Details

analyze514.0ms (7.3%)

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)

sample1.4s (20.3%)

Symmetry

(sort x y)

Results

1.0s	8256×	body	128	valid
211.0ms	1609×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify93.0ms (1.3%)

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 (0.1%)

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

4.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	7.6b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
	12.7b	(/.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))
✓	7.2b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))

series211.0ms (3%)

Counts

3 → 84

Calls

3 calls:

117.0ms	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
53.0ms	(/.f64 (/.f64 y (fma.f64 z z z)) z)
41.0ms	(/.f64 y (fma.f64 z z z))

rewrite56.0ms (0.8%)

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:

32.0ms	(*.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))

simplify167.0ms (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

prune307.0ms (4.4%)

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

1.4b

Counts

298 → 11

Alt Table

Status	Error	Program
▶	4.7b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	15.8b	(.f64 x (.f64 (sqrt.f64 (/.f64 y (fma.f64 z z z))) (/.f64 (sqrt.f64 (/.f64 y (fma.f64 z z z))) z)))
	6.4b	(.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))
	54.8b	(.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))))
	21.3b	(.f64 (.f64 x (sqrt.f64 y)) (/.f64 (/.f64 (sqrt.f64 y) (fma.f64 z z z)) z))
	32.0b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
	6.4b	(.f64 (.f64 x (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))) 1)) (/.f64 (/.f64 y (cbrt.f64 (fma.f64 z z z))) z))
	12.7b	(/.f64 (.f64 y x) (.f64 z (fma.f64 z z z)))
✓	7.6b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
	12.6b	(.f64 (.f64 y x) (/.f64 (/.f64 1 (fma.f64 z z z)) z))
	36.7b	(.f64 (.f64 x (/.f64 y (sqrt.f64 z))) (/.f64 (/.f64 1 (fma.f64 z z z)) (sqrt.f64 z)))

Compiler

Compiled 6327 to 1450 computations (77.1% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
✓	6.2b	(*.f64 x (/.f64 y (fma.f64 z z z)))
	7.0b	(/.f64 y (fma.f64 z z z))

series187.0ms (2.7%)

Counts

2 → 72

Calls

2 calls:

113.0ms	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
74.0ms	(*.f64 x (/.f64 y (fma.f64 z z z)))

rewrite13.0ms (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)))
4.0ms	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)

simplify84.0ms (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

prune155.0ms (2.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	173	2	175
Fresh	4	5	9
Picked	0	1	1
Done	0	1	1
Total	177	9	186

Error

1.2b

Counts

186 → 9

Alt Table

Status	Error	Program
	21.3b	(.f64 (.f64 x (sqrt.f64 y)) (/.f64 (/.f64 (sqrt.f64 y) (fma.f64 z z z)) z))
	32.0b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
	12.7b	(/.f64 (.f64 y x) (.f64 z (fma.f64 z z z)))
	34.0b	(/.f64 (.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
✓	4.7b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
▶	6.4b	(.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))
✓	7.6b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
	12.6b	(.f64 (.f64 y x) (/.f64 (/.f64 1 (fma.f64 z z z)) z))
	7.6b	(/.f64 (/.f64 (*.f64 y x) (fma.f64 z z z)) z)

Compiler

Compiled 3216 to 893 computations (72.2% saved)

localize9.0ms (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)))
✓	3.9b	(/.f64 x (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))
✓	3.9b	(.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))
✓	22.3b	(cbrt.f64 (fma.f64 z z z))

series894.0ms (12.8%)

Counts

4 → 84

Calls

4 calls:

773.0ms	(/.f64 x (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))
108.0ms	(.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)))
6.0ms	(cbrt.f64 (fma.f64 z z z))

rewrite64.0ms (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:

23.0ms	(.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))
5.0ms	(*.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 (2.5%)

Algorithm

1×	egg-herbie

Rules

460×	`associate-*r/_binary64`
329×	`associate-*l/_binary64`
309×	`associate-/l*_binary64`
300×	`associate-/r*_binary64`
280×	`fma-def_binary64`

Counts

279 → 337

Iterations

Useful iterations: 2 (0.0ms)

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

prune316.0ms (4.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	397	0	397
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	397	9	406

