Details

analyze530.0ms (8.8%)

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)

sample203.0ms (3.4%)

Algorithm

1×

intervals

Symmetry

(sort x y)

Results

11.0ms	256×	body	128	valid
2.0ms	47×	body	128	invalid

Compiler

Compiled 32 to 22 computations (31.3% saved)

simplify91.0ms (1.5%)

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

prune5.0ms (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

5.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	9.0b	(*.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)
✓	4.9b	(/.f64 y (fma.f64 z z z))
✓	8.5b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))

series181.0ms (3%)

Counts

3 → 84

Calls

3 calls:

99.0ms	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
48.0ms	(/.f64 (/.f64 y (fma.f64 z z z)) z)
33.0ms	(/.f64 y (fma.f64 z z z))

rewrite35.0ms (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:

11.0ms	(*.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 (2.7%)

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

prune267.0ms (4.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	288	8	296
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	288	10	298

Error

1.0b

Counts

298 → 10

Alt Table

Status	Error	Program
	39.9b	(.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z))) (/.f64 (/.f64 (sqrt.f64 y) (sqrt.f64 (fma.f64 z z z))) (sqrt.f64 z)))
✓	9.0b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
	27.0b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
	12.7b	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))
	4.7b	(.f64 (.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
▶	4.5b	(.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)))
	6.3b	(.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))
	32.7b	(.f64 (.f64 x (/.f64 (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z))) (/.f64 (/.f64 (cbrt.f64 y) (sqrt.f64 (fma.f64 z z z))) (sqrt.f64 z)))
	23.3b	(.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)))))
	4.8b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)

Compiler

Compiled 6313 to 1448 computations (77.1% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 z)
✓	0.9b	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
✓	0.9b	(/.f64 (cbrt.f64 y) (fma.f64 z z z))
✓	3.9b	(.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)))

series1.4s (23.5%)

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))))
119.0ms	(.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)))
84.0ms	(/.f64 (cbrt.f64 y) (fma.f64 z z z))
30.0ms	(cbrt.f64 z)

rewrite99.0ms (1.6%)

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)))
10.0ms	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
3.0ms	(/.f64 (cbrt.f64 y) (fma.f64 z z z))
1.0ms	(cbrt.f64 z)

simplify239.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

602×	`associate-*l/_binary64`
574×	`associate-*r/_binary64`
434×	`associate-/l*_binary64`
261×	`times-frac_binary64`
236×	`associate-/r*_binary64`

Counts

382 → 458

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	499	13000
1	1430	9034
2	4966	9026
3	5010	9026

prune398.0ms (6.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	492	0	492
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	492	10	502

Error

1.0b

Counts

502 → 10

Alt Table

Status	Error	Program
	39.9b	(.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z))) (/.f64 (/.f64 (sqrt.f64 y) (sqrt.f64 (fma.f64 z z z))) (sqrt.f64 z)))
✓	9.0b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
	27.0b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
	12.7b	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))
▶	4.7b	(.f64 (.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
✓	4.5b	(.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)))
	6.3b	(.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))
	32.7b	(.f64 (.f64 x (/.f64 (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z))) (/.f64 (/.f64 (cbrt.f64 y) (sqrt.f64 (fma.f64 z z z))) (sqrt.f64 z)))
	23.3b	(.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)))))
	4.8b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)

Compiler

Compiled 17456 to 3283 computations (81.2% saved)

localize7.0ms (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))) (/.f64 1 z))
	4.9b	(/.f64 y (fma.f64 z z z))
✓	5.4b	(*.f64 x (/.f64 y (fma.f64 z z z)))

series172.0ms (2.8%)

Counts

2 → 72

Calls

2 calls:

99.0ms	(.f64 (.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
73.0ms	(*.f64 x (/.f64 y (fma.f64 z z z)))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-exp-log_binary64`
28×	`add-cbrt-cube_binary64`
26×	`associate-r_binary64`
22×	`add-sqr-sqrt_binary64`
22×	`prod-exp_binary64`

Counts

2 → 82

Calls

2 calls:

8.0ms	(.f64 (.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
5.0ms	(*.f64 x (/.f64 y (fma.f64 z z z)))

simplify94.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

924×	`times-frac_binary64`
702×	`fma-neg_binary64`
673×	`associate-/l*_binary64`
340×	`fma-def_binary64`
280×	`cancel-sign-sub-inv_binary64`

