Details

analyze207.0ms (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)

sample2.0s (63.6%)

Results

630.0ms	5753×	body	128	valid
624.0ms	1414×	body	1024	valid
267.0ms	695×	body	1024	invalid
230.0ms	739×	body	512	valid
98.0ms	343×	body	512	invalid
80.0ms	349×	body	256	valid
42.0ms	182×	body	256	invalid
30.0ms	208×	body	128	invalid
1.0ms	1×	body	2048	valid

preprocess14.0ms (0.4%)

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)

simplify6.0ms (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)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series5.0ms (0.2%)

Counts

2 → 12

Calls

9 calls:

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

rewrite32.0ms (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	11
1	113	11
2	1324	11

Stop Event

1×	node limit

Counts

2 → 29

Calls

Call 1

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

simplify27.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

945×	`fma-def_binary64`
688×	`associate-l_binary64`
514×	`distribute-rgt-out_binary64`
434×	`associate-r_binary64`
390×	`unswap-sqr_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	49	204
1	131	200
2	331	182
3	1045	165
4	3792	160

Stop Event

1×	node limit

Counts

41 → 50

Calls

Call 1

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

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

prune69.0ms (2.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	48	2	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	48	3	51

Error

Counts

51 → 3

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 (exp.f64 re) (log1p.f64 (expm1.f64 (cos.f64 im))))
	0.2b	(*.f64 (exp.f64 re) (cbrt.f64 (pow.f64 (cos.f64 im) 3)))
✓	0.0b	(*.f64 (exp.f64 re) (cos.f64 im))

Compiler

Compiled 565 to 304 computations (46.2% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 im)
✓	0.0b	(*.f64 (exp.f64 re) (log1p.f64 (expm1.f64 (cos.f64 im))))
✓	0.2b	(log1p.f64 (expm1.f64 (cos.f64 im)))
✓	0.6b	(expm1.f64 (cos.f64 im))

series4.0ms (0.1%)

Counts

3 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	im	@	0	(expm1.f64 (cos.f64 im))
0.0ms	im	@	inf	(expm1.f64 (cos.f64 im))
0.0ms	im	@	-inf	(expm1.f64 (cos.f64 im))
0.0ms	im	@	0	(log1p.f64 (expm1.f64 (cos.f64 im)))
0.0ms	im	@	0	(*.f64 (exp.f64 re) (log1p.f64 (expm1.f64 (cos.f64 im))))

rewrite35.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

611×	`pow1_binary64`
559×	`expm1-log1p-u_binary64`
558×	`add-log-exp_binary64`
558×	`log1p-expm1-u_binary64`
66×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	135	16
2	1534	16

Stop Event

1×	node limit

Counts

3 → 49

Calls

Call 1

Inputs
(expm1.f64 (cos.f64 im))
(log1p.f64 (expm1.f64 (cos.f64 im)))
(*.f64 (exp.f64 re) (log1p.f64 (expm1.f64 (cos.f64 im))))

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

Outputs

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

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

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

simplify46.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

772×	`fma-neg_binary64`
404×	`*-commutative_binary64`
399×	`fma-def_binary64`
392×	`cancel-sign-sub-inv_binary64`
272×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	69	488
1	191	476
2	493	452
3	1642	435
4	2577	430
5	4065	428

