Details

analyze489.0ms (9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
50%	50%	0.1%	5
50%	50%	0.1%	6
50%	37.5%	12.6%	7
50%	37.5%	12.6%	8
50%	31.2%	18.8%	9
50%	31.2%	18.8%	10
50%	28.1%	22%	11
50%	28.1%	22%	12
50%	26.5%	23.5%	13
50%	26.5%	23.5%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample4.1s (76.3%)

Results

1.3s	2017×	body	1024	valid
1.0s	1982×	body	1024	invalid
645.0ms	4673×	body	128	valid
373.0ms	990×	body	512	invalid
350.0ms	1020×	body	512	valid
133.0ms	538×	body	256	invalid
131.0ms	542×	body	256	valid
107.0ms	761×	body	128	invalid
6.0ms	4×	body	2048	valid
2.0ms	2×	body	2048	invalid

Compiler

Compiled 28 to 22 computations (21.4% saved)

preprocess48.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

748×	`times-frac_binary64`
390×	`fma-def_binary64`
320×	`unswap-sqr_binary64`
302×	`associate-l_binary64`
234×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	36
1	49	36
2	131	36
3	256	34
4	373	34
5	672	34
6	1526	34
7	2651	34
8	3803	34
9	4549	34
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

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

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify37.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

529×	`associate-/l*_binary64`
430×	`unswap-sqr_binary64`
374×	`times-frac_binary64`
351×	`fma-def_binary64`
340×	`associate-/r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	28	18
2	70	18
3	134	17
4	194	17
5	347	17
6	783	17
7	1356	17
8	3975	17
9	4498	17

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

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

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.0b	(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
▶	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Compiler

Compiled 76 to 53 computations (30.3% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

series2.0ms (0%)

Counts

1 → 8

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	im	@	0	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
0.0ms	im	@	-inf	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
0.0ms	im	@	inf	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

rewrite29.0ms (0.5%)

Algorithm

1×	egg-rewrite-iter-limit
1×	batch-egg-rewrite

Rules

67×	`add-sqr-sqrt_binary64`
64×	`*-un-lft-identity_binary64`
64×	`add-log-exp_binary64`
64×	`pow1_binary64`
62×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	126	10
2	2052	10
0	6	10

Stop Event

1×	iter limit
1×	unsound

Counts

1 → 11

Calls

Call 1

Inputs
(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

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

Outputs

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

simplify28.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

700×	`fma-def_binary64`
402×	`associate-/l/_binary64`
348×	`*-commutative_binary64`
294×	`distribute-lft-out_binary64`
287×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	83
1	49	81
2	108	77
3	288	77
4	1090	77
5	3001	77
6	4049	77

Stop Event

1×	node limit

Counts

19 → 20

Calls

Call 1

Inputs
2
(+.f64 2 (pow.f64 im 2))
(+.f64 2 (+.f64 (*.f64 1/12 (pow.f64 im 4)) (pow.f64 im 2)))
(+.f64 (.f64 1/360 (pow.f64 im 6)) (+.f64 2 (+.f64 (.f64 1/12 (pow.f64 im 4)) (pow.f64 im 2))))
(+.f64 (exp.f64 (*.f64 -1 im)) (exp.f64 im))
(+.f64 (exp.f64 (*.f64 -1 im)) (exp.f64 im))
(+.f64 (exp.f64 (*.f64 -1 im)) (exp.f64 im))
(+.f64 (exp.f64 (*.f64 -1 im)) (exp.f64 im))

Outputs
2
(+.f64 2 (pow.f64 im 2))
(+.f64 2 (*.f64 im im))
(fma.f64 im im 2)
(+.f64 2 (+.f64 (*.f64 1/12 (pow.f64 im 4)) (pow.f64 im 2)))
(+.f64 2 (fma.f64 1/12 (pow.f64 im 4) (*.f64 im im)))
(+.f64 2 (fma.f64 im im (*.f64 1/12 (pow.f64 im 4))))
(fma.f64 1/12 (pow.f64 im 4) (fma.f64 im im 2))
(fma.f64 im im (fma.f64 1/12 (pow.f64 im 4) 2))
(fma.f64 im (fma.f64 1/12 (pow.f64 im 3) im) 2)
(+.f64 (.f64 1/360 (pow.f64 im 6)) (+.f64 2 (+.f64 (.f64 1/12 (pow.f64 im 4)) (pow.f64 im 2))))
(fma.f64 1/360 (pow.f64 im 6) (+.f64 2 (fma.f64 1/12 (pow.f64 im 4) (*.f64 im im))))
(+.f64 (fma.f64 im im (*.f64 1/12 (pow.f64 im 4))) (fma.f64 1/360 (pow.f64 im 6) 2))
(fma.f64 1/360 (pow.f64 im 6) (fma.f64 1/12 (pow.f64 im 4) (fma.f64 im im 2)))
(fma.f64 1/12 (pow.f64 im 4) (fma.f64 im im (fma.f64 1/360 (pow.f64 im 6) 2)))
(fma.f64 1/360 (pow.f64 im 6) (fma.f64 im (fma.f64 1/12 (pow.f64 im 3) im) 2))
(fma.f64 im (fma.f64 1/12 (pow.f64 im 3) im) (fma.f64 1/360 (pow.f64 im 6) 2))
(+.f64 (exp.f64 (*.f64 -1 im)) (exp.f64 im))
(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
(+.f64 (exp.f64 (*.f64 -1 im)) (exp.f64 im))
(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
(+.f64 (exp.f64 (*.f64 -1 im)) (exp.f64 im))
(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
(+.f64 (exp.f64 (*.f64 -1 im)) (exp.f64 im))
(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

prune19.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	18	2	20
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	19	3	22

