Details

analyze160.0ms (2.2%)

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
49.9%	49.9%	0.1%	3
49.9%	49.9%	0.1%	4
49.9%	49.9%	0.1%	5
49.9%	25%	25.1%	6
49.9%	25%	25.1%	7
49.9%	25%	25.1%	8
49.9%	12.5%	37.6%	9
49.9%	12.5%	37.6%	10
49.9%	12.5%	37.6%	11
49.9%	6.2%	43.8%	12
49.9%	6.2%	43.8%	13
49.9%	6.2%	43.8%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.5s (20.2%)

Results

1.1s	8253×	body	128	valid
141.0ms	1065×	body	128	invalid
1.0ms	2×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify177.0ms (2.5%)

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)

localize9.0ms (0.1%)

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)

series228.0ms (3.2%)

Counts

3 → 96

Calls

3 calls:

89.0ms	(-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)
87.0ms	(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))
50.0ms	(fma.f64 (+.f64 y 1/2) (log.f64 y) z)

rewrite25.0ms (0.3%)

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:

11.0ms	(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))
4.0ms	(-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)
0.0ms	(fma.f64 (+.f64 y 1/2) (log.f64 y) z)

simplify136.0ms (1.9%)

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

prune191.0ms (2.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	173	7	180
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	174	7	181

Error

0.0b

Counts

181 → 7

Alt Table

Status	Error	Program
	1.3b	(+.f64 (fma.f64 1 y (neg.f64 (.f64 (cbrt.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)) (.f64 (cbrt.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)) (cbrt.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)))))) (fma.f64 (neg.f64 (cbrt.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (.f64 (cbrt.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)) (cbrt.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (.f64 (cbrt.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)) (*.f64 (cbrt.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)) (cbrt.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))))
	45.1b	(*.f64 (+.f64 1 (log.f64 (/.f64 1 y))) y)
	1.3b	(.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))))
	26.3b	(-.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))
	34.4b	(-.f64 y (-.f64 (cbrt.f64 (.f64 (.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (fma.f64 (+.f64 y 1/2) (log.f64 y) z))) x))
▶	0.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) x))
	46.3b	(-.f64 y (-.f64 (log.f64 (*.f64 (exp.f64 z) (pow.f64 y (+.f64 1/2 y)))) x))

Compiler

Compiled 4626 to 2308 computations (50.1% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y))))
✓	0.0b	(+.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))
✓	0.2b	(*.f64 y (log.f64 y))

series335.0ms (4.7%)

Counts

4 → 74

Calls

4 calls:

185.0ms	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) x))
97.0ms	(+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y))))
41.0ms	(*.f64 y (log.f64 y))
11.0ms	(+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))

rewrite42.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`*-un-lft-identity_binary64`
44×	`add-sqr-sqrt_binary64`
32×	`add-cube-cbrt_binary64`
30×	`prod-diff_binary64`
25×	`add-log-exp_binary64`

Counts

4 → 138

Calls

4 calls:

13.0ms	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) x))
5.0ms	(+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))
5.0ms	(+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y))))
3.0ms	(*.f64 y (log.f64 y))

simplify128.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

371×	`cancel-sign-sub-inv_binary64`
367×	`fma-neg_binary64`
361×	`times-frac_binary64`
264×	`exp-sum_binary64`
255×	`associate--l+_binary64`

Counts

212 → 219

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	265	3343
1	618	2935
2	2252	2834
3	4099	2824
4	5083	2824

prune321.0ms (4.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	212	7	219
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	218	8	226

Error

0.0b

Counts

226 → 8

Alt Table

Status	Error	Program
	31.7b	(-.f64 y (-.f64 (+.f64 z (.f64 (sqrt.f64 (.f64 (log.f64 y) (+.f64 y 1/2))) (sqrt.f64 (*.f64 (log.f64 y) (+.f64 y 1/2))))) x))
	45.1b	(*.f64 y (-.f64 1 (log.f64 y)))
▶	0.1b	(+.f64 (-.f64 y (+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y))))) x)
	1.3b	(.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))))
	0.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 (log.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) y) (fma.f64 y (log.f64 (cbrt.f64 y)) (log.f64 (sqrt.f64 y))))) x))
	21.8b	(-.f64 y (-.f64 (+.f64 z (cbrt.f64 (pow.f64 (*.f64 (log.f64 y) (+.f64 y 1/2)) 3))) x))
	0.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 y)) y) (.f64 (log.f64 (sqrt.f64 y)) y)) (*.f64 1/2 (log.f64 y)))) x))
	0.4b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 (.f64 y (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))) (cbrt.f64 (log.f64 y))) (.f64 1/2 (log.f64 y)))) x))

