Details

analyze1.7s (37.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
1.8%	98%	0.3%	13
2.4%	97.3%	0.3%	14

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample98.0ms (2.2%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
5.0ms	103×	body	128	invalid

Compiler

Compiled 49 to 33 computations (32.7% saved)

simplify9.0ms (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

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.1b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	1.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 105 to 60 computations (42.9% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	1.0b	(fma.f64 a (fma.f64 z b t) x)

series43.0ms (1%)

Counts

2 → 132

Calls

2 calls:

24.0ms	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
19.0ms	(fma.f64 a (fma.f64 z b t) x)

rewrite1.0ms (0%)

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:

0.0ms	(fma.f64 a (fma.f64 z b t) x)
0.0ms	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))

simplify59.0ms (1.3%)

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

prune52.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	64	4	68

Error

0.0b

Counts

68 → 4

Alt Table

Status	Error	Program
▶	1.1b	(fma.f64 y z (+.f64 (.f64 a (.f64 b z)) (+.f64 (*.f64 a t) x)))
✓	1.1b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	1.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
	1.6b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

Compiler

Compiled 983 to 235 computations (76.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 a t) x)
✓	0.0b	(fma.f64 y z (+.f64 (.f64 a (.f64 b z)) (+.f64 (*.f64 a t) x)))
✓	0.0b	(+.f64 (.f64 a (.f64 b z)) (+.f64 (*.f64 a t) x))
✓	2.9b	(.f64 a (.f64 b z))

series56.0ms (1.3%)

Counts

4 → 145

Calls

4 calls:

24.0ms	(fma.f64 y z (+.f64 (.f64 a (.f64 b z)) (+.f64 (*.f64 a t) x)))
19.0ms	(+.f64 (.f64 a (.f64 b z)) (+.f64 (*.f64 a t) x))
8.0ms	(.f64 a (.f64 b z))
5.0ms	(+.f64 (*.f64 a t) x)

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-log-exp_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
5×	`*-un-lft-identity_binary64`

Counts

4 → 60

Calls

4 calls:

6.0ms	(+.f64 (.f64 a (.f64 b z)) (+.f64 (*.f64 a t) x))
3.0ms	(.f64 a (.f64 b z))
3.0ms	(+.f64 (*.f64 a t) x)
0.0ms	(fma.f64 y z (+.f64 (.f64 a (.f64 b z)) (+.f64 (*.f64 a t) x)))

simplify105.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

928×	`fma-neg_binary64`
614×	`fma-def_binary64`
513×	`cancel-sign-sub-inv_binary64`
477×	`distribute-rgt-in_binary64`
441×	`distribute-lft-in_binary64`

Counts

205 → 123

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	115	2441
1	317	2033
2	1061	2025
3	3412	2025
4	4613	2025
5	5046	2025

prune77.0ms (1.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	122	5	127

Error

0.0b

Counts

127 → 5

Alt Table

Status	Error	Program
	39.2b	(fma.f64 y z (/.f64 (+.f64 (pow.f64 (.f64 a (.f64 z b)) 3) (pow.f64 (fma.f64 a t x) 3)) (fma.f64 (fma.f64 a t x) (fma.f64 a t x) (.f64 (.f64 a (.f64 z b)) (fma.f64 a (-.f64 (.f64 z b) t) (neg.f64 x))))))
✓	1.1b	(fma.f64 y z (+.f64 (.f64 a (.f64 b z)) (+.f64 (*.f64 a t) x)))
✓	1.1b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
▶	1.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
	1.6b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

Compiler

Compiled 2375 to 539 computations (77.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y z))
✓	0.0b	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
✓	0.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	6.2b	(.f64 (.f64 a z) b)

series52.0ms (1.2%)

Counts

4 → 204

Calls

4 calls:

25.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
15.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
8.0ms	(.f64 (.f64 a z) b)
5.0ms	(+.f64 x (*.f64 y z))

rewrite19.0ms (0.4%)

