Details

analyze18.0ms (0.6%)

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)

sample60.0ms (1.9%)

Algorithm

1×

intervals

Symmetry

(sort x y z)

Results

14.0ms

256×

body

128

valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify8.0ms (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

38.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	38.4b	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))

Compiler

Compiled 59 to 34 computations (42.4% saved)

localize13.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (*.f64 y y))
✓	0.1b	(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)
✓	35.6b	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))

series125.0ms (3.9%)

Counts

3 → 96

Calls

3 calls:

91.0ms	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
27.0ms	(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)
6.0ms	(fma.f64 x x (*.f64 y y))

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
19×	`times-frac_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
13×	`sqrt-prod_binary64`

Counts

3 → 66

Calls

3 calls:

2.0ms	(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)
2.0ms	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
0.0ms	(fma.f64 x x (*.f64 y y))

simplify126.0ms (4%)

Algorithm

1×	egg-herbie

Rules

356×	`sub-neg_binary64`
354×	`fma-neg_binary64`
279×	`fma-def_binary64`
227×	`times-frac_binary64`
207×	`associate-r_binary64`

Counts

162 → 203

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	395	4965
1	1008	4633
2	4052	4633
3	5004	4633

prune142.0ms (4.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	199	4	203
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	200	4	204

Error

0.2b

Counts

204 → 4

Alt Table

Status	Error	Program
	38.5b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
▶	0.8b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
	30.8b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y z))
	30.3b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))

Compiler

Compiled 6328 to 3670 computations (42% 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))

series21.0ms (0.7%)

Counts

1 → 24

Calls

1 calls:

21.0ms

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

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`
4×	`sqrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`

Counts

1 → 25

Calls

1 calls:

4.0ms

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

simplify70.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

635×	`distribute-rgt-neg-in_binary64`
498×	`times-frac_binary64`
397×	`distribute-neg-frac_binary64`
345×	`associate-r_binary64`
302×	`associate-/l*_binary64`

Counts

49 → 57

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	99	1097
1	269	1061
2	905	1057
3	3923	1057
4	5279	1057

prune45.0ms (1.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	52	5	57
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	53	8	61

Error

0.0b

Counts

61 → 8

Alt Table

Status	Error	Program
	38.5b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
	1.0b	(.f64 (.f64 (sqrt.f64 1/3) (sqrt.f64 (hypot.f64 x z))) (sqrt.f64 (hypot.f64 x z)))
	1.7b	(.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)))
▶	0.8b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
	30.8b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y z))
	1.1b	(.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))))
	30.3b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
	1.7b	(.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))))

Compiler

Compiled 1267 to 912 computations (28% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series41.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

21.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
20.0ms	(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))

rewrite18.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`sqrt-prod_binary64`
18×	`associate-l_binary64`
15×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

2 → 56

Calls

2 calls:

8.0ms	(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))
7.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))

simplify97.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

785×	`fma-neg_binary64`
710×	`times-frac_binary64`
483×	`associate-/l*_binary64`
470×	`fma-def_binary64`
235×	`cancel-sign-sub-inv_binary64`

Counts

104 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	2514
1	463	2398
2	1657	2278
3	4785	2274
4	5301	2274

prune96.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	132	7	139

Error

0.0b

Counts

139 → 7

Alt Table

Status	Error	Program
	38.5b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
	1.0b	(.f64 (.f64 (sqrt.f64 1/3) (sqrt.f64 (hypot.f64 x z))) (sqrt.f64 (hypot.f64 x z)))
✓	0.8b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
	30.8b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y z))
	1.1b	(.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))))
▶	1.0b	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))))
	30.3b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))

Compiler

Compiled 2895 to 2239 computations (22.7% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))
✓	0.3b	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
✓	0.4b	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))))

series69.0ms (2.2%)

Counts

2 → 48

Calls

2 calls:

50.0ms

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

19.0ms

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

rewrite30.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`sqrt-prod_binary64`
24×	`associate-l_binary64`
16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`

Counts

2 → 63

Calls

2 calls:

17.0ms

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

8.0ms

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

simplify121.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

708×	`times-frac_binary64`
669×	`fma-neg_binary64`
449×	`fma-def_binary64`
244×	`cancel-sign-sub-inv_binary64`
239×	`associate-r_binary64`

Counts

111 → 150

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	177	3441
1	522	2910
2	1867	2694
3	4763	2690
4	5167	2690

prune167.0ms (5.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	210	2	212
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	211	8	219

Error

0.0b

Counts

219 → 8

Alt Table

Status	Error	Program
	31.5b	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (.f64 (pow.f64 (pow.f64 (sqrt.f64 1/3) 3) 1/4) z))
	38.5b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
	1.0b	(.f64 (.f64 (sqrt.f64 1/3) (sqrt.f64 (hypot.f64 x z))) (sqrt.f64 (hypot.f64 x z)))
✓	0.8b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
	30.8b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y z))
	1.1b	(.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))))
	30.3b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
	31.0b	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (neg.f64 (.f64 x (pow.f64 (*.f64 1/3 (sqrt.f64 1/3)) 1/4))))

Compiler

Compiled 5686 to 4688 computations (17.6% saved)

regimes558.0ms (17.7%)

Accuracy

Total 0.8b remaining (97.5%)

Threshold costs 0.8b (97.5%)

Counts

49 → 1

Compiler

Compiled 7800 to 5732 computations (26.5% saved)

simplify2.0ms (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 (0.5%)

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

sample1.3s (40.6%)

Algorithm

1×

intervals

Results

475.0ms

8000×

body

128

valid

Compiler

Compiled 151 to 117 computations (22.5% saved)

Details

analyze18.0ms (0.6%)

sample60.0ms (1.9%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize13.0ms (0.4%)

series125.0ms (3.9%)

rewrite8.0ms (0.3%)

simplify126.0ms (4%)

prune142.0ms (4.5%)

localize4.0ms (0.1%)

series21.0ms (0.7%)

rewrite5.0ms (0.2%)

simplify70.0ms (2.2%)

prune45.0ms (1.4%)

localize6.0ms (0.2%)

series41.0ms (1.3%)

rewrite18.0ms (0.6%)

simplify97.0ms (3.1%)

prune96.0ms (3%)

localize9.0ms (0.3%)

series69.0ms (2.2%)

rewrite30.0ms (1%)

simplify121.0ms (3.8%)

prune167.0ms (5.3%)

regimes558.0ms (17.7%)

simplify2.0ms (0.1%)

end15.0ms (0.5%)

sample1.3s (40.6%)

Profiling