Details

analyze704.0ms (5.6%)

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
10.1%	64.7%	25.1%	8
17.2%	32.8%	50.1%	9
23%	26.9%	50.1%	10
26.8%	23.1%	50.1%	11
31.6%	18.3%	50.1%	12
35.2%	14.7%	50.1%	13
37.5%	12.4%	50.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample49.0ms (0.4%)

Algorithm

1×

intervals

Results

32.0ms

256×

body

128

valid

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify171.0ms (1.4%)

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

prune6.0ms (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)

localize16.0ms (0.1%)

Local error

Found 2 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)

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
24×	`prod-diff_binary64`
19×	`add-cube-cbrt_binary64`
14×	`associate--r+_binary64`

Counts

2 → 65

Calls

2 calls:

13.0ms	(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))
1.0ms	(fma.f64 (+.f64 y 1/2) (log.f64 y) z)

series553.0ms (4.4%)

Counts

2 → 60

Calls

2 calls:

304.0ms	(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))
249.0ms	(fma.f64 (+.f64 y 1/2) (log.f64 y) z)

simplify173.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

667×	`fma-def_binary64`
547×	`distribute-rgt-in_binary64`
508×	`distribute-lft-in_binary64`
456×	`fma-neg_binary64`
232×	`exp-sum_binary64`

Counts

125 → 242

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	171	2510
1	373	2200
2	1256	1943
3	4472	1943
4	5111	1943

prune245.0ms (1.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	236	6	242
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	237	6	243

Error

0.0b

Counts

243 → 6

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) (-.f64 z x))
	1.2b	(.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))))
	27.2b	(*.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))))
	47.3b	(/.f64 (-.f64 (pow.f64 y 3) (pow.f64 (-.f64 (fma.f64 (log.f64 y) (+.f64 1/2 y) z) x) 3)) (fma.f64 y y (*.f64 (-.f64 (fma.f64 (log.f64 y) (+.f64 1/2 y) z) x) (+.f64 y (-.f64 (fma.f64 (log.f64 y) (+.f64 1/2 y) z) x)))))
	24.8b	(-.f64 y (-.f64 (.f64 -1 (.f64 y (log.f64 (/.f64 1 y)))) x))
	0.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) x))

Compiler

Compiled 3277 to 1662 computations (49.3% saved)

localize16.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) (-.f64 z x))
✓	0.2b	(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
24×	`prod-diff_binary64`
19×	`add-cube-cbrt_binary64`
13×	`associate--r+_binary64`

Counts

2 → 65

Calls

2 calls:

15.0ms	(-.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) (-.f64 z x))
1.0ms	(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

series431.0ms (3.4%)

Counts

2 → 48

Calls

2 calls:

325.0ms	(-.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) (-.f64 z x))
106.0ms	(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

simplify182.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

656×	`fma-def_binary64`
608×	`fma-neg_binary64`
469×	`associate-l_binary64`
402×	`associate-r_binary64`
352×	`distribute-rgt-in_binary64`

Counts

113 → 212

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	171	2157
1	375	1915
2	1163	1750
3	4304	1750
4	4929	1750

prune183.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	211	1	212
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	212	6	218

Error

0.0b

Counts

218 → 6

Alt Table

Status	Error	Program
	27.2b	(*.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))))
	47.3b	(/.f64 (-.f64 (pow.f64 y 3) (pow.f64 (-.f64 (fma.f64 (log.f64 y) (+.f64 1/2 y) z) x) 3)) (fma.f64 y y (*.f64 (-.f64 (fma.f64 (log.f64 y) (+.f64 1/2 y) z) x) (+.f64 y (-.f64 (fma.f64 (log.f64 y) (+.f64 1/2 y) z) x)))))
✓	0.1b	(-.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) (-.f64 z x))
	24.8b	(-.f64 y (-.f64 (.f64 -1 (.f64 y (log.f64 (/.f64 1 y)))) x))
	0.5b	(fma.f64 (*.f64 (cbrt.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y)) (cbrt.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y))) (cbrt.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y)) (-.f64 x z))
▶	0.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) x))

Compiler

Compiled 2746 to 1157 computations (57.9% saved)

localize22.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y))))
✓	0.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) x))
✓	0.3b	(*.f64 y (log.f64 y))

rewrite54.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`*-un-lft-identity_binary64`
39×	`add-sqr-sqrt_binary64`
30×	`prod-diff_binary64`
27×	`add-cube-cbrt_binary64`
22×	`add-log-exp_binary64`

Counts

3 → 111

Calls

3 calls:

25.0ms	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) x))
9.0ms	(+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y))))
6.0ms	(*.f64 y (log.f64 y))

series1.7s (13.2%)

Counts

3 → 65

Calls

3 calls:

771.0ms	(*.f64 y (log.f64 y))
540.0ms	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) x))
351.0ms	(+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y))))

simplify260.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

385×	`associate-+l+_binary64`
302×	`cancel-sign-sub-inv_binary64`
268×	`fma-neg_binary64`
261×	`exp-sum_binary64`
226×	`associate--l+_binary64`

Counts

176 → 327

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	229	2937
1	510	2549
2	1862	2443
3	4235	2440
4	4966	2440
5	4887	2440

prune333.0ms (2.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	322	5	327
Fresh	4	0	4
Picked	1	0	1
Done	0	1	1
Total	327	6	333

