3234287776531 (+ 3.0 (- z))) 0.9999999999998099)) (+ (/ 12.507343278686905 (- 5.0 z)) (/ 676.5203681218851 (- 1.0 z)))) (/ 9.984369578019572e-06 (+ 7.0 (- z)))) (/ -176.6150291621406 (+ 4.0 (- z)))))
40.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- z))) 0.9999999999998099)
78.0ms	(/ (pow (+ 7.0 (- 0.5 z)) (- 0.5 z)) (exp (+ 7.0 (- 0.5 z))))
2.0ms	(sqrt (* PI 2.0))

series404.0ms

Counts

4 → 10

Calls

4 calls:

204.0ms	(+ (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ -0.13857109526572012 (- 6.0 z))) (+ (+ (+ (+ (/ -1259.1392167224028 (+ 2.0 (- z))) (+ (/ 771.3234287776531 (+ 3.0 (- z))) 0.9999999999998099)) (+ (/ 12.507343278686905 (- 5.0 z)) (/ 676.5203681218851 (- 1.0 z)))) (/ 9.984369578019572e-06 (+ 7.0 (- z)))) (/ -176.6150291621406 (+ 4.0 (- z)))))
30.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- z))) 0.9999999999998099)
170.0ms	(/ (pow (+ 7.0 (- 0.5 z)) (- 0.5 z)) (exp (+ 7.0 (- 0.5 z))))
0.0ms	(sqrt (* PI 2.0))

simplify892.0ms

Counts

210 → 210

Iterations

Useful iterations: done (861.0ms)

Iter	Nodes	Cost
0	810	25182
1	3132	21658
done	5000	21649

prune2.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.9b	(* (* (sqrt (* PI 2.0)) (* (/ (pow (sqrt (+ 7.0 (- 0.5 z))) (- 0.5 z)) (* (cbrt (exp (+ 7.0 (- 0.5 z)))) (cbrt (exp (+ 7.0 (- 0.5 z)))))) (/ (pow (sqrt (+ 7.0 (- 0.5 z))) (- 0.5 z)) (cbrt (exp (+ 7.0 (- 0.5 z))))))) (* (/ PI (sin (* PI z))) (+ (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ -0.13857109526572012 (- 6.0 z))) (+ (+ (+ (+ (/ -1259.1392167224028 (+ 2.0 (- z))) (+ (/ 771.3234287776531 (+ 3.0 (- z))) 0.9999999999998099)) (+ (/ 12.507343278686905 (- 5.0 z)) (/ 676.5203681218851 (- 1.0 z)))) (/ 9.984369578019572e-06 (+ 7.0 (- z)))) (/ -176.6150291621406 (+ 4.0 (- z)))))))
0.9b	(+ (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ -0.13857109526572012 (- 6.0 z))) (+ (+ (+ (+ (/ -1259.1392167224028 (+ 2.0 (- z))) (+ (/ 771.3234287776531 (+ 3.0 (- z))) 0.9999999999998099)) (+ (/ 12.507343278686905 (- 5.0 z)) (/ 676.5203681218851 (- 1.0 z)))) (/ 9.984369578019572e-06 (+ 7.0 (- z)))) (/ -176.6150291621406 (+ 4.0 (- z)))))
0.9b	(+ (/ 771.3234287776531 (+ 3.0 (- z))) 0.9999999999998099)
1.0b	(sqrt (* PI 2.0))

rewrite1.8m

Algorithm

rewrite-expression-head

Rules

2052×	`frac-add`
793×	`associate-*r/`
677×	`frac-times`
571×	`add-exp-log`
523×	`flip3-+` `flip-+`
357×	`prod-exp`
165×	`div-exp`
121×	`associate-*l/` `add-cbrt-cube`
111×	`*-un-lft-identity` `add-log-exp`
88×	`sum-log` `distribute-lft-out`
85×	`cbrt-unprod`
45×	`pow-to-exp` `pow-exp`
29×	`cbrt-undiv`
28×	`pow1`
16×	`pow-prod-down`
4×	`distribute-rgt-in` `add-sqr-sqrt` `add-cube-cbrt` `distribute-lft-in`
2×	`+-commutative` `sqrt-pow1`
1×	`associate-+l+` `associate-+r+` `pow1/2` `associate-r` `associate-l` `sqrt-prod` `*-commutative`

Counts

4 → 714

Calls

4 calls:

