Metrics for math.sin on complex, real part

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 15 to 12 computations (20% saved)

sample1.5s (66.3%)

Results

767.0ms	4025×	body	256	infinite
715.0ms	4229×	body	256	valid
2.0ms	2×	body	1024	valid

Bogosity

preprocess163.0ms (7.2%)

Algorithm

1×	egg-herbie

Rules

2266×	`fma-def`
1538×	`div-sub`
1052×	`times-frac`
902×	`distribute-lft-neg-in`
784×	`distribute-rgt-neg-in`

Problems

256×

No Errors

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	36	316
1	111	308
2	394	308
3	1005	298
4	2232	294
5	5131	294
6	7600	294

Stop Event

1×	node limit

Calls

Call 1

Inputs
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
(.f64 (.f64 1/2 (sin.f64 (neg.f64 re))) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 (neg.f64 im))) (exp.f64 (neg.f64 im))))
(neg.f64 (.f64 (.f64 1/2 (sin.f64 (neg.f64 re))) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))))
(neg.f64 (.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 (neg.f64 im))) (exp.f64 (neg.f64 im)))))
(.f64 (.f64 1/2 (sin.f64 im)) (+.f64 (exp.f64 (-.f64 0 re)) (exp.f64 re)))

Outputs
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
(.f64 (.f64 1/2 (sin.f64 (neg.f64 re))) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
(.f64 1/2 (.f64 (neg.f64 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))
(.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) (.f64 (sin.f64 re) -1/2))
(.f64 (sin.f64 re) (.f64 -1/2 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))
(*.f64 (sin.f64 re) (fma.f64 (exp.f64 im) -1/2 (/.f64 -1/2 (exp.f64 im))))
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 (neg.f64 im))) (exp.f64 (neg.f64 im))))
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
(neg.f64 (.f64 (.f64 1/2 (sin.f64 (neg.f64 re))) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))))
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
(neg.f64 (.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 (neg.f64 im))) (exp.f64 (neg.f64 im)))))
(.f64 1/2 (.f64 (neg.f64 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))
(.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) (.f64 (sin.f64 re) -1/2))
(.f64 (sin.f64 re) (.f64 -1/2 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))
(*.f64 (sin.f64 re) (fma.f64 (exp.f64 im) -1/2 (/.f64 -1/2 (exp.f64 im))))
(.f64 (.f64 1/2 (sin.f64 im)) (+.f64 (exp.f64 (-.f64 0 re)) (exp.f64 re)))
(.f64 (.f64 1/2 (sin.f64 im)) (+.f64 (exp.f64 (neg.f64 re)) (exp.f64 re)))
(.f64 (sin.f64 im) (.f64 1/2 (+.f64 (exp.f64 (neg.f64 re)) (exp.f64 re))))
(*.f64 (sin.f64 im) (fma.f64 1/2 (exp.f64 re) (/.f64 1/2 (exp.f64 re))))

Symmetry

(abs im)

(negabs re)

Compiler

Compiled 55 to 36 computations (34.5% saved)

eval1.0ms (0%)

Compiler: Compiled 24 to 15 computations (37.5% saved)

prune1.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
▶	100.0%	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize50.0ms (2.2%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	100.0%	(sin.f64 re)

Compiler

Compiled 36 to 14 computations (61.1% saved)

series0.0ms (0%)

Counts

1 → 4

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	re	@	0	(sin.f64 re)
0.0ms	re	@	-inf	(sin.f64 re)
0.0ms	re	@	inf	(sin.f64 re)

rewrite150.0ms (6.7%)

Algorithm

1×	batch-egg-rewrite

Rules

990×	`log1p-expm1-u`
554×	`expm1-udef`
554×	`log1p-udef`
458×	`expm1-log1p-u`
386×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	44	8
2	453	8
3	5035	8

Stop Event

1×	node limit

Counts

1 → 50

Calls

Call 1

Inputs
(sin.f64 re)

