Details

analyze435.0ms (14.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	81.1%	18.9%	7
6.2%	74.9%	18.9%	8
9.4%	65.5%	25.1%	9
15.6%	48.4%	36%	10
20.3%	43.1%	36.6%	11
22.6%	36%	41.4%	12
27.1%	25.1%	47.8%	13
29.5%	22.5%	48%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample270.0ms (9.1%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
2.0ms	61×	body	128	nan
1.0ms	29×	body	128	invalid

Compiler

Compiled 30 to 20 computations (33.3% saved)

simplify200.0ms (6.7%)

Algorithm

1×	egg-herbie

Rules

767×	`unsub-neg_binary64`
741×	`*-commutative_binary64`
699×	`fma-def_binary64`
598×	`fma-neg_binary64`
465×	`distribute-neg-out_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	19	15
2	29	15
3	57	15
4	118	15
5	278	15
6	529	15
7	1007	15
8	1781	15
9	2585	15
10	2834	15
11	3141	15
12	3371	15
13	3485	15
14	3485	15
15	4444	15
16	4284	15
17	4604	15
18	4604	15
19	5103	15

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

22.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	22.5b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
✓	1.2b	(-.f64 (.f64 y y) (.f64 z z))
✓	22.2b	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

series58.0ms (1.9%)

Counts

3 → 84

Calls

3 calls:

37.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
14.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
6.0ms	(-.f64 (.f64 y y) (.f64 z z))

rewrite15.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
7×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`

Counts

3 → 62

Calls

3 calls:

7.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
3.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
3.0ms	(-.f64 (.f64 y y) (.f64 z z))

simplify98.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

638×	`fma-def_binary64`
337×	`fma-neg_binary64`
316×	`cancel-sign-sub-inv_binary64`
268×	`neg-mul-1_binary64`
187×	`distribute-rgt-neg-in_binary64`

Counts

146 → 179

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	206	2931
1	582	2842
2	2289	2771
3	4556	2771
4	5028	2771

prune97.0ms (3.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	173	6	179
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	174	6	180

Error

0.3b

Counts

180 → 6

Alt Table

Status	Error	Program
	35.3b	(.f64 x (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y)) (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y))) (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y))))
	36.9b	(.f64 x (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y))))
	36.9b	(fma.f64 y x (fma.f64 (.f64 (/.f64 (.f64 z z) y) x) -1/2 (.f64 (.f64 (/.f64 (pow.f64 z 4) (pow.f64 y 3)) x) -1/8)))
	31.5b	(*.f64 x (neg.f64 y))
	29.3b	(*.f64 x y)
▶	22.5b	(.f64 x (sqrt.f64 (.f64 (+.f64 y z) (-.f64 y z))))

Compiler

Compiled 3759 to 1687 computations (55.1% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (sqrt.f64 (.f64 (+.f64 y z) (-.f64 y z))))
✓	22.2b	(sqrt.f64 (*.f64 (+.f64 y z) (-.f64 y z)))

series45.0ms (1.5%)

Counts

2 → 60

Calls

2 calls:

28.0ms	(.f64 x (sqrt.f64 (.f64 (+.f64 y z) (-.f64 y z))))
17.0ms	(sqrt.f64 (*.f64 (+.f64 y z) (-.f64 y z)))

rewrite23.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`sqrt-div_binary64`
12×	`associate-*r/_binary64`
8×	`frac-times_binary64`
7×	`pow1_binary64`
6×	`flip-+_binary64`

Counts

2 → 50

Calls

2 calls:

12.0ms	(sqrt.f64 (*.f64 (+.f64 y z) (-.f64 y z)))
8.0ms	(.f64 x (sqrt.f64 (.f64 (+.f64 y z) (-.f64 y z))))

simplify101.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

725×	`fma-def_binary64`
526×	`distribute-rgt-in_binary64`
323×	`fma-neg_binary64`
285×	`cancel-sign-sub-inv_binary64`
250×	`neg-mul-1_binary64`