Error

Counts

22 → 3

Alt Table

Status	Error	Program
▶	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (/.f64 (+.f64 (pow.f64 (exp.f64 (neg.f64 im)) 3) (pow.f64 (exp.f64 im) 3)) (+.f64 (.f64 (exp.f64 (neg.f64 im)) (exp.f64 (neg.f64 im))) (-.f64 (.f64 (exp.f64 im) (exp.f64 im)) (*.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))))
	0.6b	(.f64 (.f64 1/2 (cos.f64 re)) (fma.f64 im (fma.f64 1/12 (pow.f64 im 3) im) 2))
✓	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Status

Error

Program

▶

0.0b

(*.f64 (*.f64 1/2 (cos.f64 re)) (/.f64 (+.f64 (pow.f64 (exp.f64 (neg.f64 im)) 3) (pow.f64 (exp.f64 im) 3)) (+.f64 (*.f64 (exp.f64 (neg.f64 im)) (exp.f64 (neg.f64 im))) (-.f64 (*.f64 (exp.f64 im) (exp.f64 im)) (*.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))))

0.6b

(*.f64 (*.f64 1/2 (cos.f64 re)) (fma.f64 im (fma.f64 1/12 (pow.f64 im 3) im) 2))

✓

0.0b

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

Compiler

Compiled 455 to 225 computations (50.5% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (exp.f64 (neg.f64 im)) (exp.f64 (neg.f64 im)))
✓	0.0b	(pow.f64 (exp.f64 im) 3)
✓	0.1b	(pow.f64 (exp.f64 (neg.f64 im)) 3)
✓	4.2b	(-.f64 (.f64 (exp.f64 im) (exp.f64 im)) (.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

series7.0ms (0.1%)

Counts

4 → 36

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	im	@	-inf	(pow.f64 (exp.f64 im) 3)
1.0ms	im	@	inf	(-.f64 (.f64 (exp.f64 im) (exp.f64 im)) (.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
1.0ms	im	@	inf	(pow.f64 (exp.f64 (neg.f64 im)) 3)
1.0ms	im	@	-inf	(-.f64 (.f64 (exp.f64 im) (exp.f64 im)) (.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
1.0ms	im	@	0	(-.f64 (.f64 (exp.f64 im) (exp.f64 im)) (.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

rewrite145.0ms (2.7%)

Algorithm

4×	egg-rewrite
1×	egg-rewrite-iter-limit
1×	batch-egg-rewrite

Rules

437×	`pow1_binary64`
411×	`add-log-exp_binary64`
410×	`log1p-expm1-u_binary64`
410×	`expm1-log1p-u_binary64`
405×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	60
1	277	60
2	3965	60
0	8	15
1	184	15
2	3033	15
0	8	15
0	6	8
1	128	6
2	1434	6
0	5	6
1	104	6
2	1077	6
0	5	8
1	101	6
2	1255	6

