Details

analyze701.0ms (21.3%)

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)

sample27.0ms (0.8%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
2.0ms	48×	body	128	nan
1.0ms	14×	body	128	invalid

Compiler

Compiled 30 to 20 computations (33.3% saved)

simplify194.0ms (5.9%)

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

24.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	24.4b	(.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))))
✓	2.2b	(-.f64 (.f64 y y) (.f64 z z))
✓	24.1b	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

series64.0ms (1.9%)

Counts

3 → 84

Calls

3 calls:

40.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
16.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
8.0ms	(-.f64 (.f64 y y) (.f64 z z))

rewrite15.0ms (0.4%)

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))

simplify103.0ms (3.1%)

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 (2.6%)

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

0.3b

Counts

180 → 5

Alt Table

Status	Error	Program
	35.9b	(.f64 x (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y))))
	31.8b	(*.f64 x (neg.f64 y))
✓	24.4b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
▶	29.2b	(*.f64 x y)
	30.6b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))

Compiler

Compiled 3660 to 1641 computations (55.2% saved)

localize2.0ms (0.1%)

prune3.0ms (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

0.3b

Counts

5 → 5

Alt Table

Status	Error	Program
	35.9b	(.f64 x (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y))))
	31.8b	(*.f64 x (neg.f64 y))
✓	24.4b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
✓	29.2b	(*.f64 x y)
▶	30.6b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))

Compiler

Compiled 89 to 60 computations (32.6% 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))
✓	0.2b	(*.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z)))

series84.0ms (2.5%)

Counts

3 → 60

Calls

3 calls:

41.0ms	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
24.0ms	(*.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z)))
19.0ms	(sqrt.f64 (-.f64 y z))

rewrite36.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 91

Calls

3 calls:

18.0ms	(*.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z)))
9.0ms	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
3.0ms	(sqrt.f64 (-.f64 y z))

simplify140.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

608×	`fma-def_binary64`
368×	`cancel-sign-sub-inv_binary64`
320×	`fma-neg_binary64`
278×	`neg-mul-1_binary64`
276×	`distribute-rgt-in_binary64`

Counts

151 → 209

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	261	3396
1	723	3292
2	2384	3112
3	4539	3112
4	4988	3112
5	4968	3112

prune90.0ms (2.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	208	1	209
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	208	6	214

Error

0.3b

Counts

214 → 6

Alt Table

Status	Error	Program
▶	30.7b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 y z))) (sqrt.f64 (sqrt.f64 (-.f64 y z))))))
✓	24.4b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
	35.9b	(.f64 x (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y))))
	31.8b	(*.f64 x (neg.f64 y))
✓	29.2b	(*.f64 x y)
✓	30.6b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))

Compiler

Compiled 4706 to 1916 computations (59.3% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (-.f64 y z))
✓	0.1b	(sqrt.f64 (sqrt.f64 (-.f64 y z)))
✓	0.2b	(.f64 (sqrt.f64 (+.f64 y z)) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 y z))) (sqrt.f64 (sqrt.f64 (-.f64 y z)))))
✓	0.3b	(*.f64 (sqrt.f64 (sqrt.f64 (-.f64 y z))) (sqrt.f64 (sqrt.f64 (-.f64 y z))))

series70.0ms (2.1%)

Counts

3 → 48

Calls

3 calls:

26.0ms

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

23.0ms

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

20.0ms

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

rewrite59.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

121×	`sqrt-prod_binary64`
118×	`sqrt-div_binary64`
91×	`add-sqr-sqrt_binary64`
39×	`sqrt-pow1_binary64`
37×	`*-un-lft-identity_binary64`

Counts

3 → 185

Calls

3 calls:

21.0ms

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

12.0ms

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

3.0ms

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

simplify158.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

933×	`times-frac_binary64`
582×	`fma-def_binary64`
496×	`fma-neg_binary64`
302×	`associate-r_binary64`
225×	`associate-l_binary64`

Counts

233 → 278

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	335	4928
1	818	4742
2	2657	4548
3	4984	4548
4	5332	4548

prune177.0ms (5.4%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	398	0	398
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	398	6	404

Error

0.3b

Counts

404 → 6

Alt Table

Status	Error	Program
✓	30.7b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 y z))) (sqrt.f64 (sqrt.f64 (-.f64 y z))))))
✓	24.4b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
	35.9b	(.f64 x (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y))))
	31.8b	(*.f64 x (neg.f64 y))
✓	29.2b	(*.f64 x y)
✓	30.6b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))

Compiler

Compiled 11480 to 4029 computations (64.9% saved)

regimes343.0ms (10.4%)

Accuracy

Total 0.4b remaining (72.6%)

Threshold costs 0.4b (72.6%)

Counts

12 → 2

Compiler

Compiled 1543 to 1012 computations (34.4% saved)

bsearch13.0ms (0.4%)

Steps

Iters	Range		Point
1	-3.473023437561514e-281	7.733022457936848e-274	5.49680804289364e-305

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)

sample898.0ms (27.3%)

Algorithm

1×

intervals

Results

378.0ms	8000×	body	128	valid
75.0ms	1685×	body	128	nan
32.0ms	703×	body	128	invalid

Compiler

Compiled 114 to 73 computations (36% saved)

Details

analyze701.0ms (21.3%)

sample27.0ms (0.8%)

simplify194.0ms (5.9%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

series64.0ms (1.9%)

rewrite15.0ms (0.4%)

simplify103.0ms (3.1%)

prune86.0ms (2.6%)

localize2.0ms (0.1%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series84.0ms (2.5%)

rewrite36.0ms (1.1%)

simplify140.0ms (4.3%)

prune90.0ms (2.7%)

localize9.0ms (0.3%)

series70.0ms (2.1%)

rewrite59.0ms (1.8%)

simplify158.0ms (4.8%)

prune177.0ms (5.4%)

regimes343.0ms (10.4%)

bsearch13.0ms (0.4%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample898.0ms (27.3%)

Profiling