Error

1.2b

Counts

406 → 9

Alt Table

Status	Error	Program
	21.3b	(.f64 (.f64 x (sqrt.f64 y)) (/.f64 (/.f64 (sqrt.f64 y) (fma.f64 z z z)) z))
	32.0b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
	12.7b	(/.f64 (.f64 y x) (.f64 z (fma.f64 z z z)))
	34.0b	(/.f64 (.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
✓	4.7b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
✓	6.4b	(.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))
✓	7.6b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
	12.6b	(.f64 (.f64 y x) (/.f64 (/.f64 1 (fma.f64 z z z)) z))
▶	7.6b	(/.f64 (/.f64 (*.f64 y x) (fma.f64 z z z)) z)

Compiler

Compiled 13250 to 2634 computations (80.1% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (/.f64 (*.f64 y x) (fma.f64 z z z)) z)
✓	11.1b	(/.f64 (*.f64 y x) (fma.f64 z z z))

series186.0ms (2.7%)

Counts

2 → 72

Calls

2 calls:

109.0ms	(/.f64 (/.f64 (*.f64 y x) (fma.f64 z z z)) z)
76.0ms	(/.f64 (*.f64 y x) (fma.f64 z z z))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`

Counts

2 → 73

Calls

2 calls:

5.0ms	(/.f64 (/.f64 (*.f64 y x) (fma.f64 z z z)) z)
3.0ms	(/.f64 (*.f64 y x) (fma.f64 z z z))

simplify93.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

695×	`fma-def_binary64`
525×	`associate-/r*_binary64`
470×	`associate-*l/_binary64`
392×	`associate-l_binary64`
327×	`associate-*r/_binary64`

Counts

145 → 137

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	2800
1	430	2607
2	1478	2497
3	4503	2497
4	5137	2497

prune139.0ms (2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	133	4	137
Fresh	2	3	5
Picked	0	1	1
Done	1	2	3
Total	136	10	146

Error

0.7b

Counts

146 → 10

Alt Table

Status	Error	Program
	34.7b	(*.f64 (/.f64 y (hypot.f64 z (sqrt.f64 z))) (/.f64 (/.f64 x (hypot.f64 z (sqrt.f64 z))) z))
	33.3b	(/.f64 (*.f64 (/.f64 y (hypot.f64 z (sqrt.f64 z))) (/.f64 x (hypot.f64 z (sqrt.f64 z)))) z)
	21.3b	(.f64 (.f64 x (sqrt.f64 y)) (/.f64 (/.f64 (sqrt.f64 y) (fma.f64 z z z)) z))
	32.0b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
	4.7b	(/.f64 (/.f64 y (/.f64 (fma.f64 z z z) x)) z)
	34.0b	(/.f64 (.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
	7.7b	(/.f64 (/.f64 y 1) (/.f64 z (/.f64 x (fma.f64 z z z))))
✓	6.4b	(.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))
✓	7.6b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
✓	7.6b	(/.f64 (/.f64 (*.f64 y x) (fma.f64 z z z)) z)

Compiler

Compiled 2608 to 626 computations (76% saved)

regimes1.7s (24.5%)

Accuracy

Total 2.0b remaining (66%)

Threshold costs 0b (0%)

Counts

142 → 2

Compiler

Compiled 17730 to 8890 computations (49.9% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 10 to 7 computations (30% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	84
1	35	84
2	34	84

end154.0ms (2.2%)

Remove: (sort x y)
Compiler: Compiled 397 to 189 computations (52.4% saved)

Details

analyze514.0ms (7.3%)

sample1.4s (20.3%)

simplify93.0ms (1.3%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series211.0ms (3%)

rewrite56.0ms (0.8%)

simplify167.0ms (2.4%)

prune307.0ms (4.4%)

localize7.0ms (0.1%)

series187.0ms (2.7%)

rewrite13.0ms (0.2%)

simplify84.0ms (1.2%)

prune155.0ms (2.2%)

localize9.0ms (0.1%)

series894.0ms (12.8%)

rewrite64.0ms (0.9%)

simplify173.0ms (2.5%)

prune316.0ms (4.5%)

localize6.0ms (0.1%)

series186.0ms (2.7%)

rewrite13.0ms (0.2%)

simplify93.0ms (1.3%)

prune139.0ms (2%)

regimes1.7s (24.5%)

bsearch5.0ms (0.1%)

simplify3.0ms (0%)

end154.0ms (2.2%)

Profiling