Details

analyze190.0ms (4.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
50%	50%	0.1%	2
50%	50%	0.1%	3
74.9%	25%	0.1%	4
74.9%	25%	0.1%	5
74.9%	18.7%	6.3%	6
74.9%	18.7%	6.3%	7
74.9%	15.6%	9.5%	8
74.9%	15.6%	9.5%	9
74.9%	14%	11%	10
74.9%	14%	11%	11
74.9%	13.3%	11.8%	12
74.9%	13.3%	11.8%	13
74.9%	12.9%	12.2%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample46.0ms (1.1%)

Algorithm

1×

intervals

Results

11.0ms	33×	body	1024	valid
11.0ms	190×	body	128	valid
6.0ms	25×	body	1024	invalid
3.0ms	23×	body	512	valid
2.0ms	13×	body	512	invalid
1.0ms	10×	body	256	valid
1.0ms	7×	body	256	invalid
1.0ms	11×	body	128	invalid

Compiler

Compiled 17 to 13 computations (23.5% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8
2	7	8

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (exp.f64 re) (cos.f64 im))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (exp.f64 re) (cos.f64 im))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 20

Calls

1 calls:

4.0ms

(*.f64 (exp.f64 re) (cos.f64 im))

series20.0ms (0.5%)

Counts

1 → 8

Calls

1 calls:

20.0ms

(*.f64 (exp.f64 re) (cos.f64 im))

simplify109.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

943×	`fma-neg_binary64`
594×	`cancel-sign-sub-inv_binary64`
333×	`distribute-rgt-neg-in_binary64`
263×	`*-commutative_binary64`
243×	`distribute-rgt-in_binary64`

Counts

28 → 47

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	67	406
1	167	370
2	476	352
3	1277	335
4	2313	333
5	4556	333
6	4836	333
7	4972	333
8	4841	333

prune77.0ms (1.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	45	2	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	2	48

Error

Counts

48 → 2

Alt Table

Status	Error	Program
▶	0.1b	(expm1.f64 (log1p.f64 (*.f64 (exp.f64 re) (cos.f64 im))))
	22.2b	(+.f64 (cos.f64 im) (+.f64 (.f64 (cos.f64 im) re) (.f64 1/2 (*.f64 (cos.f64 im) (pow.f64 re 2)))))

Compiler

Compiled 544 to 215 computations (60.5% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (exp.f64 re) (cos.f64 im))
✓	0.1b	(expm1.f64 (log1p.f64 (*.f64 (exp.f64 re) (cos.f64 im))))
✓	0.2b	(log1p.f64 (*.f64 (exp.f64 re) (cos.f64 im)))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(log1p.f64 (*.f64 (exp.f64 re) (cos.f64 im)))
0.0ms	(expm1.f64 (log1p.f64 (*.f64 (exp.f64 re) (cos.f64 im))))

series1.3s (31.6%)

Counts

2 → 48

Calls

2 calls:

666.0ms	(log1p.f64 (*.f64 (exp.f64 re) (cos.f64 im)))
642.0ms	(expm1.f64 (log1p.f64 (*.f64 (exp.f64 re) (cos.f64 im))))

simplify73.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

880×	`times-frac_binary64`
408×	`fma-def_binary64`
264×	`distribute-rgt-in_binary64`
236×	`distribute-lft-in_binary64`
226×	`associate-/r/_binary64`

Counts

70 → 134

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	148	1472
1	428	1373
2	1575	1127
3	5073	1127

prune71.0ms (1.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	181	2	183

Error

Counts

183 → 2

Alt Table

Status	Error	Program
✓	0.1b	(expm1.f64 (log1p.f64 (*.f64 (exp.f64 re) (cos.f64 im))))
▶	22.2b	(+.f64 (fma.f64 1/2 (.f64 (cos.f64 im) (.f64 re re)) (*.f64 (cos.f64 im) re)) (cos.f64 im))

