Details

analyze371.0ms (0.2%)

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%	74.9%	25.1%	6
6.2%	68.6%	25.1%	7
9.4%	65.5%	25.1%	8
14%	35.9%	50.1%	9
21.1%	28.9%	50.1%	10
24.6%	25.4%	50.1%	11
28.7%	21.3%	50.1%	12
33.4%	16.5%	50.1%	13
35.8%	14.1%	50.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.2s (0.8%)

Results

1.1s	8252×	body	128	valid
4.0ms	39×	body	128	invalid
1.0ms	3×	body	512	valid
0.0ms	1×	body	1024	valid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify131.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

782×	`fma-neg_binary64`
610×	`unsub-neg_binary64`
567×	`distribute-rgt-in_binary64`
442×	`sub-neg_binary64`
412×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	25	18
2	75	16
3	253	16
4	654	16
5	1767	16
6	2167	16
7	2284	16
8	2375	16
9	2374	16
10	2391	16
11	2701	16
12	3417	16
13	4877	16
14	4713	16
15	4967	16

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))

Compiler

Compiled 54 to 33 computations (38.9% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)
✓	0.1b	(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))
✓	0.1b	(fma.f64 (+.f64 y 1/2) (log.f64 y) z)

series219.0ms (0.1%)

Counts

3 → 96

Calls

3 calls:

93.0ms	(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))
81.0ms	(-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)
45.0ms	(fma.f64 (+.f64 y 1/2) (log.f64 y) z)

rewrite18.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64`
40×	`add-sqr-sqrt_binary64`
33×	`prod-diff_binary64`
28×	`add-cube-cbrt_binary64`
14×	`associate--r+_binary64`

Counts

3 → 96

Calls

3 calls:

9.0ms	(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))
3.0ms	(-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)
0.0ms	(fma.f64 (+.f64 y 1/2) (log.f64 y) z)

simplify122.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

395×	`associate-+l+_binary64`
315×	`exp-sum_binary64`
303×	`associate-+r+_binary64`
250×	`associate--r+_binary64`
246×	`associate--l+_binary64`

Counts

192 → 180

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	202	3702
1	445	3255
2	1627	2853
3	4463	2853
4	4980	2853

prune147.0ms (0.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	174	6	180
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	175	6	181

Error

0.0b

Counts

181 → 6

Alt Table

Status	Error	Program
	44.1b	(*.f64 (+.f64 1 (log.f64 (/.f64 1 y))) y)
▶	0.1b	(-.f64 (+.f64 y x) (fma.f64 (log.f64 y) (+.f64 1/2 y) z))
	25.8b	(*.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (-.f64 (sqrt.f64 y) (sqrt.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))
	1.4b	(.f64 (.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))
	45.9b	(cbrt.f64 (.f64 (.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)) (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))
	27.2b	(-.f64 y (-.f64 (*.f64 (sqrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (sqrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) x))

Compiler

Compiled 4452 to 2206 computations (50.4% saved)

localize9.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(-.f64 (+.f64 y x) (fma.f64 (log.f64 y) (+.f64 1/2 y) z))
✓	0.1b	(fma.f64 (log.f64 y) (+.f64 1/2 y) z)

series129.0ms (0.1%)

Counts

2 → 60

Calls

2 calls:

84.0ms	(-.f64 (+.f64 y x) (fma.f64 (log.f64 y) (+.f64 1/2 y) z))
45.0ms	(fma.f64 (log.f64 y) (+.f64 1/2 y) z)

rewrite11.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`prod-diff_binary64`
11×	`add-cube-cbrt_binary64`
7×	`add-log-exp_binary64`

Counts

2 → 48

Calls

2 calls:

5.0ms	(-.f64 (+.f64 y x) (fma.f64 (log.f64 y) (+.f64 1/2 y) z))
0.0ms	(fma.f64 (log.f64 y) (+.f64 1/2 y) z)

simplify125.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

554×	`fma-def_binary64`
497×	`associate-l_binary64`
423×	`associate-r_binary64`
383×	`associate-+l+_binary64`
202×	`exp-sum_binary64`

