Details

analyze107.0ms (0.5%)

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
74.9%	25%	0.2%	3
74.9%	25%	0.2%	4
74.9%	25%	0.2%	5
87.3%	12.5%	0.2%	6
93.6%	6.2%	0.2%	7
93.6%	6.2%	0.2%	8
93.6%	6.2%	0.2%	9
96.7%	3.1%	0.2%	10
98.2%	1.6%	0.2%	11
98.2%	1.6%	0.2%	12
98.2%	1.6%	0.2%	13
99%	0.8%	0.2%	14

Compiler

Compiled 42 to 20 computations (52.4% saved)

sample7.2s (35.4%)

Results

3.2s	1788×	body	1024	valid
2.5s	5373×	body	128	valid
756.0ms	692×	body	512	valid
402.0ms	122×	body	2048	valid
220.0ms	281×	body	256	valid

Compiler

Compiled 125 to 59 computations (52.8% saved)

simplify98.0ms (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

prune14.0ms (0.1%)

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

10.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	12.6b	(.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 y.re (atan2.f64 x.im x.re)))))
	34.0b	(.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))))

Status

Error

Program

▶

12.6b

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

34.0b

(*.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))))

Compiler

Compiled 206 to 96 computations (53.4% saved)

localize34.0ms (0.2%)

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)))
✓	0.9b	(*.f64 y.re (atan2.f64 x.im x.re))
✓	0.9b	(*.f64 (atan2.f64 x.im x.re) y.im)
✓	41.7b	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

series787.0ms (3.9%)

Counts

4 → 96

Calls

4 calls:

564.0ms	(fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))
195.0ms	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))
19.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
8.0ms	(*.f64 y.re (atan2.f64 x.im x.re))

rewrite13.0ms (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:

4.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
3.0ms	(*.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))))
1.0ms	(fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))

simplify286.0ms (1.4%)

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

prune501.0ms (2.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	176	10	186
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	177	11	188

Error

3.7b

Counts

188 → 11

Alt Table

Status	Error	Program
	28.0b	(.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 (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)))))))
	17.3b	(.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 y.im (log.f64 (hypot.f64 x.im x.re)))))
	21.5b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (-.f64 (fma.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (.f64 y.im (log.f64 (hypot.f64 x.im x.re))) (sin.f64 (.f64 y.re (atan2.f64 x.im x.re)))) (.f64 1/2 (.f64 (pow.f64 (log.f64 (hypot.f64 x.im x.re)) 2) (.f64 (.f64 y.im y.im) (sin.f64 (.f64 y.re (atan2.f64 x.im x.re))))))))
▶	12.6b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (expm1.f64 (log1p.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))
	42.4b	(.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 (-.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 (log.f64 (/.f64 -1 x.im)) y.im))))
	36.1b	(.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)))))))
	14.7b	(.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 (.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)))))))
	34.0b	(.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 (hypot.f64 x.re x.im)) y.im (.f64 (sqrt.f64 y.re) (.f64 (sqrt.f64 y.re) (atan2.f64 x.im x.re))))))
	22.4b	(.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 (*.f64 y.re (atan2.f64 x.im x.re))))
	38.8b	(.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 (fma.f64 (log.f64 x.im) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))

Compiler

Compiled 9670 to 3271 computations (66.2% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(log1p.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))
	0.9b	(*.f64 y.re (atan2.f64 x.im x.re))
	0.9b	(*.f64 (atan2.f64 x.im x.re) y.im)
	41.7b	(sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))

series1.7s (8.2%)

Counts

1 → 48

Calls

1 calls:

1.7s	(log1p.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 11

Calls

1 calls:

1.0ms

(log1p.f64 (sin.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))

simplify246.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

868×	`associate-/l*_binary64`
637×	`associate-/r*_binary64`
345×	`fma-def_binary64`
249×	`*-commutative_binary64`
95×	`+-commutative_binary64`

Counts

59 → 77

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	560	8118
1	2163	7529
2	4744	7529

prune734.0ms (3.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	199	2	201
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	202	10	212

