Details

analyze845.0ms (10.2%)

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)

sample1.5s (17.9%)

Symmetry

(sort x y z)

Results

1.1s	8256×	body	128	valid
294.0ms	2353×	body	128	invalid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

25×	`fma-def_binary64`
8×	`+-commutative_binary64`
8×	`*-commutative_binary64`
5×	`distribute-rgt-out_binary64`
3×	`associate-+r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	23	16
2	43	16
3	59	16
4	61	16
5	62	16
6	62	16

prune3.0ms (0%)

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

21.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	21.5b	(.f64 2 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))
▶	21.5b	(.f64 2 (sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 x z)) (.f64 y z))))

Compiler

Compiled 90 to 56 computations (37.8% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.2b	(+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z))
✓	1.2b	(+.f64 (.f64 x y) (.f64 x z))
✓	20.3b	(sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z)))

series142.0ms (1.7%)

Counts

3 → 84

Calls

3 calls:

124.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z)))
9.0ms	(+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z))
7.0ms	(+.f64 (.f64 x y) (.f64 x z))

rewrite108.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

3 → 204

Calls

3 calls:

104.0ms	(+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z))
104.0ms	(+.f64 (.f64 x y) (.f64 x z))
104.0ms	(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

simplify72.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

605×	`cancel-sign-sub-inv_binary64`
602×	`associate-l_binary64`
542×	`associate-r_binary64`
318×	`times-frac_binary64`
297×	`fma-neg_binary64`

Counts

288 → 233

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	191	1448
1	506	1389
2	1816	1344
3	4609	1344
4	5322	1344

prune255.0ms (3.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	222	11	233
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	224	11	235

Error

20.9b

Counts

235 → 11

Alt Table

Status	Error	Program
	22.0b	(.f64 2 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))
	42.1b	(.f64 2 (sqrt.f64 (.f64 y z)))
	24.9b	(.f64 2 (sqrt.f64 (fma.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) z) (.f64 x (+.f64 y z)))))
	46.6b	(.f64 2 (fma.f64 1/2 (.f64 z (+.f64 (sqrt.f64 (/.f64 x y)) (sqrt.f64 (/.f64 y x)))) (sqrt.f64 (*.f64 y x))))
	32.3b	(.f64 2 (sqrt.f64 (fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) y) (.f64 z (+.f64 x y)))))
	42.8b	(.f64 2 (sqrt.f64 (.f64 y x)))
	63.5b	(.f64 2 (+.f64 (sqrt.f64 (.f64 z x)) (.f64 y (.f64 1/2 (+.f64 (sqrt.f64 (/.f64 z x)) (sqrt.f64 (/.f64 x z)))))))
▶	21.8b	(.f64 2 (pow.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4) 2))
	62.1b	(.f64 2 (sqrt.f64 (.f64 z x)))
	50.7b	(.f64 2 (/.f64 (hypot.f64 (pow.f64 (.f64 x (+.f64 y z)) 3/2) (pow.f64 (.f64 y z) 3/2)) (hypot.f64 (.f64 x (+.f64 y z)) (sqrt.f64 (.f64 (.f64 y z) (-.f64 (.f64 y z) (.f64 x (+.f64 y z))))))))
	42.6b	(.f64 2 (sqrt.f64 (fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) z) (*.f64 x (+.f64 y z)))))

Compiler

Compiled 5450 to 2303 computations (57.7% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.5b	(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)
✓	20.7b	(pow.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)) 1/4)

series134.0ms (1.6%)

Counts

3 → 108

Calls

3 calls:

76.0ms	(pow.f64 (pow.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)) 1/4) 2)
50.0ms	(pow.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)) 1/4)
8.0ms	(fma.f64 x (+.f64 y z) (*.f64 y z))

rewrite113.0ms (1.4%)

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 → 84

Calls

3 calls:

111.0ms	(fma.f64 x (+.f64 y z) (*.f64 y z))
111.0ms	(pow.f64 (pow.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)) 1/4) 2)
111.0ms	(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

simplify108.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

718×	`times-frac_binary64`
534×	`fma-def_binary64`
469×	`associate-/l*_binary64`
251×	`*-commutative_binary64`
132×	`cancel-sign-sub-inv_binary64`

Counts

192 → 225

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	622	6589
1	2078	6304
2	5199	6304

prune225.0ms (2.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	223	2	225
Fresh	5	5	10
Picked	0	1	1
Done	0	0	0
Total	228	8	236

Error

2.2b

Counts

236 → 8

Alt Table

Status	Error	Program
✓	21.8b	(.f64 2 (pow.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4) 2))
	34.4b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (neg.f64 (+.f64 y z))) (log.f64 (/.f64 -1 x))))) 2))
	24.9b	(.f64 2 (sqrt.f64 (fma.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) z) (.f64 x (+.f64 y z)))))
	35.5b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (+.f64 y x)) (log.f64 (/.f64 1 z))))) 2))
	32.3b	(.f64 2 (sqrt.f64 (fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) y) (.f64 z (+.f64 x y)))))
	50.7b	(.f64 2 (/.f64 (hypot.f64 (pow.f64 (.f64 x (+.f64 y z)) 3/2) (pow.f64 (.f64 y z) 3/2)) (hypot.f64 (.f64 x (+.f64 y z)) (sqrt.f64 (.f64 (.f64 y z) (-.f64 (.f64 y z) (.f64 x (+.f64 y z))))))))
▶	22.0b	(.f64 2 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))
	42.6b	(.f64 2 (sqrt.f64 (fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) z) (*.f64 x (+.f64 y z)))))

Compiler

Compiled 10458 to 5950 computations (43.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))) 2)
	0.5b	(fma.f64 x (+.f64 y z) (*.f64 y z))
✓	6.3b	(sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))) 2))
✓	20.9b	(cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))

series185.0ms (2.2%)

Counts

3 → 108

Calls

3 calls:

79.0ms	(pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))) 2)
55.0ms	(sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))) 2))
50.0ms	(cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))

rewrite117.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

752×	`prod-diff_binary64`
536×	`fma-udef_binary64`
284×	`fma-def_binary64`
199×	`fma-neg_binary64`
179×	`expm1-udef_binary64`

Counts

3 → 72

Calls

3 calls:

115.0ms	(pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))) 2)
115.0ms	(sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))) 2))
115.0ms	(cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	42
1	210	42
2	2444	42
3	4790	42
4	4701	42
5	5041	42
0	0	0
1	0	0

simplify146.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

682×	`times-frac_binary64`
567×	`fma-def_binary64`
446×	`associate-/l*_binary64`
239×	`*-commutative_binary64`
180×	`sqr-pow_binary64`

Counts

180 → 184

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	614	9389
1	2155	8997
2	5390	8997

prune685.0ms (8.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	372	0	372
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	372	8	380

Error

2.2b

Counts

380 → 8

Alt Table

Status	Error	Program
✓	21.8b	(.f64 2 (pow.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4) 2))
	34.4b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (neg.f64 (+.f64 y z))) (log.f64 (/.f64 -1 x))))) 2))
▶	24.9b	(.f64 2 (sqrt.f64 (fma.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) z) (.f64 x (+.f64 y z)))))
	35.5b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (+.f64 y x)) (log.f64 (/.f64 1 z))))) 2))
	32.3b	(.f64 2 (sqrt.f64 (fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) y) (.f64 z (+.f64 x y)))))
	50.7b	(.f64 2 (/.f64 (hypot.f64 (pow.f64 (.f64 x (+.f64 y z)) 3/2) (pow.f64 (.f64 y z) 3/2)) (hypot.f64 (.f64 x (+.f64 y z)) (sqrt.f64 (.f64 (.f64 y z) (-.f64 (.f64 y z) (.f64 x (+.f64 y z))))))))
✓	22.0b	(.f64 2 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))
	42.6b	(.f64 2 (sqrt.f64 (fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) z) (*.f64 x (+.f64 y z)))))

Compiler

Compiled 20686 to 9811 computations (52.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 y)
✓	1.2b	(fma.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) z) (*.f64 x (+.f64 y z)))
✓	20.1b	(cbrt.f64 (*.f64 y y))
✓	20.3b	(sqrt.f64 (fma.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) z) (*.f64 x (+.f64 y z))))

series400.0ms (4.8%)

Counts

4 → 72

Calls

4 calls:

216.0ms	(fma.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) z) (*.f64 x (+.f64 y z)))
124.0ms	(sqrt.f64 (fma.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) z) (*.f64 x (+.f64 y z))))
30.0ms	(cbrt.f64 y)
30.0ms	(cbrt.f64 (*.f64 y y))

rewrite75.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

595×	`log-prod_binary64`
365×	`fma-def_binary64`
209×	`expm1-udef_binary64`
209×	`log1p-udef_binary64`
198×	`log-pow_binary64`

Counts

4 → 126

Calls

4 calls:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	53
1	247	37
2	2962	33
3	5465	33
0	0	0
1	0	0

simplify70.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

725×	`associate-l_binary64`
693×	`associate-r_binary64`
477×	`cancel-sign-sub-inv_binary64`
345×	`fma-neg_binary64`
212×	`times-frac_binary64`

Counts

198 → 161

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	169	1277
1	463	1233
2	1604	1195
3	4659	1192
4	5253	1192

prune110.0ms (1.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	159	2	161
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	159	10	169

Error

1.8b

Counts

169 → 10

Alt Table

Status	Error	Program
	48.3b	(.f64 2 (hypot.f64 (sqrt.f64 (.f64 x (+.f64 y z))) (*.f64 (sqrt.f64 y) (sqrt.f64 z))))
	35.5b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (+.f64 y x)) (log.f64 (/.f64 1 z))))) 2))
✓	21.8b	(.f64 2 (pow.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4) 2))
	34.4b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (neg.f64 (+.f64 y z))) (log.f64 (/.f64 -1 x))))) 2))
✓	24.9b	(.f64 2 (sqrt.f64 (fma.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) z) (.f64 x (+.f64 y z)))))
	41.1b	(.f64 2 (hypot.f64 (sqrt.f64 (.f64 x (+.f64 y z))) (.f64 (cbrt.f64 y) (sqrt.f64 (.f64 (cbrt.f64 y) z)))))
	32.3b	(.f64 2 (sqrt.f64 (fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) y) (.f64 z (+.f64 x y)))))
	50.7b	(.f64 2 (/.f64 (hypot.f64 (pow.f64 (.f64 x (+.f64 y z)) 3/2) (pow.f64 (.f64 y z) 3/2)) (hypot.f64 (.f64 x (+.f64 y z)) (sqrt.f64 (.f64 (.f64 y z) (-.f64 (.f64 y z) (.f64 x (+.f64 y z))))))))
✓	22.0b	(.f64 2 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))
	42.6b	(.f64 2 (sqrt.f64 (fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) z) (*.f64 x (+.f64 y z)))))

Compiler

Compiled 3852 to 1588 computations (58.8% saved)

regimes2.1s (24.9%)

Accuracy

Total 2.7b remaining (60.9%)

Threshold costs 0b (0%)

Counts

135 → 6

Compiler

Compiled 14810 to 9956 computations (32.8% saved)

bsearch233.0ms (2.8%)

Steps

Iters	Range		Point
7	2.1114377005974427e+77	1.5053690721256536e+79	1.4758287118476183e+79
10	2.723161989220886e-179	2.440875843614385e-169	2.748072096169368e-179
12	-2.848420278925453e-293	1.301820874721925e-282	1.2873572104499456e-282
8	-4.6384567460193974e-178	-5.045978689908405e-181	-7.353237923677478e-180
5	-4.107772779280553e+40	-1.4565604328782101e+40	-4.0550781064396446e+40

Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`*-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	55	174
1	78	174
2	92	174
3	102	174
4	106	174
5	105	174

end671.0ms (8.1%)

Compiler: Compiled 682 to 467 computations (31.5% saved)

Details

analyze845.0ms (10.2%)

sample1.5s (17.9%)

simplify11.0ms (0.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series142.0ms (1.7%)

rewrite108.0ms (1.3%)

simplify72.0ms (0.9%)

prune255.0ms (3.1%)

localize10.0ms (0.1%)

series134.0ms (1.6%)

rewrite113.0ms (1.4%)

simplify108.0ms (1.3%)

prune225.0ms (2.7%)

localize11.0ms (0.1%)

series185.0ms (2.2%)

rewrite117.0ms (1.4%)

simplify146.0ms (1.8%)

prune685.0ms (8.2%)

localize12.0ms (0.1%)

series400.0ms (4.8%)

rewrite75.0ms (0.9%)

simplify70.0ms (0.8%)

prune110.0ms (1.3%)

regimes2.1s (24.9%)

bsearch233.0ms (2.8%)

simplify7.0ms (0.1%)

end671.0ms (8.1%)

Profiling