Counts

108 → 84

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	128	2050
1	291	1842
2	1121	1676
3	4457	1676
4	4844	1674
5	4970	1674
6	4928	1674

prune60.0ms (0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	83	7	90

Error

0.0b

Counts

90 → 7

Alt Table

Status	Error	Program
	25.8b	(*.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (-.f64 (sqrt.f64 y) (sqrt.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))
	46.7b	(/.f64 (-.f64 (pow.f64 (sqrt.f64 (+.f64 y x)) 4) (pow.f64 (cbrt.f64 (fma.f64 (log.f64 y) (+.f64 1/2 y) z)) 6)) (+.f64 z (fma.f64 (log.f64 y) (+.f64 1/2 y) (+.f64 y x))))
	44.1b	(*.f64 (+.f64 1 (log.f64 (/.f64 1 y))) y)
✓	0.1b	(-.f64 (+.f64 y x) (fma.f64 (log.f64 y) (+.f64 1/2 y) z))
▶	1.4b	(.f64 (.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))
	45.9b	(cbrt.f64 (.f64 (.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)) (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))
	27.2b	(-.f64 y (-.f64 (*.f64 (sqrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (sqrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) x))

Compiler

Compiled 2174 to 1114 computations (48.8% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 (+.f64 y 1/2) (log.f64 y) z)
✓	0.4b	(.f64 (.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))
✓	0.6b	(cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)))

series8.6s (5.7%)

Counts

3 → 108

Calls

3 calls:

8.1s

(*.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))

416.0ms

(cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)))

81.0ms

(*.f64 (*.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))

rewrite70.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`*-un-lft-identity_binary64`
68×	`cbrt-div_binary64`
53×	`cbrt-prod_binary64`
36×	`add-sqr-sqrt_binary64`
34×	`flip--_binary64`

Counts

3 → 150

Calls

3 calls:

21.0ms

(*.f64 (*.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))

14.0ms

(*.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))

4.0ms

(cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)))

simplify672.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1050×	`fma-def_binary64`
404×	`times-frac_binary64`
40×	`unpow1/3_binary64`
13×	`unpow2_binary64`
10×	`cube-mult_binary64`

Counts

258 → 296

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3758	68323
1	5610	68323

prune2.5s (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	563	5	568
Fresh	4	1	5
Picked	1	0	1
Done	0	1	1
Total	568	7	575

Error

Counts

575 → 7

Alt Table

Status	Error	Program
	1.5b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)))))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))))
	44.1b	(*.f64 (+.f64 1 (neg.f64 (log.f64 y))) y)
▶	1.4b	(pow.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) 3)
	25.8b	(*.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (-.f64 (sqrt.f64 y) (sqrt.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))
	1.6b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))) (cbrt.f64 (.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)))))) (cbrt.f64 (.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)))))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))
	1.4b	(.f64 (.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))) (cbrt.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)))))) (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))
✓	0.1b	(-.f64 (+.f64 y x) (fma.f64 (log.f64 y) (+.f64 1/2 y) z))

Compiler

Compiled 131315 to 94900 computations (27.7% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))
	0.1b	(fma.f64 (+.f64 y 1/2) (log.f64 y) z)
	0.6b	(cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)))
✓	0.7b	(pow.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) 3)

Details

analyze371.0ms (0.2%)

sample1.2s (0.8%)

simplify131.0ms (0.1%)

prune3.0ms (0%)

localize8.0ms (0%)

series219.0ms (0.1%)

rewrite18.0ms (0%)

simplify122.0ms (0.1%)

prune147.0ms (0.1%)

localize9.0ms (0%)

series129.0ms (0.1%)

rewrite11.0ms (0%)

simplify125.0ms (0.1%)

prune60.0ms (0%)

localize13.0ms (0%)

series8.6s (5.7%)

rewrite70.0ms (0%)

simplify672.0ms (0.4%)

prune2.5s (1.7%)

localize10.0ms (0%)

series2.3min (90.3%)

Profiling