Details

sample23.0ms

Algorithm

intervals

Results

8.0ms	65×	body	1280	valid
4.0ms	41×	body	640	valid
3.0ms	118×	body	80	valid
1.0ms	19×	body	320	valid
1.0ms	13×	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: 33.2b

Counts

2 → 1

localize5.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.5b	(cbrt x)
3.6b	(- (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)
10.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series414.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(cbrt (+ x 1.0))
175.0ms	(cbrt x)
151.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify60.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (43.0ms)

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

prune216.0ms

Filtered

108 candidates to 69 candidates (63.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	97	11	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	11	109

Merged error: 21.1b

Counts

109 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.5b	(cbrt x)
33.3b	(fma (cbrt (* (cbrt (+ x 1.0)) (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 (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

series609.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(cbrt (+ x 1.0))
89.0ms	(cbrt (+ x 1.0))
183.0ms	(cbrt x)
248.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

simplify99.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	340	532
1	1019	485
2	3653	455
3	5001	446

prune264.0ms

Filtered

67 candidates to 61 candidates (91.0%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	58	9	67
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	63	15	78

Merged error: 21.0b

Counts

78 → 15

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0))))
0.5b	(cbrt x)
33.3b	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (* (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))))) (- (cbrt x)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

3.0ms	(cbrt (+ x 1.0))
13.0ms	(* (cbrt (cbrt (+ x 1.0))) (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 (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))))) (- (cbrt x)))

series632.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(cbrt (+ x 1.0))
104.0ms	(* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0))))
183.0ms	(cbrt x)
255.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (* (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))))) (- (cbrt x)))

simplify55.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	504	1285
1	1661	1197
2	5001	1099

prune414.0ms

Filtered

120 candidates to 87 candidates (72.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	116	4	120
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	119	16	135

Merged error: 21.0b

Counts

135 → 16

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0))))
0.5b	(cbrt x)
2.2b	(expm1 (log1p (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0))))))
32.7b	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (* (expm1 (log1p (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))))) (cbrt (cbrt (+ x 1.0))))) (- (cbrt x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

17.0ms	(* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0))))
1.0ms	(cbrt x)
1.0ms	(expm1 (log1p (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0))))))
1.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (* (expm1 (log1p (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))))) (cbrt (cbrt (+ x 1.0))))) (- (cbrt x)))

series1.6s

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0))))
175.0ms	(cbrt x)
264.0ms	(expm1 (log1p (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0))))))
1.0s	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (* (expm1 (log1p (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))))) (cbrt (cbrt (+ x 1.0))))) (- (cbrt x)))

simplify63.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	620	1377
1	2112	1263
2	5002	1171

prune396.0ms

Filtered

115 candidates to 84 candidates (73.0%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	0	15	15
Picked	1	0	1
Done	0	0	0
Total	114	17	131

Merged error: 21.0b

Counts

131 → 17

regimes93.0ms

Accuracy

98.8% (0.1b remaining)

Error of 19.3b against oracle of 19.2b and baseline of 30.2b

bsearch113.0ms

Steps

Iters	Range		Point
10	14.716166499582775	2.5158614700293387e+20	4052.180157504213
10	-1.0421590648034703e+68	-3.0756244989585523e+57	-4.4755733007566364e+61

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	32
1	51	32

end0.0ms

sample606.0ms

Algorithm

intervals

Results

228.0ms	1797×	body	1280	valid
114.0ms	1206×	body	640	valid
100.0ms	4062×	body	80	valid
43.0ms	623×	body	320	valid
14.0ms	312×	body	160	valid