Details

analyze755.0ms (5.8%)

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
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	74.9%	0.1%	8
25%	65.5%	9.5%	9
28.5%	50.9%	20.6%	10
30.4%	48.1%	21.5%	11
33.7%	37.3%	28.9%	12
37.4%	27.1%	35.5%	13
38.1%	26.2%	35.7%	14

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample2.0s (15.5%)

Symmetry

(sort x y z)

Results

1.5s	8256×	body	128	valid
460.0ms	2329×	body	128	invalid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify21.0ms (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`

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

prune6.0ms (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

17.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	17.9b	(.f64 2 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))

Compiler

Compiled 56 to 34 computations (39.3% saved)

localize17.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(fma.f64 x (+.f64 y z) (*.f64 y z))
✓	17.9b	(sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))

series436.0ms (3.3%)

Counts

2 → 48

Calls

2 calls:

419.0ms	(sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))
16.0ms	(fma.f64 x (+.f64 y z) (*.f64 y z))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-sqr-sqrt_binary64`
3×	`*-un-lft-identity_binary64`
3×	`sqrt-prod_binary64`
3×	`add-cube-cbrt_binary64`
3×	`pow1_binary64`

Counts

2 → 25

Calls

2 calls:

2.0ms	(sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))
1.0ms	(fma.f64 x (+.f64 y z) (*.f64 y z))

simplify135.0ms (1%)

Algorithm

1×	egg-herbie

Rules

631×	`associate-l_binary64`
605×	`cancel-sign-sub-inv_binary64`
565×	`associate-r_binary64`
297×	`fma-neg_binary64`
197×	`fma-def_binary64`

Counts

73 → 70

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	214	1615
1	531	1523
2	1873	1478
3	4933	1478
4	5115	1478

prune149.0ms (1.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	58	12	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	12	71

Error

17.7b

Counts

71 → 12

Alt Table

Status	Error	Program
	46.5b	(.f64 2 (sqrt.f64 (cbrt.f64 (.f64 (.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) (fma.f64 x (+.f64 y z) (.f64 y z))) (fma.f64 x (+.f64 y z) (.f64 y z))))))
	45.4b	(.f64 2 (fma.f64 1/2 (.f64 z (+.f64 (sqrt.f64 (/.f64 x y)) (sqrt.f64 (/.f64 y x)))) (sqrt.f64 (*.f64 y x))))
	18.2b	(.f64 2 (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z)))) (sqrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))
	62.7b	(.f64 2 (+.f64 (sqrt.f64 (.f64 z x)) (.f64 y (.f64 1/2 (+.f64 (sqrt.f64 (/.f64 z x)) (sqrt.f64 (/.f64 x z)))))))
▶	17.9b	(.f64 2 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/2))
	38.5b	(.f64 2 (sqrt.f64 (.f64 y z)))
	18.4b	(.f64 2 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z)))) (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))
	18.4b	(.f64 2 (.f64 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))) (sqrt.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))
	18.7b	(.f64 2 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z)))) (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))) (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))
	61.7b	(.f64 2 (sqrt.f64 (.f64 z x)))
	21.2b	(.f64 2 (exp.f64 (log.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))
	37.2b	(.f64 2 (sqrt.f64 (.f64 z (+.f64 y x))))

Compiler

Compiled 2462 to 1181 computations (52% saved)

localize22.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.5b	(fma.f64 x (+.f64 y z) (*.f64 y z))
✓	17.9b	(pow.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)) 1/2)

series139.0ms (1.1%)

Counts

1 → 36

Calls

1 calls:

139.0ms

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

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`pow-unpow_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`unpow-prod-down_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 20

Calls

1 calls:

3.0ms

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

simplify125.0ms (1%)

Algorithm

1×	egg-herbie

Rules

387×	`associate-r_binary64`
385×	`times-frac_binary64`
268×	`associate-l_binary64`
268×	`associate-/r*_binary64`
245×	`fma-def_binary64`

Counts

56 → 96

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	373	3294
1	1149	3138
2	4919	3138
3	5065	3138

prune226.0ms (1.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	116	6	122
Fresh	9	2	11
Picked	0	1	1
Done	0	0	0
Total	125	9	134

