Details

analyze586.0ms (11%)

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 (23.6%)

Symmetry

(sort x y z)

Results

969.0ms	8256×	body	128	valid
243.0ms	2383×	body	128	invalid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify32.0ms (0.6%)

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 (0.1%)

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

23.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	23.2b	(.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))
✓	1.0b	(fma.f64 x y (*.f64 z (+.f64 x y)))
✓	21.9b	(sqrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))

series116.0ms (2.2%)

Counts

3 → 84

Calls

3 calls:

101.0ms	(sqrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))
7.0ms	(fma.f64 x y (*.f64 z (+.f64 x y)))
7.0ms	(*.f64 z (+.f64 x y))

rewrite52.0ms (1%)

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

Calls

3 calls:

51.0ms	(*.f64 z (+.f64 x y))
51.0ms	(fma.f64 x y (*.f64 z (+.f64 x y)))
51.0ms	(sqrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))

simplify39.0ms (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

prune156.0ms (2.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	96	13	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	13	110

Error

22.6b

Counts

110 → 13

Alt Table

Status	Error	Program
▶	23.4b	(.f64 2 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y)))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x y (.f64 z (+.f64 x y))))) (sqrt.f64 (fma.f64 x y (.f64 z (+.f64 x y))))))))
	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)))))))
	36.3b	(.f64 2 (cbrt.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 3/2)))
	46.3b	(.f64 2 (+.f64 (sqrt.f64 (.f64 y z)) (.f64 (.f64 x 1/2) (+.f64 (sqrt.f64 (/.f64 z y)) (sqrt.f64 (/.f64 y z))))))
	23.9b	(.f64 2 (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x y (.f64 z (+.f64 x y))))) 3))
	43.2b	(.f64 2 (sqrt.f64 (.f64 y z)))
	23.6b	(.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))))))
	27.8b	(.f64 2 (sqrt.f64 (fma.f64 x y (expm1.f64 (log1p.f64 (.f64 z (+.f64 x y)))))))
	48.1b	(.f64 2 (fma.f64 1/2 (.f64 z (+.f64 (sqrt.f64 (/.f64 x y)) (sqrt.f64 (/.f64 y x)))) (sqrt.f64 (*.f64 y x))))
	23.4b	(.f64 2 (pow.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 1/4) 2))
	23.7b	(.f64 2 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y)))))))
	42.8b	(.f64 2 (sqrt.f64 (.f64 z (+.f64 y x))))
	42.4b	(.f64 2 (sqrt.f64 (.f64 (+.f64 y z) x)))

Compiler

Compiled 3081 to 1540 computations (50% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(fma.f64 x y (*.f64 z (+.f64 x y)))
	21.9b	(sqrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))
✓	21.9b	(sqrt.f64 (.f64 (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y)))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x y (.f64 z (+.f64 x y))))) (sqrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y)))))))
✓	22.5b	(cbrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))

series145.0ms (2.7%)

Counts

2 → 24

Calls

2 calls:

107.0ms

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

37.0ms

(cbrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))

rewrite49.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

858×	`prod-diff_binary64`
124×	`add-sqr-sqrt_binary64`
124×	`log1p-expm1-u_binary64`
124×	`expm1-log1p-u_binary64`
123×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	60
1	271	26
2	3448	26

Stop Event

1×	node limit

Counts

2 → 50

Calls

2 calls:

48.0ms

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

48.0ms

(cbrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))

simplify62.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

375×	`fma-def_binary64`
355×	`associate-r_binary64`
289×	`sub-neg_binary64`
252×	`associate-l_binary64`
231×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	348	2461
1	1018	2337
2	4058	2337

Stop Event

1×	node limit

Counts

74 → 95

prune365.0ms (6.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	297	0	297
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	297	13	310

Error

22.6b

Counts

310 → 13

Alt Table

Status	Error	Program
✓	23.4b	(.f64 2 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y)))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x y (.f64 z (+.f64 x y))))) (sqrt.f64 (fma.f64 x y (.f64 z (+.f64 x y))))))))
	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)))))))
	36.3b	(.f64 2 (cbrt.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 3/2)))
	46.3b	(.f64 2 (+.f64 (sqrt.f64 (.f64 y z)) (.f64 (.f64 x 1/2) (+.f64 (sqrt.f64 (/.f64 z y)) (sqrt.f64 (/.f64 y z))))))
	23.9b	(.f64 2 (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x y (.f64 z (+.f64 x y))))) 3))
	43.2b	(.f64 2 (sqrt.f64 (.f64 y z)))
	23.6b	(.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))))))
	27.8b	(.f64 2 (sqrt.f64 (fma.f64 x y (expm1.f64 (log1p.f64 (.f64 z (+.f64 x y)))))))
	48.1b	(.f64 2 (fma.f64 1/2 (.f64 z (+.f64 (sqrt.f64 (/.f64 x y)) (sqrt.f64 (/.f64 y x)))) (sqrt.f64 (*.f64 y x))))
▶	23.4b	(.f64 2 (pow.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 1/4) 2))
	23.7b	(.f64 2 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y)))))))
	42.8b	(.f64 2 (sqrt.f64 (.f64 z (+.f64 y x))))
	42.4b	(.f64 2 (sqrt.f64 (.f64 (+.f64 y z) x)))

Compiler

Compiled 14768 to 5339 computations (63.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 z (+.f64 x y))
✓	0.5b	(pow.f64 (pow.f64 (fma.f64 x y (*.f64 z (+.f64 x y))) 1/4) 2)
	1.0b	(fma.f64 x y (*.f64 z (+.f64 x y)))
✓	22.3b	(pow.f64 (fma.f64 x y (*.f64 z (+.f64 x y))) 1/4)

series121.0ms (2.3%)

