Details

sample22.0ms

Algorithm

intervals

Results

7.0ms	55×	body	1280	valid
4.0ms	39×	body	640	valid
3.0ms	132×	body	80	valid
1.0ms	21×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 29.5b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
3.0b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite18.0ms

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:

3.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
10.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series425.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(cbrt (+ x 1.0))
181.0ms	(cbrt x)
156.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify57.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (45.0ms)

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

prune221.0ms

Filtered

108 candidates to 69 candidates (63.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	98	10	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	10	109

Merged error: 18.1b

Counts

109 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.8b	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
3.0b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

117×	`cbrt-prod`
104×	`*-un-lft-identity`
84×	`prod-diff`
78×	`add-sqr-sqrt`
62×	`add-cube-cbrt`
47×	`log-prod`
44×	`exp-sum`
16×	`distribute-lft-out`
11×	`log-pow`
10×	`exp-prod`
8×	`difference-of-squares`
7×	`fma-neg`
6×	`distribute-lft-out--` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `cbrt-div` `pow1/3`
1×	`log-div` `flip3--` `flip3-+` `exp-diff` `diff-log` `rem-log-exp` `flip--` `flip-+`

Counts

4 → 168

Calls

4 calls:

3.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
14.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
10.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series567.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(cbrt (+ x 1.0))
176.0ms	(cbrt x)
151.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
151.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify74.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	567	2459
1	1651	1917
2	5001	1581

prune324.0ms

Filtered

180 candidates to 102 candidates (56.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	178	2	180
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	179	11	190

Merged error: 18.1b

Counts

190 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
29.4b	(fma (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

11×	`cbrt-prod` `*-un-lft-identity`
7×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`flip3-+` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 55

Calls

4 calls:

3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
1.0ms	(fma (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

series611.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(cbrt (+ x 1.0))
90.0ms	(cbrt (+ x 1.0))
185.0ms	(cbrt x)
248.0ms	(fma (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

simplify101.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	340	545
1	1020	489
2	3657	450
3	5001	441

prune256.0ms

Filtered

67 candidates to 61 candidates (91.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	62	5	67
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	65	13	78

Merged error: 18.1b

Counts

78 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.3b	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
0.6b	(cbrt x)
29.4b	(fma (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))) (cbrt (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))))) (- (cbrt x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-div`
28×	`cbrt-prod`
27×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`flip3-+` `flip-+`
11×	`pow1`
9×	`swap-sqr`
8×	`frac-times` `pow1/3`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `distribute-lft-out`
4×	`expm1-log1p-u` `associate-r/` `associate-l/` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 97

Calls

4 calls:

10.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
8.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
1.0ms	(cbrt x)
1.0ms	(fma (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))) (cbrt (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))))) (- (cbrt x)))

series643.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
103.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
188.0ms	(cbrt x)
252.0ms	(fma (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))) (cbrt (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))))) (- (cbrt x)))

simplify56.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	518	1099
1	1703	1011
2	5002	955

prune329.0ms

Filtered

109 candidates to 81 candidates (74.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	108	14	122

Merged error: 18.1b

Counts

122 → 14

regimes142.0ms

Accuracy

98.2% (0.2b remaining)

Error of 19.6b against oracle of 19.4b and baseline of 30.7b

bsearch109.0ms

Steps

Iters	Range		Point
10	6.398614580632226	3002406562115.273	5365.771868231847
8	-2.934539490415412e+65	-1.6430583526687275e+61	-4.4717528299524587e+61

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	43
1	62	43
2	62	43

end0.0ms

sample574.0ms

Algorithm

intervals

Results

210.0ms	1772×	body	1280	valid
113.0ms	1251×	body	640	valid
98.0ms	4002×	body	80	valid
44.0ms	647×	body	320	valid
14.0ms	328×	body	160	valid