Details

analyze191.0ms (6.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
50%	50%	0.1%	2
50%	50%	0.1%	3
74.9%	25%	0.1%	4
74.9%	25%	0.1%	5
74.9%	18.7%	6.3%	6
74.9%	18.7%	6.3%	7
74.9%	15.6%	9.5%	8
74.9%	15.6%	9.5%	9
74.9%	14%	11%	10
74.9%	14%	11%	11
74.9%	13.3%	11.8%	12
74.9%	13.3%	11.8%	13
74.9%	12.9%	12.2%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample2.1s (72%)

Results

714.0ms	1379×	body	1024	valid
631.0ms	5812×	body	128	valid
325.0ms	708×	body	1024	invalid
211.0ms	698×	body	512	valid
93.0ms	341×	body	512	invalid
69.0ms	361×	body	256	valid
40.0ms	177×	body	256	invalid
26.0ms	197×	body	128	invalid
6.0ms	6×	body	2048	valid

Compiler

Compiled 16 to 12 computations (25% saved)

preprocess17.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	11	16
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 im) (cos.f64 re))

Outputs
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 im) (cos.f64 re))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 (exp.f64 re) (cos.f64 im))

Outputs
(*.f64 (exp.f64 re) (cos.f64 im))

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (exp.f64 re) (cos.f64 im))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (exp.f64 re) (cos.f64 im))

series4.0ms (0.1%)

Counts

1 → 8

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	im	@	0	(*.f64 (exp.f64 re) (cos.f64 im))
1.0ms	re	@	inf	(*.f64 (exp.f64 re) (cos.f64 im))
1.0ms	re	@	0	(*.f64 (exp.f64 re) (cos.f64 im))
1.0ms	im	@	-inf	(*.f64 (exp.f64 re) (cos.f64 im))
1.0ms	im	@	inf	(*.f64 (exp.f64 re) (cos.f64 im))

rewrite31.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

530×	`pow1_binary64`
483×	`add-log-exp_binary64`
483×	`log1p-expm1-u_binary64`
483×	`expm1-log1p-u_binary64`
471×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	113	8
2	1324	8

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

Inputs
(*.f64 (exp.f64 re) (cos.f64 im))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (.f64 (exp.f64 re) (cos.f64 im))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (exp.f64 re) (cos.f64 im)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (exp.f64 re) (cos.f64 im)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (exp.f64 re) (cos.f64 im))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 (exp.f64 re) (cos.f64 im)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (exp.f64 re)) (cos.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (exp.f64 re) (cos.f64 im)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (exp.f64 re) 3) (pow.f64 (cos.f64 im) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (cos.f64 im) 3) (pow.f64 (exp.f64 re) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (exp.f64 re) (cos.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 re (log.f64 (cos.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (exp.f64 re) (cos.f64 im))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (exp.f64 re) (cos.f64 im))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (exp.f64 re)) (cos.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (exp.f64 re) 3) (pow.f64 (cos.f64 im) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (cos.f64 im) 3) (pow.f64 (exp.f64 re) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (exp.f64 re) (cos.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 re (log.f64 (cos.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (exp.f64 re) (cos.f64 im))))))))

simplify23.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

767×	`fma-neg_binary64`
720×	`fma-def_binary64`
541×	`cancel-sign-sub-inv_binary64`
293×	`distribute-rgt-neg-in_binary64`
237×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	38	166
1	107	160
2	307	142
3	1089	122
4	3080	119

Stop Event

1×	node limit

Counts

21 → 27

Calls

Call 1

Inputs
(cos.f64 im)
(+.f64 (cos.f64 im) (*.f64 (cos.f64 im) re))
(+.f64 (cos.f64 im) (+.f64 (.f64 (cos.f64 im) re) (.f64 1/2 (*.f64 (cos.f64 im) (pow.f64 re 2)))))
(+.f64 (.f64 1/6 (.f64 (cos.f64 im) (pow.f64 re 3))) (+.f64 (cos.f64 im) (+.f64 (.f64 (cos.f64 im) re) (.f64 1/2 (*.f64 (cos.f64 im) (pow.f64 re 2))))))
(exp.f64 re)
(-.f64 (exp.f64 re) (.f64 1/2 (.f64 (exp.f64 re) (pow.f64 im 2))))
(-.f64 (+.f64 (exp.f64 re) (.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4)))) (.f64 1/2 (.f64 (exp.f64 re) (pow.f64 im 2))))
(-.f64 (+.f64 (exp.f64 re) (.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4)))) (+.f64 (.f64 1/720 (.f64 (exp.f64 re) (pow.f64 im 6))) (.f64 1/2 (.f64 (exp.f64 re) (pow.f64 im 2)))))

Outputs
(cos.f64 im)
(+.f64 (cos.f64 im) (*.f64 (cos.f64 im) re))
(*.f64 (+.f64 re 1) (cos.f64 im))
(fma.f64 (cos.f64 im) re (cos.f64 im))
(*.f64 (cos.f64 im) (+.f64 re 1))
(+.f64 (cos.f64 im) (+.f64 (.f64 (cos.f64 im) re) (.f64 1/2 (*.f64 (cos.f64 im) (pow.f64 re 2)))))
(+.f64 (cos.f64 im) (fma.f64 (cos.f64 im) re (.f64 1/2 (.f64 (cos.f64 im) (*.f64 re re)))))
(+.f64 (cos.f64 im) (fma.f64 1/2 (.f64 (cos.f64 im) (.f64 re re)) (*.f64 (cos.f64 im) re)))
(.f64 (cos.f64 im) (+.f64 (+.f64 re 1) (.f64 re (*.f64 re 1/2))))
(.f64 (cos.f64 im) (fma.f64 re (.f64 re 1/2) (+.f64 re 1)))
(+.f64 (.f64 1/6 (.f64 (cos.f64 im) (pow.f64 re 3))) (+.f64 (cos.f64 im) (+.f64 (.f64 (cos.f64 im) re) (.f64 1/2 (*.f64 (cos.f64 im) (pow.f64 re 2))))))
(fma.f64 1/6 (.f64 (cos.f64 im) (pow.f64 re 3)) (+.f64 (cos.f64 im) (fma.f64 (cos.f64 im) re (.f64 1/2 (.f64 (cos.f64 im) (.f64 re re))))))
(+.f64 (fma.f64 1/2 (.f64 (cos.f64 im) (.f64 re re)) (.f64 (cos.f64 im) re)) (fma.f64 (.f64 (cos.f64 im) 1/6) (pow.f64 re 3) (cos.f64 im)))
(fma.f64 (cos.f64 im) (.f64 1/6 (pow.f64 re 3)) (.f64 (cos.f64 im) (+.f64 (+.f64 re 1) (.f64 re (.f64 re 1/2)))))
(.f64 (cos.f64 im) (+.f64 (+.f64 re 1) (.f64 (.f64 re re) (+.f64 1/2 (.f64 re 1/6)))))
(exp.f64 re)
(-.f64 (exp.f64 re) (.f64 1/2 (.f64 (exp.f64 re) (pow.f64 im 2))))
(+.f64 (exp.f64 re) (.f64 -1/2 (.f64 (exp.f64 re) (*.f64 im im))))
(+.f64 (exp.f64 re) (.f64 (.f64 (exp.f64 re) (*.f64 im im)) -1/2))
(.f64 (+.f64 (.f64 (*.f64 im im) -1/2) 1) (exp.f64 re))
(.f64 (exp.f64 re) (fma.f64 (.f64 im im) -1/2 1))
(-.f64 (+.f64 (exp.f64 re) (.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4)))) (.f64 1/2 (.f64 (exp.f64 re) (pow.f64 im 2))))
(+.f64 (exp.f64 re) (-.f64 (.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4))) (.f64 1/2 (.f64 (exp.f64 re) (*.f64 im im)))))
(+.f64 (exp.f64 re) (fma.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4)) (.f64 (.f64 (exp.f64 re) (.f64 im im)) -1/2)))
(+.f64 (exp.f64 re) (.f64 (exp.f64 re) (-.f64 (.f64 1/24 (pow.f64 im 4)) (.f64 im (.f64 im 1/2)))))
(.f64 (exp.f64 re) (-.f64 (fma.f64 1/24 (pow.f64 im 4) 1) (.f64 1/2 (*.f64 im im))))
(.f64 (exp.f64 re) (+.f64 (fma.f64 1/24 (pow.f64 im 4) 1) (.f64 (*.f64 im im) -1/2)))
(-.f64 (+.f64 (exp.f64 re) (.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4)))) (+.f64 (.f64 1/720 (.f64 (exp.f64 re) (pow.f64 im 6))) (.f64 1/2 (.f64 (exp.f64 re) (pow.f64 im 2)))))
(-.f64 (+.f64 (exp.f64 re) (.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4)))) (fma.f64 1/720 (.f64 (exp.f64 re) (pow.f64 im 6)) (.f64 1/2 (.f64 (exp.f64 re) (.f64 im im)))))
(-.f64 (fma.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4)) (exp.f64 re)) (fma.f64 1/2 (.f64 (exp.f64 re) (.f64 im im)) (.f64 (exp.f64 re) (*.f64 (pow.f64 im 6) 1/720))))
(-.f64 (fma.f64 (exp.f64 re) (.f64 1/24 (pow.f64 im 4)) (exp.f64 re)) (.f64 (exp.f64 re) (+.f64 (.f64 im (.f64 im 1/2)) (*.f64 1/720 (pow.f64 im 6)))))
(fma.f64 (exp.f64 re) (fma.f64 1/24 (pow.f64 im 4) (.f64 (pow.f64 im 6) -1/720)) (.f64 (exp.f64 re) (fma.f64 (*.f64 im im) -1/2 1)))
(.f64 (exp.f64 re) (-.f64 (fma.f64 1/24 (pow.f64 im 4) 1) (fma.f64 1/720 (pow.f64 im 6) (.f64 1/2 (*.f64 im im)))))