Compiler

Compiled 5967 to 2735 computations (54.2% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y))))
	0.0b	(+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))
✓	0.1b	(-.f64 y (+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))))
	0.2b	(*.f64 y (log.f64 y))

series164.0ms (2.3%)

Counts

1 → 12

Calls

1 calls:

164.0ms

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

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`prod-diff_binary64`
10×	`add-log-exp_binary64`
10×	`add-cube-cbrt_binary64`

Counts

1 → 38

Calls

1 calls:

13.0ms

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

simplify116.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

870×	`fma-neg_binary64`
541×	`fma-def_binary64`
509×	`distribute-rgt-in_binary64`
508×	`associate-r_binary64`
492×	`distribute-lft-in_binary64`

Counts

50 → 62

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	109	1308
1	258	948
2	877	789
3	4725	789
4	5411	789

prune437.0ms (6.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	185	3	188
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	189	7	196

Error

0.0b

Counts

196 → 7

Alt Table

Status	Error	Program
	21.8b	(-.f64 y (-.f64 (+.f64 z (cbrt.f64 (pow.f64 (*.f64 (log.f64 y) (+.f64 y 1/2)) 3))) x))
▶	0.1b	(+.f64 (-.f64 y (+.f64 z (+.f64 (fma.f64 y (log.f64 y) (.f64 (log.f64 y) 1/4)) (.f64 1/2 (log.f64 (sqrt.f64 y)))))) x)
	0.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 (log.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) y) (fma.f64 y (log.f64 (cbrt.f64 y)) (log.f64 (sqrt.f64 y))))) x))
	31.7b	(-.f64 y (-.f64 (+.f64 z (.f64 (sqrt.f64 (.f64 (log.f64 y) (+.f64 y 1/2))) (sqrt.f64 (*.f64 (log.f64 y) (+.f64 y 1/2))))) x))
	0.9b	(+.f64 (.f64 (.f64 (cbrt.f64 (-.f64 y (fma.f64 (log.f64 y) (+.f64 1/2 y) z))) (cbrt.f64 (-.f64 y (fma.f64 (log.f64 y) (+.f64 1/2 y) z)))) (cbrt.f64 (-.f64 y (fma.f64 (log.f64 y) (+.f64 1/2 y) z)))) x)
	19.3b	(+.f64 (fma.f64 (log.f64 y) (+.f64 (neg.f64 y) -1/2) y) x)
	0.4b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 (.f64 y (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))) (cbrt.f64 (log.f64 y))) (.f64 1/2 (log.f64 y)))) x))

Compiler

Compiled 4759 to 2270 computations (52.3% saved)

localize33.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 z (+.f64 (fma.f64 y (log.f64 y) (.f64 (log.f64 y) 1/4)) (.f64 1/2 (log.f64 (sqrt.f64 y)))))
✓	0.0b	(+.f64 (fma.f64 y (log.f64 y) (.f64 (log.f64 y) 1/4)) (.f64 1/2 (log.f64 (sqrt.f64 y))))
✓	0.1b	(-.f64 y (+.f64 z (+.f64 (fma.f64 y (log.f64 y) (.f64 (log.f64 y) 1/4)) (.f64 1/2 (log.f64 (sqrt.f64 y))))))
✓	0.1b	(fma.f64 y (log.f64 y) (*.f64 (log.f64 y) 1/4))

series450.0ms (6.3%)

Counts

4 → 42

Calls

4 calls:

228.0ms	(-.f64 y (+.f64 z (+.f64 (fma.f64 y (log.f64 y) (.f64 (log.f64 y) 1/4)) (.f64 1/2 (log.f64 (sqrt.f64 y))))))
179.0ms	(+.f64 z (+.f64 (fma.f64 y (log.f64 y) (.f64 (log.f64 y) 1/4)) (.f64 1/2 (log.f64 (sqrt.f64 y)))))
24.0ms	(fma.f64 y (log.f64 y) (*.f64 (log.f64 y) 1/4))
19.0ms	(+.f64 (fma.f64 y (log.f64 y) (.f64 (log.f64 y) 1/4)) (.f64 1/2 (log.f64 (sqrt.f64 y))))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
20×	`add-log-exp_binary64`
19×	`add-cube-cbrt_binary64`
13×	`associate-+r+_binary64`

