Details

analyze1.8s (28.4%)

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
13.3%	86.5%	0.2%	9
19.9%	79.9%	0.2%	10
24%	75.2%	0.8%	11
25.4%	72.7%	1.9%	12
35.8%	59.6%	4.6%	13
42%	52.3%	5.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample2.4s (38.3%)

Results

1.7s	8256×	body	128	valid
469.0ms	2119×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify83.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

799×	`fma-def_binary64`
661×	`fma-neg_binary64`
203×	`cancel-sign-sub-inv_binary64`
145×	`distribute-rgt-in_binary64`
99×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	30	11
3	61	11
4	129	11
5	232	11
6	397	11
7	667	11
8	1062	11
9	1355	11
10	1480	11
11	1529	11
12	1535	11
13	1540	11
14	1540	11
15	1455	11

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	7.0b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
	8.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z x) t)
✓	6.7b	(fma.f64 y (/.f64 (-.f64 z x) t) x)

series70.0ms (1.1%)

Counts

2 → 76

Calls

2 calls:

47.0ms	(fma.f64 y (/.f64 (-.f64 z x) t) x)
23.0ms	(/.f64 (-.f64 z x) t)

rewrite15.0ms (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 x) t)
1.0ms	(fma.f64 y (/.f64 (-.f64 z x) t) x)

simplify105.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

704×	`distribute-rgt-in_binary64`
694×	`distribute-lft-in_binary64`
580×	`times-frac_binary64`
456×	`fma-def_binary64`
219×	`div-sub_binary64`

Counts

126 → 76

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	112	1693
1	247	1350
2	554	1350
3	1352	1350
4	4976	1350

prune103.0ms (1.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	70	6	76
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	72	6	78

Error

Counts

78 → 6

Alt Table

Status	Error	Program
	38.7b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z x) t) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z x) t) x)))
▶	1.6b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	7.1b	(fma.f64 y (*.f64 (-.f64 z x) (/.f64 1 t)) x)
	7.1b	(fma.f64 y (/.f64 1 (/.f64 t (-.f64 z x))) x)
	25.0b	(fma.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 z x) t) 3)) x)
	8.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y x) t))

Compiler

Compiled 1222 to 373 computations (69.5% saved)

localize11.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.5b	(fma.f64 (/.f64 y t) (-.f64 z x) x)

series34.0ms (0.6%)

Counts

1 → 48

Calls

1 calls:

34.0ms

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

1.0ms

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

simplify90.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

546×	`distribute-rgt-neg-out_binary64`
522×	`distribute-lft-neg-out_binary64`
389×	`distribute-rgt-in_binary64`
386×	`distribute-lft-in_binary64`
294×	`times-frac_binary64`

Counts

58 → 24

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	946
1	87	635
2	197	623
3	473	623
4	2335	623
5	4674	623
6	5331	623

prune27.0ms (0.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	24	6	30

Error

Counts

30 → 6

Alt Table

Status	Error	Program
	38.7b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z x) t) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z x) t) x)))
✓	1.6b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
▶	7.1b	(fma.f64 y (*.f64 (-.f64 z x) (/.f64 1 t)) x)
	7.1b	(fma.f64 y (/.f64 1 (/.f64 t (-.f64 z x))) x)
	25.0b	(fma.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 z x) t) 3)) x)
	8.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y x) t))

Compiler

Compiled 439 to 164 computations (62.6% saved)

localize15.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (-.f64 z x) (/.f64 1 t))
✓	6.7b	(fma.f64 y (*.f64 (-.f64 z x) (/.f64 1 t)) x)

series59.0ms (0.9%)

Counts

2 → 84

Calls

2 calls:

39.0ms	(fma.f64 y (*.f64 (-.f64 z x) (/.f64 1 t)) x)
19.0ms	(*.f64 (-.f64 z x) (/.f64 1 t))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
13×	`*-un-lft-identity_binary64`
11×	`times-frac_binary64`
11×	`add-exp-log_binary64`

Counts

2 → 54

Calls

2 calls:

16.0ms	(*.f64 (-.f64 z x) (/.f64 1 t))
1.0ms	(fma.f64 y (*.f64 (-.f64 z x) (/.f64 1 t)) x)

simplify153.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

838×	`fma-def_binary64`
444×	`times-frac_binary64`
328×	`distribute-rgt-neg-out_binary64`
324×	`distribute-lft-neg-out_binary64`
261×	`distribute-rgt-in_binary64`

Counts

138 → 101

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	120	1703
1	269	1326
2	757	1326
3	2026	1326
4	4512	1326
5	5245	1326

prune112.0ms (1.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	101	6	107

Error

Counts

107 → 6

Alt Table

Status	Error	Program
	38.7b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z x) t) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z x) t) x)))
✓	1.6b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
✓	7.1b	(fma.f64 y (*.f64 (-.f64 z x) (/.f64 1 t)) x)
▶	7.1b	(fma.f64 y (/.f64 1 (/.f64 t (-.f64 z x))) x)
	25.0b	(fma.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 z x) t) 3)) x)
	8.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y x) t))

Compiler

Compiled 1677 to 687 computations (59% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 z x))
✓	0.2b	(/.f64 1 (/.f64 t (-.f64 z x)))
✓	6.7b	(fma.f64 y (/.f64 1 (/.f64 t (-.f64 z x))) x)

series95.0ms (1.5%)

Counts

3 → 108

Calls

3 calls:

39.0ms	(fma.f64 y (/.f64 1 (/.f64 t (-.f64 z x))) x)
35.0ms	(/.f64 t (-.f64 z x))
20.0ms	(/.f64 1 (/.f64 t (-.f64 z x)))

rewrite51.0ms (0.8%)

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:

14.0ms	(/.f64 1 (/.f64 t (-.f64 z x)))
9.0ms	(/.f64 t (-.f64 z x))
1.0ms	(fma.f64 y (/.f64 1 (/.f64 t (-.f64 z x))) x)

simplify267.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

638×	`fma-neg_binary64`
346×	`times-frac_binary64`
326×	`associate-/l*_binary64`
277×	`fma-def_binary64`
227×	`associate-/r*_binary64`

Counts

267 → 226

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	206	4467
1	433	3837
2	1250	3649
3	4124	3649
4	4958	3649
5	4962	3649

prune241.0ms (3.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	226	0	226
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	226	6	232

Error

Counts

232 → 6

Alt Table

Status	Error	Program
	38.7b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z x) t) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z x) t) x)))
✓	1.6b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
✓	7.1b	(fma.f64 y (*.f64 (-.f64 z x) (/.f64 1 t)) x)
✓	7.1b	(fma.f64 y (/.f64 1 (/.f64 t (-.f64 z x))) x)
	25.0b	(fma.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 z x) t) 3)) x)
	8.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y x) t))

Compiler

Compiled 4251 to 1486 computations (65% saved)

regimes318.0ms (5.1%)

Accuracy

Total 1.0b remaining (98.1%)

Threshold costs 1.0b (98.1%)

Counts

32 → 3

Compiler

Compiled 2536 to 1388 computations (45.3% saved)

bsearch2.0ms (0%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	73
1	27	73
2	32	73
3	34	73
4	35	73
5	35	73

end158.0ms (2.5%)

Compiler: Compiled 203 to 92 computations (54.7% saved)

Details

analyze1.8s (28.4%)

sample2.4s (38.3%)

simplify83.0ms (1.3%)

prune6.0ms (0.1%)

localize10.0ms (0.2%)

series70.0ms (1.1%)

rewrite15.0ms (0.2%)

simplify105.0ms (1.7%)

prune103.0ms (1.7%)

localize11.0ms (0.2%)

series34.0ms (0.6%)

rewrite1.0ms (0%)

simplify90.0ms (1.4%)

prune27.0ms (0.4%)

localize15.0ms (0.2%)

series59.0ms (0.9%)

rewrite23.0ms (0.4%)

simplify153.0ms (2.5%)

prune112.0ms (1.8%)

localize14.0ms (0.2%)

series95.0ms (1.5%)

rewrite51.0ms (0.8%)

simplify267.0ms (4.3%)

prune241.0ms (3.9%)

regimes318.0ms (5.1%)

bsearch2.0ms (0%)

simplify8.0ms (0.1%)

end158.0ms (2.5%)

Profiling