Details

analyze712.0ms (10.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample1.2s (18.1%)

Results

1.1s	8256×	body	128	valid
60.0ms	462×	body	128	invalid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify66.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1070×	`fma-neg_binary64`
881×	`fma-def_binary64`
768×	`times-frac_binary64`
551×	`cancel-sign-sub-inv_binary64`
514×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	25	20
2	47	20
3	78	20
4	149	20
5	228	20
6	324	20
7	500	20
8	694	20
9	867	20
10	999	20
11	2422	20
12	3920	20
13	4950	20

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

26.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	26.4b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))

Compiler

Compiled 69 to 33 computations (52.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y.re y.re (*.f64 y.im y.im))
✓	0.0b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
✓	25.9b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))

series90.0ms (1.3%)

Counts

3 → 120

Calls

3 calls:

71.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
13.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
6.0ms	(fma.f64 y.re y.re (*.f64 y.im y.im))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 58

Calls

3 calls:

6.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
3.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
0.0ms	(fma.f64 y.re y.re (*.f64 y.im y.im))

simplify133.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

523×	`fma-neg_binary64`
383×	`associate-l_binary64`
348×	`fma-def_binary64`
319×	`associate-r_binary64`
252×	`associate-/l*_binary64`

Counts

178 → 135

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	136	3054
1	326	2877
2	1095	2830
3	4407	2830
4	4995	2830
5	4946	2830

prune89.0ms (1.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	125	10	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	126	10	136

Error

1.6b

Counts

136 → 10

Alt Table

Status	Error	Program
	43.1b	(.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im))) (hypot.f64 y.im y.re)) (/.f64 (sqrt.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im))) (hypot.f64 y.im y.re)))
	36.9b	(-.f64 (fma.f64 (/.f64 y.re y.im) (/.f64 x.im y.im) (/.f64 (.f64 x.re (.f64 y.re y.re)) (pow.f64 y.im 3))) (/.f64 x.re y.im))
	26.9b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (.f64 (.f64 (cbrt.f64 (fma.f64 y.re y.re (.f64 y.im y.im))) (cbrt.f64 (fma.f64 y.re y.re (.f64 y.im y.im)))) (cbrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)))))
	37.1b	(neg.f64 (/.f64 x.re y.im))
▶	16.9b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)))
	34.3b	(-.f64 (/.f64 x.im y.re) (/.f64 (*.f64 x.re y.im) (pow.f64 y.re 2)))
	26.4b	(/.f64 (fma.f64 x.im y.re (neg.f64 (.f64 x.re y.im))) (fma.f64 y.re y.re (.f64 y.im y.im)))
	38.0b	(-.f64 (/.f64 x.im y.re) (fma.f64 (/.f64 x.re y.re) (/.f64 y.im y.re) (/.f64 (.f64 (.f64 y.im y.im) x.im) (pow.f64 y.re 3))))
	37.7b	(/.f64 x.im y.re)
	39.7b	(fma.f64 (/.f64 x.re (pow.f64 y.im 3)) (.f64 y.re y.re) (fma.f64 x.im (-.f64 (/.f64 y.re (.f64 y.im y.im)) (/.f64 (pow.f64 y.re 3) (pow.f64 y.im 4))) (neg.f64 (/.f64 x.re y.im))))

Compiler

Compiled 3354 to 748 computations (77.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 y.im y.re)
✓	0.0b	(-.f64 (.f64 y.re x.im) (.f64 x.re y.im))
✓	0.2b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)))
✓	15.9b	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im)) (hypot.f64 y.im y.re))

series202.0ms (2.9%)

Counts

4 → 132

Calls

4 calls:

96.0ms	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)))
86.0ms	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im)) (hypot.f64 y.im y.re))
10.0ms	(hypot.f64 y.im y.re)
8.0ms	(-.f64 (.f64 y.re x.im) (.f64 x.re y.im))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
34×	`times-frac_binary64`
28×	`*-un-lft-identity_binary64`
28×	`add-exp-log_binary64`
26×	`add-cube-cbrt_binary64`

Counts

4 → 116

Calls

4 calls:

9.0ms	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)))
4.0ms	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im)) (hypot.f64 y.im y.re))
3.0ms	(-.f64 (.f64 y.re x.im) (.f64 x.re y.im))
0.0ms	(hypot.f64 y.im y.re)

simplify122.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

880×	`times-frac_binary64`
525×	`fma-def_binary64`
334×	`cancel-sign-sub-inv_binary64`
217×	`fma-neg_binary64`
176×	`sub-neg_binary64`

