Details

analyze57.0ms (1.3%)

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
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
87.4%	12.5%	0.1%	7
93.6%	6.2%	0.1%	8
96.7%	3.1%	0.1%	9
98.3%	1.6%	0.1%	10
99.1%	0.8%	0.1%	11
99.5%	0.4%	0.1%	12
99.7%	0.2%	0.1%	13
99.8%	0.1%	0.1%	14

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample70.0ms (1.6%)

Algorithm

1×

intervals

Results

15.0ms

256×

body

128

valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

9×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	17	17
2	27	17
3	31	17
4	31	17

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

40.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	40.1b	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))

Compiler

Compiled 59 to 34 computations (42.4% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)
✓	37.4b	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))

rewrite27.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-cube-cbrt_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`

Counts

2 → 86

Calls

2 calls:

12.0ms	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
11.0ms	(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)

series458.0ms (10.6%)

Counts

2 → 72

Calls

2 calls:

402.0ms	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
55.0ms	(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)

simplify161.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

404×	`fma-neg_binary64`
358×	`sub-neg_binary64`
279×	`fma-def_binary64`
229×	`times-frac_binary64`
223×	`associate-r_binary64`

Counts

158 → 279

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	379	4483
1	1009	4196
2	4143	4164
3	4963	4164
4	4971	4164

prune142.0ms (3.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	276	3	279
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	276	4	280

Error

0.3b

Counts

280 → 4

Alt Table

Status	Error	Program
	29.4b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
✓	40.1b	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
	40.2b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
▶	1.1b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))

Compiler

Compiled 6002 to 3574 computations (40.5% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
6×	`add-exp-log_binary64`
5×	`pow1_binary64`
5×	`add-cbrt-cube_binary64`
5×	`add-cube-cbrt_binary64`

Counts

1 → 37

Calls

1 calls:

13.0ms

(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))

series22.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

22.0ms

(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))

simplify75.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

621×	`fma-neg_binary64`
522×	`associate-r_binary64`
508×	`associate-l_binary64`
456×	`times-frac_binary64`
311×	`associate-/l*_binary64`

Counts

61 → 103

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	106	1111
1	282	1071
2	940	1067
3	4970	1067
4	5457	1067

prune99.0ms (2.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	97	6	103
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	97	10	107

Error

0.1b

Counts

107 → 10

Alt Table

Status	Error	Program
	29.4b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
	1.8b	(.f64 (.f64 (sqrt.f64 1/3) (*.f64 (cbrt.f64 (hypot.f64 x z)) (cbrt.f64 (hypot.f64 x z)))) (cbrt.f64 (hypot.f64 x z)))
✓	40.1b	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
	1.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 1/3)) (cbrt.f64 (sqrt.f64 1/3))) (*.f64 (cbrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
▶	1.3b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (sqrt.f64 1/3))) (*.f64 (sqrt.f64 (hypot.f64 x z)) (sqrt.f64 (hypot.f64 x z))))
	40.2b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
	1.4b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (hypot.f64 x z))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (hypot.f64 x z))))
✓	1.1b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
	1.9b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 x z))) (cbrt.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 x z)))) (cbrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 x z))))
	1.9b	(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 x z))) 3)

Compiler

Compiled 1553 to 1091 computations (29.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (hypot.f64 x z))
✓	0.0b	(sqrt.f64 (hypot.f64 x z))
✓	0.4b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (sqrt.f64 1/3))) (*.f64 (sqrt.f64 (hypot.f64 x z)) (sqrt.f64 (hypot.f64 x z))))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x z)) (sqrt.f64 (hypot.f64 x z)))

rewrite44.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
25×	`rem-sqrt-square_binary64`
20×	`pow1/2_binary64`
18×	`add-exp-log_binary64`
17×	`pow2_binary64`

Counts

3 → 128

Calls

3 calls:

14.0ms

(*.f64 (sqrt.f64 (hypot.f64 x z)) (sqrt.f64 (hypot.f64 x z)))

14.0ms

(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (sqrt.f64 1/3))) (*.f64 (sqrt.f64 (hypot.f64 x z)) (sqrt.f64 (hypot.f64 x z))))

9.0ms

(sqrt.f64 (hypot.f64 x z))

series54.0ms (1.3%)

Counts

3 → 56

Calls

3 calls:

24.0ms

(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (sqrt.f64 1/3))) (*.f64 (sqrt.f64 (hypot.f64 x z)) (sqrt.f64 (hypot.f64 x z))))

16.0ms

(sqrt.f64 (hypot.f64 x z))

13.0ms

(*.f64 (sqrt.f64 (hypot.f64 x z)) (sqrt.f64 (hypot.f64 x z)))

simplify137.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

558×	`times-frac_binary64`
482×	`fma-neg_binary64`
475×	`fma-def_binary64`
395×	`unswap-sqr_binary64`
259×	`cancel-sign-sub-inv_binary64`

Counts

184 → 299

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	224	2445
1	593	2325
2	1913	2264
3	4485	2254
4	4962	2254
5	4975	2254

prune239.0ms (5.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	352	6	358
Fresh	3	4	7
Picked	1	0	1
Done	0	2	2
Total	356	12	368

