Details

analyze863.0ms (7.1%)

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
0%	99.9%	0.1%	6
25%	74.9%	0.1%	7
31.2%	68.6%	0.1%	8
35.9%	64%	0.1%	9
47.6%	49.9%	2.5%	10
49.1%	46.8%	4%	11
51.1%	44.1%	4.8%	12
60.2%	29.9%	9.9%	13
60.6%	27.9%	11.6%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample34.0ms (0.3%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
2.0ms	53×	body	128	invalid

Compiler

Compiled 32 to 22 computations (31.3% saved)

simplify114.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

826×	`associate-*r/_binary64`
769×	`associate-/l/_binary64`
660×	`associate-*l/_binary64`
522×	`associate-/l*_binary64`
421×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	30	16
2	78	14
3	195	14
4	314	14
5	383	14
6	426	14
7	631	14
8	1009	14
9	2204	14
10	2868	14
11	2967	14
12	3079	14
13	3193	14
14	3058	14
15	3712	14
16	4988	14
17	4824	14

prune7.0ms (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

4.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	7.3b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
	14.3b	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))

Compiler

Compiled 78 to 45 computations (42.3% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 y (fma.f64 z z z)) z)
✓	5.1b	(/.f64 y (fma.f64 z z z))
✓	6.9b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))

series262.0ms (2.2%)

Counts

3 → 84

Calls

3 calls:

178.0ms	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
49.0ms	(/.f64 (/.f64 y (fma.f64 z z z)) z)
34.0ms	(/.f64 y (fma.f64 z z z))

rewrite35.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

153×	`times-frac_binary64`
98×	`add-sqr-sqrt_binary64`
89×	`*-un-lft-identity_binary64`
89×	`add-cube-cbrt_binary64`
43×	`associate-r_binary64`

Counts

3 → 168

Calls

3 calls:

13.0ms	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
4.0ms	(/.f64 (/.f64 y (fma.f64 z z z)) z)
2.0ms	(/.f64 y (fma.f64 z z z))

simplify199.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

805×	`fma-def_binary64`
353×	`fma-neg_binary64`
351×	`*-commutative_binary64`
341×	`associate-/r/_binary64`
275×	`sub-neg_binary64`

Counts

252 → 296

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	287	4846
1	687	4599
2	2304	4515
3	3607	4509
4	4817	4509
5	4963	4509

prune422.0ms (3.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	286	10	296
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	287	11	298

Error

1.9b

Counts

298 → 11

Alt Table

Status	Error	Program
	7.3b	(*.f64 x (/.f64 (/.f64 1 (/.f64 (fma.f64 z z z) y)) z))
▶	3.2b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) z))
✓	7.3b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
	14.3b	(.f64 (.f64 x (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 z z z))) 1)) (/.f64 (/.f64 y (sqrt.f64 (fma.f64 z z z))) z))
	27.9b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
	12.9b	(*.f64 x (/.f64 y (/.f64 z (/.f64 1 (fma.f64 z z z)))))
	24.1b	(/.f64 (*.f64 y x) (+.f64 (pow.f64 z 2) (pow.f64 z 3)))
	4.9b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	56.0b	(.f64 (.f64 (sqrt.f64 x) (/.f64 (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z))) (*.f64 (sqrt.f64 x) (/.f64 (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z))))
	24.1b	(.f64 (sqrt.f64 (/.f64 (.f64 y x) (.f64 z (fma.f64 z z z)))) (sqrt.f64 (/.f64 (.f64 y x) (*.f64 z (fma.f64 z z z)))))
	14.6b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 y x) (.f64 z (fma.f64 z z z)))) (cbrt.f64 (/.f64 (.f64 y x) (.f64 z (fma.f64 z z z))))) (cbrt.f64 (/.f64 (.f64 y x) (.f64 z (fma.f64 z z z)))))

Compiler

Compiled 6373 to 1458 computations (77.1% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) z))
✓	2.9b	(/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))
✓	5.2b	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))))
✓	22.6b	(cbrt.f64 (fma.f64 z z z))

series3.7s (30.3%)

Counts

4 → 108

Calls

4 calls:

2.2s	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))))
1.2s	(/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))
227.0ms	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) z))
6.0ms	(cbrt.f64 (fma.f64 z z z))

rewrite213.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

231×	`times-frac_binary64`
129×	`associate-r_binary64`
127×	`add-exp-log_binary64`
126×	`add-sqr-sqrt_binary64`
123×	`*-un-lft-identity_binary64`

Counts

4 → 244

Calls

4 calls:

64.0ms	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) z))
15.0ms	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))))
13.0ms	(/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))
5.0ms	(cbrt.f64 (fma.f64 z z z))

simplify302.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

696×	`associate-*l/_binary64`
421×	`associate-/l*_binary64`
312×	`associate-/r*_binary64`
291×	`times-frac_binary64`
270×	`fma-def_binary64`

Counts

352 → 431

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	562	16302
1	1670	12076
2	4961	12036
3	5102	12036

prune742.0ms (6.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	491	0	491
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	491	11	502

Error

1.9b

Counts

502 → 11

Alt Table

Status	Error	Program
	7.3b	(*.f64 x (/.f64 (/.f64 1 (/.f64 (fma.f64 z z z) y)) z))
✓	3.2b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) z))
✓	7.3b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
	14.3b	(.f64 (.f64 x (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 z z z))) 1)) (/.f64 (/.f64 y (sqrt.f64 (fma.f64 z z z))) z))
	27.9b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
	12.9b	(*.f64 x (/.f64 y (/.f64 z (/.f64 1 (fma.f64 z z z)))))
	24.1b	(/.f64 (*.f64 y x) (+.f64 (pow.f64 z 2) (pow.f64 z 3)))
▶	4.9b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	56.0b	(.f64 (.f64 (sqrt.f64 x) (/.f64 (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z))) (*.f64 (sqrt.f64 x) (/.f64 (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z))))
	24.1b	(.f64 (sqrt.f64 (/.f64 (.f64 y x) (.f64 z (fma.f64 z z z)))) (sqrt.f64 (/.f64 (.f64 y x) (*.f64 z (fma.f64 z z z)))))
	14.6b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 y x) (.f64 z (fma.f64 z z z)))) (cbrt.f64 (/.f64 (.f64 y x) (.f64 z (fma.f64 z z z))))) (cbrt.f64 (/.f64 (.f64 y x) (.f64 z (fma.f64 z z z)))))

Compiler

Compiled 21516 to 4310 computations (80% saved)

localize16.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.2b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
✓	5.0b	(*.f64 x (/.f64 y (fma.f64 z z z)))
	5.1b	(/.f64 y (fma.f64 z z z))

series218.0ms (1.8%)

Counts

2 → 72

Calls

2 calls:

120.0ms	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
97.0ms	(*.f64 x (/.f64 y (fma.f64 z z z)))

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
13×	`associate-r_binary64`
13×	`times-frac_binary64`

Counts

2 → 60

Calls

2 calls:

10.0ms	(*.f64 x (/.f64 y (fma.f64 z z z)))
10.0ms	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)

simplify118.0ms (1%)

Algorithm

1×	egg-herbie

Rules

604×	`fma-neg_binary64`
483×	`associate-l_binary64`
433×	`associate-/r*_binary64`
417×	`associate-r_binary64`
378×	`associate-/r/_binary64`

Counts

132 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	153	2289
1	397	2096
2	1539	1990
3	4439	1990
4	4968	1990

prune160.0ms (1.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	171	4	175
Fresh	5	3	8
Picked	0	1	1
Done	1	1	2
Total	177	9	186

Error

1.4b

Counts

186 → 9

Alt Table

Status	Error	Program
	32.4b	(/.f64 (.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
✓	3.2b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) z))
	14.3b	(/.f64 (.f64 x y) (.f64 z (fma.f64 z z z)))
	27.9b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
▶	4.9b	(/.f64 (.f64 (.f64 x (/.f64 1 (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 y (cbrt.f64 (fma.f64 z z z)))) z)
	12.9b	(*.f64 x (/.f64 y (/.f64 z (/.f64 1 (fma.f64 z z z)))))
	8.9b	(/.f64 (/.f64 (*.f64 y x) (fma.f64 z z z)) z)
✓	4.9b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	14.6b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 y x) (.f64 z (fma.f64 z z z)))) (cbrt.f64 (/.f64 (.f64 y x) (.f64 z (fma.f64 z z z))))) (cbrt.f64 (/.f64 (.f64 y x) (.f64 z (fma.f64 z z z)))))

