Details

analyze709.0ms (12.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
25%	74.9%	0.2%	5
25%	74.9%	0.2%	6
31.2%	68.6%	0.2%	7
40.5%	59.3%	0.2%	8
49.9%	49.9%	0.2%	9
49.9%	49.9%	0.2%	10
54.6%	45.2%	0.2%	11
67.1%	32.7%	0.2%	12
73.3%	26.5%	0.2%	13
73.3%	26.5%	0.2%	14

Compiler

Compiled 22 to 15 computations (31.8% saved)

sample1.7s (29.7%)

Results

1.6s

8256×

body

128

valid

Compiler

Compiled 65 to 44 computations (32.3% saved)

simplify103.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

508×	`fma-neg_binary64`
504×	`associate-*l/_binary64`
466×	`div-sub_binary64`
450×	`cancel-sign-sub-inv_binary64`
403×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	30	25
2	70	25
3	177	22
4	486	19
5	1087	19
6	2534	19
7	4434	19
8	5156	19

prune7.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

2.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	11.8b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
▶	3.0b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))

Compiler

Compiled 110 to 70 computations (36.4% saved)

localize17.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
✓	4.3b	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
✓	4.9b	(/.f64 (.f64 y t) (.f64 2 z))

series193.0ms (3.4%)

Counts

3 → 120

Calls

3 calls:

89.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
75.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
28.0ms	(/.f64 (.f64 y t) (.f64 2 z))

rewrite88.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`add-sqr-sqrt_binary64`
105×	`*-un-lft-identity_binary64`
77×	`times-frac_binary64`
71×	`add-cube-cbrt_binary64`
63×	`prod-diff_binary64`

Counts

3 → 165

Calls

3 calls:

25.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
10.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
9.0ms	(/.f64 (.f64 y t) (.f64 2 z))

simplify358.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

325×	`cancel-sign-sub-inv_binary64`
304×	`distribute-neg-frac_binary64`
221×	`times-frac_binary64`
203×	`associate-/l*_binary64`
182×	`associate-*r/_binary64`

Counts

285 → 252

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	384	10579
1	1057	7887
2	3351	6717
3	4786	6717

prune443.0ms (7.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	249	3	252
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	251	3	254

Error

Counts

254 → 3

Alt Table

Status	Error	Program
	35.6b	(fma.f64 4 (/.f64 (pow.f64 z 3) (.f64 y (.f64 t t))) (fma.f64 2 (/.f64 z t) x))
	27.2b	(fma.f64 2 (/.f64 z t) x)
▶	1.1b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))

Compiler

Compiled 9891 to 5035 computations (49.1% saved)

localize19.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
✓	4.3b	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))
✓	5.2b	(*.f64 (/.f64 y 2) (/.f64 t z))

series165.0ms (2.9%)

Counts

3 → 120

Calls

3 calls:

80.0ms	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
52.0ms	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))
33.0ms	(*.f64 (/.f64 y 2) (/.f64 t z))

rewrite73.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`add-sqr-sqrt_binary64`
71×	`*-un-lft-identity_binary64`
69×	`add-cube-cbrt_binary64`
68×	`times-frac_binary64`
45×	`prod-diff_binary64`

Counts

3 → 162

Calls

3 calls:

18.0ms	(*.f64 (/.f64 y 2) (/.f64 t z))
17.0ms	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
6.0ms	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))

simplify380.0ms (6.7%)

Algorithm

1×	egg-herbie

Rules

898×	`fma-def_binary64`
241×	`associate-*r/_binary64`
221×	`associate-*l/_binary64`
198×	`fma-neg_binary64`
193×	`*-commutative_binary64`

Counts

282 → 244

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	399	9065
1	1098	7039
2	3324	6174
3	4775	6174
4	4814	6174

prune331.0ms (5.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	244	0	244
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	244	3	247

Error

Counts

247 → 3

Alt Table

Status	Error	Program
	35.6b	(fma.f64 4 (/.f64 (pow.f64 z 3) (.f64 y (.f64 t t))) (fma.f64 2 (/.f64 z t) x))
▶	27.2b	(fma.f64 2 (/.f64 z t) x)
✓	1.1b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))

Compiler

Compiled 8831 to 4528 computations (48.7% saved)

localize11.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 (/.f64 z t) x)

series21.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

21.0ms

(fma.f64 2 (/.f64 z t) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma.f64 2 (/.f64 z t) x)

simplify143.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

548×	`associate-*l/_binary64`
542×	`distribute-rgt-in_binary64`
507×	`distribute-lft-in_binary64`
443×	`associate-+l+_binary64`
396×	`fma-def_binary64`

