Details

analyze591.0ms (8.4%)

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
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)

sample1.3s (18.4%)

Symmetry

(sort x y)

Results

925.0ms	8256×	body	128	valid
179.0ms	1600×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify99.0ms (1.4%)

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

prune4.0ms (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

4.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	9.4b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
	14.9b	(/.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)
✓	7.0b	(/.f64 y (fma.f64 z z z))
✓	8.8b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))

series193.0ms (2.7%)

Counts

3 → 84

Calls

3 calls:

105.0ms	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
53.0ms	(/.f64 (/.f64 y (fma.f64 z z z)) z)
36.0ms	(/.f64 y (fma.f64 z z z))

rewrite39.0ms (0.6%)

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))

simplify166.0ms (2.4%)

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

prune321.0ms (4.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	285	11	296
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	286	12	298

Error

2.0b

Counts

298 → 12

Alt Table

Status	Error	Program
	15.3b	(.f64 (.f64 y x) (/.f64 (/.f64 1 (fma.f64 z z z)) z))
	34.7b	(.f64 (.f64 x (/.f64 y (sqrt.f64 z))) (/.f64 (/.f64 1 (fma.f64 z z z)) (sqrt.f64 z)))
	24.4b	(*.f64 x (/.f64 (/.f64 y z) z))
	31.0b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
	12.9b	(.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))
	9.4b	(.f64 x (.f64 (/.f64 y (fma.f64 z z z)) (/.f64 1 z)))
	14.9b	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))
	34.1b	(.f64 (/.f64 x (.f64 (sqrt.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))) (sqrt.f64 z)))
	14.1b	(.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))
▶	4.8b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	6.2b	(.f64 (/.f64 x (.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))) z))
	14.4b	(.f64 (.f64 x (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 z z z))) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 y (sqrt.f64 (fma.f64 z z z))) (cbrt.f64 z)))

Compiler

Compiled 6392 to 1497 computations (76.6% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.1b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
✓	5.0b	(*.f64 x (/.f64 y (fma.f64 z z z)))
	7.0b	(/.f64 y (fma.f64 z z z))

series180.0ms (2.5%)

Counts

2 → 72

Calls

2 calls:

106.0ms	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
74.0ms	(*.f64 x (/.f64 y (fma.f64 z z z)))

rewrite16.0ms (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:

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

simplify83.0ms (1.2%)

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

prune264.0ms (3.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	173	2	175
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	177	10	187

Error

1.3b

Counts

187 → 10

Alt Table

Status	Error	Program
	14.9b	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))
	32.2b	(/.f64 (.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
	24.4b	(*.f64 x (/.f64 (/.f64 y z) z))
	31.0b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
	10.3b	(/.f64 (.f64 (.f64 x y) (/.f64 1 (fma.f64 z z z))) z)
	9.4b	(.f64 x (.f64 (/.f64 y (fma.f64 z z z)) (/.f64 1 z)))
	14.1b	(.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))
✓	4.8b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
▶	6.2b	(.f64 (/.f64 x (.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))) z))
	15.3b	(.f64 (.f64 y x) (/.f64 (/.f64 1 (fma.f64 z z z)) z))

Compiler

Compiled 3273 to 932 computations (71.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))
✓	3.7b	(.f64 (/.f64 x (.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))) z))
✓	3.9b	(/.f64 x (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))
✓	23.0b	(cbrt.f64 (fma.f64 z z z))

series943.0ms (13.3%)

Counts

4 → 84

Calls

4 calls:

816.0ms	(/.f64 x (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))
110.0ms	(.f64 (/.f64 x (.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))) z))
9.0ms	(*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))
7.0ms	(cbrt.f64 (fma.f64 z z z))

rewrite67.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

140×	`times-frac_binary64`
113×	`add-sqr-sqrt_binary64`
79×	`*-un-lft-identity_binary64`
79×	`add-cube-cbrt_binary64`
76×	`associate-r_binary64`

Counts

4 → 195

Calls

4 calls:

24.0ms	(.f64 (/.f64 x (.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))) z))
7.0ms	(*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))
4.0ms	(/.f64 x (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))
1.0ms	(cbrt.f64 (fma.f64 z z z))

simplify173.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

460×	`associate-*r/_binary64`
329×	`associate-*l/_binary64`
308×	`associate-/l*_binary64`
299×	`associate-/r*_binary64`
280×	`fma-def_binary64`

Counts

279 → 329

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	412	8533
1	1210	6980
2	4720	6950
3	5002	6950

prune375.0ms (5.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	388	1	389
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	388	11	399

