Details

analyze342.0ms (6.4%)

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%	74.9%	25.1%	3
0%	74.9%	25.1%	4
0%	62.4%	37.6%	5
0%	56.2%	43.8%	6
6.2%	49.9%	43.8%	7
9.4%	43.7%	47%	8
14%	37.4%	48.5%	9
21.1%	30.4%	48.5%	10
24.6%	26.1%	49.3%	11
28.7%	21.6%	49.7%	12
33.4%	16.9%	49.7%	13
35.8%	14.3%	49.9%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.0s (19.5%)

Results

1.0s	8254×	body	128	valid
7.0ms	63×	body	128	invalid
1.0ms	1×	body	1024	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 24 to 16 computations (33.3% saved)

preprocess45.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

723×	`fma-neg_binary64`
400×	`distribute-rgt-in_binary64`
398×	`fma-def_binary64`
274×	`sub-neg_binary64`
256×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	48
1	46	48
2	112	48
3	266	48
4	544	48
5	1249	48
6	2534	48
7	4307	48
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify34.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

681×	`fma-neg_binary64`
398×	`distribute-rgt-in_binary64`
317×	`fma-def_binary64`
285×	`unsub-neg_binary64`
229×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	16	12
2	36	12
3	82	12
4	166	12
5	327	12
6	531	12
7	1282	12
8	2596	12
9	4179	12
10	4890	12

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (-.f64 (*.f64 x (log.f64 y)) z) y)

Compiler

Compiled 41 to 23 computations (43.9% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (-.f64 (*.f64 x (log.f64 y)) z) y)
✓	0.0b	(-.f64 (*.f64 x (log.f64 y)) z)
✓	0.3b	(*.f64 x (log.f64 y))

series338.0ms (6.3%)

Counts

3 → 96

Calls

24 calls:

68.0ms	(*.f64 x (log.f64 y))	x	0
48.0ms	(*.f64 x (log.f64 y))	x	inf
47.0ms	(*.f64 x (log.f64 y))	x	-inf
13.0ms	(-.f64 (-.f64 (*.f64 x (log.f64 y)) z) y)	x	-inf
12.0ms	(-.f64 (*.f64 x (log.f64 y)) z)	y	0

rewrite72.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

503×	`fma-def_binary64`
463×	`log-prod_binary64`
303×	`fma-neg_binary64`
272×	`egg-rr`
172×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	27
1	180	27
2	2591	27

Stop Event

1×	node limit

Counts

3 → 272

simplify129.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

2389×	`fma-neg_binary64`
451×	`fma-def_binary64`
413×	`sub-neg_binary64`
390×	`unsub-neg_binary64`
261×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	813
1	95	813
2	210	813
3	484	813
4	1302	813
5	3259	813
6	4001	813
7	4602	813
8	4753	813
9	4799	813
10	4809	813
11	4862	813
12	4883	813
13	4883	813

Stop Event

1×	node limit

Counts

368 → 290

prune244.0ms (4.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	281	9	290
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	282	9	291

Error

0.0b

Counts

291 → 9

Alt Table

Status	Error	Program
	31.6b	(-.f64 (-.f64 (pow.f64 (sqrt.f64 (*.f64 x (log.f64 y))) 2) z) y)
	0.5b	(-.f64 (fma.f64 (*.f64 (log.f64 y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (neg.f64 z)) y)
▶	0.1b	(-.f64 (fma.f64 (log.f64 y) x (neg.f64 y)) z)
	30.1b	(-.f64 (fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (log.f64 y)) (neg.f64 z)) y)
	0.4b	(-.f64 (fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (cbrt.f64 (log.f64 y)) (neg.f64 z)) y)
	0.4b	(-.f64 (fma.f64 (pow.f64 (cbrt.f64 (log.f64 y)) 2) (*.f64 (cbrt.f64 (log.f64 y)) x) (neg.f64 z)) y)
	0.5b	(-.f64 (fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (log.f64 y)) (neg.f64 z)) y)
	0.5b	(-.f64 (fma.f64 (cbrt.f64 (.f64 x (log.f64 y))) (pow.f64 (cbrt.f64 (.f64 x (log.f64 y))) 2) (neg.f64 z)) y)
	31.4b	(-.f64 (/.f64 1 (/.f64 (fma.f64 x (log.f64 y) z) (-.f64 (pow.f64 (.f64 x (log.f64 y)) 2) (.f64 z z)))) y)

Compiler

Compiled 4959 to 1512 computations (69.5% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 (log.f64 y) x (neg.f64 y)) z)
✓	0.1b	(fma.f64 (log.f64 y) x (neg.f64 y))

series114.0ms (2.1%)

Counts

2 → 60

Calls

15 calls:

