Details

sample420.0ms

Algorithm

intervals

Results

139.0ms	138×	body	10240	exit
99.0ms	106×	body	1280	valid
55.0ms	87×	body	640	valid
31.0ms	48×	body	1280	nan
18.0ms	37×	body	640	nan
15.0ms	33×	body	320	valid
9.0ms	25×	body	320	nan
6.0ms	23×	body	160	valid
3.0ms	13×	body	160	nan
1.0ms	9×	body	80	valid
1.0ms	8×	body	80	nan

simplify742.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (143.0ms)

Iter	Nodes	Cost
0	55	94
1	133	94
2	444	92
3	2511	89
done	5000	89

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.7b

localize49.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
1.0b	(+ (+ (/ 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))))
1.0b	(sqrt (* PI 2.0))
1.4b	(* (* (sqrt (* PI 2.0)) (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (+ (+ 0.9999999999998099 (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 676.5203681218851 z))) (+ (+ (/ 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))))))

rewrite17.9s

Algorithm

rewrite-expression-head

Rules

1314×	`*-un-lft-identity`
1227×	`frac-add`
680×	`distribute-lft-out`
447×	`flip3-+` `flip-+`
386×	`times-frac`
313×	`associate-*r/`
156×	`frac-times`
119×	`distribute-lft-out--`
38×	`associate-r`
30×	`unpow-prod-down`
28×	`add-sqr-sqrt` `add-cube-cbrt`
19×	`add-exp-log`
16×	`add-log-exp`
15×	`add-cbrt-cube`
13×	`fma-def`
12×	`pow1` `exp-sum`
11×	`associate-/l*`
9×	`prod-exp`
8×	`sum-log`
6×	`div-exp`
5×	`unpow-prod-up` `cbrt-unprod` `sqr-pow`
4×	`expm1-log1p-u` `pow-prod-down` `associate-/r*` `log1p-expm1-u`
3×	`associate-+l-`
2×	`cbrt-undiv` `pow-to-exp` `sqrt-pow1` `pow-exp`
1×	`+-commutative` `distribute-rgt-in` `associate-+l+` `associate-+r+` `frac-2neg` `distribute-lft-in` `pow1/2` `exp-diff` `associate-l` `associate-l/` `clear-num` `sqrt-prod` `associate-/r/` `-commutative` `div-inv` `associate-/l/` `pow-sub`

Counts

4 → 589

Calls

4 calls:

411.0ms	(/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
916.0ms	(+ (+ (/ 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))))
2.0ms	(sqrt (* PI 2.0))
16.5s	(* (* (sqrt (* PI 2.0)) (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (+ (+ 0.9999999999998099 (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 676.5203681218851 z))) (+ (+ (/ 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))))))

series969.0ms

Counts

4 → 10

Calls

4 calls:

177.0ms	(/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
147.0ms	(+ (+ (/ 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))))
0.0ms	(sqrt (* PI 2.0))
645.0ms	(* (* (sqrt (* PI 2.0)) (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (+ (+ 0.9999999999998099 (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 676.5203681218851 z))) (+ (+ (/ 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))))))

simplify708.0ms

Counts

599 → 599

Iterations

Useful iterations: done (555.0ms)

Iter	Nodes	Cost
0	1654	126424
done	5000	117516

prune7.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize95.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* (+ (- z 1.0) 7.0) (+ (- z 1.0) 8.0)) (+ (* (+ (pow 0.9999999999998099 3) (pow (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 3)) z) (* (+ (* (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (- (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) 676.5203681218851)))
1.0b	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
1.0b	(* (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0)))
1.0b	(sqrt (* PI 2.0))

rewrite760.0ms

Algorithm

rewrite-expression-head

Rules

197×	`*-un-lft-identity`
100×	`times-frac`
95×	`associate-*l/`
91×	`flip3-+` `flip-+`
77×	`frac-times`
73×	`add-sqr-sqrt`
56×	`add-cube-cbrt`
53×	`distribute-lft-out`
39×	`swap-sqr`
36×	`frac-add`
35×	`associate-r`
26×	`add-exp-log` `associate-l`
25×	`distribute-lft-out--`
23×	`add-cbrt-cube`
22×	`associate-*r/`
19×	`pow1`
10×	`prod-exp`
8×	`associate-/r/` `cbrt-unprod`
7×	`unpow-prod-down` `unswap-sqr`
5×	`pow-prod-down`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`*-commutative`
2×	`sqrt-pow1` `sqrt-prod` `sqr-pow`
1×	`unpow-prod-up` `pow2` `distribute-rgt-in` `pow-to-exp` `associate-+l-` `distribute-lft-in` `pow-plus` `pow1/2` `pow-exp` `pow-sqr` `pow-prod-up` `pow-sub`

Counts

4 → 241

Calls

4 calls:

360.0ms	(* (* (+ (- z 1.0) 7.0) (+ (- z 1.0) 8.0)) (+ (* (+ (pow 0.9999999999998099 3) (pow (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 3)) z) (* (+ (* (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (- (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) 676.5203681218851)))
298.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
84.0ms	(* (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0)))
2.0ms	(sqrt (* PI 2.0))

series453.0ms

Counts

4 → 10

Calls

4 calls:

127.0ms	(* (* (+ (- z 1.0) 7.0) (+ (- z 1.0) 8.0)) (+ (* (+ (pow 0.9999999999998099 3) (pow (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 3)) z) (* (+ (* (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (- (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) 676.5203681218851)))
283.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
43.0ms	(* (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0)))
0.0ms	(sqrt (* PI 2.0))

simplify623.0ms

Counts

251 → 251

Iterations

Useful iterations: done (598.0ms)

