Details

analyze609.0ms (8.9%)

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
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)

sample1.3s (18.8%)

Symmetry

(sort x y z)

Results

980.0ms	8256×	body	128	valid
259.0ms	2351×	body	128	invalid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	23	16
2	45	16
3	64	16
4	69	16
5	70	16

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

17.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	17.3b	(.f64 2 (sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 x z)) (.f64 y z))))

Compiler

Compiled 62 to 39 computations (37.1% 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))
✓	16.3b	(sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z)))

series173.0ms (2.5%)

Counts

3 → 84

Calls

3 calls:

155.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z)))
10.0ms	(+.f64 (.f64 x y) (.f64 x z))
8.0ms	(+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z))

rewrite88.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

812×	`fma-def_binary64`
367×	`fma-neg_binary64`
205×	`expm1-udef_binary64`
205×	`log1p-udef_binary64`
201×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	35
1	223	31
2	3255	31

Stop Event

1×	node limit

Counts

3 → 201

Calls

3 calls:

84.0ms	(+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z))
84.0ms	(+.f64 (.f64 x y) (.f64 x z))
84.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 x z)) (*.f64 y z)))

simplify46.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

605×	`cancel-sign-sub-inv_binary64`
591×	`associate-l_binary64`
528×	`associate-r_binary64`
198×	`fma-def_binary64`
174×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	191	1448
1	528	1389
2	1902	1344

Stop Event

1×	node limit

Counts

285 → 230

prune275.0ms (4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	216	14	230
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	217	14	231

Error

16.7b

Counts

231 → 14

Alt Table

Status	Error	Program
	44.7b	(.f64 2 (fma.f64 1/2 (.f64 z (+.f64 (sqrt.f64 (/.f64 x y)) (sqrt.f64 (/.f64 y x)))) (sqrt.f64 (*.f64 y x))))
	40.3b	(.f64 2 (sqrt.f64 (.f64 y z)))
▶	17.2b	(.f64 2 (sqrt.f64 (fma.f64 x z (fma.f64 x y (.f64 y z)))))
	39.7b	(.f64 2 (sqrt.f64 (.f64 z (+.f64 y x))))
	29.3b	(.f64 2 (sqrt.f64 (fma.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) y) (*.f64 x (+.f64 y z)))))
	63.4b	(.f64 2 (+.f64 (sqrt.f64 (.f64 z x)) (.f64 y (.f64 1/2 (+.f64 (sqrt.f64 (/.f64 z x)) (sqrt.f64 (/.f64 x z)))))))
	17.3b	(.f64 2 (sqrt.f64 (fma.f64 y z (.f64 x (+.f64 y z)))))
	61.9b	(.f64 2 (sqrt.f64 (.f64 z x)))
	50.6b	(.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)))))
	32.1b	(.f64 2 (cbrt.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 3/2)))
	17.5b	(.f64 2 (pow.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 1/4) 2))
	40.7b	(.f64 2 (sqrt.f64 (.f64 y x)))
	17.5b	(.f64 2 (sqrt.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 z (+.f64 x y))) (cbrt.f64 (.f64 z (+.f64 x y)))) (cbrt.f64 (.f64 z (+.f64 x y))) (.f64 x y))))
	26.8b	(.f64 2 (sqrt.f64 (fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) y) (.f64 z (+.f64 x y)))))

Compiler

Compiled 5471 to 2367 computations (56.7% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x z (fma.f64 x y (*.f64 y z)))
✓	1.0b	(fma.f64 x y (*.f64 y z))
✓	16.3b	(sqrt.f64 (fma.f64 x z (fma.f64 x y (*.f64 y z))))

series153.0ms (2.2%)

Counts

3 → 84

Calls

3 calls:

135.0ms	(sqrt.f64 (fma.f64 x z (fma.f64 x y (*.f64 y z))))
10.0ms	(fma.f64 x z (fma.f64 x y (*.f64 y z)))
7.0ms	(fma.f64 x y (*.f64 y z))

rewrite45.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

705×	`log1p-expm1-u_binary64`
705×	`expm1-log1p-u_binary64`
250×	`prod-diff_binary64`
144×	`log1p-udef_binary64`
80×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	34
1	159	31
2	1922	31

