Details

analyze386.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
26.5%	73.3%	0.1%	8
33.5%	66.3%	0.1%	9
49.1%	50.7%	0.1%	10
56.9%	42.9%	0.1%	11
60.8%	39%	0.1%	12
69%	30.9%	0.1%	13
72.5%	27.3%	0.1%	14

sample38.0ms

Algorithm

intervals

Results

14.0ms	81×	body	1280	valid
5.0ms	47×	body	640	valid
5.0ms	26×	body	2560	valid
2.0ms	25×	body	320	valid
2.0ms	64×	body	80	valid
1.0ms	13×	body	160	valid

simplify22.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	522	12
1	522	12

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 45.7b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (*.f64 x y) z)
11.1b	(-.f64 (fma.f64 x y z) (+.f64 1.0 (+.f64 (*.f64 x y) z)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-log-exp_binary64`
7×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64` `sum-log_binary64`
3×	`diff-log_binary64`
2×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64`

Counts

2 → 28

Calls

2 calls:

4.0ms	(+.f64 (*.f64 x y) z)
9.0ms	(-.f64 (fma.f64 x y z) (+.f64 1.0 (+.f64 (*.f64 x y) z)))

series17.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(+.f64 (*.f64 x y) z)
11.0ms	(-.f64 (fma.f64 x y z) (+.f64 1.0 (+.f64 (*.f64 x y) z)))

simplify37.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4788	439
1	4788	439

prune50.0ms

Filtered

23 candidates to 34 candidates (-47.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	27	7	34
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	8	35

Merged error: 45.1b

Counts

35 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

8.6b	(cbrt.f64 (+.f64 z (*.f64 x y)))
8.6b	(cbrt.f64 (+.f64 z (*.f64 x y)))
8.6b	(cbrt.f64 (+.f64 z (*.f64 x y)))
32.7b	(-.f64 (fma.f64 x y z) (+.f64 1.0 (.f64 (.f64 (cbrt.f64 (+.f64 z (.f64 x y))) (cbrt.f64 (+.f64 z (.f64 x y)))) (cbrt.f64 (+.f64 z (*.f64 x y))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64` `cbrt-prod_binary64`
7×	`add-cube-cbrt_binary64`
6×	`cbrt-div_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`flip3-+_binary64` `pow1/3_binary64` `flip-+_binary64`
2×	`diff-log_binary64`
1×	`sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 54

Calls

4 calls:

3.0ms	(cbrt.f64 (+.f64 z (*.f64 x y)))
3.0ms	(cbrt.f64 (+.f64 z (*.f64 x y)))
3.0ms	(cbrt.f64 (+.f64 z (*.f64 x y)))
6.0ms	(-.f64 (fma.f64 x y z) (+.f64 1.0 (.f64 (.f64 (cbrt.f64 (+.f64 z (.f64 x y))) (cbrt.f64 (+.f64 z (.f64 x y)))) (cbrt.f64 (+.f64 z (*.f64 x y))))))

series103.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(cbrt.f64 (+.f64 z (*.f64 x y)))
29.0ms	(cbrt.f64 (+.f64 z (*.f64 x y)))
29.0ms	(cbrt.f64 (+.f64 z (*.f64 x y)))
14.0ms	(-.f64 (fma.f64 x y z) (+.f64 1.0 (.f64 (.f64 (cbrt.f64 (+.f64 z (.f64 x y))) (cbrt.f64 (+.f64 z (.f64 x y)))) (cbrt.f64 (+.f64 z (*.f64 x y))))))

simplify46.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4948	812
1	4948	812

prune117.0ms

Filtered

58 candidates to 66 candidates (-13.8%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	57	9	66
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	57	17	74

Merged error: 45.0b

Counts

74 → 17

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 x y) (*.f64 x y))
5.0b	(-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 z z))
11.7b	(-.f64 (fma.f64 x y z) (+.f64 1.0 (/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 z z)) (-.f64 (*.f64 x y) z))))
30.9b	(/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 z z)) (-.f64 (*.f64 x y) z))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

43×	`pow1_binary64`
18×	`*-un-lft-identity_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
17×	`pow-prod-down_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
11×	`add-log-exp_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`difference-of-squares_binary64`
4×	`flip3--_binary64` `pow-prod-up_binary64` `associate-/l*_binary64` `pow-sqr_binary64` `flip--_binary64`
3×	`associate-/r*_binary64` `diff-log_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `associate-/r/_binary64` `pow-plus_binary64` `div-sub_binary64` `distribute-lft-out--_binary64`
1×	`associate-+r-_binary64` `associate--r+_binary64` `swap-sqr_binary64` `distribute-lft-out_binary64` `associate-r_binary64` `cbrt-undiv_binary64` `associate--r-_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 99

Calls

4 calls:

7.0ms	(.f64 (.f64 x y) (*.f64 x y))
7.0ms	(-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 z z))
17.0ms	(-.f64 (fma.f64 x y z) (+.f64 1.0 (/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 z z)) (-.f64 (*.f64 x y) z))))
13.0ms	(/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 z z)) (-.f64 (*.f64 x y) z))

series71.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(.f64 (.f64 x y) (*.f64 x y))
17.0ms	(-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 z z))
28.0ms	(-.f64 (fma.f64 x y z) (+.f64 1.0 (/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 z z)) (-.f64 (*.f64 x y) z))))
18.0ms	(/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 z z)) (-.f64 (*.f64 x y) z))

simplify48.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5020	1302

prune152.0ms

Filtered

70 candidates to 111 candidates (-58.6%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	102	9	111
Fresh	3	11	14
Picked	1	0	1
Done	1	1	2
Total	107	21	128

Merged error: 44.9b

Counts

128 → 21

localize17.0ms

Local error

Found 4 expressions with local error:

8.6b	(cbrt.f64 (-.f64 (*.f64 x y) z))
8.6b	(cbrt.f64 (-.f64 (*.f64 x y) z))
8.6b	(cbrt.f64 (-.f64 (*.f64 x y) z))
33.4b	(-.f64 (fma.f64 x y z) (+.f64 1.0 (.f64 (/.f64 (+.f64 (.f64 x y) z) (.f64 (cbrt.f64 (-.f64 (.f64 x y) z)) (cbrt.f64 (-.f64 (.f64 x y) z)))) (/.f64 (-.f64 (.f64 x y) z) (cbrt.f64 (-.f64 (*.f64 x y) z))))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64` `cbrt-prod_binary64`
7×	`add-cube-cbrt_binary64`
6×	`cbrt-div_binary64`
4×	`pow1_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`pow1/3_binary64`
2×	`diff-log_binary64`
1×	`sub-neg_binary64` `associate--r+_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `sum-log_binary64`

Counts

4 → 54

Calls

4 calls:

4.0ms	(cbrt.f64 (-.f64 (*.f64 x y) z))
4.0ms	(cbrt.f64 (-.f64 (*.f64 x y) z))
4.0ms	(cbrt.f64 (-.f64 (*.f64 x y) z))
7.0ms	(-.f64 (fma.f64 x y z) (+.f64 1.0 (.f64 (/.f64 (+.f64 (.f64 x y) z) (.f64 (cbrt.f64 (-.f64 (.f64 x y) z)) (cbrt.f64 (-.f64 (.f64 x y) z)))) (/.f64 (-.f64 (.f64 x y) z) (cbrt.f64 (-.f64 (*.f64 x y) z))))))

series115.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(cbrt.f64 (-.f64 (*.f64 x y) z))
36.0ms	(cbrt.f64 (-.f64 (*.f64 x y) z))
33.0ms	(cbrt.f64 (-.f64 (*.f64 x y) z))
13.0ms	(-.f64 (fma.f64 x y z) (+.f64 1.0 (.f64 (/.f64 (+.f64 (.f64 x y) z) (.f64 (cbrt.f64 (-.f64 (.f64 x y) z)) (cbrt.f64 (-.f64 (.f64 x y) z)))) (/.f64 (-.f64 (.f64 x y) z) (cbrt.f64 (-.f64 (*.f64 x y) z))))))

simplify35.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5089	1061

prune75.0ms

Filtered

59 candidates to 66 candidates (-11.9%)

Pruning

23 alts after pruning (21 fresh and 2 done)

	Pruned	Kept	Total
New	59	7	66
Fresh	5	14	19
Picked	0	1	1
Done	0	1	1
Total	64	23	87

Merged error: 44.8b

Counts

87 → 23

regimes349.0ms

Accuracy

0% (1.4b remaining)

Error of 46.2b against oracle of 44.8b and baseline of 46.2b

bsearch0.0ms

simplify6.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	275	39
1	275	39

end0.0ms

sample1.0s

Algorithm

intervals

Results

388.0ms	2645×	body	1280	valid
198.0ms	1632×	body	640	valid
102.0ms	590×	body	2560	valid
72.0ms	2039×	body	80	valid
69.0ms	761×	body	320	valid
20.0ms	333×	body	160	valid

Details

analyze386.0ms

sample38.0ms

simplify22.0ms

prune6.0ms

localize8.0ms

rewrite14.0ms

series17.0ms

simplify37.0ms

prune50.0ms

localize12.0ms

rewrite15.0ms

series103.0ms

simplify46.0ms

prune117.0ms

localize12.0ms

rewrite49.0ms

series71.0ms

simplify48.0ms

prune152.0ms

localize17.0ms

rewrite21.0ms

series115.0ms

simplify35.0ms

prune75.0ms

regimes349.0ms

bsearch0.0ms

simplify6.0ms

end0.0ms

sample1.0s

Profiling