Details

analyze447.0ms (15.9%)

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)

sample266.0ms (9.5%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
2.0ms	44×	body	128	nan
1.0ms	22×	body	128	invalid

Compiler

Compiled 30 to 20 computations (33.3% saved)

simplify203.0ms (7.2%)

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

25.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	25.9b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize7.0ms (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))))
✓	1.8b	(-.f64 (.f64 y y) (.f64 z z))
✓	24.9b	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

series66.0ms (2.3%)

Counts

3 → 84

Calls

3 calls:

40.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
19.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
6.0ms	(-.f64 (.f64 y y) (.f64 z z))

rewrite16.0ms (0.6%)

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:

6.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
5.0ms	(-.f64 (.f64 y y) (.f64 z z))
3.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

simplify102.0ms (3.6%)

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

prune88.0ms (3.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	173	6	179
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	173	7	180

Error

0.5b

Counts

180 → 7

Alt Table

Status	Error	Program
	32.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) (cbrt.f64 x)))
	32.9b	(.f64 (.f64 (cbrt.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x)) (cbrt.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x))) (cbrt.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x)))
	31.3b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
	32.4b	(.f64 x (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y))))
	31.4b	(*.f64 x (neg.f64 y))
▶	29.8b	(*.f64 x y)
✓	25.9b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Compiler

Compiled 3784 to 1685 computations (55.5% saved)

localize2.0ms (0.1%)

prune8.0ms (0.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	5	5
Picked	1	1
Done	1	1
Total	7	7

Error

0.5b

Counts

7 → 7

Alt Table

Status	Error	Program
	32.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) (cbrt.f64 x)))
	32.9b	(.f64 (.f64 (cbrt.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x)) (cbrt.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x))) (cbrt.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x)))
▶	31.3b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
	32.4b	(.f64 x (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y))))
	31.4b	(*.f64 x (neg.f64 y))
✓	29.8b	(*.f64 x y)
✓	25.9b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Compiler

Compiled 213 to 104 computations (51.2% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
✓	0.0b	(sqrt.f64 (+.f64 y z))
✓	0.3b	(*.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z)))

series93.0ms (3.3%)

Counts

3 → 60

Calls

3 calls:

46.0ms	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
28.0ms	(*.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z)))
19.0ms	(sqrt.f64 (+.f64 y z))

rewrite29.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`sqrt-div_binary64`
24×	`add-sqr-sqrt_binary64`
17×	`sqrt-prod_binary64`
15×	`*-un-lft-identity_binary64`
13×	`pow1_binary64`

Counts

3 → 91

Calls

3 calls:

12.0ms	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
9.0ms	(*.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z)))
3.0ms	(sqrt.f64 (+.f64 y z))

simplify142.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

662×	`fma-def_binary64`
339×	`cancel-sign-sub-inv_binary64`
280×	`fma-neg_binary64`
259×	`distribute-rgt-in_binary64`
225×	`distribute-lft-in_binary64`

Counts

151 → 216

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	264	3378
1	720	3270
2	2340	3086
3	4838	3085
4	4945	3085
5	4993	3085

prune96.0ms (3.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	215	1	216
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	216	7	223

Error

0.5b

Counts

223 → 7

Alt Table

Status	Error	Program
	38.4b	(.f64 x (/.f64 (.f64 (-.f64 y z) (sqrt.f64 (+.f64 z y))) (sqrt.f64 (-.f64 y z))))
	32.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) (cbrt.f64 x)))
	32.9b	(.f64 (.f64 (cbrt.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x)) (cbrt.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x))) (cbrt.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x)))
	32.4b	(.f64 x (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y))))
▶	31.4b	(*.f64 x (neg.f64 y))
✓	29.8b	(*.f64 x y)
✓	25.9b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Compiler

Compiled 4912 to 2012 computations (59% saved)

localize3.0ms (0.1%)

prune3.0ms (0.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	2	2
Total	7	7

Error

0.5b

Counts

7 → 7

Alt Table

Status	Error	Program
	38.4b	(.f64 x (/.f64 (.f64 (-.f64 y z) (sqrt.f64 (+.f64 z y))) (sqrt.f64 (-.f64 y z))))
	32.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) (cbrt.f64 x)))
	32.9b	(.f64 (.f64 (cbrt.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x)) (cbrt.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x))) (cbrt.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x)))
	32.4b	(.f64 x (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y))))
✓	31.4b	(*.f64 x (neg.f64 y))
✓	29.8b	(*.f64 x y)
✓	25.9b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Compiler

Compiled 120 to 59 computations (50.8% saved)

regimes231.0ms (8.2%)

Accuracy

Total 0.3b remaining (59.7%)

Threshold costs 0.3b (59.7%)

Counts

12 → 2

Compiler

Compiled 1599 to 916 computations (42.7% saved)

bsearch100.0ms (3.6%)

Steps

Iters	Range		Point
2	-4.111599505965499e-285	6.175575203135615e-259	-1.998318635537078e-303

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)

sample897.0ms (31.9%)

Algorithm

1×

intervals

Results

367.0ms	8000×	body	128	valid
108.0ms	1744×	body	128	nan
32.0ms	711×	body	128	invalid

Compiler

Compiled 159 to 85 computations (46.5% saved)

Details

analyze447.0ms (15.9%)

sample266.0ms (9.5%)

simplify203.0ms (7.2%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

series66.0ms (2.3%)

rewrite16.0ms (0.6%)

simplify102.0ms (3.6%)

prune88.0ms (3.1%)

localize2.0ms (0.1%)

prune8.0ms (0.3%)

localize7.0ms (0.2%)

series93.0ms (3.3%)

rewrite29.0ms (1%)

simplify142.0ms (5.1%)

prune96.0ms (3.4%)

localize3.0ms (0.1%)

prune3.0ms (0.1%)

regimes231.0ms (8.2%)

bsearch100.0ms (3.6%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample897.0ms (31.9%)

Profiling