Details

analyze10.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
99.7%	0%	0.3%	1

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample1.7s (30.8%)

Results

1.6s

8256×

body

128

valid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

89×	`fma-def_binary64`
24×	`associate-+l+_binary64`
22×	`associate-+r+_binary64`
19×	`+-commutative_binary64`
10×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	27	16
2	66	15
3	122	13
4	157	13
5	164	13
6	167	13
7	167	13

prune6.0ms (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

0.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	3.9b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	4.4b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 105 to 60 computations (42.9% saved)

localize28.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.8b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	3.6b	(fma.f64 a (fma.f64 z b t) x)

series79.0ms (1.4%)

Counts

2 → 132

Calls

2 calls:

49.0ms	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
29.0ms	(fma.f64 a (fma.f64 z b t) x)

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

8.0ms	(fma.f64 a (fma.f64 z b t) x)
1.0ms	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))

simplify108.0ms (2%)

Algorithm

1×	egg-herbie

Rules

739×	`associate-+l+_binary64`
732×	`associate-+r+_binary64`
701×	`fma-def_binary64`
559×	`associate-l_binary64`
480×	`associate-r_binary64`

Counts

152 → 66

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	55	1737
1	97	1579
2	249	1579
3	1063	1579
4	5721	1579

prune91.0ms (1.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	65	3	68

Error

0.0b

Counts

68 → 3

Alt Table

Status	Error	Program
✓	3.9b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	4.4b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
▶	2.4b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

Compiler

Compiled 943 to 211 computations (77.6% saved)

localize16.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
✓	2.2b	(fma.f64 z (fma.f64 a b y) x)

series80.0ms (1.5%)

Counts

2 → 132

Calls

2 calls:

54.0ms	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
26.0ms	(fma.f64 z (fma.f64 a b y) x)

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

1.0ms	(fma.f64 z (fma.f64 a b y) x)
1.0ms	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

simplify222.0ms (4%)

Algorithm

1×	egg-herbie

Rules

576×	`fma-def_binary64`
520×	`associate-+r+_binary64`
505×	`associate-l_binary64`
470×	`associate-+l+_binary64`
444×	`associate-r_binary64`

Counts

152 → 52

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	56	1796
1	103	1579
2	236	1579
3	906	1579
4	3548	1579
5	3771	1579
6	4661	1579
7	4888	1579
8	4888	1579

prune39.0ms (0.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	52	3	55

Error

0.0b

Counts

55 → 3

Alt Table

Status	Error	Program
✓	3.9b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
▶	4.4b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	2.4b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

Compiler

Compiled 702 to 160 computations (77.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y z))
✓	0.7b	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
✓	2.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	4.5b	(.f64 (.f64 a z) b)

series70.0ms (1.3%)

Counts

4 → 204

Calls

4 calls:

31.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
20.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
9.0ms	(+.f64 x (*.f64 y z))
9.0ms	(.f64 (.f64 a z) b)

rewrite44.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-log-exp_binary64`
10×	`sum-log_binary64`
9×	`fma-def_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`

Counts

4 → 73

Calls

4 calls:

18.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
7.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
7.0ms	(.f64 (.f64 a z) b)
4.0ms	(+.f64 x (*.f64 y z))

simplify183.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

846×	`fma-def_binary64`
720×	`distribute-rgt-in_binary64`
683×	`distribute-lft-in_binary64`
194×	`cancel-sign-sub-inv_binary64`
192×	`fma-neg_binary64`

Counts

277 → 134

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	135	2855
1	406	2550
2	1474	2538
3	5045	2538

prune153.0ms (2.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	132	5	137

Error

0.0b

Counts

137 → 5

Alt Table

Status	Error	Program
	33.2b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b)))
✓	2.4b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
✓	3.9b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	4.4b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
▶	4.6b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (.f64 a z) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)))

Compiler

Compiled 2777 to 539 computations (80.6% saved)

localize31.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.7b	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
✓	1.1b	(.f64 (.f64 (.f64 a z) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b))
✓	2.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (.f64 a z) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)))
✓	3.6b	(.f64 (.f64 a z) (*.f64 (cbrt.f64 b) (cbrt.f64 b)))

series1.3s (24.5%)

Counts

3 → 144

Calls

3 calls:

1.2s

(*.f64 (*.f64 a z) (*.f64 (cbrt.f64 b) (cbrt.f64 b)))

81.0ms

(+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 (*.f64 a z) (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)))

51.0ms

(*.f64 (*.f64 (*.f64 a z) (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b))

rewrite70.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-exp-log_binary64`
33×	`pow1_binary64`
21×	`cbrt-unprod_binary64`
21×	`prod-exp_binary64`
21×	`pow-prod-down_binary64`

Counts

3 → 75

Calls

3 calls:

32.0ms

(*.f64 (*.f64 (*.f64 a z) (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b))

16.0ms

(+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 (*.f64 a z) (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)))

11.0ms

(*.f64 (*.f64 a z) (*.f64 (cbrt.f64 b) (cbrt.f64 b)))

simplify223.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

626×	`distribute-rgt-in_binary64`
611×	`distribute-lft-in_binary64`
553×	`fma-def_binary64`
291×	`associate-l_binary64`
233×	`associate-r_binary64`

Counts

219 → 128

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	148	2930
1	370	2536
2	1521	2497
3	4802	2497
4	4948	2497
5	4968	2497

prune198.0ms (3.6%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	158	5	163

Error

0.0b

Counts

163 → 5

Alt Table

Status	Error	Program
	33.2b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b)))
✓	2.4b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
✓	3.9b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	4.4b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	4.6b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (.f64 a z) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)))

Compiler

Compiled 4105 to 603 computations (85.3% saved)

regimes613.0ms (11.2%)

Accuracy

Total 1.7b remaining (99.7%)

Threshold costs 0b (0%)

Counts

51 → 2

Compiler

Compiled 5411 to 3451 computations (36.2% saved)

bsearch16.0ms (0.3%)

Steps

Iters	Range		Point
4	-6.1266455606214636e+29	-2.806789467098628e+29	-5.89650849018429e+29

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	32
1	17	32

end128.0ms (2.3%)

Compiler: Compiled 166 to 92 computations (44.6% saved)

Details

analyze10.0ms (0.2%)

sample1.7s (30.8%)

simplify13.0ms (0.2%)

prune6.0ms (0.1%)

localize28.0ms (0.5%)

series79.0ms (1.4%)

rewrite10.0ms (0.2%)

simplify108.0ms (2%)

prune91.0ms (1.7%)

localize16.0ms (0.3%)

series80.0ms (1.5%)

rewrite3.0ms (0.1%)

simplify222.0ms (4%)

prune39.0ms (0.7%)

localize10.0ms (0.2%)

series70.0ms (1.3%)

rewrite44.0ms (0.8%)

simplify183.0ms (3.3%)

prune153.0ms (2.8%)

localize31.0ms (0.6%)

series1.3s (24.5%)

rewrite70.0ms (1.3%)

simplify223.0ms (4.1%)

prune198.0ms (3.6%)

regimes613.0ms (11.2%)

bsearch16.0ms (0.3%)

simplify4.0ms (0.1%)

end128.0ms (2.3%)

Profiling