Details

analyze433.0ms (14.3%)

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
37.4%	62.4%	0.1%	8
39%	60.8%	0.1%	9
51.5%	48.4%	0.1%	10
58.5%	39.8%	1.7%	11
59.3%	37.6%	3.1%	12
65.7%	28.5%	5.8%	13
69.1%	23.5%	7.4%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample1.2s (39.3%)

Results

820.0ms	8256×	body	128	valid
129.0ms	1351×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify35.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

377×	`fma-neg_binary64`
309×	`fma-def_binary64`
112×	`cancel-sign-sub-inv_binary64`
77×	`distribute-rgt-in_binary64`
56×	`unsub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	42	10
4	80	10
5	138	10
6	302	10
7	420	10
8	581	10
9	647	10
10	718	10
11	740	10
12	744	10
13	699	10

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 x (/.f64 (-.f64 y x) z))

Compiler

Compiled 30 to 18 computations (40% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 y x) z)
✓	0.0b	(+.f64 x (/.f64 (-.f64 y x) z))

series25.0ms (0.8%)

Counts

2 → 64

Calls

2 calls:

13.0ms	(/.f64 (-.f64 y x) z)
12.0ms	(+.f64 x (/.f64 (-.f64 y x) z))

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`
5×	`associate-/l*_binary64`

Counts

2 → 58

Calls

2 calls:

6.0ms	(+.f64 x (/.f64 (-.f64 y x) z))
4.0ms	(/.f64 (-.f64 y x) z)

simplify83.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-neg_binary64`
599×	`times-frac_binary64`
572×	`associate-/l*_binary64`
274×	`div-sub_binary64`
243×	`distribute-rgt-in_binary64`

Counts

122 → 74

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	1378
1	273	1269
2	636	1260
3	1893	1260
4	4435	1260
5	5003	1260

prune48.0ms (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	69	5	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	5	75

Error

Counts

75 → 5

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (+.f64 (/.f64 y z) x) (/.f64 x z))
	0.7b	(+.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (/.f64 (cbrt.f64 (-.f64 y x)) z)))
	0.7b	(+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 y x) z)) (cbrt.f64 (/.f64 (-.f64 y x) z))) (cbrt.f64 (/.f64 (-.f64 y x) z))))
	0.7b	(+.f64 x (/.f64 (/.f64 (-.f64 y x) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z)))
	0.3b	(+.f64 x (/.f64 1 (/.f64 z (-.f64 y x))))

Compiler

Compiled 1155 to 360 computations (68.8% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 y z) x)
✓	0.0b	(-.f64 (+.f64 (/.f64 y z) x) (/.f64 x z))

series20.0ms (0.7%)

Counts

2 → 18

Calls

2 calls:

13.0ms	(-.f64 (+.f64 (/.f64 y z) x) (/.f64 x z))
7.0ms	(+.f64 (/.f64 y z) x)

rewrite27.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`*-un-lft-identity_binary64`
63×	`add-sqr-sqrt_binary64`
58×	`add-cube-cbrt_binary64`
55×	`times-frac_binary64`
52×	`prod-diff_binary64`

Counts

2 → 117

Calls

2 calls:

12.0ms	(-.f64 (+.f64 (/.f64 y z) x) (/.f64 x z))
5.0ms	(+.f64 (/.f64 y z) x)

simplify124.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

575×	`fma-def_binary64`
483×	`associate-*l/_binary64`
344×	`associate-/l*_binary64`
282×	`distribute-rgt-in_binary64`
252×	`distribute-lft-in_binary64`

Counts

135 → 134

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	206	4092
1	543	1945
2	1319	1582
3	4823	1582
4	4991	1582
5	4989	1582
6	4877	1582

prune79.0ms (2.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	135	4	139

Error

Counts

139 → 4

Alt Table

Status	Error	Program
	0.5b	(-.f64 (fma.f64 (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)) x) (/.f64 x z))
	0.7b	(+.f64 x (/.f64 (/.f64 (-.f64 y x) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z)))
▶	0.1b	(+.f64 (+.f64 (/.f64 y z) x) (*.f64 (neg.f64 x) (/.f64 1 z)))
	0.3b	(+.f64 x (/.f64 1 (/.f64 z (-.f64 y x))))

Compiler

Compiled 3591 to 781 computations (78.3% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (/.f64 y z) x)
✓	0.0b	(+.f64 (+.f64 (/.f64 y z) x) (*.f64 (neg.f64 x) (/.f64 1 z)))
✓	0.2b	(*.f64 (neg.f64 x) (/.f64 1 z))

series18.0ms (0.6%)

Counts

2 → 60

Calls

2 calls:

12.0ms	(+.f64 (+.f64 (/.f64 y z) x) (*.f64 (neg.f64 x) (/.f64 1 z)))
6.0ms	(*.f64 (neg.f64 x) (/.f64 1 z))

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64`
13×	`add-cube-cbrt_binary64`
11×	`times-frac_binary64`

Counts

2 → 70

Calls

2 calls:

7.0ms	(+.f64 (+.f64 (/.f64 y z) x) (*.f64 (neg.f64 x) (/.f64 1 z)))
6.0ms	(*.f64 (neg.f64 x) (/.f64 1 z))

simplify68.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

577×	`fma-neg_binary64`
469×	`times-frac_binary64`
434×	`fma-def_binary64`
342×	`distribute-rgt-in_binary64`
312×	`distribute-lft-in_binary64`

Counts

130 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	1492
1	358	1298
2	1108	1263
3	3820	1263
4	4999	1263

prune139.0ms (4.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	148	4	152

Error

Counts

152 → 4

Alt Table

Status	Error	Program
	0.5b	(-.f64 (fma.f64 (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)) x) (/.f64 x z))
	0.7b	(+.f64 x (/.f64 (/.f64 (-.f64 y x) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z)))
✓	0.1b	(+.f64 (+.f64 (/.f64 y z) x) (*.f64 (neg.f64 x) (/.f64 1 z)))
▶	0.3b	(+.f64 x (/.f64 1 (/.f64 z (-.f64 y x))))

Compiler

Compiled 2795 to 1002 computations (64.2% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 z (-.f64 y x))
✓	0.0b	(+.f64 x (/.f64 1 (/.f64 z (-.f64 y x))))
✓	0.5b	(/.f64 1 (/.f64 z (-.f64 y x)))

series41.0ms (1.3%)

Counts

3 → 96

Calls

3 calls:

16.0ms	(/.f64 z (-.f64 y x))
14.0ms	(+.f64 x (/.f64 1 (/.f64 z (-.f64 y x))))
9.0ms	(/.f64 1 (/.f64 z (-.f64 y x)))

rewrite38.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
107×	`*-un-lft-identity_binary64`
104×	`add-sqr-sqrt_binary64`
72×	`add-cube-cbrt_binary64`
26×	`associate-/r*_binary64`

Counts

3 → 167

Calls

3 calls:

15.0ms	(+.f64 x (/.f64 1 (/.f64 z (-.f64 y x))))
6.0ms	(/.f64 1 (/.f64 z (-.f64 y x)))
3.0ms	(/.f64 z (-.f64 y x))

simplify142.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

492×	`fma-neg_binary64`
390×	`times-frac_binary64`
376×	`fma-def_binary64`
319×	`associate-/l*_binary64`
287×	`distribute-rgt-in_binary64`

Counts

263 → 229

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	201	4146
1	447	3761
2	1281	3568
3	4164	3568
4	4962	3568
5	5190	3568

prune136.0ms (4.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	229	4	233

Error

Counts

233 → 4

Alt Table

Status	Error	Program
	0.5b	(-.f64 (fma.f64 (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)) x) (/.f64 x z))
	0.7b	(+.f64 x (/.f64 (/.f64 (-.f64 y x) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z)))
✓	0.1b	(+.f64 (+.f64 (/.f64 y z) x) (*.f64 (neg.f64 x) (/.f64 1 z)))
✓	0.3b	(+.f64 x (/.f64 1 (/.f64 z (-.f64 y x))))

Compiler

Compiled 4122 to 1526 computations (63% saved)

regimes266.0ms (8.8%)

Accuracy

Total 0.0b remaining (64.6%)

Threshold costs 0.0b (64.6%)

Counts

78 → 1

Compiler

Compiled 4620 to 2766 computations (40.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	13	14
2	19	14
3	23	14
4	26	14
5	27	14
6	26	14

end58.0ms (1.9%)

Compiler: Compiled 90 to 54 computations (40% saved)

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	42	10
4	80	10
5	138	10
6	302	10
7	420	10
8	581	10
9	647	10
10	718	10
11	740	10
12	744	10
13	699	10

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	42	10
4	80	10
5	138	10
6	302	10
7	420	10
8	581	10
9	647	10
10	718	10
11	740	10
12	744	10
13	699	10

Details

analyze433.0ms (14.3%)

sample1.2s (39.3%)

simplify35.0ms (1.1%)

prune1.0ms (0%)

localize5.0ms (0.2%)

series25.0ms (0.8%)

rewrite13.0ms (0.4%)

simplify83.0ms (2.7%)

prune48.0ms (1.6%)

localize5.0ms (0.2%)

series20.0ms (0.7%)

rewrite27.0ms (0.9%)

simplify124.0ms (4.1%)

prune79.0ms (2.6%)

localize7.0ms (0.2%)

series18.0ms (0.6%)

rewrite16.0ms (0.5%)

simplify68.0ms (2.2%)

prune139.0ms (4.6%)

localize7.0ms (0.2%)

series41.0ms (1.3%)

rewrite38.0ms (1.2%)

simplify142.0ms (4.7%)

prune136.0ms (4.5%)

regimes266.0ms (8.8%)

simplify2.0ms (0.1%)

end58.0ms (1.9%)

Profiling

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	42	10
4	80	10
5	138	10
6	302	10
7	420	10
8	581	10
9	647	10
10	718	10
11	740	10
12	744	10
13	699	10