Details

sample1.5s

Algorithm

intervals

Results

781.0ms	127×	body	10240	exit
252.0ms	114×	body	1280	valid
140.0ms	77×	body	640	valid
96.0ms	42×	body	320	valid
62.0ms	45×	body	1280	nan
42.0ms	42×	body	640	nan
15.0ms	17×	body	160	valid
15.0ms	20×	body	320	nan
6.0ms	13×	body	160	nan
3.0ms	12×	body	80	nan
3.0ms	9×	body	80	valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 3 (594.0ms)

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

prune58.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize59.0ms

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))

rewrite1.5m

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))))))
858.0ms	(/ (* (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)))
826.0ms	(* (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:

958.0ms	(* (/ (* (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))))))
616.0ms	(/ (* (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)))
416.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
0.0ms	(sqrt (* PI 2.0))

simplify833.0ms

Counts

308 → 308

Iterations

Useful iterations: done (752.0ms)

Iter	Nodes	Cost
0	1114	66543
done	5000	60831

prune6.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize212.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) 3)
1.0b	(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
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))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

245×	`*-un-lft-identity`
130×	`times-frac`
91×	`add-sqr-sqrt`
74×	`add-cube-cbrt`
65×	`distribute-lft-out`
39×	`swap-sqr`
32×	`associate-l`
31×	`distribute-lft-out--`
28×	`unpow-prod-down`
25×	`associate-r`
24×	`add-exp-log`
21×	`cube-prod` `add-cbrt-cube`
15×	`pow1`
12×	`associate-/r/`
7×	`prod-exp` `unswap-sqr`
6×	`flip3-+` `flip-+` `div-inv`
5×	`cbrt-undiv` `div-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow-exp` `sqr-pow`
2×	`pow-to-exp` `sqrt-pow1` `pow-prod-down` `associate-l/` `sqrt-prod` `-commutative` `rem-cube-cbrt`
1×	`unpow-prod-up` `cube-div` `pow2` `cube-mult` `frac-times` `associate-+l-` `pow-pow` `pow-plus` `pow1/2` `unpow3` `associate-*r/` `pow-sqr` `pow-prod-up` `pow-sub`

Counts

4 → 221

Calls

4 calls:

39.0ms	(pow (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) 3)
226.0ms	(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
875.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
9.0ms	(sqrt (* PI 2.0))

series590.0ms

Counts

4 → 10

Calls

4 calls:

78.0ms	(pow (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) 3)
40.0ms	(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
472.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
0.0ms	(sqrt (* PI 2.0))

simplify2.6s

Counts

231 → 231

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	430	5158
1	1279	4725
2	4599	4215
done	5000	4213

prune3.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize122.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* (+ (- z 1.0) 6.0) (+ (- z 1.0) 3.0)) (fma 676.5203681218851 (- (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099) (* z (- (* (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (* 0.9999999999998099 0.9999999999998099)))))
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)))
1.0b	(sqrt (* PI 2.0))

rewrite2.8s

Algorithm

rewrite-expression-head

Rules

1115×	`*-un-lft-identity`
431×	`distribute-lft-out`
360×	`times-frac`
121×	`distribute-lft-out--`
87×	`swap-sqr`
25×	`associate-l`
20×	`associate-r`
19×	`pow1` `add-sqr-sqrt`
16×	`add-exp-log`
14×	`flip3-+` `associate-*l/` `flip-+`
13×	`frac-times` `add-cbrt-cube`
12×	`add-cube-cbrt`
8×	`frac-add`
7×	`unpow-prod-down` `prod-exp`
5×	`associate-*r/` `pow-prod-down` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`distribute-rgt-in` `distribute-lft-in` `sqrt-pow1` `sqrt-prod` `fma-udef` `sqr-pow`
1×	`unpow-prod-up` `pow2` `pow-to-exp` `associate-+l-` `pow-plus` `pow1/2` `pow-exp` `pow-sqr` `pow-prod-up` `pow-sub`

Counts

4 → 224

Calls

4 calls:

240.0ms	(* (* (+ (- z 1.0) 6.0) (+ (- z 1.0) 3.0)) (fma 676.5203681218851 (- (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099) (* z (- (* (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (* 0.9999999999998099 0.9999999999998099)))))
1.5s	(* (+ (/ 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))))
995.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
4.0ms	(sqrt (* PI 2.0))

series681.0ms

Counts

4 → 10

Calls

4 calls:

124.0ms	(* (* (+ (- z 1.0) 6.0) (+ (- z 1.0) 3.0)) (fma 676.5203681218851 (- (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099) (* z (- (* (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (* 0.9999999999998099 0.9999999999998099)))))
112.0ms	(* (+ (/ 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))))
445.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
0.0ms	(sqrt (* PI 2.0))

simplify528.0ms

Counts

234 → 234

Iterations

Useful iterations: done (506.0ms)

Iter	Nodes	Cost
0	348	8916
1	1073	8112
done	5001	7586

prune2.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize162.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) 3)
1.0b	(pow (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)) 3)
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))

rewrite958.0ms

Algorithm

rewrite-expression-head

Rules

114×	`*-un-lft-identity`
60×	`times-frac`
50×	`add-sqr-sqrt`
49×	`unpow-prod-down`
45×	`add-cube-cbrt`
42×	`cube-prod`
29×	`distribute-lft-out`
15×	`add-exp-log`
13×	`distribute-lft-out--`
12×	`add-cbrt-cube`
11×	`associate-l`
9×	`pow1`
8×	`associate-/r/`
6×	`pow-unpow`
5×	`pow-exp`
4×	`expm1-log1p-u` `flip3-+` `associate-r` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp` `rem-cube-cbrt` `sqr-pow`
3×	`pow-to-exp` `prod-exp` `unswap-sqr`
2×	`cbrt-undiv` `cube-div` `cube-mult` `pow-pow` `sqrt-pow1` `unpow3` `div-exp` `sqrt-prod`
1×	`unpow-prod-up` `associate-+l-` `pow1/2` `pow-prod-down` `associate-l/` `-commutative` `cbrt-unprod` `pow-sub`

Counts

4 → 174

Calls

4 calls:

66.0ms	(pow (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) 3)
39.0ms	(pow (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)) 3)
840.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
5.0ms	(sqrt (* PI 2.0))

series520.0ms

Counts

4 → 10

Calls

4 calls:

74.0ms	(pow (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) 3)
65.0ms	(pow (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)) 3)
380.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
0.0ms	(sqrt (* PI 2.0))

simplify2.3s

Counts

184 → 184

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	394	3705
1	1196	3432
2	4280	3082
done	5000	3079

prune3.0s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes316.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify20.0ms

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	73	400
1	98	400
done	98	400

end0.0ms

sample30.0s

Algorithm

intervals

Results

10.2s	3824×	body	10240	exit
7.3s	3481×	body	1280	valid
4.3s	1441×	body	1280	nan
3.4s	2419×	body	640	valid
1.4s	1323×	body	640	nan
1.2s	1243×	body	320	valid
918.0ms	631×	body	320	nan
288.0ms	608×	body	160	valid
245.0ms	289×	body	160	nan
80.0ms	349×	body	80	valid
66.0ms	317×	body	80	nan