Stop Event

1×	node limit

Counts

97 → 80

Calls

Call 1

Inputs
(-.f64 (E.f64) 1)
(-.f64 (+.f64 (E.f64) (.f64 -1/2 (.f64 (E.f64) (pow.f64 im 2)))) 1)
(-.f64 (+.f64 (E.f64) (+.f64 (.f64 -1/2 (.f64 (E.f64) (pow.f64 im 2))) (.f64 1/6 (.f64 (E.f64) (pow.f64 im 4))))) 1)
(-.f64 (+.f64 (E.f64) (+.f64 (.f64 -31/720 (.f64 (E.f64) (pow.f64 im 6))) (+.f64 (.f64 -1/2 (.f64 (E.f64) (pow.f64 im 2))) (.f64 1/6 (.f64 (E.f64) (pow.f64 im 4)))))) 1)
(-.f64 (exp.f64 (cos.f64 im)) 1)
(-.f64 (exp.f64 (cos.f64 im)) 1)
(-.f64 (exp.f64 (cos.f64 im)) 1)
(-.f64 (exp.f64 (cos.f64 im)) 1)
(-.f64 (exp.f64 (cos.f64 im)) 1)
(-.f64 (exp.f64 (cos.f64 im)) 1)
(-.f64 (exp.f64 (cos.f64 im)) 1)
(-.f64 (exp.f64 (cos.f64 im)) 1)
1
(+.f64 1 (*.f64 -1/2 (pow.f64 im 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 im 2)) (.f64 1/24 (pow.f64 im 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 im 2)) (+.f64 (.f64 1/24 (pow.f64 im 4)) (*.f64 -1/720 (pow.f64 im 6)))))
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(+.f64 (*.f64 (cos.f64 im) re) (cos.f64 im))
(+.f64 (.f64 1/2 (.f64 (cos.f64 im) (pow.f64 re 2))) (+.f64 (*.f64 (cos.f64 im) re) (cos.f64 im)))
(+.f64 (.f64 1/6 (.f64 (cos.f64 im) (pow.f64 re 3))) (+.f64 (.f64 1/2 (.f64 (cos.f64 im) (pow.f64 re 2))) (+.f64 (*.f64 (cos.f64 im) 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))
(*.f64 (exp.f64 re) (cos.f64 im))
(exp.f64 re)
(+.f64 (.f64 -1/2 (.f64 (exp.f64 re) (pow.f64 im 2))) (exp.f64 re))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 re) (pow.f64 im 2))) (+.f64 (.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4))) (exp.f64 re)))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 re) (pow.f64 im 2))) (+.f64 (.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4))) (+.f64 (exp.f64 re) (.f64 -1/720 (.f64 (exp.f64 re) (pow.f64 im 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))

