Details

analyze571.0ms (10.4%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
23.4%	51.5%	25.1%	7
24.2%	50.7%	25.1%	8
24.6%	50.3%	25.1%	9
36.9%	25.5%	37.6%	10
37.2%	25.3%	37.6%	11
37.3%	25.1%	37.6%	12
43.5%	12.7%	43.8%	13
43.6%	12.6%	43.8%	14

Compiler

Compiled 32 to 21 computations (34.4% saved)

sample1.9s (34.1%)

Results

1.6s	8256×	body	128	valid
186.0ms	999×	body	128	invalid

Compiler

Compiled 64 to 42 computations (34.4% saved)

preprocess53.0ms (1%)

Algorithm

2×	egg-herbie

Rules

752×	`fma-neg_binary64`
403×	`fma-def_binary64`
349×	`associate-/l*_binary64`
278×	`distribute-rgt-in_binary64`
264×	`div-sub_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	80
1	137	76
2	227	48
3	329	36
4	407	36
5	993	36
6	2449	36
7	3517	36
8	4122	36
9	4229	36
10	4431	36
11	4946	36
0	3	3

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
2

Call 2

Inputs
(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
(/.f64 (-.f64 (.f64 (atan2.f64 re im) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
(/.f64 (-.f64 (.f64 (atan2.f64 im base) (log.f64 re)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 base base) (.f64 im im)))) 0)) (+.f64 (.f64 (log.f64 re) (log.f64 re)) (.f64 0 0)))
(/.f64 (-.f64 (.f64 (atan2.f64 base re) (log.f64 im)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 base base)))) 0)) (+.f64 (.f64 (log.f64 im) (log.f64 im)) (.f64 0 0)))

Outputs
(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
(/.f64 (fma.f64 (atan2.f64 im re) (log.f64 base) 0) (*.f64 (log.f64 base) (log.f64 base)))
(*.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) (/.f64 (log.f64 base) (log.f64 base)))
(*.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 1)
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (-.f64 (.f64 (atan2.f64 re im) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
(/.f64 (fma.f64 (atan2.f64 re im) (log.f64 base) 0) (*.f64 (log.f64 base) (log.f64 base)))
(*.f64 (/.f64 (log.f64 base) (log.f64 base)) (/.f64 (atan2.f64 re im) (log.f64 base)))
(*.f64 1 (/.f64 (atan2.f64 re im) (log.f64 base)))
(/.f64 (atan2.f64 re im) (log.f64 base))
(/.f64 (-.f64 (.f64 (atan2.f64 im base) (log.f64 re)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 base base) (.f64 im im)))) 0)) (+.f64 (.f64 (log.f64 re) (log.f64 re)) (.f64 0 0)))
(/.f64 (fma.f64 (atan2.f64 im base) (log.f64 re) 0) (*.f64 (log.f64 re) (log.f64 re)))
(*.f64 (/.f64 (atan2.f64 im base) (log.f64 re)) (/.f64 (log.f64 re) (log.f64 re)))
(*.f64 (/.f64 (atan2.f64 im base) (log.f64 re)) 1)
(/.f64 (atan2.f64 im base) (log.f64 re))
(/.f64 (-.f64 (.f64 (atan2.f64 base re) (log.f64 im)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 base base)))) 0)) (+.f64 (.f64 (log.f64 im) (log.f64 im)) (.f64 0 0)))
(/.f64 (fma.f64 (atan2.f64 base re) (log.f64 im) 0) (*.f64 (log.f64 im) (log.f64 im)))
(/.f64 (atan2.f64 base re) (/.f64 (*.f64 (log.f64 im) (log.f64 im)) (log.f64 im)))
(/.f64 (atan2.f64 base re) (/.f64 (log.f64 im) 1))
(/.f64 (atan2.f64 base re) (log.f64 im))

Compiler

Compiled 31 to 20 computations (35.5% saved)

simplify21.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

877×	`fma-def_binary64`
692×	`fma-neg_binary64`
407×	`associate-/l*_binary64`
380×	`div-sub_binary64`
313×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	20
1	41	19
2	68	12
3	94	9
4	115	9
5	273	9
6	1005	9
7	2320	9
8	3369	9