Counts

248 → 253

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	269	6157
1	735	5482
2	2502	5423
3	4985	5423

prune196.0ms (2.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	290	5	295
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	295	10	305

Error

1.6b

Counts

305 → 10

Alt Table

Status	Error	Program
	34.3b	(-.f64 (/.f64 x.im y.re) (/.f64 (*.f64 x.re y.im) (pow.f64 y.re 2)))
▶	17.1b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (/.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))))
✓	16.9b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)))
	46.8b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 x.re (/.f64 (.f64 y.re x.im) y.im)))
	45.1b	(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.im))
	37.1b	(neg.f64 (/.f64 x.re y.im))
	45.0b	(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.re))
	40.7b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im)) (*.f64 (hypot.f64 y.im y.re) (hypot.f64 y.im y.re))) 3))
	38.0b	(-.f64 (/.f64 x.im y.re) (fma.f64 (/.f64 x.re y.re) (/.f64 y.im y.re) (/.f64 (.f64 (.f64 y.im y.im) x.im) (pow.f64 y.re 3))))
	39.7b	(fma.f64 (/.f64 x.re (pow.f64 y.im 3)) (.f64 y.re y.re) (fma.f64 x.im (-.f64 (/.f64 y.re (.f64 y.im y.im)) (/.f64 (pow.f64 y.re 3) (pow.f64 y.im 4))) (neg.f64 (/.f64 x.re y.im))))

Compiler

Compiled 8096 to 2551 computations (68.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (.f64 y.re x.im) (.f64 x.re y.im))
✓	0.2b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (/.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))))
✓	7.2b	(/.f64 (/.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re)))
✓	8.8b	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re)))

series332.0ms (4.8%)

Counts

3 → 128

Calls

3 calls:

151.0ms

(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re)))

94.0ms

(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re)))

86.0ms

(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))))

rewrite145.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

569×	`times-frac_binary64`
364×	`add-sqr-sqrt_binary64`
292×	`*-un-lft-identity_binary64`
285×	`add-cube-cbrt_binary64`
279×	`sqrt-prod_binary64`

Counts

3 → 424

Calls

3 calls:

41.0ms

(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))))

9.0ms

(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re)))

7.0ms

(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re)))

simplify401.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

546×	`fma-def_binary64`
362×	`associate-/l*_binary64`
353×	`associate-/l/_binary64`
314×	`associate-*l/_binary64`
298×	`associate-*r/_binary64`

Counts

552 → 574

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	477	21592
1	1302	19563
2	4087	18923
3	5093	18923

prune402.0ms (5.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	596	2	598
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	597	11	608

Error

1.6b

Counts

608 → 11

Alt Table

Status	Error	Program
	34.3b	(-.f64 (/.f64 x.im y.re) (/.f64 (*.f64 x.re y.im) (pow.f64 y.re 2)))
✓	17.1b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (/.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))))
✓	16.9b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)))
	46.8b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 x.re (/.f64 (.f64 y.re x.im) y.im)))
	45.1b	(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.im))
	37.1b	(neg.f64 (/.f64 x.re y.im))
	45.0b	(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.re))
	50.0b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (neg.f64 (.f64 x.re (sqrt.f64 y.im))) (sqrt.f64 (hypot.f64 y.im y.re))))
▶	26.6b	(pow.f64 (/.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im)) (pow.f64 (sqrt.f64 (hypot.f64 y.im y.re)) 4)) 1)
	38.0b	(-.f64 (/.f64 x.im y.re) (fma.f64 (/.f64 x.re y.re) (/.f64 y.im y.re) (/.f64 (.f64 (.f64 y.im y.im) x.im) (pow.f64 y.re 3))))
	39.7b	(fma.f64 (/.f64 x.re (pow.f64 y.im 3)) (.f64 y.re y.re) (fma.f64 x.im (-.f64 (/.f64 y.re (.f64 y.im y.im)) (/.f64 (pow.f64 y.re 3) (pow.f64 y.im 4))) (neg.f64 (/.f64 x.re y.im))))

Compiler

Compiled 23260 to 4381 computations (81.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 y.im y.re)
	0.0b	(-.f64 (.f64 y.re x.im) (.f64 x.re y.im))
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 y.im y.re)) 4)
✓	25.9b	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im)) (pow.f64 (sqrt.f64 (hypot.f64 y.im y.re)) 4))

series149.0ms (2.2%)

