Details

analyze800.0ms (9.2%)

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)

sample35.0ms (0.4%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
2.0ms	61×	body	128	invalid

Compiler

Compiled 32 to 22 computations (31.3% saved)

simplify101.0ms (1.2%)

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

prune3.0ms (0%)

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

5.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	8.7b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
	15.8b	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))

Compiler

Compiled 78 to 45 computations (42.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 y (fma.f64 z z z)) z)
✓	6.1b	(/.f64 y (fma.f64 z z z))
✓	8.0b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))

rewrite30.0ms (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:

12.0ms	(*.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))

series227.0ms (2.6%)

Counts

3 → 84

Calls

3 calls:

131.0ms	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
56.0ms	(/.f64 (/.f64 y (fma.f64 z z z)) z)
39.0ms	(/.f64 y (fma.f64 z z z))

simplify224.0ms (2.6%)

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 → 433

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

prune359.0ms (4.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	421	12	433
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	423	12	435

Error

2.2b

Counts

435 → 12

Alt Table

Status	Error	Program
	23.6b	(.f64 x (cbrt.f64 (.f64 (*.f64 (/.f64 (/.f64 y (fma.f64 z z z)) z) (/.f64 (/.f64 y (fma.f64 z z z)) z)) (/.f64 (/.f64 y (fma.f64 z z z)) z))))
	36.6b	(.f64 (.f64 x (/.f64 y (sqrt.f64 z))) (/.f64 (/.f64 1 (fma.f64 z z z)) (sqrt.f64 z)))
	36.3b	(.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 (/.f64 y z) (hypot.f64 z (sqrt.f64 z)))))
	6.4b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	16.6b	(.f64 (.f64 y x) (/.f64 (/.f64 1 (fma.f64 z z z)) z))
	7.3b	(.f64 (/.f64 x (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 y (cbrt.f64 (fma.f64 z z z))) (cbrt.f64 z)))
	8.7b	(.f64 (.f64 x (/.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 1 (fma.f64 z z z)) (cbrt.f64 z)))
	9.2b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 (/.f64 y (fma.f64 z z z)) z)))
▶	5.1b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (fma.f64 z z z)) (cbrt.f64 z)))
	15.5b	(.f64 (.f64 x (/.f64 (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (sqrt.f64 (fma.f64 z z z))) 1)) (/.f64 (/.f64 (cbrt.f64 y) (sqrt.f64 (fma.f64 z z z))) z))
	8.7b	(*.f64 (/.f64 (/.f64 y (fma.f64 z z z)) z) x)
	16.5b	(.f64 (.f64 x (sqrt.f64 (/.f64 y (fma.f64 z z z)))) (/.f64 (sqrt.f64 (/.f64 y (fma.f64 z z z))) z))

Compiler

Compiled 6431 to 1504 computations (76.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 z)
✓	0.7b	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
✓	2.0b	(/.f64 (cbrt.f64 y) (fma.f64 z z z))
✓	4.2b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (fma.f64 z z z)) (cbrt.f64 z)))

rewrite70.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

260×	`times-frac_binary64`
148×	`add-sqr-sqrt_binary64`
145×	`*-un-lft-identity_binary64`
145×	`add-cube-cbrt_binary64`
141×	`associate-r_binary64`

Counts

4 → 274

Calls

4 calls:

30.0ms	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (fma.f64 z z z)) (cbrt.f64 z)))
8.0ms	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
5.0ms	(/.f64 (cbrt.f64 y) (fma.f64 z z z))
1.0ms	(cbrt.f64 z)

series1.9s (21.6%)

Counts

4 → 108

Calls

4 calls:

1.2s	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
264.0ms	(/.f64 (cbrt.f64 y) (fma.f64 z z z))
221.0ms	(cbrt.f64 z)
162.0ms	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (fma.f64 z z z)) (cbrt.f64 z)))

simplify209.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

609×	`associate-*l/_binary64`
582×	`associate-*r/_binary64`
467×	`associate-/l*_binary64`
319×	`times-frac_binary64`
272×	`associate-/r*_binary64`

Counts

382 → 716

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	518	13048
1	1503	9055
2	5232	9055

prune563.0ms (6.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	712	4	716
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	715	13	728