Counts

4 → 96

Calls

4 calls:

8.0ms	(-.f64 y (+.f64 z (+.f64 (fma.f64 y (log.f64 y) (.f64 (log.f64 y) 1/4)) (.f64 1/2 (log.f64 (sqrt.f64 y))))))
4.0ms	(+.f64 z (+.f64 (fma.f64 y (log.f64 y) (.f64 (log.f64 y) 1/4)) (.f64 1/2 (log.f64 (sqrt.f64 y)))))
3.0ms	(+.f64 (fma.f64 y (log.f64 y) (.f64 (log.f64 y) 1/4)) (.f64 1/2 (log.f64 (sqrt.f64 y))))
0.0ms	(fma.f64 y (log.f64 y) (*.f64 (log.f64 y) 1/4))

simplify114.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

637×	`sub-neg_binary64`
333×	`associate--r+_binary64`
307×	`*-commutative_binary64`
271×	`unsub-neg_binary64`
255×	`+-commutative_binary64`

Counts

138 → 166

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	185	3422
1	438	2870
2	1736	2577
3	3648	2550
4	4964	2550

prune324.0ms (4.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	166	7	173

Error

Counts

173 → 7

Alt Table

Status	Error	Program
	31.7b	(-.f64 y (-.f64 (+.f64 z (.f64 (sqrt.f64 (.f64 (log.f64 y) (+.f64 y 1/2))) (sqrt.f64 (*.f64 (log.f64 y) (+.f64 y 1/2))))) x))
	0.1b	(+.f64 (fma.f64 (sqrt.f64 y) (sqrt.f64 y) (-.f64 (*.f64 (log.f64 y) (-.f64 -1/4 y)) (fma.f64 1/2 (log.f64 (sqrt.f64 y)) z))) x)
	0.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 (log.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) y) (fma.f64 y (log.f64 (cbrt.f64 y)) (log.f64 (sqrt.f64 y))))) x))
	21.8b	(-.f64 y (-.f64 (+.f64 z (cbrt.f64 (pow.f64 (*.f64 (log.f64 y) (+.f64 y 1/2)) 3))) x))
	0.9b	(+.f64 (.f64 (.f64 (cbrt.f64 (-.f64 y (fma.f64 (log.f64 y) (+.f64 1/2 y) z))) (cbrt.f64 (-.f64 y (fma.f64 (log.f64 y) (+.f64 1/2 y) z)))) (cbrt.f64 (-.f64 y (fma.f64 (log.f64 y) (+.f64 1/2 y) z)))) x)
	19.3b	(+.f64 (fma.f64 (log.f64 y) (+.f64 (neg.f64 y) -1/2) y) x)
	0.4b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 (.f64 y (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))) (cbrt.f64 (log.f64 y))) (.f64 1/2 (log.f64 y)))) x))

Compiler

Compiled 5439 to 2681 computations (50.7% saved)

regimes2.1s (29.8%)

Accuracy

Total 0.1b remaining (82.2%)

Threshold costs 0.1b (82.2%)

Counts

305 → 1

Compiler

Compiled 30422 to 19618 computations (35.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	31
1	21	31
2	29	31
3	33	31
4	35	31
5	35	31

end121.0ms (1.7%)

Compiler: Compiled 214 to 131 computations (38.8% saved)

Details

analyze160.0ms (2.2%)

sample1.5s (20.2%)

simplify177.0ms (2.5%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series228.0ms (3.2%)

rewrite25.0ms (0.3%)

simplify136.0ms (1.9%)

prune191.0ms (2.7%)

localize17.0ms (0.2%)

series335.0ms (4.7%)

rewrite42.0ms (0.6%)

simplify128.0ms (1.8%)

prune321.0ms (4.5%)

localize18.0ms (0.3%)

series164.0ms (2.3%)

rewrite26.0ms (0.4%)

simplify116.0ms (1.6%)

prune437.0ms (6.1%)

localize33.0ms (0.5%)

series450.0ms (6.3%)

rewrite23.0ms (0.3%)

simplify114.0ms (1.6%)

prune324.0ms (4.5%)

regimes2.1s (29.8%)

simplify3.0ms (0%)

end121.0ms (1.7%)

Profiling