Details

analyze3.0ms (0.1%)

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)

sample954.0ms (25.8%)

Infinites

32.9% of outputs are infinite.

Results

868.0ms

8256×

body

128

valid

Compiler

Compiled 65 to 41 computations (36.9% 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

prune5.0ms (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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	3.1b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	3.8b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 105 to 60 computations (42.9% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	2.9b	(fma.f64 a (fma.f64 z b t) x)

series45.0ms (1.2%)

Counts

2 → 132

Calls

2 calls:

25.0ms	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
20.0ms	(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))

simplify74.0ms (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

prune48.0ms (1.3%)

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
	4.7b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
	5.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 a t (fma.f64 z (fma.f64 a b y) x))) (cbrt.f64 (fma.f64 a t (fma.f64 z (fma.f64 a b y) x)))) (cbrt.f64 (fma.f64 a t (fma.f64 z (fma.f64 a b y) x))))
✓	3.1b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
▶	3.8b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 1025 to 235 computations (77.1% saved)

localize11.0ms (0.3%)

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))
✓	1.9b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	4.7b	(.f64 (.f64 a z) b)

series64.0ms (1.7%)

Counts

4 → 204

Calls

4 calls:

37.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
12.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
8.0ms	(.f64 (.f64 a z) b)
6.0ms	(+.f64 x (*.f64 y z))

rewrite19.0ms (0.5%)

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:

6.0ms	(+.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))

simplify93.0ms (2.5%)

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

prune115.0ms (3.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	134	4	138

Error

0.0b

Counts

138 → 4

Alt Table

Status	Error	Program
	4.7b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
▶	3.9b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a z) b)) (cbrt.f64 (.f64 (.f64 a z) b))) (cbrt.f64 (.f64 (.f64 a z) b))))
✓	3.1b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	3.8b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 2759 to 518 computations (81.2% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.7b	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
✓	1.9b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a z) b)) (cbrt.f64 (.f64 (.f64 a z) b))) (cbrt.f64 (.f64 (.f64 a z) b))))
	4.7b	(.f64 (.f64 a z) b)
✓	19.4b	(cbrt.f64 (.f64 (.f64 a z) b))

series781.0ms (21.1%)

Counts

2 → 108

Calls

2 calls:

720.0ms	(cbrt.f64 (.f64 (.f64 a z) b))
61.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a z) b)) (cbrt.f64 (.f64 (.f64 a z) b))) (cbrt.f64 (.f64 (.f64 a z) b))))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-log-exp_binary64`
6×	`sum-log_binary64`
3×	`fma-def_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`

Counts

2 → 30

Calls

2 calls:

11.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a z) b)) (cbrt.f64 (.f64 (.f64 a z) b))) (cbrt.f64 (.f64 (.f64 a z) b))))
2.0ms	(cbrt.f64 (.f64 (.f64 a z) b))

simplify69.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

778×	`associate-l_binary64`
686×	`distribute-rgt-in_binary64`
663×	`distribute-lft-in_binary64`
529×	`fma-def_binary64`
150×	`cancel-sign-sub-inv_binary64`

Counts

138 → 83

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	129	2156
1	320	1930
2	1051	1835
3	5178	1835

prune173.0ms (4.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	258	1	259
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	259	4	263

Error

0.0b

Counts

263 → 4

Alt Table

Status	Error	Program
	4.7b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
▶	3.9b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a z) b)) (cbrt.f64 (.f64 (.f64 a z) b))) (.f64 (cbrt.f64 (.f64 a z)) (cbrt.f64 b))))
✓	3.1b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	3.8b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 8796 to 1220 computations (86.1% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.9b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a z) b)) (cbrt.f64 (.f64 (.f64 a z) b))) (.f64 (cbrt.f64 (.f64 a z)) (cbrt.f64 b))))
	4.7b	(.f64 (.f64 a z) b)
✓	13.1b	(cbrt.f64 (*.f64 a z))
	19.4b	(cbrt.f64 (.f64 (.f64 a z) b))

series442.0ms (11.9%)

Counts

2 → 96

Calls

2 calls:

381.0ms	(cbrt.f64 (*.f64 a z))
60.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a z) b)) (cbrt.f64 (.f64 (.f64 a z) b))) (.f64 (cbrt.f64 (.f64 a z)) (cbrt.f64 b))))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-log-exp_binary64`
6×	`sum-log_binary64`
3×	`fma-def_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`

Counts

2 → 30

Calls

2 calls:

9.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a z) b)) (cbrt.f64 (.f64 (.f64 a z) b))) (.f64 (cbrt.f64 (.f64 a z)) (cbrt.f64 b))))
2.0ms	(cbrt.f64 (*.f64 a z))

simplify82.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

619×	`associate-l_binary64`
543×	`distribute-rgt-in_binary64`
524×	`distribute-lft-in_binary64`
511×	`associate-r_binary64`
459×	`fma-def_binary64`

Counts

126 → 74

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	114	2416
1	280	2169
2	930	2060
3	4792	2060
4	5022	2060

prune121.0ms (3.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	192	4	196

Error

0.0b

Counts

196 → 4

Alt Table

Status	Error	Program
	4.7b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
✓	3.9b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a z) b)) (cbrt.f64 (.f64 (.f64 a z) b))) (.f64 (cbrt.f64 (.f64 a z)) (cbrt.f64 b))))
✓	3.1b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	3.8b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 6738 to 1021 computations (84.8% saved)

regimes433.0ms (11.7%)

Accuracy

Total 0.6b remaining (99%)

Threshold costs 0.6b (99%)

Counts

52 → 3

Compiler

Compiled 7462 to 4123 computations (44.7% saved)

bsearch19.0ms (0.5%)

Steps

Iters	Range		Point
1	4.839712821328201e-70	1.655477426466457e-51	9.051060819995496e-61
8	-1.1989106663485614e+87	-3.408111744416856e+82	-2.6664490440212043e+83

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`if-if-or-not_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	40
1	23	40
2	23	40

end70.0ms (1.9%)

Compiler: Compiled 160 to 88 computations (45% saved)

Details

analyze3.0ms (0.1%)

sample954.0ms (25.8%)

simplify9.0ms (0.2%)

prune5.0ms (0.1%)

localize8.0ms (0.2%)

series45.0ms (1.2%)

rewrite1.0ms (0%)

simplify74.0ms (2%)

prune48.0ms (1.3%)

localize11.0ms (0.3%)

series64.0ms (1.7%)

rewrite19.0ms (0.5%)

simplify93.0ms (2.5%)

prune115.0ms (3.1%)

localize15.0ms (0.4%)

series781.0ms (21.1%)

rewrite15.0ms (0.4%)

simplify69.0ms (1.9%)

prune173.0ms (4.7%)

localize16.0ms (0.4%)

series442.0ms (11.9%)

rewrite12.0ms (0.3%)

simplify82.0ms (2.2%)

prune121.0ms (3.3%)

regimes433.0ms (11.7%)

bsearch19.0ms (0.5%)

simplify6.0ms (0.2%)

end70.0ms (1.9%)

Profiling