Details

analyze575.0ms (4.6%)

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)

sample116.0ms (0.9%)

Algorithm

1×

intervals

Results

37.0ms	74×	body	1024	valid
20.0ms	53×	body	1024	invalid
12.0ms	76×	body	128	invalid
11.0ms	38×	body	512	valid
11.0ms	135×	body	128	valid
6.0ms	27×	body	512	invalid
2.0ms	2×	body	2048	valid
1.0ms	7×	body	256	valid
1.0ms	6×	body	256	invalid

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify85.0ms (0.7%)

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

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 51 to 34 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1/2 (exp.f64 im))
✓	0.0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
✓	0.0b	(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-cbrt-cube_binary64`

Counts

3 → 61

Calls

3 calls:

3.0ms	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
3.0ms	(/.f64 1/2 (exp.f64 im))
0.0ms	(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))

series87.0ms (0.7%)

Counts

3 → 40

Calls

3 calls:

60.0ms	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
17.0ms	(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
10.0ms	(/.f64 1/2 (exp.f64 im))

simplify86.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

686×	`fma-neg_binary64`
500×	`associate-l_binary64`
496×	`fma-def_binary64`
422×	`associate-r_binary64`
311×	`times-frac_binary64`

Counts

101 → 164

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	168	1824
1	395	1671
2	1184	1647
3	3869	1643
4	5027	1643

prune98.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	161	3	164
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	162	3	165

Error

Counts

165 → 3

Alt Table

Status	Error	Program
	0.0b	(*.f64 (sin.f64 re) (exp.f64 (log.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))))
	0.4b	(+.f64 (sin.f64 re) (.f64 (sin.f64 re) (fma.f64 1/2 (.f64 im im) (*.f64 1/24 (pow.f64 im 4)))))
▶	0.0b	(.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (exp.f64 im)))))

Compiler

Compiled 2096 to 1162 computations (44.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (exp.f64 im)))))
✓	0.0b	(fma.f64 1/2 (exp.f64 im) (*.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (exp.f64 im))))
✓	0.0b	(/.f64 (sqrt.f64 1/2) (exp.f64 im))
✓	1.0b	(*.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (exp.f64 im)))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
36×	`*-un-lft-identity_binary64`
36×	`add-cube-cbrt_binary64`
29×	`sqrt-prod_binary64`

Counts

4 → 123

Calls

4 calls:

9.0ms	(*.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (exp.f64 im)))
5.0ms	(.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (exp.f64 im)))))
4.0ms	(/.f64 (sqrt.f64 1/2) (exp.f64 im))
0.0ms	(fma.f64 1/2 (exp.f64 im) (*.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (exp.f64 im))))

series152.0ms (1.2%)

Counts

4 → 52

Calls

4 calls:

82.0ms	(.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (exp.f64 im)))))
33.0ms	(fma.f64 1/2 (exp.f64 im) (*.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (exp.f64 im))))
20.0ms	(*.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (exp.f64 im)))
17.0ms	(/.f64 (sqrt.f64 1/2) (exp.f64 im))

simplify133.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

532×	`fma-neg_binary64`
444×	`cancel-sign-sub-inv_binary64`
360×	`distribute-rgt-in_binary64`
348×	`distribute-lft-in_binary64`
194×	`associate-r_binary64`

Counts

175 → 310

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	250	3220
1	646	2845
2	2250	2749
3	4817	2740
4	5046	2740

prune183.0ms (1.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	310	0	310
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	310	3	313

Error

Counts

313 → 3

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (sin.f64 re) (exp.f64 (log.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))))
	0.4b	(+.f64 (sin.f64 re) (.f64 (sin.f64 re) (fma.f64 1/2 (.f64 im im) (*.f64 1/24 (pow.f64 im 4)))))
✓	0.0b	(.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (exp.f64 im)))))

Compiler

Compiled 4754 to 3037 computations (36.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (sin.f64 re) (exp.f64 (log.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))))
	0.0b	(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
✓	0.0b	(exp.f64 (log.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))))
✓	3.5b	(log.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
10×	`log-prod_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`
7×	`exp-sum_binary64`

Counts

3 → 55

Calls

3 calls:

5.0ms

(*.f64 (sin.f64 re) (exp.f64 (log.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))))

2.0ms

(exp.f64 (log.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))))

1.0ms

(log.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

series3.1s (24.9%)

Counts

3 → 48

Calls

3 calls:

1.8s

(*.f64 (sin.f64 re) (exp.f64 (log.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))))

809.0ms

(exp.f64 (log.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))))

