Details

analyze858.0ms (10.6%)

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
6.2%	93.6%	0.1%	6
12.5%	87.4%	0.1%	7
15.6%	84.3%	0.1%	8
18.7%	71.8%	9.5%	9
23.4%	56%	20.6%	10
26.3%	52.2%	21.5%	11
31%	40.1%	28.9%	12
35.6%	28.9%	35.5%	13
36.8%	27.5%	35.7%	14

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample1.6s (19.4%)

Alt Table

Status	Error	Program
▶	21.1b	(.f64 2 (sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 x z)) (.f64 y z))))

Symmetry

(sort x y z)

Results

1.2s	8256×	body	128	valid
274.0ms	2379×	body	128	invalid

Compiler

Compiled 87 to 57 computations (34.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(+.f64 (.f64 x y) (.f64 x z))
✓	0.4b	(+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z))
✓	20.0b	(sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z)))

series229.0ms (2.8%)

Counts

3 → 84

Calls

3 calls:

213.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z)))
10.0ms	(+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z))
7.0ms	(+.f64 (.f64 x y) (.f64 x z))

rewrite116.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

812×	`fma-def_binary64`
462×	`fma-neg_binary64`
205×	`expm1-udef_binary64`
205×	`log1p-udef_binary64`
203×	`egg-rr`

Counts

3 → 203

Calls

3 calls:

111.0ms	(+.f64 (.f64 x y) (.f64 x z))
111.0ms	(+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z))
111.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	35
1	222	31
2	3032	31
3	4992	31
4	5043	31
0	0	0
1	0	0

prune329.0ms (4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	275	12	287
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	276	12	288

Error

20.4b

Counts

288 → 12

Alt Table

Status	Error	Program
▶	21.3b	(.f64 2 (pow.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4) 2))
	63.3b	(.f64 2 (+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 z x)))) (+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 x z)))) (sqrt.f64 (.f64 z x)))))
	21.8b	(.f64 2 (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z)))) 3))
	61.7b	(.f64 2 (sqrt.f64 (.f64 z x)))
	22.7b	(.f64 2 (sqrt.f64 (fma.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) z) (.f64 x (+.f64 y z)))))
	43.7b	(.f64 2 (sqrt.f64 (.f64 y z)))
	43.9b	(.f64 2 (+.f64 (sqrt.f64 (.f64 y x)) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 x y)) z)) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 y x)) z)))))
	40.9b	(.f64 2 (sqrt.f64 (.f64 y x)))
	52.7b	(.f64 2 (/.f64 (sqrt.f64 (-.f64 (pow.f64 (.f64 x (+.f64 y z)) 2) (pow.f64 (.f64 y z) 2))) (sqrt.f64 (-.f64 (.f64 x (+.f64 y z)) (*.f64 y z)))))
	24.2b	(.f64 2 (sqrt.f64 (fma.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) x) (.f64 z (+.f64 x y)))))
	21.6b	(.f64 2 (.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))
	42.7b	(.f64 2 (sqrt.f64 (.f64 z (+.f64 y x))))

Compiler

Compiled 5773 to 2176 computations (62.3% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (+.f64 y z) (*.f64 y z))
✓	0.5b	(pow.f64 (pow.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)) 1/4) 2)
✓	20.3b	(pow.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)) 1/4)

series213.0ms (2.6%)

Counts

3 → 108

Calls

3 calls:

129.0ms	(pow.f64 (pow.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)) 1/4) 2)
75.0ms	(pow.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)) 1/4)
8.0ms	(fma.f64 x (+.f64 y z) (*.f64 y z))

rewrite118.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

750×	`prod-diff_binary64`
542×	`fma-udef_binary64`
304×	`fma-def_binary64`
203×	`fma-neg_binary64`
194×	`expm1-udef_binary64`

Counts

3 → 82

Calls

3 calls:

116.0ms	(fma.f64 x (+.f64 y z) (*.f64 y z))
116.0ms	(pow.f64 (pow.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)) 1/4) 2)
116.0ms	(pow.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)) 1/4)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	240	38
2	2631	38
3	4734	38
4	4706	38
5	4972	38
0	0	0
1	0	0

prune240.0ms (3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	188	2	190
Fresh	6	5	11
Picked	0	1	1
Done	0	0	0
Total	194	8	202

Error

2.2b

Counts

202 → 8

Alt Table

Status	Error	Program
	21.8b	(.f64 2 (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z)))) 3))
	33.0b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (neg.f64 (+.f64 y z))) (log.f64 (/.f64 -1 x))))) 2))
	36.9b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (+.f64 y x)) (log.f64 (/.f64 1 z))))) 2))
✓	21.3b	(.f64 2 (pow.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4) 2))
	22.7b	(.f64 2 (sqrt.f64 (fma.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) z) (.f64 x (+.f64 y z)))))
	52.7b	(.f64 2 (/.f64 (sqrt.f64 (-.f64 (pow.f64 (.f64 x (+.f64 y z)) 2) (pow.f64 (.f64 y z) 2))) (sqrt.f64 (-.f64 (.f64 x (+.f64 y z)) (*.f64 y z)))))
	24.2b	(.f64 2 (sqrt.f64 (fma.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) x) (.f64 z (+.f64 x y)))))
▶	21.6b	(.f64 2 (.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))

Compiler

Compiled 6922 to 3962 computations (42.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))))
✓	0.6b	(cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))
✓	20.0b	(sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))
✓	20.6b	(cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))

series568.0ms (7%)

Counts

4 → 96

Calls

4 calls:

212.0ms	(.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))))
207.0ms	(sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))
77.0ms	(cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))
73.0ms	(cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))

rewrite125.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

752×	`prod-diff_binary64`
536×	`fma-udef_binary64`
292×	`fma-def_binary64`
216×	`fma-neg_binary64`
174×	`expm1-udef_binary64`

Counts

4 → 101

Calls

4 calls:

122.0ms	(.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))))
122.0ms	(cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))
122.0ms	(sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))
122.0ms	(cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	54
1	204	53
2	2414	53
3	4755	53
4	4666	53
5	5086	53
0	0	0
1	0	0

prune174.0ms (2.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	196	1	197
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	196	9	205

Error

2.2b

Counts

205 → 9

Alt Table

Status	Error	Program
▶	21.8b	(.f64 2 (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z)))) 3))
	33.0b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (neg.f64 (+.f64 y z))) (log.f64 (/.f64 -1 x))))) 2))
	52.7b	(.f64 2 (/.f64 (sqrt.f64 (-.f64 (pow.f64 (.f64 x (+.f64 y z)) 2) (pow.f64 (.f64 y z) 2))) (sqrt.f64 (-.f64 (.f64 x (+.f64 y z)) (*.f64 y z)))))
	22.0b	(.f64 2 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z)))) 3) (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))
	36.9b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (+.f64 y x)) (log.f64 (/.f64 1 z))))) 2))
✓	21.3b	(.f64 2 (pow.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4) 2))
	22.7b	(.f64 2 (sqrt.f64 (fma.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) z) (.f64 x (+.f64 y z)))))
	24.2b	(.f64 2 (sqrt.f64 (fma.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) x) (.f64 z (+.f64 x y)))))
✓	21.6b	(.f64 2 (.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))

Compiler

Compiled 9443 to 4635 computations (50.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (+.f64 y z) (*.f64 y z))
✓	0.6b	(cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))
✓	0.7b	(pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))) 3)
✓	20.0b	(sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))

series511.0ms (6.3%)

Counts

4 → 120

Calls

4 calls:

223.0ms	(pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))) 3)
209.0ms	(sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))
71.0ms	(cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))
8.0ms	(fma.f64 x (+.f64 y z) (*.f64 y z))

rewrite132.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

750×	`prod-diff_binary64`
541×	`fma-udef_binary64`
304×	`fma-def_binary64`
205×	`fma-neg_binary64`
182×	`expm1-udef_binary64`