Outputs
(-.f64 (E.f64) 1)
(+.f64 (E.f64) -1)
(expm1.f64 1)
(-.f64 (+.f64 (E.f64) (.f64 -1/2 (.f64 (E.f64) (pow.f64 im 2)))) 1)
(+.f64 (E.f64) (-.f64 (.f64 -1/2 (.f64 (E.f64) (*.f64 im im))) 1))
(+.f64 (E.f64) (fma.f64 (.f64 (E.f64) -1/2) (.f64 im im) -1))
(fma.f64 (E.f64) (.f64 im (.f64 -1/2 im)) (expm1.f64 1))
(fma.f64 (fma.f64 -1/2 (*.f64 im im) 1) (E.f64) -1)
(fma.f64 (E.f64) (fma.f64 -1/2 (*.f64 im im) 1) -1)
(-.f64 (+.f64 (E.f64) (+.f64 (.f64 -1/2 (.f64 (E.f64) (pow.f64 im 2))) (.f64 1/6 (.f64 (E.f64) (pow.f64 im 4))))) 1)
(+.f64 (E.f64) (-.f64 (fma.f64 -1/2 (.f64 (E.f64) (.f64 im im)) (.f64 1/6 (.f64 (E.f64) (pow.f64 im 4)))) 1))
(+.f64 (fma.f64 -1/2 (.f64 (E.f64) (.f64 im im)) (.f64 (.f64 1/6 (pow.f64 im 4)) (E.f64))) (expm1.f64 1))
(+.f64 (.f64 (E.f64) (+.f64 (.f64 im (.f64 -1/2 im)) (.f64 1/6 (pow.f64 im 4)))) (expm1.f64 1))
(+.f64 (.f64 (E.f64) (+.f64 (.f64 1/6 (pow.f64 im 4)) (fma.f64 -1/2 (*.f64 im im) 1))) -1)
(fma.f64 (E.f64) (+.f64 (fma.f64 -1/2 (.f64 im im) 1) (.f64 1/6 (pow.f64 im 4))) -1)
(-.f64 (+.f64 (E.f64) (+.f64 (.f64 -31/720 (.f64 (E.f64) (pow.f64 im 6))) (+.f64 (.f64 -1/2 (.f64 (E.f64) (pow.f64 im 2))) (.f64 1/6 (.f64 (E.f64) (pow.f64 im 4)))))) 1)
(+.f64 (E.f64) (-.f64 (fma.f64 -31/720 (.f64 (E.f64) (pow.f64 im 6)) (fma.f64 -1/2 (.f64 (E.f64) (.f64 im im)) (.f64 1/6 (*.f64 (E.f64) (pow.f64 im 4))))) 1))
(+.f64 (fma.f64 -31/720 (.f64 (E.f64) (pow.f64 im 6)) (fma.f64 -1/2 (.f64 (E.f64) (.f64 im im)) (.f64 (*.f64 1/6 (pow.f64 im 4)) (E.f64)))) (expm1.f64 1))
(+.f64 (fma.f64 (E.f64) (.f64 im (.f64 -1/2 im)) (.f64 (E.f64) (+.f64 (.f64 1/6 (pow.f64 im 4)) (*.f64 -31/720 (pow.f64 im 6))))) (expm1.f64 1))
(+.f64 (.f64 (E.f64) (+.f64 (.f64 -1/2 (.f64 im im)) (+.f64 (.f64 1/6 (pow.f64 im 4)) (*.f64 -31/720 (pow.f64 im 6))))) (expm1.f64 1))
(+.f64 (.f64 (E.f64) (+.f64 (fma.f64 -1/2 (.f64 im im) 1) (+.f64 (.f64 1/6 (pow.f64 im 4)) (.f64 -31/720 (pow.f64 im 6))))) -1)
(fma.f64 (E.f64) (+.f64 (fma.f64 -1/2 (.f64 im im) 1) (+.f64 (.f64 1/6 (pow.f64 im 4)) (*.f64 -31/720 (pow.f64 im 6)))) -1)
(-.f64 (exp.f64 (cos.f64 im)) 1)
(expm1.f64 (cos.f64 im))
(-.f64 (exp.f64 (cos.f64 im)) 1)
(expm1.f64 (cos.f64 im))
(-.f64 (exp.f64 (cos.f64 im)) 1)
(expm1.f64 (cos.f64 im))
(-.f64 (exp.f64 (cos.f64 im)) 1)
(expm1.f64 (cos.f64 im))
(-.f64 (exp.f64 (cos.f64 im)) 1)
(expm1.f64 (cos.f64 im))
(-.f64 (exp.f64 (cos.f64 im)) 1)
(expm1.f64 (cos.f64 im))
(-.f64 (exp.f64 (cos.f64 im)) 1)
(expm1.f64 (cos.f64 im))
(-.f64 (exp.f64 (cos.f64 im)) 1)
(expm1.f64 (cos.f64 im))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 im 2)))
(+.f64 1 (.f64 -1/2 (.f64 im im)))
(fma.f64 -1/2 (*.f64 im im) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 im 2)) (.f64 1/24 (pow.f64 im 4))))
(+.f64 1 (fma.f64 -1/2 (.f64 im im) (.f64 (pow.f64 im 4) 1/24)))
(+.f64 1 (fma.f64 (pow.f64 im 4) 1/24 (.f64 im (.f64 im -1/2))))
(fma.f64 -1/2 (*.f64 im im) (fma.f64 (pow.f64 im 4) 1/24 1))
(fma.f64 (pow.f64 im 4) 1/24 (fma.f64 -1/2 (*.f64 im im) 1))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 im 2)) (+.f64 (.f64 1/24 (pow.f64 im 4)) (*.f64 -1/720 (pow.f64 im 6)))))
(+.f64 1 (fma.f64 -1/2 (.f64 im im) (fma.f64 1/24 (pow.f64 im 4) (.f64 (pow.f64 im 6) -1/720))))
(+.f64 (fma.f64 -1/2 (.f64 im im) 1) (fma.f64 (pow.f64 im 4) 1/24 (.f64 (pow.f64 im 6) -1/720)))
