Details

sample389.0ms

Algorithm

intervals

Results

111.0ms	104×	body	10240	exit
95.0ms	107×	body	1280	valid
56.0ms	91×	body	640	valid
30.0ms	48×	body	1280	nan
22.0ms	44×	body	640	nan
15.0ms	35×	body	320	valid
9.0ms	15×	body	320	nan
4.0ms	13×	body	160	valid
2.0ms	9×	body	160	nan
2.0ms	13×	body	80	nan
1.0ms	11×	body	80	valid

simplify730.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (140.0ms)

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize45.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (* (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))))))
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))

rewrite18.0s

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:

16.6s	(* (* (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))))))
422.0ms	(/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
931.0ms	(+ (+ (/ 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))

series962.0ms

Counts

4 → 10

Calls

4 calls:

638.0ms	(* (* (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))))))
175.0ms	(/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
149.0ms	(+ (+ (/ 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))

simplify696.0ms

Counts

599 → 599

Iterations

Useful iterations: done (546.0ms)

Iter	Nodes	Cost
0	1654	126424
done	5000	117516

prune7.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize108.0ms

Local error

Found 4 expressions with local error:

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	(* (+ (/ 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	(pow (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) 3)
1.0b	(sqrt (* PI 2.0))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

2315×	`*-un-lft-identity`
896×	`distribute-lft-out`
756×	`times-frac`
252×	`distribute-lft-out--`
174×	`swap-sqr`
26×	`associate-r` `associate-l`
22×	`pow1`
19×	`add-sqr-sqrt`
18×	`frac-times`
17×	`flip3-+` `frac-add` `flip-+`
15×	`add-cube-cbrt`
13×	`unpow-prod-down` `cube-prod`
9×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r/` `associate-l/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cube-div` `pow-unpow` `pow-prod-down`
2×	`pow2` `distribute-rgt-in` `distribute-lft-in` `sqrt-pow1` `pow-plus` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`cube-mult` `pow-to-exp` `pow-pow` `pow1/2` `unpow3` `pow-exp` `sqrt-prod` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 357

Calls

4 calls:

696.0ms	(* (+ (/ 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))))
687.0ms	(* (+ (/ 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))))
179.0ms	(pow (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) 3)
2.0ms	(sqrt (* PI 2.0))

series296.0ms

Counts

4 → 10

Calls

4 calls:

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))))
92.0ms	(* (+ (/ 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))))
111.0ms	(pow (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) 3)
0.0ms	(sqrt (* PI 2.0))

simplify1.5s

Counts

367 → 367

Iterations

Useful iterations: 2 (339.0ms)

Iter	Nodes	Cost
0	259	13573
1	875	11671
2	4198	11361
done	5000	11361

prune2.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize91.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
1.0b	(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
1.0b	(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
1.0b	(sqrt (* PI 2.0))

rewrite278.0ms

Algorithm

rewrite-expression-head

Rules

544×	`*-un-lft-identity`
300×	`times-frac`
184×	`add-sqr-sqrt`
148×	`add-cube-cbrt`
144×	`distribute-lft-out`
117×	`swap-sqr`
72×	`distribute-lft-out--`
63×	`associate-r` `associate-l`
40×	`add-exp-log` `add-cbrt-cube`
28×	`pow1`
24×	`associate-/r/`
12×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up`
2×	`sqrt-pow1`
1×	`pow1/2` `sqrt-prod`

Counts

4 → 346

Calls

4 calls:

82.0ms	(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
83.0ms	(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
89.0ms	(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
2.0ms	(sqrt (* PI 2.0))

series115.0ms

Counts

4 → 10

Calls

4 calls:

37.0ms	(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
35.0ms	(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
41.0ms	(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
0.0ms	(sqrt (* PI 2.0))

simplify1.1s

Counts

356 → 356

Iterations

Useful iterations: 2 (260.0ms)

Iter	Nodes	Cost
0	242	8253
1	759	7159
2	3341	6419
done	5000	6419

prune4.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize103.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)) 3)
1.0b	(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
1.0b	(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
1.0b	(sqrt (* PI 2.0))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

413×	`*-un-lft-identity`
230×	`times-frac`
143×	`add-sqr-sqrt`
119×	`add-cube-cbrt`
108×	`distribute-lft-out`
78×	`swap-sqr`
54×	`distribute-lft-out--`
42×	`associate-r` `associate-l`
31×	`add-exp-log` `add-cbrt-cube`
22×	`pow1`
21×	`unpow-prod-down` `cube-prod`
20×	`associate-/r/`
10×	`flip3-+` `flip-+` `div-inv`
9×	`cbrt-undiv` `div-exp`
8×	`prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow-prod-down`
2×	`pow2` `frac-times` `sqrt-pow1` `pow-plus` `associate-r/` `associate-l/` `pow-exp` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cube-cbrt`
1×	`cube-div` `cube-mult` `pow-to-exp` `pow-pow` `pow1/2` `unpow3` `sqrt-prod` `sqr-pow`

Counts

4 → 299

Calls

4 calls:

22.0ms	(pow (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)) 3)
82.0ms	(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
82.0ms	(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
2.0ms	(sqrt (* PI 2.0))

series128.0ms

Counts

4 → 10

Calls

4 calls:

52.0ms	(pow (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)) 3)
41.0ms	(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
35.0ms	(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
0.0ms	(sqrt (* PI 2.0))

simplify389.0ms

Counts

309 → 309

Iterations

Useful iterations: done (372.0ms)

Iter	Nodes	Cost
0	349	6809
1	1114	5968
done	5000	5342

prune3.9s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes200.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	86	411
1	128	411
done	128	411

end0.0ms

sample11.4s

Algorithm

intervals

Results

3.9s	3840×	body	10240	exit
2.9s	3413×	body	1280	valid
1.5s	2499×	body	640	valid
1.0s	1538×	body	1280	nan
642.0ms	1268×	body	640	nan
509.0ms	1187×	body	320	valid
217.0ms	590×	body	320	nan
176.0ms	634×	body	160	valid
76.0ms	307×	body	160	nan
50.0ms	357×	body	80	valid
36.0ms	309×	body	80	nan