prune22.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	25	3	28

Error

0.0b

Counts

28 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (exp.f64 re) (cos.f64 im))
▶	0.5b	(pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 3)
	22.2b	(+.f64 (cos.f64 im) (*.f64 (cos.f64 im) re))

Compiler

Compiled 340 to 184 computations (45.9% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (exp.f64 re) (cos.f64 im))
✓	0.2b	(cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im)))
✓	0.2b	(pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 3)

series23.0ms (0.8%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
6.0ms	re	@	0	(cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im)))
4.0ms	im	@	-inf	(pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 3)
3.0ms	re	@	inf	(pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 3)
2.0ms	re	@	0	(pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 3)
2.0ms	im	@	inf	(pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 3)

rewrite38.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

706×	`pow1_binary64`
657×	`add-log-exp_binary64`
657×	`log1p-expm1-u_binary64`
657×	`expm1-log1p-u_binary64`
79×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	182	18
2	1847	18

Stop Event

1×	node limit

Counts

2 → 56

Calls

Call 1

Inputs
(pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 3)
(cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (exp.f64 re) (cos.f64 im)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (exp.f64 re) (cos.f64 im))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cos.f64 im) (exp.f64 re))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (exp.f64 re) (cos.f64 im)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im))) (pow.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 (exp.f64 re) (cos.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im))) 2) (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (cos.f64 im)) 2) (.f64 (cbrt.f64 (cos.f64 im)) (exp.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (exp.f64 re)) (.f64 (cbrt.f64 (cos.f64 im)) (pow.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (exp.f64 re) 2)) (.f64 (cbrt.f64 (exp.f64 re)) (cos.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im)))) 2) (.f64 (cbrt.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im)))) (pow.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (cos.f64 im)) (.f64 (sqrt.f64 (cos.f64 im)) (exp.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (exp.f64 re) (cos.f64 im))) (sqrt.f64 (.f64 (exp.f64 re) (cos.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (exp.f64 re)) (.f64 (sqrt.f64 (exp.f64 re)) (cos.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (exp.f64 re) (cos.f64 im)) 1/6) (.f64 (pow.f64 (.f64 (exp.f64 re) (cos.f64 im)) 1/6) (pow.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im)))) 2) 3) (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (.f64 (exp.f64 re) (cos.f64 im)) 1/6) 3) (pow.f64 (pow.f64 (.f64 (exp.f64 re) (cos.f64 im)) 1/6) 3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (exp.f64 re) (pow.f64 (cbrt.f64 (cos.f64 im)) 2)) (cbrt.f64 (cos.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (exp.f64 re) (sqrt.f64 (cos.f64 im))) (sqrt.f64 (cos.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (cos.f64 im) (cbrt.f64 (pow.f64 (exp.f64 re) 2))) (cbrt.f64 (exp.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (cos.f64 im) (sqrt.f64 (exp.f64 re))) (sqrt.f64 (exp.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im))) 2) 1) (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im))) 2) (cbrt.f64 (exp.f64 re))) (cbrt.f64 (cos.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im))) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im)))) 2)) (cbrt.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im))) 2) (pow.f64 (.f64 (exp.f64 re) (cos.f64 im)) 1/6)) (pow.f64 (.f64 (exp.f64 re) (cos.f64 im)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 (exp.f64 re) (cos.f64 im)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 im)) (exp.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (exp.f64 re) (cos.f64 im)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (exp.f64 re) (cos.f64 im)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (exp.f64 re) 3) (pow.f64 (cos.f64 im) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (cos.f64 im) 3) (pow.f64 (exp.f64 re) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (exp.f64 re) (cos.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 re (log.f64 (cos.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (exp.f64 re) (cos.f64 im))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (cos.f64 im)) (cbrt.f64 (exp.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (exp.f64 re)) (cbrt.f64 (cos.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im)))) (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im)))) (pow.f64 (pow.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im))) 2) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im)))) 2) (cbrt.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (exp.f64 re) (cos.f64 im)) 1/6) (pow.f64 (.f64 (exp.f64 re) (cos.f64 im)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im))) 2) 1/3) (cbrt.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/3) (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (.f64 (exp.f64 re) (cos.f64 im))) 1/3) (pow.f64 (sqrt.f64 (.f64 (exp.f64 re) (cos.f64 im))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (exp.f64 re) (cos.f64 im)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (exp.f64 re) (cos.f64 im)) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (.f64 (exp.f64 re) (cos.f64 im)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (+.f64 re (log.f64 (cos.f64 im))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im)))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (exp.f64 re) (cos.f64 im)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 re) (cos.f64 im))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cos.f64 im) (exp.f64 re))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) (pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (exp.f64 re) (cos.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 2) (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cos.f64 im)) 2) (*.f64 (cbrt.f64 (cos.f64 im)) (exp.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (exp.f64 re)) (*.f64 (cbrt.f64 (cos.f64 im)) (pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (exp.f64 re) 2)) (*.f64 (cbrt.f64 (exp.f64 re)) (cos.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im)))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im)))) (pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cos.f64 im)) (*.f64 (sqrt.f64 (cos.f64 im)) (exp.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) (sqrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (exp.f64 re)) (*.f64 (sqrt.f64 (exp.f64 re)) (cos.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/6) (*.f64 (pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/6) (pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im)))) 2) 3) (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/6) 3) (pow.f64 (pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/6) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (exp.f64 re) (pow.f64 (cbrt.f64 (cos.f64 im)) 2)) (cbrt.f64 (cos.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (exp.f64 re) (sqrt.f64 (cos.f64 im))) (sqrt.f64 (cos.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cos.f64 im) (cbrt.f64 (pow.f64 (exp.f64 re) 2))) (cbrt.f64 (exp.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cos.f64 im) (sqrt.f64 (exp.f64 re))) (sqrt.f64 (exp.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 2) 1) (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 2) (cbrt.f64 (exp.f64 re))) (cbrt.f64 (cos.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im)))) 2)) (cbrt.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 2) (pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/6)) (pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 im)) (exp.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (exp.f64 re) (cos.f64 im)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (exp.f64 re) 3) (pow.f64 (cos.f64 im) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (cos.f64 im) 3) (pow.f64 (exp.f64 re) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (exp.f64 re) (cos.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 re (log.f64 (cos.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (exp.f64 re) (cos.f64 im))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cos.f64 im)) (cbrt.f64 (exp.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (exp.f64 re)) (cbrt.f64 (cos.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im)))) (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im)))) (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 2) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im)))) 2) (cbrt.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/6) (pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 2) 1/3) (cbrt.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 1/3) (pow.f64 (sqrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (+.f64 re (log.f64 (cos.f64 im))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im)))))))))

simplify42.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

527×	`fma-def_binary64`
497×	`associate-r_binary64`
475×	`associate-l_binary64`
248×	`cancel-sign-sub-inv_binary64`
207×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	92	860
1	292	848
2	1013	810
3	4732	810

