Details

sample1.0s

Algorithm

intervals

Results

302.0ms	131×	body	10240	exit
223.0ms	110×	body	1280	valid
177.0ms	80×	body	640	valid
64.0ms	51×	body	1280	nan
57.0ms	12×	body	80	valid
46.0ms	41×	body	640	nan
35.0ms	37×	body	320	valid
23.0ms	32×	body	320	nan
10.0ms	19×	body	160	valid
6.0ms	14×	body	160	nan
3.0ms	10×	body	80	nan

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 3 (507.0ms)

Iter	Nodes	Cost
0	55	94
1	133	94
2	449	92
3	2515	89
done	5001	89

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.1b

localize89.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (/ (* (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))) (+ (+ (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (+ (/ 676.5203681218851 z) (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099))))))
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))

rewrite1.6m

Algorithm

rewrite-expression-head

Rules

648×	`frac-add`
186×	`flip3-+` `flip-+`
159×	`*-un-lft-identity`
119×	`distribute-lft-out`
82×	`frac-times` `associate-*r/`
31×	`associate-r`
27×	`add-exp-log`
20×	`associate-l` `add-cbrt-cube`
19×	`add-sqr-sqrt`
14×	`prod-exp`
12×	`add-cube-cbrt`
9×	`pow1`
8×	`times-frac` `div-exp`
7×	`unpow-prod-down`
6×	`associate-+l-` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `exp-sum` `associate-*l/` `pow-exp`
2×	`sqrt-pow1` `exp-diff` `pow-prod-down` `sqrt-prod` `associate-/r/` `*-commutative` `div-inv` `pow-sub` `sqr-pow`
1×	`unpow-prod-up` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow1/2` `clear-num` `associate-/l/` `associate-/l*` `distribute-lft-out--`

Counts

4 → 298

Calls

4 calls:

1.5m	(* (/ (* (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))) (+ (+ (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (+ (/ 676.5203681218851 z) (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099))))))
996.0ms	(/ (* (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)))
1.1s	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
5.0ms	(sqrt (* PI 2.0))

series2.0s

Counts

4 → 10

Calls

4 calls:

963.0ms	(* (/ (* (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))) (+ (+ (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (+ (/ 676.5203681218851 z) (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099))))))
670.0ms	(/ (* (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)))
353.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
0.0ms	(sqrt (* PI 2.0))

simplify936.0ms

Counts

308 → 308

Iterations

Useful iterations: done (844.0ms)

Iter	Nodes	Cost
0	1114	66543
done	5000	60831

prune5.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize162.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
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))

rewrite2.5s

Algorithm

rewrite-expression-head

Rules

1116×	`*-un-lft-identity`
431×	`distribute-lft-out`
364×	`times-frac`
121×	`distribute-lft-out--`
87×	`swap-sqr`
24×	`associate-l`
20×	`add-sqr-sqrt`
17×	`add-exp-log` `associate-r`
14×	`pow1`
13×	`add-cube-cbrt` `add-cbrt-cube`
9×	`frac-times`
8×	`flip3-+` `frac-add` `flip-+`
7×	`unpow-prod-down` `prod-exp`
5×	`associate-*l/`
4×	`expm1-log1p-u` `associate-+l-` `div-exp` `associate-/r*` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-*r/` `cbrt-unprod`
2×	`cbrt-undiv` `pow-to-exp` `sqrt-pow1` `exp-sum` `pow-prod-down` `pow-exp` `sqrt-prod` `*-commutative` `pow-sub` `sqr-pow`
1×	`unpow-prod-up` `pow2` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-plus` `pow1/2` `exp-diff` `clear-num` `associate-/r/` `pow-sqr` `pow-prod-up` `div-inv` `associate-/l/` `associate-/l*`

Counts

4 → 223

Calls

4 calls:

1.2s	(* (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
603.0ms	(/ (* (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)))
637.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
5.0ms	(sqrt (* PI 2.0))

series826.0ms

Counts

4 → 10

Calls

4 calls:

95.0ms	(* (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
440.0ms	(/ (* (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)))
291.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
0.0ms	(sqrt (* PI 2.0))

simplify1.5s

Counts

233 → 233

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	349	8368
1	1044	7519
2	4614	7104
done	5000	7101

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize166.0ms

Local error

Found 4 expressions with local error:

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

rewrite4.3s

Algorithm

rewrite-expression-head

Rules

1138×	`*-un-lft-identity`
431×	`distribute-lft-out`
416×	`times-frac`
121×	`distribute-lft-out--`
94×	`swap-sqr`
74×	`add-sqr-sqrt`
57×	`add-exp-log`
53×	`associate-r`
40×	`cbrt-prod`
38×	`associate-l`
35×	`add-cube-cbrt`
23×	`pow1`
22×	`prod-exp`
20×	`add-cbrt-cube`
19×	`div-exp`
18×	`associate-+l-`
17×	`unswap-sqr`
12×	`frac-times`
10×	`cbrt-unprod`
9×	`unpow-prod-down` `cbrt-div` `exp-diff`
8×	`flip3-+` `exp-sum` `frac-add` `sqrt-prod` `flip-+`
7×	`cbrt-undiv`
6×	`pow1/3` `associate-r/` `associate-l/`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `pow-to-exp` `pow-exp` `associate-/r/` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`pow-sqr` `*-commutative` `pow-prod-up`
2×	`pow2` `sqrt-pow1` `pow-plus` `div-inv`
1×	`unpow-prod-up` `distribute-rgt-in` `distribute-lft-in` `pow1/2`

Counts

4 → 306

Calls

4 calls:

1.2s	(* (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
773.0ms	(* (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))) (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))))
2.3s	(* (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (* (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))) (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))))) (/ (sqrt (* PI 2.0)) (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5)))))
5.0ms	(sqrt (* PI 2.0))

series683.0ms

Counts

4 → 10

Calls

4 calls:

89.0ms	(* (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
148.0ms	(* (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))) (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))))
446.0ms	(* (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (* (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))) (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))))) (/ (sqrt (* PI 2.0)) (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5)))))
0.0ms	(sqrt (* PI 2.0))

simplify525.0ms

Counts

316 → 316

Iterations

Useful iterations: done (508.0ms)

Iter	Nodes	Cost
0	422	12914
1	1256	11812
done	5000	10993

prune3.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize184.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (cbrt (* (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (* (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))) (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))))) (/ (sqrt (* PI 2.0)) (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5)))))) (cbrt (* (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (* (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))) (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))))) (/ (sqrt (* PI 2.0)) (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5)))))))
1.0b	(sqrt (* PI 2.0))
1.0b	(sqrt (* PI 2.0))
1.0b	(sqrt (* PI 2.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-div`
20×	`pow1`
17×	`frac-times`
11×	`associate-r/` `associate-l/`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-pow1` `pow1/3`
5×	`pow-prod-down`
4×	`cbrt-prod` `expm1-log1p-u` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2` `sqrt-prod`
2×	`pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

14.0ms	(* (cbrt (* (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (* (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))) (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))))) (/ (sqrt (* PI 2.0)) (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5)))))) (cbrt (* (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (* (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))) (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))))) (/ (sqrt (* PI 2.0)) (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5)))))))
4.0ms	(sqrt (* PI 2.0))
5.0ms	(sqrt (* PI 2.0))
5.0ms	(sqrt (* PI 2.0))

series1.1s

Counts

4 → 6

Calls

4 calls:

1.1s	(* (cbrt (* (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (* (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))) (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))))) (/ (sqrt (* PI 2.0)) (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5)))))) (cbrt (* (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (* (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))) (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))))) (/ (sqrt (* PI 2.0)) (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5)))))))
0.0ms	(sqrt (* PI 2.0))
0.0ms	(sqrt (* PI 2.0))
0.0ms	(sqrt (* PI 2.0))

simplify675.0ms

Counts

93 → 93

Iterations

Useful iterations: done (671.0ms)

Iter	Nodes	Cost
0	199	5639
1	457	5170
2	1536	3528
done	5001	2848

prune1.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes180.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	69	305
1	92	305
done	92	305

end0.0ms

sample22.8s

Algorithm

intervals

Results

9.0s	3795×	body	10240	exit
4.9s	3365×	body	1280	valid
3.0s	2496×	body	640	valid
1.8s	1247×	body	640	nan
1.6s	1497×	body	1280	nan
1.1s	1257×	body	320	valid
411.0ms	663×	body	320	nan
346.0ms	635×	body	160	valid
94.0ms	289×	body	160	nan
61.0ms	329×	body	80	valid
45.0ms	294×	body	80	nan