Stop Event

1×	node limit
1×	node limit
1×	node limit
1×	iter limit
1×	unsound
1×	unsound

Counts

4 → 70

Calls

Call 1

Inputs
(-.f64 (.f64 (exp.f64 im) (exp.f64 im)) (.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(pow.f64 (exp.f64 (neg.f64 im)) 3)
(pow.f64 (exp.f64 im) 3)
(*.f64 (exp.f64 (neg.f64 im)) (exp.f64 (neg.f64 im)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (exp.f64 im) 2) (neg.f64 (exp.f64 (+.f64 (neg.f64 im) im))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (exp.f64 im) 2) (.f64 (neg.f64 (exp.f64 (neg.f64 im))) (exp.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (exp.f64 im) (-.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))) (fma.f64 (neg.f64 (exp.f64 im)) (exp.f64 (neg.f64 im)) (exp.f64 (+.f64 (neg.f64 im) im))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (exp.f64 im) (-.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 (exp.f64 im) (-.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (cbrt.f64 (.f64 (exp.f64 im) (-.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))) (cbrt.f64 (.f64 (exp.f64 im) (-.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))) (cbrt.f64 (.f64 (exp.f64 im) (-.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (exp.f64 im) (-.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))) (sqrt.f64 (.f64 (exp.f64 im) (-.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 im) 2) 3) (pow.f64 (exp.f64 (+.f64 (neg.f64 im) im)) 3)) (+.f64 (.f64 (pow.f64 (exp.f64 im) 2) (pow.f64 (exp.f64 im) 2)) (+.f64 (.f64 (exp.f64 (+.f64 (neg.f64 im) im)) (exp.f64 (+.f64 (neg.f64 im) im))) (.f64 (pow.f64 (exp.f64 im) 2) (exp.f64 (+.f64 (neg.f64 im) im))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (pow.f64 (exp.f64 im) 2) (pow.f64 (exp.f64 im) 2)) (.f64 (exp.f64 (+.f64 (neg.f64 im) im)) (exp.f64 (+.f64 (neg.f64 im) im)))) (+.f64 (pow.f64 (exp.f64 im) 2) (exp.f64 (+.f64 (neg.f64 im) im))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (exp.f64 im) (-.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (.f64 (exp.f64 im) (-.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (.f64 (.f64 (exp.f64 im) (-.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))) (.f64 (exp.f64 im) (-.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))) (.f64 (exp.f64 im) (-.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (exp.f64 im) (exp.f64 im) (neg.f64 (exp.f64 (+.f64 (neg.f64 im) im))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (exp.f64 im) (-.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (exp.f64 im) (-.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (exp.f64 im) (-.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (exp.f64 im) 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (exp.f64 im) (pow.f64 (exp.f64 im) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (exp.f64 im) 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (exp.f64 im) 3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (exp.f64 im) 2) (exp.f64 im))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (exp.f64 im)) 2) (.f64 (cbrt.f64 (exp.f64 im)) (pow.f64 (exp.f64 im) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (exp.f64 im)) (.f64 (sqrt.f64 (exp.f64 im)) (pow.f64 (exp.f64 im) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (exp.f64 (.f64 im 3/2)) (exp.f64 (.f64 im 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 im)) 2) 3) (exp.f64 im))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (exp.f64 im)) 3) (pow.f64 (sqrt.f64 (exp.f64 im)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 (exp.f64 im) 2) 1) (exp.f64 im))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 (exp.f64 im) 2) (pow.f64 (cbrt.f64 (exp.f64 im)) 2)) (cbrt.f64 (exp.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 (exp.f64 im) 2) (sqrt.f64 (exp.f64 im))) (sqrt.f64 (exp.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (pow.f64 (exp.f64 im) 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (exp.f64 im) 2) (exp.f64 im))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 (exp.f64 im) 2) 1) (exp.f64 im))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 im) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (exp.f64 im) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (exp.f64 im) 3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 im 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (exp.f64 im) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (exp.f64 im) 3)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (exp.f64 im) 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (exp.f64 im) (pow.f64 (exp.f64 im) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (exp.f64 im) 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (exp.f64 im) 3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (exp.f64 im) 2) (exp.f64 im))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (exp.f64 im)) 2) (.f64 (cbrt.f64 (exp.f64 im)) (pow.f64 (exp.f64 im) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (exp.f64 im)) (.f64 (sqrt.f64 (exp.f64 im)) (pow.f64 (exp.f64 im) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (exp.f64 (.f64 im 3/2)) (exp.f64 (.f64 im 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 im)) 2) 3) (exp.f64 im))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (exp.f64 im)) 3) (pow.f64 (sqrt.f64 (exp.f64 im)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 (exp.f64 im) 2) 1) (exp.f64 im))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 (exp.f64 im) 2) (pow.f64 (cbrt.f64 (exp.f64 im)) 2)) (cbrt.f64 (exp.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 (exp.f64 im) 2) (sqrt.f64 (exp.f64 im))) (sqrt.f64 (exp.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 im) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (exp.f64 im) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (exp.f64 im) 3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 im 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (exp.f64 im) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (exp.f64 im) 3)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (exp.f64 im) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (exp.f64 im) (exp.f64 im))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (pow.f64 (exp.f64 im) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 im) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 im) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (exp.f64 im) 2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (exp.f64 im)) 2) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 im) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (exp.f64 im) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (exp.f64 im) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 im im))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (exp.f64 im) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (exp.f64 im) 2)))))))

simplify24.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

414×	`associate-l_binary64`
339×	`associate-r_binary64`
327×	`cancel-sign-sub-inv_binary64`
264×	`fma-neg_binary64`
239×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	416
1	169	342
2	451	287
3	1487	272

