Details

sample2.5s

Algorithm

intervals

Results

2.2s	129×	body	10240	exit
97.0ms	50×	body	1280	nan
87.0ms	258×	body	80	valid
42.0ms	31×	body	640	nan
20.0ms	18×	body	320	nan
5.0ms	8×	body	160	nan
4.0ms	11×	body	80	nan

simplify2.4s

Counts

1 → 1

Iterations

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

prune78.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize233.0ms

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	(+ (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) 0.9999999999998099)
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	(sqrt (* 2.0 PI))

rewrite2.3m

Algorithm

rewrite-expression-head

Rules

187×	`*-un-lft-identity`
121×	`distribute-lft-out`
78×	`frac-add`
44×	`times-frac`
30×	`add-sqr-sqrt` `unpow-prod-down` `associate-*l/`
28×	`flip3-+` `add-cube-cbrt` `flip-+`
23×	`associate-l`
13×	`add-log-exp`
12×	`exp-sum`
11×	`associate-/l*`
9×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
6×	`sum-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 → 176

Calls

4 calls:

304.0ms	(/ (pow (+ 7.0 (+ 0.5 (- z))) (+ 0.5 (- z))) (exp (+ 7.0 (+ 0.5 (- z)))))
2.6s	(+ (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) 0.9999999999998099)
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)))
3.0ms	(sqrt (* 2.0 PI))

series681.0ms

Counts

4 → 10

Calls

4 calls:

245.0ms	(/ (pow (+ 7.0 (+ 0.5 (- z))) (+ 0.5 (- z))) (exp (+ 7.0 (+ 0.5 (- z)))))
84.0ms	(+ (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) 0.9999999999998099)
352.0ms	(* (+ (+ (+ (+ (+ (/ 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)))
0.0ms	(sqrt (* 2.0 PI))

simplify669.0ms

Counts

186 → 186

Iterations

Iter	Nodes
done	5002
1	1623
0	532

prune3.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize229.0ms

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)))
1.0b	(+ (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) 0.9999999999998099)
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	(sqrt (* 2.0 PI))

rewrite1.7m

Algorithm

rewrite-expression-head

Rules

139×	`*-un-lft-identity`
106×	`distribute-lft-out`
80×	`frac-add`
30×	`flip3-+` `associate-*l/` `flip-+`
27×	`add-log-exp`
23×	`associate-l`
16×	`sum-log`
9×	`pow1`
8×	`add-sqr-sqrt`
6×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`associate-r`
2×	`+-commutative` `associate-+l+` `sqrt-pow1` `pow-prod-down` `sqrt-prod`
1×	`pow1/2` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 118

Calls

4 calls:

6.8s	(+ (+ (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) 0.9999999999998099) (/ 12.507343278686905 (+ (- z) 5.0)))
1.6s	(+ (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) 0.9999999999998099)
1.6m	(* (+ (+ (+ (+ (+ (/ 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)))
3.0ms	(sqrt (* 2.0 PI))

series460.0ms

Counts

4 → 10

Calls

4 calls:

103.0ms	(+ (+ (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) 0.9999999999998099) (/ 12.507343278686905 (+ (- z) 5.0)))
78.0ms	(+ (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) 0.9999999999998099)
278.0ms	(* (+ (+ (+ (+ (+ (/ 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)))
0.0ms	(sqrt (* 2.0 PI))

simplify402.0ms

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
1	1346
0	402

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize188.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.5s

Algorithm

rewrite-expression-head

Rules

288×	`frac-add`
162×	`*-un-lft-identity`
126×	`distribute-lft-out`
88×	`flip3-+` `flip-+`
72×	`associate-*l/`
27×	`associate-l`
24×	`add-log-exp`
14×	`sum-log`
9×	`pow1`
8×	`add-sqr-sqrt`
6×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`associate-r`
2×	`+-commutative` `sqrt-pow1` `pow-prod-down` `sqrt-prod`
1×	`associate-+l+` `pow1/2` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 167

Calls

4 calls:

1.6s	(+ (+ (+ (/ -1259.1392167224028 (- 2.0 z)) (/ 676.5203681218851 (- 1.0 z))) (+ 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z)))) (/ 12.507343278686905 (+ 5.0 (- z))))
18.0ms	(+ 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z)))
23.8s	(* (+ (+ (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z)))) (/ -176.6150291621406 (+ (- z) 4.0))) (+ (+ (+ (/ -1259.1392167224028 (- 2.0 z)) (/ 676.5203681218851 (- 1.0 z))) (+ 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z)))) (/ 12.507343278686905 (+ 5.0 (- z))))) (sqrt (* 2.0 PI)))
3.0ms	(sqrt (* 2.0 PI))

series420.0ms

Counts

4 → 10

Calls

4 calls:

105.0ms	(+ (+ (+ (/ -1259.1392167224028 (- 2.0 z)) (/ 676.5203681218851 (- 1.0 z))) (+ 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z)))) (/ 12.507343278686905 (+ 5.0 (- z))))
26.0ms	(+ 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z)))
288.0ms	(* (+ (+ (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z)))) (/ -176.6150291621406 (+ (- z) 4.0))) (+ (+ (+ (/ -1259.1392167224028 (- 2.0 z)) (/ 676.5203681218851 (- 1.0 z))) (+ 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z)))) (/ 12.507343278686905 (+ 5.0 (- z))))) (sqrt (* 2.0 PI)))
0.0ms	(sqrt (* 2.0 PI))

simplify584.0ms

Counts

177 → 177

Iterations

Iter	Nodes
done	5000
1	2416
0	637

prune3.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize736.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (+ (* (- 2.0 z) (* (- 1.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 771.3234287776531 (- 3.0 z)) 3)))) (* (+ (* (/ 771.3234287776531 (- 3.0 z)) (- (/ 771.3234287776531 (- 3.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) (+ (* (- 2.0 z) 676.5203681218851) (* (- 1.0 z) -1259.1392167224028)))) (- 5.0 z))
1.0b	(pow (/ 771.3234287776531 (- 3.0 z)) 3)
1.0b	(pow (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z)))) 3)
1.0b	(sqrt (* 2.0 PI))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

3660×	`frac-times`
3030×	`associate-*l/`
2541×	`flip3--` `flip--`
2500×	`frac-add`
1325×	`flip3-+` `flip-+`
1310×	`associate-*r/`
172×	`*-un-lft-identity`
78×	`times-frac`
44×	`add-sqr-sqrt`
38×	`distribute-lft-out`
34×	`unpow-prod-down` `cube-prod`
31×	`distribute-lft-out--`
28×	`add-cube-cbrt`
11×	`pow1`
10×	`add-cbrt-cube` `add-exp-log`
7×	`difference-of-squares`
6×	`cube-div` `pow-unpow`
5×	`associate-r`
4×	`associate-/r/` `add-log-exp`
3×	`associate-l` `pow-exp` `rem-cube-cbrt`
2×	`distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `distribute-lft-in` `sqrt-pow1` `unpow3` `pow-prod-down` `div-inv` `sqr-pow`
1×	`cbrt-undiv` `pow1/2` `div-exp` `prod-exp` `*-commutative` `sqrt-prod` `cbrt-unprod` `unswap-sqr`

Counts

4 → 1713

Calls

4 calls:

890.0ms	(* (+ (* (- 2.0 z) (* (- 1.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 771.3234287776531 (- 3.0 z)) 3)))) (* (+ (* (/ 771.3234287776531 (- 3.0 z)) (- (/ 771.3234287776531 (- 3.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) (+ (* (- 2.0 z) 676.5203681218851) (* (- 1.0 z) -1259.1392167224028)))) (- 5.0 z))
11.0ms	(pow (/ 771.3234287776531 (- 3.0 z)) 3)
295.0ms	(pow (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z)))) 3)
3.0ms	(sqrt (* 2.0 PI))

series377.0ms

Counts

4 → 10

Calls

4 calls:

190.0ms	(* (+ (* (- 2.0 z) (* (- 1.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 771.3234287776531 (- 3.0 z)) 3)))) (* (+ (* (/ 771.3234287776531 (- 3.0 z)) (- (/ 771.3234287776531 (- 3.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) (+ (* (- 2.0 z) 676.5203681218851) (* (- 1.0 z) -1259.1392167224028)))) (- 5.0 z))
50.0ms	(pow (/ 771.3234287776531 (- 3.0 z)) 3)
137.0ms	(pow (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z)))) 3)
0.0ms	(sqrt (* 2.0 PI))

simplify1.5s

Counts

1723 → 1723

Iterations

Iter	Nodes
done	5225
0	5225

prune1.4m

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes374.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify18.0ms

Iterations

Iter	Nodes
done	141
2	141
1	140
0	100

end0.0ms

sample52.4s

Algorithm

intervals

Results

44.0s	3939×	body	10240	exit
2.9s	1549×	body	1280	nan
2.3s	8087×	body	80	valid
1.6s	1324×	body	640	nan
987.0ms	567×	body	320	nan
152.0ms	316×	body	160	nan
60.0ms	304×	body	80	nan