Details

analyze613.0ms (7.4%)

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
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
43.7%	56.2%	0.1%	8
62.4%	37.4%	0.1%	9
65.5%	34.3%	0.1%	10
71.8%	27.7%	0.5%	11
79.2%	19.7%	1.1%	12
80.2%	18.7%	1.1%	13
82.8%	15%	2.2%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample50.0ms (0.6%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
1.0ms	16×	body	128	invalid

Compiler

Compiled 32 to 24 computations (25% saved)

simplify20.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

44×	`fma-def_binary64`
37×	`associate-l_binary64`
36×	`associate-r_binary64`
20×	`*-commutative_binary64`
19×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	24	14
2	41	14
3	94	14
4	122	14
5	149	14
6	153	14
7	146	14

prune5.0ms (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

5.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.4b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))

Compiler

Compiled 50 to 34 computations (32% saved)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	2.6b	(*.f64 y (fma.f64 z z 1))
✓	4.2b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`times-frac_binary64`
26×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`

Counts

2 → 74

Calls

2 calls:

12.0ms	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
4.0ms	(*.f64 y (fma.f64 z z 1))

series217.0ms (2.6%)

Counts

2 → 60

Calls

2 calls:

176.0ms	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
41.0ms	(*.f64 y (fma.f64 z z 1))

simplify213.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

469×	`associate-/r*_binary64`
453×	`associate-l_binary64`
414×	`associate-/l*_binary64`
336×	`associate-/l/_binary64`
297×	`associate-r_binary64`

Counts

134 → 256

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	154	2203
1	330	1967
2	1107	1965
3	3956	1963
4	4482	1963
5	4806	1963
6	4938	1963

prune247.0ms (3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	247	9	256
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	248	9	257

Error

3.3b

Counts

257 → 9

Alt Table

Status	Error	Program
	5.4b	(/.f64 (/.f64 1 x) (.f64 (.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1))))
	5.5b	(/.f64 1 (.f64 (.f64 y (fma.f64 z z 1)) x))
	20.8b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
	48.7b	(*.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (sqrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))
	5.2b	(/.f64 (/.f64 (/.f64 1 x) y) (fma.f64 z z 1))
	6.1b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 (.f64 y (fma.f64 z z 1)) (/.f64 1 (cbrt.f64 x))))
	6.0b	(/.f64 (/.f64 1 x) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (fma.f64 z z 1))))
▶	5.2b	(.f64 (/.f64 1 y) (/.f64 1 (.f64 x (fma.f64 z z 1))))
	5.9b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))

Compiler

Compiled 2522 to 1454 computations (42.3% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (*.f64 x (fma.f64 z z 1)))
✓	2.6b	(.f64 (/.f64 1 y) (/.f64 1 (.f64 x (fma.f64 z z 1))))
✓	3.8b	(*.f64 x (fma.f64 z z 1))

rewrite38.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`add-exp-log_binary64`
44×	`prod-exp_binary64`
34×	`div-exp_binary64`
31×	`add-cbrt-cube_binary64`
25×	`add-sqr-sqrt_binary64`

Counts

3 → 127

Calls

3 calls:

16.0ms	(.f64 (/.f64 1 y) (/.f64 1 (.f64 x (fma.f64 z z 1))))
5.0ms	(/.f64 1 (*.f64 x (fma.f64 z z 1)))
4.0ms	(*.f64 x (fma.f64 z z 1))

series281.0ms (3.4%)

Counts

3 → 84

Calls

3 calls:

170.0ms	(.f64 (/.f64 1 y) (/.f64 1 (.f64 x (fma.f64 z z 1))))
65.0ms	(/.f64 1 (*.f64 x (fma.f64 z z 1)))
45.0ms	(*.f64 x (fma.f64 z z 1))

simplify260.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

457×	`associate-/r*_binary64`
414×	`associate-/l*_binary64`
361×	`associate-*l/_binary64`
308×	`fma-def_binary64`
264×	`associate-/l/_binary64`

Counts

211 → 407

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	192	3383
1	418	3024
2	1367	2996
3	4201	2992
4	4650	2992
5	4992	2992
6	4942	2992

prune370.0ms (4.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	403	4	407
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	408	8	416

Error

2.1b

Counts

416 → 8

Alt Table

Status	Error	Program
	5.4b	(/.f64 (/.f64 1 x) (.f64 (.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1))))
	5.5b	(/.f64 1 (.f64 (.f64 y (fma.f64 z z 1)) x))
▶	5.2b	(/.f64 (/.f64 1 y) (*.f64 x (fma.f64 z z 1)))
	47.5b	(.f64 (/.f64 1 y) (/.f64 1 (.f64 (.f64 (sqrt.f64 x) (hypot.f64 1 z)) (.f64 (sqrt.f64 x) (hypot.f64 1 z)))))
	6.0b	(/.f64 (/.f64 1 x) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (fma.f64 z z 1))))
	36.4b	(/.f64 1 (.f64 (.f64 z z) (*.f64 x y)))
	20.8b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
	25.7b	(.f64 (/.f64 1 y) (cbrt.f64 (/.f64 1 (pow.f64 (.f64 (fma.f64 z z 1) x) 3))))

Compiler

Compiled 4134 to 2750 computations (33.5% saved)

localize13.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	2.6b	(/.f64 (/.f64 1 y) (*.f64 x (fma.f64 z z 1)))
	3.8b	(*.f64 x (fma.f64 z z 1))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`times-frac_binary64`
23×	`add-exp-log_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`

Counts

1 → 52

Calls

1 calls:

11.0ms

(/.f64 (/.f64 1 y) (*.f64 x (fma.f64 z z 1)))

series211.0ms (2.5%)

Counts

1 → 36

Calls

1 calls:

210.0ms

(/.f64 (/.f64 1 y) (*.f64 x (fma.f64 z z 1)))

simplify142.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

801×	`times-frac_binary64`
421×	`associate-/r*_binary64`
377×	`associate-/l*_binary64`
370×	`associate-l_binary64`
275×	`associate-/l/_binary64`

Counts

88 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	1756
1	301	1563
2	873	1561
3	4022	1561
4	4682	1561
5	4927	1561

prune196.0ms (2.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	254	2	256
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	255	9	264

Error

2.1b

Counts

264 → 9

Alt Table

Status	Error	Program
	47.5b	(/.f64 (/.f64 1 y) (.f64 (.f64 (sqrt.f64 x) (hypot.f64 1 z)) (*.f64 (sqrt.f64 x) (hypot.f64 1 z))))
✓	5.2b	(/.f64 (/.f64 1 y) (*.f64 x (fma.f64 z z 1)))
	5.4b	(/.f64 (/.f64 1 x) (.f64 (.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1))))
	5.5b	(/.f64 1 (.f64 (.f64 y (fma.f64 z z 1)) x))
▶	5.3b	(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
	47.5b	(.f64 (/.f64 1 y) (/.f64 1 (.f64 (.f64 (sqrt.f64 x) (hypot.f64 1 z)) (.f64 (sqrt.f64 x) (hypot.f64 1 z)))))
	6.0b	(/.f64 (/.f64 1 x) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (fma.f64 z z 1))))
	20.8b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
	25.7b	(.f64 (/.f64 1 y) (cbrt.f64 (/.f64 1 (pow.f64 (.f64 (fma.f64 z z 1) x) 3))))

Compiler

Compiled 2486 to 1472 computations (40.8% saved)

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.6b	(/.f64 1 (*.f64 y x))
✓	5.0b	(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
32×	`add-exp-log_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`

Counts

2 → 84

Calls

2 calls:

9.0ms	(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
6.0ms	(/.f64 1 (*.f64 y x))

series397.0ms (4.8%)

Counts

2 → 36

Calls

2 calls:

345.0ms	(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
51.0ms	(/.f64 1 (*.f64 y x))

simplify247.0ms (3%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-def_binary64`
468×	`fma-neg_binary64`
445×	`times-frac_binary64`
368×	`associate-/r*_binary64`
345×	`cancel-sign-sub-inv_binary64`

Counts

120 → 216

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	148	2243
1	332	2008
2	900	2006
3	3270	2000
4	4421	2000
5	4793	2000
6	4985	2000
7	4929	2000

prune242.0ms (2.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	213	3	216
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	216	9	225

Error

0.0b

Counts

225 → 9

Alt Table

Status	Error	Program
	5.4b	(/.f64 (/.f64 1 x) (.f64 (.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1))))
	2.1b	(*.f64 (/.f64 (/.f64 1 y) (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
	5.5b	(/.f64 1 (.f64 (.f64 y (fma.f64 z z 1)) x))
	28.6b	(.f64 (/.f64 (sqrt.f64 (/.f64 1 (.f64 y x))) (hypot.f64 1 z)) (/.f64 (sqrt.f64 (/.f64 1 (*.f64 y x))) (hypot.f64 1 z)))
	47.5b	(.f64 (/.f64 1 y) (/.f64 1 (.f64 (.f64 (sqrt.f64 x) (hypot.f64 1 z)) (.f64 (sqrt.f64 x) (hypot.f64 1 z)))))
✓	5.2b	(/.f64 (/.f64 1 y) (*.f64 x (fma.f64 z z 1)))
	2.8b	(.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 (.f64 y x)) (hypot.f64 1 z)))
	6.0b	(/.f64 (/.f64 1 x) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (fma.f64 z z 1))))
	25.7b	(.f64 (/.f64 1 y) (cbrt.f64 (/.f64 1 (pow.f64 (.f64 (fma.f64 z z 1) x) 3))))

Compiler

Compiled 2278 to 1326 computations (41.8% saved)

regimes2.5s (29.8%)

Accuracy

Total 1.2b remaining (96.8%)

Threshold costs 0b (0%)

Compiler

Compiled 21809 to 15562 computations (28.6% saved)

bsearch67.0ms (0.8%)

Steps

Iters	Range		Point
7	7.19144164695389e-75	8.416835601946818e-73	4.5355777734533977e-73

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	50
1	25	50
2	24	50

end18.0ms (0.2%)

Compiler: Compiled 111 to 84 computations (24.3% saved)

sample1.9s (22.4%)

Algorithm

1×

intervals

Results

723.0ms	8000×	body	128	valid
40.0ms	462×	body	128	invalid

Compiler

Compiled 219 to 160 computations (26.9% saved)

Details

analyze613.0ms (7.4%)

sample50.0ms (0.6%)

simplify20.0ms (0.2%)

prune5.0ms (0.1%)

localize11.0ms (0.1%)

rewrite23.0ms (0.3%)

series217.0ms (2.6%)

simplify213.0ms (2.6%)

prune247.0ms (3%)

localize13.0ms (0.2%)

rewrite38.0ms (0.5%)

series281.0ms (3.4%)

simplify260.0ms (3.1%)

prune370.0ms (4.5%)

localize13.0ms (0.2%)

rewrite22.0ms (0.3%)

series211.0ms (2.5%)

simplify142.0ms (1.7%)

prune196.0ms (2.4%)

localize12.0ms (0.1%)

rewrite22.0ms (0.3%)

series397.0ms (4.8%)

simplify247.0ms (3%)

prune242.0ms (2.9%)

regimes2.5s (29.8%)

bsearch67.0ms (0.8%)

simplify6.0ms (0.1%)

end18.0ms (0.2%)

sample1.9s (22.4%)

Profiling