Details

analyze393.0ms

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

12.0ms	81×	body	1280	valid
6.0ms	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

simplify21.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	503	12
1	503	12

prune9.0ms

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 (+.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:

5.0ms	(+.f64 (*.f64 x y) z)
9.0ms	(-.f64 (fma.f64 x y z) (+.f64 1 (+.f64 (*.f64 x y) z)))

series20.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(+.f64 (*.f64 x y) z)
13.0ms	(-.f64 (fma.f64 x y z) (+.f64 1 (+.f64 (*.f64 x y) z)))

simplify42.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5067	438

prune34.0ms

Filtered

23 candidates to 34 candidates (-47.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	32	2	34
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	33	2	35

Merged error: 8.8b

Counts

35 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 z (*.f64 x y))
8.4b	(-.f64 (fma.f64 x y z) (+.f64 z (*.f64 x y)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

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

series17.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(+.f64 z (*.f64 x y))
10.0ms	(-.f64 (fma.f64 x y z) (+.f64 z (*.f64 x y)))

simplify38.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5066	364

prune31.0ms

Filtered

23 candidates to 32 candidates (-39.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	32	0	32
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	32	2	34

Merged error: 8.8b

Counts

34 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (fma.f64 x y z) (+.f64 1 (+.f64 z (*.f64 x y))))
0.1b	(.f64 (+.f64 1 (+.f64 z (.f64 x y))) (+.f64 1 (+.f64 z (*.f64 x y))))
0.1b	(*.f64 (fma.f64 x y z) (fma.f64 x y z))
33.0b	(-.f64 (.f64 (fma.f64 x y z) (fma.f64 x y z)) (.f64 (+.f64 1 (+.f64 z (.f64 x y))) (+.f64 1 (+.f64 z (.f64 x y)))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64`
18×	`pow1_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-log-exp_binary64`
12×	`add-cube-cbrt_binary64`
9×	`swap-sqr_binary64` `distribute-lft-out_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`flip3-+_binary64` `associate-r_binary64` `associate-l_binary64` `flip-+_binary64`
6×	`sum-log_binary64`
4×	`frac-times_binary64`
2×	`pow-prod-down_binary64` `associate--r+_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow-sqr_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `flip--_binary64` `associate-+r+_binary64`

Counts

4 → 95

Calls

4 calls:

8.0ms	(+.f64 (fma.f64 x y z) (+.f64 1 (+.f64 z (*.f64 x y))))
12.0ms	(.f64 (+.f64 1 (+.f64 z (.f64 x y))) (+.f64 1 (+.f64 z (*.f64 x y))))
4.0ms	(*.f64 (fma.f64 x y z) (fma.f64 x y z))
4.0ms	(-.f64 (.f64 (fma.f64 x y z) (fma.f64 x y z)) (.f64 (+.f64 1 (+.f64 z (.f64 x y))) (+.f64 1 (+.f64 z (.f64 x y)))))

series75.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+.f64 (fma.f64 x y z) (+.f64 1 (+.f64 z (*.f64 x y))))
15.0ms	(.f64 (+.f64 1 (+.f64 z (.f64 x y))) (+.f64 1 (+.f64 z (*.f64 x y))))
6.0ms	(*.f64 (fma.f64 x y z) (fma.f64 x y z))
42.0ms	(-.f64 (.f64 (fma.f64 x y z) (fma.f64 x y z)) (.f64 (+.f64 1 (+.f64 z (.f64 x y))) (+.f64 1 (+.f64 z (.f64 x y)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4976	1457
1	4976	1457

prune88.0ms

Filtered

64 candidates to 107 candidates (-67.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	107	2	109