Stop Event

1×	node limit

Counts

3 → 76

Calls

3 calls:

43.0ms	(fma.f64 x z (fma.f64 x y (*.f64 y z)))
43.0ms	(fma.f64 x y (*.f64 y z))
43.0ms	(sqrt.f64 (fma.f64 x z (fma.f64 x y (*.f64 y z))))

simplify39.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

605×	`cancel-sign-sub-inv_binary64`
592×	`associate-l_binary64`
531×	`associate-r_binary64`
196×	`fma-def_binary64`
171×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	191	1448
1	527	1389
2	1901	1344

Stop Event

1×	node limit

Counts

160 → 107

prune122.0ms (1.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	108	13	121

Error

16.7b

Counts

121 → 13

Alt Table

Status	Error	Program
	39.6b	(.f64 2 (sqrt.f64 (fma.f64 x z (.f64 y x))))
	44.7b	(.f64 2 (fma.f64 1/2 (.f64 z (+.f64 (sqrt.f64 (/.f64 x y)) (sqrt.f64 (/.f64 y x)))) (sqrt.f64 (*.f64 y x))))
	40.3b	(.f64 2 (sqrt.f64 (.f64 y z)))
	29.3b	(.f64 2 (sqrt.f64 (fma.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) y) (*.f64 x (+.f64 y z)))))
	63.4b	(.f64 2 (+.f64 (sqrt.f64 (.f64 z x)) (.f64 y (.f64 1/2 (+.f64 (sqrt.f64 (/.f64 z x)) (sqrt.f64 (/.f64 x z)))))))
	50.6b	(.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)))))
	32.1b	(.f64 2 (cbrt.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 3/2)))
	39.7b	(.f64 2 (sqrt.f64 (.f64 z (+.f64 y x))))
	17.5b	(.f64 2 (pow.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 1/4) 2))
	40.7b	(.f64 2 (sqrt.f64 (.f64 y x)))
	17.5b	(.f64 2 (sqrt.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 z (+.f64 x y))) (cbrt.f64 (.f64 z (+.f64 x y)))) (cbrt.f64 (.f64 z (+.f64 x y))) (.f64 x y))))
	26.8b	(.f64 2 (sqrt.f64 (fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) y) (.f64 z (+.f64 x y)))))
▶	17.3b	(.f64 2 (sqrt.f64 (fma.f64 y (+.f64 z x) (.f64 z x))))

Compiler

Compiled 2992 to 1485 computations (50.4% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	2.0b	(fma.f64 y (+.f64 z x) (*.f64 z x))
✓	16.3b	(sqrt.f64 (fma.f64 y (+.f64 z x) (*.f64 z x)))

series142.0ms (2.1%)

Counts

2 → 48

Calls

2 calls:

132.0ms	(sqrt.f64 (fma.f64 y (+.f64 z x) (*.f64 z x)))
9.0ms	(fma.f64 y (+.f64 z x) (*.f64 z x))

rewrite47.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

834×	`expm1-log1p-u_binary64`
750×	`prod-diff_binary64`
85×	`add-sqr-sqrt_binary64`
81×	`log1p-expm1-u_binary64`
80×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	168	24
2	2236	24

Stop Event

1×	node limit

Counts

2 → 51

Calls

2 calls:

46.0ms	(fma.f64 y (+.f64 z x) (*.f64 z x))
46.0ms	(sqrt.f64 (fma.f64 y (+.f64 z x) (*.f64 z x)))

simplify37.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

605×	`cancel-sign-sub-inv_binary64`
593×	`associate-l_binary64`
531×	`associate-r_binary64`
194×	`fma-def_binary64`
175×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	1214
1	524	1155
2	1897	1110