(+.f64 (fma.f64 (pow.f64 im 4) 1/24 (.f64 im (.f64 -1/2 im))) (fma.f64 (pow.f64 im 6) -1/720 1))
(+.f64 1 (fma.f64 (pow.f64 im 4) 1/24 (fma.f64 -1/2 (.f64 im im) (.f64 (pow.f64 im 6) -1/720))))
(+.f64 1 (fma.f64 -1/2 (.f64 im im) (fma.f64 (pow.f64 im 4) 1/24 (.f64 (pow.f64 im 6) -1/720))))
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(+.f64 (*.f64 (cos.f64 im) re) (cos.f64 im))
(fma.f64 (cos.f64 im) re (cos.f64 im))
(*.f64 (+.f64 re 1) (cos.f64 im))
(*.f64 (cos.f64 im) (+.f64 1 re))
(+.f64 (.f64 1/2 (.f64 (cos.f64 im) (pow.f64 re 2))) (+.f64 (*.f64 (cos.f64 im) re) (cos.f64 im)))
(fma.f64 1/2 (.f64 (cos.f64 im) (.f64 re re)) (fma.f64 (cos.f64 im) re (cos.f64 im)))
(fma.f64 1/2 (.f64 (cos.f64 im) (.f64 re re)) (*.f64 (+.f64 re 1) (cos.f64 im)))
(.f64 (cos.f64 im) (+.f64 (+.f64 1 re) (.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 (.f64 1/2 (.f64 (cos.f64 im) (pow.f64 re 2))) (+.f64 (*.f64 (cos.f64 im) re) (cos.f64 im))))
(fma.f64 1/6 (.f64 (cos.f64 im) (pow.f64 re 3)) (fma.f64 1/2 (.f64 (cos.f64 im) (*.f64 re re)) (fma.f64 (cos.f64 im) re (cos.f64 im))))
(fma.f64 1/6 (.f64 (cos.f64 im) (pow.f64 re 3)) (fma.f64 1/2 (.f64 (cos.f64 im) (.f64 re re)) (.f64 (+.f64 re 1) (cos.f64 im))))
(fma.f64 1/6 (.f64 (cos.f64 im) (pow.f64 re 3)) (.f64 (cos.f64 im) (+.f64 (+.f64 1 re) (.f64 re (.f64 re 1/2)))))
(.f64 (cos.f64 im) (+.f64 (+.f64 1 re) (.f64 (.f64 re re) (+.f64 1/2 (.f64 1/6 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))
(*.f64 (exp.f64 re) (cos.f64 im))
(*.f64 (cos.f64 im) (exp.f64 re))
(exp.f64 re)
(+.f64 (.f64 -1/2 (.f64 (exp.f64 re) (pow.f64 im 2))) (exp.f64 re))
(fma.f64 -1/2 (.f64 (.f64 im im) (exp.f64 re)) (exp.f64 re))
(.f64 (fma.f64 -1/2 (.f64 im im) 1) (exp.f64 re))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 re) (pow.f64 im 2))) (+.f64 (.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4))) (exp.f64 re)))
(fma.f64 -1/2 (.f64 (.f64 im im) (exp.f64 re)) (fma.f64 1/24 (*.f64 (pow.f64 im 4) (exp.f64 re)) (exp.f64 re)))
(+.f64 (exp.f64 re) (.f64 (exp.f64 re) (fma.f64 (pow.f64 im 4) 1/24 (.f64 im (*.f64 -1/2 im)))))
(.f64 (exp.f64 re) (fma.f64 (pow.f64 im 4) 1/24 (fma.f64 -1/2 (.f64 im im) 1)))
(.f64 (exp.f64 re) (fma.f64 -1/2 (.f64 im im) (fma.f64 (pow.f64 im 4) 1/24 1)))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 re) (pow.f64 im 2))) (+.f64 (.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4))) (+.f64 (exp.f64 re) (.f64 -1/720 (.f64 (exp.f64 re) (pow.f64 im 6))))))
(fma.f64 -1/2 (.f64 (.f64 im im) (exp.f64 re)) (fma.f64 1/24 (.f64 (pow.f64 im 4) (exp.f64 re)) (+.f64 (exp.f64 re) (.f64 (*.f64 -1/720 (exp.f64 re)) (pow.f64 im 6)))))
(fma.f64 -1/2 (.f64 (.f64 im im) (exp.f64 re)) (fma.f64 1/24 (.f64 (pow.f64 im 4) (exp.f64 re)) (fma.f64 -1/720 (.f64 (pow.f64 im 6) (exp.f64 re)) (exp.f64 re))))
(+.f64 (.f64 (fma.f64 (pow.f64 im 6) -1/720 1) (exp.f64 re)) (.f64 (exp.f64 re) (fma.f64 (pow.f64 im 4) 1/24 (.f64 im (.f64 -1/2 im)))))
(+.f64 (exp.f64 re) (.f64 (exp.f64 re) (fma.f64 (pow.f64 im 4) 1/24 (fma.f64 -1/2 (.f64 im im) (*.f64 (pow.f64 im 6) -1/720)))))
(.f64 (exp.f64 re) (+.f64 1 (fma.f64 -1/2 (.f64 im im) (fma.f64 (pow.f64 im 4) 1/24 (*.f64 (pow.f64 im 6) -1/720)))))
(*.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))

