Details

analyze412.0ms (8.2%)

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)

sample913.0ms (18.3%)

Results

877.0ms

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

17.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	17.0b	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z z) (*.f64 t t)))
	23.3b	(+.f64 (/.f64 (.f64 x x) (.f64 y y)) (/.f64 (.f64 z z) (.f64 t t)))

Compiler

Compiled 107 to 55 computations (48.6% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	2.1b	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z z) (*.f64 t t)))
✓	9.2b	(/.f64 x (*.f64 y y))
✓	14.8b	(/.f64 (.f64 z z) (.f64 t t))

series168.0ms (3.4%)

Counts

3 → 96

Calls

3 calls:

113.0ms	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z z) (*.f64 t t)))
29.0ms	(/.f64 (.f64 z z) (.f64 t t))
26.0ms	(/.f64 x (*.f64 y y))

rewrite10.0ms (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 (.f64 z z) (.f64 t t))
3.0ms	(/.f64 x (*.f64 y y))
0.0ms	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z z) (*.f64 t t)))

simplify109.0ms (2.2%)

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

prune78.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	66	9	75
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	68	9	77

Error

0.1b

Counts

77 → 9

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
	9.0b	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z (/.f64 z t)) t))
	14.0b	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (/.f64 (.f64 z z) t) t))
	8.6b	(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))
	13.5b	(fma.f64 x (/.f64 (/.f64 x y) y) (/.f64 (.f64 z z) (.f64 t t)))
	17.8b	(fma.f64 x (.f64 x (/.f64 1 (.f64 y y))) (/.f64 (.f64 z z) (.f64 t t)))
	13.5b	(fma.f64 x (/.f64 1 (/.f64 y (/.f64 x y))) (/.f64 (.f64 z z) (.f64 t t)))
	15.2b	(fma.f64 x (/.f64 x (*.f64 y y)) (cbrt.f64 (pow.f64 (/.f64 z t) 6)))
	34.8b	(/.f64 (pow.f64 x 2) (pow.f64 y 2))

Compiler

Compiled 1738 to 457 computations (73.7% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series303.0ms (6.1%)

Counts

1 → 48

Calls

1 calls:

303.0ms

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

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 29

Calls

1 calls:

3.0ms

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

simplify99.0ms (2%)

Algorithm

1×	egg-herbie

Rules

894×	`fma-def_binary64`
358×	`distribute-rgt-out_binary64`
262×	`sqr-pow_binary64`
244×	`associate-*l/_binary64`
213×	`associate-*r/_binary64`

Counts

77 → 44

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	48	1634
1	100	1440
2	223	1309
3	661	1295
4	2497	1216
5	4140	1215
6	4858	1028
7	4917	1028

prune55.0ms (1.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	39	5	44
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	44	9	53

Error

0.0b

Counts

53 → 9

Alt Table

Status	Error	Program
	0.3b	(.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
	8.6b	(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))
	0.7b	(.f64 (.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (*.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
	17.8b	(fma.f64 x (.f64 x (/.f64 1 (.f64 y y))) (/.f64 (.f64 z z) (.f64 t t)))
	9.0b	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z (/.f64 z t)) t))
	13.5b	(fma.f64 x (/.f64 1 (/.f64 y (/.f64 x y))) (/.f64 (.f64 z z) (.f64 t t)))
	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)))))
	18.6b	(cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 6))
▶	0.2b	(+.f64 (pow.f64 (/.f64 x y) 2) (pow.f64 (/.f64 z t) 2))

Compiler

Compiled 1346 to 351 computations (73.9% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 (/.f64 x y) 2) (pow.f64 (/.f64 z t) 2))
✓	0.2b	(pow.f64 (/.f64 x y) 2)
✓	0.2b	(pow.f64 (/.f64 z t) 2)

series117.0ms (2.3%)

Counts

3 → 96

Calls

3 calls:

98.0ms	(+.f64 (pow.f64 (/.f64 x y) 2) (pow.f64 (/.f64 z t) 2))
10.0ms	(pow.f64 (/.f64 z t) 2)
9.0ms	(pow.f64 (/.f64 x y) 2)

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`unpow-prod-down_binary64`
35×	`*-un-lft-identity_binary64`
29×	`times-frac_binary64`
27×	`add-sqr-sqrt_binary64`
27×	`add-cube-cbrt_binary64`

Counts

3 → 96

Calls

3 calls:

18.0ms	(+.f64 (pow.f64 (/.f64 x y) 2) (pow.f64 (/.f64 z t) 2))
3.0ms	(pow.f64 (/.f64 x y) 2)
3.0ms	(pow.f64 (/.f64 z t) 2)

simplify143.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

358×	`fma-neg_binary64`
321×	`associate-l_binary64`
314×	`associate-*l/_binary64`
306×	`associate-r_binary64`
269×	`associate-*r/_binary64`

Counts

192 → 132

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	169	2612
1	389	2023
2	901	1969
3	3512	1965
4	4771	1965
5	4997	1965
6	4939	1965

prune186.0ms (3.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	126	6	132
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	132	9	141