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))

Outputs
(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
(/.f64 (fma.f64 (atan2.f64 im re) (log.f64 base) 0) (*.f64 (log.f64 base) (log.f64 base)))
(*.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) (/.f64 (log.f64 base) (log.f64 base)))
(*.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 1)
(/.f64 (atan2.f64 im re) (log.f64 base))

prune14.0ms (0.3%)

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	31.5b	(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
▶	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))

Status

Error

Program

31.5b

(/.f64 (-.f64 (*.f64 (atan2.f64 im re) (log.f64 base)) (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) 0)) (+.f64 (*.f64 (log.f64 base) (log.f64 base)) (*.f64 0 0)))

▶

0.3b

(/.f64 (atan2.f64 im re) (log.f64 base))

Compiler

Compiled 117 to 73 computations (37.6% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))

series341.0ms (6.2%)

Counts

1 → 8

Calls

9 calls:

Time	Variable		Point	Expression
54.0ms	im	@	0	(/.f64 (atan2.f64 im re) (log.f64 base))
54.0ms	re	@	0	(/.f64 (atan2.f64 im re) (log.f64 base))
51.0ms	re	@	-inf	(/.f64 (atan2.f64 im re) (log.f64 base))
50.0ms	re	@	inf	(/.f64 (atan2.f64 im re) (log.f64 base))
49.0ms	im	@	-inf	(/.f64 (atan2.f64 im re) (log.f64 base))

rewrite37.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

702×	`pow1_binary64`
643×	`add-log-exp_binary64`
643×	`log1p-expm1-u_binary64`
643×	`expm1-log1p-u_binary64`
72×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	139	9
2	1734	9

Stop Event

1×	node limit

Counts

1 → 32

Calls

Call 1

Inputs
(/.f64 (atan2.f64 im re) (log.f64 base))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (atan2.f64 im re) (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (pow.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 2) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (atan2.f64 im re)) 2) (.f64 (cbrt.f64 (atan2.f64 im re)) (/.f64 1 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (atan2.f64 im re)) (.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 1 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (atan2.f64 im re)) (/.f64 1 (neg.f64 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (log.f64 base)) (atan2.f64 im re))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (atan2.f64 im re)) 2) 1) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (atan2.f64 im re)) 1) (/.f64 (sqrt.f64 (atan2.f64 im re)) (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (atan2.f64 im re)) 2) (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (atan2.f64 im re)) (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (cbrt.f64 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (atan2.f64 im re)) 2) (sqrt.f64 (log.f64 base))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (sqrt.f64 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (atan2.f64 im re) (neg.f64 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (atan2.f64 im re) 3) (pow.f64 (log.f64 base) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (atan2.f64 im re) (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (pow.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 2) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 im re)) 2) (*.f64 (cbrt.f64 (atan2.f64 im re)) (/.f64 1 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 im re)) (*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 1 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (atan2.f64 im re)) (/.f64 1 (neg.f64 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (log.f64 base)) (atan2.f64 im re))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (atan2.f64 im re)) 2) 1) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (atan2.f64 im re)) 1) (/.f64 (sqrt.f64 (atan2.f64 im re)) (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (atan2.f64 im re)) 2) (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (atan2.f64 im re)) (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (cbrt.f64 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (atan2.f64 im re)) 2) (sqrt.f64 (log.f64 base))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (sqrt.f64 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (atan2.f64 im re) (neg.f64 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (atan2.f64 im re) 3) (pow.f64 (log.f64 base) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))))

simplify29.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

762×	`div-sub_binary64`
628×	`fma-neg_binary64`
494×	`fma-def_binary64`
292×	`distribute-rgt-in_binary64`
231×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	16	104
1	29	104
2	43	96
3	92	72
4	189	72
5	583	72
6	2308	72
7	4815	72

Stop Event

1×	node limit

Counts

40 → 35

Calls

Call 1

Inputs
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))

