Details

sample3.1s

Algorithm

intervals

Results

2.5s	111×	body	10240	exit
149.0ms	43×	body	1280	nan
148.0ms	258×	body	80	valid
145.0ms	41×	body	640	nan
22.0ms	12×	body	320	nan
9.0ms	13×	body	80	nan
8.0ms	7×	body	160	nan

simplify3.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5014
3	4020
2	623
1	155
0	60

prune61.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize217.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (+ (/ 676.5203681218851 (- 1 z)) (+ (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (/ 771.3234287776531 (- 3 z))))) (+ (/ -176.6150291621406 (- 4 z)) (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))))
1.0b	(+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))
1.0b	(/ (pow (+ (- 7 z) 0.5) (+ (- 0 z) 0.5)) (exp (+ (- 7 z) 0.5)))
1.0b	(sqrt (* 2 PI))

rewrite7.2s

Algorithm

rewrite-expression-head

Rules

225×	`*-un-lft-identity`
216×	`frac-add`
119×	`distribute-lft-out` `add-log-exp`
93×	`sum-log`
64×	`times-frac`
55×	`flip3-+` `flip-+`
25×	`add-sqr-sqrt` `unpow-prod-down` `add-cube-cbrt`
17×	`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×	`associate-/r*` `insert-posit16`
3×	`div-exp`
2×	`+-commutative` `associate-+l+` `sqrt-pow1` `associate-+l-`
1×	`pow-to-exp` `cbrt-undiv` `associate-+r+` `clear-num` `frac-2neg` `pow1/2` `exp-diff` `pow-prod-down` `pow-exp` `associate-/r/` `sqrt-prod` `div-inv` `pow-sub` `associate-/l/`

Counts

4 → 219

Calls

4 calls:

6.8s	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (+ (/ 676.5203681218851 (- 1 z)) (+ (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (/ 771.3234287776531 (- 3 z))))) (+ (/ -176.6150291621406 (- 4 z)) (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))))
295.0ms	(+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))
173.0ms	(/ (pow (+ (- 7 z) 0.5) (+ (- 0 z) 0.5)) (exp (+ (- 7 z) 0.5)))
3.0ms	(sqrt (* 2 PI))

series611.0ms

Counts

4 → 10

Calls

4 calls:

255.0ms	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (+ (/ 676.5203681218851 (- 1 z)) (+ (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (/ 771.3234287776531 (- 3 z))))) (+ (/ -176.6150291621406 (- 4 z)) (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))))
122.0ms	(+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))
233.0ms	(/ (pow (+ (- 7 z) 0.5) (+ (- 0 z) 0.5)) (exp (+ (- 7 z) 0.5)))
0.0ms	(sqrt (* 2 PI))

simplify5.5s

Counts

229 → 229

Iterations

Iter	Nodes
done	5002
1	2473
0	723

prune4.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize153.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (+ (/ 676.5203681218851 (- 1 z)) (+ (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (/ 771.3234287776531 (- 3 z))))) (+ (/ -176.6150291621406 (- 4 z)) (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))))
1.0b	(+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))
1.0b	(sqrt (* 2 PI))
1.6b	(exp (- (* (log (- 7.5 z)) (- 0.5 z)) (- 7.5 z)))

rewrite6.7s

Algorithm

rewrite-expression-head

Rules

216×	`frac-add`
180×	`*-un-lft-identity`
125×	`add-log-exp`
109×	`distribute-lft-out`
93×	`sum-log`
55×	`flip3-+` `flip-+`
24×	`times-frac`
12×	`distribute-lft-out--`
7×	`pow1` `exp-sum`
5×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`add-cbrt-cube` `associate--l+` `add-exp-log` `insert-posit16`
3×	`exp-prod` `sub-neg` `diff-log` `rem-exp-log`
2×	`distribute-rgt-in` `+-commutative` `associate-+l+` `distribute-lft-in` `sqrt-pow1`
1×	`associate-+r+` `pow1/2` `exp-diff` `pow-prod-down` `sqrt-prod` `associate--r-`

Counts

4 → 170

Calls

4 calls:

6.4s	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (+ (/ 676.5203681218851 (- 1 z)) (+ (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (/ 771.3234287776531 (- 3 z))))) (+ (/ -176.6150291621406 (- 4 z)) (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))))
216.0ms	(+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))
5.0ms	(sqrt (* 2 PI))
58.0ms	(exp (- (* (log (- 7.5 z)) (- 0.5 z)) (- 7.5 z)))

series470.0ms

Counts

4 → 10

Calls

4 calls:

246.0ms	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (+ (/ 676.5203681218851 (- 1 z)) (+ (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (/ 771.3234287776531 (- 3 z))))) (+ (/ -176.6150291621406 (- 4 z)) (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))))
88.0ms	(+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))
0.0ms	(sqrt (* 2 PI))
136.0ms	(exp (- (* (log (- 7.5 z)) (- 0.5 z)) (- 7.5 z)))

simplify6.8s

Counts

180 → 180

Iterations

Iter	Nodes
done	5001
1	2292
0	625

prune3.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize254.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (+ (/ 676.5203681218851 (- 1 z)) (+ (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (/ 771.3234287776531 (- 3 z))))) (+ (/ -176.6150291621406 (- 4 z)) (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))))
1.0b	(+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))
1.0b	(sqrt (* 2 PI))
1.6b	(exp (- (+ (* 0.5 (log (- 7.5 z))) z) (+ (* (log (- 7.5 z)) z) 7.5)))

rewrite7.0s

Algorithm

rewrite-expression-head

Rules

216×	`frac-add`
182×	`*-un-lft-identity`
132×	`add-log-exp`
109×	`distribute-lft-out`
97×	`sum-log`
55×	`flip3-+` `flip-+`
24×	`times-frac`
13×	`distribute-lft-out--`
7×	`add-sqr-sqrt` `pow1`
5×	`exp-prod` `add-cube-cbrt` `rem-exp-log`
4×	`add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16`
3×	`exp-sum`
2×	`+-commutative` `associate-+l+` `sqrt-pow1`
1×	`associate-+r+` `sub-neg` `pow1/2` `exp-diff` `pow-prod-down` `associate--l+` `sqrt-prod` `difference-of-squares`

Counts

4 → 170

Calls

4 calls:

6.6s	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (+ (/ 676.5203681218851 (- 1 z)) (+ (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (/ 771.3234287776531 (- 3 z))))) (+ (/ -176.6150291621406 (- 4 z)) (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))))
231.0ms	(+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))
5.0ms	(sqrt (* 2 PI))
176.0ms	(exp (- (+ (* 0.5 (log (- 7.5 z))) z) (+ (* (log (- 7.5 z)) z) 7.5)))

series517.0ms

Counts

4 → 10

Calls

4 calls:

231.0ms	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (+ (/ 676.5203681218851 (- 1 z)) (+ (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (/ 771.3234287776531 (- 3 z))))) (+ (/ -176.6150291621406 (- 4 z)) (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))))
124.0ms	(+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))
0.0ms	(sqrt (* 2 PI))
161.0ms	(exp (- (+ (* 0.5 (log (- 7.5 z))) z) (+ (* (log (- 7.5 z)) z) 7.5)))

simplify7.5s

Counts

180 → 180

Iterations

Iter	Nodes
done	5002
1	2253
0	609

prune3.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize246.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (+ (/ 676.5203681218851 (- 1 z)) (+ (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (/ 771.3234287776531 (- 3 z))))) (+ (/ -176.6150291621406 (- 4 z)) (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))))
1.0b	(+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))
1.0b	(/ (pow (+ (- 7 z) 0.5) (+ (- 0 z) 0.5)) (exp (+ (- 7 z) 0.5)))
1.0b	(sqrt PI)

rewrite6.9s

Algorithm

rewrite-expression-head

Rules

226×	`*-un-lft-identity`
216×	`frac-add`
119×	`distribute-lft-out` `add-log-exp`
93×	`sum-log`
64×	`times-frac`
55×	`flip3-+` `flip-+`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`unpow-prod-down`
17×	`distribute-lft-out--`
11×	`exp-sum`
10×	`associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `unpow-prod-up` `sqr-pow`
4×	`associate-/r*` `insert-posit16`
3×	`div-exp` `sqrt-prod`
2×	`+-commutative` `associate-+l+` `associate-+l-`
1×	`pow-to-exp` `cbrt-undiv` `rem-sqrt-square` `associate-+r+` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `exp-diff` `pow-exp` `associate-/r/` `div-inv` `pow-sub` `associate-/l/`

Counts

4 → 221

Calls

4 calls:

6.4s	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (+ (/ 676.5203681218851 (- 1 z)) (+ (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (/ 771.3234287776531 (- 3 z))))) (+ (/ -176.6150291621406 (- 4 z)) (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))))
233.0ms	(+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))
254.0ms	(/ (pow (+ (- 7 z) 0.5) (+ (- 0 z) 0.5)) (exp (+ (- 7 z) 0.5)))
2.0ms	(sqrt PI)

series664.0ms

Counts

4 → 10

Calls

4 calls:

259.0ms	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (+ (/ 676.5203681218851 (- 1 z)) (+ (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2 z))) (/ 771.3234287776531 (- 3 z))))) (+ (/ -176.6150291621406 (- 4 z)) (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))))
123.0ms	(+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- 5 z))) (/ 9.984369578019572e-06 (- 7 z)))
282.0ms	(/ (pow (+ (- 7 z) 0.5) (+ (- 0 z) 0.5)) (exp (+ (- 7 z) 0.5)))
0.0ms	(sqrt PI)

simplify5.6s

Counts

231 → 231

Iterations

Iter	Nodes
done	5002
1	2458
0	720

prune3.9s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

regimes606.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

bsearch0.0ms

simplify23.0ms

Iterations

Iter	Nodes
done	80
1	80
0	61

end0.0ms

sample1.5m

Algorithm

intervals

Results

1.2m	3678×	body	10240	exit
6.6s	8091×	body	80	valid
6.0s	1401×	body	1280	nan
4.1s	1181×	body	640	nan
1.4s	601×	body	320	nan
471.0ms	319×	body	160	nan
176.0ms	287×	body	80	nan