Details

sample2.7s

Algorithm

intervals

Results

2.2s	130×	body	10240	exit
111.0ms	56×	body	1280	nan
91.0ms	259×	body	80	valid
69.0ms	47×	body	640	nan
20.0ms	19×	body	320	nan
7.0ms	13×	body	160	nan
3.0ms	9×	body	80	nan

simplify3.9s

Counts

1 → 1

Iterations

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

prune54.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize225.0ms

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)
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) (/ 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:

2.5s	(+ (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) 0.9999999999998099)
320.0ms	(/ (pow (+ 7.0 (+ 0.5 (- z))) (+ 0.5 (- z))) (exp (+ 7.0 (+ 0.5 (- z)))))
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))

series841.0ms

Counts

4 → 10

Calls

4 calls:

114.0ms	(+ (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) 0.9999999999998099)
285.0ms	(/ (pow (+ 7.0 (+ 0.5 (- z))) (+ 0.5 (- z))) (exp (+ 7.0 (+ 0.5 (- z)))))
442.0ms	(* (+ (+ (+ (+ (+ (/ 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))

simplify5.9s

Counts

186 → 186

Iterations

Iter	Nodes
done	5001
1	1622
0	532

prune3.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize200.0ms

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))

rewrite1.9m

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)
1.7m	(* (+ (+ (+ (+ (+ (/ 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)))
5.0ms	(sqrt (* 2.0 PI))

series489.0ms

Counts

4 → 10

Calls

4 calls:

109.0ms	(+ (+ (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) 0.9999999999998099) (/ 12.507343278686905 (+ (- z) 5.0)))
83.0ms	(+ (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) 0.9999999999998099)
297.0ms	(* (+ (+ (+ (+ (+ (/ 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))

simplify4.1s

Counts

128 → 128

Iterations

Iter	Nodes
done	5002
1	1321
0	393

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize482.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (/ 12.507343278686905 (+ (- z) 5.0)) (/ 12.507343278686905 (+ (- z) 5.0)))
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))
1.6b	(pow (/ 12.507343278686905 (+ (- z) 5.0)) 3)

rewrite767.0ms

Algorithm

rewrite-expression-head

Rules

648×	`*-un-lft-identity`
292×	`times-frac`
282×	`distribute-lft-out`
86×	`add-sqr-sqrt`
84×	`distribute-rgt-neg-in`
74×	`add-cube-cbrt`
53×	`unpow-prod-down` `cube-prod`
39×	`swap-sqr`
21×	`associate-r` `associate-l`
20×	`add-cbrt-cube` `add-exp-log`
16×	`pow1`
12×	`associate-/r/`
8×	`flip3-+` `flip-+`
6×	`cube-div` `pow-unpow` `div-inv`
5×	`cbrt-undiv` `div-exp`
4×	`frac-add` `prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-exp` `rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `pow-pow` `sqrt-pow1` `unpow3` `pow-prod-down` `sqr-pow`
1×	`pow2` `frac-times` `pow-plus` `pow1/2` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `sqrt-prod`

Counts

4 → 268

Calls

4 calls:

69.0ms	(* (/ 12.507343278686905 (+ (- z) 5.0)) (/ 12.507343278686905 (+ (- z) 5.0)))
657.0ms	(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))
18.0ms	(pow (/ 12.507343278686905 (+ (- z) 5.0)) 3)

series244.0ms

Counts

4 → 10

Calls

4 calls:

38.0ms	(* (/ 12.507343278686905 (+ (- z) 5.0)) (/ 12.507343278686905 (+ (- z) 5.0)))
147.0ms	(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))
59.0ms	(pow (/ 12.507343278686905 (+ (- z) 5.0)) 3)

simplify1.7s

Counts

278 → 278

Iterations

Iter	Nodes
done	5000
1	1450
0	363

prune2.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize79.0ms

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	(sqrt PI)
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
44×	`times-frac`
32×	`add-sqr-sqrt`
30×	`unpow-prod-down`
29×	`add-cube-cbrt`
25×	`distribute-lft-out`
12×	`exp-sum`
11×	`associate-/l*`
9×	`sqrt-prod`
7×	`pow1`
6×	`add-cbrt-cube` `add-exp-log`
5×	`unpow-prod-up` `associate-+r-` `distribute-rgt-neg-in` `sqr-pow`
4×	`associate-/r*` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `exp-diff` `div-exp` `associate-/r/` `pow-sub` `associate-/l/`
2×	`neg-sub0` `unsub-neg`
1×	`pow-to-exp` `cbrt-undiv` `clear-num` `frac-2neg` `pow-exp` `div-inv`

Counts

4 → 118

Calls

4 calls:

194.0ms	(/ (pow (+ 7.0 (+ 0.5 (- z))) (+ 0.5 (- z))) (exp (+ 7.0 (+ 0.5 (- z)))))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)

series164.0ms

Counts

4 → 6

Calls

4 calls:

164.0ms	(/ (pow (+ 7.0 (+ 0.5 (- z))) (+ 0.5 (- z))) (exp (+ 7.0 (+ 0.5 (- z)))))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify1.4s

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
2	1754
1	454
0	214

prune734.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes129.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify35.0ms

Iterations

Iter	Nodes
done	108
1	108
0	79

end0.0ms

sample53.4s

Algorithm

intervals

Results

45.1s	3848×	body	10240	exit
2.9s	1547×	body	1280	nan
2.7s	8085×	body	80	valid
1.6s	1254×	body	640	nan
489.0ms	630×	body	320	nan
161.0ms	311×	body	160	nan
57.0ms	265×	body	80	nan