Counts

110 → 163

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	210	2700
1	607	2637
2	2329	2577
3	4725	2577
4	5103	2577

prune83.0ms (2.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	163	6	169

Error

0.3b

Counts

169 → 6

Alt Table

Status	Error	Program
	35.3b	(.f64 x (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y)) (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y))) (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y))))
	36.9b	(.f64 x (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y))))
	36.9b	(fma.f64 y x (fma.f64 (.f64 (/.f64 (.f64 z z) y) x) -1/2 (.f64 (.f64 (/.f64 (pow.f64 z 4) (pow.f64 y 3)) x) -1/8)))
	31.5b	(*.f64 x (neg.f64 y))
▶	29.3b	(*.f64 x y)
✓	22.5b	(.f64 x (sqrt.f64 (.f64 (+.f64 y z) (-.f64 y z))))

Compiler

Compiled 3768 to 1713 computations (54.5% saved)

localize2.0ms (0.1%)

prune5.0ms (0.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	1	1
Total	6	6

Error

0.3b

Counts

6 → 6

Alt Table

Status	Error	Program
	35.3b	(.f64 x (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y)) (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y))) (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y))))
	36.9b	(.f64 x (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y))))
	36.9b	(fma.f64 y x (fma.f64 (.f64 (/.f64 (.f64 z z) y) x) -1/2 (.f64 (.f64 (/.f64 (pow.f64 z 4) (pow.f64 y 3)) x) -1/8)))
▶	31.5b	(*.f64 x (neg.f64 y))
✓	29.3b	(*.f64 x y)
✓	22.5b	(.f64 x (sqrt.f64 (.f64 (+.f64 y z) (-.f64 y z))))

Compiler

Compiled 175 to 98 computations (44% saved)

localize3.0ms (0.1%)

prune3.0ms (0.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	2	2
Total	6	6

Error

0.3b

Counts

6 → 6

Alt Table

Status	Error	Program
	35.3b	(.f64 x (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y)) (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y))) (cbrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y))))
	36.9b	(.f64 x (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y))))
	36.9b	(fma.f64 y x (fma.f64 (.f64 (/.f64 (.f64 z z) y) x) -1/2 (.f64 (.f64 (/.f64 (pow.f64 z 4) (pow.f64 y 3)) x) -1/8)))
✓	31.5b	(*.f64 x (neg.f64 y))
✓	29.3b	(*.f64 x y)
✓	22.5b	(.f64 x (sqrt.f64 (.f64 (+.f64 y z) (-.f64 y z))))

Compiler

Compiled 97 to 55 computations (43.3% saved)

regimes590.0ms (19.8%)

Accuracy

Total 0.3b remaining (48.3%)

Threshold costs 0.3b (48.3%)

Counts

26 → 2

Compiler

Compiled 4737 to 2555 computations (46.1% saved)

bsearch67.0ms (2.2%)

Steps

Iters	Range		Point
1	-2.2133289492771425e-286	1.5385331351348065e-273	3.0464164926915463e-302

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	29
1	28	29
2	38	29
3	46	29
4	50	29
5	51	29
6	51	29

end1.0ms (0%)

Compiler: Compiled 22 to 14 computations (36.4% saved)

sample872.0ms (29.2%)

Algorithm

1×

intervals

Results

357.0ms	8000×	body	128	valid
88.0ms	1834×	body	128	nan
28.0ms	685×	body	128	invalid

Compiler

Compiled 136 to 81 computations (40.4% saved)

Details

analyze435.0ms (14.6%)

sample270.0ms (9.1%)

simplify200.0ms (6.7%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series58.0ms (1.9%)

rewrite15.0ms (0.5%)

simplify98.0ms (3.3%)

prune97.0ms (3.3%)

localize6.0ms (0.2%)

series45.0ms (1.5%)

rewrite23.0ms (0.8%)

simplify101.0ms (3.4%)

prune83.0ms (2.8%)

localize2.0ms (0.1%)

prune5.0ms (0.2%)

localize3.0ms (0.1%)

prune3.0ms (0.1%)

regimes590.0ms (19.8%)

bsearch67.0ms (2.2%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample872.0ms (29.2%)

Profiling