Outputs
(+.f64 (+.f64 (sin.f64 re) 1) -1)
(+.f64 0 (sin.f64 re))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 re)) 2))) (log.f64 (cbrt.f64 (exp.f64 (sin.f64 re)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sin.f64 re)))) (log.f64 (sqrt.f64 (exp.f64 (sin.f64 re)))))
(-.f64 (+.f64 (sin.f64 re) 1) 1)
(-.f64 (.f64 (sin.f64 (+.f64 re 1)) (cos.f64 1)) (.f64 (cos.f64 (+.f64 re 1)) (sin.f64 1)))
(*.f64 (sin.f64 re) 1)
(*.f64 (sin.f64 re) (log.f64 (E.f64)))
(*.f64 1 (sin.f64 re))
(*.f64 (cbrt.f64 (sin.f64 re)) (pow.f64 (cbrt.f64 (sin.f64 re)) 2))
(*.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 2) (cbrt.f64 (sin.f64 re)))
(*.f64 (sqrt.f64 (sin.f64 re)) (sqrt.f64 (sin.f64 re)))
(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 re))) 2) (.f64 (cbrt.f64 (cbrt.f64 (sin.f64 re))) (pow.f64 (cbrt.f64 (sin.f64 re)) 2)))
(.f64 (pow.f64 (sin.f64 re) 1/6) (.f64 (pow.f64 (sin.f64 re) 1/6) (pow.f64 (cbrt.f64 (sin.f64 re)) 2)))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 4)) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 re))) 2) (cbrt.f64 (sin.f64 re))))
(*.f64 (pow.f64 (sin.f64 re) 1/4) (sqrt.f64 (pow.f64 (sin.f64 re) 3/2)))
(.f64 (pow.f64 (sin.f64 re) 1/4) (.f64 (pow.f64 (sin.f64 re) 1/4) (sqrt.f64 (sin.f64 re))))
(.f64 (.f64 (sqrt.f64 (sin.f64 re)) (cbrt.f64 (sin.f64 re))) (pow.f64 (sin.f64 re) 1/6))
(*.f64 (pow.f64 1 1/3) (sin.f64 re))
(*.f64 (pow.f64 (pow.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 4) 2) 1/3) (cbrt.f64 (cbrt.f64 (sin.f64 re))))
(*.f64 (pow.f64 (pow.f64 (sin.f64 re) 5/2) 1/3) (pow.f64 (sin.f64 re) 1/6))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 4) 2)) (cbrt.f64 (cbrt.f64 (sin.f64 re))))
(*.f64 (cbrt.f64 (pow.f64 (sin.f64 re) 5/2)) (pow.f64 (sin.f64 re) 1/6))
(.f64 (.f64 (sqrt.f64 (sin.f64 re)) (pow.f64 (sin.f64 re) 1/4)) (pow.f64 (sin.f64 re) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (sin.f64 re) 3/2)) (pow.f64 (sin.f64 re) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 5)) (pow.f64 (sin.f64 re) 1/6))
(.f64 (.f64 (cbrt.f64 (sin.f64 re)) (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 4))) (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 re))) 2))
(.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 re))) 2)) (cbrt.f64 (cbrt.f64 (sin.f64 re))))
(.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 2) (pow.f64 (sin.f64 re) 1/6)) (pow.f64 (sin.f64 re) 1/6))
(/.f64 (sqrt.f64 (-.f64 (cos.f64 0) (cos.f64 (*.f64 re 2)))) (sqrt.f64 2))
(/.f64 (-.f64 (pow.f64 (+.f64 (sin.f64 re) 1) 3) 1) (+.f64 (*.f64 (+.f64 (sin.f64 re) 1) (+.f64 (sin.f64 re) 1)) (+.f64 1 (+.f64 (sin.f64 re) 1))))
(/.f64 (-.f64 (*.f64 (+.f64 (sin.f64 re) 1) (+.f64 (sin.f64 re) 1)) 1) (+.f64 (+.f64 (sin.f64 re) 1) 1))
(pow.f64 (sin.f64 re) 1)
(pow.f64 (cbrt.f64 (sin.f64 re)) 3)
(pow.f64 (pow.f64 (sin.f64 re) 2) 1/2)
(pow.f64 (pow.f64 (sin.f64 re) 3) 1/3)
(pow.f64 (sqrt.f64 (sin.f64 re)) 2)
(pow.f64 (E.f64) (log.f64 (sin.f64 re)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sin.f64 re))) 2)) (cbrt.f64 (log.f64 (sin.f64 re))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sin.f64 re)))) (sqrt.f64 (log.f64 (sin.f64 re))))
(sqrt.f64 (pow.f64 (sin.f64 re) 2))
(fabs.f64 (sin.f64 re))
(log.f64 (exp.f64 (sin.f64 re)))
(cbrt.f64 (pow.f64 (sin.f64 re) 3))
(expm1.f64 (log1p.f64 (sin.f64 re)))
(exp.f64 (log.f64 (sin.f64 re)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (sin.f64 re))) 3))
(exp.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 re) 3)) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (sin.f64 re))) 2))
(log1p.f64 (expm1.f64 (sin.f64 re)))

