Details

analyze2.4s (27.8%)

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)

sample62.0ms (0.7%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
7.0ms	90×	body	128	invalid

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify77.0ms (0.9%)

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

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
	5.9b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
▶	5.7b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 76 to 45 computations (40.8% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	0.0b	(*.f64 y (-.f64 z t))
✓	5.7b	(/.f64 (*.f64 y (-.f64 z t)) a)

series113.0ms (1.3%)

Counts

3 → 144

Calls

3 calls:

56.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
42.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
14.0ms	(*.f64 y (-.f64 z t))

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 92

Calls

3 calls:

13.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
11.0ms	(*.f64 y (-.f64 z t))
7.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

simplify149.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

599×	`times-frac_binary64`
517×	`distribute-rgt-in_binary64`
492×	`distribute-lft-in_binary64`
448×	`fma-def_binary64`
124×	`associate-l_binary64`

Counts

236 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	199	2898
1	425	2525
2	1558	2355
3	5186	2355

prune269.0ms (3.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	143	5	148
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	144	6	150

Error

0.0b

Counts

150 → 6

Alt Table

Status	Error	Program
	5.9b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	33.0b	(+.f64 x (*.f64 (/.f64 y (sqrt.f64 a)) (/.f64 (-.f64 z t) (sqrt.f64 a))))
	6.1b	(+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 y (-.f64 z t)) a)) (cbrt.f64 (/.f64 (.f64 y (-.f64 z t)) a))) (cbrt.f64 (/.f64 (*.f64 y (-.f64 z t)) a))))
▶	5.7b	(+.f64 x (-.f64 (/.f64 (.f64 y z) a) (/.f64 (.f64 y t) a)))
	15.4b	(fma.f64 (/.f64 y a) z x)
	5.7b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))

Compiler

Compiled 2649 to 763 computations (71.2% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (-.f64 (/.f64 (.f64 y z) a) (/.f64 (.f64 y t) a)))
✓	0.0b	(-.f64 (/.f64 (.f64 y z) a) (/.f64 (.f64 y t) a))
✓	3.6b	(/.f64 (*.f64 y z) a)
✓	5.8b	(/.f64 (*.f64 y t) a)

series162.0ms (1.9%)

Counts

4 → 90

Calls

4 calls:

55.0ms	(+.f64 x (-.f64 (/.f64 (.f64 y z) a) (/.f64 (.f64 y t) a)))
46.0ms	(-.f64 (/.f64 (.f64 y z) a) (/.f64 (.f64 y t) a))
33.0ms	(/.f64 (*.f64 y z) a)
26.0ms	(/.f64 (*.f64 y t) a)

rewrite103.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

105×	`times-frac_binary64`
98×	`prod-diff_binary64`
80×	`*-un-lft-identity_binary64`
75×	`add-sqr-sqrt_binary64`
73×	`add-cube-cbrt_binary64`

Counts

4 → 207

Calls

4 calls:

31.0ms	(+.f64 x (-.f64 (/.f64 (.f64 y z) a) (/.f64 (.f64 y t) a)))
15.0ms	(-.f64 (/.f64 (.f64 y z) a) (/.f64 (.f64 y t) a))
6.0ms	(/.f64 (*.f64 y t) a)
6.0ms	(/.f64 (*.f64 y z) a)

simplify298.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

925×	`times-frac_binary64`
507×	`fma-neg_binary64`
195×	`cancel-sign-sub-inv_binary64`
182×	`exp-prod_binary64`
174×	`distribute-rgt-neg-in_binary64`

Counts

297 → 320

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	287	5726
1	623	4778
2	1992	4266
3	4193	4266
4	4886	4266

prune474.0ms (5.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	317	3	320
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	320	6	326

Error

0.0b

Counts

326 → 6

Alt Table

Status	Error	Program
✓	5.7b	(+.f64 x (-.f64 (/.f64 (.f64 y z) a) (/.f64 (.f64 y t) a)))
	27.5b	(+.f64 x (-.f64 (/.f64 (.f64 y z) a) (.f64 (sqrt.f64 (/.f64 (.f64 y t) a)) (sqrt.f64 (/.f64 (.f64 y t) a)))))
	33.0b	(+.f64 x (*.f64 (/.f64 y (sqrt.f64 a)) (/.f64 (-.f64 z t) (sqrt.f64 a))))
▶	2.5b	(+.f64 x (*.f64 (/.f64 y a) (-.f64 z t)))
	5.9b	(+.f64 x (*.f64 (-.f64 (/.f64 z a) (/.f64 t a)) y))
	5.7b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))