Counts

2 → 56

Calls

2 calls:

97.0ms	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im)) (pow.f64 (sqrt.f64 (hypot.f64 y.im y.re)) 4))
52.0ms	(pow.f64 (sqrt.f64 (hypot.f64 y.im y.re)) 4)

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`times-frac_binary64`
30×	`unpow-prod-down_binary64`
28×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
28×	`add-cube-cbrt_binary64`

Counts

2 → 87

Calls

2 calls:

6.0ms	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im)) (pow.f64 (sqrt.f64 (hypot.f64 y.im y.re)) 4))
2.0ms	(pow.f64 (sqrt.f64 (hypot.f64 y.im y.re)) 4)

simplify111.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

450×	`times-frac_binary64`
425×	`associate-/l*_binary64`
398×	`associate-/r*_binary64`
367×	`associate-l_binary64`
262×	`fma-neg_binary64`

Counts

143 → 138

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	167	3967
1	388	3483
2	1207	3422
3	4799	3421
4	4960	3421

prune152.0ms (2.2%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	204	11	215

Error

1.6b

Counts

215 → 11

Alt Table

Status	Error	Program
	34.3b	(-.f64 (/.f64 x.im y.re) (/.f64 (*.f64 x.re y.im) (pow.f64 y.re 2)))
✓	17.1b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (/.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))))
✓	16.9b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)))
	46.8b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 x.re (/.f64 (.f64 y.re x.im) y.im)))
	45.1b	(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.im))
	37.1b	(neg.f64 (/.f64 x.re y.im))
	45.0b	(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.re))
	50.0b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (neg.f64 (.f64 x.re (sqrt.f64 y.im))) (sqrt.f64 (hypot.f64 y.im y.re))))
✓	26.6b	(pow.f64 (/.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im)) (pow.f64 (sqrt.f64 (hypot.f64 y.im y.re)) 4)) 1)
	38.0b	(-.f64 (/.f64 x.im y.re) (fma.f64 (/.f64 x.re y.re) (/.f64 y.im y.re) (/.f64 (.f64 (.f64 y.im y.im) x.im) (pow.f64 y.re 3))))
	39.7b	(fma.f64 (/.f64 x.re (pow.f64 y.im 3)) (.f64 y.re y.re) (fma.f64 x.im (-.f64 (/.f64 y.re (.f64 y.im y.im)) (/.f64 (pow.f64 y.re 3) (pow.f64 y.im 4))) (neg.f64 (/.f64 x.re y.im))))

Compiler

Compiled 5331 to 2106 computations (60.5% saved)

regimes1.7s (25.3%)

Accuracy

Total 11.4b remaining (85%)

Threshold costs 0b (0%)

Counts

147 → 5

Compiler

Compiled 15823 to 9584 computations (39.4% saved)

bsearch70.0ms (1%)

Steps

Iters	Range		Point
4	1.782276665126511e+98	3.450029335556712e+98	2.723673641056143e+98
9	2.595895121154282e-116	1.012025539378144e-109	3.0839218551021475e-116
9	-1.475479794932978e-191	-6.931373179042015e-199	-6.426786380723436e-198
5	-5.502833891950998e+208	-1.7983961528141233e+208	-1.9259002861513078e+208

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
7×	`+-commutative_binary64`
7×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	100
1	52	100
2	66	100
3	75	100
4	80	100
5	81	100
6	80	100

end444.0ms (6.4%)

Compiler: Compiled 352 to 200 computations (43.2% saved)

Details

analyze712.0ms (10.3%)

sample1.2s (18.1%)

simplify66.0ms (0.9%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series90.0ms (1.3%)

rewrite12.0ms (0.2%)

simplify133.0ms (1.9%)

prune89.0ms (1.3%)

localize9.0ms (0.1%)

series202.0ms (2.9%)

rewrite26.0ms (0.4%)

simplify122.0ms (1.8%)

prune196.0ms (2.8%)

localize13.0ms (0.2%)

series332.0ms (4.8%)

rewrite145.0ms (2.1%)

simplify401.0ms (5.8%)

prune402.0ms (5.8%)

localize10.0ms (0.1%)

series149.0ms (2.2%)

rewrite16.0ms (0.2%)

simplify111.0ms (1.6%)

prune152.0ms (2.2%)

regimes1.7s (25.3%)

bsearch70.0ms (1%)

simplify5.0ms (0.1%)

end444.0ms (6.4%)

Profiling