Error

3.7b

Counts

212 → 10

Alt Table

Status	Error	Program
	42.4b	(.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 (-.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 (log.f64 (/.f64 -1 x.im)) y.im))))
	36.1b	(.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)))))))
▶	14.7b	(.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 (.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)))))))
	34.0b	(.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))))
	28.0b	(.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 (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)))))))
	39.7b	(.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 (hypot.f64 x.re x.im)) y.im (.f64 (sqrt.f64 y.re) (.f64 (sqrt.f64 y.re) (atan2.f64 x.im x.re))))))
	21.5b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (-.f64 (fma.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (.f64 y.im (log.f64 (hypot.f64 x.im x.re))) (sin.f64 (.f64 y.re (atan2.f64 x.im x.re)))) (.f64 1/2 (.f64 (pow.f64 (log.f64 (hypot.f64 x.im x.re)) 2) (.f64 (.f64 y.im y.im) (sin.f64 (.f64 y.re (atan2.f64 x.im x.re))))))))
	17.3b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (expm1.f64 (log1p.f64 (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re)))))))
	22.4b	(.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 (*.f64 y.re (atan2.f64 x.im x.re))))
	38.8b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (expm1.f64 (log1p.f64 (sin.f64 (fma.f64 (log.f64 x.im) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))

Compiler

Compiled 18397 to 7397 computations (59.8% saved)

localize42.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (*.f64 y.re (atan2.f64 x.im x.re))))
	0.9b	(*.f64 y.re (atan2.f64 x.im x.re))
	0.9b	(*.f64 (atan2.f64 x.im x.re) y.im)
✓	41.4b	(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))))))

series594.0ms (2.9%)

Counts

2 → 96

Calls

2 calls:

413.0ms

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

180.0ms

(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))))))

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`cbrt-prod_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

3.0ms

(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))))))

1.0ms

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

simplify309.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

643×	`fma-def_binary64`
567×	`times-frac_binary64`
472×	`associate-/l*_binary64`
262×	`*-commutative_binary64`
188×	`cancel-sign-sub-inv_binary64`

Counts

118 → 187

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	674	9673
1	2243	8712
2	4689	8660
3	4885	8660

prune1.6s (7.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	507	2	509
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	509	10	519

Error

3.7b

Counts

519 → 10

Alt Table

Status	Error	Program
	36.1b	(.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)))))))
	53.5b	(.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 (.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))))) (pow.f64 (-.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 (log.f64 (/.f64 -1 x.im)) y.im)) 1/3))))
	34.0b	(.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))))
	28.0b	(.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 (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)))))))
	39.7b	(.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 (hypot.f64 x.re x.im)) y.im (.f64 (sqrt.f64 y.re) (.f64 (sqrt.f64 y.re) (atan2.f64 x.im x.re))))))
	21.5b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (-.f64 (fma.f64 (cos.f64 (.f64 y.re (atan2.f64 x.im x.re))) (.f64 y.im (log.f64 (hypot.f64 x.im x.re))) (sin.f64 (.f64 y.re (atan2.f64 x.im x.re)))) (.f64 1/2 (.f64 (pow.f64 (log.f64 (hypot.f64 x.im x.re)) 2) (.f64 (.f64 y.im y.im) (sin.f64 (.f64 y.re (atan2.f64 x.im x.re))))))))
▶	17.3b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (expm1.f64 (log1p.f64 (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re)))))))
	22.4b	(.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 (*.f64 y.re (atan2.f64 x.im x.re))))
	20.3b	(.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 (.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)))))) (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))))))) (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)))))))))
	38.8b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (expm1.f64 (log1p.f64 (sin.f64 (fma.f64 (log.f64 x.im) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))

Compiler

Compiled 47396 to 15553 computations (67.2% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(log1p.f64 (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re)))))
✓	0.3b	(*.f64 y.im (log.f64 (hypot.f64 x.im x.re)))
	0.9b	(*.f64 (atan2.f64 x.im x.re) y.im)
✓	27.7b	(sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))

series1.8s (9.1%)

Counts

3 → 108

Calls

3 calls:

1.1s	(*.f64 y.im (log.f64 (hypot.f64 x.im x.re)))
658.0ms	(log1p.f64 (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re)))))
123.0ms	(sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))

rewrite9.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`log-prod_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`
6×	`pow1_binary64`

Counts

3 → 53

Calls

3 calls:

3.0ms	(*.f64 y.im (log.f64 (hypot.f64 x.im x.re)))
2.0ms	(sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re))))
0.0ms	(log1p.f64 (sin.f64 (*.f64 y.im (log.f64 (hypot.f64 x.im x.re)))))

simplify333.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

739×	`fma-def_binary64`
698×	`associate-/r*_binary64`
291×	`*-commutative_binary64`
144×	`sub-neg_binary64`
134×	`+-commutative_binary64`

Counts

161 → 232

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	753	9632
1	2595	8719
2	4924	8703
3	4904	8703

prune717.0ms (3.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	258	4	262
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	262	10	272

