Details

analyze410.0ms (6.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
25%	74.9%	0.2%	5
25%	74.9%	0.2%	6
37.4%	62.4%	0.2%	7
37.4%	62.4%	0.2%	8
56.1%	43.7%	0.2%	9
56.1%	43.7%	0.2%	10
65.5%	34.3%	0.2%	11
65.5%	34.3%	0.2%	12
76.4%	23.4%	0.2%	13
76.4%	23.4%	0.2%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample870.0ms (14.7%)

Infinites

48.6% of outputs are infinite.

Results

822.0ms

8256×

body

128

valid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`associate-/l*_binary64`
6×	`associate-*r/_binary64`
6×	`associate-/r/_binary64`
6×	`fma-def_binary64`
4×	`associate-/r*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	25	20
2	45	20
3	55	20
4	55	20
5	55	20

prune3.0ms (0.1%)

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

19.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	19.6b	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z z) (*.f64 t t)))
	23.8b	(+.f64 (/.f64 (.f64 x x) (.f64 y y)) (/.f64 (.f64 z z) (.f64 t t)))

Compiler

Compiled 107 to 55 computations (48.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.6b	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z z) (*.f64 t t)))
✓	6.4b	(/.f64 x (*.f64 y y))
✓	17.7b	(/.f64 (.f64 z z) (.f64 t t))

series159.0ms (2.7%)

Counts

3 → 96

Calls

3 calls:

104.0ms	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z z) (*.f64 t t)))
28.0ms	(/.f64 (.f64 z z) (.f64 t t))
26.0ms	(/.f64 x (*.f64 y y))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`
6×	`cbrt-undiv_binary64`
6×	`div-exp_binary64`
5×	`*-un-lft-identity_binary64`

Counts

3 → 56

Calls

3 calls:

5.0ms	(/.f64 x (*.f64 y y))
5.0ms	(/.f64 (.f64 z z) (.f64 t t))
0.0ms	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z z) (*.f64 t t)))

simplify106.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

652×	`times-frac_binary64`
469×	`unswap-sqr_binary64`
438×	`associate-/l*_binary64`
258×	`associate-*l/_binary64`
229×	`associate-/r*_binary64`

Counts

152 → 75

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	106	2182
1	224	1962
2	656	1913
3	2597	1888
4	4392	1885
5	4944	1885
6	4965	1885

prune77.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	69	6	75
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	71	6	77

Error

0.0b

Counts

77 → 6

Alt Table

Status	Error	Program
	16.5b	(fma.f64 x (/.f64 1 (/.f64 y (/.f64 x y))) (/.f64 (.f64 z z) (.f64 t t)))
	16.3b	(fma.f64 x (.f64 (/.f64 1 y) (/.f64 x y)) (/.f64 (.f64 z z) (*.f64 t t)))
▶	0.2b	(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
	8.1b	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z (/.f64 z t)) t))
	12.2b	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (/.f64 (.f64 z z) t) t))
	8.3b	(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))

Compiler

Compiled 1646 to 397 computations (75.9% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 (/.f64 z t) (/.f64 x y))
✓	0.2b	(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))

series319.0ms (5.4%)

Counts

2 → 96

Calls

2 calls:

270.0ms	(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
48.0ms	(hypot.f64 (/.f64 z t) (/.f64 x y))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`
5×	`hypot-udef_binary64`

Counts

2 → 39

Calls

2 calls:

3.0ms	(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
0.0ms	(hypot.f64 (/.f64 z t) (/.f64 x y))

simplify76.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

928×	`associate-/l*_binary64`
772×	`associate-/r*_binary64`
212×	`fma-def_binary64`
151×	`unswap-sqr_binary64`
148×	`associate-/r/_binary64`

Counts

135 → 87

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	117	3714
1	342	3389
2	1314	3211
3	5268	3211

prune317.0ms (5.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	124	5	129
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	125	10	135

Error

0.0b

Counts

135 → 10

Alt Table

Status	Error	Program
	0.5b	(pow.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4) 1)
	16.5b	(fma.f64 x (/.f64 1 (/.f64 y (/.f64 x y))) (/.f64 (.f64 z z) (.f64 t t)))
	16.3b	(fma.f64 x (.f64 (/.f64 1 y) (/.f64 x y)) (/.f64 (.f64 z z) (*.f64 t t)))
	0.7b	(.f64 (.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (*.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))
▶	0.4b	(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3))
	0.6b	(.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (.f64 (*.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))))
	0.7b	(.f64 (.f64 (cbrt.f64 (.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))) (cbrt.f64 (.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y))))) (cbrt.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))))
✓	0.2b	(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
	12.2b	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (/.f64 (.f64 z z) t) t))
	8.3b	(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))