Error

1.3b

Counts

399 → 11

Alt Table

Status	Error	Program
	14.9b	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))
	32.2b	(/.f64 (.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
▶	6.3b	(.f64 (/.f64 x (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))) (/.f64 (/.f64 y (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z z z))) (cbrt.f64 (cbrt.f64 (fma.f64 z z z)))) (cbrt.f64 (cbrt.f64 (fma.f64 z z z))))) z))
✓	6.2b	(.f64 (/.f64 x (.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))) z))
	24.4b	(*.f64 x (/.f64 (/.f64 y z) z))
	31.0b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
	10.3b	(/.f64 (.f64 (.f64 x y) (/.f64 1 (fma.f64 z z z))) z)
	9.4b	(.f64 x (.f64 (/.f64 y (fma.f64 z z z)) (/.f64 1 z)))
	14.1b	(.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))
✓	4.8b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	15.3b	(.f64 (.f64 y x) (/.f64 (/.f64 1 (fma.f64 z z z)) z))

Compiler

Compiled 13040 to 2688 computations (79.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z z z))) (cbrt.f64 (cbrt.f64 (fma.f64 z z z))))
✓	3.7b	(.f64 (/.f64 x (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))) (/.f64 (/.f64 y (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z z z))) (cbrt.f64 (cbrt.f64 (fma.f64 z z z)))) (cbrt.f64 (cbrt.f64 (fma.f64 z z z))))) z))
	3.9b	(/.f64 x (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))
	23.0b	(cbrt.f64 (fma.f64 z z z))

series122.0ms (1.7%)

Counts

2 → 48

Calls

2 calls:

114.0ms

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

7.0ms

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

rewrite61.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`add-exp-log_binary64`
58×	`add-sqr-sqrt_binary64`
55×	`add-cbrt-cube_binary64`
54×	`cbrt-prod_binary64`
37×	`times-frac_binary64`

Counts

2 → 136

Calls

2 calls:

23.0ms

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

6.0ms

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

simplify128.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

484×	`associate-/r/_binary64`
332×	`associate-/r*_binary64`
320×	`times-frac_binary64`
291×	`fma-def_binary64`
264×	`associate-*r/_binary64`

Counts

184 → 234

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	310	6622
1	750	4546
2	3343	4074
3	5189	4074

prune427.0ms (6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	428	1	429
Fresh	2	6	8
Picked	0	1	1
Done	0	2	2
Total	430	10	440

Error

1.3b

Counts

440 → 10

Alt Table

Status	Error	Program
	14.9b	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))
	32.2b	(/.f64 (.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
✓	6.3b	(.f64 (/.f64 x (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))) (/.f64 (/.f64 y (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z z z))) (cbrt.f64 (cbrt.f64 (fma.f64 z z z)))) (cbrt.f64 (cbrt.f64 (fma.f64 z z z))))) z))
✓	6.2b	(.f64 (/.f64 x (.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))) z))
	10.3b	(/.f64 (.f64 (.f64 x y) (/.f64 1 (fma.f64 z z z))) z)
	14.1b	(.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))
✓	4.8b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	15.3b	(.f64 (.f64 y x) (/.f64 (/.f64 1 (fma.f64 z z z)) z))
	9.4b	(.f64 x (/.f64 1 (.f64 (/.f64 (fma.f64 z z z) y) z)))
	31.0b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))

Compiler

Compiled 19966 to 3616 computations (81.9% saved)

regimes1.2s (17%)

Accuracy

Total 3.7b remaining (77.9%)

Threshold costs 0b (0%)

Counts

203 → 1

Compiler

Compiled 25416 to 13085 computations (48.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	38
1	16	38
2	16	38

end284.0ms (4%)

Compiler: Compiled 303 to 149 computations (50.8% saved)

Details

analyze591.0ms (8.4%)

sample1.3s (18.4%)

simplify99.0ms (1.4%)

prune4.0ms (0%)

localize6.0ms (0.1%)

series193.0ms (2.7%)

rewrite39.0ms (0.6%)

simplify166.0ms (2.4%)

prune321.0ms (4.5%)

localize6.0ms (0.1%)

series180.0ms (2.5%)

rewrite16.0ms (0.2%)

simplify83.0ms (1.2%)

prune264.0ms (3.7%)

localize10.0ms (0.1%)

series943.0ms (13.3%)

rewrite67.0ms (0.9%)

simplify173.0ms (2.4%)

prune375.0ms (5.3%)

localize13.0ms (0.2%)

series122.0ms (1.7%)

rewrite61.0ms (0.9%)

simplify128.0ms (1.8%)

prune427.0ms (6%)

regimes1.2s (17%)

simplify3.0ms (0%)

end284.0ms (4%)

Profiling