Details

analyze612.0ms (11.3%)

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
25%	74.9%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
62.4%	31.2%	6.3%	7
62.4%	31.2%	6.3%	8
62.4%	28.1%	9.5%	9
62.4%	28.1%	9.5%	10
62.4%	26.5%	11%	11
62.4%	26.5%	11%	12
62.4%	25.8%	11.8%	13
62.4%	25.8%	11.8%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample122.0ms (2.3%)

Algorithm

1×

intervals

Results

36.0ms	66×	body	1024	valid
27.0ms	63×	body	1024	invalid
12.0ms	145×	body	128	valid
11.0ms	33×	body	512	valid
10.0ms	33×	body	512	invalid
6.0ms	77×	body	128	invalid
2.0ms	12×	body	256	valid
1.0ms	8×	body	256	invalid

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify77.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

778×	`unswap-sqr_binary64`
536×	`fma-def_binary64`
491×	`associate-/r*_binary64`
476×	`fabs-mul_binary64`
360×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	27	18
2	65	18
3	104	17
4	137	17
5	196	17
6	329	17
7	736	17
8	2242	17
9	2250	17
10	2619	17
11	4128	17
12	4563	17
13	5391	17

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
▶	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))

Compiler

Compiled 79 to 56 computations (29.1% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))

series20.0ms (0.4%)

Counts

2 → 36

Calls

2 calls:

18.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
2.0ms	(+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`fma-def_binary64`
15×	`*-un-lft-identity_binary64`
13×	`exp-sum_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 55

Calls

2 calls:

12.0ms	(+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))
12.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))

simplify75.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

682×	`fma-def_binary64`
579×	`fma-neg_binary64`
407×	`times-frac_binary64`
388×	`*-commutative_binary64`
341×	`distribute-rgt-in_binary64`

Counts

91 → 102

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	146	1574
1	410	1348
2	1452	1317
3	4116	1316
4	5087	1316

prune75.0ms (1.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	101	3	104

Error

Counts

104 → 3

Alt Table

Status	Error	Program
▶	1.0b	(.f64 (.f64 (*.f64 1/2 (sin.f64 re)) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))))
	31.1b	(*.f64 1/2 (fma.f64 (exp.f64 im) re (/.f64 re (exp.f64 im))))
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))

Compiler

Compiled 2260 to 1251 computations (44.6% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
	0.0b	(+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))
✓	0.5b	(.f64 (.f64 1/2 (sin.f64 re)) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))
✓	0.5b	(.f64 (.f64 (*.f64 1/2 (sin.f64 re)) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))))

series50.0ms (0.9%)

Counts

3 → 56

Calls

3 calls:

28.0ms

(*.f64 (*.f64 1/2 (sin.f64 re)) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))

17.0ms

(*.f64 (*.f64 (*.f64 1/2 (sin.f64 re)) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))))

4.0ms

(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

rewrite43.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
17×	`pow1_binary64`
14×	`associate-r_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 78

Calls

3 calls:

22.0ms

(*.f64 (*.f64 (*.f64 1/2 (sin.f64 re)) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))))

9.0ms

(*.f64 (*.f64 1/2 (sin.f64 re)) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))

5.0ms

(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

simplify93.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

904×	`fma-def_binary64`
450×	`distribute-rgt-in_binary64`
358×	`associate-l_binary64`
337×	`cancel-sign-sub-inv_binary64`
265×	`associate-r_binary64`

Counts

134 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	258	3621
1	672	3081
2	2365	2954
3	4955	2954

prune110.0ms (2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	194	3	197

Error

Counts

197 → 3

Alt Table

Status	Error	Program
✓	1.0b	(.f64 (.f64 (*.f64 1/2 (sin.f64 re)) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))))
▶	31.1b	(*.f64 1/2 (fma.f64 (exp.f64 im) re (/.f64 re (exp.f64 im))))
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))

Compiler

Compiled 6098 to 2844 computations (53.4% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (exp.f64 im) re (/.f64 re (exp.f64 im)))
✓	0.0b	(/.f64 re (exp.f64 im))

series39.0ms (0.7%)

Counts

2 → 28

Calls

2 calls:

21.0ms	(fma.f64 (exp.f64 im) re (/.f64 re (exp.f64 im)))
17.0ms	(/.f64 re (exp.f64 im))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

3.0ms	(/.f64 re (exp.f64 im))
0.0ms	(fma.f64 (exp.f64 im) re (/.f64 re (exp.f64 im)))

simplify89.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

837×	`fma-def_binary64`
716×	`fma-neg_binary64`
418×	`associate-/l*_binary64`
299×	`cancel-sign-sub-inv_binary64`
244×	`associate-*l/_binary64`

Counts

67 → 68

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	897
1	208	844
2	502	833
3	1406	822
4	4321	822
5	4973	822
6	4928	822

prune35.0ms (0.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	68	3	71

Error

Counts

71 → 3

Alt Table

Status	Error	Program
✓	1.0b	(.f64 (.f64 (*.f64 1/2 (sin.f64 re)) (sqrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (sqrt.f64 (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))))
✓	31.1b	(*.f64 1/2 (fma.f64 (exp.f64 im) re (/.f64 re (exp.f64 im))))
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))

Compiler

Compiled 1099 to 450 computations (59.1% saved)

regimes140.0ms (2.6%)

Accuracy

Total 0.0b remaining (53.6%)

Threshold costs 0.0b (53.6%)

Counts

21 → 1

Compiler

Compiled 1802 to 1320 computations (26.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	18	18
2	20	18
3	21	18
4	21	18

end1.0ms (0%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

sample3.7s (69.3%)

Algorithm

1×

intervals

Results

1.1s	2043×	body	1024	valid
742.0ms	1916×	body	1024	invalid
394.0ms	4493×	body	128	valid
321.0ms	956×	body	512	valid
231.0ms	967×	body	512	invalid
221.0ms	2556×	body	128	invalid
85.0ms	500×	body	256	valid
83.0ms	513×	body	256	invalid
9.0ms	8×	body	2048	valid

Compiler

Compiled 79 to 59 computations (25.3% saved)

Details

analyze612.0ms (11.3%)

sample122.0ms (2.3%)

simplify77.0ms (1.4%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series20.0ms (0.4%)

rewrite28.0ms (0.5%)

simplify75.0ms (1.4%)

prune75.0ms (1.4%)

localize15.0ms (0.3%)

series50.0ms (0.9%)

rewrite43.0ms (0.8%)

simplify93.0ms (1.7%)

prune110.0ms (2%)

localize11.0ms (0.2%)

series39.0ms (0.7%)

rewrite5.0ms (0.1%)

simplify89.0ms (1.7%)

prune35.0ms (0.6%)

regimes140.0ms (2.6%)

simplify3.0ms (0%)

end1.0ms (0%)

sample3.7s (69.3%)

Profiling