Outputs
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(neg.f64 (/.f64 (atan2.f64 im re) (neg.f64 (log.f64 base))))
(/.f64 (neg.f64 (atan2.f64 im re)) (neg.f64 (log.f64 base)))
(*.f64 1 (/.f64 (atan2.f64 im re) (log.f64 base)))
(/.f64 (atan2.f64 im re) (log.f64 base))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(neg.f64 (/.f64 (atan2.f64 im re) (neg.f64 (log.f64 base))))
(/.f64 (neg.f64 (atan2.f64 im re)) (neg.f64 (log.f64 base)))
(*.f64 1 (/.f64 (atan2.f64 im re) (log.f64 base)))
(/.f64 (atan2.f64 im re) (log.f64 base))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(neg.f64 (/.f64 (atan2.f64 im re) (neg.f64 (log.f64 base))))
(/.f64 (neg.f64 (atan2.f64 im re)) (neg.f64 (log.f64 base)))
(*.f64 1 (/.f64 (atan2.f64 im re) (log.f64 base)))
(/.f64 (atan2.f64 im re) (log.f64 base))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(neg.f64 (/.f64 (atan2.f64 im re) (neg.f64 (log.f64 base))))
(/.f64 (neg.f64 (atan2.f64 im re)) (neg.f64 (log.f64 base)))
(*.f64 1 (/.f64 (atan2.f64 im re) (log.f64 base)))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(neg.f64 (/.f64 (atan2.f64 im re) (neg.f64 (log.f64 base))))
(/.f64 (neg.f64 (atan2.f64 im re)) (neg.f64 (log.f64 base)))
(*.f64 1 (/.f64 (atan2.f64 im re) (log.f64 base)))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(neg.f64 (/.f64 (atan2.f64 im re) (neg.f64 (log.f64 base))))
(/.f64 (neg.f64 (atan2.f64 im re)) (neg.f64 (log.f64 base)))
(*.f64 1 (/.f64 (atan2.f64 im re) (log.f64 base)))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(neg.f64 (/.f64 (atan2.f64 im re) (neg.f64 (log.f64 base))))
(/.f64 (neg.f64 (atan2.f64 im re)) (neg.f64 (log.f64 base)))
(*.f64 1 (/.f64 (atan2.f64 im re) (log.f64 base)))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(neg.f64 (/.f64 (atan2.f64 im re) (neg.f64 (log.f64 base))))
(/.f64 (neg.f64 (atan2.f64 im re)) (neg.f64 (log.f64 base)))
(*.f64 1 (/.f64 (atan2.f64 im re) (log.f64 base)))
(/.f64 (atan2.f64 im re) (log.f64 base))

prune30.0ms (0.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	26	9	35
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	26	11	37

Error

0.0b

Counts

37 → 11

Alt Table

Status	Error	Program
	33.3b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))))
	31.5b	(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
	1.4b	(*.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (pow.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 2))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	30.6b	(pow.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3) 1/3)
	1.2b	(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))
▶	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	5.5b	(cbrt.f64 (/.f64 (pow.f64 (atan2.f64 im re) 3) (pow.f64 (log.f64 base) 3)))
	5.6b	(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3))
	0.7b	(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -1)
	27.8b	(pow.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 2)

Compiler

Compiled 725 to 354 computations (51.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (log.f64 base))
✓	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))

series363.0ms (6.6%)

Counts

2 → 44

Calls

12 calls:

Time	Variable		Point	Expression
51.0ms	re	@	0	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
50.0ms	im	@	-inf	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
49.0ms	re	@	-inf	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
48.0ms	im	@	0	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
48.0ms	im	@	inf	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))

rewrite39.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

779×	`pow1_binary64`
712×	`log1p-expm1-u_binary64`
712×	`expm1-log1p-u_binary64`
86×	`add-sqr-sqrt_binary64`
84×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	175	15
2	2031	15