Stop Event

1×	node limit

Counts

104 → 87

Calls

Call 1

Inputs
(cos.f64 im)
(+.f64 (*.f64 (pow.f64 (pow.f64 (cos.f64 im) 13) 1/9) re) (cos.f64 im))
(+.f64 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 13) 1/9) re) (+.f64 (cos.f64 im) (.f64 1/2 (*.f64 (cos.f64 im) (pow.f64 re 2)))))
(+.f64 (.f64 1/6 (.f64 (cos.f64 im) (pow.f64 re 3))) (+.f64 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 13) 1/9) re) (+.f64 (cos.f64 im) (.f64 1/2 (*.f64 (cos.f64 im) (pow.f64 re 2))))))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(exp.f64 re)
(-.f64 (exp.f64 re) (.f64 1/2 (.f64 (exp.f64 re) (pow.f64 im 2))))
(-.f64 (+.f64 (exp.f64 re) (.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4)))) (.f64 1/2 (.f64 (exp.f64 re) (pow.f64 im 2))))
(-.f64 (+.f64 (exp.f64 re) (.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4)))) (+.f64 (.f64 1/720 (.f64 (exp.f64 re) (pow.f64 im 6))) (.f64 1/2 (.f64 (exp.f64 re) (pow.f64 im 2)))))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(pow.f64 (cos.f64 im) 1/3)
(+.f64 (.f64 1/3 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 7) 1/9) re)) (pow.f64 (cos.f64 im) 1/3))
(-.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 7) 1/9) re)) (+.f64 (.f64 1/6 (.f64 (pow.f64 (cos.f64 im) 1/3) (pow.f64 re 2))) (pow.f64 (cos.f64 im) 1/3))) (.f64 1/9 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 11) 1/9) (pow.f64 re 2))))
(-.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 7) 1/9) re)) (+.f64 (.f64 1/18 (.f64 (pow.f64 (cos.f64 im) 1/3) (pow.f64 re 3))) (+.f64 (.f64 5/81 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 5) 1/3) (pow.f64 re 3))) (+.f64 (.f64 1/6 (.f64 (pow.f64 (cos.f64 im) 1/3) (pow.f64 re 2))) (pow.f64 (cos.f64 im) 1/3))))) (+.f64 (.f64 1/9 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 11) 1/9) (pow.f64 re 2))) (.f64 1/9 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 7) 1/9) (pow.f64 re 3)))))
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(pow.f64 (exp.f64 re) 1/3)
(-.f64 (pow.f64 (exp.f64 re) 1/3) (.f64 1/6 (.f64 (pow.f64 (exp.f64 re) 1/3) (pow.f64 im 2))))
(-.f64 (pow.f64 (exp.f64 re) 1/3) (+.f64 (.f64 1/6 (.f64 (pow.f64 (exp.f64 re) 1/3) (pow.f64 im 2))) (.f64 1/72 (.f64 (pow.f64 (exp.f64 re) 1/3) (pow.f64 im 4)))))
(-.f64 (pow.f64 (exp.f64 re) 1/3) (+.f64 (.f64 23/6480 (.f64 (pow.f64 (exp.f64 re) 1/3) (pow.f64 im 6))) (+.f64 (.f64 1/6 (.f64 (pow.f64 (exp.f64 re) 1/3) (pow.f64 im 2))) (.f64 1/72 (.f64 (pow.f64 (exp.f64 re) 1/3) (pow.f64 im 4))))))
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)