Compiler

Compiled 2062 to 975 computations (52.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (fma.f64 1/2 (.f64 (cos.f64 im) (.f64 re re)) (*.f64 (cos.f64 im) re)) (cos.f64 im))
✓	0.0b	(fma.f64 1/2 (.f64 (cos.f64 im) (.f64 re re)) (*.f64 (cos.f64 im) re))
✓	0.1b	(.f64 (cos.f64 im) (.f64 re re))
✓	0.1b	(*.f64 (cos.f64 im) re)

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
11×	`pow1_binary64`
10×	`*-un-lft-identity_binary64`

Counts

4 → 69

Calls

4 calls:

4.0ms	(.f64 (cos.f64 im) (.f64 re re))
3.0ms	(*.f64 (cos.f64 im) re)
3.0ms	(+.f64 (fma.f64 1/2 (.f64 (cos.f64 im) (.f64 re re)) (*.f64 (cos.f64 im) re)) (cos.f64 im))
0.0ms	(fma.f64 1/2 (.f64 (cos.f64 im) (.f64 re re)) (*.f64 (cos.f64 im) re))

series142.0ms (3.4%)

Counts

4 → 76

Calls

4 calls:

46.0ms	(fma.f64 1/2 (.f64 (cos.f64 im) (.f64 re re)) (*.f64 (cos.f64 im) re))
40.0ms	(+.f64 (fma.f64 1/2 (.f64 (cos.f64 im) (.f64 re re)) (*.f64 (cos.f64 im) re)) (cos.f64 im))
32.0ms	(.f64 (cos.f64 im) (.f64 re re))
23.0ms	(*.f64 (cos.f64 im) re)

simplify105.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

918×	`fma-def_binary64`
813×	`fma-neg_binary64`
520×	`cancel-sign-sub-inv_binary64`
478×	`associate--l+_binary64`
283×	`distribute-rgt-in_binary64`

Counts

145 → 271

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	164	2721
1	449	2553
2	1560	2118
3	4732	2113
4	5364	2113

prune139.0ms (3.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	271	0	271
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	271	2	273

Error

Counts

273 → 2

Alt Table

Status	Error	Program
✓	0.1b	(expm1.f64 (log1p.f64 (*.f64 (exp.f64 re) (cos.f64 im))))
✓	22.2b	(+.f64 (fma.f64 1/2 (.f64 (cos.f64 im) (.f64 re re)) (*.f64 (cos.f64 im) re)) (cos.f64 im))

Compiler

Compiled 3494 to 1371 computations (60.8% saved)

regimes334.0ms (8.1%)

Accuracy

Total -0.0b remaining (-227.6%)

Threshold costs -0.0b (-227.6%)

Compiler

Compiled 3758 to 2547 computations (32.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8
2	7	8

end0.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

sample1.5s (35.6%)

Algorithm

1×

intervals

Results

453.0ms	1341×	body	1024	valid
285.0ms	5625×	body	128	valid
172.0ms	645×	body	1024	invalid
128.0ms	690×	body	512	valid
44.0ms	314×	body	512	invalid
35.0ms	341×	body	256	valid
18.0ms	190×	body	256	invalid
12.0ms	211×	body	128	invalid
3.0ms	3×	body	2048	valid

Compiler

Compiled 43 to 29 computations (32.6% saved)

Details

analyze190.0ms (4.6%)

sample46.0ms (1.1%)

simplify9.0ms (0.2%)

prune1.0ms (0%)

localize4.0ms (0.1%)

rewrite4.0ms (0.1%)

series20.0ms (0.5%)

simplify109.0ms (2.6%)

prune77.0ms (1.9%)

localize7.0ms (0.2%)

rewrite2.0ms (0%)

series1.3s (31.6%)

simplify73.0ms (1.8%)

prune71.0ms (1.7%)

localize10.0ms (0.2%)

rewrite13.0ms (0.3%)

series142.0ms (3.4%)

simplify105.0ms (2.5%)

prune139.0ms (3.4%)

regimes334.0ms (8.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.5s (35.6%)

Profiling