Details

analyze2.2s (17.5%)

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
9.4%	90.4%	0.2%	6
17.2%	82.7%	0.2%	7
19.5%	80.3%	0.2%	8
30.8%	69%	0.2%	9
35.5%	64.3%	0.2%	10
42.4%	57.4%	0.2%	11
47.1%	52.7%	0.2%	12
48.9%	50.9%	0.2%	13
50%	49.7%	0.2%	14

Compiler

Compiled 42 to 20 computations (52.4% saved)

sample6.3s (50.8%)

Results

2.5s	2543×	body	1024	invalid
1.8s	7883×	body	128	valid
746.0ms	931×	body	512	invalid
483.0ms	214×	body	2048	invalid
157.0ms	347×	body	256	invalid
150.0ms	156×	body	1024	valid
133.0ms	510×	body	128	invalid
75.0ms	118×	body	512	valid
36.0ms	85×	body	256	valid
22.0ms	14×	body	2048	valid

Compiler

Compiled 125 to 59 computations (52.8% saved)

simplify67.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

892×	`unswap-sqr_binary64`
461×	`associate-/l*_binary64`
323×	`associate-/r*_binary64`
296×	`associate-*l/_binary64`
286×	`associate-*r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	40
1	39	38
2	70	38
3	118	38
4	263	38
5	996	38
6	3043	38
7	4085	38
8	4541	38
9	4866	38
10	4932	38

prune5.0ms (0%)

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

5.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	33.0b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))))
▶	6.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))

Status

Error

Program

33.0b

(*.f64 (exp.f64 (-.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.re) (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))))

▶

6.4b

(*.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))

Compiler

Compiled 206 to 96 computations (53.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))
✓	0.6b	(*.f64 y.re (atan2.f64 x.im x.re))
✓	0.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
✓	32.1b	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

series398.0ms (3.2%)

Counts

4 → 96

Calls

4 calls:

276.0ms	(fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))
107.0ms	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))
7.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
7.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`

Counts

4 → 60

Calls

4 calls:

2.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
2.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
1.0ms	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))
0.0ms	(fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))

simplify142.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

433×	`associate-r_binary64`
296×	`sub-neg_binary64`
295×	`fma-neg_binary64`
279×	`fma-def_binary64`
278×	`associate-l_binary64`

Counts

156 → 186

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	424	5775
1	1273	5176
2	4198	5164
3	4994	5164
4	4931	5164

prune245.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	177	9	186
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	178	10	188

Error

4.6b

Counts

188 → 10

Alt Table

Status	Error	Program
	19.8b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (expm1.f64 (log1p.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
	39.3b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (-.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 (log.f64 (/.f64 -1 x.im)) y.im))))
	33.0b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))))
	39.7b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 x.im) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	32.2b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (.f64 (sqrt.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))) (sqrt.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
	6.8b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))) (cbrt.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re))))) (cbrt.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
	18.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (pow.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
▶	6.5b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re))))))
	39.2b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (cbrt.f64 (.f64 (.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re))) (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))) (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
	25.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (cbrt.f64 (.f64 (.f64 (.f64 y.re y.re) y.re) (.f64 (*.f64 (atan2.f64 x.im x.re) (atan2.f64 x.im x.re)) (atan2.f64 x.im x.re)))))))

Compiler

Compiled 9664 to 3245 computations (66.4% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re)))
✓	0.6b	(cbrt.f64 y.re)
	0.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
✓	32.4b	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re)))))

series151.0ms (1.2%)

Counts

3 → 96

Calls

3 calls:

98.0ms

(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re)))))

33.0ms

(cbrt.f64 y.re)

19.0ms

(*.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re)))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-exp-log_binary64`
15×	`pow1_binary64`
9×	`add-cbrt-cube_binary64`
8×	`cbrt-unprod_binary64`
8×	`prod-exp_binary64`

Counts

3 → 47

Calls

3 calls:

7.0ms

(*.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re)))

1.0ms

(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re)))))

1.0ms

(cbrt.f64 y.re)

simplify96.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

677×	`fma-def_binary64`
467×	`associate-r_binary64`
321×	`associate-l_binary64`
255×	`*-commutative_binary64`
250×	`unswap-sqr_binary64`

Counts

143 → 122

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	372	4492
1	1077	4087
2	3715	4081
3	4952	4081

prune287.0ms (2.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	183	5	188
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	184	14	198