Error

2.0b

Counts

134 → 9

Alt Table

Status	Error	Program
✓	17.9b	(.f64 2 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/2))
	33.1b	(*.f64 2 (pow.f64 (exp.f64 1/2) (+.f64 (log.f64 (+.f64 y x)) (log.f64 z))))
	36.9b	(.f64 2 (exp.f64 (.f64 1/2 (-.f64 (log.f64 (neg.f64 (+.f64 y z))) (log.f64 (/.f64 -1 x))))))
	18.4b	(.f64 2 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z)))) (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))
	46.5b	(.f64 2 (sqrt.f64 (cbrt.f64 (.f64 (.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) (fma.f64 x (+.f64 y z) (.f64 y z))) (fma.f64 x (+.f64 y z) (.f64 y z))))))
▶	18.1b	(.f64 2 (.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4) (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4)))
	33.9b	(.f64 2 (cbrt.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 3/2)))
	18.4b	(.f64 2 (.f64 (fabs.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z)))) (sqrt.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))
	33.1b	(.f64 2 (exp.f64 (.f64 1/2 (-.f64 (log.f64 (+.f64 y x)) (log.f64 (/.f64 1 z))))))

Compiler

Compiled 5213 to 2706 computations (48.1% saved)

localize22.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4) (pow.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)) 1/4))
	0.5b	(fma.f64 x (+.f64 y z) (*.f64 y z))
✓	18.2b	(pow.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)) 1/4)

series457.0ms (3.5%)

Counts

2 → 48

Calls

2 calls:

317.0ms	(.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4) (pow.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)) 1/4))
139.0ms	(pow.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)) 1/4)

rewrite28.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
21×	`unpow-prod-down_binary64`
15×	`add-exp-log_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

2 → 73

Calls

2 calls:

11.0ms	(.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4) (pow.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)) 1/4))
3.0ms	(pow.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)) 1/4)

simplify179.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

493×	`associate-l_binary64`
448×	`fma-def_binary64`
385×	`times-frac_binary64`
317×	`associate-/r*_binary64`
245×	`associate-/l*_binary64`

Counts

121 → 176

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	585	5877
1	1718	5500
2	5498	5500

prune642.0ms (4.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	313	4	317
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	317	9	326

Error

2.0b

Counts

326 → 9

Alt Table

Status	Error	Program
	18.2b	(.f64 2 (.f64 (pow.f64 (.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z)))) 1/4) (.f64 (pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) 1/4) (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4))))
	18.3b	(.f64 2 (.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4) (cbrt.f64 (.f64 (.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4) (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4)) (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4)))))
✓	17.9b	(.f64 2 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/2))
	33.1b	(*.f64 2 (pow.f64 (exp.f64 1/2) (+.f64 (log.f64 (+.f64 y x)) (log.f64 z))))
▶	18.2b	(.f64 2 (.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) (/.f64 1/4 2)) (.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) (/.f64 1/4 2)) (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4))))
	33.1b	(.f64 2 (exp.f64 (.f64 1/2 (-.f64 (log.f64 (+.f64 y x)) (log.f64 (/.f64 1 z))))))
	36.9b	(.f64 2 (exp.f64 (.f64 1/2 (-.f64 (log.f64 (neg.f64 (+.f64 y z))) (log.f64 (/.f64 -1 x))))))
	18.4b	(.f64 2 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z)))) (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))
	39.9b	(.f64 2 (pow.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 2) 1/4))

Compiler

Compiled 16406 to 8015 computations (51.1% saved)

localize34.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) (/.f64 1/4 2)) (.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) (/.f64 1/4 2)) (pow.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)) 1/4)))
	0.5b	(fma.f64 x (+.f64 y z) (*.f64 y z))
	18.2b	(pow.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)) 1/4)
✓	18.2b	(pow.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)) (/.f64 1/4 2))

series505.0ms (3.9%)

Counts

2 → 48

Calls

2 calls:

385.0ms

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

120.0ms

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

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`add-exp-log_binary64`
57×	`prod-exp_binary64`
29×	`pow-exp_binary64`
29×	`pow-to-exp_binary64`
13×	`pow-unpow_binary64`

