Details

analyze1.3s (20.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
10.1%	89.6%	0.2%	11
15.2%	84.6%	0.2%	12
20.5%	79.3%	0.2%	13
21.6%	77.1%	1.3%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.4s (23.5%)

Results

1.0s	8256×	body	128	valid
316.0ms	2595×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify67.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

946×	`fma-def_binary64`
719×	`fma-neg_binary64`
235×	`cancel-sign-sub-inv_binary64`
163×	`distribute-rgt-in_binary64`
116×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	16	13
2	31	11
3	62	11
4	130	11
5	231	11
6	390	11
7	639	11
8	955	11
9	1272	11
10	1381	11
11	1449	11
12	1474	11
13	1471	11
14	1471	11
15	1398	11

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
▶	6.3b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	7.9b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 76 to 45 computations (40.8% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) a)
✓	5.9b	(fma.f64 y (/.f64 (-.f64 z t) a) x)

series36.0ms (0.6%)

Counts

2 → 88

Calls

2 calls:

26.0ms	(fma.f64 y (/.f64 (-.f64 z t) a) x)
9.0ms	(/.f64 (-.f64 z t) a)

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`associate-/l*_binary64`

Counts

2 → 50

Calls

2 calls:

9.0ms	(/.f64 (-.f64 z t) a)
0.0ms	(fma.f64 y (/.f64 (-.f64 z t) a) x)

simplify87.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

699×	`distribute-rgt-in_binary64`
686×	`distribute-lft-in_binary64`
589×	`times-frac_binary64`
434×	`fma-def_binary64`
215×	`div-sub_binary64`

Counts

138 → 77

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	109	1877
1	238	1462
2	529	1460
3	1344	1460
4	4947	1460
5	5050	1460

prune47.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	72	5	77
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	73	6	79

Error

0.0b

Counts

79 → 6

Alt Table

Status	Error	Program
	3.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))
✓	6.3b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
▶	2.5b	(fma.f64 (/.f64 y a) (-.f64 z t) x)
	7.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) a) x) (/.f64 (.f64 y t) a))
	6.4b	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 z t))) x)
	6.8b	(fma.f64 y (.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a))) x)

Compiler

Compiled 1248 to 369 computations (70.4% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.4b	(fma.f64 (/.f64 y a) (-.f64 z t) x)

series22.0ms (0.4%)

Counts

1 → 60

Calls

1 calls:

22.0ms

(fma.f64 (/.f64 y a) (-.f64 z t) 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 (/.f64 y a) (-.f64 z t) x)

simplify66.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

429×	`distribute-lft-neg-out_binary64`
429×	`distribute-rgt-neg-out_binary64`
368×	`distribute-rgt-in_binary64`
367×	`distribute-lft-in_binary64`
237×	`distribute-rgt-out_binary64`

Counts

70 → 26

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	38	1133
1	75	750
2	165	733
3	447	733
4	2165	733
5	4627	733
6	4940	733

prune15.0ms (0.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	26	6	32

Error

0.0b

Counts

32 → 6

Alt Table

Status	Error	Program
▶	3.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))
✓	6.3b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
✓	2.5b	(fma.f64 (/.f64 y a) (-.f64 z t) x)
	7.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) a) x) (/.f64 (.f64 y t) a))
	6.4b	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 z t))) x)
	6.8b	(fma.f64 y (.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a))) x)

Compiler

Compiled 480 to 164 computations (65.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))
✓	0.5b	(cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))
	2.4b	(fma.f64 (/.f64 y a) (-.f64 z t) x)

series684.0ms (11.2%)

Counts

3 → 180

Calls

3 calls:

478.0ms

(*.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))

181.0ms

(cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))

24.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))

rewrite18.0ms (0.3%)

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 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))

4.0ms

(*.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))

1.0ms

(cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))

simplify302.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

625×	`*-commutative_binary64`
281×	`associate-r_binary64`
256×	`+-commutative_binary64`
230×	`fma-def_binary64`
175×	`associate-/l*_binary64`

Counts

273 → 298

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1378	22896
1	4987	22896
2	4998	22896

prune862.0ms (14.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	588	0	588
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	588	6	594

Error

0.0b

Counts

594 → 6

Alt Table

Status	Error	Program
✓	3.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))
✓	6.3b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
✓	2.5b	(fma.f64 (/.f64 y a) (-.f64 z t) x)
	7.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) a) x) (/.f64 (.f64 y t) a))
▶	6.4b	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 z t))) x)
	6.8b	(fma.f64 y (.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a))) x)

Compiler

Compiled 51429 to 21048 computations (59.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 a (-.f64 z t))
✓	0.3b	(/.f64 1 (/.f64 a (-.f64 z t)))
✓	5.9b	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 z t))) x)

series50.0ms (0.8%)

Counts

3 → 120

Calls

3 calls:

23.0ms	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 z t))) x)
18.0ms	(/.f64 a (-.f64 z t))
9.0ms	(/.f64 1 (/.f64 a (-.f64 z t)))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
103×	`*-un-lft-identity_binary64`
103×	`add-sqr-sqrt_binary64`
71×	`add-cube-cbrt_binary64`
26×	`associate-/r*_binary64`

Counts

3 → 159

Calls

3 calls:

6.0ms	(/.f64 1 (/.f64 a (-.f64 z t)))
3.0ms	(/.f64 a (-.f64 z t))
0.0ms	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 z t))) x)

simplify133.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

727×	`fma-neg_binary64`
346×	`times-frac_binary64`
328×	`associate-/l*_binary64`
274×	`fma-def_binary64`
229×	`associate-/r*_binary64`

Counts

279 → 228

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	202	4651
1	421	3949
2	1216	3759
3	4143	3759
4	4963	3759

prune327.0ms (5.3%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	228	0	228
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	228	6	234

Error

0.0b

Counts

234 → 6

Alt Table

Status	Error	Program
✓	3.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x))) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)))
✓	6.3b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
✓	2.5b	(fma.f64 (/.f64 y a) (-.f64 z t) x)
	7.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) a) x) (/.f64 (.f64 y t) a))
✓	6.4b	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 z t))) x)
	6.8b	(fma.f64 y (.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a))) x)

Compiler

Compiled 4286 to 1485 computations (65.4% saved)

regimes533.0ms (8.7%)

Accuracy

Total 0.4b remaining (95.2%)

Threshold costs 0.4b (95.2%)

Counts

38 → 3

Compiler

Compiled 6655 to 3856 computations (42.1% saved)

bsearch1.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
7×	`*-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	71
1	34	71
2	44	71
3	55	71
4	61	71
5	64	71
6	65	71
7	65	71

end86.0ms (1.4%)

Compiler: Compiled 223 to 109 computations (51.1% saved)

Details

analyze1.3s (20.7%)

sample1.4s (23.5%)

simplify67.0ms (1.1%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series36.0ms (0.6%)

rewrite12.0ms (0.2%)

simplify87.0ms (1.4%)

prune47.0ms (0.8%)

localize6.0ms (0.1%)

series22.0ms (0.4%)

rewrite1.0ms (0%)

simplify66.0ms (1.1%)

prune15.0ms (0.2%)

localize9.0ms (0.2%)

series684.0ms (11.2%)

rewrite18.0ms (0.3%)

simplify302.0ms (4.9%)

prune862.0ms (14.1%)

localize8.0ms (0.1%)

series50.0ms (0.8%)

rewrite24.0ms (0.4%)

simplify133.0ms (2.2%)

prune327.0ms (5.3%)

regimes533.0ms (8.7%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end86.0ms (1.4%)

Profiling