Details

analyze690.0ms (11.9%)

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)

sample1.5s (25.1%)

Results

1.1s	8256×	body	128	valid
375.0ms	2389×	body	128	invalid

Compiler

Compiled 36 to 24 computations (33.3% saved)

preprocess25.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

25×	`fma-def_binary64`
11×	`*-commutative_binary64`
10×	`+-commutative_binary64`
4×	`associate-+l+_binary64`
4×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	72
1	58	64
2	84	64
3	87	64
0	3	3
1	3	3

Stop Event

1×	unsound
1×	saturated

Symmetry

(sort x y z)

Compiler

Compiled 17 to 11 computations (35.3% saved)

simplify18.0ms (0.3%)

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

1 alts after pruning (1 fresh and 0 done)

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

Error

23.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	23.3b	(.f64 2 (sqrt.f64 (fma.f64 x y (.f64 z (+.f64 x y)))))

Compiler

Compiled 56 to 35 computations (37.5% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 z (+.f64 x y))
✓	0.8b	(fma.f64 x y (*.f64 z (+.f64 x y)))
✓	22.1b	(sqrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))

series115.0ms (2%)

Counts

3 → 84

Calls

27 calls:

20.0ms	(sqrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))	x	inf
16.0ms	(sqrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))	x	-inf
15.0ms	(sqrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))	z	inf
15.0ms	(sqrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))	y	inf
14.0ms	(sqrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))	z	-inf

rewrite48.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

887×	`expm1-log1p-u_binary64`
858×	`prod-diff_binary64`
89×	`add-sqr-sqrt_binary64`
85×	`log1p-expm1-u_binary64`
84×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	31
1	174	31
2	2422	31

Stop Event

1×	node limit

Counts

3 → 78

simplify38.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	1448
1	525	1389
2	1898	1344

Stop Event

1×	node limit

Counts

162 → 109

prune108.0ms (1.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	97	12	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	12	110

Error

22.6b

Counts

110 → 12

Alt Table

Status	Error	Program
▶	23.6b	(.f64 2 (pow.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 1/4) 2))
	41.1b	(.f64 2 (sqrt.f64 (.f64 y z)))
	23.8b	(.f64 2 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x y (.f64 z (+.f64 x y))))) (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y))))))
	40.5b	(.f64 2 (sqrt.f64 (.f64 z (+.f64 y x))))
	44.7b	(.f64 2 (sqrt.f64 (.f64 (+.f64 y z) x)))
	49.7b	(.f64 2 (fma.f64 1/2 (.f64 z (+.f64 (sqrt.f64 (/.f64 x y)) (sqrt.f64 (/.f64 y x)))) (sqrt.f64 (*.f64 y x))))
	45.6b	(.f64 2 (sqrt.f64 (.f64 y x)))
	63.3b	(.f64 2 (+.f64 (sqrt.f64 (.f64 z x)) (.f64 y (.f64 1/2 (+.f64 (sqrt.f64 (/.f64 z x)) (sqrt.f64 (/.f64 x z)))))))
	45.3b	(.f64 2 (sqrt.f64 (fma.f64 x y (/.f64 (.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) z) (fma.f64 x x (*.f64 y (-.f64 y x)))))))
	47.9b	(.f64 2 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 3))))
	26.2b	(.f64 2 (exp.f64 (log.f64 (sqrt.f64 (fma.f64 x y (.f64 z (+.f64 x y)))))))
	33.5b	(.f64 2 (cbrt.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 3/2)))

Compiler

Compiled 2979 to 1500 computations (49.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 z (+.f64 x y))
✓	0.6b	(pow.f64 (pow.f64 (fma.f64 x y (*.f64 z (+.f64 x y))) 1/4) 2)
	0.8b	(fma.f64 x y (*.f64 z (+.f64 x y)))
✓	22.4b	(pow.f64 (fma.f64 x y (*.f64 z (+.f64 x y))) 1/4)

series131.0ms (2.2%)

Counts

2 → 72

Calls

18 calls:

12.0ms	(pow.f64 (pow.f64 (fma.f64 x y (*.f64 z (+.f64 x y))) 1/4) 2)	y	0
12.0ms	(pow.f64 (pow.f64 (fma.f64 x y (*.f64 z (+.f64 x y))) 1/4) 2)	z	inf
11.0ms	(pow.f64 (fma.f64 x y (*.f64 z (+.f64 x y))) 1/4)	y	0
9.0ms	(pow.f64 (pow.f64 (fma.f64 x y (*.f64 z (+.f64 x y))) 1/4) 2)	z	-inf
8.0ms	(pow.f64 (fma.f64 x y (*.f64 z (+.f64 x y))) 1/4)	z	-inf

rewrite47.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

858×	`prod-diff_binary64`
198×	`log1p-udef_binary64`
116×	`log1p-expm1-u_binary64`
116×	`expm1-log1p-u_binary64`
114×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	246	27
2	3073	27

Stop Event

1×	node limit

Counts

2 → 42

simplify87.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	620	6238
1	2112	5953

Stop Event

1×	node limit

Counts

114 → 180

prune251.0ms (4.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	241	4	245
Fresh	5	6	11
Picked	0	1	1
Done	0	0	0
Total	246	11	257

Error

2.5b

Counts

257 → 11

Alt Table

Status	Error	Program
	34.7b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (+.f64 y x)) (log.f64 (/.f64 1 z))))) 2))
	44.7b	(.f64 2 (sqrt.f64 (.f64 (+.f64 y z) x)))
	36.5b	(*.f64 2 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (-.f64 (neg.f64 y) z)) (log.f64 (/.f64 -1 x)))) 2))
	45.3b	(.f64 2 (sqrt.f64 (fma.f64 x y (/.f64 (.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) z) (fma.f64 x x (*.f64 y (-.f64 y x)))))))
	35.3b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (neg.f64 (+.f64 y z))) (log.f64 (/.f64 -1 x))))) 2))
	47.9b	(.f64 2 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 3))))
▶	23.8b	(.f64 2 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x y (.f64 z (+.f64 x y))))) (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y))))))
	40.5b	(.f64 2 (sqrt.f64 (.f64 z (+.f64 y x))))
	35.1b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (+.f64 z x)) (log.f64 (/.f64 1 y))))) 2))
	33.5b	(.f64 2 (cbrt.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 3/2)))
✓	23.6b	(.f64 2 (pow.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 1/4) 2))

Compiler

Compiled 10924 to 6276 computations (42.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (sqrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y)))))
	0.8b	(fma.f64 x y (*.f64 z (+.f64 x y)))
	22.1b	(sqrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))
✓	22.7b	(cbrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))

series105.0ms (1.8%)

Counts

2 → 72

Calls

18 calls:

16.0ms	(cbrt.f64 (sqrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y)))))	x	0
10.0ms	(cbrt.f64 (sqrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y)))))	z	0
7.0ms	(cbrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))	y	inf
6.0ms	(cbrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))	z	0
6.0ms	(cbrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))	x	0

rewrite49.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

858×	`prod-diff_binary64`
178×	`expm1-udef_binary64`
178×	`log1p-udef_binary64`
103×	`add-sqr-sqrt_binary64`
98×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	209	27
2	2766	27

Stop Event

1×	node limit

Counts

2 → 49

simplify86.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

710×	`times-frac_binary64`
542×	`fma-def_binary64`
256×	`*-commutative_binary64`
171×	`sqr-pow_binary64`
130×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	636	6155
1	2227	5898

Stop Event

1×	node limit

Counts

121 → 190

prune252.0ms (4.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	309	1	310
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	310	11	321

Error

2.5b

Counts

321 → 11

Alt Table

Status	Error	Program
	34.7b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (+.f64 y x)) (log.f64 (/.f64 1 z))))) 2))
	44.7b	(.f64 2 (sqrt.f64 (.f64 (+.f64 y z) x)))
	36.5b	(*.f64 2 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (-.f64 (neg.f64 y) z)) (log.f64 (/.f64 -1 x)))) 2))
	45.3b	(.f64 2 (sqrt.f64 (fma.f64 x y (/.f64 (.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) z) (fma.f64 x x (*.f64 y (-.f64 y x)))))))
	35.3b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (neg.f64 (+.f64 y z))) (log.f64 (/.f64 -1 x))))) 2))
	47.9b	(.f64 2 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 3))))
	40.5b	(.f64 2 (sqrt.f64 (.f64 z (+.f64 y x))))
▶	23.8b	(.f64 2 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x y (.f64 z (+.f64 x y))))) (cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y)))) 2) (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y))))))))
	35.1b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (+.f64 z x)) (log.f64 (/.f64 1 y))))) 2))
	33.5b	(.f64 2 (cbrt.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 3/2)))
✓	23.6b	(.f64 2 (pow.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 1/4) 2))