Iter	Nodes	Cost
0	577	17178
1	2301	15352
done	5001	15346

prune4.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize100.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (* (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))))
1.0b	(* (* (+ (- z 1.0) 7.0) (+ (- z 1.0) 8.0)) (+ (* (+ (pow 0.9999999999998099 3) (pow (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 3)) z) (* (+ (* (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (- (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) 676.5203681218851)))
1.0b	(* (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0)))
1.0b	(sqrt (* 2.0 PI))

rewrite489.0ms

Algorithm

rewrite-expression-head

Rules

185×	`*-un-lft-identity`
101×	`associate-*l/`
100×	`times-frac`
91×	`flip3-+` `flip-+`
83×	`frac-times`
65×	`add-sqr-sqrt`
53×	`add-cube-cbrt`
48×	`distribute-lft-out`
39×	`swap-sqr`
36×	`frac-add`
27×	`associate-*r/`
24×	`associate-r` `distribute-lft-out--`
22×	`associate-l`
21×	`add-exp-log` `add-cbrt-cube`
19×	`pow1`
9×	`frac-sub`
8×	`associate-/r/`
7×	`prod-exp` `cbrt-unprod`
6×	`add-log-exp`
5×	`pow-prod-down`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `div-inv` `unswap-sqr`
2×	`sqrt-pow1` `*-commutative`
1×	`pow2` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `pow-plus` `pow1/2` `fma-neg` `diff-log` `prod-diff` `sqrt-prod` `pow-sqr` `pow-prod-up` `flip--` `difference-of-squares`

Counts

4 → 234

Calls

4 calls:

23.0ms	(- (* (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (* (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))))
359.0ms	(* (* (+ (- z 1.0) 7.0) (+ (- z 1.0) 8.0)) (+ (* (+ (pow 0.9999999999998099 3) (pow (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 3)) z) (* (+ (* (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (- (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) 676.5203681218851)))
87.0ms	(* (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0)))
2.0ms	(sqrt (* 2.0 PI))

series243.0ms

Counts

4 → 10

Calls

4 calls:

88.0ms	(- (* (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (* (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))))
121.0ms	(* (* (+ (- z 1.0) 7.0) (+ (- z 1.0) 8.0)) (+ (* (+ (pow 0.9999999999998099 3) (pow (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 3)) z) (* (+ (* (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (- (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) 676.5203681218851)))
35.0ms	(* (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0)))
0.0ms	(sqrt (* 2.0 PI))

simplify615.0ms

Counts

244 → 244

Iterations

Useful iterations: done (589.0ms)

Iter	Nodes	Cost
0	553	17541
1	2265	15711
done	5001	15615

prune4.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize79.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (* 0.9999999999998099 0.9999999999998099) (* (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) z)
1.0b	(/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
1.0b	(* (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))))
1.0b	(sqrt (* PI 2.0))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

1171×	`*-un-lft-identity`
451×	`distribute-lft-out`
404×	`times-frac`
125×	`distribute-lft-out--`
87×	`swap-sqr`
36×	`add-sqr-sqrt`
32×	`add-cube-cbrt`
30×	`unpow-prod-down`
17×	`associate-l`
16×	`pow1` `associate-r`
12×	`exp-sum`
11×	`associate-/l*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`frac-times`
8×	`flip3-+` `frac-add` `flip-+`
5×	`unpow-prod-up` `associate-*l/` `sqr-pow`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`associate-+l-` `associate-*r/` `div-exp` `pow-prod-down`
2×	`sqrt-pow1` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `distribute-rgt-in` `pow-to-exp` `flip3--` `frac-2neg` `distribute-lft-in` `pow-plus` `pow1/2` `exp-diff` `pow-exp` `clear-num` `sqrt-prod` `associate-/r/` `pow-sqr` `pow-prod-up` `flip--` `div-inv` `associate-/l/` `pow-sub` `difference-of-squares`

Counts

4 → 261

Calls

4 calls:

9.0ms	(* (- (* 0.9999999999998099 0.9999999999998099) (* (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) z)
419.0ms	(/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
695.0ms	(* (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))))
2.0ms	(sqrt (* PI 2.0))

series337.0ms

Counts

4 → 10

Calls

4 calls:

68.0ms	(* (- (* 0.9999999999998099 0.9999999999998099) (* (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) z)
176.0ms	(/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
93.0ms	(* (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))))
0.0ms	(sqrt (* PI 2.0))

simplify1.8s

Counts

271 → 271

Iterations

Useful iterations: 2 (389.0ms)

Iter	Nodes	Cost
0	391	9763
1	1032	8855
2	4700	8452
done	5000	8452

prune1.8s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes250.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify11.0ms

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	86	344
1	132	344
done	132	344

end0.0ms

sample11.6s

Algorithm

intervals

Results

4.0s	3935×	body	10240	exit
2.9s	3325×	body	1280	valid
1.6s	2515×	body	640	valid
987.0ms	1518×	body	1280	nan
617.0ms	1211×	body	640	nan
530.0ms	1239×	body	320	valid
228.0ms	614×	body	320	nan
185.0ms	652×	body	160	valid
77.0ms	297×	body	160	nan
50.0ms	351×	body	80	valid
35.0ms	305×	body	80	nan