simplify56.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1258×	`fma-def`
634×	`associate-+r-`
600×	`times-frac`
592×	`log-prod`
512×	`distribute-lft-out`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	162	1123
1	355	1107
2	1042	1094
3	4429	1034

Stop Event

1×	node limit

Counts

54 → 75

Calls

Call 1

Inputs
re
(+.f64 re (*.f64 -1/6 (pow.f64 re 3)))
(+.f64 re (+.f64 (.f64 -1/6 (pow.f64 re 3)) (.f64 1/120 (pow.f64 re 5))))
(+.f64 re (+.f64 (.f64 -1/6 (pow.f64 re 3)) (+.f64 (.f64 -1/5040 (pow.f64 re 7)) (*.f64 1/120 (pow.f64 re 5)))))
(+.f64 (+.f64 (sin.f64 re) 1) -1)
(+.f64 0 (sin.f64 re))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 re)) 2))) (log.f64 (cbrt.f64 (exp.f64 (sin.f64 re)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sin.f64 re)))) (log.f64 (sqrt.f64 (exp.f64 (sin.f64 re)))))
(-.f64 (+.f64 (sin.f64 re) 1) 1)
(-.f64 (.f64 (sin.f64 (+.f64 re 1)) (cos.f64 1)) (.f64 (cos.f64 (+.f64 re 1)) (sin.f64 1)))
(*.f64 (sin.f64 re) 1)
(*.f64 (sin.f64 re) (log.f64 (E.f64)))
(*.f64 1 (sin.f64 re))
(*.f64 (cbrt.f64 (sin.f64 re)) (pow.f64 (cbrt.f64 (sin.f64 re)) 2))
(*.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 2) (cbrt.f64 (sin.f64 re)))
(*.f64 (sqrt.f64 (sin.f64 re)) (sqrt.f64 (sin.f64 re)))
(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 re))) 2) (.f64 (cbrt.f64 (cbrt.f64 (sin.f64 re))) (pow.f64 (cbrt.f64 (sin.f64 re)) 2)))
(.f64 (pow.f64 (sin.f64 re) 1/6) (.f64 (pow.f64 (sin.f64 re) 1/6) (pow.f64 (cbrt.f64 (sin.f64 re)) 2)))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 4)) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 re))) 2) (cbrt.f64 (sin.f64 re))))
(*.f64 (pow.f64 (sin.f64 re) 1/4) (sqrt.f64 (pow.f64 (sin.f64 re) 3/2)))
(.f64 (pow.f64 (sin.f64 re) 1/4) (.f64 (pow.f64 (sin.f64 re) 1/4) (sqrt.f64 (sin.f64 re))))
(.f64 (.f64 (sqrt.f64 (sin.f64 re)) (cbrt.f64 (sin.f64 re))) (pow.f64 (sin.f64 re) 1/6))
(*.f64 (pow.f64 1 1/3) (sin.f64 re))
(*.f64 (pow.f64 (pow.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 4) 2) 1/3) (cbrt.f64 (cbrt.f64 (sin.f64 re))))
(*.f64 (pow.f64 (pow.f64 (sin.f64 re) 5/2) 1/3) (pow.f64 (sin.f64 re) 1/6))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 4) 2)) (cbrt.f64 (cbrt.f64 (sin.f64 re))))
(*.f64 (cbrt.f64 (pow.f64 (sin.f64 re) 5/2)) (pow.f64 (sin.f64 re) 1/6))
(.f64 (.f64 (sqrt.f64 (sin.f64 re)) (pow.f64 (sin.f64 re) 1/4)) (pow.f64 (sin.f64 re) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (sin.f64 re) 3/2)) (pow.f64 (sin.f64 re) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 5)) (pow.f64 (sin.f64 re) 1/6))
(.f64 (.f64 (cbrt.f64 (sin.f64 re)) (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 4))) (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 re))) 2))
(.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 re))) 2)) (cbrt.f64 (cbrt.f64 (sin.f64 re))))
(.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 2) (pow.f64 (sin.f64 re) 1/6)) (pow.f64 (sin.f64 re) 1/6))
(/.f64 (sqrt.f64 (-.f64 (cos.f64 0) (cos.f64 (*.f64 re 2)))) (sqrt.f64 2))
(/.f64 (-.f64 (pow.f64 (+.f64 (sin.f64 re) 1) 3) 1) (+.f64 (*.f64 (+.f64 (sin.f64 re) 1) (+.f64 (sin.f64 re) 1)) (+.f64 1 (+.f64 (sin.f64 re) 1))))
(/.f64 (-.f64 (*.f64 (+.f64 (sin.f64 re) 1) (+.f64 (sin.f64 re) 1)) 1) (+.f64 (+.f64 (sin.f64 re) 1) 1))
(pow.f64 (sin.f64 re) 1)
(pow.f64 (cbrt.f64 (sin.f64 re)) 3)
(pow.f64 (pow.f64 (sin.f64 re) 2) 1/2)
(pow.f64 (pow.f64 (sin.f64 re) 3) 1/3)
(pow.f64 (sqrt.f64 (sin.f64 re)) 2)
(pow.f64 (E.f64) (log.f64 (sin.f64 re)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sin.f64 re))) 2)) (cbrt.f64 (log.f64 (sin.f64 re))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sin.f64 re)))) (sqrt.f64 (log.f64 (sin.f64 re))))
(sqrt.f64 (pow.f64 (sin.f64 re) 2))
(fabs.f64 (sin.f64 re))
(log.f64 (exp.f64 (sin.f64 re)))
(cbrt.f64 (pow.f64 (sin.f64 re) 3))
(expm1.f64 (log1p.f64 (sin.f64 re)))
(exp.f64 (log.f64 (sin.f64 re)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (sin.f64 re))) 3))
(exp.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 re) 3)) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (sin.f64 re))) 2))
(log1p.f64 (expm1.f64 (sin.f64 re)))