Stop Event

1×	node limit

Counts

106 → 86

Calls

Call 1

Inputs
(*.f64 2 im)
(+.f64 (.f64 2 (pow.f64 im 2)) (.f64 2 im))
(+.f64 (.f64 4/3 (pow.f64 im 3)) (+.f64 (.f64 2 (pow.f64 im 2)) (*.f64 2 im)))
(+.f64 (.f64 2/3 (pow.f64 im 4)) (+.f64 (.f64 4/3 (pow.f64 im 3)) (+.f64 (.f64 2 (pow.f64 im 2)) (.f64 2 im))))
(-.f64 (pow.f64 (exp.f64 im) 2) (*.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(-.f64 (pow.f64 (exp.f64 im) 2) (*.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(-.f64 (pow.f64 (exp.f64 im) 2) (*.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(-.f64 (pow.f64 (exp.f64 im) 2) (*.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(-.f64 (pow.f64 (exp.f64 im) 2) (.f64 (exp.f64 (.f64 -1 im)) (exp.f64 im)))
(-.f64 (pow.f64 (exp.f64 im) 2) (.f64 (exp.f64 (.f64 -1 im)) (exp.f64 im)))
(-.f64 (pow.f64 (exp.f64 im) 2) (.f64 (exp.f64 (.f64 -1 im)) (exp.f64 im)))
(-.f64 (pow.f64 (exp.f64 im) 2) (.f64 (exp.f64 (.f64 -1 im)) (exp.f64 im)))
1
(-.f64 1 (*.f64 3 im))
(-.f64 (+.f64 1 (.f64 9/2 (pow.f64 im 2))) (.f64 3 im))
(-.f64 (+.f64 1 (.f64 9/2 (pow.f64 im 2))) (+.f64 (.f64 9/2 (pow.f64 im 3)) (*.f64 3 im)))
(pow.f64 (exp.f64 (*.f64 -1 im)) 3)
(pow.f64 (exp.f64 (*.f64 -1 im)) 3)
(pow.f64 (exp.f64 (*.f64 -1 im)) 3)
(pow.f64 (exp.f64 (*.f64 -1 im)) 3)
1
(+.f64 1 (*.f64 3 im))
(+.f64 1 (+.f64 (.f64 9/2 (pow.f64 im 2)) (.f64 3 im)))
(+.f64 1 (+.f64 (.f64 9/2 (pow.f64 im 3)) (+.f64 (.f64 9/2 (pow.f64 im 2)) (*.f64 3 im))))
1
(-.f64 1 (*.f64 2 im))
(-.f64 (+.f64 1 (.f64 2 (pow.f64 im 2))) (.f64 2 im))
(-.f64 (+.f64 1 (.f64 2 (pow.f64 im 2))) (+.f64 (.f64 4/3 (pow.f64 im 3)) (*.f64 2 im)))
(pow.f64 (exp.f64 (neg.f64 im)) 2)
(pow.f64 (exp.f64 (neg.f64 im)) 2)
(pow.f64 (exp.f64 (neg.f64 im)) 2)
(pow.f64 (exp.f64 (neg.f64 im)) 2)
(pow.f64 (exp.f64 (*.f64 -1 im)) 2)
(pow.f64 (exp.f64 (*.f64 -1 im)) 2)
(pow.f64 (exp.f64 (*.f64 -1 im)) 2)
(pow.f64 (exp.f64 (*.f64 -1 im)) 2)

Outputs
(*.f64 2 im)
(+.f64 im im)
(+.f64 (.f64 2 (pow.f64 im 2)) (.f64 2 im))
(.f64 2 (+.f64 (.f64 im im) im))
(*.f64 2 (fma.f64 im im im))
(+.f64 (.f64 4/3 (pow.f64 im 3)) (+.f64 (.f64 2 (pow.f64 im 2)) (*.f64 2 im)))
(fma.f64 4/3 (pow.f64 im 3) (.f64 2 (+.f64 (.f64 im im) im)))
(fma.f64 2 (fma.f64 im im im) (*.f64 4/3 (pow.f64 im 3)))
(+.f64 (.f64 2/3 (pow.f64 im 4)) (+.f64 (.f64 4/3 (pow.f64 im 3)) (+.f64 (.f64 2 (pow.f64 im 2)) (.f64 2 im))))
(fma.f64 2/3 (pow.f64 im 4) (fma.f64 4/3 (pow.f64 im 3) (.f64 2 (+.f64 (.f64 im im) im))))
(fma.f64 2/3 (pow.f64 im 4) (fma.f64 2 (fma.f64 im im im) (*.f64 4/3 (pow.f64 im 3))))
(fma.f64 2 (fma.f64 im im im) (fma.f64 4/3 (pow.f64 im 3) (*.f64 2/3 (pow.f64 im 4))))
(fma.f64 2 (fma.f64 im im im) (.f64 (pow.f64 im 3) (+.f64 4/3 (.f64 im 2/3))))
(-.f64 (pow.f64 (exp.f64 im) 2) (*.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(-.f64 (pow.f64 (exp.f64 im) 2) (exp.f64 (+.f64 (neg.f64 im) im)))
(fma.f64 (exp.f64 im) (exp.f64 im) -1)
(expm1.f64 (+.f64 im im))
(-.f64 (pow.f64 (exp.f64 im) 2) (*.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(-.f64 (pow.f64 (exp.f64 im) 2) (exp.f64 (+.f64 (neg.f64 im) im)))
(fma.f64 (exp.f64 im) (exp.f64 im) -1)
(expm1.f64 (+.f64 im im))
(-.f64 (pow.f64 (exp.f64 im) 2) (*.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(-.f64 (pow.f64 (exp.f64 im) 2) (exp.f64 (+.f64 (neg.f64 im) im)))
(fma.f64 (exp.f64 im) (exp.f64 im) -1)
(expm1.f64 (+.f64 im im))
(-.f64 (pow.f64 (exp.f64 im) 2) (*.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(-.f64 (pow.f64 (exp.f64 im) 2) (exp.f64 (+.f64 (neg.f64 im) im)))
(fma.f64 (exp.f64 im) (exp.f64 im) -1)
(expm1.f64 (+.f64 im im))
(-.f64 (pow.f64 (exp.f64 im) 2) (.f64 (exp.f64 (.f64 -1 im)) (exp.f64 im)))
(-.f64 (pow.f64 (exp.f64 im) 2) (exp.f64 (+.f64 (neg.f64 im) im)))
(fma.f64 (exp.f64 im) (exp.f64 im) -1)
(expm1.f64 (+.f64 im im))
(-.f64 (pow.f64 (exp.f64 im) 2) (.f64 (exp.f64 (.f64 -1 im)) (exp.f64 im)))
(-.f64 (pow.f64 (exp.f64 im) 2) (exp.f64 (+.f64 (neg.f64 im) im)))
(fma.f64 (exp.f64 im) (exp.f64 im) -1)
(expm1.f64 (+.f64 im im))
(-.f64 (pow.f64 (exp.f64 im) 2) (.f64 (exp.f64 (.f64 -1 im)) (exp.f64 im)))
(-.f64 (pow.f64 (exp.f64 im) 2) (exp.f64 (+.f64 (neg.f64 im) im)))
(fma.f64 (exp.f64 im) (exp.f64 im) -1)
(expm1.f64 (+.f64 im im))
(-.f64 (pow.f64 (exp.f64 im) 2) (.f64 (exp.f64 (.f64 -1 im)) (exp.f64 im)))
(-.f64 (pow.f64 (exp.f64 im) 2) (exp.f64 (+.f64 (neg.f64 im) im)))
(fma.f64 (exp.f64 im) (exp.f64 im) -1)
(expm1.f64 (+.f64 im im))
1
(-.f64 1 (*.f64 3 im))
(+.f64 1 (*.f64 -3 im))
(+.f64 1 (*.f64 im -3))
(fma.f64 im -3 1)
(-.f64 (+.f64 1 (.f64 9/2 (pow.f64 im 2))) (.f64 3 im))
(+.f64 1 (-.f64 (.f64 (.f64 im im) 9/2) (*.f64 im 3)))
(+.f64 1 (fma.f64 (.f64 im im) 9/2 (.f64 im -3)))
(fma.f64 im (*.f64 im 9/2) (fma.f64 im -3 1))
(+.f64 1 (*.f64 im (fma.f64 im 9/2 -3)))
(-.f64 (+.f64 1 (.f64 9/2 (pow.f64 im 2))) (+.f64 (.f64 9/2 (pow.f64 im 3)) (*.f64 3 im)))
(+.f64 1 (-.f64 (.f64 (.f64 im im) 9/2) (fma.f64 9/2 (pow.f64 im 3) (*.f64 im 3))))
(-.f64 (fma.f64 (.f64 im im) 9/2 1) (fma.f64 im 3 (.f64 (pow.f64 im 3) 9/2)))
(+.f64 (.f64 (pow.f64 im 3) -9/2) (fma.f64 im (.f64 im 9/2) (fma.f64 im -3 1)))
(+.f64 1 (fma.f64 im (fma.f64 im 9/2 -3) (*.f64 (pow.f64 im 3) -9/2)))
(pow.f64 (exp.f64 (*.f64 -1 im)) 3)
(pow.f64 (exp.f64 (neg.f64 im)) 3)
(exp.f64 (*.f64 im -3))
(pow.f64 (exp.f64 (*.f64 -1 im)) 3)
(pow.f64 (exp.f64 (neg.f64 im)) 3)
(exp.f64 (*.f64 im -3))
(pow.f64 (exp.f64 (*.f64 -1 im)) 3)
(pow.f64 (exp.f64 (neg.f64 im)) 3)
(exp.f64 (*.f64 im -3))
(pow.f64 (exp.f64 (*.f64 -1 im)) 3)
(pow.f64 (exp.f64 (neg.f64 im)) 3)
(exp.f64 (*.f64 im -3))
1
(+.f64 1 (*.f64 3 im))
(+.f64 1 (*.f64 im 3))
(fma.f64 im 3 1)
(+.f64 1 (+.f64 (.f64 9/2 (pow.f64 im 2)) (.f64 3 im)))
(+.f64 1 (fma.f64 9/2 (.f64 im im) (.f64 im 3)))
(+.f64 1 (fma.f64 im 3 (.f64 (.f64 im im) 9/2)))
(fma.f64 im (*.f64 im 9/2) (fma.f64 im 3 1))
(+.f64 1 (+.f64 (.f64 9/2 (pow.f64 im 3)) (+.f64 (.f64 9/2 (pow.f64 im 2)) (*.f64 3 im))))
(+.f64 1 (fma.f64 9/2 (pow.f64 im 3) (fma.f64 9/2 (.f64 im im) (.f64 im 3))))
(+.f64 (.f64 9/2 (+.f64 (pow.f64 im 3) (.f64 im im))) (fma.f64 im 3 1))
(fma.f64 9/2 (*.f64 im (fma.f64 im im im)) (fma.f64 im 3 1))
1
(-.f64 1 (*.f64 2 im))
(+.f64 1 (*.f64 -2 im))
(+.f64 1 (*.f64 im -2))
(fma.f64 im -2 1)
(-.f64 (+.f64 1 (.f64 2 (pow.f64 im 2))) (.f64 2 im))
(+.f64 1 (-.f64 (.f64 2 (.f64 im im)) (*.f64 2 im)))
(+.f64 1 (.f64 2 (-.f64 (.f64 im im) im)))
(fma.f64 2 (-.f64 (*.f64 im im) im) 1)
(+.f64 1 (*.f64 im (fma.f64 2 im -2)))
(-.f64 (+.f64 1 (.f64 2 (pow.f64 im 2))) (+.f64 (.f64 4/3 (pow.f64 im 3)) (*.f64 2 im)))
(+.f64 1 (-.f64 (.f64 2 (.f64 im im)) (fma.f64 4/3 (pow.f64 im 3) (*.f64 2 im))))
(-.f64 (fma.f64 2 (.f64 im im) 1) (fma.f64 4/3 (pow.f64 im 3) (.f64 2 im)))
(+.f64 (.f64 (pow.f64 im 3) -4/3) (fma.f64 2 (-.f64 (.f64 im im) im) 1))
(-.f64 (*.f64 im (fma.f64 2 im -2)) (fma.f64 4/3 (pow.f64 im 3) -1))
(pow.f64 (exp.f64 (neg.f64 im)) 2)
(pow.f64 (exp.f64 im) -2)
(pow.f64 (exp.f64 -2) im)
(pow.f64 (exp.f64 (neg.f64 im)) 2)
(pow.f64 (exp.f64 im) -2)
(pow.f64 (exp.f64 -2) im)
(pow.f64 (exp.f64 (neg.f64 im)) 2)
(pow.f64 (exp.f64 im) -2)
(pow.f64 (exp.f64 -2) im)
(pow.f64 (exp.f64 (neg.f64 im)) 2)
(pow.f64 (exp.f64 im) -2)
(pow.f64 (exp.f64 -2) im)
(pow.f64 (exp.f64 (*.f64 -1 im)) 2)
(pow.f64 (exp.f64 (neg.f64 im)) 2)
(pow.f64 (exp.f64 im) -2)
(pow.f64 (exp.f64 -2) im)
(pow.f64 (exp.f64 (*.f64 -1 im)) 2)
(pow.f64 (exp.f64 (neg.f64 im)) 2)
(pow.f64 (exp.f64 im) -2)
(pow.f64 (exp.f64 -2) im)
(pow.f64 (exp.f64 (*.f64 -1 im)) 2)
(pow.f64 (exp.f64 (neg.f64 im)) 2)
(pow.f64 (exp.f64 im) -2)
(pow.f64 (exp.f64 -2) im)
(pow.f64 (exp.f64 (*.f64 -1 im)) 2)
(pow.f64 (exp.f64 (neg.f64 im)) 2)
(pow.f64 (exp.f64 im) -2)
(pow.f64 (exp.f64 -2) im)

prune98.0ms (1.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	87	2	89

Error

Counts

89 → 2

Alt Table

Status

Error

Program

▶

0.0b

(*.f64 (*.f64 1/2 (cos.f64 re)) (/.f64 (+.f64 (pow.f64 (exp.f64 (neg.f64 im)) 3) (pow.f64 (exp.f64 im) 3)) (+.f64 (*.f64 (exp.f64 (neg.f64 im)) (exp.f64 (neg.f64 im))) (fma.f64 (exp.f64 im) (exp.f64 im) (neg.f64 (exp.f64 (+.f64 (neg.f64 im) im)))))))

✓

0.0b

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

Compiler

Compiled 3390 to 1246 computations (63.2% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (exp.f64 (neg.f64 im)) (exp.f64 (neg.f64 im)))
	0.0b	(pow.f64 (exp.f64 im) 3)
	0.1b	(pow.f64 (exp.f64 (neg.f64 im)) 3)
✓	4.2b	(fma.f64 (exp.f64 im) (exp.f64 im) (neg.f64 (exp.f64 (+.f64 (neg.f64 im) im))))

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

0.0ms

im

(fma.f64 (exp.f64 im) (exp.f64 im) (neg.f64 (exp.f64 (+.f64 (neg.f64 im) im))))

0.0ms

im

inf

(fma.f64 (exp.f64 im) (exp.f64 im) (neg.f64 (exp.f64 (+.f64 (neg.f64 im) im))))

0.0ms

im

-inf

(fma.f64 (exp.f64 im) (exp.f64 im) (neg.f64 (exp.f64 (+.f64 (neg.f64 im) im))))

rewrite40.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

597×	`pow1_binary64`
554×	`add-log-exp_binary64`
553×	`log1p-expm1-u_binary64`
553×	`expm1-log1p-u_binary64`
87×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	167	11
2	2446	11

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

Inputs
(fma.f64 (exp.f64 im) (exp.f64 im) (neg.f64 (exp.f64 (+.f64 (neg.f64 im) im))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (exp.f64 im) 2) (pow.f64 (exp.f64 im) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (exp.f64 im) 2) (pow.f64 (exp.f64 im) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (hypot.f64 (exp.f64 im) (exp.f64 im)) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (pow.f64 (exp.f64 im) 2) 0) (pow.f64 (exp.f64 im) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 (exp.f64 im) (exp.f64 im)) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (hypot.f64 (exp.f64 im) (exp.f64 im)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (hypot.f64 (exp.f64 im) (exp.f64 im)) 2)) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 (exp.f64 im) (exp.f64 im)) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 (exp.f64 im) (exp.f64 im)) 2)) 2) (cbrt.f64 (pow.f64 (hypot.f64 (exp.f64 im) (exp.f64 im)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 (exp.f64 im) (exp.f64 im)) (hypot.f64 (exp.f64 im) (exp.f64 im)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (pow.f64 (exp.f64 im) 2) 3) (pow.f64 (pow.f64 (exp.f64 im) 2) 3)) (+.f64 (pow.f64 (pow.f64 (exp.f64 im) 2) 2) (-.f64 (pow.f64 (pow.f64 (exp.f64 im) 2) 2) (pow.f64 (pow.f64 (exp.f64 im) 2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 im) 2) 2) (pow.f64 (pow.f64 (exp.f64 im) 2) 2)) (pow.f64 (hypot.f64 (exp.f64 im) (exp.f64 im)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 (exp.f64 im) (exp.f64 im)) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (hypot.f64 (exp.f64 im) (exp.f64 im)) 2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 (exp.f64 im) (exp.f64 im)) 2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 (exp.f64 im) (exp.f64 im)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (pow.f64 (hypot.f64 (exp.f64 im) (exp.f64 im)) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (hypot.f64 (exp.f64 im) (exp.f64 im)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 (exp.f64 im) (exp.f64 im)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 (exp.f64 im) (exp.f64 im)) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (hypot.f64 (exp.f64 im) (exp.f64 im)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 (exp.f64 im) (exp.f64 im)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 (exp.f64 im) (exp.f64 im)) 2)))))))

simplify38.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

478×	`distribute-rgt-out_binary64`
424×	`associate-+l+_binary64`
420×	`*-commutative_binary64`
319×	`fma-def_binary64`
318×	`associate-+r+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	127
1	58	121
2	139	97
3	420	95
4	1440	95
5	3042	95
6	4851	95

Stop Event

1×	node limit

Counts

34 → 32

Calls

Call 1

Inputs
(*.f64 2 im)
(+.f64 (.f64 2 (pow.f64 im 2)) (.f64 2 im))
(+.f64 (.f64 4/3 (pow.f64 im 3)) (+.f64 (.f64 2 (pow.f64 im 2)) (*.f64 2 im)))
(+.f64 (.f64 2/3 (pow.f64 im 4)) (+.f64 (.f64 4/3 (pow.f64 im 3)) (+.f64 (.f64 2 (pow.f64 im 2)) (.f64 2 im))))
(-.f64 (pow.f64 (exp.f64 im) 2) 1)
(-.f64 (pow.f64 (exp.f64 im) 2) 1)
(-.f64 (pow.f64 (exp.f64 im) 2) 1)
(-.f64 (pow.f64 (exp.f64 im) 2) 1)
(-.f64 (pow.f64 (exp.f64 im) 2) 1)
(-.f64 (pow.f64 (exp.f64 im) 2) 1)
(-.f64 (pow.f64 (exp.f64 im) 2) 1)
(-.f64 (pow.f64 (exp.f64 im) 2) 1)

Outputs
(*.f64 2 im)
(+.f64 im im)
(+.f64 (.f64 2 (pow.f64 im 2)) (.f64 2 im))
(.f64 2 (+.f64 (.f64 im im) im))
(*.f64 2 (fma.f64 im im im))
(+.f64 (.f64 4/3 (pow.f64 im 3)) (+.f64 (.f64 2 (pow.f64 im 2)) (*.f64 2 im)))
(fma.f64 4/3 (pow.f64 im 3) (.f64 2 (+.f64 (.f64 im im) im)))
(fma.f64 2 (fma.f64 im im im) (*.f64 4/3 (pow.f64 im 3)))
(.f64 im (+.f64 2 (.f64 im (fma.f64 im 4/3 2))))
(+.f64 (.f64 2/3 (pow.f64 im 4)) (+.f64 (.f64 4/3 (pow.f64 im 3)) (+.f64 (.f64 2 (pow.f64 im 2)) (.f64 2 im))))
(fma.f64 2/3 (pow.f64 im 4) (fma.f64 4/3 (pow.f64 im 3) (.f64 2 (+.f64 (.f64 im im) im))))
(fma.f64 2/3 (pow.f64 im 4) (fma.f64 2 (fma.f64 im im im) (*.f64 4/3 (pow.f64 im 3))))
(fma.f64 2 (fma.f64 im im im) (fma.f64 4/3 (pow.f64 im 3) (*.f64 2/3 (pow.f64 im 4))))
(fma.f64 2 (fma.f64 im im im) (.f64 (pow.f64 im 3) (+.f64 4/3 (.f64 im 2/3))))
(-.f64 (pow.f64 (exp.f64 im) 2) 1)
(+.f64 (pow.f64 (exp.f64 im) 2) -1)
(expm1.f64 (+.f64 im im))
(-.f64 (pow.f64 (exp.f64 im) 2) 1)
(+.f64 (pow.f64 (exp.f64 im) 2) -1)
(expm1.f64 (+.f64 im im))
(-.f64 (pow.f64 (exp.f64 im) 2) 1)
(+.f64 (pow.f64 (exp.f64 im) 2) -1)
(expm1.f64 (+.f64 im im))
(-.f64 (pow.f64 (exp.f64 im) 2) 1)
(+.f64 (pow.f64 (exp.f64 im) 2) -1)
(expm1.f64 (+.f64 im im))
(-.f64 (pow.f64 (exp.f64 im) 2) 1)
(+.f64 (pow.f64 (exp.f64 im) 2) -1)
(expm1.f64 (+.f64 im im))
(-.f64 (pow.f64 (exp.f64 im) 2) 1)
(+.f64 (pow.f64 (exp.f64 im) 2) -1)
(expm1.f64 (+.f64 im im))
(-.f64 (pow.f64 (exp.f64 im) 2) 1)
(+.f64 (pow.f64 (exp.f64 im) 2) -1)
(expm1.f64 (+.f64 im im))
(-.f64 (pow.f64 (exp.f64 im) 2) 1)
(+.f64 (pow.f64 (exp.f64 im) 2) -1)
(expm1.f64 (+.f64 im im))

prune84.0ms (1.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	91	2	93

Error

Counts

93 → 2

Alt Table

Status

Error

Program

✓

0.0b

(*.f64 (*.f64 1/2 (cos.f64 re)) (/.f64 (+.f64 (pow.f64 (exp.f64 (neg.f64 im)) 3) (pow.f64 (exp.f64 im) 3)) (+.f64 (*.f64 (exp.f64 (neg.f64 im)) (exp.f64 (neg.f64 im))) (fma.f64 (exp.f64 im) (exp.f64 im) (neg.f64 (exp.f64 (+.f64 (neg.f64 im) im)))))))

✓

0.0b

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

Compiler

Compiled 3369 to 1341 computations (60.2% saved)

regimes80.0ms (1.5%)

Accuracy

Total 0.1b remaining (93%)

Threshold costs 0.1b (93%)

Counts

27 → 1

Compiler

Compiled 778 to 341 computations (56.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`*-commutative_binary64`
2×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	54
1	33	52
2	38	52
3	40	52

Stop Event

1×

saturated

Calls

Call 1

Inputs

(*.f64 (*.f64 1/2 (cos.f64 re)) (/.f64 (+.f64 (pow.f64 (exp.f64 (neg.f64 im)) 3) (pow.f64 (exp.f64 im) 3)) (+.f64 (pow.f64 (exp.f64 (neg.f64 im)) 2) (fma.f64 (exp.f64 im) (exp.f64 im) (neg.f64 (exp.f64 (+.f64 (neg.f64 im) im)))))))

Outputs

(*.f64 (*.f64 1/2 (cos.f64 re)) (/.f64 (+.f64 (pow.f64 (exp.f64 (neg.f64 im)) 3) (pow.f64 (exp.f64 im) 3)) (+.f64 (pow.f64 (exp.f64 (neg.f64 im)) 2) (fma.f64 (exp.f64 im) (exp.f64 im) (neg.f64 (exp.f64 (+.f64 (neg.f64 im) im)))))))

(*.f64 (*.f64 1/2 (cos.f64 re)) (/.f64 (+.f64 (pow.f64 (exp.f64 (neg.f64 im)) 3) (pow.f64 (exp.f64 im) 3)) (+.f64 (pow.f64 (exp.f64 (neg.f64 im)) 2) (fma.f64 (exp.f64 im) (exp.f64 im) (neg.f64 (exp.f64 (+.f64 im (neg.f64 im))))))))

(*.f64 (*.f64 1/2 (cos.f64 re)) (/.f64 (+.f64 (pow.f64 (exp.f64 (neg.f64 im)) 3) (pow.f64 (exp.f64 im) 3)) (+.f64 (pow.f64 (exp.f64 (neg.f64 im)) 2) (fma.f64 (exp.f64 im) (exp.f64 im) (neg.f64 (exp.f64 (-.f64 im im)))))))

end71.0ms (1.3%)

Stop Event

1×

done

Compiler

Compiled 118 to 75 computations (36.4% saved)

Details

analyze489.0ms (9%)

sample4.1s (76.3%)

preprocess48.0ms (0.9%)

simplify37.0ms (0.7%)

prune3.0ms (0.1%)

localize8.0ms (0.1%)

series2.0ms (0%)

rewrite29.0ms (0.5%)

simplify28.0ms (0.5%)

prune19.0ms (0.4%)

localize18.0ms (0.3%)

series7.0ms (0.1%)

rewrite145.0ms (2.7%)

simplify24.0ms (0.4%)

prune98.0ms (1.8%)

localize18.0ms (0.3%)

series1.0ms (0%)

rewrite40.0ms (0.7%)

simplify38.0ms (0.7%)

prune84.0ms (1.5%)

regimes80.0ms (1.5%)

simplify3.0ms (0%)

end71.0ms (1.3%)

Profiling