Stop Event

1×	node limit

Counts

99 → 86

prune97.0ms (1.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	86	13	99

Error

16.7b

Counts

99 → 13

Alt Table

Status	Error	Program
	39.6b	(.f64 2 (sqrt.f64 (fma.f64 x z (.f64 y x))))
	44.7b	(.f64 2 (fma.f64 1/2 (.f64 z (+.f64 (sqrt.f64 (/.f64 x y)) (sqrt.f64 (/.f64 y x)))) (sqrt.f64 (*.f64 y x))))
	40.3b	(.f64 2 (sqrt.f64 (.f64 y z)))
	29.3b	(.f64 2 (sqrt.f64 (fma.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) y) (*.f64 x (+.f64 y z)))))
	63.4b	(.f64 2 (+.f64 (sqrt.f64 (.f64 z x)) (.f64 y (.f64 1/2 (+.f64 (sqrt.f64 (/.f64 z x)) (sqrt.f64 (/.f64 x z)))))))
	50.6b	(.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)))))
	32.1b	(.f64 2 (cbrt.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 3/2)))
	39.7b	(.f64 2 (sqrt.f64 (.f64 z (+.f64 y x))))
	17.5b	(.f64 2 (pow.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 1/4) 2))
	40.7b	(.f64 2 (sqrt.f64 (.f64 y x)))
▶	17.5b	(.f64 2 (sqrt.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 z (+.f64 x y))) (cbrt.f64 (.f64 z (+.f64 x y)))) (cbrt.f64 (.f64 z (+.f64 x y))) (.f64 x y))))
	26.8b	(.f64 2 (sqrt.f64 (fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) y) (.f64 z (+.f64 x y)))))
✓	17.3b	(.f64 2 (sqrt.f64 (fma.f64 y (+.f64 z x) (.f64 z x))))

Compiler

Compiled 2592 to 1319 computations (49.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (cbrt.f64 (.f64 z (+.f64 x y))) (cbrt.f64 (*.f64 z (+.f64 x y))))
✓	0.5b	(fma.f64 (.f64 (cbrt.f64 (.f64 z (+.f64 x y))) (cbrt.f64 (.f64 z (+.f64 x y)))) (cbrt.f64 (.f64 z (+.f64 x y))) (*.f64 x y))
✓	11.7b	(cbrt.f64 (*.f64 z (+.f64 x y)))
✓	16.3b	(sqrt.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 z (+.f64 x y))) (cbrt.f64 (.f64 z (+.f64 x y)))) (cbrt.f64 (.f64 z (+.f64 x y))) (*.f64 x y)))

series2.2s (31.7%)

Counts

4 → 128

Calls

4 calls:

1.0s	(fma.f64 (.f64 (cbrt.f64 (.f64 z (+.f64 x y))) (cbrt.f64 (.f64 z (+.f64 x y)))) (cbrt.f64 (.f64 z (+.f64 x y))) (*.f64 x y))
608.0ms	(sqrt.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 z (+.f64 x y))) (cbrt.f64 (.f64 z (+.f64 x y)))) (cbrt.f64 (.f64 z (+.f64 x y))) (*.f64 x y)))
321.0ms	(.f64 (cbrt.f64 (.f64 z (+.f64 x y))) (cbrt.f64 (*.f64 z (+.f64 x y))))
208.0ms	(cbrt.f64 (*.f64 z (+.f64 x y)))

rewrite57.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

557×	`log-prod_binary64`
401×	`fma-def_binary64`
197×	`expm1-udef_binary64`
197×	`log1p-udef_binary64`
185×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	49
1	234	45
2	3102	45

Stop Event

1×	node limit

Counts

4 → 112

Calls

4 calls:

55.0ms	(.f64 (cbrt.f64 (.f64 z (+.f64 x y))) (cbrt.f64 (*.f64 z (+.f64 x y))))
55.0ms	(fma.f64 (.f64 (cbrt.f64 (.f64 z (+.f64 x y))) (cbrt.f64 (.f64 z (+.f64 x y)))) (cbrt.f64 (.f64 z (+.f64 x y))) (*.f64 x y))
55.0ms	(cbrt.f64 (*.f64 z (+.f64 x y)))
55.0ms	(sqrt.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 z (+.f64 x y))) (cbrt.f64 (.f64 z (+.f64 x y)))) (cbrt.f64 (.f64 z (+.f64 x y))) (*.f64 x y)))

simplify109.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

348×	`fma-def_binary64`
288×	`associate-r_binary64`
248×	`*-commutative_binary64`
211×	`fma-neg_binary64`
203×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	466	5872
1	1395	5297
2	4547	5167

Stop Event

1×	node limit

Counts

240 → 265

prune467.0ms (6.8%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	426	1	427
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	426	14	440

Error

16.7b

Counts

440 → 14

Alt Table

Status	Error	Program
	39.6b	(.f64 2 (sqrt.f64 (fma.f64 x z (.f64 y x))))
	44.7b	(.f64 2 (fma.f64 1/2 (.f64 z (+.f64 (sqrt.f64 (/.f64 x y)) (sqrt.f64 (/.f64 y x)))) (sqrt.f64 (*.f64 y x))))
	40.3b	(.f64 2 (sqrt.f64 (.f64 y z)))
	29.3b	(.f64 2 (sqrt.f64 (fma.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) y) (*.f64 x (+.f64 y z)))))
	63.4b	(.f64 2 (+.f64 (sqrt.f64 (.f64 z x)) (.f64 y (.f64 1/2 (+.f64 (sqrt.f64 (/.f64 z x)) (sqrt.f64 (/.f64 x z)))))))
	50.6b	(.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)))))
	32.1b	(.f64 2 (cbrt.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 3/2)))
	39.7b	(.f64 2 (sqrt.f64 (.f64 z (+.f64 y x))))
	17.5b	(.f64 2 (pow.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 1/4) 2))
	40.7b	(.f64 2 (sqrt.f64 (.f64 y x)))
✓	17.5b	(.f64 2 (sqrt.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 z (+.f64 x y))) (cbrt.f64 (.f64 z (+.f64 x y)))) (cbrt.f64 (.f64 z (+.f64 x y))) (.f64 x y))))
	26.8b	(.f64 2 (sqrt.f64 (fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) y) (.f64 z (+.f64 x y)))))
	63.1b	(.f64 2 (sqrt.f64 (fma.f64 y x (pow.f64 (exp.f64 1/3) (+.f64 (.f64 2 (+.f64 (log.f64 z) (log.f64 x))) (+.f64 (log.f64 z) (log.f64 x)))))))
✓	17.3b	(.f64 2 (sqrt.f64 (fma.f64 y (+.f64 z x) (.f64 z x))))

Compiler

Compiled 16960 to 7594 computations (55.2% saved)

regimes638.0ms (9.4%)

Accuracy

Total 0.5b remaining (2.6%)

Threshold costs 0.5b (2.6%)

Counts

106 → 1

Compiler

Compiled 12434 to 7586 computations (39% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	13	16

Stop Event

1×

saturated

end185.0ms (2.7%)

Remove: (sort x y z)
Compiler: Compiled 311 to 198 computations (36.3% saved)

Details

analyze609.0ms (8.9%)

sample1.3s (18.8%)

simplify10.0ms (0.2%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series173.0ms (2.5%)

rewrite88.0ms (1.3%)

simplify46.0ms (0.7%)

prune275.0ms (4%)

localize7.0ms (0.1%)

series153.0ms (2.2%)

rewrite45.0ms (0.7%)

simplify39.0ms (0.6%)

prune122.0ms (1.8%)

localize7.0ms (0.1%)

series142.0ms (2.1%)

rewrite47.0ms (0.7%)

simplify37.0ms (0.5%)

prune97.0ms (1.4%)

localize10.0ms (0.1%)

series2.2s (31.7%)

rewrite57.0ms (0.8%)

simplify109.0ms (1.6%)

prune467.0ms (6.8%)

regimes638.0ms (9.4%)

simplify2.0ms (0%)

end185.0ms (2.7%)

Profiling