Details

analyze208.0ms (2.5%)

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
49.9%	49.9%	0.1%	4
49.9%	49.9%	0.1%	5
49.9%	49.9%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
74.9%	25%	0.1%	9
74.9%	25%	0.1%	10
74.9%	25%	0.1%	11
74.9%	25%	0.1%	12
87.4%	12.5%	0.1%	13
87.4%	12.5%	0.1%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample951.0ms (11.3%)

Infinites

25.5% of outputs are infinite.

Symmetry

(sort x y)

Results

725.0ms

8256×

body

128

valid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify97.0ms (1.1%)

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

4.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	7.4b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
	11.7b	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))

Compiler

Compiled 78 to 45 computations (42.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 y (fma.f64 z z z)) z)
✓	4.3b	(/.f64 y (fma.f64 z z z))
✓	6.6b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))

series196.0ms (2.3%)

Counts

3 → 84

Calls

3 calls:

111.0ms	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
49.0ms	(/.f64 (/.f64 y (fma.f64 z z z)) z)
36.0ms	(/.f64 y (fma.f64 z z z))

rewrite36.0ms (0.4%)

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))

simplify175.0ms (2.1%)

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

prune332.0ms (3.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

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

Error

1.4b

Counts

298 → 11

Alt Table

Status	Error	Program
	41.1b	(.f64 x (/.f64 (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z)))) z))
	11.7b	(.f64 (.f64 y x) (/.f64 (/.f64 1 (fma.f64 z z z)) z))
	18.4b	(*.f64 x (/.f64 y (+.f64 (pow.f64 z 2) (pow.f64 z 3))))
	21.6b	(.f64 (.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (sqrt.f64 (fma.f64 z z z))) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (sqrt.f64 (fma.f64 z z z))) (cbrt.f64 z)))
	4.7b	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (/.f64 y (fma.f64 z z z)) (cbrt.f64 z)))
	19.5b	(.f64 (.f64 x (/.f64 (sqrt.f64 y) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (sqrt.f64 y) (cbrt.f64 (fma.f64 z z z))) z))
	4.3b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
▶	3.0b	(.f64 (.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) (cbrt.f64 z)))
	11.7b	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))
	7.4b	(.f64 x (/.f64 (.f64 1 (/.f64 y (fma.f64 z z z))) z))
	24.1b	(.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 6394 to 1489 computations (76.7% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 z)
✓	3.3b	(/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))
✓	5.8b	(.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))) (.f64 (cbrt.f64 z) (cbrt.f64 z))))
✓	15.5b	(cbrt.f64 (fma.f64 z z z))

series2.9s (34.8%)

Counts

4 → 84

Calls

4 calls:

2.2s	(.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))) (.f64 (cbrt.f64 z) (cbrt.f64 z))))
693.0ms	(/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))
29.0ms	(cbrt.f64 z)
8.0ms	(cbrt.f64 (fma.f64 z z z))

rewrite33.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-exp-log_binary64`
35×	`add-cbrt-cube_binary64`
28×	`cbrt-unprod_binary64`
28×	`prod-exp_binary64`
22×	`cbrt-undiv_binary64`

Counts

4 → 98

Calls

4 calls:

12.0ms	(.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))) (.f64 (cbrt.f64 z) (cbrt.f64 z))))
6.0ms	(/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))
1.0ms	(cbrt.f64 (fma.f64 z z z))
1.0ms	(cbrt.f64 z)

simplify150.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

809×	`fma-def_binary64`
301×	`fma-neg_binary64`
285×	`times-frac_binary64`
231×	`associate-r_binary64`
230×	`associate-l_binary64`

Counts

182 → 200

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	351	7046
1	925	5135
2	3568	4514
3	4932	4514
4	4963	4514

prune336.0ms (4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	294	0	294
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	294	11	305

Error

1.4b

Counts

305 → 11

Alt Table

Status	Error	Program
	41.1b	(.f64 x (/.f64 (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z)))) z))
	11.7b	(.f64 (.f64 y x) (/.f64 (/.f64 1 (fma.f64 z z z)) z))
	18.4b	(*.f64 x (/.f64 y (+.f64 (pow.f64 z 2) (pow.f64 z 3))))
	21.6b	(.f64 (.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (sqrt.f64 (fma.f64 z z z))) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (sqrt.f64 (fma.f64 z z z))) (cbrt.f64 z)))
	4.7b	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (/.f64 y (fma.f64 z z z)) (cbrt.f64 z)))
	19.5b	(.f64 (.f64 x (/.f64 (sqrt.f64 y) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (sqrt.f64 y) (cbrt.f64 (fma.f64 z z z))) z))
▶	4.3b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
✓	3.0b	(.f64 (.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) (cbrt.f64 z)))
	11.7b	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))
	7.4b	(.f64 x (/.f64 (.f64 1 (/.f64 y (fma.f64 z z z))) z))
	24.1b	(.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 14160 to 3782 computations (73.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.5b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	4.3b	(/.f64 y (fma.f64 z z z))
✓	5.3b	(*.f64 x (/.f64 y (fma.f64 z z z)))

series167.0ms (2%)

Counts

2 → 72

Calls

2 calls:

