Details

analyze551.0ms (9.3%)

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
25%	74.9%	0.1%	7
31.2%	68.6%	0.1%	8
35.9%	64%	0.1%	9
47.6%	49.9%	2.5%	10
49.1%	46.8%	4%	11
51.1%	44.1%	4.8%	12
60.2%	29.9%	9.9%	13
60.6%	27.9%	11.6%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.2s (20.8%)

Symmetry

(sort x y)

Results

868.0ms	8256×	body	128	valid
170.0ms	1572×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify94.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

826×	`associate-*r/_binary64`
769×	`associate-/l/_binary64`
660×	`associate-*l/_binary64`
522×	`associate-/l*_binary64`
421×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	30	16
2	78	14
3	195	14
4	314	14
5	383	14
6	426	14
7	631	14
8	1009	14
9	2204	14
10	2868	14
11	2967	14
12	3079	14
13	3193	14
14	3058	14
15	3712	14
16	4988	14
17	4824	14

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

7.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	10.5b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
	17.2b	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))

Compiler

Compiled 78 to 45 computations (42.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 y (fma.f64 z z z)) z)
✓	3.9b	(/.f64 y (fma.f64 z z z))
✓	9.7b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))

series187.0ms (3.2%)

Counts

3 → 84

Calls

3 calls:

103.0ms	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
52.0ms	(/.f64 (/.f64 y (fma.f64 z z z)) z)
32.0ms	(/.f64 y (fma.f64 z z z))

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

153×	`times-frac_binary64`
98×	`add-sqr-sqrt_binary64`
89×	`*-un-lft-identity_binary64`
89×	`add-cube-cbrt_binary64`
43×	`associate-r_binary64`

Counts

3 → 168

Calls

3 calls:

10.0ms	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
4.0ms	(/.f64 (/.f64 y (fma.f64 z z z)) z)
2.0ms	(/.f64 y (fma.f64 z z z))

simplify156.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

805×	`fma-def_binary64`
353×	`fma-neg_binary64`
351×	`*-commutative_binary64`
341×	`associate-/r/_binary64`
275×	`sub-neg_binary64`

Counts

252 → 296

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	287	4846
1	687	4599
2	2304	4515
3	3607	4509
4	4817	4509
5	4963	4509

prune251.0ms (4.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	286	10	296
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	288	10	298

Error

2.6b

Counts

298 → 10

Alt Table

Status	Error	Program
	14.9b	(*.f64 x (/.f64 y (/.f64 z (/.f64 1 (fma.f64 z z z)))))
	8.4b	(.f64 (/.f64 x (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 y (cbrt.f64 (fma.f64 z z z))) (cbrt.f64 z)))
	10.5b	(*.f64 (/.f64 (/.f64 y (fma.f64 z z z)) z) x)
	37.1b	(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 (/.f64 y (fma.f64 z z z)) (sqrt.f64 z)))
	9.8b	(.f64 (.f64 x (/.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 1 (fma.f64 z z z)) (cbrt.f64 z)))
	6.7b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (fma.f64 z z z)) (cbrt.f64 z)))
▶	5.8b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	27.7b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
	39.9b	(.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 (/.f64 y z) (hypot.f64 z (sqrt.f64 z)))))
	24.0b	(/.f64 (*.f64 y x) (+.f64 (pow.f64 z 2) (pow.f64 z 3)))

Compiler

Compiled 6292 to 1451 computations (76.9% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.8b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	3.9b	(/.f64 y (fma.f64 z z z))
✓	5.4b	(*.f64 x (/.f64 y (fma.f64 z z z)))

series165.0ms (2.8%)

Counts

2 → 72

Calls

2 calls:

100.0ms	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
66.0ms	(*.f64 x (/.f64 y (fma.f64 z z z)))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
13×	`associate-r_binary64`
13×	`times-frac_binary64`

Counts

2 → 60

Calls

2 calls:

4.0ms	(*.f64 x (/.f64 y (fma.f64 z z z)))
4.0ms	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)

simplify82.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

604×	`fma-neg_binary64`
483×	`associate-l_binary64`
433×	`associate-/r*_binary64`
417×	`associate-r_binary64`
378×	`associate-/r/_binary64`

