Details

analyze79.0ms (2%)

Algorithm

1×

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
49.9%	49.9%	0.1%	4
49.9%	49.9%	0.1%	5
49.9%	49.9%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
74.9%	25%	0.1%	9
87.4%	12.5%	0.1%	10
87.4%	12.5%	0.1%	11
87.4%	12.5%	0.1%	12
93.6%	6.2%	0.1%	13
93.6%	6.2%	0.1%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample601.0ms (15.1%)

Infinites

25.4% of outputs are infinite.

Results

550.0ms

8256×

body

128

valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-def_binary64`
1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`associate-/l*_binary64`
1×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	10	10
2	12	8
3	14	8
4	15	8
5	15	8

prune3.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 y (/.f64 y z) x)
	5.0b	(+.f64 x (/.f64 (*.f64 y y) z))

Compiler

Compiled 54 to 30 computations (44.4% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (/.f64 y z) x)

series15.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

15.0ms

(fma.f64 y (/.f64 y z) 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:

0.0ms

(fma.f64 y (/.f64 y z) x)

simplify51.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

611×	`associate-/l/_binary64`
604×	`associate-+l+_binary64`
543×	`associate-l_binary64`
462×	`fma-def_binary64`
424×	`associate-/r*_binary64`

Counts

46 → 17

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	376
1	28	359
2	59	359
3	151	359
4	551	359
5	2861	359
6	5394	359

prune11.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	15	2	17
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	15	4	19

Error

0.0b

Counts

19 → 4

Alt Table

Status	Error	Program
▶	1.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (fma.f64 y (/.f64 y z) x)))
	26.4b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (/.f64 y z) x) (fma.f64 y (/.f64 y z) x)) (fma.f64 y (/.f64 y z) x)))
✓	0.1b	(fma.f64 y (/.f64 y z) x)
	5.0b	(+.f64 x (/.f64 (*.f64 y y) z))

Compiler

Compiled 286 to 89 computations (68.9% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 y (/.f64 y z) x)
✓	0.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (fma.f64 y (/.f64 y z) x)))
✓	0.4b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x)))
✓	17.7b	(cbrt.f64 (fma.f64 y (/.f64 y z) x))

series136.0ms (3.4%)

Counts

3 → 108

Calls

3 calls:

64.0ms

(*.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x)))

59.0ms

(cbrt.f64 (fma.f64 y (/.f64 y z) x))

12.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (fma.f64 y (/.f64 y z) x)))

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

6.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (fma.f64 y (/.f64 y z) x)))

4.0ms

(*.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x)))

1.0ms

(cbrt.f64 (fma.f64 y (/.f64 y z) x))

simplify180.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

688×	`fma-def_binary64`
298×	`associate-r_binary64`
276×	`cancel-sign-sub-inv_binary64`
257×	`unswap-sqr_binary64`
188×	`*-commutative_binary64`

Counts

201 → 199

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	316	6172
1	905	5625
2	2738	5166
3	4604	4783
4	4960	4783
5	4920	4783

prune302.0ms (7.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	362	4	366
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	363	7	370

Error

0.0b

Counts

370 → 7

Alt Table

Status	Error	Program
	1.1b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (fma.f64 y (/.f64 y z) x)))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (fma.f64 y (/.f64 y z) x))))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (fma.f64 y (/.f64 y z) x)))))
✓	0.1b	(fma.f64 y (/.f64 y z) x)
	20.3b	(.f64 (cbrt.f64 (.f64 (fma.f64 y (/.f64 y z) x) (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (fma.f64 y (/.f64 y z) x)))
▶	1.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)))))
	26.4b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (/.f64 y z) x) (fma.f64 y (/.f64 y z) x)) (fma.f64 y (/.f64 y z) x)))
	5.0b	(+.f64 x (/.f64 (*.f64 y y) z))
	33.0b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 y z) x)))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 y z) x))))) (cbrt.f64 (fma.f64 y (/.f64 y z) x)))

Compiler

Compiled 14619 to 5309 computations (63.7% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x)))
✓	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)))
✓	9.8b	(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))))
	17.7b	(cbrt.f64 (fma.f64 y (/.f64 y z) x))

series127.0ms (3.2%)

Counts

2 → 72

Calls

2 calls:

66.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))))
60.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`cbrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 27

Calls

2 calls:

2.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))))
1.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)))

simplify124.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

697×	`fma-def_binary64`
291×	`cancel-sign-sub-inv_binary64`
247×	`associate-/r/_binary64`
243×	`associate-r_binary64`
240×	`fma-neg_binary64`

Counts

99 → 115

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	297	4757
1	869	4481
2	2582	4234
3	4924	4232
4	4960	4232

prune575.0ms (14.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	588	1	589
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	588	8	596

Error

0.0b

Counts

596 → 8

Alt Table

Status	Error	Program
	1.1b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (fma.f64 y (/.f64 y z) x)))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (fma.f64 y (/.f64 y z) x))))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (fma.f64 y (/.f64 y z) x)))))
✓	0.1b	(fma.f64 y (/.f64 y z) x)
	20.3b	(.f64 (cbrt.f64 (.f64 (fma.f64 y (/.f64 y z) x) (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (fma.f64 y (/.f64 y z) x)))
✓	1.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)))))
	26.4b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (/.f64 y z) x) (fma.f64 y (/.f64 y z) x)) (fma.f64 y (/.f64 y z) x)))
	5.0b	(+.f64 x (/.f64 (*.f64 y y) z))
▶	1.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))) (.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))))) (cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x))))) (cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)))))
	33.0b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 y z) x)))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 y z) x))))) (cbrt.f64 (fma.f64 y (/.f64 y z) x)))

Compiler

Compiled 37096 to 11908 computations (67.9% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)))
	9.8b	(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))))
✓	9.8b	(cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))))) (cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)))))
	17.7b	(cbrt.f64 (fma.f64 y (/.f64 y z) x))

series70.0ms (1.8%)

Counts

1 → 36

Calls

1 calls:

70.0ms

(cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))))) (cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)))))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`cbrt-prod_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 11

Calls

1 calls:

4.0ms

(cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))))) (cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)))))

simplify84.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

827×	`fma-def_binary64`
712×	`times-frac_binary64`
453×	`associate-/l*_binary64`
341×	`associate-/r*_binary64`
147×	`fma-neg_binary64`

Counts

47 → 48

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	159	2700
1	453	2530
2	1254	2474
3	4849	2472
4	5396	2472

prune865.0ms (21.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	629	1	630
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	629	9	638

Error

0.0b

Counts

638 → 9

Alt Table

Status	Error	Program
	20.3b	(.f64 (cbrt.f64 (.f64 (fma.f64 y (/.f64 y z) x) (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (fma.f64 y (/.f64 y z) x)))
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x))))) (.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))))) (cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x))))) (cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)))))
	1.1b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (fma.f64 y (/.f64 y z) x)))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (fma.f64 y (/.f64 y z) x))))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (fma.f64 y (/.f64 y z) x)))))
✓	0.1b	(fma.f64 y (/.f64 y z) x)
✓	1.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)))))
	26.4b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (/.f64 y z) x) (fma.f64 y (/.f64 y z) x)) (fma.f64 y (/.f64 y z) x)))
	5.0b	(+.f64 x (/.f64 (*.f64 y y) z))
✓	1.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))) (.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))))) (cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x))))) (cbrt.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)))))
	33.0b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 y z) x)))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 y z) x))))) (cbrt.f64 (fma.f64 y (/.f64 y z) x)))

Compiler

Compiled 52147 to 15177 computations (70.9% saved)

regimes580.0ms (14.6%)

Accuracy

Total 0.0b remaining (69.1%)

Threshold costs 0.0b (69.1%)

Counts

95 → 1

Compiler

Compiled 18822 to 6694 computations (64.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	6	8

end105.0ms (2.6%)

Compiler: Compiled 396 to 102 computations (74.2% saved)

Details

analyze79.0ms (2%)

sample601.0ms (15.1%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series15.0ms (0.4%)

rewrite1.0ms (0%)

simplify51.0ms (1.3%)

prune11.0ms (0.3%)

localize7.0ms (0.2%)

series136.0ms (3.4%)

rewrite19.0ms (0.5%)

simplify180.0ms (4.5%)

prune302.0ms (7.6%)

localize11.0ms (0.3%)

series127.0ms (3.2%)

rewrite5.0ms (0.1%)

simplify124.0ms (3.1%)

prune575.0ms (14.4%)

localize15.0ms (0.4%)

series70.0ms (1.8%)

rewrite5.0ms (0.1%)

simplify84.0ms (2.1%)

prune865.0ms (21.7%)

regimes580.0ms (14.6%)

simplify2.0ms (0.1%)

end105.0ms (2.6%)

Profiling