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:

7.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
4.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
4.0ms	(.f64 (.f64 a z) b)
2.0ms	(+.f64 x (*.f64 y z))

simplify81.0ms (1.8%)

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

prune98.0ms (2.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	133	6	139

Error

0.0b

Counts

139 → 6

Alt Table

Status	Error	Program
	39.2b	(fma.f64 y z (/.f64 (+.f64 (pow.f64 (.f64 a (.f64 z b)) 3) (pow.f64 (fma.f64 a t x) 3)) (fma.f64 (fma.f64 a t x) (fma.f64 a t x) (.f64 (.f64 a (.f64 z b)) (fma.f64 a (-.f64 (.f64 z b) t) (neg.f64 x))))))
✓	1.1b	(fma.f64 y z (+.f64 (.f64 a (.f64 b z)) (+.f64 (*.f64 a t) x)))
✓	1.1b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	1.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
▶	1.6b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
	32.4b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b)))

Compiler

Compiled 2853 to 570 computations (80% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
✓	1.5b	(fma.f64 z (fma.f64 a b y) x)

series38.0ms (0.9%)

Counts

2 → 132

Calls

2 calls:

24.0ms	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
14.0ms	(fma.f64 z (fma.f64 a b y) x)

rewrite1.0ms (0%)

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:

0.0ms	(fma.f64 z (fma.f64 a b y) x)
0.0ms	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

simplify117.0ms (2.7%)

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

prune38.0ms (0.9%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	52	6	58

Error

0.0b

Counts

58 → 6

Alt Table

Status	Error	Program
	39.2b	(fma.f64 y z (/.f64 (+.f64 (pow.f64 (.f64 a (.f64 z b)) 3) (pow.f64 (fma.f64 a t x) 3)) (fma.f64 (fma.f64 a t x) (fma.f64 a t x) (.f64 (.f64 a (.f64 z b)) (fma.f64 a (-.f64 (.f64 z b) t) (neg.f64 x))))))
✓	1.1b	(fma.f64 y z (+.f64 (.f64 a (.f64 b z)) (+.f64 (*.f64 a t) x)))
✓	1.1b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	1.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	1.6b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
	32.4b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b)))

Compiler

Compiled 774 to 195 computations (74.8% saved)

regimes459.0ms (10.4%)

Accuracy

Total 2.5b remaining (99.7%)

Threshold costs 0b (0%)

Counts

63 → 2

Compiler

Compiled 7196 to 4410 computations (38.7% saved)

bsearch4.0ms (0.1%)

Steps

Iters	Range		Point
1	6.1256629865547295e-233	7.83485857666472e-232	2.204489919394036e-232

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	44
1	30	44
2	30	44

end1.0ms (0%)

Compiler: Compiled 37 to 20 computations (45.9% saved)

sample1.3s (29.4%)

Algorithm

1×

intervals

Results

472.0ms	8000×	body	128	valid
200.0ms	3769×	body	128	invalid

Compiler

Compiled 211 to 119 computations (43.6% saved)

Details

analyze1.7s (37.6%)

sample98.0ms (2.2%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series43.0ms (1%)

rewrite1.0ms (0%)

simplify59.0ms (1.3%)

prune52.0ms (1.2%)

localize9.0ms (0.2%)

series56.0ms (1.3%)

rewrite14.0ms (0.3%)

simplify105.0ms (2.4%)

prune77.0ms (1.7%)

localize9.0ms (0.2%)

series52.0ms (1.2%)

rewrite19.0ms (0.4%)

simplify81.0ms (1.8%)

prune98.0ms (2.2%)

localize9.0ms (0.2%)

series38.0ms (0.9%)

rewrite1.0ms (0%)

simplify117.0ms (2.7%)

prune38.0ms (0.9%)

regimes459.0ms (10.4%)

bsearch4.0ms (0.1%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.3s (29.4%)

Profiling