Details

analyze678.0ms (21.9%)

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)

sample26.0ms (0.9%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
3.0ms	54×	body	128	nan
1.0ms	22×	body	128	invalid

Compiler

Compiled 30 to 20 computations (33.3% saved)

simplify193.0ms (6.2%)

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

24.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	24.6b	(.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))))
✓	1.8b	(-.f64 (.f64 y y) (.f64 z z))
✓	24.7b	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

series67.0ms (2.2%)

Counts

3 → 84

Calls

3 calls:

41.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
15.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
11.0ms	(-.f64 (.f64 y y) (.f64 z z))

rewrite16.0ms (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:

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

simplify108.0ms (3.5%)

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

prune89.0ms (2.9%)

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
	30.4b	(-.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 z 2) x) y)) (*.f64 y x))
	32.6b	(fma.f64 (.f64 (/.f64 (.f64 z z) y) x) -1/2 (*.f64 y x))
▶	29.4b	(*.f64 x (neg.f64 y))
	31.7b	(*.f64 x y)
✓	24.6b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Compiler

Compiled 3666 to 1643 computations (55.2% saved)

localize3.0ms (0.1%)

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
▶	30.4b	(-.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 z 2) x) y)) (*.f64 y x))
	32.6b	(fma.f64 (.f64 (/.f64 (.f64 z z) y) x) -1/2 (*.f64 y x))
✓	29.4b	(*.f64 x (neg.f64 y))
	31.7b	(*.f64 x y)
✓	24.6b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Compiler

Compiled 94 to 61 computations (35.1% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 z 2) x) y)) (*.f64 y x))
✓	2.8b	(/.f64 (*.f64 (pow.f64 z 2) x) y)
✓	5.2b	(*.f64 (pow.f64 z 2) x)

series72.0ms (2.3%)

Counts

3 → 18

Calls

3 calls:

38.0ms	(-.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 z 2) x) y)) (*.f64 y x))
23.0ms	(/.f64 (*.f64 (pow.f64 z 2) x) y)
10.0ms	(*.f64 (pow.f64 z 2) x)

rewrite15.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64`
14×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
8×	`associate-l_binary64`
8×	`*-un-lft-identity_binary64`

Counts

3 → 70

Calls

3 calls:

5.0ms	(-.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 z 2) x) y)) (*.f64 y x))
4.0ms	(/.f64 (*.f64 (pow.f64 z 2) x) y)
4.0ms	(*.f64 (pow.f64 z 2) x)

simplify74.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

744×	`times-frac_binary64`
624×	`associate-/l*_binary64`
478×	`fma-def_binary64`
417×	`associate-*l/_binary64`
232×	`associate-/l/_binary64`

Counts

88 → 118

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	130	1403
1	304	1206
2	1063	1159
3	4460	1159
4	4942	1159

prune64.0ms (2.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	0	2	2
Picked	1	0	1
Done	1	1	2
Total	119	4	123

Error

Counts

123 → 4

Alt Table

Status	Error	Program
▶	29.1b	(-.f64 (.f64 1/2 (/.f64 (.f64 z (.f64 z x)) y)) (.f64 y x))
	32.6b	(fma.f64 (.f64 (/.f64 (.f64 z z) y) x) -1/2 (*.f64 y x))
	31.7b	(*.f64 x y)
✓	24.6b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Compiler

Compiled 2303 to 1162 computations (49.5% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 1/2 (/.f64 (.f64 z (.f64 z x)) y)) (.f64 y x))
✓	0.1b	(.f64 z (.f64 z x))
✓	2.8b	(/.f64 (.f64 z (.f64 z x)) y)

series67.0ms (2.2%)

Counts

3 → 96

Calls

3 calls:

34.0ms	(-.f64 (.f64 1/2 (/.f64 (.f64 z (.f64 z x)) y)) (.f64 y x))
26.0ms	(/.f64 (.f64 z (.f64 z x)) y)
8.0ms	(.f64 z (.f64 z x))

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
8×	`pow1_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`

Counts

3 → 61

Calls

3 calls:

5.0ms	(-.f64 (.f64 1/2 (/.f64 (.f64 z (.f64 z x)) y)) (.f64 y x))
4.0ms	(/.f64 (.f64 z (.f64 z x)) y)
4.0ms	(.f64 z (.f64 z x))

simplify79.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

809×	`associate-/l*_binary64`
528×	`associate-*l/_binary64`
476×	`fma-def_binary64`
443×	`associate-*r/_binary64`
317×	`associate-/r*_binary64`

Counts

157 → 106

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	2213
1	312	2034
2	1138	1900
3	4577	1900
4	4955	1900

prune51.0ms (1.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	106	4	110

Error

Counts

110 → 4

Alt Table

Status	Error	Program
✓	29.1b	(-.f64 (.f64 1/2 (/.f64 (.f64 z (.f64 z x)) y)) (.f64 y x))
	32.6b	(fma.f64 (.f64 (/.f64 (.f64 z z) y) x) -1/2 (*.f64 y x))
	31.7b	(*.f64 x y)
✓	24.6b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Compiler

Compiled 2022 to 705 computations (65.1% saved)

regimes359.0ms (11.6%)

Accuracy

Total 0.4b remaining (33.5%)

Threshold costs 0.4b (33.5%)

Counts

18 → 2

Compiler

Compiled 2039 to 1372 computations (32.7% saved)

bsearch214.0ms (6.9%)

Steps

Iters	Range		Point
10	-3.538714094681241e-257	-3.676704133685205e-270	-3.7165584773607825e-270

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	29
1	24	29
2	34	29
3	40	29
4	44	29
5	45	29
6	45	29

end1.0ms (0%)

Compiler: Compiled 23 to 13 computations (43.5% saved)

sample875.0ms (28.2%)

Algorithm

1×

intervals

Results

380.0ms	8000×	body	128	valid
82.0ms	1821×	body	128	nan
35.0ms	723×	body	128	invalid

Compiler

Compiled 90 to 56 computations (37.8% saved)

Details

analyze678.0ms (21.9%)

sample26.0ms (0.9%)

simplify193.0ms (6.2%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series67.0ms (2.2%)

rewrite16.0ms (0.5%)

simplify108.0ms (3.5%)

prune89.0ms (2.9%)

localize3.0ms (0.1%)

prune4.0ms (0.1%)

localize9.0ms (0.3%)

series72.0ms (2.3%)

rewrite15.0ms (0.5%)

simplify74.0ms (2.4%)

prune64.0ms (2.1%)

localize8.0ms (0.3%)

series67.0ms (2.2%)

rewrite16.0ms (0.5%)

simplify79.0ms (2.6%)

prune51.0ms (1.6%)

regimes359.0ms (11.6%)

bsearch214.0ms (6.9%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample875.0ms (28.2%)

Profiling