Details

sample20.0ms

Algorithm

intervals

Results

6.0ms	56×	body	1280	valid
3.0ms	41×	body	640	valid
3.0ms	128×	body	80	valid
1.0ms	22×	body	320	valid
0.0ms	9×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize6.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
3.1b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

64×	`cbrt-prod`
56×	`*-un-lft-identity`
42×	`prod-diff`
41×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
9×	`distribute-lft-out`
7×	`fma-neg`
5×	`add-log-exp`
4×	`difference-of-squares`
3×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
2×	`cbrt-div` `pow1/3`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

3 → 99

Calls

3 calls:

2.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
29.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series423.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(cbrt (+ x 1.0))
179.0ms	(cbrt x)
152.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify55.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	430	1315
1	1394	1045
2	5001	981

prune260.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 19.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
3.2b	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `flip--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
0.0ms	(cbrt x)
11.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

series720.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(cbrt x)
177.0ms	(cbrt x)
178.0ms	(cbrt x)
180.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

simplify145.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (139.0ms)

Iter	Nodes	Cost
0	260	403
1	906	328
2	4583	314
3	5001	311

prune248.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
3.2b	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `flip--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
0.0ms	(cbrt x)
11.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

series730.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt x)
182.0ms	(cbrt x)
188.0ms	(cbrt x)
182.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

simplify147.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (135.0ms)

Iter	Nodes	Cost
0	260	403
1	906	328
2	4583	314
3	5001	311

prune285.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
3.2b	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))
3.2b	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))
3.2b	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-prod` `sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `flip--` `difference-of-squares`
1×	`pow1/3`

Counts

4 → 64

Calls

4 calls:

0.0ms	(cbrt x)
11.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))
11.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))
11.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

series713.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(cbrt x)
175.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))
177.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))
177.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

simplify142.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (134.0ms)

Iter	Nodes	Cost
0	260	865
1	906	680
2	4583	638
3	5001	629

prune356.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 13.2b

regimes77.0ms

Accuracy

98.9% (0.2b remaining)

Error of 12.4b against oracle of 12.2b and baseline of 30.3b

bsearch103.0ms

Steps

Iters	Range		Point
10	488.5072251079851	29561296481055.625	3308.7385413926622
8	-1.4333731922804479e+62	-3.8658731844659564e+59	-4.515229856998832e+61

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	57
1	73	57

end0.0ms

sample511.0ms

Algorithm

intervals

Results

184.0ms	1743×	body	1280	valid
99.0ms	1253×	body	640	valid
85.0ms	4031×	body	80	valid
37.0ms	658×	body	320	valid
12.0ms	315×	body	160	valid