Details

analyze537.0ms (6.3%)

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
50%	50%	0.1%	5
50%	50%	0.1%	6
50%	40.6%	9.5%	7
50%	39%	11%	8
50%	33.6%	16.5%	9
50%	32.4%	17.7%	10
50%	29.5%	20.6%	11
50%	28.8%	21.3%	12
50%	27.3%	22.8%	13
50%	26.9%	23.1%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample6.2s (72.7%)

Results

3.0s	4208×	body	1024	valid
1.1s	2035×	body	1024	invalid
838.0ms	2090×	body	512	valid
381.0ms	1034×	body	512	invalid
292.0ms	222×	body	2048	valid
271.0ms	1046×	body	256	valid
131.0ms	527×	body	256	invalid
110.0ms	746×	body	128	invalid
108.0ms	690×	body	128	valid
1.0ms	1×	body	2048	invalid

Compiler

Compiled 28 to 22 computations (21.4% saved)

preprocess89.0ms (1%)

Algorithm

2×	egg-herbie

Rules

816×	`fma-def_binary64`
600×	`times-frac_binary64`
456×	`fma-neg_binary64`
228×	`distribute-rgt-neg-in_binary64`
146×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	36
1	39	36
2	93	36
3	247	36
4	557	34
5	1130	34
6	2092	34
7	4019	34
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify24.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

454×	`fma-def_binary64`
444×	`times-frac_binary64`
365×	`distribute-rgt-neg-in_binary64`
340×	`fma-neg_binary64`
297×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	23	18
2	51	18
3	126	18
4	286	17
5	581	17
6	1384	17
7	2793	17

Stop Event

1×	node limit

Counts

1 → 2

prune2.0ms (0%)

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

41.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	41.4b	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Compiler

Compiled 50 to 35 computations (30% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	5.4b	(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

series17.0ms (0.2%)

Counts

2 → 32

Calls

9 calls:

4.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))	im	-inf
3.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))	im	inf
2.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))	re	0
2.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))	re	-inf
2.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))	re	inf

rewrite76.0ms (0.9%)

Algorithm

2×	egg-rewrite-iter-limit
2×	egg-rewrite
1×	batch-egg-rewrite

Rules

116×	`add-sqr-sqrt_binary64`
116×	`add-sqr-sqrt_binary64`
109×	`log1p-expm1-u_binary64`
109×	`expm1-log1p-u_binary64`
109×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	228	20
2	3503	20
0	6	10
1	127	10
2	2077	10
0	6	10
0	11	18
1	228	18
2	3499	18
0	11	18

Stop Event

1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	unsound

Counts

2 → 18

simplify40.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

698×	`fma-def_binary64`
411×	`sub-neg_binary64`
240×	`associate-l_binary64`
225×	`cancel-sign-sub-inv_binary64`
221×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	100	734
1	305	716
2	1029	666
3	4524	666

Stop Event

1×	node limit

Counts

50 → 46

prune38.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	44	2	46
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	3	47

Error

0.1b

Counts

47 → 3

Alt Table

Status	Error	Program
	43.5b	(fma.f64 1/2 (/.f64 re (exp.f64 im)) (+.f64 (.f64 (.f64 1/12 (pow.f64 re 3)) (-.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))) (.f64 (exp.f64 im) (.f64 re -1/2))))
✓	41.4b	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
▶	1.0b	(neg.f64 (+.f64 (.f64 (sin.f64 re) im) (+.f64 (.f64 1/120 (.f64 (sin.f64 re) (pow.f64 im 5))) (.f64 1/6 (*.f64 (sin.f64 re) (pow.f64 im 3))))))

Compiler

Compiled 1062 to 552 computations (48% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (sin.f64 re) (pow.f64 im 5))
✓	0.1b	(*.f64 (sin.f64 re) (pow.f64 im 3))
✓	0.1b	(.f64 1/6 (.f64 (sin.f64 re) (pow.f64 im 3)))
✓	0.1b	(*.f64 (sin.f64 re) im)

series51.0ms (0.6%)

Counts

4 → 16

Calls

24 calls:

4.0ms	(.f64 1/6 (.f64 (sin.f64 re) (pow.f64 im 3)))	re	0
3.0ms	(*.f64 (sin.f64 re) (pow.f64 im 5))	re	-inf
3.0ms	(*.f64 (sin.f64 re) (pow.f64 im 5))	re	inf
3.0ms	(.f64 1/6 (.f64 (sin.f64 re) (pow.f64 im 3)))	re	-inf
3.0ms	(.f64 1/6 (.f64 (sin.f64 re) (pow.f64 im 3)))	re	inf

rewrite50.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

614×	`log-prod_binary64`
225×	`expm1-udef_binary64`
225×	`log1p-udef_binary64`
201×	`log-pow_binary64`
130×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	36
1	271	36
2	3099	36

Stop Event

1×	node limit

Counts

4 → 70

simplify34.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

580×	`associate-l_binary64`
525×	`associate-r_binary64`
413×	`fma-def_binary64`
360×	`cancel-sign-sub-inv_binary64`
272×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	62	430
1	207	362
2	855	302
3	4536	302

Stop Event

1×	node limit

Counts

86 → 99

prune100.0ms (1.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	97	5	102

Error

0.1b

Counts

102 → 5

Alt Table

Status	Error	Program
▶	2.0b	(neg.f64 (+.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 re) im)) 3) (+.f64 (.f64 1/120 (.f64 (sin.f64 re) (pow.f64 im 5))) (.f64 1/6 (*.f64 (sin.f64 re) (pow.f64 im 3))))))
✓	1.0b	(neg.f64 (+.f64 (.f64 (sin.f64 re) im) (+.f64 (.f64 1/120 (.f64 (sin.f64 re) (pow.f64 im 5))) (.f64 1/6 (*.f64 (sin.f64 re) (pow.f64 im 3))))))
	43.5b	(fma.f64 1/2 (/.f64 re (exp.f64 im)) (+.f64 (.f64 (.f64 1/12 (pow.f64 re 3)) (-.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))) (.f64 (exp.f64 im) (.f64 re -1/2))))
✓	41.4b	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
	35.3b	(neg.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 re) im) 3)) (+.f64 (.f64 1/120 (.f64 (sin.f64 re) (pow.f64 im 5))) (.f64 1/6 (*.f64 (sin.f64 re) (pow.f64 im 3))))))

Compiler

Compiled 3139 to 1988 computations (36.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 1/6 (.f64 (sin.f64 re) (pow.f64 im 3)))
	0.1b	(*.f64 (sin.f64 re) im)
✓	0.6b	(pow.f64 (cbrt.f64 (*.f64 (sin.f64 re) im)) 3)
✓	16.3b	(cbrt.f64 (*.f64 (sin.f64 re) im))

series135.0ms (1.6%)

Counts

2 → 16

Calls

12 calls:

25.0ms	(pow.f64 (cbrt.f64 (*.f64 (sin.f64 re) im)) 3)	re	-inf
24.0ms	(pow.f64 (cbrt.f64 (*.f64 (sin.f64 re) im)) 3)	re	inf
22.0ms	(cbrt.f64 (*.f64 (sin.f64 re) im))	re	-inf
21.0ms	(cbrt.f64 (*.f64 (sin.f64 re) im))	re	inf
18.0ms	(pow.f64 (cbrt.f64 (*.f64 (sin.f64 re) im)) 3)	im	-inf

rewrite37.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

596×	`log1p-expm1-u_binary64`
596×	`expm1-log1p-u_binary64`
319×	`log-prod_binary64`
121×	`expm1-udef_binary64`
121×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	159	14
2	1674	14

Stop Event

1×	node limit

Counts

2 → 63

simplify69.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

730×	`sqr-pow_binary64`
370×	`cube-prod_binary64`
362×	`unswap-sqr_binary64`
313×	`pow-sqr_binary64`
283×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	112
1	14	112
2	19	112
3	28	112
4	50	112
5	139	112
6	519	112
7	1180	112
8	1270	112
9	1406	112
10	1567	112
11	1798	112
12	2123	112
13	2547	112
14	3050	112
15	3650	112
16	4375	112
17	4698	112
18	4984	112

Stop Event

1×	node limit

Counts

79 → 64

prune123.0ms (1.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	109	4	113
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	109	9	118

Error

0.0b

Counts

118 → 9

Alt Table

Status	Error	Program
✓	2.0b	(neg.f64 (+.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 re) im)) 3) (+.f64 (.f64 1/120 (.f64 (sin.f64 re) (pow.f64 im 5))) (.f64 1/6 (*.f64 (sin.f64 re) (pow.f64 im 3))))))
✓	1.0b	(neg.f64 (+.f64 (.f64 (sin.f64 re) im) (+.f64 (.f64 1/120 (.f64 (sin.f64 re) (pow.f64 im 5))) (.f64 1/6 (*.f64 (sin.f64 re) (pow.f64 im 3))))))
	43.5b	(fma.f64 1/2 (/.f64 re (exp.f64 im)) (+.f64 (.f64 (.f64 1/12 (pow.f64 re 3)) (-.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))) (.f64 (exp.f64 im) (.f64 re -1/2))))
✓	41.4b	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
	36.2b	(neg.f64 (+.f64 (.f64 (sqrt.f64 im) (.f64 (sqrt.f64 im) (sin.f64 re))) (+.f64 (.f64 1/120 (.f64 (sin.f64 re) (pow.f64 im 5))) (.f64 1/6 (.f64 (sin.f64 re) (pow.f64 im 3))))))
	32.7b	(neg.f64 (+.f64 (.f64 (sqrt.f64 (sin.f64 re)) (.f64 (sqrt.f64 (sin.f64 re)) im)) (+.f64 (.f64 1/120 (.f64 (sin.f64 re) (pow.f64 im 5))) (.f64 1/6 (.f64 (sin.f64 re) (pow.f64 im 3))))))
	2.0b	(neg.f64 (+.f64 (.f64 (pow.f64 (cbrt.f64 im) 2) (.f64 (cbrt.f64 im) (sin.f64 re))) (+.f64 (.f64 1/120 (.f64 (sin.f64 re) (pow.f64 im 5))) (.f64 1/6 (.f64 (sin.f64 re) (pow.f64 im 3))))))
	35.3b	(neg.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 re) im) 3)) (+.f64 (.f64 1/120 (.f64 (sin.f64 re) (pow.f64 im 5))) (.f64 1/6 (*.f64 (sin.f64 re) (pow.f64 im 3))))))
▶	2.0b	(neg.f64 (+.f64 (.f64 (cbrt.f64 (sin.f64 re)) (.f64 (cbrt.f64 im) (pow.f64 (cbrt.f64 (.f64 (sin.f64 re) im)) 2))) (+.f64 (.f64 1/120 (.f64 (sin.f64 re) (pow.f64 im 5))) (.f64 1/6 (*.f64 (sin.f64 re) (pow.f64 im 3))))))

Compiler

Compiled 3956 to 2393 computations (39.5% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 (sin.f64 re) im)) 2)
✓	0.6b	(cbrt.f64 (sin.f64 re))
✓	0.6b	(cbrt.f64 im)
	16.3b	(cbrt.f64 (*.f64 (sin.f64 re) im))

series130.0ms (1.5%)

Counts

3 → 16

Calls

12 calls:

26.0ms	(pow.f64 (cbrt.f64 (*.f64 (sin.f64 re) im)) 2)	re	inf
25.0ms	(pow.f64 (cbrt.f64 (*.f64 (sin.f64 re) im)) 2)	re	-inf
20.0ms	(pow.f64 (cbrt.f64 (*.f64 (sin.f64 re) im)) 2)	im	-inf
20.0ms	(cbrt.f64 (sin.f64 re))	re	-inf
19.0ms	(cbrt.f64 (sin.f64 re))	re	inf

rewrite43.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

726×	`log1p-expm1-u_binary64`
726×	`expm1-log1p-u_binary64`
153×	`expm1-udef_binary64`
153×	`log1p-udef_binary64`
89×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	193	19
2	2100	19

Stop Event

1×	node limit

Counts

3 → 63

simplify93.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

2215×	`associate-l_binary64`
724×	`sqr-pow_binary64`
290×	`pow-sqr_binary64`
276×	`unswap-sqr_binary64`
248×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	152
1	28	152
2	56	152
3	137	152
4	512	152
5	1058	152
6	1149	152
7	1288	152
8	1461	152
9	1650	152
10	1886	152
11	2163	152
12	2483	152
13	2855	152
14	3264	152
15	3697	152
16	3893	152
17	3997	152
18	4069	152
19	4123	152

Stop Event

1×	node limit

Counts

79 → 66

prune144.0ms (1.7%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	93	10	103

Error

0.0b

Counts

103 → 10

Alt Table

Status	Error	Program
✓	2.0b	(neg.f64 (+.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 re) im)) 3) (+.f64 (.f64 1/120 (.f64 (sin.f64 re) (pow.f64 im 5))) (.f64 1/6 (*.f64 (sin.f64 re) (pow.f64 im 3))))))
✓	1.0b	(neg.f64 (+.f64 (.f64 (sin.f64 re) im) (+.f64 (.f64 1/120 (.f64 (sin.f64 re) (pow.f64 im 5))) (.f64 1/6 (*.f64 (sin.f64 re) (pow.f64 im 3))))))
	2.6b	(neg.f64 (+.f64 (.f64 (cbrt.f64 (sin.f64 re)) (.f64 (cbrt.f64 im) (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (sin.f64 re) im))) 3) 2))) (+.f64 (.f64 1/120 (.f64 (sin.f64 re) (pow.f64 im 5))) (.f64 1/6 (*.f64 (sin.f64 re) (pow.f64 im 3))))))
	43.5b	(fma.f64 1/2 (/.f64 re (exp.f64 im)) (+.f64 (.f64 (.f64 1/12 (pow.f64 re 3)) (-.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))) (.f64 (exp.f64 im) (.f64 re -1/2))))
✓	41.4b	(.f64 (.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
	36.2b	(neg.f64 (+.f64 (.f64 (sqrt.f64 im) (.f64 (sqrt.f64 im) (sin.f64 re))) (+.f64 (.f64 1/120 (.f64 (sin.f64 re) (pow.f64 im 5))) (.f64 1/6 (.f64 (sin.f64 re) (pow.f64 im 3))))))
	32.7b	(neg.f64 (+.f64 (.f64 (sqrt.f64 (sin.f64 re)) (.f64 (sqrt.f64 (sin.f64 re)) im)) (+.f64 (.f64 1/120 (.f64 (sin.f64 re) (pow.f64 im 5))) (.f64 1/6 (.f64 (sin.f64 re) (pow.f64 im 3))))))
	2.0b	(neg.f64 (+.f64 (.f64 (pow.f64 (cbrt.f64 im) 2) (.f64 (cbrt.f64 im) (sin.f64 re))) (+.f64 (.f64 1/120 (.f64 (sin.f64 re) (pow.f64 im 5))) (.f64 1/6 (.f64 (sin.f64 re) (pow.f64 im 3))))))
	35.3b	(neg.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 re) im) 3)) (+.f64 (.f64 1/120 (.f64 (sin.f64 re) (pow.f64 im 5))) (.f64 1/6 (*.f64 (sin.f64 re) (pow.f64 im 3))))))
✓	2.0b	(neg.f64 (+.f64 (.f64 (cbrt.f64 (sin.f64 re)) (.f64 (cbrt.f64 im) (pow.f64 (cbrt.f64 (.f64 (sin.f64 re) im)) 2))) (+.f64 (.f64 1/120 (.f64 (sin.f64 re) (pow.f64 im 5))) (.f64 1/6 (*.f64 (sin.f64 re) (pow.f64 im 3))))))

Compiler

Compiled 3798 to 2067 computations (45.6% saved)

regimes239.0ms (2.8%)

Accuracy

Total 0.8b remaining (89.1%)

Threshold costs 0.8b (89.1%)

Counts

33 → 1

Compiler

Compiled 5026 to 3517 computations (30% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
13×	`+-commutative_binary64`
11×	`sub-neg_binary64`
11×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	36
1	32	36
2	50	34
3	80	34
4	104	34
5	116	34
6	122	34
7	124	34

Stop Event

1×

saturated

end215.0ms (2.5%)

Stop Event

1×

fuel

Compiler

Compiled 332 to 227 computations (31.6% saved)

Details

analyze537.0ms (6.3%)

sample6.2s (72.7%)

preprocess89.0ms (1%)

simplify24.0ms (0.3%)

prune2.0ms (0%)

localize10.0ms (0.1%)

series17.0ms (0.2%)

rewrite76.0ms (0.9%)

simplify40.0ms (0.5%)

prune38.0ms (0.4%)

localize12.0ms (0.1%)

series51.0ms (0.6%)

rewrite50.0ms (0.6%)

simplify34.0ms (0.4%)

prune100.0ms (1.2%)

localize15.0ms (0.2%)

series135.0ms (1.6%)

rewrite37.0ms (0.4%)

simplify69.0ms (0.8%)

prune123.0ms (1.4%)

localize20.0ms (0.2%)

series130.0ms (1.5%)

rewrite43.0ms (0.5%)

simplify93.0ms (1.1%)

prune144.0ms (1.7%)

regimes239.0ms (2.8%)

simplify4.0ms (0%)

end215.0ms (2.5%)

Profiling