Outputs
(cos.f64 im)
(+.f64 (*.f64 (pow.f64 (pow.f64 (cos.f64 im) 13) 1/9) re) (cos.f64 im))
(fma.f64 (*.f64 (pow.f64 (pow.f64 (cos.f64 im) 13) 1/18) (pow.f64 (pow.f64 (cos.f64 im) 13) 1/18)) re (cos.f64 im))
(+.f64 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 13) 1/9) re) (+.f64 (cos.f64 im) (.f64 1/2 (*.f64 (cos.f64 im) (pow.f64 re 2)))))
(+.f64 (fma.f64 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 13) 1/18) (pow.f64 (pow.f64 (cos.f64 im) 13) 1/18)) re (cos.f64 im)) (.f64 1/2 (.f64 (cos.f64 im) (.f64 re re))))
(fma.f64 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 13) 1/18) (pow.f64 (pow.f64 (cos.f64 im) 13) 1/18)) re (fma.f64 1/2 (.f64 (cos.f64 im) (*.f64 re re)) (cos.f64 im)))
(fma.f64 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 13) 1/18) (pow.f64 (pow.f64 (cos.f64 im) 13) 1/18)) re (fma.f64 (cos.f64 im) (.f64 1/2 (*.f64 re re)) (cos.f64 im)))
(+.f64 (.f64 1/6 (.f64 (cos.f64 im) (pow.f64 re 3))) (+.f64 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 13) 1/9) re) (+.f64 (cos.f64 im) (.f64 1/2 (*.f64 (cos.f64 im) (pow.f64 re 2))))))
(fma.f64 1/6 (.f64 (cos.f64 im) (pow.f64 re 3)) (+.f64 (fma.f64 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 13) 1/18) (pow.f64 (pow.f64 (cos.f64 im) 13) 1/18)) re (cos.f64 im)) (.f64 1/2 (.f64 (cos.f64 im) (*.f64 re re)))))
(fma.f64 1/6 (.f64 (cos.f64 im) (pow.f64 re 3)) (fma.f64 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 13) 1/18) (pow.f64 (pow.f64 (cos.f64 im) 13) 1/18)) re (fma.f64 1/2 (.f64 (cos.f64 im) (.f64 re re)) (cos.f64 im))))
(+.f64 (fma.f64 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 13) 1/18) (pow.f64 (pow.f64 (cos.f64 im) 13) 1/18)) re (cos.f64 im)) (.f64 (cos.f64 im) (+.f64 (.f64 1/2 (.f64 re re)) (*.f64 1/6 (pow.f64 re 3)))))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (cos.f64 im) (exp.f64 re))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (cos.f64 im) (exp.f64 re))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (cos.f64 im) (exp.f64 re))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (cos.f64 im) (exp.f64 re))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (cos.f64 im) (exp.f64 re))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (cos.f64 im) (exp.f64 re))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (cos.f64 im) (exp.f64 re))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (cos.f64 im) (exp.f64 re))
(exp.f64 re)
(-.f64 (exp.f64 re) (.f64 1/2 (.f64 (exp.f64 re) (pow.f64 im 2))))
(-.f64 (exp.f64 re) (.f64 (.f64 1/2 (exp.f64 re)) (*.f64 im im)))
(+.f64 (exp.f64 re) (.f64 (.f64 im (*.f64 im (exp.f64 re))) -1/2))
(.f64 (+.f64 (.f64 (*.f64 im im) -1/2) 1) (exp.f64 re))
(-.f64 (+.f64 (exp.f64 re) (.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4)))) (.f64 1/2 (.f64 (exp.f64 re) (pow.f64 im 2))))
(+.f64 (exp.f64 re) (-.f64 (.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4))) (.f64 (.f64 1/2 (exp.f64 re)) (*.f64 im im))))
(+.f64 (exp.f64 re) (fma.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4)) (.f64 (.f64 im (.f64 im (exp.f64 re))) -1/2)))
(+.f64 (exp.f64 re) (.f64 (exp.f64 re) (-.f64 (.f64 1/24 (pow.f64 im 4)) (.f64 im (.f64 im 1/2)))))
(-.f64 (+.f64 (exp.f64 re) (.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4)))) (+.f64 (.f64 1/720 (.f64 (exp.f64 re) (pow.f64 im 6))) (.f64 1/2 (.f64 (exp.f64 re) (pow.f64 im 2)))))
(+.f64 (exp.f64 re) (-.f64 (.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4))) (fma.f64 1/720 (.f64 (exp.f64 re) (pow.f64 im 6)) (.f64 (.f64 1/2 (exp.f64 re)) (.f64 im im)))))
(-.f64 (fma.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4)) (exp.f64 re)) (fma.f64 1/2 (.f64 im (.f64 im (exp.f64 re))) (.f64 (exp.f64 re) (*.f64 (pow.f64 im 6) 1/720))))
(-.f64 (.f64 (+.f64 (.f64 1/24 (pow.f64 im 4)) 1) (exp.f64 re)) (.f64 (exp.f64 re) (+.f64 (.f64 1/720 (pow.f64 im 6)) (.f64 im (.f64 im 1/2)))))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (cos.f64 im) (exp.f64 re))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (cos.f64 im) (exp.f64 re))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (cos.f64 im) (exp.f64 re))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (cos.f64 im) (exp.f64 re))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (cos.f64 im) (exp.f64 re))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (cos.f64 im) (exp.f64 re))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (cos.f64 im) (exp.f64 re))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (cos.f64 im) (exp.f64 re))
(pow.f64 (cos.f64 im) 1/3)
(cbrt.f64 (cos.f64 im))
(+.f64 (.f64 1/3 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 7) 1/9) re)) (pow.f64 (cos.f64 im) 1/3))
(fma.f64 1/3 (.f64 re (.f64 (pow.f64 (pow.f64 (cos.f64 im) 7) 1/18) (pow.f64 (pow.f64 (cos.f64 im) 7) 1/18))) (cbrt.f64 (cos.f64 im)))
(fma.f64 1/3 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 7) 1/18) (.f64 (pow.f64 (pow.f64 (cos.f64 im) 7) 1/18) re)) (cbrt.f64 (cos.f64 im)))
(-.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 7) 1/9) re)) (+.f64 (.f64 1/6 (.f64 (pow.f64 (cos.f64 im) 1/3) (pow.f64 re 2))) (pow.f64 (cos.f64 im) 1/3))) (.f64 1/9 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 11) 1/9) (pow.f64 re 2))))
(+.f64 (fma.f64 1/3 (.f64 re (.f64 (pow.f64 (pow.f64 (cos.f64 im) 7) 1/18) (pow.f64 (pow.f64 (cos.f64 im) 7) 1/18))) (fma.f64 1/6 (.f64 (.f64 re re) (cbrt.f64 (cos.f64 im))) (cbrt.f64 (cos.f64 im)))) (.f64 -1/9 (.f64 (.f64 re re) (.f64 (pow.f64 (pow.f64 (cos.f64 im) 11) 1/18) (pow.f64 (pow.f64 (cos.f64 im) 11) 1/18)))))
(+.f64 (fma.f64 1/3 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 7) 1/18) (.f64 (pow.f64 (pow.f64 (cos.f64 im) 7) 1/18) re)) (fma.f64 1/6 (.f64 (.f64 re re) (cbrt.f64 (cos.f64 im))) (cbrt.f64 (cos.f64 im)))) (.f64 (.f64 (.f64 re re) (.f64 (pow.f64 (pow.f64 (cos.f64 im) 11) 1/18) (pow.f64 (pow.f64 (cos.f64 im) 11) 1/18))) -1/9))
(+.f64 (fma.f64 1/3 (.f64 re (.f64 (pow.f64 (pow.f64 (cos.f64 im) 7) 1/18) (pow.f64 (pow.f64 (cos.f64 im) 7) 1/18))) (cbrt.f64 (cos.f64 im))) (.f64 (.f64 re re) (-.f64 (.f64 1/6 (cbrt.f64 (cos.f64 im))) (.f64 (pow.f64 (pow.f64 (cos.f64 im) 11) 1/18) (*.f64 1/9 (pow.f64 (pow.f64 (cos.f64 im) 11) 1/18))))))
(+.f64 (fma.f64 1/3 (.f64 re (.f64 (pow.f64 (pow.f64 (cos.f64 im) 7) 1/18) (pow.f64 (pow.f64 (cos.f64 im) 7) 1/18))) (cbrt.f64 (cos.f64 im))) (.f64 (.f64 re re) (+.f64 (.f64 1/6 (cbrt.f64 (cos.f64 im))) (.f64 (*.f64 (pow.f64 (pow.f64 (cos.f64 im) 11) 1/18) (pow.f64 (pow.f64 (cos.f64 im) 11) 1/18)) -1/9))))
(-.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 7) 1/9) re)) (+.f64 (.f64 1/18 (.f64 (pow.f64 (cos.f64 im) 1/3) (pow.f64 re 3))) (+.f64 (.f64 5/81 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 5) 1/3) (pow.f64 re 3))) (+.f64 (.f64 1/6 (.f64 (pow.f64 (cos.f64 im) 1/3) (pow.f64 re 2))) (pow.f64 (cos.f64 im) 1/3))))) (+.f64 (.f64 1/9 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 11) 1/9) (pow.f64 re 2))) (.f64 1/9 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 7) 1/9) (pow.f64 re 3)))))
(-.f64 (fma.f64 1/3 (.f64 re (.f64 (pow.f64 (pow.f64 (cos.f64 im) 7) 1/18) (pow.f64 (pow.f64 (cos.f64 im) 7) 1/18))) (fma.f64 1/18 (.f64 (pow.f64 re 3) (cbrt.f64 (cos.f64 im))) (fma.f64 5/81 (.f64 (pow.f64 re 3) (cbrt.f64 (pow.f64 (cos.f64 im) 5))) (fma.f64 1/6 (.f64 (.f64 re re) (cbrt.f64 (cos.f64 im))) (cbrt.f64 (cos.f64 im)))))) (.f64 1/9 (+.f64 (.f64 (.f64 re re) (.f64 (pow.f64 (pow.f64 (cos.f64 im) 11) 1/18) (pow.f64 (pow.f64 (cos.f64 im) 11) 1/18))) (.f64 (pow.f64 re 3) (.f64 (pow.f64 (pow.f64 (cos.f64 im) 7) 1/18) (pow.f64 (pow.f64 (cos.f64 im) 7) 1/18))))))
(+.f64 (+.f64 (.f64 (pow.f64 re 3) (+.f64 (.f64 (cbrt.f64 (cos.f64 im)) 1/18) (.f64 5/81 (cbrt.f64 (pow.f64 (cos.f64 im) 5))))) (fma.f64 1/3 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 7) 1/18) (.f64 (pow.f64 (pow.f64 (cos.f64 im) 7) 1/18) re)) (fma.f64 1/6 (.f64 (.f64 re re) (cbrt.f64 (cos.f64 im))) (cbrt.f64 (cos.f64 im))))) (.f64 -1/9 (fma.f64 (.f64 re re) (.f64 (pow.f64 (pow.f64 (cos.f64 im) 11) 1/18) (pow.f64 (pow.f64 (cos.f64 im) 11) 1/18)) (.f64 (pow.f64 re 3) (.f64 (pow.f64 (pow.f64 (cos.f64 im) 7) 1/18) (pow.f64 (pow.f64 (cos.f64 im) 7) 1/18))))))
(fma.f64 -1/9 (.f64 (.f64 re re) (+.f64 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 11) 1/18) (pow.f64 (pow.f64 (cos.f64 im) 11) 1/18)) (.f64 re (.f64 (pow.f64 (pow.f64 (cos.f64 im) 7) 1/18) (pow.f64 (pow.f64 (cos.f64 im) 7) 1/18))))) (fma.f64 re (.f64 1/3 (.f64 (pow.f64 (pow.f64 (cos.f64 im) 7) 1/18) (pow.f64 (pow.f64 (cos.f64 im) 7) 1/18))) (fma.f64 (pow.f64 re 3) (fma.f64 (cbrt.f64 (cos.f64 im)) 1/18 (.f64 5/81 (cbrt.f64 (pow.f64 (cos.f64 im) 5)))) (.f64 (+.f64 (.f64 (*.f64 re re) 1/6) 1) (cbrt.f64 (cos.f64 im))))))
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(cbrt.f64 (*.f64 (cos.f64 im) (exp.f64 re)))
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(cbrt.f64 (*.f64 (cos.f64 im) (exp.f64 re)))
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(cbrt.f64 (*.f64 (cos.f64 im) (exp.f64 re)))
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(cbrt.f64 (*.f64 (cos.f64 im) (exp.f64 re)))
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(cbrt.f64 (*.f64 (cos.f64 im) (exp.f64 re)))
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(cbrt.f64 (*.f64 (cos.f64 im) (exp.f64 re)))
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(cbrt.f64 (*.f64 (cos.f64 im) (exp.f64 re)))
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(cbrt.f64 (*.f64 (cos.f64 im) (exp.f64 re)))
(pow.f64 (exp.f64 re) 1/3)
(cbrt.f64 (exp.f64 re))
(-.f64 (pow.f64 (exp.f64 re) 1/3) (.f64 1/6 (.f64 (pow.f64 (exp.f64 re) 1/3) (pow.f64 im 2))))
(-.f64 (cbrt.f64 (exp.f64 re)) (.f64 (.f64 1/6 (cbrt.f64 (exp.f64 re))) (*.f64 im im)))
(+.f64 (cbrt.f64 (exp.f64 re)) (.f64 (.f64 (*.f64 (cbrt.f64 (exp.f64 re)) im) im) -1/6))
(.f64 (+.f64 (.f64 (*.f64 im im) -1/6) 1) (cbrt.f64 (exp.f64 re)))
(-.f64 (pow.f64 (exp.f64 re) 1/3) (+.f64 (.f64 1/6 (.f64 (pow.f64 (exp.f64 re) 1/3) (pow.f64 im 2))) (.f64 1/72 (.f64 (pow.f64 (exp.f64 re) 1/3) (pow.f64 im 4)))))
(-.f64 (cbrt.f64 (exp.f64 re)) (fma.f64 1/6 (.f64 (.f64 im im) (cbrt.f64 (exp.f64 re))) (.f64 1/72 (.f64 (pow.f64 im 4) (cbrt.f64 (exp.f64 re))))))
(-.f64 (cbrt.f64 (exp.f64 re)) (fma.f64 1/6 (.f64 (.f64 (cbrt.f64 (exp.f64 re)) im) im) (.f64 (pow.f64 im 4) (.f64 (cbrt.f64 (exp.f64 re)) 1/72))))
(-.f64 (cbrt.f64 (exp.f64 re)) (.f64 (cbrt.f64 (exp.f64 re)) (+.f64 (.f64 im (.f64 im 1/6)) (.f64 (pow.f64 im 4) 1/72))))
(-.f64 (pow.f64 (exp.f64 re) 1/3) (+.f64 (.f64 23/6480 (.f64 (pow.f64 (exp.f64 re) 1/3) (pow.f64 im 6))) (+.f64 (.f64 1/6 (.f64 (pow.f64 (exp.f64 re) 1/3) (pow.f64 im 2))) (.f64 1/72 (.f64 (pow.f64 (exp.f64 re) 1/3) (pow.f64 im 4))))))
(-.f64 (cbrt.f64 (exp.f64 re)) (fma.f64 23/6480 (.f64 (pow.f64 im 6) (cbrt.f64 (exp.f64 re))) (fma.f64 1/6 (.f64 (.f64 im im) (cbrt.f64 (exp.f64 re))) (.f64 1/72 (*.f64 (pow.f64 im 4) (cbrt.f64 (exp.f64 re)))))))
(-.f64 (cbrt.f64 (exp.f64 re)) (fma.f64 23/6480 (.f64 (pow.f64 im 6) (cbrt.f64 (exp.f64 re))) (fma.f64 1/6 (.f64 (.f64 (cbrt.f64 (exp.f64 re)) im) im) (.f64 (pow.f64 im 4) (*.f64 (cbrt.f64 (exp.f64 re)) 1/72)))))
(-.f64 (.f64 (+.f64 (.f64 (.f64 im im) -1/6) 1) (cbrt.f64 (exp.f64 re))) (.f64 (cbrt.f64 (exp.f64 re)) (+.f64 (.f64 (pow.f64 im 4) 1/72) (.f64 (pow.f64 im 6) 23/6480))))
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(cbrt.f64 (*.f64 (cos.f64 im) (exp.f64 re)))
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(cbrt.f64 (*.f64 (cos.f64 im) (exp.f64 re)))
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(cbrt.f64 (*.f64 (cos.f64 im) (exp.f64 re)))
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(cbrt.f64 (*.f64 (cos.f64 im) (exp.f64 re)))
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(cbrt.f64 (*.f64 (cos.f64 im) (exp.f64 re)))
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(cbrt.f64 (*.f64 (cos.f64 im) (exp.f64 re)))
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(cbrt.f64 (*.f64 (cos.f64 im) (exp.f64 re)))
(pow.f64 (*.f64 (exp.f64 re) (cos.f64 im)) 1/3)
(cbrt.f64 (*.f64 (cos.f64 im) (exp.f64 re)))