prune245.0ms (7.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	103	3	106

Error

Counts

106 → 3

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (exp.f64 re) (log1p.f64 (expm1.f64 (cos.f64 im))))
▶	0.2b	(*.f64 (exp.f64 re) (cbrt.f64 (pow.f64 (cos.f64 im) 3)))
✓	0.0b	(*.f64 (exp.f64 re) (cos.f64 im))

Compiler

Compiled 1216 to 646 computations (46.9% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (exp.f64 re) (cbrt.f64 (pow.f64 (cos.f64 im) 3)))
	0.0b	(cos.f64 im)
✓	0.3b	(cbrt.f64 (pow.f64 (cos.f64 im) 3))
✓	0.3b	(pow.f64 (cos.f64 im) 3)

series5.0ms (0.1%)

Counts

3 → 40

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	im	@	0	(pow.f64 (cos.f64 im) 3)
1.0ms	im	@	-inf	(pow.f64 (cos.f64 im) 3)
1.0ms	im	@	inf	(pow.f64 (cos.f64 im) 3)
0.0ms	re	@	0	(*.f64 (exp.f64 re) (cbrt.f64 (pow.f64 (cos.f64 im) 3)))
0.0ms	im	@	0	(*.f64 (exp.f64 re) (cbrt.f64 (pow.f64 (cos.f64 im) 3)))

rewrite46.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

700×	`pow1_binary64`
651×	`add-log-exp_binary64`
651×	`log1p-expm1-u_binary64`
651×	`expm1-log1p-u_binary64`
79×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	182	17
2	1831	17

Stop Event

1×	node limit

Counts

3 → 55

Calls

Call 1

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

Outputs

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

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

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

simplify62.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1884×	`fma-def_binary64`
421×	`*-commutative_binary64`
236×	`distribute-lft-out_binary64`
179×	`unswap-sqr_binary64`
178×	`sqr-pow_binary64`

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	60	408
1	155	402
2	396	380
3	1259	367
4	1889	365
5	2650	365
6	2868	365
7	3139	365
8	3673	353

Stop Event

1×	node limit

Counts

95 → 83

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -3/2 (pow.f64 im 2)))
(+.f64 1 (+.f64 (.f64 -3/2 (pow.f64 im 2)) (.f64 7/8 (pow.f64 im 4))))
(+.f64 (.f64 -61/240 (pow.f64 im 6)) (+.f64 1 (+.f64 (.f64 -3/2 (pow.f64 im 2)) (*.f64 7/8 (pow.f64 im 4)))))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 im 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 im 2)) (.f64 1/24 (pow.f64 im 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 im 2)) (+.f64 (.f64 1/24 (pow.f64 im 4)) (*.f64 -1/720 (pow.f64 im 6)))))
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(+.f64 (*.f64 (cos.f64 im) re) (cos.f64 im))
(+.f64 (.f64 1/2 (.f64 (cos.f64 im) (pow.f64 re 2))) (+.f64 (*.f64 (cos.f64 im) re) (cos.f64 im)))
(+.f64 (.f64 1/6 (.f64 (cos.f64 im) (pow.f64 re 3))) (+.f64 (.f64 1/2 (.f64 (cos.f64 im) (pow.f64 re 2))) (+.f64 (*.f64 (cos.f64 im) 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))
(*.f64 (exp.f64 re) (cos.f64 im))
(exp.f64 re)
(+.f64 (.f64 -1/2 (.f64 (exp.f64 re) (pow.f64 im 2))) (exp.f64 re))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 re) (pow.f64 im 2))) (+.f64 (.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4))) (exp.f64 re)))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 re) (pow.f64 im 2))) (+.f64 (.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4))) (+.f64 (exp.f64 re) (.f64 -1/720 (.f64 (exp.f64 re) (pow.f64 im 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))