Error

1.9b

Counts

728 → 13

Alt Table

Status	Error	Program
	8.7b	(.f64 (.f64 x (/.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 1 (fma.f64 z z z)) (cbrt.f64 z)))
▶	6.2b	(.f64 (.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (cbrt.f64 y) (.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z))))) (/.f64 (/.f64 1 (fma.f64 z z z)) (cbrt.f64 (cbrt.f64 z))))
	7.7b	(/.f64 (.f64 (.f64 x (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 y) (fma.f64 z z z))) (.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 z)))
	21.4b	(.f64 (.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 (sqrt.f64 y)) 1) (.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z))))) (/.f64 (/.f64 (cbrt.f64 (sqrt.f64 y)) (fma.f64 z z z)) (cbrt.f64 (cbrt.f64 z))))
	6.4b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	36.3b	(.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 (/.f64 y z) (hypot.f64 z (sqrt.f64 z)))))
	26.1b	(*.f64 (/.f64 y -1) (-.f64 (/.f64 x (pow.f64 z 4)) (/.f64 x (pow.f64 z 3))))
	16.6b	(.f64 (.f64 y x) (/.f64 (/.f64 1 (fma.f64 z z z)) z))
	23.6b	(.f64 x (cbrt.f64 (.f64 (*.f64 (/.f64 (/.f64 y (fma.f64 z z z)) z) (/.f64 (/.f64 y (fma.f64 z z z)) z)) (/.f64 (/.f64 y (fma.f64 z z z)) z))))
	9.2b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 (/.f64 y (fma.f64 z z z)) z)))
	15.5b	(.f64 (.f64 x (/.f64 (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (sqrt.f64 (fma.f64 z z z))) 1)) (/.f64 (/.f64 (cbrt.f64 y) (sqrt.f64 (fma.f64 z z z))) z))
	8.7b	(*.f64 (/.f64 (/.f64 y (fma.f64 z z z)) z) x)
	16.5b	(.f64 (.f64 x (sqrt.f64 (/.f64 y (fma.f64 z z z)))) (/.f64 (sqrt.f64 (/.f64 y (fma.f64 z z z))) z))

Compiler

Compiled 16956 to 3428 computations (79.8% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 z)
✓	0.6b	(/.f64 1 (fma.f64 z z z))
	0.7b	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
✓	5.4b	(.f64 (.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (cbrt.f64 y) (.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z))))) (/.f64 (/.f64 1 (fma.f64 z z z)) (cbrt.f64 (cbrt.f64 z))))

rewrite93.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

666×	`add-exp-log_binary64`
350×	`prod-exp_binary64`
236×	`div-exp_binary64`
218×	`add-cbrt-cube_binary64`
210×	`cbrt-unprod_binary64`

Counts

2 → 327

Calls

2 calls:

40.0ms

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

2.0ms

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

series149.0ms (1.7%)

Counts

2 → 48

Calls

2 calls:

146.0ms

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

3.0ms

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

simplify514.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

523×	`associate-r_binary64`
467×	`associate-*r/_binary64`
442×	`associate-*l/_binary64`
347×	`*-commutative_binary64`
329×	`fma-def_binary64`

Counts

375 → 732

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	460	24359
1	1144	13982
2	4175	13265
3	4605	12785
4	4987	12785
5	4992	12785

prune559.0ms (6.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	902	1	903
Fresh	4	8	12
Picked	0	1	1
Done	0	0	0
Total	906	10	916

Error

1.9b

Counts

916 → 10

Alt Table

Status	Error	Program
	10.4b	(/.f64 (/.f64 (*.f64 y x) (fma.f64 z z z)) z)
	23.6b	(.f64 x (cbrt.f64 (.f64 (*.f64 (/.f64 (/.f64 y (fma.f64 z z z)) z) (/.f64 (/.f64 y (fma.f64 z z z)) z)) (/.f64 (/.f64 y (fma.f64 z z z)) z))))
	36.3b	(.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 (/.f64 y z) (hypot.f64 z (sqrt.f64 z)))))
▶	6.4b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	16.6b	(.f64 (.f64 y x) (/.f64 (/.f64 1 (fma.f64 z z z)) z))
✓	6.2b	(.f64 (.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (cbrt.f64 y) (.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z))))) (/.f64 (/.f64 1 (fma.f64 z z z)) (cbrt.f64 (cbrt.f64 z))))
	9.2b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 (/.f64 y (fma.f64 z z z)) z)))
	15.5b	(.f64 (.f64 x (/.f64 (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (sqrt.f64 (fma.f64 z z z))) 1)) (/.f64 (/.f64 (cbrt.f64 y) (sqrt.f64 (fma.f64 z z z))) z))
	8.7b	(*.f64 (/.f64 (/.f64 y (fma.f64 z z z)) z) x)
	16.5b	(.f64 (.f64 x (sqrt.f64 (/.f64 y (fma.f64 z z z)))) (/.f64 (sqrt.f64 (/.f64 y (fma.f64 z z z))) z))