prune68.0ms (2.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	113	4	117

Error

Counts

117 → 4

Alt Table

Status	Error	Program
	22.2b	(+.f64 (cos.f64 im) (*.f64 (cos.f64 im) re))
▶	15.3b	(.f64 (sqrt.f64 (cos.f64 im)) (.f64 (sqrt.f64 (cos.f64 im)) (exp.f64 re)))
✓	0.0b	(*.f64 (exp.f64 re) (cos.f64 im))
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 3)

Compiler

Compiled 1851 to 956 computations (48.4% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (cos.f64 im))
✓	0.1b	(.f64 (sqrt.f64 (cos.f64 im)) (.f64 (sqrt.f64 (cos.f64 im)) (exp.f64 re)))

series3.0ms (0.1%)

Counts

2 → 28

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	im	@	0	(sqrt.f64 (cos.f64 im))
0.0ms	im	@	0	(.f64 (sqrt.f64 (cos.f64 im)) (.f64 (sqrt.f64 (cos.f64 im)) (exp.f64 re)))
0.0ms	im	@	inf	(sqrt.f64 (cos.f64 im))
0.0ms	im	@	-inf	(sqrt.f64 (cos.f64 im))
0.0ms	im	@	inf	(.f64 (sqrt.f64 (cos.f64 im)) (.f64 (sqrt.f64 (cos.f64 im)) (exp.f64 re)))

rewrite39.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

709×	`pow1_binary64`
649×	`add-log-exp_binary64`
649×	`log1p-expm1-u_binary64`
649×	`expm1-log1p-u_binary64`
77×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	154	13
2	1818	13

Stop Event

1×	node limit

Counts

2 → 36

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (cos.f64 im)) (.f64 (sqrt.f64 (cos.f64 im)) (exp.f64 re)))
(sqrt.f64 (cos.f64 im))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (cos.f64 im) (exp.f64 re)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cos.f64 im) (exp.f64 re)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (cos.f64 im) (exp.f64 re)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (cos.f64 im) (exp.f64 re))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (cos.f64 im) (exp.f64 re))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (cos.f64 im) (exp.f64 re)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 im)) (exp.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (cos.f64 im) (exp.f64 re)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (cos.f64 im) (exp.f64 re)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (cos.f64 im) 3) (pow.f64 (exp.f64 re) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (cos.f64 im) 3/2) (pow.f64 (*.f64 (sqrt.f64 (cos.f64 im)) (exp.f64 re)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 (sqrt.f64 (cos.f64 im)) (exp.f64 re)) 3) (pow.f64 (cos.f64 im) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (cos.f64 im) (exp.f64 re))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log.f64 (cos.f64 im)) re))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (cos.f64 im) (exp.f64 re))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (cos.f64 im)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cos.f64 im)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (cos.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cos.f64 im)) (cbrt.f64 (sqrt.f64 (cos.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (cos.f64 im))) (cbrt.f64 (cos.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cos.f64 im) 1/4) (pow.f64 (cos.f64 im) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cos.f64 im)) 2)) (sqrt.f64 (cbrt.f64 (cos.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (cos.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cos.f64 im)) 2) 1/2) (pow.f64 (cbrt.f64 (cos.f64 im)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cos.f64 im) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (cos.f64 im)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cos.f64 im) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (cos.f64 im))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cos.f64 im) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (cos.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (cos.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (cos.f64 im)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (cos.f64 im) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (cos.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (cos.f64 im))))))))

simplify31.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

460×	`distribute-rgt-neg-in_binary64`
436×	`cancel-sign-sub-inv_binary64`
353×	`fma-neg_binary64`
271×	`*-commutative_binary64`
249×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	346
1	145	340
2	419	320
3	1521	307
4	3765	307

Stop Event

1×	node limit

Counts

64 → 58

Calls

Call 1

Inputs
(exp.f64 re)
(-.f64 (exp.f64 re) (.f64 1/2 (.f64 (exp.f64 re) (pow.f64 im 2))))
(-.f64 (+.f64 (exp.f64 re) (.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4)))) (.f64 1/2 (.f64 (exp.f64 re) (pow.f64 im 2))))
(-.f64 (+.f64 (exp.f64 re) (.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4)))) (+.f64 (.f64 1/720 (.f64 (exp.f64 re) (pow.f64 im 6))) (.f64 1/2 (.f64 (exp.f64 re) (pow.f64 im 2)))))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(cos.f64 im)
(+.f64 (cos.f64 im) (*.f64 (cos.f64 im) re))
(+.f64 (cos.f64 im) (+.f64 (.f64 (cos.f64 im) re) (.f64 1/2 (*.f64 (cos.f64 im) (pow.f64 re 2)))))
(+.f64 (.f64 1/6 (.f64 (cos.f64 im) (pow.f64 re 3))) (+.f64 (cos.f64 im) (+.f64 (.f64 (cos.f64 im) re) (.f64 1/2 (*.f64 (cos.f64 im) (pow.f64 re 2))))))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
1
(-.f64 1 (*.f64 1/4 (pow.f64 im 2)))
(-.f64 1 (+.f64 (.f64 1/96 (pow.f64 im 4)) (.f64 1/4 (pow.f64 im 2))))
(-.f64 1 (+.f64 (.f64 19/5760 (pow.f64 im 6)) (+.f64 (.f64 1/96 (pow.f64 im 4)) (*.f64 1/4 (pow.f64 im 2)))))