Error

0.0b

Counts

141 → 9

Alt Table

Status	Error	Program
	9.0b	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z (/.f64 z t)) t))
	0.7b	(.f64 (.f64 (cbrt.f64 (+.f64 (pow.f64 (/.f64 x y) 2) (pow.f64 (/.f64 z t) 2))) (cbrt.f64 (+.f64 (pow.f64 (/.f64 x y) 2) (pow.f64 (/.f64 z t) 2)))) (cbrt.f64 (+.f64 (pow.f64 (/.f64 x y) 2) (pow.f64 (/.f64 z t) 2))))
▶	0.3b	(.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
	0.7b	(.f64 (.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (*.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
	2.1b	(+.f64 (pow.f64 (/.f64 x y) 2) (*.f64 z (/.f64 (/.f64 z t) t)))
	27.7b	(+.f64 (pow.f64 (/.f64 x y) 2) (*.f64 (pow.f64 (/.f64 (sqrt.f64 z) 1) 2) (pow.f64 (/.f64 (sqrt.f64 z) t) 2)))
	2.3b	(+.f64 (.f64 (/.f64 1 y) (.f64 x (/.f64 x y))) (pow.f64 (/.f64 z t) 2))
	2.3b	(+.f64 (*.f64 x (/.f64 (/.f64 x y) y)) (pow.f64 (/.f64 z t) 2))
	0.4b	(+.f64 (.f64 (.f64 (/.f64 x y) (cbrt.f64 x)) (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) y)) (pow.f64 (/.f64 z t) 2))

Compiler

Compiled 2840 to 1438 computations (49.4% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
✓	0.2b	(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y)))
✓	12.5b	(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

series492.0ms (9.8%)

Counts

3 → 96

Calls

3 calls:

291.0ms

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

120.0ms

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

81.0ms

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

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`pow1_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`pow-prod-up_binary64`
12×	`associate-l_binary64`
11×	`sqrt-pow1_binary64`

Counts

3 → 78

Calls

3 calls:

7.0ms

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

4.0ms

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

1.0ms

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

simplify128.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

777×	`fma-def_binary64`
751×	`times-frac_binary64`
417×	`associate-/r*_binary64`
388×	`associate-/l*_binary64`
288×	`associate-*l/_binary64`

Counts

174 → 133

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	198	5187
1	476	4629
2	1384	4233
3	4848	4233
4	5322	4233

prune197.0ms (4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	163	9	172

Error

0.0b

Counts

172 → 9

Alt Table

Status	Error	Program
	9.0b	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z (/.f64 z t)) t))
	0.7b	(.f64 (.f64 (cbrt.f64 (+.f64 (pow.f64 (/.f64 x y) 2) (pow.f64 (/.f64 z t) 2))) (cbrt.f64 (+.f64 (pow.f64 (/.f64 x y) 2) (pow.f64 (/.f64 z t) 2)))) (cbrt.f64 (+.f64 (pow.f64 (/.f64 x y) 2) (pow.f64 (/.f64 z t) 2))))
✓	0.3b	(.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
	2.1b	(+.f64 (pow.f64 (/.f64 x y) 2) (*.f64 z (/.f64 (/.f64 z t) t)))
	27.7b	(+.f64 (pow.f64 (/.f64 x y) 2) (*.f64 (pow.f64 (/.f64 (sqrt.f64 z) 1) 2) (pow.f64 (/.f64 (sqrt.f64 z) t) 2)))
	2.3b	(+.f64 (.f64 (/.f64 1 y) (.f64 x (/.f64 x y))) (pow.f64 (/.f64 z t) 2))
	2.3b	(+.f64 (*.f64 x (/.f64 (/.f64 x y) y)) (pow.f64 (/.f64 z t) 2))
	0.4b	(+.f64 (.f64 (.f64 (/.f64 x y) (cbrt.f64 x)) (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) y)) (pow.f64 (/.f64 z t) 2))
	0.5b	(.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (.f64 (*.f64 (fabs.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (sqrt.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))) (hypot.f64 (/.f64 z t) (/.f64 x y))))

Compiler

Compiled 5913 to 1570 computations (73.4% saved)

regimes1.4s (27.1%)

Accuracy

Total 0.2b remaining (85.9%)

Threshold costs 0.2b (85.9%)

Counts

103 → 1

Compiler

Compiled 28216 to 15792 computations (44% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	17
1	14	17
2	13	17

end131.0ms (2.6%)

Compiler: Compiled 261 to 150 computations (42.5% saved)

Details

analyze412.0ms (8.2%)

sample913.0ms (18.3%)

simplify7.0ms (0.1%)

prune3.0ms (0.1%)

localize12.0ms (0.2%)

series168.0ms (3.4%)

rewrite10.0ms (0.2%)

simplify109.0ms (2.2%)

prune78.0ms (1.6%)

localize6.0ms (0.1%)

series303.0ms (6.1%)

rewrite5.0ms (0.1%)

simplify99.0ms (2%)

prune55.0ms (1.1%)

localize7.0ms (0.1%)

series117.0ms (2.3%)

rewrite28.0ms (0.6%)

simplify143.0ms (2.9%)

prune186.0ms (3.7%)

localize9.0ms (0.2%)

series492.0ms (9.8%)

rewrite17.0ms (0.3%)

simplify128.0ms (2.6%)

prune197.0ms (4%)

regimes1.4s (27.1%)

simplify3.0ms (0.1%)

end131.0ms (2.6%)

Profiling