Stop Event

1×	node limit

Counts

2 → 49

Calls

Call 1

Inputs
(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
(/.f64 1 (log.f64 base))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (atan2.f64 im re) (log.f64 base))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (atan2.f64 im re) 2)) (/.f64 (log.f64 base) (cbrt.f64 (atan2.f64 im re))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (log.f64 base) (sqrt.f64 (atan2.f64 im re))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (atan2.f64 im re)) (neg.f64 (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (atan2.f64 im re) 1) (log.f64 base))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (log.f64 base) 2))) (cbrt.f64 (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 -1 (atan2.f64 im re)) (neg.f64 (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (atan2.f64 im re) -1) (neg.f64 (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (atan2.f64 im re) 3) (pow.f64 (log.f64 base) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (atan2.f64 im re) 3) (pow.f64 (/.f64 1 (log.f64 base)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3) (pow.f64 (atan2.f64 im re) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (log.f64 base)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 1 (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (log.f64 base)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 (log.f64 base))) (cbrt.f64 (pow.f64 (log.f64 base) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (log.f64 base) -2)) (/.f64 1 (cbrt.f64 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (log.f64 base) -1/2) (pow.f64 (log.f64 base) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (/.f64 1 (neg.f64 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 (log.f64 base) 2)) -1) (pow.f64 (cbrt.f64 (log.f64 base)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (log.f64 base)) -1) (pow.f64 (sqrt.f64 (log.f64 base)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 base) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (log.f64 base)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (log.f64 base))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log.f64 base) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log.f64 base) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (log.f64 base)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (log.f64 base)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (neg.f64 (log.f64 (log.f64 base))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (log.f64 base))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (atan2.f64 im re) (log.f64 base))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (atan2.f64 im re) 2)) (/.f64 (log.f64 base) (cbrt.f64 (atan2.f64 im re))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (log.f64 base) (sqrt.f64 (atan2.f64 im re))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (atan2.f64 im re)) (neg.f64 (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (atan2.f64 im re) 1) (log.f64 base))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (log.f64 base) 2))) (cbrt.f64 (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (atan2.f64 im re)) (neg.f64 (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (atan2.f64 im re) -1) (neg.f64 (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (atan2.f64 im re) 3) (pow.f64 (log.f64 base) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (atan2.f64 im re) 3) (pow.f64 (/.f64 1 (log.f64 base)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3) (pow.f64 (atan2.f64 im re) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))))

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

simplify38.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

767×	`div-sub_binary64`
628×	`fma-neg_binary64`
493×	`fma-def_binary64`
292×	`distribute-rgt-in_binary64`
231×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	388
1	32	388
2	46	372
3	94	372
4	190	372
5	581	372
6	2294	372
7	4778	372

Stop Event

1×	node limit

Counts

93 → 54

Calls

Call 1

Inputs
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 -1 (log.f64 (/.f64 1 base)))
(/.f64 -1 (log.f64 (/.f64 1 base)))
(/.f64 -1 (log.f64 (/.f64 1 base)))
(/.f64 -1 (log.f64 (/.f64 1 base)))
(/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))

Outputs
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 -1 (log.f64 (/.f64 1 base)))
(/.f64 -1 (neg.f64 (log.f64 base)))
(/.f64 1 (log.f64 base))
(/.f64 -1 (log.f64 (/.f64 1 base)))
(/.f64 -1 (neg.f64 (log.f64 base)))
(/.f64 1 (log.f64 base))
(/.f64 -1 (log.f64 (/.f64 1 base)))
(/.f64 -1 (neg.f64 (log.f64 base)))
(/.f64 1 (log.f64 base))
(/.f64 -1 (log.f64 (/.f64 1 base)))
(/.f64 -1 (neg.f64 (log.f64 base)))
(/.f64 1 (log.f64 base))
(/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 -1 (neg.f64 (log.f64 base)))
(/.f64 1 (log.f64 base))
(/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 -1 (neg.f64 (log.f64 base)))
(/.f64 1 (log.f64 base))
(/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 -1 (neg.f64 (log.f64 base)))
(/.f64 1 (log.f64 base))
(/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 -1 (neg.f64 (log.f64 base)))
(/.f64 1 (log.f64 base))

prune43.0ms (0.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	50	4	54
Fresh	3	6	9
Picked	0	1	1
Done	0	1	1
Total	53	12	65