Error

0.0b

Counts

333 → 6

Alt Table

Status	Error	Program
	0.2b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (log.f64 y))) (*.f64 1/2 (log.f64 y)))) x))
	0.4b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (log.f64 y))) (.f64 1/2 (log.f64 y)))) x))
	28.9b	(-.f64 y (-.f64 (*.f64 (sqrt.f64 (fma.f64 (log.f64 y) (+.f64 y 1/2) z)) (sqrt.f64 (fma.f64 (log.f64 y) (+.f64 y 1/2) z))) x))
✓	0.1b	(-.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) (-.f64 z x))
▶	0.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (+.f64 (.f64 y (.f64 2 (log.f64 (cbrt.f64 y)))) (.f64 y (log.f64 (cbrt.f64 y)))) (.f64 1/2 (log.f64 y)))) x))
	0.5b	(-.f64 y (-.f64 (fma.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 z) (+.f64 (.f64 y (log.f64 y)) (*.f64 1/2 (log.f64 y)))) x))

Compiler

Compiled 4805 to 2196 computations (54.3% saved)

localize34.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 y (log.f64 (cbrt.f64 y)))
✓	0.3b	(.f64 y (.f64 2 (log.f64 (cbrt.f64 y))))
	0.6b	(cbrt.f64 y)
✓	0.6b	(cbrt.f64 y)

rewrite29.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`log-prod_binary64`
30×	`distribute-lft-in_binary64`
30×	`distribute-rgt-in_binary64`
21×	`add-sqr-sqrt_binary64`
21×	`cbrt-prod_binary64`

Counts

3 → 91

Calls

3 calls:

10.0ms	(.f64 y (.f64 2 (log.f64 (cbrt.f64 y))))
8.0ms	(*.f64 y (log.f64 (cbrt.f64 y)))
1.0ms	(cbrt.f64 y)

series3.7s (29.3%)

Counts

3 → 36

Calls

3 calls:

1.7s	(.f64 y (.f64 2 (log.f64 (cbrt.f64 y))))
1.6s	(*.f64 y (log.f64 (cbrt.f64 y)))
439.0ms	(cbrt.f64 y)

simplify185.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

981×	`fma-def_binary64`
479×	`*-commutative_binary64`
342×	`associate-+l+_binary64`
268×	`fma-neg_binary64`
235×	`unswap-sqr_binary64`

Counts

127 → 225

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	1720
1	258	1506
2	1024	1486
3	2094	1486
4	4665	1486
5	4996	1486
6	4865	1486

prune355.0ms (2.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	265	1	266
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	265	7	272

Error

Counts

272 → 7

Alt Table

Status	Error	Program
	0.3b	(-.f64 y (-.f64 (+.f64 z (+.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 y (log.f64 y)) 2/3)) (cbrt.f64 (.f64 (.f64 y (log.f64 y)) 2/3))) (cbrt.f64 (.f64 (.f64 y (log.f64 y)) 2/3))) (.f64 y (log.f64 (cbrt.f64 y)))) (.f64 1/2 (log.f64 y)))) x))
	0.2b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (log.f64 y))) (*.f64 1/2 (log.f64 y)))) x))
	0.4b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (log.f64 y))) (.f64 1/2 (log.f64 y)))) x))
	28.9b	(-.f64 y (-.f64 (*.f64 (sqrt.f64 (fma.f64 (log.f64 y) (+.f64 y 1/2) z)) (sqrt.f64 (fma.f64 (log.f64 y) (+.f64 y 1/2) z))) x))
✓	0.1b	(-.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) (-.f64 z x))
✓	0.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (+.f64 (.f64 y (.f64 2 (log.f64 (cbrt.f64 y)))) (.f64 y (log.f64 (cbrt.f64 y)))) (.f64 1/2 (log.f64 y)))) x))
	0.5b	(-.f64 y (-.f64 (fma.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 z) (+.f64 (.f64 y (log.f64 y)) (*.f64 1/2 (log.f64 y)))) x))

Compiler

Compiled 4268 to 1940 computations (54.5% saved)

regimes1.6s (13%)

Accuracy

Total 0.1b remaining (83.3%)

Threshold costs 0.1b (83.3%)

Compiler

Compiled 16387 to 10238 computations (37.5% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`sub-neg_binary64`
7×	`+-commutative_binary64`
6×	`cancel-sign-sub-inv_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	16	16
2	30	16
3	45	16
4	58	16
5	61	16
6	57	16

end1.0ms (0%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

sample1.6s (12.3%)

Algorithm

1×

intervals

Results

875.0ms	7999×	body	128	valid
4.0ms	42×	body	128	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 212 to 130 computations (38.7% saved)

Details

analyze704.0ms (5.6%)

sample49.0ms (0.4%)

simplify171.0ms (1.4%)

prune6.0ms (0%)

localize16.0ms (0.1%)

rewrite25.0ms (0.2%)

series553.0ms (4.4%)

simplify173.0ms (1.4%)

prune245.0ms (1.9%)

localize16.0ms (0.1%)

rewrite23.0ms (0.2%)

series431.0ms (3.4%)

simplify182.0ms (1.4%)

prune183.0ms (1.5%)

localize22.0ms (0.2%)

rewrite54.0ms (0.4%)

series1.7s (13.2%)

simplify260.0ms (2.1%)

prune333.0ms (2.6%)

localize34.0ms (0.3%)

rewrite29.0ms (0.2%)

series3.7s (29.3%)

simplify185.0ms (1.5%)

prune355.0ms (2.8%)

regimes1.6s (13%)

simplify7.0ms (0.1%)

end1.0ms (0%)

sample1.6s (12.3%)

Profiling