15.0ms	(-.f64 (fma.f64 (log.f64 y) x (neg.f64 y)) z)	x	inf
13.0ms	(fma.f64 (log.f64 y) x (neg.f64 y))	x	inf
12.0ms	(-.f64 (fma.f64 (log.f64 y) x (neg.f64 y)) z)	x	-inf
11.0ms	(fma.f64 (log.f64 y) x (neg.f64 y))	x	-inf
10.0ms	(-.f64 (fma.f64 (log.f64 y) x (neg.f64 y)) z)	z	0

rewrite73.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

771×	`log1p-expm1-u_binary64`
771×	`expm1-log1p-u_binary64`
570×	`prod-diff_binary64`
206×	`egg-rr`
89×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	170	17
2	2284	17

Stop Event

1×	node limit

Counts

2 → 206

simplify42.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

828×	`fma-neg_binary64`
438×	`fma-def_binary64`
369×	`distribute-rgt-in_binary64`
338×	`sub-neg_binary64`
314×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	561
1	83	561
2	177	561
3	471	561
4	1328	561
5	2956	561

Stop Event

1×	node limit

Counts

266 → 221

prune166.0ms (3.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	221	0	221
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	221	9	230

Error

0.0b

Counts

230 → 9

Alt Table

Status	Error	Program
	31.6b	(-.f64 (-.f64 (pow.f64 (sqrt.f64 (*.f64 x (log.f64 y))) 2) z) y)
	0.5b	(-.f64 (fma.f64 (*.f64 (log.f64 y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (neg.f64 z)) y)
✓	0.1b	(-.f64 (fma.f64 (log.f64 y) x (neg.f64 y)) z)
	30.1b	(-.f64 (fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (log.f64 y)) (neg.f64 z)) y)
▶	0.4b	(-.f64 (fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (cbrt.f64 (log.f64 y)) (neg.f64 z)) y)
	0.4b	(-.f64 (fma.f64 (pow.f64 (cbrt.f64 (log.f64 y)) 2) (*.f64 (cbrt.f64 (log.f64 y)) x) (neg.f64 z)) y)
	0.5b	(-.f64 (fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (log.f64 y)) (neg.f64 z)) y)
	0.5b	(-.f64 (fma.f64 (cbrt.f64 (.f64 x (log.f64 y))) (pow.f64 (cbrt.f64 (.f64 x (log.f64 y))) 2) (neg.f64 z)) y)
	31.4b	(-.f64 (/.f64 1 (/.f64 (fma.f64 x (log.f64 y) z) (-.f64 (pow.f64 (.f64 x (log.f64 y)) 2) (.f64 z z)))) y)

Compiler

Compiled 4837 to 1626 computations (66.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (cbrt.f64 (log.f64 y)) (neg.f64 z))
✓	0.3b	(*.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2))
✓	0.5b	(cbrt.f64 (log.f64 y))
✓	0.5b	(pow.f64 (cbrt.f64 (log.f64 y)) 2)

series1.1s (20.7%)

Counts

4 → 84

Calls

21 calls:

121.0ms	(fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (cbrt.f64 (log.f64 y)) (neg.f64 z))	y	inf
89.0ms	(pow.f64 (cbrt.f64 (log.f64 y)) 2)	y	inf
86.0ms	(cbrt.f64 (log.f64 y))	y	inf
86.0ms	(*.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2))	x	0
67.0ms	(*.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2))	x	inf

rewrite78.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

798×	`log1p-expm1-u_binary64`
798×	`expm1-log1p-u_binary64`
237×	`egg-rr`
172×	`prod-diff_binary64`
106×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	45
1	219	33
2	2536	33

Stop Event

1×	node limit

Counts

4 → 237

simplify48.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

804×	`fma-def_binary64`
548×	`unswap-sqr_binary64`
355×	`associate-l_binary64`
325×	`associate-r_binary64`
239×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	41	813
1	107	805
2	209	805
3	641	805
4	2484	797

Stop Event

1×	node limit

Counts

321 → 257

prune236.0ms (4.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	281	3	284
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	286	7	293

Error

0.0b

Counts

293 → 7

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (fma.f64 (log.f64 y) x (neg.f64 y)) z)
	30.1b	(-.f64 (fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (log.f64 y)) (neg.f64 z)) y)
	0.5b	(-.f64 (fma.f64 (*.f64 (log.f64 y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (neg.f64 z)) y)
	28.4b	(-.f64 (fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (expm1.f64 (log1p.f64 (cbrt.f64 (log.f64 y)))) (neg.f64 z)) y)
	0.4b	(-.f64 (fma.f64 (pow.f64 (cbrt.f64 (log.f64 y)) 2) (*.f64 (cbrt.f64 (log.f64 y)) x) (neg.f64 z)) y)
▶	0.3b	(-.f64 (fma.f64 (*.f64 x (cbrt.f64 (pow.f64 (log.f64 y) 2))) (cbrt.f64 (log.f64 y)) (neg.f64 z)) y)
	0.3b	(-.f64 (fma.f64 (*.f64 x (pow.f64 (pow.f64 (log.f64 y) 2) 1/3)) (cbrt.f64 (log.f64 y)) (neg.f64 z)) y)