431.0ms

(log.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

simplify194.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

794×	`fma-neg_binary64`
538×	`associate-l_binary64`
477×	`associate-r_binary64`
338×	`fma-def_binary64`
333×	`distribute-rgt-neg-in_binary64`

Counts

103 → 186

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	136	2070
1	283	1873
2	899	1815
3	3267	1795
4	4734	1794
5	4922	1794

prune212.0ms (1.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	220	3	223

Error

Counts

223 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (sin.f64 re) (exp.f64 (log.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))))
▶	0.4b	(+.f64 (sin.f64 re) (.f64 (sin.f64 re) (fma.f64 1/2 (.f64 im im) (*.f64 1/24 (pow.f64 im 4)))))
✓	0.0b	(.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (exp.f64 im)))))

Compiler

Compiled 2678 to 1628 computations (39.2% saved)

localize18.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/2 (.f64 im im) (.f64 1/24 (pow.f64 im 4)))
✓	0.1b	(*.f64 1/24 (pow.f64 im 4))
✓	0.1b	(.f64 (sin.f64 re) (fma.f64 1/2 (.f64 im im) (*.f64 1/24 (pow.f64 im 4))))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
10×	`associate-r_binary64`
10×	`add-exp-log_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`

Counts

3 → 59

Calls

3 calls:

6.0ms	(*.f64 1/24 (pow.f64 im 4))
5.0ms	(.f64 (sin.f64 re) (fma.f64 1/2 (.f64 im im) (*.f64 1/24 (pow.f64 im 4))))
1.0ms	(fma.f64 1/2 (.f64 im im) (.f64 1/24 (pow.f64 im 4)))

series145.0ms (1.2%)

Counts

3 → 36

Calls

3 calls:

95.0ms	(.f64 (sin.f64 re) (fma.f64 1/2 (.f64 im im) (*.f64 1/24 (pow.f64 im 4))))
26.0ms	(fma.f64 1/2 (.f64 im im) (.f64 1/24 (pow.f64 im 4)))
24.0ms	(*.f64 1/24 (pow.f64 im 4))

simplify158.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

751×	`fma-neg_binary64`
456×	`fma-def_binary64`
300×	`*-commutative_binary64`
264×	`sub-neg_binary64`
199×	`cancel-sign-sub-inv_binary64`

Counts

95 → 170

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	144	1808
1	324	1676
2	1062	1628
3	2997	1623
4	4903	1623
5	4933	1623

prune206.0ms (1.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	170	3	173

Error

Counts

173 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (sin.f64 re) (exp.f64 (log.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))))
✓	0.4b	(+.f64 (sin.f64 re) (.f64 (sin.f64 re) (fma.f64 1/2 (.f64 im im) (*.f64 1/24 (pow.f64 im 4)))))
✓	0.0b	(.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (exp.f64 im)))))

Compiler

Compiled 2544 to 1493 computations (41.3% saved)

regimes488.0ms (3.9%)

Accuracy

Total 0.0b remaining (40.7%)

Threshold costs 0.0b (40.7%)

Compiler

Compiled 4200 to 3059 computations (27.2% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	13	24
2	13	24

end1.0ms (0%)

Compiler: Compiled 17 to 13 computations (23.5% saved)

sample6.3s (50.6%)

Algorithm

1×

intervals

Results

1.9s	1991×	body	1024	valid
1.4s	1990×	body	1024	invalid
608.0ms	4468×	body	128	valid
442.0ms	958×	body	512	invalid
438.0ms	2520×	body	128	invalid
430.0ms	1003×	body	512	valid
141.0ms	532×	body	256	valid
135.0ms	484×	body	256	invalid
9.0ms	6×	body	2048	valid

Compiler

Compiled 84 to 63 computations (25% saved)

Details

analyze575.0ms (4.6%)

sample116.0ms (0.9%)

simplify85.0ms (0.7%)

prune3.0ms (0%)

localize7.0ms (0.1%)

rewrite9.0ms (0.1%)

series87.0ms (0.7%)

simplify86.0ms (0.7%)

prune98.0ms (0.8%)

localize9.0ms (0.1%)

rewrite25.0ms (0.2%)

series152.0ms (1.2%)

simplify133.0ms (1.1%)

prune183.0ms (1.5%)

localize11.0ms (0.1%)

rewrite10.0ms (0.1%)

series3.1s (24.9%)

simplify194.0ms (1.6%)

prune212.0ms (1.7%)

localize18.0ms (0.1%)

rewrite18.0ms (0.1%)

series145.0ms (1.2%)

simplify158.0ms (1.3%)

prune206.0ms (1.7%)

regimes488.0ms (3.9%)

simplify5.0ms (0%)

end1.0ms (0%)

sample6.3s (50.6%)

Profiling