Details

sample1.5s

Algorithm

intervals

Results

1.3s	126×	body	10240	exit
50.0ms	259×	body	80	valid
36.0ms	35×	body	1280	nan
29.0ms	42×	body	640	nan
7.0ms	13×	body	320	nan
3.0ms	8×	body	160	nan
1.0ms	7×	body	80	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	3587	88
done	5000	78

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.1b

localize50.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* (pow (+ 0.5 (- 7.0 z)) (- 0.5 z)) (sqrt (* PI 2.0))) (+ (+ (+ (/ 771.3234287776531 (- 3.0 z)) (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z)))) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))) (/ 12.507343278686905 (- 5.0 z)))))
1.0b	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
1.0b	(sqrt (* PI 2.0))
2.6b	(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z)))

rewrite16.4s

Algorithm

rewrite-expression-head

Rules

427×	`frac-add`
142×	`*-un-lft-identity`
109×	`flip3-+` `flip-+`
98×	`distribute-lft-out`
60×	`associate-*l/`
59×	`pow-sub`
58×	`frac-times` `associate-*r/`
23×	`associate-r`
14×	`add-exp-log`
11×	`add-log-exp`
9×	`pow1` `add-cbrt-cube`
8×	`times-frac`
7×	`prod-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`sum-log` `distribute-lft-out--`
3×	`cbrt-unprod`
2×	`+-commutative` `sqrt-pow1` `pow-prod-down`
1×	`distribute-rgt-in` `pow-to-exp` `associate-+l+` `distribute-lft-in` `pow1/2` `associate-l` `pow-exp` `sqrt-prod` `*-commutative`

Counts

4 → 203

Calls

4 calls:

16.2s	(* (* (pow (+ 0.5 (- 7.0 z)) (- 0.5 z)) (sqrt (* PI 2.0))) (+ (+ (+ (/ 771.3234287776531 (- 3.0 z)) (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z)))) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))) (/ 12.507343278686905 (- 5.0 z)))))
42.0ms	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
1.0ms	(sqrt (* PI 2.0))
96.0ms	(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z)))

series620.0ms

Counts

4 → 10

Calls

4 calls:

491.0ms	(* (* (pow (+ 0.5 (- 7.0 z)) (- 0.5 z)) (sqrt (* PI 2.0))) (+ (+ (+ (/ 771.3234287776531 (- 3.0 z)) (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z)))) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))) (/ 12.507343278686905 (- 5.0 z)))))
71.0ms	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
0.0ms	(sqrt (* PI 2.0))
57.0ms	(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z)))

simplify1.1s

Counts

213 → 213

Iterations

Useful iterations: 1 (405.0ms)

Iter	Nodes	Cost
0	791	34065
1	3626	31616
done	5001	31616

prune2.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize95.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3)) (- 2.0 z)) (* (+ (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) -1259.1392167224028)) (- 3.0 z))
1.0b	(* (/ 12.507343278686905 (- 5.0 z)) (/ 12.507343278686905 (- 5.0 z)))
1.0b	(sqrt (* PI 2.0))
2.6b	(+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3)) (- 2.0 z)) (* (+ (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) -1259.1392167224028))

rewrite355.0ms

Algorithm

rewrite-expression-head

Rules

99×	`associate-*l/`
90×	`*-un-lft-identity`
86×	`add-sqr-sqrt`
76×	`times-frac`
69×	`frac-times`
64×	`frac-add`
60×	`flip3-+` `flip-+`
47×	`flip3--` `flip--`
46×	`add-cube-cbrt`
27×	`swap-sqr`
26×	`associate-r`
24×	`associate-l`
19×	`associate-*r/` `distribute-lft-out--`
18×	`add-exp-log` `add-cbrt-cube`
16×	`pow1`
13×	`difference-of-squares`
8×	`associate-/r/`
6×	`add-log-exp`
5×	`prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `associate-+l+` `distribute-lft-in` `div-exp` `div-inv`
3×	`pow-prod-down`
2×	`sqrt-pow1` `*-commutative`
1×	`+-commutative` `pow2` `pow-plus` `pow1/2` `sum-log` `sqrt-prod` `pow-sqr` `pow-prod-up`

Counts

4 → 219

Calls

4 calls:

229.0ms	(* (+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3)) (- 2.0 z)) (* (+ (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) -1259.1392167224028)) (- 3.0 z))
33.0ms	(* (/ 12.507343278686905 (- 5.0 z)) (/ 12.507343278686905 (- 5.0 z)))
2.0ms	(sqrt (* PI 2.0))
72.0ms	(+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3)) (- 2.0 z)) (* (+ (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) -1259.1392167224028))

series471.0ms

Counts

4 → 10

Calls

4 calls:

130.0ms	(* (+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3)) (- 2.0 z)) (* (+ (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) -1259.1392167224028)) (- 3.0 z))
36.0ms	(* (/ 12.507343278686905 (- 5.0 z)) (/ 12.507343278686905 (- 5.0 z)))
0.0ms	(sqrt (* PI 2.0))
304.0ms	(+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3)) (- 2.0 z)) (* (+ (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) -1259.1392167224028))

simplify537.0ms

Counts

229 → 229

Iterations

Useful iterations: done (513.0ms)