Counts

4 → 126

Calls

4 calls:

125.0ms	(fma.f64 x (+.f64 y z) (*.f64 y z))
125.0ms	(cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))
125.0ms	(pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))) 3)
125.0ms	(sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	52
1	214	51
2	2523	51
3	4727	51
4	4703	51
5	4981	51
0	0	0
1	0	0

prune201.0ms (2.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	244	2	246
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	244	11	255

Error

2.2b

Counts

255 → 11

Alt Table

Status	Error	Program
✓	21.8b	(.f64 2 (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z)))) 3))
	33.0b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (neg.f64 (+.f64 y z))) (log.f64 (/.f64 -1 x))))) 2))
	52.7b	(.f64 2 (/.f64 (sqrt.f64 (-.f64 (pow.f64 (.f64 x (+.f64 y z)) 2) (pow.f64 (.f64 y z) 2))) (sqrt.f64 (-.f64 (.f64 x (+.f64 y z)) (*.f64 y z)))))
	22.0b	(.f64 2 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z)))) 3) (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))
	36.9b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (+.f64 y x)) (log.f64 (/.f64 1 z))))) 2))
✓	21.3b	(.f64 2 (pow.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4) 2))
	22.7b	(.f64 2 (sqrt.f64 (fma.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) z) (.f64 x (+.f64 y z)))))
	24.2b	(.f64 2 (sqrt.f64 (fma.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) x) (.f64 z (+.f64 x y)))))
✓	21.6b	(.f64 2 (.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))
	38.2b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 (+.f64 z x)) (log.f64 (/.f64 1 y))))) 3))
	33.2b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/6 (-.f64 (log.f64 (neg.f64 (+.f64 y z))) (log.f64 (/.f64 -1 x))))) 3))

Compiler

Compiled 8499 to 4622 computations (45.6% saved)

regimes1.9s (23.1%)

Accuracy

Total 3.2b remaining (61%)

Threshold costs 0b (0%)

Counts

133 → 4

Compiler

Compiled 14354 to 9704 computations (32.4% saved)

bsearch151.0ms (1.9%)

Steps

Iters	Range	Point
12	-4.1017965464249906e-289	2.0905494539134198e-268	2.0611617972601002e-268
7	-2.2306878865165007e-172	-1.3938296011750175e-174	-5.029427106894932e-174
7	-3.554471203990684e+22	-2.543246854412101e+20	-3.5016519017157693e+22

Iters

Range

Point

-4.1017965464249906e-289

2.0905494539134198e-268

2.0611617972601002e-268

-2.2306878865165007e-172

-1.3938296011750175e-174

-5.029427106894932e-174

-3.554471203990684e+22

-2.543246854412101e+20

-3.5016519017157693e+22

Compiler

Compiled 4 to 3 computations (25% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary64`
10×	`+-commutative_binary64`
7×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	119
1	66	119
2	80	119
3	90	119
4	94	119
5	93	119

end655.0ms (8.1%)

Compiler: Compiled 555 to 396 computations (28.6% saved)

Details

analyze858.0ms (10.6%)

sample1.6s (19.4%)

localize9.0ms (0.1%)

series229.0ms (2.8%)

rewrite116.0ms (1.4%)

prune329.0ms (4%)

localize11.0ms (0.1%)

series213.0ms (2.6%)

rewrite118.0ms (1.5%)

prune240.0ms (3%)

localize12.0ms (0.2%)

series568.0ms (7%)

rewrite125.0ms (1.5%)

prune174.0ms (2.1%)

localize12.0ms (0.1%)

series511.0ms (6.3%)

rewrite132.0ms (1.6%)

prune201.0ms (2.5%)

regimes1.9s (23.1%)

bsearch151.0ms (1.9%)

simplify8.0ms (0.1%)

end655.0ms (8.1%)

Profiling