Counts

46 → 14

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	376
1	23	359
2	49	359
3	126	359
4	432	359
5	1628	359
6	4283	359
7	4686	359
8	4929	359
9	4999	359

prune14.0ms (0.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	14	0	14
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	14	3	17

Error

Counts

17 → 3

Alt Table

Status	Error	Program
▶	35.6b	(fma.f64 4 (/.f64 (pow.f64 z 3) (.f64 y (.f64 t t))) (fma.f64 2 (/.f64 z t) x))
✓	27.2b	(fma.f64 2 (/.f64 z t) x)
✓	1.1b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))

Compiler

Compiled 208 to 114 computations (45.2% saved)

localize28.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 2 (/.f64 z t) x)
✓	4.7b	(fma.f64 4 (/.f64 (pow.f64 z 3) (.f64 y (.f64 t t))) (fma.f64 2 (/.f64 z t) x))
✓	6.9b	(.f64 y (.f64 t t))
✓	11.0b	(/.f64 (pow.f64 z 3) (.f64 y (.f64 t t)))

series252.0ms (4.4%)

Counts

3 → 108

Calls

3 calls:

125.0ms	(fma.f64 4 (/.f64 (pow.f64 z 3) (.f64 y (.f64 t t))) (fma.f64 2 (/.f64 z t) x))
117.0ms	(/.f64 (pow.f64 z 3) (.f64 y (.f64 t t)))
9.0ms	(.f64 y (.f64 t t))

rewrite43.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64`
17×	`add-cbrt-cube_binary64`
12×	`associate-/l*_binary64`
12×	`times-frac_binary64`
12×	`prod-exp_binary64`

Counts

3 → 80

Calls

3 calls:

25.0ms	(/.f64 (pow.f64 z 3) (.f64 y (.f64 t t)))
8.0ms	(.f64 y (.f64 t t))
1.0ms	(fma.f64 4 (/.f64 (pow.f64 z 3) (.f64 y (.f64 t t))) (fma.f64 2 (/.f64 z t) x))

simplify158.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

439×	`associate-*l/_binary64`
389×	`fma-def_binary64`
386×	`associate-*r/_binary64`
272×	`associate-/l/_binary64`
262×	`log-div_binary64`

Counts

188 → 107

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	2953
1	259	2751
2	1148	2739
3	3948	2739
4	4988	2739

prune117.0ms (2.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	121	3	124

Error

Counts

124 → 3

Alt Table

Status	Error	Program
✓	35.6b	(fma.f64 4 (/.f64 (pow.f64 z 3) (.f64 y (.f64 t t))) (fma.f64 2 (/.f64 z t) x))
✓	27.2b	(fma.f64 2 (/.f64 z t) x)
✓	1.1b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))

Compiler

Compiled 2723 to 1266 computations (53.5% saved)

regimes230.0ms (4%)

Accuracy

Total 1.0b remaining (99.3%)

Threshold costs 0b (0%)

Counts

17 → 1

Compiler

Compiled 1912 to 1288 computations (32.6% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
7×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	20	19
2	36	19
3	48	19
4	57	19
5	61	19
6	62	19
7	62	19

end96.0ms (1.7%)

Compiler: Compiled 82 to 54 computations (34.1% saved)

Details

analyze709.0ms (12.5%)

sample1.7s (29.7%)

simplify103.0ms (1.8%)

prune7.0ms (0.1%)

localize17.0ms (0.3%)

series193.0ms (3.4%)

rewrite88.0ms (1.5%)

simplify358.0ms (6.3%)

prune443.0ms (7.8%)

localize19.0ms (0.3%)

series165.0ms (2.9%)

rewrite73.0ms (1.3%)

simplify380.0ms (6.7%)

prune331.0ms (5.8%)

localize11.0ms (0.2%)

series21.0ms (0.4%)

rewrite1.0ms (0%)

simplify143.0ms (2.5%)

prune14.0ms (0.2%)

localize28.0ms (0.5%)

series252.0ms (4.4%)

rewrite43.0ms (0.8%)

simplify158.0ms (2.8%)

prune117.0ms (2.1%)

regimes230.0ms (4%)

simplify6.0ms (0.1%)

end96.0ms (1.7%)

Profiling