Details

analyze696.0ms (6.8%)

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)

sample55.0ms (0.5%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
2.0ms	20×	body	128	invalid

Compiler

Compiled 32 to 24 computations (25% saved)

simplify19.0ms (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

prune6.0ms (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

5.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.8b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))

Compiler

Compiled 50 to 34 computations (32% saved)

localize15.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.6b	(*.f64 y (fma.f64 z z 1))
✓	3.9b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))

series288.0ms (2.8%)

Counts

2 → 60

Calls

2 calls:

270.0ms	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
18.0ms	(*.f64 y (fma.f64 z z 1))

rewrite30.0ms (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:

15.0ms	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
6.0ms	(*.f64 y (fma.f64 z z 1))

simplify179.0ms (1.7%)

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 → 132

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

prune253.0ms (2.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	122	10	132
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	122	11	133

Error

2.6b

Counts

133 → 11

Alt Table

Status	Error	Program
	5.9b	(.f64 (/.f64 1 y) (/.f64 1 (.f64 x (fma.f64 z z 1))))
✓	5.8b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
	49.2b	(/.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 y (/.f64 (sqrt.f64 (/.f64 1 x)) (fma.f64 z z 1))))
	5.7b	(*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (fma.f64 z z 1)))
	6.0b	(/.f64 1 (.f64 y (.f64 (+.f64 1 (pow.f64 z 2)) x)))
	6.0b	(/.f64 1 (.f64 (fma.f64 y (.f64 z z) y) x))
▶	5.7b	(.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)))
	20.4b	(.f64 (sqrt.f64 (/.f64 (/.f64 1 x) (.f64 y (fma.f64 z z 1)))) (sqrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))))
	6.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 1 x) (.f64 y (fma.f64 z z 1)))) (cbrt.f64 (/.f64 (/.f64 1 x) (.f64 y (fma.f64 z z 1))))) (cbrt.f64 (/.f64 (/.f64 1 x) (*.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))))
	25.4b	(/.f64 (/.f64 1 x) (cbrt.f64 (.f64 (.f64 (.f64 y (fma.f64 z z 1)) (.f64 y (fma.f64 z z 1))) (*.f64 y (fma.f64 z z 1)))))

Compiler

Compiled 2631 to 1533 computations (41.7% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x)))
✓	0.6b	(cbrt.f64 (/.f64 1 x))
✓	1.7b	(/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1))
✓	3.9b	(.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)))

series427.0ms (4.2%)

Counts

4 → 84

Calls

4 calls:

237.0ms	(.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)))
100.0ms	(/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1))
57.0ms	(*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x)))
32.0ms	(cbrt.f64 (/.f64 1 x))

rewrite142.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

240×	`times-frac_binary64`
205×	`add-sqr-sqrt_binary64`
190×	`cbrt-prod_binary64`
147×	`*-un-lft-identity_binary64`
135×	`add-cube-cbrt_binary64`

Counts

4 → 290

Calls

4 calls:

43.0ms	(.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)))
22.0ms	(*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x)))
10.0ms	(/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1))
5.0ms	(cbrt.f64 (/.f64 1 x))

simplify579.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

539×	`unswap-sqr_binary64`
472×	`fma-def_binary64`
333×	`fma-neg_binary64`
304×	`associate-l_binary64`
295×	`cancel-sign-sub-inv_binary64`

Counts

374 → 446

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	304	8811
1	724	7584
2	2899	7460
3	3853	7377
4	5241	7377

prune743.0ms (7.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	494	6	500
Fresh	4	5	9
Picked	1	0	1
Done	0	1	1
Total	499	12	511

