Details

analyze537.0ms (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%	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)

sample6.0s (72%)

Results

2.9s	4208×	body	1024	valid
1.1s	2035×	body	1024	invalid
796.0ms	2090×	body	512	valid
363.0ms	1034×	body	512	invalid
265.0ms	1046×	body	256	valid
240.0ms	222×	body	2048	valid
128.0ms	527×	body	256	invalid
111.0ms	746×	body	128	invalid
95.0ms	690×	body	128	valid
1.0ms	1×	body	2048	invalid

Compiler

Compiled 28 to 22 computations (21.4% saved)

preprocess44.0ms (0.5%)

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)

simplify26.0ms (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)

localize8.0ms (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))

series19.0ms (0.2%)

Counts

2 → 32

Calls

9 calls:

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

rewrite78.0ms (0.9%)

Algorithm

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

Rules

118×	`add-sqr-sqrt_binary64`
118×	`add-sqr-sqrt_binary64`
113×	`*-un-lft-identity_binary64`
113×	`pow1_binary64`
113×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	228	20
2	3510	20
0	6	10
1	127	10
2	2085	10
0	6	10
0	11	18
1	228	18
2	3509	18
0	11	18

Stop Event

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

Counts

2 → 18

simplify41.0ms (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

prune40.0ms (0.5%)

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
✓	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))))))
	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))))

Compiler

Compiled 1062 to 552 computations (48% saved)

localize13.0ms (0.2%)

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)

series56.0ms (0.7%)

Counts

4 → 16

Calls

24 calls:

5.0ms	(*.f64 (sin.f64 re) (pow.f64 im 5))	re	-inf
4.0ms	(.f64 1/6 (.f64 (sin.f64 re) (pow.f64 im 3)))	im	-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

rewrite51.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	36
1	275	36
2	3057	36

Stop Event

1×	node limit

Counts

4 → 70

simplify35.0ms (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

prune103.0ms (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
✓	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))))))
▶	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))))

Compiler

Compiled 3139 to 2002 computations (36.2% saved)

localize17.0ms (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))

series150.0ms (1.8%)

Counts

2 → 16

Calls

12 calls:

28.0ms	(pow.f64 (cbrt.f64 (*.f64 (sin.f64 re) im)) 3)	re	-inf
28.0ms	(pow.f64 (cbrt.f64 (*.f64 (sin.f64 re) im)) 3)	re	inf
25.0ms	(cbrt.f64 (*.f64 (sin.f64 re) im))	re	inf
23.0ms	(cbrt.f64 (*.f64 (sin.f64 re) im))	re	-inf
19.0ms	(pow.f64 (cbrt.f64 (*.f64 (sin.f64 re) im)) 3)	im	-inf

rewrite39.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

638×	`pow1_binary64`
596×	`add-log-exp_binary64`
596×	`log1p-expm1-u_binary64`
596×	`expm1-log1p-u_binary64`
71×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	166	14
2	1669	14

Stop Event

1×	node limit

Counts

2 → 56

simplify71.0ms (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

72 → 57

prune120.0ms (1.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	102	4	106
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	102	9	111

Error

0.0b

Counts

111 → 9

Alt Table

Status	Error	Program
✓	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))))))
▶	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))))))
	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))))))
	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))))))
✓	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))))

Compiler

Compiled 3729 to 2291 computations (38.6% saved)

localize22.0ms (0.3%)

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))

series129.0ms (1.5%)

Counts

3 → 16

Calls

12 calls:

25.0ms	(pow.f64 (cbrt.f64 (*.f64 (sin.f64 re) im)) 2)	re	inf
24.0ms	(pow.f64 (cbrt.f64 (*.f64 (sin.f64 re) im)) 2)	re	-inf
20.0ms	(cbrt.f64 (sin.f64 re))	re	inf
19.0ms	(pow.f64 (cbrt.f64 (*.f64 (sin.f64 re) im)) 2)	im	-inf
19.0ms	(cbrt.f64 (sin.f64 re))	re	-inf

rewrite47.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

790×	`pow1_binary64`
726×	`log1p-expm1-u_binary64`
726×	`expm1-log1p-u_binary64`
90×	`add-sqr-sqrt_binary64`
87×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	194	19
2	2078	19

Stop Event

1×	node limit

Counts

3 → 63

simplify95.0ms (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

prune110.0ms (1.3%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	88	10	98

Error

0.0b

Counts

98 → 10

Alt Table

Status	Error	Program
✓	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))))))
✓	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))))))
	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))))))
	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))))))
✓	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))))

Compiler

Compiled 3592 to 1965 computations (45.3% saved)

regimes229.0ms (2.7%)

Accuracy

Total 0.8b remaining (89.1%)

Threshold costs 0.8b (89.1%)

Counts

33 → 1

Compiler

Compiled 5026 to 3517 computations (30% saved)

simplify7.0ms (0.1%)

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

end263.0ms (3.1%)

Stop Event

1×

fuel

Compiler

Compiled 332 to 227 computations (31.6% saved)

Details

analyze537.0ms (6.4%)

sample6.0s (72%)

preprocess44.0ms (0.5%)

simplify26.0ms (0.3%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series19.0ms (0.2%)

rewrite78.0ms (0.9%)

simplify41.0ms (0.5%)

prune40.0ms (0.5%)

localize13.0ms (0.2%)

series56.0ms (0.7%)

rewrite51.0ms (0.6%)

simplify35.0ms (0.4%)

prune103.0ms (1.2%)

localize17.0ms (0.2%)

series150.0ms (1.8%)

rewrite39.0ms (0.5%)

simplify71.0ms (0.8%)

prune120.0ms (1.4%)

localize22.0ms (0.3%)

series129.0ms (1.5%)

rewrite47.0ms (0.6%)

simplify95.0ms (1.1%)

prune110.0ms (1.3%)

regimes229.0ms (2.7%)

simplify7.0ms (0.1%)

end263.0ms (3.1%)

Profiling