Details

sample3.0s

Algorithm

intervals

Results

2.6s	143×	body	10240	exit
177.0ms	256×	body	80	valid
86.0ms	44×	body	1280	nan
51.0ms	39×	body	640	nan
20.0ms	22×	body	320	nan
4.0ms	6×	body	160	nan
2.0ms	8×	body	80	nan

simplify3.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	4551
2	612
1	148
0	60

prune54.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize150.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.4m

Algorithm

rewrite-expression-head

Rules

192×	`*-un-lft-identity`
125×	`distribute-lft-out`
80×	`frac-add`
44×	`times-frac`
30×	`add-sqr-sqrt` `unpow-prod-down` `associate-*l/`
29×	`flip3-+` `flip-+`
28×	`add-cube-cbrt`
23×	`associate-l`
18×	`add-log-exp`
12×	`exp-sum`
11×	`associate-/l*`
10×	`sum-log`
9×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
5×	`unpow-prod-up` `associate-+r-` `distribute-rgt-neg-in` `sqr-pow`
4×	`associate-/r` `associate-r*`
3×	`exp-diff` `div-exp` `associate-/r/` `pow-sub` `associate-/l/`
2×	`neg-sub0` `sqrt-pow1` `unsub-neg` `pow-prod-down` `sqrt-prod`
1×	`pow-to-exp` `cbrt-undiv` `+-commutative` `associate-+l+` `clear-num` `frac-2neg` `pow1/2` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 180

Calls

4 calls:

2.3m	(* (+ (+ (+ (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) 0.9999999999998099) (/ 12.507343278686905 (+ (- z) 5.0))) (+ (/ -176.6150291621406 (+ (- z) 4.0)) (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ 1.5056327351493116e-07 (+ 8.0 (- z)))) (/ 9.984369578019572e-06 (+ 7.0 (- z)))))) (sqrt (* 2.0 PI)))
10.2s	(+ (+ (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) 0.9999999999998099) (/ 12.507343278686905 (+ (- z) 5.0)))
309.0ms	(/ (pow (+ 7.0 (+ 0.5 (- z))) (+ 0.5 (- z))) (exp (+ 7.0 (+ 0.5 (- z)))))
3.0ms	(sqrt (* 2.0 PI))

series877.0ms

Counts

4 → 10

Calls

4 calls:

473.0ms	(* (+ (+ (+ (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) 0.9999999999998099) (/ 12.507343278686905 (+ (- z) 5.0))) (+ (/ -176.6150291621406 (+ (- z) 4.0)) (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ 1.5056327351493116e-07 (+ 8.0 (- z)))) (/ 9.984369578019572e-06 (+ 7.0 (- z)))))) (sqrt (* 2.0 PI)))
142.0ms	(+ (+ (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) 0.9999999999998099) (/ 12.507343278686905 (+ (- z) 5.0)))
262.0ms	(/ (pow (+ 7.0 (+ 0.5 (- z))) (+ 0.5 (- z))) (exp (+ 7.0 (+ 0.5 (- z)))))
0.0ms	(sqrt (* 2.0 PI))

simplify4.2s

Counts

190 → 190

Iterations

Iter	Nodes
done	5000
1	1649
0	542

prune3.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize221.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.0m

Algorithm

rewrite-expression-head

Rules

224×	`*-un-lft-identity`
150×	`distribute-lft-out`
80×	`frac-add`
52×	`cbrt-prod`
35×	`flip3-+` `flip-+`
32×	`associate-l` `associate-*l/`
24×	`add-sqr-sqrt`
21×	`swap-sqr`
18×	`add-log-exp`
16×	`pow1`
14×	`add-cube-cbrt`
13×	`associate-r`
12×	`cbrt-div`
10×	`sum-log` `distribute-rgt-neg-in`
8×	`add-exp-log`
6×	`add-cbrt-cube` `pow1/3`
5×	`unswap-sqr`
4×	`frac-times` `pow-prod-down`
2×	`sqrt-pow1` `prod-exp` `associate-r/` `pow-sqr` `-commutative` `pow-prod-up` `sqrt-prod` `cbrt-unprod`
1×	`pow2` `+-commutative` `associate-+l+` `pow-plus` `pow1/2`

Counts

4 → 170

Calls

4 calls:

1.8m	(* (+ (+ (+ (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) 0.9999999999998099) (/ 12.507343278686905 (+ (- z) 5.0))) (+ (/ -176.6150291621406 (+ (- z) 4.0)) (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ 1.5056327351493116e-07 (+ 8.0 (- z)))) (/ 9.984369578019572e-06 (+ 7.0 (- z)))))) (sqrt (* 2.0 PI)))
10.8s	(+ (+ (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) 0.9999999999998099) (/ 12.507343278686905 (+ (- z) 5.0)))
216.0ms	(* (cbrt (+ 7.0 (+ 0.5 (- z)))) (cbrt (+ 7.0 (+ 0.5 (- z)))))
3.0ms	(sqrt (* 2.0 PI))

series496.0ms

Counts

4 → 10

Calls

4 calls:

283.0ms	(* (+ (+ (+ (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) 0.9999999999998099) (/ 12.507343278686905 (+ (- z) 5.0))) (+ (/ -176.6150291621406 (+ (- z) 4.0)) (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ 1.5056327351493116e-07 (+ 8.0 (- z)))) (/ 9.984369578019572e-06 (+ 7.0 (- z)))))) (sqrt (* 2.0 PI)))
105.0ms	(+ (+ (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) 0.9999999999998099) (/ 12.507343278686905 (+ (- z) 5.0)))
107.0ms	(* (cbrt (+ 7.0 (+ 0.5 (- z)))) (cbrt (+ 7.0 (+ 0.5 (- z)))))
0.0ms	(sqrt (* 2.0 PI))

simplify3.6s

Counts

180 → 180

Iterations

Iter	Nodes
done	5001
1	1521
0	472

prune2.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize75.0ms

Local error

Found 4 expressions with local error:

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

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
44×	`times-frac`
32×	`add-sqr-sqrt`
30×	`unpow-prod-down`
29×	`add-cube-cbrt`
25×	`distribute-lft-out`
12×	`exp-sum`
11×	`associate-/l*`
9×	`sqrt-prod`
7×	`pow1`
6×	`add-cbrt-cube` `add-exp-log`
5×	`unpow-prod-up` `associate-+r-` `distribute-rgt-neg-in` `sqr-pow`
4×	`associate-/r*` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `exp-diff` `div-exp` `associate-/r/` `pow-sub` `associate-/l/`
2×	`neg-sub0` `unsub-neg`
1×	`pow-to-exp` `cbrt-undiv` `clear-num` `frac-2neg` `pow-exp` `div-inv`

Counts

4 → 118

Calls

4 calls:

196.0ms	(/ (pow (+ 7.0 (+ 0.5 (- z))) (+ 0.5 (- z))) (exp (+ 7.0 (+ 0.5 (- z)))))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)

series167.0ms

Counts

4 → 6

Calls

4 calls:

166.0ms	(/ (pow (+ 7.0 (+ 0.5 (- z))) (+ 0.5 (- z))) (exp (+ 7.0 (+ 0.5 (- z)))))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify1.3s

Counts

124 → 124

Iterations

Iter	Nodes
done	5001
2	1753
1	453
0	214

prune814.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize84.0ms

Local error

Found 4 expressions with local error:

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

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

59×	`*-un-lft-identity`
33×	`times-frac`
30×	`add-sqr-sqrt`
27×	`add-cube-cbrt`
24×	`unpow-prod-down`
20×	`distribute-lft-out`
11×	`associate-/l*`
9×	`sqrt-prod`
7×	`pow1`
6×	`add-cbrt-cube` `add-exp-log`
4×	`unpow-prod-up` `distribute-rgt-neg-in` `add-log-exp` `sqr-pow`
3×	`rem-sqrt-square` `associate-/r*` `sqrt-pow1` `pow1/2` `div-exp` `pow-sub` `associate-/l/`
1×	`neg-sub0` `pow-to-exp` `cbrt-undiv` `clear-num` `associate-+r-` `frac-2neg` `unsub-neg` `pow-exp` `div-inv`

Counts

4 → 103

Calls

4 calls:

113.0ms	(/ (pow (+ 7.0 (+ 0.5 (- z))) (+ 0.5 (- z))) (exp 7.0))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)

series196.0ms

Counts

4 → 6

Calls

4 calls:

196.0ms	(/ (pow (+ 7.0 (+ 0.5 (- z))) (+ 0.5 (- z))) (exp 7.0))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify1.2s

Counts

109 → 109

Iterations

Iter	Nodes
done	5001
2	1267
1	343
0	164

prune712.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes113.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify15.0ms

Iterations

Iter	Nodes
done	84
1	84
0	62

end0.0ms

sample56.6s

Algorithm

intervals

Results

47.6s	4012×	body	10240	exit
3.1s	1571×	body	1280	nan
2.8s	8086×	body	80	valid
1.5s	1243×	body	640	nan
799.0ms	619×	body	320	nan
176.0ms	315×	body	160	nan
97.0ms	301×	body	80	nan