Merged error: 8.8b

Counts

109 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

4.7b	(+.f64 (.f64 2 (.f64 x (.f64 y z))) (.f64 (.f64 x y) (+.f64 2 (.f64 x y))))
4.9b	(.f64 x (.f64 y z))
14.8b	(/.f64 (-.f64 (.f64 (fma.f64 x y z) (fma.f64 x y z)) (+.f64 (.f64 2 (.f64 x (.f64 y z))) (.f64 (.f64 x y) (+.f64 2 (.f64 x y))))) (+.f64 (fma.f64 x y z) (+.f64 1 (+.f64 z (.f64 x y)))))
18.1b	(-.f64 (.f64 (fma.f64 x y z) (fma.f64 x y z)) (+.f64 (.f64 2 (.f64 x (.f64 y z))) (.f64 (.f64 x y) (+.f64 2 (*.f64 x y)))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64`
23×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
15×	`distribute-lft-out_binary64`
11×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow1_binary64`
7×	`difference-of-squares_binary64`
5×	`associate-/r*_binary64`
4×	`associate-/l*_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `diff-log_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `associate-+r+_binary64` `sum-log_binary64`
1×	`sub-neg_binary64` `associate--r+_binary64` `associate-r_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `*-commutative_binary64`

Counts

4 → 91

Calls

4 calls:

12.0ms	(+.f64 (.f64 2 (.f64 x (.f64 y z))) (.f64 (.f64 x y) (+.f64 2 (.f64 x y))))
5.0ms	(.f64 x (.f64 y z))
17.0ms	(/.f64 (-.f64 (.f64 (fma.f64 x y z) (fma.f64 x y z)) (+.f64 (.f64 2 (.f64 x (.f64 y z))) (.f64 (.f64 x y) (+.f64 2 (.f64 x y))))) (+.f64 (fma.f64 x y z) (+.f64 1 (+.f64 z (.f64 x y)))))
10.0ms	(-.f64 (.f64 (fma.f64 x y z) (fma.f64 x y z)) (+.f64 (.f64 2 (.f64 x (.f64 y z))) (.f64 (.f64 x y) (+.f64 2 (*.f64 x y)))))

series111.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+.f64 (.f64 2 (.f64 x (.f64 y z))) (.f64 (.f64 x y) (+.f64 2 (.f64 x y))))
7.0ms	(.f64 x (.f64 y z))
58.0ms	(/.f64 (-.f64 (.f64 (fma.f64 x y z) (fma.f64 x y z)) (+.f64 (.f64 2 (.f64 x (.f64 y z))) (.f64 (.f64 x y) (+.f64 2 (.f64 x y))))) (+.f64 (fma.f64 x y z) (+.f64 1 (+.f64 z (.f64 x y)))))
25.0ms	(-.f64 (.f64 (fma.f64 x y z) (fma.f64 x y z)) (+.f64 (.f64 2 (.f64 x (.f64 y z))) (.f64 (.f64 x y) (+.f64 2 (*.f64 x y)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5054	3065

prune105.0ms

Filtered

74 candidates to 103 candidates (-39.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	103	2	105

Merged error: 8.8b

Counts

105 → 2

regimes122.0ms

Accuracy

0% (0.0b remaining)

Error of 7.9b against oracle of 7.9b and baseline of 7.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	14
1	59	14

end0.0ms

sample1.1s

Algorithm

intervals

Results

406.0ms	2645×	body	1280	valid
205.0ms	1632×	body	640	valid
107.0ms	590×	body	2560	valid
69.0ms	761×	body	320	valid
69.0ms	2039×	body	80	valid
23.0ms	333×	body	160	valid

Details

analyze393.0ms

sample38.0ms

simplify21.0ms

prune9.0ms

localize8.0ms

rewrite14.0ms

series20.0ms

simplify42.0ms

prune34.0ms

localize10.0ms

rewrite10.0ms

series17.0ms

simplify38.0ms

prune31.0ms

localize12.0ms

rewrite31.0ms

series75.0ms

simplify64.0ms

prune88.0ms

localize18.0ms

rewrite48.0ms

series111.0ms

simplify56.0ms

prune105.0ms

regimes122.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling