Details

analyze957.0ms (18.4%)

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
0%	81.1%	18.9%	8
0%	76.5%	23.5%	9
0%	65.5%	34.5%	10
0%	65.2%	34.8%	11
0%	61.7%	38.3%	12
0.2%	55.4%	44.4%	13
0.5%	55%	44.6%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample2.2s (43%)

Results

996.0ms	8256×	body	128	valid
697.0ms	1069×	body	8192	exit
281.0ms	2231×	body	128	invalid

Compiler

Compiled 27 to 17 computations (37% saved)

simplify200.0ms (3.8%)

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%)

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

25.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	25.7b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
✓	4.0b	(-.f64 (.f64 y y) (.f64 z z))
✓	24.5b	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

series63.0ms (1.2%)

Counts

3 → 84

Calls

3 calls:

39.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
15.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
8.0ms	(-.f64 (.f64 y y) (.f64 z z))

rewrite14.0ms (0.3%)

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))))
3.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
3.0ms	(-.f64 (.f64 y y) (.f64 z z))

simplify102.0ms (2%)

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

prune86.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	175	4	179
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	175	5	180

Error

0.1b

Counts

180 → 5

Alt Table

Status	Error	Program
	50.8b	(exp.f64 (log.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x)))
	33.3b	(*.f64 x (neg.f64 y))
▶	28.5b	(*.f64 x y)
✓	25.7b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
	30.0b	(.f64 (.f64 x (sqrt.f64 (+.f64 y z))) (sqrt.f64 (-.f64 y z)))

Compiler

Compiled 3660 to 1641 computations (55.2% saved)

localize2.0ms (0%)

prune4.0ms (0.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	1	1
Total	5	5

Error

0.1b

Counts

5 → 5

Alt Table

Status	Error	Program
	50.8b	(exp.f64 (log.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x)))
	33.3b	(*.f64 x (neg.f64 y))
✓	28.5b	(*.f64 x y)
✓	25.7b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
▶	30.0b	(.f64 (.f64 x (sqrt.f64 (+.f64 y z))) (sqrt.f64 (-.f64 y z)))

Compiler

Compiled 89 to 60 computations (32.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 y z))
✓	0.0b	(sqrt.f64 (-.f64 y z))
✓	0.1b	(*.f64 x (sqrt.f64 (+.f64 y z)))
✓	0.2b	(.f64 (.f64 x (sqrt.f64 (+.f64 y z))) (sqrt.f64 (-.f64 y z)))

series119.0ms (2.3%)

Counts

4 → 68

Calls

4 calls:

42.0ms	(.f64 (.f64 x (sqrt.f64 (+.f64 y z))) (sqrt.f64 (-.f64 y z)))
35.0ms	(*.f64 x (sqrt.f64 (+.f64 y z)))
22.0ms	(sqrt.f64 (+.f64 y z))
19.0ms	(sqrt.f64 (-.f64 y z))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
19×	`sqrt-prod_binary64`
19×	`*-un-lft-identity_binary64`
18×	`sqrt-div_binary64`
15×	`associate-r_binary64`

Counts

4 → 98

Calls

4 calls:

9.0ms	(.f64 (.f64 x (sqrt.f64 (+.f64 y z))) (sqrt.f64 (-.f64 y z)))
5.0ms	(sqrt.f64 (-.f64 y z))
5.0ms	(*.f64 x (sqrt.f64 (+.f64 y z)))
2.0ms	(sqrt.f64 (+.f64 y z))

simplify126.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

410×	`cancel-sign-sub-inv_binary64`
370×	`fma-neg_binary64`
294×	`associate-l_binary64`
278×	`associate-r_binary64`
245×	`neg-mul-1_binary64`

Counts

166 → 195

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	275	3232
1	765	3105
2	2708	3068
3	4604	3003
4	5009	3003

prune82.0ms (1.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	194	1	195
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	194	6	200

Error

0.1b

Counts

200 → 6

Alt Table

Status	Error	Program
	50.8b	(exp.f64 (log.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x)))
	33.3b	(*.f64 x (neg.f64 y))
✓	28.5b	(*.f64 x y)
✓	25.7b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
▶	30.1b	(.f64 (.f64 (*.f64 x (sqrt.f64 (+.f64 y z))) (sqrt.f64 (sqrt.f64 (-.f64 y z)))) (sqrt.f64 (sqrt.f64 (-.f64 y z))))
✓	30.0b	(.f64 (.f64 x (sqrt.f64 (+.f64 y z))) (sqrt.f64 (-.f64 y z)))