Counts

132 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	153	2289
1	397	2096
2	1539	1990
3	4439	1990
4	4968	1990

prune154.0ms (2.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	170	5	175
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	176	9	185

Error

1.9b

Counts

185 → 9

Alt Table

Status	Error	Program
	10.3b	(/.f64 x (/.f64 z (/.f64 y (fma.f64 z z z))))
	19.3b	(.f64 (sqrt.f64 (/.f64 (.f64 x (/.f64 y (fma.f64 z z z))) z)) (sqrt.f64 (/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)))
	36.5b	(/.f64 (.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
	24.0b	(/.f64 (*.f64 y x) (+.f64 (pow.f64 z 2) (pow.f64 z 3)))
	11.1b	(/.f64 (/.f64 (*.f64 y x) (fma.f64 z z z)) z)
	10.5b	(*.f64 (/.f64 (/.f64 y (fma.f64 z z z)) z) x)
▶	5.8b	(/.f64 (.f64 x (.f64 y (/.f64 1 (fma.f64 z z z)))) z)
	37.1b	(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 (/.f64 y (fma.f64 z z z)) (sqrt.f64 z)))
	39.9b	(.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 (/.f64 y z) (hypot.f64 z (sqrt.f64 z)))))

Compiler

Compiled 3260 to 919 computations (71.8% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(/.f64 (.f64 x (.f64 y (/.f64 1 (fma.f64 z z z)))) z)
✓	0.9b	(/.f64 1 (fma.f64 z z z))
✓	3.8b	(*.f64 y (/.f64 1 (fma.f64 z z z)))
✓	5.4b	(.f64 x (.f64 y (/.f64 1 (fma.f64 z z z))))

series202.0ms (3.4%)

Counts

4 → 108

Calls

4 calls:

100.0ms	(/.f64 (.f64 x (.f64 y (/.f64 1 (fma.f64 z z z)))) z)
66.0ms	(.f64 x (.f64 y (/.f64 1 (fma.f64 z z z))))
33.0ms	(*.f64 y (/.f64 1 (fma.f64 z z z)))
2.0ms	(/.f64 1 (fma.f64 z z z))

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-exp-log_binary64`
34×	`add-cbrt-cube_binary64`
30×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
23×	`times-frac_binary64`

Counts

4 → 128

Calls

4 calls:

7.0ms	(/.f64 (.f64 x (.f64 y (/.f64 1 (fma.f64 z z z)))) z)
5.0ms	(.f64 x (.f64 y (/.f64 1 (fma.f64 z z z))))
5.0ms	(*.f64 y (/.f64 1 (fma.f64 z z z)))
4.0ms	(/.f64 1 (fma.f64 z z z))

simplify128.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

653×	`associate-/r*_binary64`
477×	`fma-neg_binary64`
401×	`associate-/l/_binary64`
364×	`fma-def_binary64`
362×	`associate-/r/_binary64`

Counts

236 → 238

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	210	3645
1	504	3287
2	1786	3174
3	4541	3174
4	4998	3174
5	4977	3174

prune179.0ms (3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	238	9	247

Error

1.9b

Counts

247 → 9

Alt Table

Status	Error	Program
▶	10.3b	(/.f64 x (/.f64 z (/.f64 y (fma.f64 z z z))))
	19.3b	(.f64 (sqrt.f64 (/.f64 (.f64 x (/.f64 y (fma.f64 z z z))) z)) (sqrt.f64 (/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)))
	36.5b	(/.f64 (.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
	24.0b	(/.f64 (*.f64 y x) (+.f64 (pow.f64 z 2) (pow.f64 z 3)))
	11.1b	(/.f64 (/.f64 (*.f64 y x) (fma.f64 z z z)) z)
	10.5b	(*.f64 (/.f64 (/.f64 y (fma.f64 z z z)) z) x)
✓	5.8b	(/.f64 (.f64 x (.f64 y (/.f64 1 (fma.f64 z z z)))) z)
	37.1b	(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 (/.f64 y (fma.f64 z z z)) (sqrt.f64 z)))
	39.9b	(.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 (/.f64 y z) (hypot.f64 z (sqrt.f64 z)))))

