Details

analyze564.0ms (5.7%)

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 15 to 12 computations (20% saved)

sample5.6s (56.6%)

Results

1.8s	2066×	body	1024	valid
1.4s	2042×	body	1024	invalid
818.0ms	4697×	body	128	valid
509.0ms	1019×	body	512	valid
417.0ms	1018×	body	512	invalid
160.0ms	532×	body	256	invalid
148.0ms	467×	body	256	valid
139.0ms	814×	body	128	invalid
17.0ms	7×	body	2048	valid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify81.0ms (0.8%)

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

prune5.0ms (0.1%)

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)

localize16.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series73.0ms (0.7%)

Counts

3 → 40

Calls

3 calls:

46.0ms	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
16.0ms	(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
11.0ms	(/.f64 1/2 (exp.f64 im))

rewrite16.0ms (0.2%)

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:

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

simplify113.0ms (1.1%)

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 → 109

Iterations

Useful iterations: 3 (0.0ms)

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

prune203.0ms (2.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	3	110

Error

Counts

110 → 3

Alt Table

Status	Error	Program
	0.8b	(+.f64 (sin.f64 re) (.f64 1/2 (.f64 (sin.f64 re) (pow.f64 im 2))))
	19.4b	(cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 re) (sin.f64 re)) (sin.f64 re)) (.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))))
▶	0.0b	(.f64 (.f64 (sin.f64 re) (sqrt.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))) (sqrt.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))))

Compiler

Compiled 2141 to 1181 computations (44.8% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series120.0ms (1.2%)

Counts

3 → 60

Calls

3 calls:

54.0ms

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

47.0ms

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

18.0ms

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

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`associate-r_binary64`
11×	`pow1_binary64`
10×	`sqrt-prod_binary64`
10×	`add-cbrt-cube_binary64`

Counts

3 → 62

Calls

3 calls:

11.0ms

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

9.0ms

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

2.0ms

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

simplify190.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

694×	`fma-neg_binary64`
596×	`fma-def_binary64`
342×	`sub-neg_binary64`
331×	`*-commutative_binary64`
244×	`distribute-rgt-in_binary64`

Counts

122 → 123

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	2812
1	430	2612
2	1369	2530
3	3753	2528
4	4844	2528
5	4978	2528

prune460.0ms (4.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	228	2	230
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	230	3	233

Error

Counts

233 → 3

Alt Table

Status	Error	Program
▶	0.0b	(.f64 (.f64 (*.f64 (sin.f64 re) (sqrt.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))) (sqrt.f64 (sqrt.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))))) (sqrt.f64 (sqrt.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))))
	0.8b	(fma.f64 1/2 (.f64 (sin.f64 re) (.f64 im im)) (sin.f64 re))
✓	0.0b	(.f64 (.f64 (sin.f64 re) (sqrt.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))) (sqrt.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))))

Compiler

Compiled 6738 to 3943 computations (41.5% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series44.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

44.0ms

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

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`
9×	`sqrt-prod_binary64`
9×	`associate-r_binary64`

Counts

1 → 29

Calls

1 calls:

20.0ms

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

simplify133.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

697×	`fma-neg_binary64`
515×	`cancel-sign-sub-inv_binary64`
373×	`fma-def_binary64`
356×	`*-commutative_binary64`
257×	`sub-neg_binary64`

Counts

53 → 55

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	125	1924
1	338	1281
2	1131	1273
3	2983	1264
4	4565	1261
5	5170	1261

prune740.0ms (7.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	302	0	302
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	302	3	305

Error

Counts

305 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (.f64 (*.f64 (sin.f64 re) (sqrt.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))) (sqrt.f64 (sqrt.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))))) (sqrt.f64 (sqrt.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))))
▶	0.8b	(fma.f64 1/2 (.f64 (sin.f64 re) (.f64 im im)) (sin.f64 re))
✓	0.0b	(.f64 (.f64 (sin.f64 re) (sqrt.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))) (sqrt.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))))

Compiler

Compiled 12121 to 7383 computations (39.1% saved)

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series50.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

27.0ms	(fma.f64 1/2 (.f64 (sin.f64 re) (.f64 im im)) (sin.f64 re))
22.0ms	(.f64 (sin.f64 re) (.f64 im im))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
4×	`add-sqr-sqrt_binary64`
3×	`associate-l_binary64`

Counts

2 → 31

Calls

2 calls:

8.0ms	(.f64 (sin.f64 re) (.f64 im im))
1.0ms	(fma.f64 1/2 (.f64 (sin.f64 re) (.f64 im im)) (sin.f64 re))

simplify145.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

474×	`associate-l_binary64`
408×	`fma-def_binary64`
381×	`associate-r_binary64`
338×	`distribute-rgt-neg-in_binary64`
328×	`distribute-lft-neg-in_binary64`

Counts

79 → 71

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	98	1249
1	247	1133
2	809	1043
3	3073	1043
4	4999	1043
5	4930	1043

prune128.0ms (1.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	71	3	74

Error

Counts

74 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (.f64 (*.f64 (sin.f64 re) (sqrt.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))) (sqrt.f64 (sqrt.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))))) (sqrt.f64 (sqrt.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))))
✓	0.8b	(fma.f64 1/2 (.f64 (sin.f64 re) (.f64 im im)) (sin.f64 re))
✓	0.0b	(.f64 (.f64 (sin.f64 re) (sqrt.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))) (sqrt.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))))

Compiler

Compiled 1293 to 607 computations (53.1% saved)

regimes903.0ms (9.1%)

Accuracy

Total 0.0b remaining (67.2%)

Threshold costs 0.0b (67.2%)

Counts

67 → 1

Compiler

Compiled 7248 to 5031 computations (30.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	55
1	16	55
2	16	55

end174.0ms (1.8%)

Compiler: Compiled 144 to 95 computations (34% saved)

Details

analyze564.0ms (5.7%)

sample5.6s (56.6%)

simplify81.0ms (0.8%)

prune5.0ms (0.1%)

localize16.0ms (0.2%)

series73.0ms (0.7%)

rewrite16.0ms (0.2%)

simplify113.0ms (1.1%)

prune203.0ms (2.1%)

localize22.0ms (0.2%)

series120.0ms (1.2%)

rewrite27.0ms (0.3%)

simplify190.0ms (1.9%)

prune460.0ms (4.7%)

localize23.0ms (0.2%)

series44.0ms (0.4%)

rewrite27.0ms (0.3%)

simplify133.0ms (1.3%)

prune740.0ms (7.5%)

localize12.0ms (0.1%)

series50.0ms (0.5%)

rewrite11.0ms (0.1%)

simplify145.0ms (1.5%)

prune128.0ms (1.3%)

regimes903.0ms (9.1%)

simplify3.0ms (0%)

end174.0ms (1.8%)

Profiling