Details

sample23.0ms

Algorithm

intervals

Results

6.0ms	59×	body	640	valid
4.0ms	125×	body	80	valid
3.0ms	26×	body	1280	valid
2.0ms	25×	body	320	valid
1.0ms	21×	body	160	valid

simplify17.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	31	7
2	43	7
3	57	7
4	73	7
5	92	7
6	126	7
7	158	7
8	207	7
9	209	7
10	209	7
done	209	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.6b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite504.0ms

Algorithm

rewrite-expression-head

Rules

725×	`*-un-lft-identity`
703×	`times-frac`
524×	`add-sqr-sqrt`
492×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
95×	`distribute-lft-out`
65×	`div-inv`
58×	`associate-/r/`
29×	`flip3-+` `flip-+`
18×	`fma-neg`
17×	`distribute-lft-out--`
12×	`difference-of-squares`
11×	`add-log-exp`
10×	`fma-def`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub`
1×	`+-commutative` `associate-+l-`

Counts

4 → 618

Calls

4 calls:

11.0ms	(/ 1.0 (- x 1.0))
12.0ms	(/ 1.0 (+ x 1.0))
78.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
341.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ 1.0 (- x 1.0))
25.0ms	(/ 1.0 (+ x 1.0))
43.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
209.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify152.0ms

Counts

630 → 630

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	1156	10955
1	3607	8288
2	5001	7670
done	5001	7670

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))
2.6b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
2.6b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
2.6b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

1097×	`*-un-lft-identity`
1026×	`times-frac`
734×	`add-sqr-sqrt`
708×	`associate-+l+`
702×	`prod-diff`
698×	`add-cube-cbrt`
152×	`distribute-lft-out`
93×	`div-inv`
78×	`associate-/r/`
43×	`flip3-+` `flip-+`
37×	`distribute-lft-out--`
30×	`fma-def`
19×	`add-log-exp`
12×	`frac-add` `difference-of-squares`
9×	`cbrt-prod`
6×	`sum-log`
5×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `frac-sub` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`+-commutative` `associate-+l-` `sub-neg` `diff-log`
1×	`pow1/3`

Counts

4 → 834

Calls

4 calls:

166.0ms	(cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))
330.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
330.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
331.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

463.0ms	(cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))
216.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
215.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
217.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify142.0ms

Counts

846 → 846

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	627	12772
1	2312	9865
2	5001	7203
done	5001	7203

prune3.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.5b

localize22.0ms

Local error

Found 4 expressions with local error:

2.0b	(cbrt (fma (* (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (/ 1.0 (- x 1.0))))
2.6b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
2.6b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
29.9b	(fma (* (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (/ 1.0 (- x 1.0)))

rewrite741.0ms

Algorithm

rewrite-expression-head

Rules

711×	`*-un-lft-identity`
676×	`times-frac`
491×	`add-sqr-sqrt`
472×	`associate-+l+`
468×	`prod-diff`
467×	`add-cube-cbrt`
96×	`distribute-lft-out`
62×	`div-inv`
52×	`associate-/r/`
28×	`flip3-+` `flip-+`
20×	`fma-def` `distribute-lft-out--`
14×	`add-log-exp`
8×	`difference-of-squares`
6×	`frac-add`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sum-log` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-prod`
2×	`+-commutative` `associate-+l-` `sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`
1×	`pow1/3` `fma-udef`

Counts

4 → 563

Calls

4 calls:

1.0ms	(cbrt (fma (* (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (/ 1.0 (- x 1.0))))
337.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
340.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
0.0ms	(fma (* (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (/ 1.0 (- x 1.0)))

series1.4s

Counts

4 → 12

Calls

4 calls:

559.0ms	(cbrt (fma (* (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (/ 1.0 (- x 1.0))))
218.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
214.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
393.0ms	(fma (* (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (/ 1.0 (- x 1.0)))

simplify162.0ms

Counts

575 → 575

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	1149	9635
1	4743	7596
2	5001	6624
done	5001	6624

prune3.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize30.0ms

Local error

Found 4 expressions with local error:

2.6b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
29.9b	(fma (* (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (/ 1.0 (- x 1.0)))
29.9b	(fma (* (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (/ 1.0 (- x 1.0)))
29.9b	(fma (* (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (/ 1.0 (- x 1.0)))

rewrite369.0ms

Algorithm

rewrite-expression-head

Rules

357×	`*-un-lft-identity`
338×	`times-frac`
247×	`add-sqr-sqrt`
236×	`associate-+l+`
235×	`add-cube-cbrt`
234×	`prod-diff`
48×	`distribute-lft-out`
31×	`div-inv`
26×	`associate-/r/`
14×	`flip3-+` `flip-+`
10×	`fma-def` `distribute-lft-out--`
9×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `difference-of-squares`
3×	`frac-add` `fma-udef`
2×	`sum-log`
1×	`+-commutative` `associate-+l-` `sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 300

Calls

4 calls:

339.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
0.0ms	(fma (* (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (/ 1.0 (- x 1.0)))
0.0ms	(fma (* (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (/ 1.0 (- x 1.0)))
0.0ms	(fma (* (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (/ 1.0 (- x 1.0)))

series1.4s

Counts

4 → 12

Calls

4 calls:

222.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
395.0ms	(fma (* (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (/ 1.0 (- x 1.0)))
389.0ms	(fma (* (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (/ 1.0 (- x 1.0)))
396.0ms	(fma (* (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (/ 1.0 (- x 1.0)))

simplify97.0ms

Counts

312 → 312

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	754	5570
1	2923	4389
2	5001	3133
done	5001	3133

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

regimes63.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 10.7b

bsearch66.0ms

Steps

Iters	Range		Point
7	27.68840223478076	5364.146891578128	129.30183772681997
5	-392.4425927342909	-100.46129226371261	-139.67380485985092

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	22
1	42	22
done	42	22

end0.0ms

sample607.0ms

Algorithm

intervals

Results

191.0ms	1897×	body	640	valid
118.0ms	4158×	body	80	valid
80.0ms	576×	body	1280	valid
71.0ms	904×	body	320	valid
24.0ms	465×	body	160	valid