Outputs
(exp.f64 re)
(-.f64 (exp.f64 re) (.f64 1/2 (.f64 (exp.f64 re) (pow.f64 im 2))))
(-.f64 (exp.f64 re) (.f64 1/2 (.f64 (exp.f64 re) (*.f64 im im))))
(+.f64 (exp.f64 re) (.f64 (.f64 (exp.f64 re) (*.f64 im im)) -1/2))
(fma.f64 (.f64 (exp.f64 re) (.f64 im im)) -1/2 (exp.f64 re))
(-.f64 (+.f64 (exp.f64 re) (.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4)))) (.f64 1/2 (.f64 (exp.f64 re) (pow.f64 im 2))))
(+.f64 (exp.f64 re) (-.f64 (.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4))) (.f64 1/2 (.f64 (exp.f64 re) (*.f64 im im)))))
(+.f64 (fma.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4)) (exp.f64 re)) (.f64 (.f64 (exp.f64 re) (.f64 im im)) -1/2))
(+.f64 (exp.f64 re) (.f64 (exp.f64 re) (+.f64 (.f64 1/24 (pow.f64 im 4)) (.f64 (.f64 im im) -1/2))))
(.f64 (exp.f64 re) (-.f64 (+.f64 1 (.f64 1/24 (pow.f64 im 4))) (.f64 1/2 (.f64 im im))))
(.f64 (exp.f64 re) (+.f64 (+.f64 1 (.f64 1/24 (pow.f64 im 4))) (.f64 im (.f64 im -1/2))))
(-.f64 (+.f64 (exp.f64 re) (.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4)))) (+.f64 (.f64 1/720 (.f64 (exp.f64 re) (pow.f64 im 6))) (.f64 1/2 (.f64 (exp.f64 re) (pow.f64 im 2)))))
(+.f64 (exp.f64 re) (-.f64 (.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4))) (fma.f64 1/720 (.f64 (exp.f64 re) (pow.f64 im 6)) (.f64 1/2 (.f64 (exp.f64 re) (.f64 im im))))))
(-.f64 (fma.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4)) (exp.f64 re)) (fma.f64 1/720 (.f64 (exp.f64 re) (pow.f64 im 6)) (.f64 (exp.f64 re) (.f64 (*.f64 im im) 1/2))))
(-.f64 (fma.f64 (exp.f64 re) (.f64 1/24 (pow.f64 im 4)) (exp.f64 re)) (.f64 (exp.f64 re) (+.f64 (.f64 1/720 (pow.f64 im 6)) (.f64 1/2 (*.f64 im im)))))
(+.f64 (exp.f64 re) (.f64 (exp.f64 re) (-.f64 (fma.f64 1/24 (pow.f64 im 4) (.f64 (.f64 im im) -1/2)) (.f64 1/720 (pow.f64 im 6)))))
(+.f64 (exp.f64 re) (.f64 (exp.f64 re) (+.f64 (fma.f64 1/24 (pow.f64 im 4) (.f64 (pow.f64 im 6) -1/720)) (.f64 im (.f64 im -1/2)))))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(cos.f64 im)
(+.f64 (cos.f64 im) (*.f64 (cos.f64 im) re))
(+.f64 (cos.f64 im) (*.f64 re (cos.f64 im)))
(*.f64 (+.f64 re 1) (cos.f64 im))
(*.f64 (cos.f64 im) (+.f64 re 1))
(+.f64 (cos.f64 im) (+.f64 (.f64 (cos.f64 im) re) (.f64 1/2 (*.f64 (cos.f64 im) (pow.f64 re 2)))))
(+.f64 (cos.f64 im) (fma.f64 (cos.f64 im) re (.f64 1/2 (.f64 (cos.f64 im) (*.f64 re re)))))
(+.f64 (cos.f64 im) (fma.f64 re (cos.f64 im) (.f64 (cos.f64 im) (.f64 (*.f64 re re) 1/2))))
(.f64 (cos.f64 im) (+.f64 (+.f64 re 1) (.f64 1/2 (*.f64 re re))))
(.f64 (cos.f64 im) (+.f64 (+.f64 re 1) (.f64 re (*.f64 re 1/2))))
(.f64 (cos.f64 im) (+.f64 re (+.f64 1 (.f64 re (*.f64 re 1/2)))))
(+.f64 (.f64 1/6 (.f64 (cos.f64 im) (pow.f64 re 3))) (+.f64 (cos.f64 im) (+.f64 (.f64 (cos.f64 im) re) (.f64 1/2 (*.f64 (cos.f64 im) (pow.f64 re 2))))))
(fma.f64 1/6 (.f64 (cos.f64 im) (pow.f64 re 3)) (+.f64 (cos.f64 im) (fma.f64 (cos.f64 im) re (.f64 1/2 (.f64 (cos.f64 im) (.f64 re re))))))
(+.f64 (fma.f64 re (cos.f64 im) (.f64 (cos.f64 im) (.f64 (.f64 re re) 1/2))) (fma.f64 1/6 (.f64 (cos.f64 im) (pow.f64 re 3)) (cos.f64 im)))
(fma.f64 (cos.f64 im) (.f64 1/6 (pow.f64 re 3)) (.f64 (cos.f64 im) (+.f64 (+.f64 re 1) (.f64 1/2 (.f64 re re)))))
(.f64 (cos.f64 im) (+.f64 (+.f64 re 1) (.f64 (.f64 re re) (+.f64 1/2 (.f64 re 1/6)))))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (exp.f64 re) (cos.f64 im))
1
(-.f64 1 (*.f64 1/4 (pow.f64 im 2)))
(+.f64 1 (.f64 -1/4 (.f64 im im)))
(-.f64 1 (.f64 (.f64 im im) 1/4))
(fma.f64 (*.f64 im im) -1/4 1)
(-.f64 1 (+.f64 (.f64 1/96 (pow.f64 im 4)) (.f64 1/4 (pow.f64 im 2))))
(-.f64 1 (fma.f64 1/96 (pow.f64 im 4) (.f64 (.f64 im im) 1/4)))
(-.f64 1 (fma.f64 (pow.f64 im 4) 1/96 (.f64 (.f64 im im) 1/4)))
(+.f64 (.f64 (pow.f64 im 4) -1/96) (fma.f64 (.f64 im im) -1/4 1))
(+.f64 1 (fma.f64 im (.f64 im -1/4) (.f64 (pow.f64 im 4) -1/96)))
(-.f64 1 (+.f64 (.f64 19/5760 (pow.f64 im 6)) (+.f64 (.f64 1/96 (pow.f64 im 4)) (*.f64 1/4 (pow.f64 im 2)))))
(-.f64 1 (fma.f64 19/5760 (pow.f64 im 6) (fma.f64 1/96 (pow.f64 im 4) (.f64 (.f64 im im) 1/4))))
(-.f64 1 (fma.f64 (pow.f64 im 6) 19/5760 (fma.f64 (pow.f64 im 4) 1/96 (.f64 (.f64 im im) 1/4))))
(-.f64 1 (fma.f64 (.f64 im im) 1/4 (fma.f64 (pow.f64 im 4) 1/96 (.f64 (pow.f64 im 6) 19/5760))))
(+.f64 (fma.f64 (.f64 im im) -1/4 1) (fma.f64 (pow.f64 im 6) -19/5760 (.f64 (pow.f64 im 4) -1/96)))
(+.f64 1 (fma.f64 (pow.f64 im 4) -1/96 (fma.f64 (pow.f64 im 6) -19/5760 (.f64 (.f64 im im) -1/4))))

prune48.0ms (1.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	86	4	90

Error

Counts

90 → 4

Alt Table

Status	Error	Program
▶	22.2b	(+.f64 (cos.f64 im) (*.f64 (cos.f64 im) re))
✓	15.3b	(.f64 (sqrt.f64 (cos.f64 im)) (.f64 (sqrt.f64 (cos.f64 im)) (exp.f64 re)))
✓	0.0b	(*.f64 (exp.f64 re) (cos.f64 im))
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 3)