Compiler

Compiled 15638 to 7079 computations (54.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.8b	(fma.f64 x y (*.f64 z (+.f64 x y)))
	22.1b	(sqrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))
✓	22.7b	(cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y)))) 2) (cbrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))))
	22.7b	(cbrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))

series50.0ms (0.9%)

Counts

1 → 36

Calls

9 calls:

8.0ms	(cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y)))) 2) (cbrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))))	x	0
6.0ms	(cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y)))) 2) (cbrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))))	y	inf
6.0ms	(cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y)))) 2) (cbrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))))	y	0
6.0ms	(cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y)))) 2) (cbrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))))	z	inf
6.0ms	(cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y)))) 2) (cbrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))))	z	0

rewrite40.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

858×	`prod-diff_binary64`
182×	`expm1-udef_binary64`
182×	`log1p-udef_binary64`
105×	`add-sqr-sqrt_binary64`
104×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	13
1	242	13
2	2838	13

Stop Event

1×	node limit

Counts

1 → 23

simplify78.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

423×	`associate-r_binary64`
366×	`times-frac_binary64`
282×	`associate-l_binary64`
270×	`fma-def_binary64`
249×	`associate-/r*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	345	3044
1	1204	2918

Stop Event

1×	node limit

Counts

59 → 95

prune352.0ms (6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	447	0	447
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	447	11	458

Error

2.5b

Counts

458 → 11

Alt Table

Status	Error	Program
	34.7b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (+.f64 y x)) (log.f64 (/.f64 1 z))))) 2))
	44.7b	(.f64 2 (sqrt.f64 (.f64 (+.f64 y z) x)))
	36.5b	(*.f64 2 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (-.f64 (neg.f64 y) z)) (log.f64 (/.f64 -1 x)))) 2))
	45.3b	(.f64 2 (sqrt.f64 (fma.f64 x y (/.f64 (.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) z) (fma.f64 x x (*.f64 y (-.f64 y x)))))))
	35.3b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (neg.f64 (+.f64 y z))) (log.f64 (/.f64 -1 x))))) 2))
	47.9b	(.f64 2 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 3))))
	40.5b	(.f64 2 (sqrt.f64 (.f64 z (+.f64 y x))))
✓	23.8b	(.f64 2 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x y (.f64 z (+.f64 x y))))) (cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y)))) 2) (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y))))))))
	35.1b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (+.f64 z x)) (log.f64 (/.f64 1 y))))) 2))
	33.5b	(.f64 2 (cbrt.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 3/2)))
✓	23.6b	(.f64 2 (pow.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 1/4) 2))

Compiler

Compiled 26769 to 10925 computations (59.2% saved)

regimes1.1s (18.7%)

Accuracy

Total 3.8b remaining (63.6%)

Threshold costs 0b (0%)

Counts

92 → 2

Compiler

Compiled 13376 to 8102 computations (39.4% saved)

bsearch58.0ms (1%)

Algorithm

1×	binary-search

Calls

1 calls:

55.0ms

Steps

Iters	Point		Range
7.036781764230213e-307	∈ [	-1.4296436999830294e-292	,	7.886326688639638e-284	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
9×	`*-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	31	58
1	48	58
2	62	58
3	72	58
4	76	58

Stop Event

1×

saturated

end589.0ms (10.1%)

Stop Event

1×

fuel

Compiler

Compiled 375 to 282 computations (24.8% saved)

Details

analyze690.0ms (11.9%)

sample1.5s (25.1%)

preprocess25.0ms (0.4%)

simplify18.0ms (0.3%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series115.0ms (2%)

rewrite48.0ms (0.8%)

simplify38.0ms (0.7%)

prune108.0ms (1.9%)

localize10.0ms (0.2%)

series131.0ms (2.2%)

rewrite47.0ms (0.8%)

simplify87.0ms (1.5%)

prune251.0ms (4.3%)

localize12.0ms (0.2%)

series105.0ms (1.8%)

rewrite49.0ms (0.9%)

simplify86.0ms (1.5%)

prune252.0ms (4.3%)

localize14.0ms (0.2%)

series50.0ms (0.9%)

rewrite40.0ms (0.7%)

simplify78.0ms (1.4%)

prune352.0ms (6%)

regimes1.1s (18.7%)

bsearch58.0ms (1%)

simplify4.0ms (0.1%)

end589.0ms (10.1%)

Profiling