Details

analyze1.7s (37.1%)

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
13.2%	86.5%	0.2%	11
16.8%	83%	0.2%	12
22.7%	77.1%	0.2%	13
24.1%	74.7%	1.3%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample43.0ms (0.9%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
3.0ms	82×	body	128	invalid

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify69.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

783×	`fma-neg_binary64`
721×	`fma-def_binary64`
244×	`cancel-sign-sub-inv_binary64`
187×	`distribute-rgt-in_binary64`
138×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	17	13
2	39	13
3	98	13
4	258	11
5	542	11
6	1019	11
7	1302	11
8	1414	11
9	1470	11
10	1476	11
11	1481	11
12	1481	11
13	1408	11

prune4.0ms (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
▶	7.9b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
	9.1b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 76 to 46 computations (39.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) a)
✓	7.5b	(fma.f64 y (/.f64 (-.f64 t z) a) x)

series36.0ms (0.8%)

Counts

2 → 88

Calls

2 calls:

22.0ms	(fma.f64 y (/.f64 (-.f64 t z) a) x)
13.0ms	(/.f64 (-.f64 t z) a)

rewrite8.0ms (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:

5.0ms	(/.f64 (-.f64 t z) a)
0.0ms	(fma.f64 y (/.f64 (-.f64 t z) a) x)

simplify85.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

696×	`distribute-rgt-in_binary64`
684×	`distribute-lft-in_binary64`
583×	`times-frac_binary64`
453×	`fma-def_binary64`
215×	`div-sub_binary64`

Counts

138 → 78

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	1607
1	238	1462
2	525	1460
3	1333	1460
4	4886	1460
5	4983	1460

prune52.0ms (1.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	73	5	78
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	73	7	80

Error

0.0b

Counts

80 → 7

Alt Table

Status	Error	Program
	40.9b	(cbrt.f64 (pow.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x) 3))
	36.6b	(fma.f64 y (/.f64 (/.f64 (-.f64 t z) (sqrt.f64 a)) (sqrt.f64 a)) x)
	7.9b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 a)) x)
▶	1.6b	(fma.f64 (/.f64 y a) (-.f64 t z) x)
✓	7.9b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
	36.4b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)) (sqrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)))
	9.1b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 1255 to 381 computations (69.6% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.6b	(fma.f64 (/.f64 y a) (-.f64 t z) x)

series27.0ms (0.6%)

Counts

1 → 60

Calls

1 calls:

27.0ms

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

simplify70.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

426×	`distribute-lft-neg-out_binary64`
425×	`distribute-rgt-neg-out_binary64`
378×	`distribute-rgt-in_binary64`
375×	`distribute-lft-in_binary64`
225×	`distribute-rgt-out_binary64`

Counts

70 → 27

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	863
1	76	750
2	164	733
3	450	733
4	2142	733
5	4579	733
6	5069	733

prune18.0ms (0.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	27	7	34

Error

0.0b

Counts

34 → 7

Alt Table

Status	Error	Program
	40.9b	(cbrt.f64 (pow.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x) 3))
	36.6b	(fma.f64 y (/.f64 (/.f64 (-.f64 t z) (sqrt.f64 a)) (sqrt.f64 a)) x)
▶	7.9b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 a)) x)
✓	1.6b	(fma.f64 (/.f64 y a) (-.f64 t z) x)
✓	7.9b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
	36.4b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)) (sqrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)))
	9.1b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 487 to 176 computations (63.9% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (-.f64 t z) (/.f64 1 a))
✓	7.5b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 a)) x)

series35.0ms (0.8%)

Counts

2 → 96

Calls

2 calls:

23.0ms	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 a)) x)
12.0ms	(*.f64 (-.f64 t z) (/.f64 1 a))

rewrite11.0ms (0.2%)

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:

8.0ms	(*.f64 (-.f64 t z) (/.f64 1 a))
0.0ms	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 a)) x)

simplify86.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

827×	`fma-def_binary64`
427×	`times-frac_binary64`
324×	`distribute-rgt-neg-out_binary64`
320×	`distribute-lft-neg-out_binary64`
254×	`distribute-rgt-in_binary64`

Counts

150 → 104

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	119	1617
1	260	1438
2	729	1436
3	2014	1436
4	4433	1436
5	5099	1436

prune59.0ms (1.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	104	7	111

Error

0.0b

Counts

111 → 7

Alt Table

Status	Error	Program
	40.9b	(cbrt.f64 (pow.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x) 3))
	36.6b	(fma.f64 y (/.f64 (/.f64 (-.f64 t z) (sqrt.f64 a)) (sqrt.f64 a)) x)
✓	7.9b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 a)) x)
✓	1.6b	(fma.f64 (/.f64 y a) (-.f64 t z) x)
✓	7.9b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
	36.4b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)) (sqrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)))
▶	9.1b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 1724 to 696 computations (59.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (-.f64 z t))
✓	9.7b	(/.f64 (*.f64 y (-.f64 z t)) a)

series25.0ms (0.5%)

Counts

2 → 84

Calls

2 calls:

18.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
6.0ms	(*.f64 y (-.f64 z t))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 75

Calls

2 calls:

7.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
5.0ms	(*.f64 y (-.f64 z t))

simplify77.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

667×	`associate-/l*_binary64`
508×	`times-frac_binary64`
338×	`fma-def_binary64`
275×	`distribute-rgt-in_binary64`
261×	`distribute-lft-in_binary64`

Counts

159 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	167	1706
1	335	1575
2	1241	1521
3	4826	1521
4	4942	1521

prune141.0ms (3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	110	3	113
Fresh	1	2	3
Picked	0	1	1
Done	1	2	3
Total	112	8	120

Error

Counts

120 → 8

Alt Table

Status	Error	Program
	9.2b	(-.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
✓	1.6b	(fma.f64 (/.f64 y a) (-.f64 t z) x)
	36.6b	(fma.f64 y (/.f64 (/.f64 (-.f64 t z) (sqrt.f64 a)) (sqrt.f64 a)) x)
	7.5b	(-.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
✓	7.9b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
	36.4b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)) (sqrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)))
✓	9.1b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	9.5b	(-.f64 x (/.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (-.f64 z t))) a))

Compiler

Compiled 2048 to 636 computations (68.9% saved)

regimes474.0ms (10.2%)

Accuracy

Total 2.4b remaining (99.7%)

Threshold costs 0b (0%)

Counts

35 → 1

Compiler

Compiled 5841 to 3367 computations (42.4% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	11	11
2	16	11
3	18	11
4	19	11
5	19	11

end1.0ms (0%)

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

sample1.6s (33.5%)

Algorithm

1×

intervals

Results

552.0ms	8000×	body	128	valid
171.0ms	2555×	body	128	invalid

Compiler

Compiled 165 to 100 computations (39.4% saved)

Details

analyze1.7s (37.1%)

sample43.0ms (0.9%)

simplify69.0ms (1.5%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series36.0ms (0.8%)

rewrite8.0ms (0.2%)

simplify85.0ms (1.8%)

prune52.0ms (1.1%)

localize6.0ms (0.1%)

series27.0ms (0.6%)

rewrite1.0ms (0%)

simplify70.0ms (1.5%)

prune18.0ms (0.4%)

localize7.0ms (0.2%)

series35.0ms (0.8%)

rewrite11.0ms (0.2%)

simplify86.0ms (1.9%)

prune59.0ms (1.3%)

localize6.0ms (0.1%)

series25.0ms (0.5%)

rewrite17.0ms (0.4%)

simplify77.0ms (1.7%)

prune141.0ms (3%)

regimes474.0ms (10.2%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.6s (33.5%)

Profiling