Error

1.6b

Counts

511 → 12

Alt Table

Status	Error	Program
	48.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (*.f64 (/.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 x))) (hypot.f64 1 z)) (/.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 x))) (hypot.f64 1 z))))
	5.8b	(/.f64 (/.f64 1 (*.f64 x (fma.f64 z z 1))) y)
	5.7b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (/.f64 (cbrt.f64 1) (*.f64 (fma.f64 z z 1) (cbrt.f64 x))))
✓	5.8b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
	25.4b	(/.f64 (/.f64 1 x) (cbrt.f64 (.f64 (.f64 (.f64 y (fma.f64 z z 1)) (.f64 y (fma.f64 z z 1))) (*.f64 y (fma.f64 z z 1)))))
▶	4.7b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z))))
	47.8b	(*.f64 (/.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) (hypot.f64 1 z)) (sqrt.f64 y)) (/.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) (hypot.f64 1 z)) (sqrt.f64 y)))
	6.0b	(/.f64 1 (.f64 (fma.f64 y (.f64 z z) y) x))
	5.6b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))
	20.4b	(.f64 (sqrt.f64 (/.f64 (/.f64 1 x) (.f64 y (fma.f64 z z 1)))) (sqrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))))
	6.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 1 x) (.f64 y (fma.f64 z z 1)))) (cbrt.f64 (/.f64 (/.f64 1 x) (.f64 y (fma.f64 z z 1))))) (cbrt.f64 (/.f64 (/.f64 1 x) (*.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))))

Compiler

Compiled 15685 to 11214 computations (28.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y)
	0.5b	(*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x)))
	0.6b	(cbrt.f64 (/.f64 1 x))
✓	3.9b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z))))

series807.0ms (7.9%)

Counts

2 → 60

Calls

2 calls:

660.0ms

(/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y)

146.0ms

(*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z))))

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`add-exp-log_binary64`
61×	`prod-exp_binary64`
58×	`add-cbrt-cube_binary64`
44×	`div-exp_binary64`
33×	`cbrt-unprod_binary64`

Counts

2 → 95

Calls

2 calls:

19.0ms

(*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z))))

7.0ms

(/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y)

simplify148.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

687×	`times-frac_binary64`
445×	`associate-/l/_binary64`
433×	`*-commutative_binary64`
427×	`associate-/r*_binary64`
355×	`fma-def_binary64`

Counts

155 → 149

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	209	5464
1	532	2954
2	1503	2851
3	4184	2795
4	4962	2795
5	4995	2795

prune471.0ms (4.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	345	4	349
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	348	13	361

Error

0.0b

Counts

361 → 13

Alt Table

Status	Error	Program
	48.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (*.f64 (/.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 x))) (hypot.f64 1 z)) (/.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 x))) (hypot.f64 1 z))))
	5.8b	(/.f64 (/.f64 1 (*.f64 x (fma.f64 z z 1))) y)
	5.7b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (/.f64 (cbrt.f64 1) (*.f64 (fma.f64 z z 1) (cbrt.f64 x))))
✓	5.8b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
	2.7b	(/.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (*.f64 (/.f64 1 (hypot.f64 1 z)) (cbrt.f64 (/.f64 1 x)))) (hypot.f64 1 z))
	20.8b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
▶	0.8b	(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))
	6.0b	(/.f64 1 (.f64 (fma.f64 y (.f64 z z) y) x))
	5.6b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))
	20.3b	(.f64 (/.f64 (cbrt.f64 (/.f64 1 (.f64 x x))) (*.f64 y (hypot.f64 1 z))) (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z)))
	20.4b	(.f64 (sqrt.f64 (/.f64 (/.f64 1 x) (.f64 y (fma.f64 z z 1)))) (sqrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))))
	6.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 1 x) (.f64 y (fma.f64 z z 1)))) (cbrt.f64 (/.f64 (/.f64 1 x) (.f64 y (fma.f64 z z 1))))) (cbrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))))
	3.2b	(/.f64 (/.f64 (/.f64 1 (*.f64 y x)) (hypot.f64 1 z)) (hypot.f64 1 z))

Compiler

Compiled 12056 to 9084 computations (24.7% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (hypot.f64 1 z))
✓	0.1b	(/.f64 (/.f64 1 x) (hypot.f64 1 z))
✓	0.8b	(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))

series296.0ms (2.9%)

Counts

3 → 84

Calls

3 calls:

186.0ms	(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))
90.0ms	(/.f64 (/.f64 1 x) (hypot.f64 1 z))
19.0ms	(*.f64 y (hypot.f64 1 z))

rewrite42.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

250×	`times-frac_binary64`
119×	`add-sqr-sqrt_binary64`
117×	`*-un-lft-identity_binary64`
117×	`add-cube-cbrt_binary64`
56×	`associate-/l*_binary64`

Counts

3 → 210

Calls

3 calls:

12.0ms	(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))
5.0ms	(/.f64 (/.f64 1 x) (hypot.f64 1 z))
3.0ms	(*.f64 y (hypot.f64 1 z))

simplify213.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

522×	`associate-*l/_binary64`
502×	`fma-def_binary64`
499×	`associate-/r/_binary64`
350×	`associate-*r/_binary64`
242×	`associate-/r*_binary64`

Counts

294 → 343

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	317	6694
1	789	5989
2	2417	5673
3	4433	5667
4	4971	5667
5	4930	5667

prune435.0ms (4.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	338	5	343
Fresh	6	5	11
Picked	1	0	1
Done	0	1	1
Total	345	11	356

Error

Counts

356 → 11

Alt Table

Status	Error	Program
	5.0b	(*.f64 (/.f64 (/.f64 1 x) y) (/.f64 (/.f64 1 (hypot.f64 1 z)) (hypot.f64 1 z)))
	6.0b	(/.f64 1 (.f64 (fma.f64 y (.f64 z z) y) x))
	5.7b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (/.f64 (cbrt.f64 1) (*.f64 (fma.f64 z z 1) (cbrt.f64 x))))
✓	5.8b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
	1.4b	(*.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 1 z))) y) (/.f64 (/.f64 (/.f64 1 x) (sqrt.f64 (hypot.f64 1 z))) (hypot.f64 1 z)))
	5.6b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))
	1.1b	(/.f64 1 (/.f64 (*.f64 y (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z))))
	0.9b	(/.f64 (/.f64 1 (.f64 x (hypot.f64 1 z))) (.f64 y (hypot.f64 1 z)))
	20.4b	(.f64 (sqrt.f64 (/.f64 (/.f64 1 x) (.f64 y (fma.f64 z z 1)))) (sqrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))))
	47.8b	(/.f64 (/.f64 (/.f64 1 (sqrt.f64 x)) (.f64 (hypot.f64 1 z) (sqrt.f64 x))) (.f64 y (hypot.f64 1 z)))
	3.2b	(/.f64 (/.f64 (/.f64 1 (*.f64 y x)) (hypot.f64 1 z)) (hypot.f64 1 z))

Compiler

Compiled 8121 to 5570 computations (31.4% saved)

regimes2.6s (25%)

Accuracy

Total 1.5b remaining (98.2%)

Threshold costs 0b (0%)

Counts

191 → 1

Compiler

Compiled 40725 to 30536 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	17	21
2	19	21
3	20	21
4	19	21

end8.0ms (0.1%)

Compiler: Compiled 51 to 39 computations (23.5% saved)

sample1.8s (17.1%)

Algorithm

1×

intervals

Results

764.0ms	8000×	body	128	valid
36.0ms	469×	body	128	invalid

Compiler

Compiled 246 to 181 computations (26.4% saved)

Details

analyze696.0ms (6.8%)

sample55.0ms (0.5%)

simplify19.0ms (0.2%)

prune6.0ms (0.1%)

localize15.0ms (0.2%)

series288.0ms (2.8%)

rewrite30.0ms (0.3%)

simplify179.0ms (1.7%)

prune253.0ms (2.5%)

localize18.0ms (0.2%)

series427.0ms (4.2%)

rewrite142.0ms (1.4%)

simplify579.0ms (5.6%)

prune743.0ms (7.2%)

localize12.0ms (0.1%)

series807.0ms (7.9%)

rewrite40.0ms (0.4%)

simplify148.0ms (1.4%)

prune471.0ms (4.6%)

localize7.0ms (0.1%)

series296.0ms (2.9%)

rewrite42.0ms (0.4%)

simplify213.0ms (2.1%)

prune435.0ms (4.2%)

regimes2.6s (25%)

simplify3.0ms (0%)

end8.0ms (0.1%)

sample1.8s (17.1%)

Profiling