Compiler

Compiled 7059 to 2756 computations (61% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 x (cbrt.f64 (pow.f64 (log.f64 y) 2)))
	0.5b	(cbrt.f64 (log.f64 y))
✓	0.5b	(cbrt.f64 (pow.f64 (log.f64 y) 2))
✓	0.6b	(pow.f64 (log.f64 y) 2)

series452.0ms (8.4%)

Counts

3 → 44

Calls

12 calls:

88.0ms	(*.f64 x (cbrt.f64 (pow.f64 (log.f64 y) 2)))	x	0
67.0ms	(*.f64 x (cbrt.f64 (pow.f64 (log.f64 y) 2)))	x	-inf
66.0ms	(*.f64 x (cbrt.f64 (pow.f64 (log.f64 y) 2)))	x	inf
39.0ms	(*.f64 x (cbrt.f64 (pow.f64 (log.f64 y) 2)))	y	inf
36.0ms	(cbrt.f64 (pow.f64 (log.f64 y) 2))	y	-inf

rewrite41.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

581×	`log1p-expm1-u_binary64`
581×	`expm1-log1p-u_binary64`
319×	`log-prod_binary64`
125×	`expm1-udef_binary64`
125×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	25
1	156	25
2	1702	25

Stop Event

1×	node limit

Counts

3 → 66

simplify37.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

650×	`fma-neg_binary64`
585×	`associate-l_binary64`
546×	`unswap-sqr_binary64`
428×	`fma-def_binary64`
241×	`unsub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	424
1	55	408
2	97	408
3	276	408
4	954	408
5	3642	408

Stop Event

1×	node limit

Counts

110 → 76

prune116.0ms (2.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	102	8	110

Error

Counts

110 → 8

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (fma.f64 (log.f64 y) x (neg.f64 y)) z)
	30.1b	(-.f64 (fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (log.f64 y)) (neg.f64 z)) y)
	0.5b	(-.f64 (fma.f64 (*.f64 (log.f64 y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (neg.f64 z)) y)
	28.4b	(-.f64 (fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (expm1.f64 (log1p.f64 (cbrt.f64 (log.f64 y)))) (neg.f64 z)) y)
	0.4b	(-.f64 (fma.f64 (pow.f64 (cbrt.f64 (log.f64 y)) 2) (*.f64 (cbrt.f64 (log.f64 y)) x) (neg.f64 z)) y)
	0.3b	(-.f64 (fma.f64 (.f64 x (cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (log.f64 y)) 2) (cbrt.f64 (pow.f64 (log.f64 y) 4))))) (cbrt.f64 (log.f64 y)) (neg.f64 z)) y)
	0.3b	(-.f64 (fma.f64 (*.f64 x (pow.f64 (pow.f64 (log.f64 y) 2) 1/3)) (cbrt.f64 (log.f64 y)) (neg.f64 z)) y)
	0.4b	(-.f64 (fma.f64 (.f64 x (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (log.f64 y)) 2)) (cbrt.f64 (cbrt.f64 (pow.f64 (log.f64 y) 4))))) (cbrt.f64 (log.f64 y)) (neg.f64 z)) y)

Compiler

Compiled 2124 to 1014 computations (52.3% saved)

regimes443.0ms (8.3%)

Accuracy

Total 0.1b remaining (72.1%)

Threshold costs 0.1b (72.1%)

Counts

113 → 1

Compiler

Compiled 7598 to 5068 computations (33.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	17	12
2	31	12
3	49	12
4	57	12
5	58	12

Stop Event

1×

saturated

end111.0ms (2.1%)

Stop Event

1×

fuel

Compiler

Compiled 173 to 111 computations (35.8% saved)

Details

analyze342.0ms (6.4%)

sample1.0s (19.5%)

preprocess45.0ms (0.8%)

simplify34.0ms (0.6%)

prune5.0ms (0.1%)

localize6.0ms (0.1%)

series338.0ms (6.3%)

rewrite72.0ms (1.3%)

simplify129.0ms (2.4%)

prune244.0ms (4.5%)

localize8.0ms (0.2%)

series114.0ms (2.1%)

rewrite73.0ms (1.4%)

simplify42.0ms (0.8%)

prune166.0ms (3.1%)

localize10.0ms (0.2%)

series1.1s (20.7%)

rewrite78.0ms (1.4%)

simplify48.0ms (0.9%)

prune236.0ms (4.4%)

localize12.0ms (0.2%)

series452.0ms (8.4%)

rewrite41.0ms (0.8%)

simplify37.0ms (0.7%)

prune116.0ms (2.2%)

regimes443.0ms (8.3%)

simplify2.0ms (0%)

end111.0ms (2.1%)

Profiling