Error

0.0b

Counts

368 → 12

Alt Table

Status	Error	Program
	1.2b	(.f64 (.f64 (sqrt.f64 1/3) (sqrt.f64 (hypot.f64 x z))) (sqrt.f64 (hypot.f64 x z)))
✓	40.1b	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
	2.0b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (sqrt.f64 1/3))) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x z))) (cbrt.f64 (sqrt.f64 (hypot.f64 x z)))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x z))) (sqrt.f64 (hypot.f64 x z)))))
	1.9b	(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 x z))) 3)
	1.9b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (sqrt.f64 1/3))) (.f64 (.f64 (cbrt.f64 (hypot.f64 x z)) (cbrt.f64 (hypot.f64 x z))) (cbrt.f64 (hypot.f64 x z))))
	1.4b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (sqrt.f64 1/3))) (*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x z))) 2) (sqrt.f64 (hypot.f64 x z))))
	29.4b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
	40.2b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
▶	0.9b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (hypot.f64 x z) (sqrt.f64 (sqrt.f64 1/3))))
✓	1.1b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
	1.9b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 x z))) (cbrt.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 x z)))) (cbrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 x z))))
	1.4b	(pow.f64 (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (hypot.f64 x z))) 2)

Compiler

Compiled 6151 to 3782 computations (38.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (hypot.f64 x z) (sqrt.f64 (sqrt.f64 1/3)))
✓	0.3b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (hypot.f64 x z) (sqrt.f64 (sqrt.f64 1/3))))

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-exp-log_binary64`
14×	`add-sqr-sqrt_binary64`
10×	`pow1_binary64`
10×	`add-cbrt-cube_binary64`
9×	`sqrt-unprod_binary64`

Counts

2 → 74

Calls

2 calls:

13.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (hypot.f64 x z) (sqrt.f64 (sqrt.f64 1/3))))
11.0ms	(*.f64 (hypot.f64 x z) (sqrt.f64 (sqrt.f64 1/3)))

series46.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

25.0ms	(*.f64 (hypot.f64 x z) (sqrt.f64 (sqrt.f64 1/3)))
20.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (hypot.f64 x z) (sqrt.f64 (sqrt.f64 1/3))))

simplify107.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

686×	`times-frac_binary64`
673×	`fma-neg_binary64`
462×	`fma-def_binary64`
272×	`unswap-sqr_binary64`
246×	`cancel-sign-sub-inv_binary64`

Counts

122 → 210

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	169	2652
1	463	2391
2	1671	2256
3	4732	2252
4	5143	2252

prune116.0ms (2.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	208	2	210
Fresh	4	5	9
Picked	0	1	1
Done	0	2	2
Total	212	10	222

Error

Counts

222 → 10

Alt Table

Status	Error	Program
	29.4b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
	1.4b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (sqrt.f64 (.f64 (hypot.f64 x z) (sqrt.f64 (sqrt.f64 1/3))))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (sqrt.f64 (*.f64 (hypot.f64 x z) (sqrt.f64 (sqrt.f64 1/3))))))
	1.2b	(.f64 (.f64 (sqrt.f64 1/3) (sqrt.f64 (hypot.f64 x z))) (sqrt.f64 (hypot.f64 x z)))
✓	40.1b	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
	1.9b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (sqrt.f64 1/3))) (.f64 (.f64 (cbrt.f64 (hypot.f64 x z)) (cbrt.f64 (hypot.f64 x z))) (cbrt.f64 (hypot.f64 x z))))
	1.4b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (sqrt.f64 1/3))) (*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x z))) 2) (sqrt.f64 (hypot.f64 x z))))
✓	0.9b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (hypot.f64 x z) (sqrt.f64 (sqrt.f64 1/3))))
✓	1.1b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
	1.5b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3)))) (.f64 (sqrt.f64 (.f64 (hypot.f64 x z) (sqrt.f64 (sqrt.f64 1/3)))) (sqrt.f64 (*.f64 (hypot.f64 x z) (sqrt.f64 (sqrt.f64 1/3))))))
	2.0b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (sqrt.f64 1/3))) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x z))) (cbrt.f64 (sqrt.f64 (hypot.f64 x z)))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x z))) (sqrt.f64 (hypot.f64 x z)))))

Compiler

Compiled 3322 to 2529 computations (23.9% saved)

regimes948.0ms (22%)

Accuracy

Total 0.7b remaining (81.1%)

Threshold costs 0.7b (81.1%)

Compiler

Compiled 16419 to 11855 computations (27.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	11	18
2	11	18

end15.0ms (0.3%)

Compiler: Compiled 42 to 36 computations (14.3% saved)

sample1.4s (32.7%)

Algorithm

1×

intervals

Results

514.0ms

8000×

body

128

valid

Compiler

Compiled 238 to 170 computations (28.6% saved)

Details

analyze57.0ms (1.3%)

sample70.0ms (1.6%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

rewrite27.0ms (0.6%)

series458.0ms (10.6%)

simplify161.0ms (3.7%)

prune142.0ms (3.3%)

localize4.0ms (0.1%)

rewrite14.0ms (0.3%)

series22.0ms (0.5%)

simplify75.0ms (1.7%)

prune99.0ms (2.3%)

localize8.0ms (0.2%)

rewrite44.0ms (1%)

series54.0ms (1.3%)

simplify137.0ms (3.2%)

prune239.0ms (5.5%)

localize6.0ms (0.1%)

rewrite29.0ms (0.7%)

series46.0ms (1.1%)

simplify107.0ms (2.5%)

prune116.0ms (2.7%)

regimes948.0ms (22%)

simplify3.0ms (0.1%)

end15.0ms (0.3%)

sample1.4s (32.7%)

Profiling