Counts

154 → 152

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	173	2699
1	441	2409
2	1622	2310
3	4889	2310
4	5349	2310

prune174.0ms (2.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	200	3	203
Fresh	4	3	7
Picked	0	1	1
Done	1	1	2
Total	205	8	213

Error

0.7b

Counts

213 → 8

Alt Table

Status	Error	Program
	34.0b	(.f64 (.f64 x (*.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) (/.f64 1 z))
✓	9.0b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
	27.0b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
	34.1b	(.f64 (.f64 (/.f64 (*.f64 y x) (fma.f64 z z z)) (sqrt.f64 (/.f64 1 z))) (sqrt.f64 (/.f64 1 z)))
✓	4.7b	(.f64 (.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
	6.3b	(.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))
▶	4.8b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	7.1b	(/.f64 (/.f64 (*.f64 y x) z) (fma.f64 z z z))

Compiler

Compiled 4077 to 1413 computations (65.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.0b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	4.9b	(/.f64 y (fma.f64 z z z))
	5.4b	(*.f64 x (/.f64 y (fma.f64 z z z)))

series105.0ms (1.7%)

Counts

1 → 36

Calls

1 calls:

104.0ms

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

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
4×	`cbrt-undiv_binary64`
4×	`div-exp_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 26

Calls

1 calls:

4.0ms

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

simplify60.0ms (1%)

Algorithm

1×	egg-herbie

Rules

860×	`times-frac_binary64`
690×	`associate-/l*_binary64`
435×	`associate-/l/_binary64`
399×	`associate-*l/_binary64`
323×	`fma-def_binary64`

Counts

62 → 55

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	100	1178
1	264	1060
2	952	1016
3	4879	1016
4	5112	1016

prune126.0ms (2.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	175	8	183

Error

0.7b

Counts

183 → 8

Alt Table

Status	Error	Program
	34.0b	(.f64 (.f64 x (*.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) (/.f64 1 z))
✓	9.0b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
	27.0b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
	34.1b	(.f64 (.f64 (/.f64 (*.f64 y x) (fma.f64 z z z)) (sqrt.f64 (/.f64 1 z))) (sqrt.f64 (/.f64 1 z)))
✓	4.7b	(.f64 (.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
	6.3b	(.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))
✓	4.8b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	7.1b	(/.f64 (/.f64 (*.f64 y x) z) (fma.f64 z z z))

Compiler

Compiled 3083 to 832 computations (73% saved)

regimes807.0ms (13.3%)

Accuracy

Total 2.5b remaining (68.9%)

Threshold costs 0b (0%)

Counts

136 → 1

Compiler

Compiled 16144 to 8525 computations (47.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	41
1	21	41
2	20	41

end7.0ms (0.1%)

Remove: (sort x y)
Compiler: Compiled 87 to 45 computations (48.3% saved)

sample804.0ms (13.3%)

Algorithm

1×

intervals

Results

341.0ms	8000×	body	128	valid
70.0ms	1507×	body	128	invalid

Compiler

Compiled 182 to 102 computations (44% saved)

Details

analyze530.0ms (8.8%)

sample203.0ms (3.4%)

simplify91.0ms (1.5%)

prune5.0ms (0.1%)

localize6.0ms (0.1%)

series181.0ms (3%)

rewrite35.0ms (0.6%)

simplify166.0ms (2.7%)

prune267.0ms (4.4%)

localize15.0ms (0.3%)

series1.4s (23.5%)

rewrite99.0ms (1.6%)

simplify239.0ms (3.9%)

prune398.0ms (6.6%)

localize7.0ms (0.1%)

series172.0ms (2.8%)

rewrite20.0ms (0.3%)

simplify94.0ms (1.6%)

prune174.0ms (2.9%)

localize8.0ms (0.1%)

series105.0ms (1.7%)

rewrite6.0ms (0.1%)

simplify60.0ms (1%)

prune126.0ms (2.1%)

regimes807.0ms (13.3%)

simplify3.0ms (0%)

end7.0ms (0.1%)

sample804.0ms (13.3%)

Profiling