Error

3.7b

Counts

272 → 10

Alt Table

Status	Error	Program
	53.5b	(.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 (.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))))) (pow.f64 (-.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 (log.f64 (/.f64 -1 x.im)) y.im)) 1/3))))
	38.4b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (expm1.f64 (log1p.f64 (sin.f64 (.f64 (sqrt.f64 y.im) (.f64 (sqrt.f64 y.im) (log.f64 (hypot.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 (hypot.f64 x.re x.im)) y.im (.f64 (sqrt.f64 y.re) (.f64 (sqrt.f64 y.re) (atan2.f64 x.im x.re))))))
	15.6b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (expm1.f64 (fma.f64 (log.f64 (hypot.f64 x.re x.im)) y.im (.f64 (.f64 (*.f64 y.im y.im) (pow.f64 (log.f64 (hypot.f64 x.re x.im)) 2)) -1/2))))
	30.3b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (expm1.f64 (log1p.f64 (sin.f64 (.f64 (.f64 y.im (sqrt.f64 (log.f64 (hypot.f64 x.im x.re)))) (sqrt.f64 (log.f64 (hypot.f64 x.im x.re))))))))
	17.3b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (expm1.f64 (log1p.f64 (sin.f64 (+.f64 (.f64 y.im (.f64 2 (log.f64 (cbrt.f64 (hypot.f64 x.re x.im))))) (*.f64 y.im (log.f64 (cbrt.f64 (hypot.f64 x.re x.im)))))))))
	36.1b	(.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)))))))
	34.0b	(.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))))
	28.0b	(.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 (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)))))))
	38.8b	(.f64 (/.f64 (pow.f64 (hypot.f64 x.re x.im) y.re) (exp.f64 (.f64 (atan2.f64 x.im x.re) y.im))) (expm1.f64 (log1p.f64 (sin.f64 (fma.f64 (log.f64 x.im) y.im (*.f64 y.re (atan2.f64 x.im x.re)))))))

Compiler

Compiled 16143 to 7797 computations (51.7% saved)

regimes2.5s (12.3%)

Accuracy

Total 10.9b remaining (58.9%)

Threshold costs 0b (0%)

Counts

145 → 4

Compiler

Compiled 27292 to 14900 computations (45.4% saved)

bsearch272.0ms (1.3%)

Steps

Iters	Range		Point
10	2.358490417143299e+93	2.613798834517674e+103	5.908482168426287e+93
9	-139272022830439380.0	-155833206590.852	-859914823969486.9
4	-2.0007988624962592e+137	-4.2982492127340007e+133	-7.512750821835541e+133

Compiler

Compiled 5 to 4 computations (20% saved)

simplify18.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

20×	`*-commutative_binary64`
8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
7×	`distribute-lft-neg-in_binary64`
7×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	196
1	74	196
2	82	196
3	92	196
4	105	196
5	117	196
6	125	196
7	129	196
8	130	196
9	129	196

end353.0ms (1.7%)

Compiler: Compiled 631 to 297 computations (52.9% saved)

Iter	Nodes	Cost
0	53	196
1	74	196
2	82	196
3	92	196
4	105	196
5	117	196
6	125	196
7	129	196
8	130	196
9	129	196

Iter	Nodes	Cost
0	53	196
1	74	196
2	82	196
3	92	196
4	105	196
5	117	196
6	125	196
7	129	196
8	130	196
9	129	196

Details

analyze107.0ms (0.5%)

sample7.2s (35.4%)

simplify98.0ms (0.5%)

prune14.0ms (0.1%)

localize34.0ms (0.2%)

series787.0ms (3.9%)

rewrite13.0ms (0.1%)

simplify286.0ms (1.4%)

prune501.0ms (2.5%)

localize29.0ms (0.1%)

series1.7s (8.2%)

rewrite1.0ms (0%)

simplify246.0ms (1.2%)

prune734.0ms (3.6%)

localize42.0ms (0.2%)

series594.0ms (2.9%)

rewrite7.0ms (0%)

simplify309.0ms (1.5%)

prune1.6s (7.7%)

localize36.0ms (0.2%)

series1.8s (9.1%)

rewrite9.0ms (0%)

simplify333.0ms (1.6%)

prune717.0ms (3.5%)

regimes2.5s (12.3%)

bsearch272.0ms (1.3%)

simplify18.0ms (0.1%)

end353.0ms (1.7%)

Profiling

Iter	Nodes	Cost
0	53	196
1	74	196
2	82	196
3	92	196
4	105	196
5	117	196
6	125	196
7	129	196
8	130	196
9	129	196