Compiler

Compiled 4164 to 1439 computations (65.4% saved)

localize57.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 (/.f64 z t) (/.f64 x y))
✓	0.2b	(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3))
✓	0.3b	(pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3)
✓	14.9b	(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

series505.0ms (8.5%)

Counts

3 → 96

Calls

3 calls:

271.0ms

(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3))

163.0ms

(pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3)

70.0ms

(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
28×	`sqrt-prod_binary64`
18×	`associate-r_binary64`
16×	`cube-prod_binary64`
16×	`unpow-prod-down_binary64`

Counts

3 → 100

Calls

3 calls:

7.0ms

(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3))

2.0ms

(pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3)

1.0ms

(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

simplify128.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

777×	`fma-def_binary64`
743×	`times-frac_binary64`
413×	`associate-/r*_binary64`
396×	`associate-/l*_binary64`
161×	`associate-l_binary64`

Counts

196 → 139

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	207	5351
1	485	4949
2	1662	4639
3	4696	4639
4	5150	4639

prune356.0ms (6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	251	3	254
Fresh	4	4	8
Picked	1	0	1
Done	0	1	1
Total	256	8	264

Error

0.0b

Counts

264 → 8

Alt Table

Status	Error	Program
	0.6b	(.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (.f64 (*.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))))
▶	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4)
	8.3b	(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))
	0.6b	(.f64 (.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) 3)) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) 3))
	0.5b	(.f64 (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))) (*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3)))
	16.5b	(fma.f64 x (/.f64 1 (/.f64 y (/.f64 x y))) (/.f64 (.f64 z z) (.f64 t t)))
✓	0.2b	(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
	12.2b	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (/.f64 (.f64 z z) t) t))

Compiler

Compiled 8653 to 3223 computations (62.8% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 (/.f64 z t) (/.f64 x y))
✓	0.4b	(pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4)
	14.9b	(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

series407.0ms (6.9%)

Counts

1 → 24

Calls

1 calls:

407.0ms

(pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4)

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`unpow-prod-down_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`pow1_binary64`

Counts

1 → 25

Calls

1 calls:

2.0ms

(pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4)

simplify66.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

785×	`fma-def_binary64`
661×	`associate-/l*_binary64`
537×	`associate-l_binary64`
379×	`associate-/r*_binary64`
340×	`associate-r_binary64`

Counts

49 → 36

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	56	966
1	95	863
2	165	815
3	450	810
4	1823	802
5	4744	802
6	5206	802

prune119.0ms (2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	109	8	117

Error

0.0b

Counts

117 → 8

Alt Table

Status	Error	Program
	0.6b	(.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (.f64 (*.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))))
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4)
	8.3b	(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))
	0.6b	(.f64 (.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) 3)) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) 3))
	0.5b	(.f64 (sqrt.f64 (.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))) (*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3)))
	16.5b	(fma.f64 x (/.f64 1 (/.f64 y (/.f64 x y))) (/.f64 (.f64 z z) (.f64 t t)))
✓	0.2b	(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
	12.2b	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (/.f64 (.f64 z z) t) t))

Compiler

Compiled 2708 to 1334 computations (50.7% saved)

regimes1.8s (29.7%)

Accuracy

Total 0.2b remaining (82.2%)

Threshold costs 0.2b (82.2%)

Counts

154 → 1

Compiler

Compiled 42060 to 22187 computations (47.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	10	13

end113.0ms (1.9%)

Compiler: Compiled 232 to 110 computations (52.6% saved)

Details

analyze410.0ms (6.9%)

sample870.0ms (14.7%)

simplify7.0ms (0.1%)

prune3.0ms (0.1%)

localize9.0ms (0.1%)

series159.0ms (2.7%)

rewrite12.0ms (0.2%)

simplify106.0ms (1.8%)

prune77.0ms (1.3%)

localize6.0ms (0.1%)

series319.0ms (5.4%)

rewrite5.0ms (0.1%)

simplify76.0ms (1.3%)

prune317.0ms (5.4%)

localize57.0ms (1%)

series505.0ms (8.5%)

rewrite16.0ms (0.3%)

simplify128.0ms (2.2%)

prune356.0ms (6%)

localize7.0ms (0.1%)

series407.0ms (6.9%)

rewrite3.0ms (0.1%)

simplify66.0ms (1.1%)

prune119.0ms (2%)

regimes1.8s (29.7%)

simplify2.0ms (0%)

end113.0ms (1.9%)

Profiling