Compiler

Compiled 3282 to 905 computations (72.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.2b	(/.f64 1 (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))
✓	2.4b	(.f64 (.f64 x (/.f64 1 (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 y (cbrt.f64 (fma.f64 z z z))))
✓	4.5b	(.f64 x (/.f64 1 (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))))
	22.6b	(cbrt.f64 (fma.f64 z z z))

series1.3s (10.5%)

Counts

3 → 72

Calls

3 calls:

1.1s

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

212.0ms

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

14.0ms

(/.f64 1 (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))

rewrite92.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`add-exp-log_binary64`
49×	`prod-exp_binary64`
37×	`add-cbrt-cube_binary64`
29×	`associate-r_binary64`
26×	`times-frac_binary64`

Counts

3 → 137

Calls

3 calls:

28.0ms

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

19.0ms

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

10.0ms

(/.f64 1 (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))

simplify258.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

867×	`times-frac_binary64`
503×	`fma-def_binary64`
378×	`fma-neg_binary64`
366×	`cancel-sign-sub-inv_binary64`
312×	`associate-l_binary64`

Counts

209 → 242

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	268	5476
1	679	3825
2	2475	3574
3	4366	3574
4	4886	3574
5	4936	3574

prune562.0ms (4.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	331	1	332
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	331	10	341

Error

1.0b

Counts

341 → 10

Alt Table

Status	Error	Program
	32.4b	(/.f64 (.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
✓	3.2b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) z))
	14.3b	(/.f64 (.f64 x y) (.f64 z (fma.f64 z z z)))
	27.9b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
	24.6b	(/.f64 (-.f64 (fma.f64 (/.f64 x z) (/.f64 y z) (/.f64 (.f64 x y) (pow.f64 z 4))) (/.f64 (.f64 x y) (pow.f64 z 3))) z)
	12.9b	(*.f64 x (/.f64 y (/.f64 z (/.f64 1 (fma.f64 z z z)))))
✓	4.9b	(/.f64 (.f64 (.f64 x (/.f64 1 (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 y (cbrt.f64 (fma.f64 z z z)))) z)
	8.9b	(/.f64 (/.f64 (*.f64 y x) (fma.f64 z z z)) z)
✓	4.9b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	14.6b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 y x) (.f64 z (fma.f64 z z z)))) (cbrt.f64 (/.f64 (.f64 y x) (.f64 z (fma.f64 z z z))))) (cbrt.f64 (/.f64 (.f64 y x) (.f64 z (fma.f64 z z z)))))

Compiler

Compiled 10562 to 3512 computations (66.7% saved)

regimes1.3s (11%)

Accuracy

Total 3.4b remaining (80.3%)

Threshold costs 0b (0%)

Counts

152 → 1

Compiler

Compiled 20324 to 10326 computations (49.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	46
1	16	46
2	16	46

end6.0ms (0.1%)

Compiler: Compiled 99 to 39 computations (60.6% saved)

sample1.1s (9.3%)

Algorithm

1×

intervals

Results

355.0ms	8000×	body	128	valid
66.0ms	1589×	body	128	invalid

Compiler

Compiled 263 to 124 computations (52.9% saved)

Details

analyze863.0ms (7.1%)

sample34.0ms (0.3%)

simplify114.0ms (0.9%)

prune7.0ms (0.1%)

localize13.0ms (0.1%)

series262.0ms (2.2%)

rewrite35.0ms (0.3%)

simplify199.0ms (1.6%)

prune422.0ms (3.5%)

localize17.0ms (0.1%)

series3.7s (30.3%)

rewrite213.0ms (1.8%)

simplify302.0ms (2.5%)

prune742.0ms (6.1%)

localize16.0ms (0.1%)

series218.0ms (1.8%)

rewrite31.0ms (0.3%)

simplify118.0ms (1%)

prune160.0ms (1.3%)

localize12.0ms (0.1%)

series1.3s (10.5%)

rewrite92.0ms (0.8%)

simplify258.0ms (2.1%)

prune562.0ms (4.6%)

regimes1.3s (11%)

simplify3.0ms (0%)

end6.0ms (0.1%)

sample1.1s (9.3%)

Profiling