Error

0.0b

Counts

65 → 12

Alt Table

Status	Error	Program
	30.6b	(pow.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3) 1/3)
▶	0.7b	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
	33.3b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))))
	33.3b	(*.f64 (atan2.f64 im re) (pow.f64 (pow.f64 (log.f64 base) -1/2) 2))
	31.5b	(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
	1.4b	(*.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (pow.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 2))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
✓	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	0.8b	(/.f64 (/.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (log.f64 base) 2))) (cbrt.f64 (log.f64 base)))
	1.2b	(*.f64 (atan2.f64 im re) (pow.f64 (/.f64 1 (cbrt.f64 (log.f64 base))) 3))
	5.5b	(cbrt.f64 (/.f64 (pow.f64 (atan2.f64 im re) 3) (pow.f64 (log.f64 base) 3)))
	0.7b	(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -1)

Compiler

Compiled 911 to 491 computations (46.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f64 1 (log.f64 base))
✓	0.4b	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
✓	0.6b	(cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3))
✓	0.7b	(pow.f64 (/.f64 1 (log.f64 base)) 3)

series424.0ms (7.8%)

Counts

3 → 60

Calls

15 calls:

Time	Variable		Point	Expression
58.0ms	im	@	-inf	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
56.0ms	re	@	0	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
52.0ms	re	@	inf	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
48.0ms	im	@	inf	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
48.0ms	im	@	0	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))

rewrite47.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

868×	`log1p-expm1-u_binary64`
868×	`expm1-log1p-u_binary64`
107×	`add-sqr-sqrt_binary64`
101×	`pow1_binary64`
100×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	27
1	244	21
2	2516	21

Stop Event

1×	node limit

Counts

3 → 79

Calls

Call 1

Inputs
(pow.f64 (/.f64 1 (log.f64 base)) 3)
(cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3))
(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))

Outputs

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

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

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (atan2.f64 im re) (log.f64 base))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (atan2.f64 im re)) (neg.f64 (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (atan2.f64 im re) -1) (neg.f64 (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (log.f64 base) -3) (pow.f64 (atan2.f64 im re) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (atan2.f64 im re) 3) (pow.f64 (log.f64 base) -3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))))

simplify40.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

681×	`fma-neg_binary64`
491×	`fma-def_binary64`
460×	`distribute-rgt-in_binary64`
357×	`distribute-lft-in_binary64`
266×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	504
1	58	504
2	115	504
3	353	504
4	1178	504
5	4481	504

Stop Event

1×	node limit

Counts

139 → 85

Calls

Call 1

Inputs
(/.f64 1 (pow.f64 (log.f64 base) 3))
(/.f64 1 (pow.f64 (log.f64 base) 3))
(/.f64 1 (pow.f64 (log.f64 base) 3))
(/.f64 1 (pow.f64 (log.f64 base) 3))
(/.f64 -1 (pow.f64 (log.f64 (/.f64 1 base)) 3))
(/.f64 -1 (pow.f64 (log.f64 (/.f64 1 base)) 3))
(/.f64 -1 (pow.f64 (log.f64 (/.f64 1 base)) 3))
(/.f64 -1 (pow.f64 (log.f64 (/.f64 1 base)) 3))
(/.f64 1 (pow.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))) 3))
(/.f64 1 (pow.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))) 3))
(/.f64 1 (pow.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))) 3))
(/.f64 1 (pow.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))) 3))
(/.f64 1 (log.f64 base))
(/.f64 1 (log.f64 base))
(/.f64 1 (log.f64 base))
(/.f64 1 (log.f64 base))
(/.f64 -1 (log.f64 (/.f64 1 base)))
(/.f64 -1 (log.f64 (/.f64 1 base)))
(/.f64 -1 (log.f64 (/.f64 1 base)))
(/.f64 -1 (log.f64 (/.f64 1 base)))
(/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))