Outputs
1
(+.f64 1 (*.f64 -3/2 (pow.f64 im 2)))
(+.f64 1 (.f64 -3/2 (.f64 im im)))
(fma.f64 -3/2 (*.f64 im im) 1)
(+.f64 1 (+.f64 (.f64 -3/2 (pow.f64 im 2)) (.f64 7/8 (pow.f64 im 4))))
(+.f64 1 (fma.f64 -3/2 (.f64 im im) (.f64 7/8 (pow.f64 im 4))))
(+.f64 (fma.f64 -3/2 (.f64 im im) 1) (.f64 7/8 (pow.f64 im 4)))
(fma.f64 -3/2 (*.f64 im im) (fma.f64 7/8 (pow.f64 im 4) 1))
(+.f64 (.f64 -61/240 (pow.f64 im 6)) (+.f64 1 (+.f64 (.f64 -3/2 (pow.f64 im 2)) (*.f64 7/8 (pow.f64 im 4)))))
(fma.f64 -61/240 (pow.f64 im 6) (+.f64 1 (fma.f64 -3/2 (.f64 im im) (.f64 7/8 (pow.f64 im 4)))))
(+.f64 (fma.f64 -3/2 (.f64 im im) (.f64 7/8 (pow.f64 im 4))) (fma.f64 -61/240 (pow.f64 im 6) 1))
(fma.f64 -61/240 (pow.f64 im 6) (fma.f64 -3/2 (*.f64 im im) (fma.f64 7/8 (pow.f64 im 4) 1)))
(fma.f64 -3/2 (*.f64 im im) (fma.f64 -61/240 (pow.f64 im 6) (fma.f64 7/8 (pow.f64 im 4) 1)))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 im 2)))
(+.f64 1 (.f64 (.f64 im im) -1/2))
(fma.f64 (*.f64 im im) -1/2 1)
(fma.f64 im (*.f64 im -1/2) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 im 2)) (.f64 1/24 (pow.f64 im 4))))
(+.f64 1 (fma.f64 -1/2 (.f64 im im) (.f64 (pow.f64 im 4) 1/24)))
(+.f64 (fma.f64 (.f64 im im) -1/2 1) (.f64 (pow.f64 im 4) 1/24))
(fma.f64 im (*.f64 im -1/2) (fma.f64 (pow.f64 im 4) 1/24 1))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 im 2)) (+.f64 (.f64 1/24 (pow.f64 im 4)) (*.f64 -1/720 (pow.f64 im 6)))))
(+.f64 1 (fma.f64 -1/2 (.f64 im im) (fma.f64 1/24 (pow.f64 im 4) (.f64 (pow.f64 im 6) -1/720))))
(+.f64 (fma.f64 (.f64 im im) -1/2 1) (fma.f64 (pow.f64 im 4) 1/24 (.f64 (pow.f64 im 6) -1/720)))
(+.f64 (fma.f64 im (.f64 im -1/2) (.f64 (pow.f64 im 4) 1/24)) (fma.f64 (pow.f64 im 6) -1/720 1))
(+.f64 (fma.f64 im (.f64 im -1/2) 1) (fma.f64 (pow.f64 im 4) 1/24 (.f64 (pow.f64 im 6) -1/720)))
(fma.f64 im (*.f64 im -1/2) (fma.f64 (pow.f64 im 4) 1/24 (fma.f64 (pow.f64 im 6) -1/720 1)))
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(cos.f64 im)
(+.f64 (*.f64 (cos.f64 im) re) (cos.f64 im))
(fma.f64 (cos.f64 im) re (cos.f64 im))
(*.f64 (+.f64 re 1) (cos.f64 im))
(*.f64 (cos.f64 im) (+.f64 1 re))
(+.f64 (.f64 1/2 (.f64 (cos.f64 im) (pow.f64 re 2))) (+.f64 (*.f64 (cos.f64 im) re) (cos.f64 im)))
(fma.f64 1/2 (.f64 (cos.f64 im) (.f64 re re)) (fma.f64 (cos.f64 im) re (cos.f64 im)))
(fma.f64 1/2 (.f64 (cos.f64 im) (.f64 re re)) (*.f64 (+.f64 re 1) (cos.f64 im)))
(.f64 (cos.f64 im) (+.f64 (.f64 re (*.f64 re 1/2)) (+.f64 1 re)))
(.f64 (cos.f64 im) (+.f64 1 (+.f64 re (.f64 1/2 (*.f64 re re)))))
(*.f64 (cos.f64 im) (fma.f64 re (fma.f64 re 1/2 1) 1))
