Details

sample2.6s

Algorithm

intervals

Results

2.2s	125×	body	10240	exit
130.0ms	38×	body	1280	nan
98.0ms	259×	body	80	valid
42.0ms	32×	body	640	nan
17.0ms	17×	body	320	nan
5.0ms	9×	body	160	nan
5.0ms	15×	body	80	nan

simplify4.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	4112
2	625
1	155
0	60

prune45.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize197.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))))) (/ 12.507343278686905 (- 5 z)))
1.0b	(/ (pow (+ (- 7 z) 0.5) (+ 0.5 (- 0 z))) (exp (+ (- 7 z) 0.5)))
1.0b	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
1.0b	(sqrt (* 2 PI))

rewrite1.3m

Algorithm

rewrite-expression-head

Rules

385×	`*-un-lft-identity`
241×	`distribute-lft-out`
141×	`frac-add`
132×	`add-log-exp`
106×	`sum-log`
79×	`times-frac`
46×	`flip3-+` `flip-+`
44×	`fma-def`
35×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`unpow-prod-down`
15×	`distribute-lft-out--`
11×	`exp-sum`
10×	`associate-/l*`
7×	`pow1`
6×	`add-cbrt-cube` `add-exp-log`
5×	`unpow-prod-up` `sqr-pow`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u`
3×	`div-exp` `associate-/r/` `pow-sub` `associate-/l/`
2×	`+-commutative` `sqrt-pow1` `div-inv` `sub0-neg`
1×	`pow-to-exp` `cbrt-undiv` `associate-+l+` `clear-num` `associate-+r-` `frac-2neg` `pow1/2` `exp-diff` `unsub-neg` `pow-prod-down` `pow-exp` `associate-+l-` `sqrt-prod`

Counts

4 → 255

Calls

4 calls:

1.3m	(+ (+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))))) (/ 12.507343278686905 (- 5 z)))
160.0ms	(/ (pow (+ (- 7 z) 0.5) (+ 0.5 (- 0 z))) (exp (+ (- 7 z) 0.5)))
333.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
5.0ms	(sqrt (* 2 PI))

series541.0ms

Counts

4 → 10

Calls

4 calls:

233.0ms	(+ (+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))))) (/ 12.507343278686905 (- 5 z)))
232.0ms	(/ (pow (+ (- 7 z) 0.5) (+ 0.5 (- 0 z))) (exp (+ (- 7 z) 0.5)))
76.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
0.0ms	(sqrt (* 2 PI))

simplify4.0s

Counts

265 → 265

Iterations

Iter	Nodes
done	5004
1	2505
0	786

prune3.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize184.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))))) (/ 12.507343278686905 (- 5 z)))
1.0b	(/ (pow (- 7 (- z 0.5)) (- 0.5 z)) (exp 7))
1.0b	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
1.0b	(sqrt (* 2 PI))

rewrite1.3m

Algorithm

rewrite-expression-head

Rules

413×	`*-un-lft-identity`
231×	`distribute-lft-out`
141×	`frac-add`
132×	`add-log-exp`
106×	`sum-log`
102×	`times-frac`
76×	`add-sqr-sqrt`
68×	`add-cube-cbrt`
46×	`flip3-+` `flip-+`
44×	`unpow-prod-up` `fma-def`
36×	`prod-diff`
24×	`unpow-prod-down`
22×	`distribute-lft-out--`
21×	`associate-/l*`
7×	`pow1`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `sub-neg` `insert-posit16` `log1p-expm1-u` `difference-of-squares` `sqr-pow`
3×	`associate-/r*` `div-exp`
2×	`+-commutative` `sqrt-pow1` `associate-/r/` `div-inv`
1×	`pow-to-exp` `cbrt-undiv` `associate-+l+` `clear-num` `frac-2neg` `pow1/2` `pow-prod-down` `pow-exp` `sqrt-prod` `pow-sub` `associate-/l/`

Counts

4 → 285

Calls

4 calls:

1.3m	(+ (+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))))) (/ 12.507343278686905 (- 5 z)))
52.0ms	(/ (pow (- 7 (- z 0.5)) (- 0.5 z)) (exp 7))
755.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
8.0ms	(sqrt (* 2 PI))

series609.0ms

Counts

4 → 10

Calls

4 calls:

224.0ms	(+ (+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))))) (/ 12.507343278686905 (- 5 z)))
281.0ms	(/ (pow (- 7 (- z 0.5)) (- 0.5 z)) (exp 7))
103.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
0.0ms	(sqrt (* 2 PI))

simplify4.3s

Counts

295 → 295

Iterations

Iter	Nodes
done	5000
1	2659
0	854

prune4.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize206.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))))) (/ 12.507343278686905 (- 5 z)))
1.0b	(/ (exp 7) (pow (- 7 (- z 0.5)) (/ (- 0.5 z) 2)))
1.0b	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
1.0b	(sqrt (* 2 PI))

rewrite52.3s

Algorithm

rewrite-expression-head

Rules

378×	`*-un-lft-identity`
231×	`distribute-lft-out`
141×	`frac-add`
132×	`add-log-exp`
106×	`sum-log`
69×	`times-frac`
46×	`flip3-+` `flip-+`
44×	`fma-def`
41×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
24×	`unpow-prod-down`
22×	`distribute-lft-out--`
10×	`associate-/r*`
7×	`pow1`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `difference-of-squares` `sqr-pow`
3×	`div-exp` `associate-/r/` `associate-/l*`
2×	`+-commutative` `sqrt-pow1` `div-inv`
1×	`pow-to-exp` `cbrt-undiv` `associate-+l+` `clear-num` `frac-2neg` `pow1/2` `div-sub` `pow-prod-down` `pow-exp` `sqrt-prod` `pow-sub`

Counts

4 → 241

Calls

4 calls:

51.9s	(+ (+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))))) (/ 12.507343278686905 (- 5 z)))
44.0ms	(/ (exp 7) (pow (- 7 (- z 0.5)) (/ (- 0.5 z) 2)))
314.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
4.0ms	(sqrt (* 2 PI))

series447.0ms

Counts

4 → 10

Calls

4 calls:

169.0ms	(+ (+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))))) (/ 12.507343278686905 (- 5 z)))
222.0ms	(/ (exp 7) (pow (- 7 (- z 0.5)) (/ (- 0.5 z) 2)))
56.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
0.0ms	(sqrt (* 2 PI))

simplify3.0s

Counts

251 → 251

Iterations

Iter	Nodes
done	5002
1	2451
0	761

prune2.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize150.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))))) (/ 12.507343278686905 (- 5 z)))
1.0b	(* (cbrt (+ (- 7 z) 0.5)) (cbrt (+ (- 7 z) 0.5)))
1.0b	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
1.0b	(sqrt (* 2 PI))

rewrite49.9s

Algorithm

rewrite-expression-head

Rules

391×	`*-un-lft-identity`
247×	`distribute-lft-out`
141×	`frac-add`
132×	`add-log-exp`
106×	`sum-log`
52×	`flip3-+` `flip-+`
44×	`fma-def`
39×	`times-frac`
36×	`cbrt-prod`
30×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
18×	`distribute-lft-out--`
14×	`pow1` `swap-sqr`
12×	`cbrt-div`
8×	`associate-r` `associate-l`
6×	`pow1/3` `add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`pow-prod-down`
2×	`+-commutative` `sqrt-pow1` `associate-l/` `associate-r/` `associate-/r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `associate-+l+` `pow-plus` `pow1/2` `prod-exp` `*-commutative` `sqrt-prod` `cbrt-unprod` `div-inv`

Counts

4 → 243

Calls

4 calls:

49.6s	(+ (+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))))) (/ 12.507343278686905 (- 5 z)))
80.0ms	(* (cbrt (+ (- 7 z) 0.5)) (cbrt (+ (- 7 z) 0.5)))
201.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
4.0ms	(sqrt (* 2 PI))

series331.0ms

Counts

4 → 10

Calls

4 calls:

168.0ms	(+ (+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))))) (/ 12.507343278686905 (- 5 z)))
107.0ms	(* (cbrt (+ (- 7 z) 0.5)) (cbrt (+ (- 7 z) 0.5)))
56.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
0.0ms	(sqrt (* 2 PI))

simplify2.8s

Counts

253 → 253

Iterations

Iter	Nodes
done	5000
1	2387
0	723

prune2.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

regimes352.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify20.0ms

Iterations

Iter	Nodes
done	78
1	78
0	60

end0.0ms

sample56.3s

Algorithm

intervals

Results

47.2s	3998×	body	10240	exit
2.8s	8098×	body	80	valid
2.6s	1419×	body	1280	nan
1.4s	1251×	body	640	nan
869.0ms	628×	body	320	nan
633.0ms	299×	body	80	nan
477.0ms	327×	body	160	nan