Counts

2 → 72

Calls

2 calls:

72.0ms	(pow.f64 (pow.f64 (fma.f64 x y (*.f64 z (+.f64 x y))) 1/4) 2)
48.0ms	(pow.f64 (fma.f64 x y (*.f64 z (+.f64 x y))) 1/4)

rewrite52.0ms (1%)

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

Calls

2 calls:

51.0ms	(pow.f64 (pow.f64 (fma.f64 x y (*.f64 z (+.f64 x y))) 1/4) 2)
51.0ms	(pow.f64 (fma.f64 x y (*.f64 z (+.f64 x y))) 1/4)

simplify98.0ms (1.8%)

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

prune260.0ms (4.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	241	4	245
Fresh	6	5	11
Picked	0	1	1
Done	0	1	1
Total	247	11	258

Error

2.5b

Counts

258 → 11

Alt Table

Status	Error	Program
✓	23.4b	(.f64 2 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y)))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x y (.f64 z (+.f64 x y))))) (sqrt.f64 (fma.f64 x y (.f64 z (+.f64 x y))))))))
▶	23.2b	(.f64 2 (fabs.f64 (sqrt.f64 (fma.f64 x y (.f64 z (+.f64 x y))))))
	23.6b	(.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))))))
	37.1b	(*.f64 2 (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (+.f64 y x)) (log.f64 z))) 2))
	27.8b	(.f64 2 (sqrt.f64 (fma.f64 x y (expm1.f64 (log1p.f64 (.f64 z (+.f64 x y)))))))
	34.1b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (neg.f64 (+.f64 y z))) (log.f64 (/.f64 -1 x))))) 2))
	36.3b	(.f64 2 (cbrt.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 3/2)))
✓	23.4b	(.f64 2 (pow.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 1/4) 2))
	23.9b	(.f64 2 (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x y (.f64 z (+.f64 x y))))) 3))
	23.7b	(.f64 2 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y)))))))
	36.0b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (+.f64 y x)) (log.f64 (/.f64 1 z))))) 2))

Compiler

Compiled 10936 to 6256 computations (42.8% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 z (+.f64 x y))
	1.0b	(fma.f64 x y (*.f64 z (+.f64 x y)))
	21.9b	(sqrt.f64 (fma.f64 x y (*.f64 z (+.f64 x y))))

prune83.0ms (1.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	109	11	120

Error

2.5b

Counts

120 → 11

Alt Table

Status	Error	Program
✓	23.4b	(.f64 2 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y)))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x y (.f64 z (+.f64 x y))))) (sqrt.f64 (fma.f64 x y (.f64 z (+.f64 x y))))))))
✓	23.2b	(.f64 2 (fabs.f64 (sqrt.f64 (fma.f64 x y (.f64 z (+.f64 x y))))))
	23.6b	(.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))))))
	37.1b	(*.f64 2 (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (+.f64 y x)) (log.f64 z))) 2))
	27.8b	(.f64 2 (sqrt.f64 (fma.f64 x y (expm1.f64 (log1p.f64 (.f64 z (+.f64 x y)))))))
	34.1b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (neg.f64 (+.f64 y z))) (log.f64 (/.f64 -1 x))))) 2))
	36.3b	(.f64 2 (cbrt.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 3/2)))
✓	23.4b	(.f64 2 (pow.f64 (pow.f64 (fma.f64 x y (.f64 z (+.f64 x y))) 1/4) 2))
	23.9b	(.f64 2 (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x y (.f64 z (+.f64 x y))))) 3))
	23.7b	(.f64 2 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x y (.f64 z (+.f64 x y)))))))
	36.0b	(.f64 2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (+.f64 y x)) (log.f64 (/.f64 1 z))))) 2))

Compiler

Compiled 2908 to 1477 computations (49.2% saved)

regimes965.0ms (18.1%)

Accuracy

Total 2.4b remaining (52.9%)

Threshold costs 0b (0%)

Counts

77 → 6

Compiler

Compiled 9686 to 6176 computations (36.2% saved)

bsearch232.0ms (4.3%)

Steps

Iters	Range		Point
7	2632165710693298700.0	7.387001778290783e+21	6.965577108647369e+21
11	1.1609401247143697e-207	3.733633490384838e-183	1.1764325343930836e-207
12	-1.967252303492221e-289	5.637836101992725e-266	5.248403633372559e-266
8	-2.2074341187827674e-220	-3.384336718055756e-225	-1.3866893327893407e-224
9	-3.0541820842655216e+44	-1.6737180928486003e+37	-3.0121278070499345e+44

Compiler

Compiled 4 to 3 computations (25% saved)

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

13×	`*-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	56	171
1	77	171
2	91	171
3	101	171
4	105	171

Stop Event

1×

saturated

end615.0ms (11.5%)

Compiler: Compiled 678 to 463 computations (31.7% saved)

Details

analyze586.0ms (11%)

sample1.3s (23.6%)

simplify32.0ms (0.6%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series116.0ms (2.2%)

rewrite52.0ms (1%)

simplify39.0ms (0.7%)

prune156.0ms (2.9%)

localize13.0ms (0.2%)

series145.0ms (2.7%)

rewrite49.0ms (0.9%)

simplify62.0ms (1.2%)

prune365.0ms (6.8%)

localize11.0ms (0.2%)

series121.0ms (2.3%)

rewrite52.0ms (1%)

simplify98.0ms (1.8%)

prune260.0ms (4.9%)

localize8.0ms (0.2%)

prune83.0ms (1.5%)

regimes965.0ms (18.1%)

bsearch232.0ms (4.3%)

simplify13.0ms (0.2%)

end615.0ms (11.5%)

Profiling