Outputs
re
(+.f64 re (*.f64 -1/6 (pow.f64 re 3)))
(fma.f64 -1/6 (pow.f64 re 3) re)
(+.f64 re (+.f64 (.f64 -1/6 (pow.f64 re 3)) (.f64 1/120 (pow.f64 re 5))))
(+.f64 re (fma.f64 -1/6 (pow.f64 re 3) (*.f64 1/120 (pow.f64 re 5))))
(fma.f64 -1/6 (pow.f64 re 3) (fma.f64 1/120 (pow.f64 re 5) re))
(+.f64 re (+.f64 (.f64 -1/6 (pow.f64 re 3)) (+.f64 (.f64 -1/5040 (pow.f64 re 7)) (*.f64 1/120 (pow.f64 re 5)))))
(+.f64 re (fma.f64 -1/6 (pow.f64 re 3) (fma.f64 -1/5040 (pow.f64 re 7) (*.f64 1/120 (pow.f64 re 5)))))
(+.f64 re (fma.f64 -1/6 (pow.f64 re 3) (fma.f64 1/120 (pow.f64 re 5) (*.f64 -1/5040 (pow.f64 re 7)))))
(+.f64 (fma.f64 -1/6 (pow.f64 re 3) re) (fma.f64 1/120 (pow.f64 re 5) (*.f64 -1/5040 (pow.f64 re 7))))
(+.f64 (+.f64 (sin.f64 re) 1) -1)
(sin.f64 re)
(+.f64 0 (sin.f64 re))
(sin.f64 re)
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sin.f64 re)) 2))) (log.f64 (cbrt.f64 (exp.f64 (sin.f64 re)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sin.f64 re)))) (log.f64 (sqrt.f64 (exp.f64 (sin.f64 re)))))
(sin.f64 re)
(-.f64 (+.f64 (sin.f64 re) 1) 1)
(sin.f64 re)
(-.f64 (.f64 (sin.f64 (+.f64 re 1)) (cos.f64 1)) (.f64 (cos.f64 (+.f64 re 1)) (sin.f64 1)))
(*.f64 (sin.f64 re) 1)
(sin.f64 re)
(*.f64 (sin.f64 re) (log.f64 (E.f64)))
(sin.f64 re)
(*.f64 1 (sin.f64 re))
(sin.f64 re)
(*.f64 (cbrt.f64 (sin.f64 re)) (pow.f64 (cbrt.f64 (sin.f64 re)) 2))
(sin.f64 re)
(*.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 2) (cbrt.f64 (sin.f64 re)))
(sin.f64 re)
(*.f64 (sqrt.f64 (sin.f64 re)) (sqrt.f64 (sin.f64 re)))
(sin.f64 re)
(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 re))) 2) (.f64 (cbrt.f64 (cbrt.f64 (sin.f64 re))) (pow.f64 (cbrt.f64 (sin.f64 re)) 2)))
(sin.f64 re)
(.f64 (pow.f64 (sin.f64 re) 1/6) (.f64 (pow.f64 (sin.f64 re) 1/6) (pow.f64 (cbrt.f64 (sin.f64 re)) 2)))
(sin.f64 re)
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 4)) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 re))) 2) (cbrt.f64 (sin.f64 re))))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 4)) (.f64 (cbrt.f64 (sin.f64 re)) (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 re))) 2)))
(.f64 (cbrt.f64 (sin.f64 re)) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 re))) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 4))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 4)) (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 re))) 5))
(*.f64 (pow.f64 (sin.f64 re) 1/4) (sqrt.f64 (pow.f64 (sin.f64 re) 3/2)))
(sin.f64 re)
(.f64 (pow.f64 (sin.f64 re) 1/4) (.f64 (pow.f64 (sin.f64 re) 1/4) (sqrt.f64 (sin.f64 re))))
(sin.f64 re)
(.f64 (.f64 (sqrt.f64 (sin.f64 re)) (cbrt.f64 (sin.f64 re))) (pow.f64 (sin.f64 re) 1/6))
(.f64 (sqrt.f64 (sin.f64 re)) (.f64 (cbrt.f64 (sin.f64 re)) (pow.f64 (sin.f64 re) 1/6)))
(.f64 (cbrt.f64 (sin.f64 re)) (.f64 (sqrt.f64 (sin.f64 re)) (pow.f64 (sin.f64 re) 1/6)))
(*.f64 (sqrt.f64 (sin.f64 re)) (pow.f64 (pow.f64 (sin.f64 re) 1/6) 3))
(*.f64 (pow.f64 1 1/3) (sin.f64 re))
(sin.f64 re)
(*.f64 (pow.f64 (pow.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 4) 2) 1/3) (cbrt.f64 (cbrt.f64 (sin.f64 re))))
(*.f64 (cbrt.f64 (cbrt.f64 (sin.f64 re))) (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 4) 2)))
(*.f64 (cbrt.f64 (cbrt.f64 (sin.f64 re))) (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 8)))
(*.f64 (pow.f64 (pow.f64 (sin.f64 re) 5/2) 1/3) (pow.f64 (sin.f64 re) 1/6))
(*.f64 (pow.f64 (sin.f64 re) 1/6) (cbrt.f64 (pow.f64 (sin.f64 re) 5/2)))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 4) 2)) (cbrt.f64 (cbrt.f64 (sin.f64 re))))
(*.f64 (cbrt.f64 (cbrt.f64 (sin.f64 re))) (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 4) 2)))
(*.f64 (cbrt.f64 (cbrt.f64 (sin.f64 re))) (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 8)))
(*.f64 (cbrt.f64 (pow.f64 (sin.f64 re) 5/2)) (pow.f64 (sin.f64 re) 1/6))
(*.f64 (pow.f64 (sin.f64 re) 1/6) (cbrt.f64 (pow.f64 (sin.f64 re) 5/2)))
(.f64 (.f64 (sqrt.f64 (sin.f64 re)) (pow.f64 (sin.f64 re) 1/4)) (pow.f64 (sin.f64 re) 1/4))
(sin.f64 re)
(*.f64 (sqrt.f64 (pow.f64 (sin.f64 re) 3/2)) (pow.f64 (sin.f64 re) 1/4))
(sin.f64 re)
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 5)) (pow.f64 (sin.f64 re) 1/6))
(.f64 (sqrt.f64 (sin.f64 re)) (.f64 (cbrt.f64 (sin.f64 re)) (pow.f64 (sin.f64 re) 1/6)))
(.f64 (cbrt.f64 (sin.f64 re)) (.f64 (sqrt.f64 (sin.f64 re)) (pow.f64 (sin.f64 re) 1/6)))
(*.f64 (sqrt.f64 (sin.f64 re)) (pow.f64 (pow.f64 (sin.f64 re) 1/6) 3))
(.f64 (.f64 (cbrt.f64 (sin.f64 re)) (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 4))) (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 re))) 2))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 4)) (.f64 (cbrt.f64 (sin.f64 re)) (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 re))) 2)))
(.f64 (cbrt.f64 (sin.f64 re)) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 re))) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 4))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 4)) (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 re))) 5))
(.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 re))) 2)) (cbrt.f64 (cbrt.f64 (sin.f64 re))))
(sin.f64 re)
(.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 re)) 2) (pow.f64 (sin.f64 re) 1/6)) (pow.f64 (sin.f64 re) 1/6))
(sin.f64 re)
(/.f64 (sqrt.f64 (-.f64 (cos.f64 0) (cos.f64 (*.f64 re 2)))) (sqrt.f64 2))
(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 (*.f64 re 2)))) (sqrt.f64 2))
(/.f64 (-.f64 (pow.f64 (+.f64 (sin.f64 re) 1) 3) 1) (+.f64 (*.f64 (+.f64 (sin.f64 re) 1) (+.f64 (sin.f64 re) 1)) (+.f64 1 (+.f64 (sin.f64 re) 1))))
(/.f64 (+.f64 (pow.f64 (+.f64 (sin.f64 re) 1) 3) -1) (fma.f64 (+.f64 (sin.f64 re) 1) (+.f64 (sin.f64 re) 1) (+.f64 (sin.f64 re) 2)))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 (sin.f64 re) 1) 3)) (fma.f64 (+.f64 (sin.f64 re) 1) (+.f64 (sin.f64 re) 1) (+.f64 (sin.f64 re) 2)))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 (sin.f64 re) 1) 3)) (+.f64 1 (*.f64 (+.f64 (sin.f64 re) 1) (+.f64 (sin.f64 re) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 (sin.f64 re) 1) 3)) (fma.f64 (+.f64 (sin.f64 re) 1) (+.f64 (sin.f64 re) 2) 1))
(/.f64 (-.f64 (*.f64 (+.f64 (sin.f64 re) 1) (+.f64 (sin.f64 re) 1)) 1) (+.f64 (+.f64 (sin.f64 re) 1) 1))
(sin.f64 re)
(pow.f64 (sin.f64 re) 1)
(sin.f64 re)
(pow.f64 (cbrt.f64 (sin.f64 re)) 3)
(sin.f64 re)
(pow.f64 (pow.f64 (sin.f64 re) 2) 1/2)
(sin.f64 re)
(pow.f64 (pow.f64 (sin.f64 re) 3) 1/3)
(sin.f64 re)
(pow.f64 (sqrt.f64 (sin.f64 re)) 2)
(sin.f64 re)
(pow.f64 (E.f64) (log.f64 (sin.f64 re)))
(sin.f64 re)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sin.f64 re))) 2)) (cbrt.f64 (log.f64 (sin.f64 re))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sin.f64 re)))) (sqrt.f64 (log.f64 (sin.f64 re))))
(sqrt.f64 (pow.f64 (sin.f64 re) 2))
(sin.f64 re)
(fabs.f64 (sin.f64 re))
(sin.f64 re)
(log.f64 (exp.f64 (sin.f64 re)))
(sin.f64 re)
(cbrt.f64 (pow.f64 (sin.f64 re) 3))
(sin.f64 re)
(expm1.f64 (log1p.f64 (sin.f64 re)))
(sin.f64 re)
(exp.f64 (log.f64 (sin.f64 re)))
(sin.f64 re)
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (sin.f64 re))) 3))
(sin.f64 re)
(exp.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 re) 3)) 1/3))
(sin.f64 re)
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (sin.f64 re))) 2))
(sin.f64 re)
(log1p.f64 (expm1.f64 (sin.f64 re)))
(sin.f64 re)

eval23.0ms (1%)

Compiler: Compiled 1479 to 682 computations (53.9% saved)

prune12.0ms (0.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	2	76

Accuracy

100.0%

Counts

76 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
▶	61.0%	(.f64 (.f64 1/2 re) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	100.0%	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
▶	61.0%	(.f64 (.f64 1/2 re) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Compiler

Compiled 50 to 38 computations (24% saved)

localize40.0ms (1.8%)

Compiler: Compiled 32 to 13 computations (59.4% saved)

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune2.0ms (0.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Accuracy

100.0%

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	61.0%	(.f64 (.f64 1/2 re) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Compiler

Compiled 60 to 39 computations (35% saved)

regimes21.0ms (0.9%)

Counts

3 → 1

Calls

Call 1

Inputs

(*.f64 (*.f64 1/2 re) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

(*.f64 (*.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

(*.f64 (*.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))

Outputs
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Calls

6 calls:

4.0ms	im
3.0ms	(*.f64 1/2 (sin.f64 re))
3.0ms	(sin.f64 re)
3.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
3.0ms	re

Results

Accuracy	Segments	Branch
100.0%	1	`re`
100.0%	1	`im`
100.0%	1	`(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))`
100.0%	1	`(*.f64 1/2 (sin.f64 re))`
100.0%	1	`(sin.f64 re)`
100.0%	1	`(+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))`

Compiler

Compiled 74 to 50 computations (32.4% saved)

regimes6.0ms (0.3%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(.f64 (.f64 1/2 re) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Outputs
(.f64 (.f64 1/2 re) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Calls

2 calls:

3.0ms	im
3.0ms	re

Results

Accuracy	Segments	Branch
61.0%	1	`re`
61.0%	1	`im`

Compiler

Compiled 18 to 13 computations (27.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative`
4×	`+-commutative`
2×	`sub-neg`
2×	`neg-mul-1`
2×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	84
1	27	84
2	29	84
3	30	84

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(.f64 (.f64 1/2 re) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Outputs

(*.f64 (*.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

(*.f64 (*.f64 1/2 re) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

(*.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) (*.f64 1/2 re))

Compiler

Compiled 25 to 19 computations (24% saved)

soundness196.0ms (8.7%)

Rules

2266×	`fma-def`
1538×	`div-sub`
1052×	`times-frac`
902×	`distribute-lft-neg-in`
784×	`distribute-rgt-neg-in`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	36	316
1	111	308
2	394	308
3	1005	298
4	2232	294
5	5131	294
6	7600	294

Stop Event

1×	node limit

Compiler

Compiled 100 to 57 computations (43% saved)

end0.0ms (0%)

preprocess35.0ms (1.5%)

Remove

(negabs re)

(abs im)

Compiler

Compiled 126 to 88 computations (30.2% saved)

analyze0.0ms (0%)

sample1.5s (66.3%)

preprocess163.0ms (7.2%)

eval1.0ms (0%)

prune1.0ms (0.1%)

localize50.0ms (2.2%)

series0.0ms (0%)

rewrite150.0ms (6.7%)

simplify56.0ms (2.5%)

eval23.0ms (1%)

prune12.0ms (0.5%)

localize40.0ms (1.8%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes21.0ms (0.9%)

regimes6.0ms (0.3%)

simplify3.0ms (0.1%)

soundness196.0ms (8.7%)

end0.0ms (0%)

preprocess35.0ms (1.5%)

Profiling