Error

4.6b

Counts

198 → 14

Alt Table

Status	Error	Program
	19.8b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (expm1.f64 (log1p.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
	39.3b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (-.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 (log.f64 (/.f64 -1 x.im)) y.im))))
	33.0b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))))
▶	6.5b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (.f64 (cbrt.f64 (.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (cbrt.f64 y.re))) (atan2.f64 x.im x.re))))))
	18.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (.f64 (.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re))))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re)))))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re))))))))
	39.7b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 x.im) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	37.9b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (cbrt.f64 y.re) (.f64 (atan2.f64 x.im x.re) (pow.f64 y.re 2/3))))))
	18.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (pow.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
	6.5b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 (cbrt.f64 y.re) (.f64 (cbrt.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re))) (cbrt.f64 (cbrt.f64 y.re)))) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re))))))
	6.6b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (.f64 (.f64 (*.f64 (cbrt.f64 (cbrt.f64 y.re)) (cbrt.f64 (cbrt.f64 y.re))) (cbrt.f64 (cbrt.f64 y.re))) (atan2.f64 x.im x.re))))))
	32.2b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (.f64 (sqrt.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))) (sqrt.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
	6.8b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))) (cbrt.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re))))) (cbrt.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
	39.2b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (cbrt.f64 (.f64 (.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re))) (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))) (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
	25.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (cbrt.f64 (.f64 (.f64 (.f64 y.re y.re) y.re) (.f64 (*.f64 (atan2.f64 x.im x.re) (atan2.f64 x.im x.re)) (atan2.f64 x.im x.re)))))))

Compiler

Compiled 10433 to 3070 computations (70.6% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (cbrt.f64 y.re)))
	0.6b	(cbrt.f64 y.re)
	0.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
✓	32.4b	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (.f64 (cbrt.f64 (.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (cbrt.f64 y.re))) (atan2.f64 x.im x.re)))))

series132.0ms (1.1%)

Counts

2 → 60

Calls

2 calls:

102.0ms

(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (cbrt.f64 y.re))) (atan2.f64 x.im x.re)))))

30.0ms

(cbrt.f64 (*.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (cbrt.f64 y.re)))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 22

Calls

2 calls:

5.0ms

(cbrt.f64 (*.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (cbrt.f64 y.re)))

1.0ms

(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (cbrt.f64 y.re))) (atan2.f64 x.im x.re)))))

simplify84.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

661×	`fma-def_binary64`
534×	`cancel-sign-sub-inv_binary64`
377×	`associate-r_binary64`
231×	`*-commutative_binary64`
226×	`times-frac_binary64`

Counts

82 → 96

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	342	3939
1	1008	3616
2	3409	3610
3	5010	3610

prune455.0ms (3.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	215	1	216
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	215	15	230

Error

4.6b

Counts

230 → 15

Alt Table

Status	Error	Program
	19.8b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (expm1.f64 (log1p.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
	39.3b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (-.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 (log.f64 (/.f64 -1 x.im)) y.im))))
	33.0b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))))
✓	6.5b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (.f64 (cbrt.f64 (.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (cbrt.f64 y.re))) (atan2.f64 x.im x.re))))))
	18.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (.f64 (.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re))))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re)))))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re))))))))
	39.7b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 x.im) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	32.9b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (.f64 (pow.f64 (*.f64 -1 y.re) 1/3) (cbrt.f64 -1)))) (atan2.f64 x.im x.re))))))
	37.9b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (cbrt.f64 y.re) (.f64 (atan2.f64 x.im x.re) (pow.f64 y.re 2/3))))))
	18.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (pow.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
▶	6.5b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 (cbrt.f64 y.re) (.f64 (cbrt.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re))) (cbrt.f64 (cbrt.f64 y.re)))) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re))))))
	6.6b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (.f64 (.f64 (*.f64 (cbrt.f64 (cbrt.f64 y.re)) (cbrt.f64 (cbrt.f64 y.re))) (cbrt.f64 (cbrt.f64 y.re))) (atan2.f64 x.im x.re))))))
	32.2b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (.f64 (sqrt.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))) (sqrt.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
	6.8b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))) (cbrt.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re))))) (cbrt.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
	39.2b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (cbrt.f64 (.f64 (.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re))) (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))) (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
	25.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (cbrt.f64 (.f64 (.f64 (.f64 y.re y.re) y.re) (.f64 (*.f64 (atan2.f64 x.im x.re) (atan2.f64 x.im x.re)) (atan2.f64 x.im x.re)))))))

Compiler

Compiled 12530 to 3446 computations (72.5% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(.f64 (.f64 (cbrt.f64 y.re) (.f64 (cbrt.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re))) (cbrt.f64 (cbrt.f64 y.re)))) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re)))
	0.6b	(cbrt.f64 y.re)
	0.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
✓	32.2b	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 (cbrt.f64 y.re) (.f64 (cbrt.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re))) (cbrt.f64 (cbrt.f64 y.re)))) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re)))))

series128.0ms (1%)

Counts

2 → 84

Calls

2 calls:

107.0ms

(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 (*.f64 (cbrt.f64 y.re) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re))) (cbrt.f64 (cbrt.f64 y.re)))) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re)))))

