Details

analyze1.6s (36.7%)

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)

sample94.0ms (2.2%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
7.0ms	128×	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

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.8b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
▶	2.3b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))

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))
✓	2.2b	(fma.f64 a (fma.f64 z b t) x)

series40.0ms (0.9%)

Counts

2 → 132

Calls

2 calls:

26.0ms	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
14.0ms	(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))

simplify54.0ms (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

prune45.0ms (1.1%)

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
	2.8b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
▶	2.3b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
	39.9b	(fma.f64 y z (cbrt.f64 (pow.f64 (fma.f64 a (fma.f64 b z t) x) 3)))
✓	2.3b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))

Compiler

Compiled 981 to 235 computations (76% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series14.0ms (0.3%)

Counts

1 → 60

Calls

1 calls:

14.0ms

(fma.f64 z (fma.f64 a b y) 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 z (fma.f64 a b y) x)

simplify119.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

889×	`distribute-rgt-in_binary64`
886×	`distribute-lft-in_binary64`
636×	`unswap-sqr_binary64`
394×	`associate-l_binary64`
337×	`associate-r_binary64`

Counts

70 → 26

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	32	626
1	51	607
2	127	607
3	510	607
4	3225	607
5	3357	607
6	3579	607
7	3869	607
8	4363	607
9	4411	607
10	5048	607

prune22.0ms (0.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	26	4	30

Error

0.0b

Counts

30 → 4

Alt Table

Status	Error	Program
▶	2.8b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	2.3b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
	39.9b	(fma.f64 y z (cbrt.f64 (pow.f64 (fma.f64 a (fma.f64 b z t) x) 3)))
✓	2.3b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))

Compiler

Compiled 425 to 144 computations (66.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series51.0ms (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))
11.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
10.0ms	(.f64 (.f64 a z) b)
5.0ms	(+.f64 x (*.f64 y z))

rewrite18.0ms (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:

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))

simplify69.0ms (1.6%)

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

prune76.0ms (1.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

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

Error

Counts

138 → 4

Alt Table

Status	Error	Program
✓	2.3b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
▶	35.2b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b)))
✓	2.8b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	2.3b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

Compiler

Compiled 2801 to 521 computations (81.4% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
	0.0b	(+.f64 x (*.f64 y z))
✓	1.1b	(.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b))
✓	1.5b	(.f64 (.f64 a z) (sqrt.f64 b))

series37.0ms (0.9%)

Counts

2 → 32

Calls

2 calls:

26.0ms	(.f64 (.f64 a z) (sqrt.f64 b))
11.0ms	(.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`
12×	`associate-r_binary64`
9×	`cbrt-unprod_binary64`

Counts

2 → 49

Calls

2 calls:

7.0ms	(.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b))
5.0ms	(.f64 (.f64 a z) (sqrt.f64 b))

simplify107.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

395×	`unswap-sqr_binary64`
364×	`*-commutative_binary64`
348×	`log-div_binary64`
322×	`sqr-pow_binary64`
223×	`associate-l_binary64`

Counts

81 → 60

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	71	823
1	172	727
2	661	727
3	979	727
4	1277	727
5	1827	727
6	3254	727
7	4264	719
8	4987	719
9	4938	719

prune63.0ms (1.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	124	4	128

Error

Counts

128 → 4

Alt Table

Status	Error	Program
✓	2.3b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	35.2b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b)))
✓	2.8b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	2.3b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

Compiler

Compiled 3076 to 541 computations (82.4% saved)

regimes570.0ms (13.5%)

Accuracy

Total 0.5b remaining (98.4%)

Threshold costs 0.5b (98.4%)

Counts

63 → 3

Compiler

Compiled 7490 to 4648 computations (37.9% saved)

bsearch32.0ms (0.8%)

Steps

Iters	Range		Point
6	4.108146850221084e-144	1.9558946806520643e-143	1.845139882369355e-143
5	-2.720523313767427e+67	-4.5179230586137154e+47	-1.8881264951566855e+48

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`if-if-or-not_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	42
1	26	42
2	26	42

end1.0ms (0%)

Compiler: Compiled 36 to 20 computations (44.4% saved)

sample1.2s (28.3%)

Algorithm

1×

intervals

Results

426.0ms	8000×	body	128	valid
201.0ms	3816×	body	128	invalid

Compiler

Compiled 142 to 86 computations (39.4% saved)

Details

analyze1.6s (36.7%)

sample94.0ms (2.2%)

simplify9.0ms (0.2%)

prune6.0ms (0.1%)

localize7.0ms (0.2%)

series40.0ms (0.9%)

rewrite1.0ms (0%)

simplify54.0ms (1.3%)

prune45.0ms (1.1%)

localize7.0ms (0.2%)

series14.0ms (0.3%)

rewrite1.0ms (0%)

simplify119.0ms (2.8%)

prune22.0ms (0.5%)

localize10.0ms (0.2%)

series51.0ms (1.2%)

rewrite18.0ms (0.4%)

simplify69.0ms (1.6%)

prune76.0ms (1.8%)

localize11.0ms (0.3%)

series37.0ms (0.9%)

rewrite15.0ms (0.3%)

simplify107.0ms (2.5%)

prune63.0ms (1.5%)

regimes570.0ms (13.5%)

bsearch32.0ms (0.8%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.2s (28.3%)

Profiling