Compiler

Compiled 25467 to 4904 computations (80.7% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.3b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	6.1b	(/.f64 y (fma.f64 z z z))
✓	7.5b	(*.f64 x (/.f64 y (fma.f64 z z z)))

rewrite20.0ms (0.2%)

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:

9.0ms	(*.f64 x (/.f64 y (fma.f64 z z z)))
7.0ms	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)

series202.0ms (2.3%)

Counts

2 → 72

Calls

2 calls:

107.0ms	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
95.0ms	(*.f64 x (/.f64 y (fma.f64 z z z)))

simplify110.0ms (1.3%)

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 → 246

Iterations

Useful iterations: 2 (0.0ms)

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

prune183.0ms (2.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	327	5	332
Fresh	5	3	8
Picked	1	0	1
Done	0	1	1
Total	333	9	342

Error

1.7b

Counts

342 → 9

Alt Table

Status	Error	Program
	9.2b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 (/.f64 y (fma.f64 z z z)) z)))
	8.6b	(/.f64 x (/.f64 z (/.f64 y (fma.f64 z z z))))
	34.4b	(/.f64 (.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
✓	6.2b	(.f64 (.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (cbrt.f64 y) (.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z))))) (/.f64 (/.f64 1 (fma.f64 z z z)) (cbrt.f64 (cbrt.f64 z))))
	10.5b	(/.f64 (.f64 (.f64 x y) (/.f64 1 (fma.f64 z z z))) z)
	10.4b	(/.f64 (/.f64 (*.f64 y x) (+.f64 (pow.f64 z 2) z)) z)
	6.4b	(/.f64 (*.f64 x (/.f64 y (+.f64 (pow.f64 z 2) z))) z)
	8.7b	(*.f64 (/.f64 (/.f64 y (fma.f64 z z z)) z) x)
	16.5b	(.f64 (.f64 x (sqrt.f64 (/.f64 y (fma.f64 z z z)))) (/.f64 (sqrt.f64 (/.f64 y (fma.f64 z z z))) z))

Compiler

Compiled 3112 to 851 computations (72.7% saved)

regimes1.2s (13.8%)

Accuracy

Total 2.8b remaining (69.6%)

Threshold costs 0b (0%)

Compiler

Compiled 27205 to 13856 computations (49.1% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	84
1	23	84
2	23	84

end8.0ms (0.1%)

Compiler: Compiled 165 to 57 computations (65.5% saved)

sample1.1s (12.7%)

Algorithm

1×

intervals

Results

353.0ms	8000×	body	128	valid
71.0ms	1582×	body	128	invalid

Compiler

Compiled 242 to 121 computations (50% saved)

Details

analyze800.0ms (9.2%)

sample35.0ms (0.4%)

simplify101.0ms (1.2%)

prune3.0ms (0%)

localize6.0ms (0.1%)

rewrite30.0ms (0.3%)

series227.0ms (2.6%)

simplify224.0ms (2.6%)

prune359.0ms (4.1%)

localize14.0ms (0.2%)

rewrite70.0ms (0.8%)

series1.9s (21.6%)

simplify209.0ms (2.4%)

prune563.0ms (6.5%)

localize21.0ms (0.2%)

rewrite93.0ms (1.1%)

series149.0ms (1.7%)

simplify514.0ms (5.9%)

prune559.0ms (6.4%)

localize14.0ms (0.2%)

rewrite20.0ms (0.2%)

series202.0ms (2.3%)

simplify110.0ms (1.3%)

prune183.0ms (2.1%)

regimes1.2s (13.8%)

simplify4.0ms (0%)

end8.0ms (0.1%)

sample1.1s (12.7%)

Profiling