21.0ms

(*.f64 (*.f64 (cbrt.f64 y.re) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re))) (cbrt.f64 (cbrt.f64 y.re)))) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re)))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-exp-log_binary64`
23×	`pow1_binary64`
15×	`cbrt-unprod_binary64`
15×	`prod-exp_binary64`
15×	`pow-prod-down_binary64`

Counts

2 → 40

Calls

2 calls:

9.0ms

(*.f64 (*.f64 (cbrt.f64 y.re) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re))) (cbrt.f64 (cbrt.f64 y.re)))) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re)))

1.0ms

(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 (*.f64 (cbrt.f64 y.re) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re))) (cbrt.f64 (cbrt.f64 y.re)))) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re)))))

simplify131.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

624×	`fma-def_binary64`
541×	`associate-r_binary64`
400×	`associate-l_binary64`
284×	`*-commutative_binary64`
226×	`times-frac_binary64`

Counts

124 → 110

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	373	5776
1	1118	5038
2	3891	5029
3	4925	5029

prune540.0ms (4.4%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	230	0	230
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	230	15	245

Error

4.6b

Counts

245 → 15

Alt Table

Status	Error	Program
	19.8b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (expm1.f64 (log1p.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
	39.3b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (-.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 (log.f64 (/.f64 -1 x.im)) y.im))))
	33.0b	(.f64 (exp.f64 (-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))))
✓	6.5b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (.f64 (cbrt.f64 (.f64 (*.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (cbrt.f64 y.re))) (atan2.f64 x.im x.re))))))
	18.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (.f64 (.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re))))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re)))))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re))))))))
	39.7b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 x.im) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	32.9b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (.f64 (pow.f64 (*.f64 -1 y.re) 1/3) (cbrt.f64 -1)))) (atan2.f64 x.im x.re))))))
	37.9b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (cbrt.f64 y.re) (.f64 (atan2.f64 x.im x.re) (pow.f64 y.re 2/3))))))
	18.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (pow.f64 (sin.f64 (fma.f64 y.im (log.f64 (hypot.f64 x.im x.re)) (*.f64 y.re (atan2.f64 x.im x.re)))) 3)))
✓	6.5b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 (cbrt.f64 y.re) (.f64 (cbrt.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re))) (cbrt.f64 (cbrt.f64 y.re)))) (*.f64 (cbrt.f64 y.re) (atan2.f64 x.im x.re))))))
	6.6b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 (cbrt.f64 y.re) (cbrt.f64 y.re)) (.f64 (.f64 (*.f64 (cbrt.f64 (cbrt.f64 y.re)) (cbrt.f64 (cbrt.f64 y.re))) (cbrt.f64 (cbrt.f64 y.re))) (atan2.f64 x.im x.re))))))
	32.2b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (.f64 (sqrt.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))) (sqrt.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
	6.8b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))) (cbrt.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re))))) (cbrt.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
	39.2b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (cbrt.f64 (.f64 (.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re))) (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 y.re (atan2.f64 x.im x.re)))) (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
	25.0b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (cbrt.f64 (.f64 (.f64 (.f64 y.re y.re) y.re) (.f64 (*.f64 (atan2.f64 x.im x.re) (atan2.f64 x.im x.re)) (atan2.f64 x.im x.re)))))))

Compiler

Compiled 13157 to 3246 computations (75.3% saved)

regimes599.0ms (4.9%)

Accuracy

Total 0.3b remaining (6%)

Threshold costs 0.3b (6%)

Counts

96 → 2

Compiler

Compiled 18467 to 9245 computations (49.9% saved)

bsearch7.0ms (0.1%)

Compiler: Compiled 41 to 19 computations (53.7% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
6×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	159
1	45	159
2	54	159
3	60	159
4	64	159
5	65	159
6	65	159

end306.0ms (2.5%)

Compiler: Compiled 860 to 351 computations (59.2% saved)

Details

analyze2.2s (17.5%)

sample6.3s (50.8%)

simplify67.0ms (0.5%)

prune5.0ms (0%)

localize16.0ms (0.1%)

series398.0ms (3.2%)

rewrite8.0ms (0.1%)

simplify142.0ms (1.2%)

prune245.0ms (2%)

localize20.0ms (0.2%)

series151.0ms (1.2%)

rewrite11.0ms (0.1%)

simplify96.0ms (0.8%)

prune287.0ms (2.3%)

localize21.0ms (0.2%)

series132.0ms (1.1%)

rewrite7.0ms (0.1%)

simplify84.0ms (0.7%)

prune455.0ms (3.7%)

localize26.0ms (0.2%)

series128.0ms (1%)

rewrite14.0ms (0.1%)

simplify131.0ms (1.1%)

prune540.0ms (4.4%)

regimes599.0ms (4.9%)

bsearch7.0ms (0.1%)

simplify5.0ms (0%)

end306.0ms (2.5%)

Profiling