Iter	Nodes	Cost
0	548	15859
1	1891	14345
done	5001	14333

prune4.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize90.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3)) (- 2.0 z)) (* (+ (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) -1259.1392167224028)) (- 3.0 z))
1.0b	(* (/ 12.507343278686905 (- 5.0 z)) (/ 12.507343278686905 (- 5.0 z)))
1.0b	(sqrt (* PI 2.0))
2.6b	(+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3)) (- 2.0 z)) (* (+ (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) -1259.1392167224028))

rewrite350.0ms

Algorithm

rewrite-expression-head

Rules

99×	`associate-*l/`
90×	`*-un-lft-identity`
86×	`add-sqr-sqrt`
76×	`times-frac`
69×	`frac-times`
64×	`frac-add`
60×	`flip3-+` `flip-+`
47×	`flip3--` `flip--`
46×	`add-cube-cbrt`
27×	`swap-sqr`
26×	`associate-r`
24×	`associate-l`
19×	`associate-*r/` `distribute-lft-out--`
18×	`add-exp-log` `add-cbrt-cube`
16×	`pow1`
13×	`difference-of-squares`
8×	`associate-/r/`
6×	`add-log-exp`
5×	`prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `associate-+l+` `distribute-lft-in` `div-exp` `div-inv`
3×	`pow-prod-down`
2×	`sqrt-pow1` `*-commutative`
1×	`+-commutative` `pow2` `pow-plus` `pow1/2` `sum-log` `sqrt-prod` `pow-sqr` `pow-prod-up`

Counts

4 → 219

Calls

4 calls:

232.0ms	(* (+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3)) (- 2.0 z)) (* (+ (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) -1259.1392167224028)) (- 3.0 z))
32.0ms	(* (/ 12.507343278686905 (- 5.0 z)) (/ 12.507343278686905 (- 5.0 z)))
1.0ms	(sqrt (* PI 2.0))
69.0ms	(+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3)) (- 2.0 z)) (* (+ (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) -1259.1392167224028))

series286.0ms

Counts

4 → 10

Calls

4 calls:

131.0ms	(* (+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3)) (- 2.0 z)) (* (+ (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) -1259.1392167224028)) (- 3.0 z))
37.0ms	(* (/ 12.507343278686905 (- 5.0 z)) (/ 12.507343278686905 (- 5.0 z)))
0.0ms	(sqrt (* PI 2.0))
117.0ms	(+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3)) (- 2.0 z)) (* (+ (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) -1259.1392167224028))

simplify550.0ms

Counts

229 → 229

Iterations

Useful iterations: done (519.0ms)

Iter	Nodes	Cost
0	543	15859
1	1875	14351
done	5001	14339

prune4.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize92.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (* PI 2.0))
2.6b	(+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3)) (- 2.0 z)) (* (+ (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) -1259.1392167224028))
2.6b	(+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3)) (- 2.0 z)) (* (+ (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) -1259.1392167224028))
2.6b	(+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3)) (- 2.0 z)) (* (+ (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) -1259.1392167224028))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

60×	`associate-*l/`
48×	`frac-add`
45×	`flip3-+` `flip-+`
24×	`frac-times`
18×	`flip3--` `flip--`
12×	`associate-+l+` `associate-*r/`
10×	`add-log-exp`
7×	`pow1`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
4×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`+-commutative` `sum-log`
2×	`sqrt-pow1`
1×	`pow1/2` `pow-prod-down` `sqrt-prod`

Counts

4 → 104

Calls

4 calls:

1.0ms	(sqrt (* PI 2.0))
69.0ms	(+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3)) (- 2.0 z)) (* (+ (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) -1259.1392167224028))
69.0ms	(+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3)) (- 2.0 z)) (* (+ (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) -1259.1392167224028))
70.0ms	(+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3)) (- 2.0 z)) (* (+ (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) -1259.1392167224028))

series333.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(sqrt (* PI 2.0))
108.0ms	(+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3)) (- 2.0 z)) (* (+ (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) -1259.1392167224028))
110.0ms	(+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3)) (- 2.0 z)) (* (+ (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) -1259.1392167224028))
114.0ms	(+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3)) (- 2.0 z)) (* (+ (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) -1259.1392167224028))

simplify876.0ms

Counts

114 → 114

Iterations

Useful iterations: 2 (217.0ms)

Iter	Nodes	Cost
0	185	10979
1	661	9898
2	3099	9544
done	5001	9544

prune2.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes221.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	83	359
1	114	359
done	114	359

end0.0ms

sample46.5s

Algorithm

intervals

Results

41.5s	3916×	body	10240	exit
1.6s	1486×	body	1280	nan
1.5s	8078×	body	80	valid
913.0ms	1234×	body	640	nan
346.0ms	640×	body	320	nan
97.0ms	281×	body	160	nan
55.0ms	293×	body	80	nan