(+.f64 (.f64 1/6 (.f64 (cos.f64 im) (pow.f64 re 3))) (+.f64 (.f64 1/2 (.f64 (cos.f64 im) (pow.f64 re 2))) (+.f64 (*.f64 (cos.f64 im) re) (cos.f64 im))))
(fma.f64 1/6 (.f64 (cos.f64 im) (pow.f64 re 3)) (fma.f64 1/2 (.f64 (cos.f64 im) (*.f64 re re)) (fma.f64 (cos.f64 im) re (cos.f64 im))))
(fma.f64 1/6 (.f64 (cos.f64 im) (pow.f64 re 3)) (fma.f64 1/2 (.f64 (cos.f64 im) (.f64 re re)) (.f64 (+.f64 re 1) (cos.f64 im))))
(fma.f64 (cos.f64 im) (.f64 1/6 (pow.f64 re 3)) (.f64 (cos.f64 im) (+.f64 (.f64 re (.f64 re 1/2)) (+.f64 1 re))))
(.f64 (cos.f64 im) (+.f64 (+.f64 1 re) (.f64 (.f64 re re) (+.f64 1/2 (.f64 re 1/6)))))
(.f64 (cos.f64 im) (+.f64 re (+.f64 1 (.f64 (.f64 re re) (+.f64 1/2 (.f64 re 1/6))))))
(fma.f64 (cos.f64 im) (fma.f64 (*.f64 re re) (fma.f64 re 1/6 1/2) re) (cos.f64 im))
(*.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 (.f64 -1/2 (.f64 (exp.f64 re) (pow.f64 im 2))) (exp.f64 re))
(fma.f64 -1/2 (.f64 (.f64 im im) (exp.f64 re)) (exp.f64 re))
(fma.f64 -1/2 (.f64 im (.f64 im (exp.f64 re))) (exp.f64 re))
(.f64 (fma.f64 im (.f64 im -1/2) 1) (exp.f64 re))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 re) (pow.f64 im 2))) (+.f64 (.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4))) (exp.f64 re)))
(fma.f64 -1/2 (.f64 (.f64 im im) (exp.f64 re)) (fma.f64 1/24 (*.f64 (pow.f64 im 4) (exp.f64 re)) (exp.f64 re)))
(fma.f64 -1/2 (.f64 im (.f64 im (exp.f64 re))) (fma.f64 1/24 (*.f64 (pow.f64 im 4) (exp.f64 re)) (exp.f64 re)))
(+.f64 (exp.f64 re) (.f64 (exp.f64 re) (fma.f64 im (.f64 im -1/2) (*.f64 (pow.f64 im 4) 1/24))))
(.f64 (exp.f64 re) (fma.f64 im (.f64 im -1/2) (fma.f64 (pow.f64 im 4) 1/24 1)))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 re) (pow.f64 im 2))) (+.f64 (.f64 1/24 (.f64 (exp.f64 re) (pow.f64 im 4))) (+.f64 (exp.f64 re) (.f64 -1/720 (.f64 (exp.f64 re) (pow.f64 im 6))))))
(fma.f64 -1/2 (.f64 (.f64 im im) (exp.f64 re)) (fma.f64 1/24 (.f64 (pow.f64 im 4) (exp.f64 re)) (+.f64 (exp.f64 re) (.f64 -1/720 (*.f64 (pow.f64 im 6) (exp.f64 re))))))
(fma.f64 -1/2 (.f64 im (.f64 im (exp.f64 re))) (fma.f64 1/24 (.f64 (pow.f64 im 4) (exp.f64 re)) (fma.f64 -1/720 (.f64 (pow.f64 im 6) (exp.f64 re)) (exp.f64 re))))
(+.f64 (.f64 (fma.f64 (pow.f64 im 4) 1/24 1) (exp.f64 re)) (.f64 (exp.f64 re) (fma.f64 im (.f64 im -1/2) (.f64 (pow.f64 im 6) -1/720))))
(+.f64 (exp.f64 re) (.f64 (exp.f64 re) (fma.f64 im (.f64 im -1/2) (fma.f64 (pow.f64 im 4) 1/24 (*.f64 (pow.f64 im 6) -1/720)))))
(.f64 (exp.f64 re) (+.f64 (fma.f64 im (.f64 im -1/2) 1) (fma.f64 (pow.f64 im 4) 1/24 (*.f64 (pow.f64 im 6) -1/720))))
(.f64 (exp.f64 re) (fma.f64 im (.f64 im -1/2) (fma.f64 (pow.f64 im 4) 1/24 (fma.f64 (pow.f64 im 6) -1/720 1))))
(*.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))

