Details

sample22.0ms

Algorithm

intervals

Results

6.0ms	56×	body	1280	valid
4.0ms	42×	body	640	valid
3.0ms	113×	body	80	valid
1.0ms	22×	body	320	valid
1.0ms	23×	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: 33.9b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
6.5b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite17.0ms

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)
9.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series417.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(cbrt (+ x 1.0))
174.0ms	(cbrt x)
153.0ms	(- (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

prune231.0ms

Filtered

108 candidates to 69 candidates (63.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	95	13	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	13	109

Merged error: 20.9b

Counts

109 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
0.3b	(cbrt (cbrt (+ x 1.0)))
0.6b	(cbrt x)
33.9b	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-div`
15×	`cbrt-prod`
9×	`*-un-lft-identity`
7×	`add-sqr-sqrt` `add-cube-cbrt` `flip3-+` `flip-+`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`associate-r/` `associate-l/`
1×	`fma-udef` `distribute-lft-out`

Counts

4 → 61

Calls

4 calls:

8.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
3.0ms	(cbrt (cbrt (+ x 1.0)))
1.0ms	(cbrt x)
1.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

series626.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
89.0ms	(cbrt (cbrt (+ x 1.0)))
182.0ms	(cbrt x)
251.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

simplify132.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (123.0ms)

Iter	Nodes	Cost
0	458	716
1	1307	661
2	4689	636
3	5001	634

prune302.0ms

Filtered

73 candidates to 65 candidates (89.0%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	64	9	73
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	68	18	86

Merged error: 20.8b

Counts

86 → 18

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cbrt (+ x 1.0)))
0.4b	(* (sqrt (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))) (sqrt (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))))
0.6b	(cbrt x)
33.6b	(fma (* (sqrt (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))) (sqrt (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

364×	`cbrt-div`
144×	`sqrt-div`
136×	`frac-times`
109×	`flip3-+` `flip-+`
44×	`associate-r/` `associate-l/`
31×	`add-sqr-sqrt`
30×	`sqrt-prod`
24×	`cbrt-prod`
19×	`pow1`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
14×	`sqrt-pow1`
9×	`swap-sqr` `unswap-sqr`
8×	`pow1/2` `pow1/3`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `pow-prod-up` `add-cbrt-cube`
4×	`expm1-log1p-u` `pow-prod-down` `pow-sqr` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `fma-udef` `distribute-lft-out`

Counts

4 → 184

Calls

4 calls:

3.0ms	(cbrt (cbrt (+ x 1.0)))
14.0ms	(* (sqrt (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))) (sqrt (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))))
1.0ms	(cbrt x)
1.0ms	(fma (* (sqrt (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))) (sqrt (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

series631.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(cbrt (cbrt (+ x 1.0)))
103.0ms	(* (sqrt (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))) (sqrt (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))))
182.0ms	(cbrt x)
256.0ms	(fma (* (sqrt (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))) (sqrt (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

simplify84.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	677	3797
1	2119	3625
2	5001	3562

prune493.0ms

Filtered

196 candidates to 95 candidates (48.5%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	2	15	17
Picked	0	1	1
Done	0	0	0
Total	195	19	214

Merged error: 20.8b

Counts

214 → 19

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
0.3b	(cbrt (cbrt (+ x 1.0)))
0.6b	(cbrt x)
33.7b	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (* (cbrt (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))) (cbrt (cbrt (cbrt (+ x 1.0))))) (- (cbrt x)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-div`
15×	`cbrt-prod`
9×	`*-un-lft-identity`
7×	`add-sqr-sqrt` `add-cube-cbrt` `flip3-+` `flip-+`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`associate-r/` `associate-l/`
1×	`fma-udef` `distribute-lft-out`

Counts

4 → 61

Calls

4 calls:

8.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
3.0ms	(cbrt (cbrt (+ x 1.0)))
1.0ms	(cbrt x)
1.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (* (cbrt (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))) (cbrt (cbrt (cbrt (+ x 1.0))))) (- (cbrt x)))

series633.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
90.0ms	(cbrt (cbrt (+ x 1.0)))
178.0ms	(cbrt x)
259.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (* (cbrt (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))) (cbrt (cbrt (cbrt (+ x 1.0))))) (- (cbrt x)))

simplify140.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (124.0ms)

Iter	Nodes	Cost
0	462	833
1	1319	760
2	4747	735
3	5001	733

prune285.0ms

Filtered

73 candidates to 65 candidates (89.0%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	3	14	17
Picked	1	0	1
Done	0	1	1
Total	73	19	92

Merged error: 20.8b

Counts

92 → 19

regimes104.0ms

Accuracy

98.2% (0.2b remaining)

Error of 19.0b against oracle of 18.8b and baseline of 30.1b

bsearch121.0ms

Steps

Iters	Range		Point
10	0.00022027325057658872	62623256.830634765	4941.535701226754
10	-9.540315001687748e+64	-2.1978783347321447e+55	-4.4405013780138126e+61

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	36
1	54	36

end0.0ms

sample571.0ms

Algorithm

intervals

Results

196.0ms	1711×	body	1280	valid
116.0ms	1284×	body	640	valid
103.0ms	4078×	body	80	valid
44.0ms	637×	body	320	valid
15.0ms	290×	body	160	valid

Details

sample22.0ms

simplify5.0ms

prune2.0ms

localize6.0ms

rewrite17.0ms

series417.0ms

simplify55.0ms

prune231.0ms

localize11.0ms

rewrite14.0ms

series626.0ms

simplify132.0ms

prune302.0ms

localize15.0ms

rewrite36.0ms

series631.0ms

simplify84.0ms

prune493.0ms

localize20.0ms

rewrite15.0ms

series633.0ms

simplify140.0ms

prune285.0ms

regimes104.0ms

bsearch121.0ms

simplify2.0ms

end0.0ms

sample571.0ms

Profiling