Compiler

Compiled 1193 to 504 computations (57.8% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (cos.f64 im) (*.f64 (cos.f64 im) re))
✓	0.1b	(*.f64 (cos.f64 im) re)

series5.0ms (0.2%)

Counts

2 → 11

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	im	@	0	(*.f64 (cos.f64 im) re)
1.0ms	im	@	0	(+.f64 (cos.f64 im) (*.f64 (cos.f64 im) re))
1.0ms	re	@	0	(*.f64 (cos.f64 im) re)
0.0ms	re	@	inf	(*.f64 (cos.f64 im) re)
0.0ms	re	@	-inf	(*.f64 (cos.f64 im) re)

rewrite42.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

718×	`pow1_binary64`
666×	`add-log-exp_binary64`
666×	`log1p-expm1-u_binary64`
666×	`expm1-log1p-u_binary64`
69×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	17
1	128	15
2	1786	15

Stop Event

1×	node limit

Counts

2 → 51

Calls

Call 1

Inputs
(*.f64 (cos.f64 im) re)
(+.f64 (cos.f64 im) (*.f64 (cos.f64 im) re))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (cos.f64 im) re))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cos.f64 im) re) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (cos.f64 im) re)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (cos.f64 im) re)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (cos.f64 im) re) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (cos.f64 im) re) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 re) (cos.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (cos.f64 im) re))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (cos.f64 im) re) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (cos.f64 im) re)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (cos.f64 im) re)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (cos.f64 im) re)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (cos.f64 im) (+.f64 1 re)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (cos.f64 im) 2) (*.f64 (cos.f64 im) (-.f64 1 re))) (/.f64 (pow.f64 (*.f64 (cos.f64 im) re) 2) (*.f64 (cos.f64 im) (-.f64 1 re))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cos.f64 im) (+.f64 1 re))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cos.f64 im) (+.f64 re 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cos.f64 im) (+.f64 1 re)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (cos.f64 im) (+.f64 1 re)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (cos.f64 im) (+.f64 1 re))) (cbrt.f64 (pow.f64 (*.f64 (cos.f64 im) (+.f64 1 re)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 im) (+.f64 1 re)) 2)) (cbrt.f64 (*.f64 (cos.f64 im) (+.f64 1 re))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (cos.f64 im) (+.f64 1 re))) (sqrt.f64 (*.f64 (cos.f64 im) (+.f64 1 re))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (cos.f64 im) 3) (pow.f64 (*.f64 (cos.f64 im) re) 3)) (/.f64 1 (+.f64 (pow.f64 (cos.f64 im) 2) (*.f64 (*.f64 (cos.f64 im) re) (-.f64 (*.f64 (cos.f64 im) re) (cos.f64 im))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (cos.f64 im) 2) (pow.f64 (*.f64 (cos.f64 im) re) 2)) (/.f64 1 (*.f64 (cos.f64 im) (-.f64 1 re))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 re 1) (cos.f64 im))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (cos.f64 im) 2) (*.f64 (*.f64 (cos.f64 im) re) (-.f64 (*.f64 (cos.f64 im) re) (cos.f64 im)))) (+.f64 (pow.f64 (cos.f64 im) 3) (pow.f64 (*.f64 (cos.f64 im) re) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 (cos.f64 im) (-.f64 1 re)) (-.f64 (pow.f64 (cos.f64 im) 2) (pow.f64 (*.f64 (cos.f64 im) re) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (cos.f64 im) 3) (pow.f64 (*.f64 (cos.f64 im) re) 3)) (+.f64 (pow.f64 (cos.f64 im) 2) (*.f64 (*.f64 (cos.f64 im) re) (-.f64 (*.f64 (cos.f64 im) re) (cos.f64 im)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (cos.f64 im) 3) (pow.f64 (*.f64 (cos.f64 im) re) 3)) (+.f64 (pow.f64 (*.f64 (cos.f64 im) re) 2) (-.f64 (pow.f64 (cos.f64 im) 2) (*.f64 (pow.f64 (cos.f64 im) 2) re))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (cos.f64 im) 2) (pow.f64 (*.f64 (cos.f64 im) re) 2)) (*.f64 (cos.f64 im) (-.f64 1 re)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (cos.f64 im) 3) (pow.f64 (*.f64 (cos.f64 im) re) 3))) (neg.f64 (+.f64 (pow.f64 (cos.f64 im) 2) (*.f64 (*.f64 (cos.f64 im) re) (-.f64 (*.f64 (cos.f64 im) re) (cos.f64 im))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 im) 2) (pow.f64 (*.f64 (cos.f64 im) re) 2))) (neg.f64 (*.f64 (cos.f64 im) (-.f64 1 re))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 im) re) 2) (pow.f64 (cos.f64 im) 2)) (-.f64 (*.f64 (cos.f64 im) re) (cos.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cos.f64 im) (+.f64 1 re)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (cos.f64 im) (+.f64 1 re)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (cos.f64 im) (+.f64 1 re))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (cos.f64 im) (+.f64 1 re))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (cos.f64 im) (+.f64 1 re)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 (cos.f64 im) (+.f64 1 re))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (cos.f64 im) (+.f64 1 re)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (cos.f64 im) (+.f64 1 re)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cos.f64 im) re (cos.f64 im))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 re (cos.f64 im) (cos.f64 im))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (cos.f64 im) (*.f64 (cos.f64 im) re))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 (cos.f64 im) re) (cos.f64 im))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (cos.f64 im)) 2) (cbrt.f64 (cos.f64 im)) (*.f64 (cos.f64 im) re))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 (cos.f64 im) re)) 2) (cbrt.f64 (*.f64 (cos.f64 im) re)) (cos.f64 im))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cos.f64 im)) (sqrt.f64 (cos.f64 im)) (*.f64 (cos.f64 im) re))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 (cos.f64 im) re)) (sqrt.f64 (*.f64 (cos.f64 im) re)) (cos.f64 im))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (cos.f64 im) (+.f64 1 re))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (cos.f64 im) (+.f64 1 re))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (cos.f64 im) (+.f64 1 re))))))))

simplify21.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

640×	`fma-neg_binary64`
511×	`associate--r+_binary64`
397×	`associate-+l-_binary64`
291×	`sub-neg_binary64`
235×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	207
1	126	197
2	445	182
3	2122	169

Stop Event

1×	node limit

Counts

62 → 69

Calls

Call 1

Inputs
re
(-.f64 re (.f64 1/2 (.f64 re (pow.f64 im 2))))
(-.f64 (+.f64 (.f64 1/24 (.f64 re (pow.f64 im 4))) re) (.f64 1/2 (.f64 re (pow.f64 im 2))))
(-.f64 (+.f64 (.f64 1/24 (.f64 re (pow.f64 im 4))) re) (+.f64 (.f64 1/2 (.f64 re (pow.f64 im 2))) (.f64 1/720 (.f64 re (pow.f64 im 6)))))
(+.f64 1 re)
(-.f64 (+.f64 1 re) (+.f64 (.f64 1/2 (.f64 re (pow.f64 im 2))) (*.f64 1/2 (pow.f64 im 2))))
(-.f64 (+.f64 (.f64 1/24 (.f64 re (pow.f64 im 4))) (+.f64 1 (+.f64 (.f64 1/24 (pow.f64 im 4)) re))) (+.f64 (.f64 1/2 (.f64 re (pow.f64 im 2))) (.f64 1/2 (pow.f64 im 2))))
(-.f64 (+.f64 (.f64 1/24 (.f64 re (pow.f64 im 4))) (+.f64 1 (+.f64 (.f64 1/24 (pow.f64 im 4)) re))) (+.f64 (.f64 1/720 (pow.f64 im 6)) (+.f64 (.f64 1/2 (.f64 re (pow.f64 im 2))) (+.f64 (.f64 1/2 (pow.f64 im 2)) (.f64 1/720 (*.f64 re (pow.f64 im 6)))))))
(cos.f64 im)
(*.f64 (cos.f64 im) re)
(*.f64 (cos.f64 im) re)