prune299.0ms (9.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	106	3	109

Error

Counts

109 → 3

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (exp.f64 re) (log1p.f64 (expm1.f64 (cos.f64 im))))
✓	0.2b	(*.f64 (exp.f64 re) (cbrt.f64 (pow.f64 (cos.f64 im) 3)))
✓	0.0b	(*.f64 (exp.f64 re) (cos.f64 im))

Compiler

Compiled 1259 to 695 computations (44.8% saved)

regimes16.0ms (0.5%)

Accuracy

Total -0.2b remaining (-2817%)

Threshold costs -0.2b (-2817%)

Counts

3 → 1

Calls

Call 1

Inputs
(*.f64 (exp.f64 re) (log1p.f64 (expm1.f64 (cos.f64 im))))
(*.f64 (exp.f64 re) (cbrt.f64 (pow.f64 (cos.f64 im) 3)))
(*.f64 (exp.f64 re) (cos.f64 im))

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

Results

3.0ms	0.0b	`re`
4.0ms	0.0b	`im`
3.0ms	0.0b	`(*.f64 (exp.f64 re) (cos.f64 im))`
2.0ms	0.0b	`(exp.f64 re)`
3.0ms	0.0b	`(cos.f64 im)`

Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify2.0ms (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))

end14.0ms (0.4%)

Stop Event

1×

done

Compiler

Compiled 14 to 10 computations (28.6% saved)

Details

analyze207.0ms (6.5%)

sample2.0s (63.6%)

preprocess14.0ms (0.4%)

simplify6.0ms (0.2%)

prune1.0ms (0%)

localize6.0ms (0.2%)

series5.0ms (0.2%)

rewrite32.0ms (1%)

simplify27.0ms (0.9%)

prune69.0ms (2.2%)

localize7.0ms (0.2%)

series4.0ms (0.1%)

rewrite35.0ms (1.1%)

simplify46.0ms (1.4%)

prune245.0ms (7.7%)

localize7.0ms (0.2%)

series5.0ms (0.1%)

rewrite46.0ms (1.4%)

simplify62.0ms (2%)

prune299.0ms (9.4%)

regimes16.0ms (0.5%)

simplify2.0ms (0.1%)

end14.0ms (0.4%)

Profiling