99.0ms	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
68.0ms	(*.f64 x (/.f64 y (fma.f64 z z z)))

rewrite17.0ms (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)

simplify82.0ms (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

prune213.0ms (2.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	173	2	175
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	175	11	186

Error

0.7b

Counts

186 → 11

Alt Table

Status	Error	Program
	19.5b	(.f64 (.f64 x (/.f64 (sqrt.f64 y) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (sqrt.f64 y) (cbrt.f64 (fma.f64 z z z))) z))
	11.7b	(/.f64 (.f64 x y) (.f64 z (fma.f64 z z z)))
	41.1b	(.f64 x (/.f64 (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z)))) z))
	11.7b	(.f64 (.f64 y x) (/.f64 (/.f64 1 (fma.f64 z z z)) z))
	18.4b	(*.f64 x (/.f64 y (+.f64 (pow.f64 z 2) (pow.f64 z 3))))
	38.9b	(/.f64 (.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
	21.6b	(.f64 (.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (sqrt.f64 (fma.f64 z z z))) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (sqrt.f64 (fma.f64 z z z))) (cbrt.f64 z)))
▶	4.7b	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (/.f64 y (fma.f64 z z z)) (cbrt.f64 z)))
✓	4.3b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
✓	3.0b	(.f64 (.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) (cbrt.f64 z)))
	7.4b	(.f64 x (/.f64 (.f64 1 (/.f64 y (fma.f64 z z z))) z))

Compiler

Compiled 3373 to 970 computations (71.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
	0.6b	(cbrt.f64 z)
✓	3.4b	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (/.f64 y (fma.f64 z z z)) (cbrt.f64 z)))
	4.3b	(/.f64 y (fma.f64 z z z))

series142.0ms (1.7%)

Counts

2 → 48

Calls

2 calls:

101.0ms	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (/.f64 y (fma.f64 z z z)) (cbrt.f64 z)))
41.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))

rewrite88.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

152×	`times-frac_binary64`
121×	`add-sqr-sqrt_binary64`
88×	`associate-r_binary64`
81×	`*-un-lft-identity_binary64`
81×	`add-cube-cbrt_binary64`

Counts

2 → 173

Calls

2 calls:

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

simplify200.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

485×	`fma-def_binary64`
461×	`associate-*r/_binary64`
325×	`associate-*l/_binary64`
319×	`associate-/l*_binary64`
264×	`times-frac_binary64`

Counts

221 → 294

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	314	5866
1	914	4878
2	4058	4574
3	4728	4574
4	4956	4574

prune489.0ms (5.8%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	392	1	393
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	393	11	404

Error

0.7b

Counts

404 → 11

Alt Table

Status	Error	Program
	11.7b	(/.f64 (.f64 y x) (.f64 z (+.f64 (pow.f64 z 2) z)))
✓	4.3b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	41.1b	(.f64 x (/.f64 (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z)))) z))
	11.7b	(.f64 (.f64 y x) (/.f64 (/.f64 1 (fma.f64 z z z)) z))
	18.4b	(*.f64 x (/.f64 y (+.f64 (pow.f64 z 2) (pow.f64 z 3))))
	38.9b	(/.f64 (.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
	21.6b	(.f64 (.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (sqrt.f64 (fma.f64 z z z))) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (sqrt.f64 (fma.f64 z z z))) (cbrt.f64 z)))
✓	4.7b	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (/.f64 y (fma.f64 z z z)) (cbrt.f64 z)))
	19.5b	(.f64 (.f64 x (/.f64 (sqrt.f64 y) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (sqrt.f64 y) (cbrt.f64 (fma.f64 z z z))) z))
✓	3.0b	(.f64 (.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) (cbrt.f64 z)))
	7.4b	(.f64 x (/.f64 (.f64 1 (/.f64 y (fma.f64 z z z))) z))

Compiler

Compiled 10749 to 1839 computations (82.9% saved)

regimes1.2s (14.8%)

Accuracy

Total 2.0b remaining (67.2%)

Threshold costs 0b (0%)

Counts

208 → 1

Compiler

Compiled 28669 to 14504 computations (49.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	58
1	19	58
2	19	58

end288.0ms (3.4%)

Compiler: Compiled 395 to 183 computations (53.7% saved)

Details

analyze208.0ms (2.5%)

sample951.0ms (11.3%)

simplify97.0ms (1.1%)

prune4.0ms (0%)

localize7.0ms (0.1%)

series196.0ms (2.3%)

rewrite36.0ms (0.4%)

simplify175.0ms (2.1%)

prune332.0ms (3.9%)

localize19.0ms (0.2%)

series2.9s (34.8%)

rewrite33.0ms (0.4%)

simplify150.0ms (1.8%)

prune336.0ms (4%)

localize6.0ms (0.1%)

series167.0ms (2%)

rewrite17.0ms (0.2%)

simplify82.0ms (1%)

prune213.0ms (2.5%)

localize12.0ms (0.1%)

series142.0ms (1.7%)

rewrite88.0ms (1%)

simplify200.0ms (2.4%)

prune489.0ms (5.8%)

regimes1.2s (14.8%)

simplify3.0ms (0%)

end288.0ms (3.4%)

Profiling