Counts

2 → 80

Calls

2 calls:

7.0ms

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

5.0ms

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

simplify194.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

757×	`fma-def_binary64`
366×	`times-frac_binary64`
321×	`associate-/r*_binary64`
240×	`associate-/l*_binary64`
214×	`*-commutative_binary64`

Counts

128 → 180

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	623	5499
1	1843	5187
2	4967	5134
3	5239	5134

prune1.3s (9.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	459	1	460
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	459	10	469

Error

2.0b

Counts

469 → 10

Alt Table

Status	Error	Program
	18.2b	(.f64 2 (.f64 (pow.f64 (.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z)))) 1/4) (.f64 (pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) 1/4) (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4))))
	18.3b	(.f64 2 (.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4) (cbrt.f64 (.f64 (.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4) (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4)) (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4)))))
✓	17.9b	(.f64 2 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/2))
	33.1b	(*.f64 2 (pow.f64 (exp.f64 1/2) (+.f64 (log.f64 (+.f64 y x)) (log.f64 z))))
✓	18.2b	(.f64 2 (.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) (/.f64 1/4 2)) (.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) (/.f64 1/4 2)) (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/4))))
	33.1b	(.f64 2 (exp.f64 (.f64 1/2 (-.f64 (log.f64 (+.f64 y x)) (log.f64 (/.f64 1 z))))))
	36.9b	(.f64 2 (exp.f64 (.f64 1/2 (-.f64 (log.f64 (neg.f64 (+.f64 y z))) (log.f64 (/.f64 -1 x))))))
	18.4b	(.f64 2 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z)))) (cbrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))))))
	39.9b	(.f64 2 (pow.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 2) 1/4))
	18.4b	(.f64 2 (.f64 (pow.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) (/.f64 1/4 2)) (.f64 (pow.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (.f64 y z))) 1/8) (pow.f64 (pow.f64 (fma.f64 x (+.f64 y z) (.f64 y z)) 1/8) 3))))

Compiler

Compiled 29243 to 14076 computations (51.9% saved)

regimes4.0s (30.8%)

Accuracy

Total 3.1b remaining (60.4%)

Threshold costs 0b (0%)

Counts

163 → 5

Compiler

Compiled 28664 to 15848 computations (44.7% saved)

bsearch271.0ms (2.1%)

Steps

Iters	Range		Point
7	2.5277842608173215e+91	1.0319103201538945e+93	1.0208539709101426e+93
11	-2.4161171264377086e-251	-2.221401343227022e-279	-2.7214926907983235e-253
11	-1.6233304406267663e-175	-7.777286448998501e-199	-1.1343957496177142e-192
3	-2.1955296947950985e+23	-1.6939739310864924e+23	-1.7253211663182805e+23

Compiler

Compiled 4 to 3 computations (25% saved)

simplify11.0ms (0.1%)

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	45	123
1	66	123
2	80	123
3	90	123
4	94	123
5	93	123

end1.3s (10.2%)

Compiler: Compiled 631 to 382 computations (39.5% saved)

Details

analyze755.0ms (5.8%)

sample2.0s (15.5%)

simplify21.0ms (0.2%)

prune6.0ms (0%)

localize17.0ms (0.1%)

series436.0ms (3.3%)

rewrite5.0ms (0%)

simplify135.0ms (1%)

prune149.0ms (1.1%)

localize22.0ms (0.2%)

series139.0ms (1.1%)

rewrite4.0ms (0%)

simplify125.0ms (1%)

prune226.0ms (1.7%)

localize22.0ms (0.2%)

series457.0ms (3.5%)

rewrite28.0ms (0.2%)

simplify179.0ms (1.4%)

prune642.0ms (4.9%)

localize34.0ms (0.3%)

series505.0ms (3.9%)

rewrite23.0ms (0.2%)

simplify194.0ms (1.5%)

prune1.3s (9.9%)

regimes4.0s (30.8%)

bsearch271.0ms (2.1%)

simplify11.0ms (0.1%)

end1.3s (10.2%)

Profiling