1.3m	(* (* (sqrt (* PI 2.0)) (* (/ (pow (sqrt (+ 7.0 (- 0.5 z))) (- 0.5 z)) (* (cbrt (exp (+ 7.0 (- 0.5 z)))) (cbrt (exp (+ 7.0 (- 0.5 z)))))) (/ (pow (sqrt (+ 7.0 (- 0.5 z))) (- 0.5 z)) (cbrt (exp (+ 7.0 (- 0.5 z))))))) (* (/ PI (sin (* PI z))) (+ (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ -0.13857109526572012 (- 6.0 z))) (+ (+ (+ (+ (/ -1259.1392167224028 (+ 2.0 (- z))) (+ (/ 771.3234287776531 (+ 3.0 (- z))) 0.9999999999998099)) (+ (/ 12.507343278686905 (- 5.0 z)) (/ 676.5203681218851 (- 1.0 z)))) (/ 9.984369578019572e-06 (+ 7.0 (- z)))) (/ -176.6150291621406 (+ 4.0 (- z)))))))
35.3s	(+ (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ -0.13857109526572012 (- 6.0 z))) (+ (+ (+ (+ (/ -1259.1392167224028 (+ 2.0 (- z))) (+ (/ 771.3234287776531 (+ 3.0 (- z))) 0.9999999999998099)) (+ (/ 12.507343278686905 (- 5.0 z)) (/ 676.5203681218851 (- 1.0 z)))) (/ 9.984369578019572e-06 (+ 7.0 (- z)))) (/ -176.6150291621406 (+ 4.0 (- z)))))
43.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- z))) 0.9999999999998099)
2.0ms	(sqrt (* PI 2.0))

series1.2s

Counts

4 → 10

Calls

4 calls:

945.0ms	(* (* (sqrt (* PI 2.0)) (* (/ (pow (sqrt (+ 7.0 (- 0.5 z))) (- 0.5 z)) (* (cbrt (exp (+ 7.0 (- 0.5 z)))) (cbrt (exp (+ 7.0 (- 0.5 z)))))) (/ (pow (sqrt (+ 7.0 (- 0.5 z))) (- 0.5 z)) (cbrt (exp (+ 7.0 (- 0.5 z))))))) (* (/ PI (sin (* PI z))) (+ (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ -0.13857109526572012 (- 6.0 z))) (+ (+ (+ (+ (/ -1259.1392167224028 (+ 2.0 (- z))) (+ (/ 771.3234287776531 (+ 3.0 (- z))) 0.9999999999998099)) (+ (/ 12.507343278686905 (- 5.0 z)) (/ 676.5203681218851 (- 1.0 z)))) (/ 9.984369578019572e-06 (+ 7.0 (- z)))) (/ -176.6150291621406 (+ 4.0 (- z)))))))
203.0ms	(+ (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ -0.13857109526572012 (- 6.0 z))) (+ (+ (+ (+ (/ -1259.1392167224028 (+ 2.0 (- z))) (+ (/ 771.3234287776531 (+ 3.0 (- z))) 0.9999999999998099)) (+ (/ 12.507343278686905 (- 5.0 z)) (/ 676.5203681218851 (- 1.0 z)))) (/ 9.984369578019572e-06 (+ 7.0 (- z)))) (/ -176.6150291621406 (+ 4.0 (- z)))))
26.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- z))) 0.9999999999998099)
0.0ms	(sqrt (* PI 2.0))

simplify1.1s

Counts

724 → 724

Iterations

Useful iterations: done (821.0ms)

Iter	Nodes	Cost
0	1921	221195
done	5001	205151

prune14.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z)))
0.9b	(+ (+ (/ -0.13857109526572012 (- 6.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (+ (+ (+ 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z))) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (/ 676.5203681218851 (- 1.0 z)))) (/ 9.984369578019572e-06 (- 7.0 z)))))
0.9b	(* (+ (+ (/ -0.13857109526572012 (- 6.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (+ (+ (+ 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z))) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (/ 676.5203681218851 (- 1.0 z)))) (/ 9.984369578019572e-06 (- 7.0 z))))) PI)
1.0b	(sqrt (* PI 2.0))

rewrite1.1m

Algorithm

rewrite-expression-head

Rules

456×	`frac-add`
218×	`*-un-lft-identity`
175×	`distribute-lft-out`
117×	`flip3-+` `flip-+`
111×	`add-log-exp`
88×	`sum-log`
56×	`associate-*l/`
21×	`associate-l`
9×	`pow1`
8×	`add-sqr-sqrt`
6×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r`
2×	`+-commutative` `sqrt-pow1` `pow-prod-down`
1×	`associate-+l+` `associate-+r+` `pow1/2` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 217

Calls

4 calls:

12.0ms	(+ 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z)))
14.2s	(+ (+ (/ -0.13857109526572012 (- 6.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (+ (+ (+ 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z))) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (/ 676.5203681218851 (- 1.0 z)))) (/ 9.984369578019572e-06 (- 7.0 z)))))
50.4s	(* (+ (+ (/ -0.13857109526572012 (- 6.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (+ (+ (+ 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z))) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (/ 676.5203681218851 (- 1.0 z)))) (/ 9.984369578019572e-06 (- 7.0 z))))) PI)
2.0ms	(sqrt (* PI 2.0))

series426.0ms

Counts

4 → 10

Calls

4 calls:

24.0ms	(+ 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z)))
191.0ms	(+ (+ (/ -0.13857109526572012 (- 6.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (+ (+ (+ 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z))) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (/ 676.5203681218851 (- 1.0 z)))) (/ 9.984369578019572e-06 (- 7.0 z)))))
210.0ms	(* (+ (+ (/ -0.13857109526572012 (- 6.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) (+ (/ -176.6150291621406 (- 4.0 z)) (+ (+ (+ (+ 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z))) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (/ 676.5203681218851 (- 1.0 z)))) (/ 9.984369578019572e-06 (- 7.0 z))))) PI)
0.0ms	(sqrt (* PI 2.0))

simplify761.0ms

Counts

227 → 227

Iterations

Useful iterations: 1 (246.0ms)

Iter	Nodes	Cost
0	752	37309
1	2667	34468
done	5000	34468

prune3.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize112.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* (- 7.0 z) (* (* (+ (* (/ 771.3234287776531 (- 3.0 z)) (/ 771.3234287776531 (- 3.0 z))) (- (* 0.9999999999998099 0.9999999999998099) (* 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z))))) (- 2.0 z)) (* (- 5.0 z) (- 1.0 z)))) -176.6150291621406)
1.0b	(* (+ (* 12.507343278686905 (- 1.0 z)) (* (- 5.0 z) 676.5203681218851)) (* (+ (* (/ 771.3234287776531 (- 3.0 z)) (/ 771.3234287776531 (- 3.0 z))) (- (* 0.9999999999998099 0.9999999999998099) (* 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z))))) (- 2.0 z)))
1.0b	(pow (/ 771.3234287776531 (- 3.0 z)) 3)
1.0b	(sqrt (* PI 2.0))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

2336×	`frac-times`
1560×	`associate-*l/`
1451×	`flip3--` `flip--`
834×	`associate-*r/`
720×	`frac-add`
129×	`flip3-+` `flip-+`
38×	`pow1`
37×	`add-exp-log` `add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube`
30×	`times-frac`
25×	`add-cube-cbrt`
23×	`pow-prod-down`
22×	`prod-exp` `cbrt-unprod`
21×	`unpow-prod-down` `cube-prod`
8×	`distribute-rgt-in` `distribute-lft-in`
6×	`distribute-lft-out--` `difference-of-squares`
4×	`sub-neg` `associate-r` `associate-l` `associate-/r/` `add-log-exp`
3×	`pow-unpow`
2×	`sqrt-pow1` `pow-exp` `*-commutative` `div-inv` `rem-cube-cbrt`
1×	`cbrt-undiv` `cube-div` `cube-mult` `pow-to-exp` `pow-pow` `pow1/2` `unpow3` `div-exp` `sqrt-prod` `sqr-pow`

Counts

4 → 1045

Calls

4 calls:

1.2s	(* (* (- 7.0 z) (* (* (+ (* (/ 771.3234287776531 (- 3.0 z)) (/ 771.3234287776531 (- 3.0 z))) (- (* 0.9999999999998099 0.9999999999998099) (* 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z))))) (- 2.0 z)) (* (- 5.0 z) (- 1.0 z)))) -176.6150291621406)
85.0ms	(* (+ (* 12.507343278686905 (- 1.0 z)) (* (- 5.0 z) 676.5203681218851)) (* (+ (* (/ 771.3234287776531 (- 3.0 z)) (/ 771.3234287776531 (- 3.0 z))) (- (* 0.9999999999998099 0.9999999999998099) (* 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z))))) (- 2.0 z)))
8.0ms	(pow (/ 771.3234287776531 (- 3.0 z)) 3)
2.0ms	(sqrt (* PI 2.0))

series277.0ms

Counts

4 → 10

Calls

4 calls:

130.0ms	(* (* (- 7.0 z) (* (* (+ (* (/ 771.3234287776531 (- 3.0 z)) (/ 771.3234287776531 (- 3.0 z))) (- (* 0.9999999999998099 0.9999999999998099) (* 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z))))) (- 2.0 z)) (* (- 5.0 z) (- 1.0 z)))) -176.6150291621406)
90.0ms	(* (+ (* 12.507343278686905 (- 1.0 z)) (* (- 5.0 z) 676.5203681218851)) (* (+ (* (/ 771.3234287776531 (- 3.0 z)) (/ 771.3234287776531 (- 3.0 z))) (- (* 0.9999999999998099 0.9999999999998099) (* 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z))))) (- 2.0 z)))
55.0ms	(pow (/ 771.3234287776531 (- 3.0 z)) 3)
0.0ms	(sqrt (* PI 2.0))

simplify811.0ms

Counts

1055 → 1055

Iterations

Useful iterations: 0 (221.0ms)

Iter	Nodes	Cost
0	2521	84339
done	5000	84339

prune28.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes207.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	107
1	77	107
done	77	107

end0.0ms

sample43.6s

Algorithm

intervals

Results

39.2s	3954×	body	10240	exit
1.5s	1470×	body	1280	nan
1.4s	8084×	body	80	valid
847.0ms	1261×	body	640	nan
292.0ms	612×	body	320	nan
100.0ms	319×	body	160	nan
53.0ms	323×	body	80	nan
0.0ms	1×	body	160	valid