Outputs
re
(-.f64 re (.f64 1/2 (.f64 re (pow.f64 im 2))))
(+.f64 re (.f64 -1/2 (.f64 re (*.f64 im im))))
(+.f64 re (.f64 (.f64 -1/2 re) (*.f64 im im)))
(fma.f64 (.f64 re (.f64 im im)) -1/2 re)
(-.f64 (+.f64 (.f64 1/24 (.f64 re (pow.f64 im 4))) re) (.f64 1/2 (.f64 re (pow.f64 im 2))))
(+.f64 (fma.f64 1/24 (.f64 re (pow.f64 im 4)) re) (.f64 -1/2 (.f64 re (.f64 im im))))
(fma.f64 (.f64 re 1/24) (pow.f64 im 4) (+.f64 re (.f64 (.f64 -1/2 re) (.f64 im im))))
(fma.f64 re (.f64 1/24 (pow.f64 im 4)) (fma.f64 (.f64 re (*.f64 im im)) -1/2 re))
(.f64 re (+.f64 (fma.f64 1/24 (pow.f64 im 4) 1) (.f64 im (*.f64 im -1/2))))
(-.f64 (+.f64 (.f64 1/24 (.f64 re (pow.f64 im 4))) re) (+.f64 (.f64 1/2 (.f64 re (pow.f64 im 2))) (.f64 1/720 (.f64 re (pow.f64 im 6)))))
(-.f64 (fma.f64 1/24 (.f64 re (pow.f64 im 4)) re) (fma.f64 1/2 (.f64 re (.f64 im im)) (.f64 1/720 (*.f64 re (pow.f64 im 6)))))
(-.f64 (fma.f64 1/24 (.f64 re (pow.f64 im 4)) re) (fma.f64 1/2 (.f64 re (.f64 im im)) (.f64 (pow.f64 im 6) (*.f64 re 1/720))))
(+.f64 (.f64 (fma.f64 1/24 (pow.f64 im 4) 1) re) (.f64 re (-.f64 (.f64 (.f64 im im) -1/2) (*.f64 1/720 (pow.f64 im 6)))))
(fma.f64 (fma.f64 1/24 (pow.f64 im 4) 1) re (.f64 re (fma.f64 im (.f64 im -1/2) (*.f64 (pow.f64 im 6) -1/720))))
(+.f64 1 re)
(+.f64 re 1)
(-.f64 (+.f64 1 re) (+.f64 (.f64 1/2 (.f64 re (pow.f64 im 2))) (*.f64 1/2 (pow.f64 im 2))))
(+.f64 1 (-.f64 re (.f64 1/2 (+.f64 (.f64 re (.f64 im im)) (.f64 im im)))))
(+.f64 re (-.f64 1 (.f64 (.f64 im im) (+.f64 1/2 (*.f64 re 1/2)))))
(+.f64 1 (-.f64 re (.f64 im (.f64 im (fma.f64 re 1/2 1/2)))))
(-.f64 re (fma.f64 im (*.f64 im (fma.f64 re 1/2 1/2)) -1))
(-.f64 (+.f64 (.f64 1/24 (.f64 re (pow.f64 im 4))) (+.f64 1 (+.f64 (.f64 1/24 (pow.f64 im 4)) re))) (+.f64 (.f64 1/2 (.f64 re (pow.f64 im 2))) (.f64 1/2 (pow.f64 im 2))))
(-.f64 (fma.f64 1/24 (.f64 re (pow.f64 im 4)) (+.f64 1 (fma.f64 1/24 (pow.f64 im 4) re))) (.f64 1/2 (+.f64 (.f64 re (.f64 im im)) (*.f64 im im))))
(+.f64 (+.f64 (fma.f64 1/24 (pow.f64 im 4) re) (fma.f64 (.f64 re 1/24) (pow.f64 im 4) 1)) (.f64 -1/2 (.f64 (+.f64 re 1) (.f64 im im))))
(+.f64 (fma.f64 re (.f64 1/24 (pow.f64 im 4)) (fma.f64 1/24 (pow.f64 im 4) 1)) (-.f64 re (.f64 im (*.f64 im (fma.f64 re 1/2 1/2)))))
(+.f64 (-.f64 1 (.f64 im (.f64 im (fma.f64 re 1/2 1/2)))) (+.f64 re (.f64 (pow.f64 im 4) (+.f64 1/24 (.f64 re 1/24)))))
(-.f64 (+.f64 (.f64 1/24 (.f64 re (pow.f64 im 4))) (+.f64 1 (+.f64 (.f64 1/24 (pow.f64 im 4)) re))) (+.f64 (.f64 1/720 (pow.f64 im 6)) (+.f64 (.f64 1/2 (.f64 re (pow.f64 im 2))) (+.f64 (.f64 1/2 (pow.f64 im 2)) (.f64 1/720 (*.f64 re (pow.f64 im 6)))))))
(-.f64 (fma.f64 1/24 (.f64 re (pow.f64 im 4)) (+.f64 1 (fma.f64 1/24 (pow.f64 im 4) re))) (fma.f64 1/720 (pow.f64 im 6) (fma.f64 1/2 (.f64 re (.f64 im im)) (fma.f64 1/2 (.f64 im im) (.f64 1/720 (.f64 re (pow.f64 im 6)))))))
(+.f64 (fma.f64 (.f64 re 1/24) (pow.f64 im 4) 1) (-.f64 (fma.f64 1/24 (pow.f64 im 4) re) (fma.f64 1/720 (pow.f64 im 6) (fma.f64 1/2 (.f64 (+.f64 re 1) (.f64 im im)) (.f64 (pow.f64 im 6) (*.f64 re 1/720))))))
(+.f64 (fma.f64 1/24 (pow.f64 im 4) 1) (-.f64 (.f64 (fma.f64 1/24 (pow.f64 im 4) 1) re) (fma.f64 (.f64 im im) (fma.f64 re 1/2 1/2) (.f64 (pow.f64 im 6) (+.f64 (.f64 re 1/720) 1/720)))))
(+.f64 1 (-.f64 (+.f64 re (.f64 (pow.f64 im 4) (+.f64 1/24 (.f64 re 1/24)))) (.f64 (+.f64 re 1) (+.f64 (.f64 1/2 (.f64 im im)) (.f64 1/720 (pow.f64 im 6))))))
(cos.f64 im)
(*.f64 (cos.f64 im) re)
(*.f64 re (cos.f64 im))
(*.f64 (cos.f64 im) re)
(*.f64 re (cos.f64 im))

prune43.0ms (1.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	69	4	73

Error

Counts

73 → 4

Alt Table

Status	Error	Program
✓	22.2b	(+.f64 (cos.f64 im) (*.f64 (cos.f64 im) re))
✓	15.3b	(.f64 (sqrt.f64 (cos.f64 im)) (.f64 (sqrt.f64 (cos.f64 im)) (exp.f64 re)))
✓	0.0b	(*.f64 (exp.f64 re) (cos.f64 im))
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (cos.f64 im))) 3)

Compiler

Compiled 987 to 522 computations (47.1% saved)

regimes33.0ms (1.1%)

Accuracy

Total 0.0b remaining (59.8%)

Threshold costs 0.0b (59.8%)

Counts

13 → 1

Compiler

Compiled 91 to 40 computations (56% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8

Stop Event

1×

saturated

Calls

Call 1

Inputs
(*.f64 (exp.f64 re) (cos.f64 im))

Outputs
(*.f64 (exp.f64 re) (cos.f64 im))

end70.0ms (2.4%)

Stop Event

1×

done

Compiler

Compiled 52 to 35 computations (32.7% saved)

Details

analyze191.0ms (6.5%)

sample2.1s (72%)

preprocess17.0ms (0.6%)

simplify5.0ms (0.2%)

prune1.0ms (0%)

localize4.0ms (0.1%)

series4.0ms (0.1%)

rewrite31.0ms (1%)

simplify23.0ms (0.8%)

prune22.0ms (0.7%)

localize6.0ms (0.2%)

series23.0ms (0.8%)

rewrite38.0ms (1.3%)

simplify42.0ms (1.4%)

prune68.0ms (2.3%)

localize6.0ms (0.2%)

series3.0ms (0.1%)

rewrite39.0ms (1.3%)

simplify31.0ms (1.1%)

prune48.0ms (1.6%)

localize5.0ms (0.2%)

series5.0ms (0.2%)

rewrite42.0ms (1.4%)

simplify21.0ms (0.7%)

prune43.0ms (1.5%)

regimes33.0ms (1.1%)

simplify3.0ms (0.1%)

end70.0ms (2.4%)

Profiling