Compiler

Compiled 4423 to 1737 computations (60.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (sqrt.f64 (-.f64 y z)))
	0.1b	(*.f64 x (sqrt.f64 (+.f64 y z)))
✓	0.2b	(.f64 (.f64 (*.f64 x (sqrt.f64 (+.f64 y z))) (sqrt.f64 (sqrt.f64 (-.f64 y z)))) (sqrt.f64 (sqrt.f64 (-.f64 y z))))
✓	0.2b	(.f64 (.f64 x (sqrt.f64 (+.f64 y z))) (sqrt.f64 (sqrt.f64 (-.f64 y z))))

series437.0ms (8.4%)

Counts

3 → 72

Calls

3 calls:

365.0ms

(*.f64 (*.f64 x (sqrt.f64 (+.f64 y z))) (sqrt.f64 (sqrt.f64 (-.f64 y z))))

46.0ms

(*.f64 (*.f64 (*.f64 x (sqrt.f64 (+.f64 y z))) (sqrt.f64 (sqrt.f64 (-.f64 y z)))) (sqrt.f64 (sqrt.f64 (-.f64 y z))))

26.0ms

(sqrt.f64 (sqrt.f64 (-.f64 y z)))

rewrite48.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`sqrt-div_binary64`
40×	`sqrt-prod_binary64`
34×	`associate-*r/_binary64`
32×	`frac-times_binary64`
22×	`associate-r_binary64`

Counts

3 → 118

Calls

3 calls:

16.0ms

(*.f64 (*.f64 (*.f64 x (sqrt.f64 (+.f64 y z))) (sqrt.f64 (sqrt.f64 (-.f64 y z)))) (sqrt.f64 (sqrt.f64 (-.f64 y z))))

11.0ms

(*.f64 (*.f64 x (sqrt.f64 (+.f64 y z))) (sqrt.f64 (sqrt.f64 (-.f64 y z))))

3.0ms

(sqrt.f64 (sqrt.f64 (-.f64 y z)))

simplify165.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

778×	`fma-def_binary64`
535×	`associate-l_binary64`
420×	`associate-r_binary64`
263×	`*-commutative_binary64`
256×	`fma-neg_binary64`

Counts

190 → 239

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	361	5632
1	1035	5308
2	3534	5184
3	4963	5184
4	4943	5184

prune152.0ms (2.9%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	334	0	334
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	334	6	340

Error

0.1b

Counts

340 → 6

Alt Table

Status	Error	Program
	50.8b	(exp.f64 (log.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x)))
	33.3b	(*.f64 x (neg.f64 y))
✓	28.5b	(*.f64 x y)
✓	25.7b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
✓	30.1b	(.f64 (.f64 (*.f64 x (sqrt.f64 (+.f64 y z))) (sqrt.f64 (sqrt.f64 (-.f64 y z)))) (sqrt.f64 (sqrt.f64 (-.f64 y z))))
✓	30.0b	(.f64 (.f64 x (sqrt.f64 (+.f64 y z))) (sqrt.f64 (-.f64 y z)))

Compiler

Compiled 10531 to 3451 computations (67.2% saved)

regimes253.0ms (4.9%)

Accuracy

Total 0.4b remaining (77.1%)

Threshold costs 0.4b (77.1%)

Counts

13 → 2

Compiler

Compiled 1783 to 1028 computations (42.3% saved)

bsearch12.0ms (0.2%)

Steps

Iters	Range		Point
1	-2.1945270859879633e-284	2.677262489569739e-267	4.105738868846895e-300

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

end76.0ms (1.5%)

Compiler: Compiled 119 to 75 computations (37% saved)

Details

analyze957.0ms (18.4%)

sample2.2s (43%)

simplify200.0ms (3.8%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series63.0ms (1.2%)

rewrite14.0ms (0.3%)

simplify102.0ms (2%)

prune86.0ms (1.6%)

localize2.0ms (0%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

series119.0ms (2.3%)

rewrite27.0ms (0.5%)

simplify126.0ms (2.4%)

prune82.0ms (1.6%)

localize11.0ms (0.2%)

series437.0ms (8.4%)

rewrite48.0ms (0.9%)

simplify165.0ms (3.2%)

prune152.0ms (2.9%)

regimes253.0ms (4.9%)

bsearch12.0ms (0.2%)

simplify4.0ms (0.1%)

end76.0ms (1.5%)

Profiling