Compiler

Compiled 9374 to 1681 computations (82.1% saved)

localize13.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 (/.f64 y a) (-.f64 z t)))
✓	6.4b	(*.f64 (/.f64 y a) (-.f64 z t))

series98.0ms (1.1%)

Counts

2 → 108

Calls

2 calls:

60.0ms	(+.f64 x (*.f64 (/.f64 y a) (-.f64 z t)))
38.0ms	(*.f64 (/.f64 y a) (-.f64 z t))

rewrite72.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
39×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
26×	`associate-+r+_binary64`

Counts

2 → 108

Calls

2 calls:

19.0ms	(*.f64 (/.f64 y a) (-.f64 z t))
9.0ms	(+.f64 x (*.f64 (/.f64 y a) (-.f64 z t)))

simplify274.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

645×	`fma-def_binary64`
487×	`distribute-rgt-in_binary64`
459×	`distribute-lft-in_binary64`
308×	`fma-neg_binary64`
161×	`exp-prod_binary64`

Counts

216 → 173

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	222	3201
1	471	2589
2	1518	2535
3	4658	2535
4	4989	2535
5	4996	2535
6	4999	2535
7	4946	2535

prune187.0ms (2.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	174	5	179

Error

0.0b

Counts

179 → 5

Alt Table

Status	Error	Program
▶	2.5b	(fma.f64 (-.f64 z t) (/.f64 y a) x)
	5.9b	(+.f64 x (*.f64 (-.f64 (/.f64 z a) (/.f64 t a)) y))
	33.0b	(+.f64 x (*.f64 (/.f64 y (sqrt.f64 a)) (/.f64 (-.f64 z t) (sqrt.f64 a))))
✓	5.7b	(+.f64 x (-.f64 (/.f64 (.f64 y z) a) (/.f64 (.f64 y t) a)))
	5.7b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))

Compiler

Compiled 3589 to 833 computations (76.8% saved)

localize13.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.5b	(fma.f64 (-.f64 z t) (/.f64 y a) x)

series44.0ms (0.5%)

Counts

1 → 60

Calls

1 calls:

44.0ms

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

simplify102.0ms (1.2%)

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`
244×	`distribute-rgt-out_binary64`

Counts

70 → 26

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	38	1133
1	77	750
2	164	733
3	445	733
4	2171	733
5	4663	733
6	4961	733

prune28.0ms (0.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	26	5	31

Error

0.0b

Counts

31 → 5

Alt Table

Status	Error	Program
✓	2.5b	(fma.f64 (-.f64 z t) (/.f64 y a) x)
	5.9b	(+.f64 x (*.f64 (-.f64 (/.f64 z a) (/.f64 t a)) y))
	33.0b	(+.f64 x (*.f64 (/.f64 y (sqrt.f64 a)) (/.f64 (-.f64 z t) (sqrt.f64 a))))
✓	5.7b	(+.f64 x (-.f64 (/.f64 (.f64 y z) a) (/.f64 (.f64 y t) a)))
	5.7b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))

Compiler

Compiled 355 to 107 computations (69.9% saved)

regimes1.8s (20.1%)

Accuracy

Total 0.3b remaining (95.8%)

Threshold costs 0.3b (95.8%)

Counts

80 → 3

Compiler

Compiled 11748 to 7762 computations (33.9% saved)

bsearch4.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	57
1	41	55
2	50	55
3	56	55
4	59	55
5	60	55
6	60	55

end1.0ms (0%)

Compiler: Compiled 42 to 22 computations (47.6% saved)

sample1.9s (21.8%)

Algorithm

1×

intervals

Results

658.0ms	8000×	body	128	valid
206.0ms	2625×	body	128	invalid

Compiler

Compiled 141 to 86 computations (39% saved)

Details

analyze2.4s (27.8%)

sample62.0ms (0.7%)

simplify77.0ms (0.9%)

prune6.0ms (0.1%)

localize13.0ms (0.2%)

series113.0ms (1.3%)

rewrite44.0ms (0.5%)

simplify149.0ms (1.7%)

prune269.0ms (3.1%)

localize27.0ms (0.3%)

series162.0ms (1.9%)

rewrite103.0ms (1.2%)

simplify298.0ms (3.4%)

prune474.0ms (5.4%)

localize13.0ms (0.1%)

series98.0ms (1.1%)

rewrite72.0ms (0.8%)

simplify274.0ms (3.1%)

prune187.0ms (2.1%)

localize13.0ms (0.1%)

series44.0ms (0.5%)

rewrite1.0ms (0%)

simplify102.0ms (1.2%)

prune28.0ms (0.3%)

regimes1.8s (20.1%)

bsearch4.0ms (0%)

simplify9.0ms (0.1%)

end1.0ms (0%)

sample1.9s (21.8%)

Profiling