Compiler

Compiled 4539 to 1881 computations (58.6% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 z (/.f64 y (fma.f64 z z z)))
	3.9b	(/.f64 y (fma.f64 z z z))
✓	9.8b	(/.f64 x (/.f64 z (/.f64 y (fma.f64 z z z))))

series109.0ms (1.8%)

Counts

2 → 60

Calls

2 calls:

94.0ms	(/.f64 x (/.f64 z (/.f64 y (fma.f64 z z z))))
15.0ms	(/.f64 z (/.f64 y (fma.f64 z z z)))

rewrite50.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

471×	`times-frac_binary64`
229×	`*-un-lft-identity_binary64`
229×	`add-sqr-sqrt_binary64`
229×	`add-cube-cbrt_binary64`
57×	`associate-/r*_binary64`

Counts

2 → 270

Calls

2 calls:

10.0ms	(/.f64 x (/.f64 z (/.f64 y (fma.f64 z z z))))
4.0ms	(/.f64 z (/.f64 y (fma.f64 z z z)))

simplify233.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

579×	`associate-/r/_binary64`
431×	`associate-/l/_binary64`
401×	`fma-def_binary64`
378×	`associate-*l/_binary64`
332×	`associate-*r/_binary64`

Counts

330 → 488

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	487	9126
1	1085	8731
2	4136	8600
3	4639	8600
4	4989	8600

prune376.0ms (6.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	537	2	539
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	539	9	548

Error

1.8b

Counts

548 → 9

Alt Table

Status	Error	Program
✓	10.3b	(/.f64 x (/.f64 z (/.f64 y (fma.f64 z z z))))
	19.3b	(.f64 (sqrt.f64 (/.f64 (.f64 x (/.f64 y (fma.f64 z z z))) z)) (sqrt.f64 (/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)))
	36.5b	(/.f64 (.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
	34.9b	(.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (hypot.f64 z (sqrt.f64 z))) (*.f64 (/.f64 (cbrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (/.f64 x z)))
	24.0b	(/.f64 (*.f64 y x) (+.f64 (pow.f64 z 2) (pow.f64 z 3)))
	10.5b	(*.f64 (/.f64 (/.f64 y (fma.f64 z z z)) z) x)
✓	5.8b	(/.f64 (.f64 x (.f64 y (/.f64 1 (fma.f64 z z z)))) z)
	11.1b	(/.f64 (/.f64 (*.f64 y x) z) (fma.f64 z z z))
	39.9b	(.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 (/.f64 y z) (hypot.f64 z (sqrt.f64 z)))))

Compiler

Compiled 12433 to 2253 computations (81.9% saved)

regimes1.3s (22.6%)

Accuracy

Total 2.0b remaining (68.6%)

Threshold costs 0b (0%)

Counts

196 → 2

Compiler

Compiled 22641 to 12028 computations (46.9% saved)

bsearch65.0ms (1.1%)

Steps

Iters	Range		Point
4	-8.919213842090535e-284	2.6267638808657615e-298	-5.332363795460978e-308

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	87
1	29	87
2	29	87

end261.0ms (4.4%)

Compiler: Compiled 395 to 175 computations (55.7% saved)

Details

analyze551.0ms (9.3%)

sample1.2s (20.8%)

simplify94.0ms (1.6%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series187.0ms (3.2%)

rewrite33.0ms (0.6%)

simplify156.0ms (2.6%)

prune251.0ms (4.2%)

localize7.0ms (0.1%)

series165.0ms (2.8%)

rewrite13.0ms (0.2%)

simplify82.0ms (1.4%)

prune154.0ms (2.6%)

localize7.0ms (0.1%)

series202.0ms (3.4%)

rewrite28.0ms (0.5%)

simplify128.0ms (2.2%)

prune179.0ms (3%)

localize7.0ms (0.1%)

series109.0ms (1.8%)

rewrite50.0ms (0.8%)

simplify233.0ms (3.9%)

prune376.0ms (6.4%)

regimes1.3s (22.6%)

bsearch65.0ms (1.1%)

simplify3.0ms (0.1%)

end261.0ms (4.4%)

Profiling