Details

sample1.1s

Algorithm

intervals

Results

347.0ms	131×	body	10240	exit
212.0ms	95×	body	1280	valid
120.0ms	88×	body	640	valid
109.0ms	50×	body	1280	nan
87.0ms	32×	body	640	nan
40.0ms	43×	body	320	valid
20.0ms	27×	body	320	nan
12.0ms	22×	body	160	valid
5.0ms	12×	body	160	nan
4.0ms	13×	body	80	valid
2.0ms	10×	body	80	nan

simplify1.8s

Counts

1 → 1

Iterations

Useful iterations: 3 (513.0ms)

Iter	Nodes	Cost
0	55	94
1	133	94
2	447	92
3	2474	89
done	5002	89

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize121.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (* (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))) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 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	(/ (* (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))

rewrite1.2m

Algorithm

rewrite-expression-head

Rules

624×	`frac-add`
176×	`flip3-+` `flip-+`
157×	`*-un-lft-identity`
117×	`distribute-lft-out`
80×	`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` `associate-/r*` `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 → 286

Calls

4 calls:

1.2m	(* (/ (* (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))) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 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)))))))
962.0ms	(/ (* (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)))
1.4s	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
8.0ms	(sqrt (* PI 2.0))

series1.8s

Counts

4 → 10

Calls

4 calls:

884.0ms	(* (/ (* (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))) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 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)))))))
517.0ms	(/ (* (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))

simplify692.0ms

Counts

296 → 296

Iterations

Useful iterations: done (613.0ms)

Iter	Nodes	Cost
0	1073	63253
done	5000	58696

prune6.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize126.0ms

Local error

Found 4 expressions with local error:

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))
1.0b	(sqrt (* PI 2.0))
1.0b	(sqrt (* PI 2.0))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
13×	`pow1`
12×	`add-sqr-sqrt`
11×	`associate-l`
9×	`add-exp-log`
7×	`add-cube-cbrt` `unpow-prod-down`
6×	`sqrt-pow1` `add-cbrt-cube`
5×	`distribute-lft-out`
4×	`associate-r` `sqrt-prod` `add-log-exp`
3×	`pow1/2` `pow-prod-down` `prod-exp` `unswap-sqr`
2×	`sqr-pow`
1×	`unpow-prod-up` `pow-to-exp` `associate-+l-` `associate-l/` `pow-exp` `-commutative` `cbrt-unprod` `distribute-lft-out--` `pow-sub`

Counts

4 → 64

Calls

4 calls:

1.4s	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
7.0ms	(sqrt (* PI 2.0))
7.0ms	(sqrt (* PI 2.0))
8.0ms	(sqrt (* PI 2.0))

series451.0ms

Counts

4 → 6

Calls

4 calls:

451.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
0.0ms	(sqrt (* PI 2.0))
0.0ms	(sqrt (* PI 2.0))
0.0ms	(sqrt (* PI 2.0))

simplify4.2s

Counts

70 → 70

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	120	1239
1	310	1165
2	1055	1090
3	4542	1069
done	5000	1069

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize165.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (* (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)) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 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))))))))
0.4b	(* (exp (- (- 1.0 7.0) 0.5)) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 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	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
1.0b	(sqrt (* PI 2.0))

rewrite1.5m

Algorithm

rewrite-expression-head

Rules

1872×	`frac-add`
528×	`flip3-+` `flip-+`
401×	`frac-times` `associate-*r/`
243×	`exp-diff`
156×	`*-un-lft-identity`
117×	`distribute-lft-out`
34×	`add-exp-log`
32×	`associate-r`
29×	`add-cbrt-cube`
25×	`associate-l` `prod-exp`
18×	`add-sqr-sqrt`
14×	`pow1`
13×	`cbrt-unprod`
11×	`add-cube-cbrt`
8×	`div-exp`
7×	`unpow-prod-down`
5×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-*l/`
4×	`cbrt-undiv` `exp-sum` `add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `times-frac` `pow-exp` `*-commutative`
2×	`sub-neg` `sqrt-pow1` `associate--l+` `sqrt-prod` `sqr-pow`
1×	`unpow-prod-up` `associate-+l-` `pow1/2` `div-inv` `distribute-lft-out--` `pow-sub`

Counts

4 → 612

Calls

4 calls:

35.5s	(* (/ (* (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)) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 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))))))))
54.2s	(* (exp (- (- 1.0 7.0) 0.5)) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 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)))))))
963.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
7.0ms	(sqrt (* PI 2.0))

series1.2s

Counts

4 → 10

Calls

4 calls:

749.0ms	(* (/ (* (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)) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 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))))))))
207.0ms	(* (exp (- (- 1.0 7.0) 0.5)) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 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)))))))
280.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
0.0ms	(sqrt (* PI 2.0))

simplify829.0ms

Counts

622 → 622

Iterations

Useful iterations: done (648.0ms)

Iter	Nodes	Cost
0	1566	174720
done	5000	161364

prune12.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize83.0ms

Local error

Found 4 expressions with local error:

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

rewrite725.0ms

Algorithm

rewrite-expression-head

Rules

27×	`pow1`
17×	`*-un-lft-identity`
14×	`add-exp-log`
13×	`add-sqr-sqrt`
12×	`associate-l`
10×	`add-cbrt-cube`
9×	`pow-prod-down`
8×	`add-cube-cbrt` `associate-r`
7×	`unpow-prod-down`
6×	`sqrt-pow1` `prod-exp` `pow-prod-up`
5×	`distribute-lft-out`
4×	`cbrt-unprod` `add-log-exp`
3×	`pow1/2` `unswap-sqr`
2×	`cbrt-prod` `sqrt-prod` `*-commutative` `sqr-pow`
1×	`unpow-prod-up` `pow-to-exp` `associate-+l-` `pow1/3` `associate-*l/` `pow-exp` `distribute-lft-out--` `pow-sub`

Counts

4 → 76

Calls

4 calls:

666.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (cbrt (* (* PI 2.0) (sqrt (* PI 2.0)))))
3.0ms	(sqrt (* PI 2.0))
31.0ms	(* (* PI 2.0) (sqrt (* PI 2.0)))
22.0ms	(cbrt (* (* PI 2.0) (sqrt (* PI 2.0))))

series527.0ms

Counts

4 → 6

Calls

4 calls:

526.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (cbrt (* (* PI 2.0) (sqrt (* PI 2.0)))))
0.0ms	(sqrt (* PI 2.0))
0.0ms	(* (* PI 2.0) (sqrt (* PI 2.0)))
0.0ms	(cbrt (* (* PI 2.0) (sqrt (* PI 2.0))))

simplify904.0ms

Counts

82 → 82

Iterations

Useful iterations: done (901.0ms)

Iter	Nodes	Cost
0	207	1796
1	535	1702
2	2010	1482
done	5000	1291

prune763.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes114.0ms

Accuracy

0% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 0.8b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	130
1	77	130
done	77	130

end0.0ms

sample22.7s

Algorithm

intervals

Results

8.0s	3758×	body	10240	exit
5.3s	3333×	body	1280	valid
2.8s	2505×	body	640	valid
2.4s	1492×	body	1280	nan
1.3s	1156×	body	640	nan
1.2s	1282×	body	320	valid
427.0ms	330×	body	160	nan
341.0ms	651×	body	320	nan
311.0ms	620×	body	160	valid
95.0ms	339×	body	80	valid
43.0ms	283×	body	80	nan