Outputs
(/.f64 1 (pow.f64 (log.f64 base) 3))
(/.f64 1 (pow.f64 (log.f64 base) 3))
(/.f64 1 (pow.f64 (log.f64 base) 3))
(/.f64 1 (pow.f64 (log.f64 base) 3))
(/.f64 -1 (pow.f64 (log.f64 (/.f64 1 base)) 3))
(/.f64 1 (pow.f64 (log.f64 base) 3))
(/.f64 -1 (pow.f64 (log.f64 (/.f64 1 base)) 3))
(/.f64 1 (pow.f64 (log.f64 base) 3))
(/.f64 -1 (pow.f64 (log.f64 (/.f64 1 base)) 3))
(/.f64 1 (pow.f64 (log.f64 base) 3))
(/.f64 -1 (pow.f64 (log.f64 (/.f64 1 base)) 3))
(/.f64 1 (pow.f64 (log.f64 base) 3))
(/.f64 1 (pow.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))) 3))
(/.f64 1 (pow.f64 (log.f64 base) 3))
(/.f64 1 (pow.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))) 3))
(/.f64 1 (pow.f64 (log.f64 base) 3))
(/.f64 1 (pow.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))) 3))
(/.f64 1 (pow.f64 (log.f64 base) 3))
(/.f64 1 (pow.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))) 3))
(/.f64 1 (pow.f64 (log.f64 base) 3))
(/.f64 1 (log.f64 base))
(/.f64 1 (log.f64 base))
(/.f64 1 (log.f64 base))
(/.f64 1 (log.f64 base))
(/.f64 -1 (log.f64 (/.f64 1 base)))
(/.f64 1 (log.f64 base))
(/.f64 -1 (log.f64 (/.f64 1 base)))
(/.f64 1 (log.f64 base))
(/.f64 -1 (log.f64 (/.f64 1 base)))
(/.f64 1 (log.f64 base))
(/.f64 -1 (log.f64 (/.f64 1 base)))
(/.f64 1 (log.f64 base))
(/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 1 (log.f64 base))
(/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 1 (log.f64 base))
(/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 1 (log.f64 base))
(/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 1 (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))

prune97.0ms (1.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	3	6	9
Picked	0	1	1
Done	1	1	2
Total	113	10	123

Error

0.0b

Counts

123 → 10

Alt Table

Status	Error	Program
	30.6b	(pow.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3) 1/3)
✓	0.7b	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
	33.3b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))))
	31.5b	(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
	1.3b	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (pow.f64 (/.f64 1 (cbrt.f64 (log.f64 base))) 3) 3)))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	0.8b	(/.f64 (/.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (log.f64 base) 2))) (cbrt.f64 (log.f64 base)))
	5.5b	(cbrt.f64 (/.f64 (pow.f64 (atan2.f64 im re) 3) (pow.f64 (log.f64 base) 3)))
▶	0.7b	(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -1)
	0.9b	(.f64 (atan2.f64 im re) (.f64 (/.f64 1 (cbrt.f64 (log.f64 base))) (pow.f64 (pow.f64 (log.f64 base) -2) 1/3)))

Compiler

Compiled 1686 to 940 computations (44.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (log.f64 base) (atan2.f64 im re))
✓	0.6b	(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -1)

series715.0ms (13.1%)

Counts

2 → 44

Calls

18 calls:

Time	Variable		Point	Expression
60.0ms	im	@	inf	(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -1)
59.0ms	im	@	-inf	(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -1)
58.0ms	im	@	0	(/.f64 (log.f64 base) (atan2.f64 im re))
56.0ms	im	@	inf	(/.f64 (log.f64 base) (atan2.f64 im re))
55.0ms	re	@	inf	(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -1)

rewrite42.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

791×	`log1p-expm1-u_binary64`
791×	`expm1-log1p-u_binary64`
91×	`add-sqr-sqrt_binary64`
89×	`pow1_binary64`
88×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	181	18
2	2188	18

Stop Event

1×	node limit

Counts

2 → 76

Calls

Call 1

Inputs
(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -1)
(/.f64 (log.f64 base) (atan2.f64 im re))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (atan2.f64 im re) (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (pow.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 2) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (log.f64 base) -1) (pow.f64 (/.f64 1 (atan2.f64 im re)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) 2) -1) (pow.f64 (cbrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) -1) (pow.f64 (sqrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (atan2.f64 im re)) 2) 1) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (atan2.f64 im re)) 1) (/.f64 (sqrt.f64 (atan2.f64 im re)) (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (atan2.f64 im re)) 2) (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (/.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (atan2.f64 im re)) (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (cbrt.f64 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (atan2.f64 im re)) 2) (sqrt.f64 (log.f64 base))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (sqrt.f64 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (atan2.f64 im re)) (sqrt.f64 (log.f64 base))) (/.f64 (sqrt.f64 (atan2.f64 im re)) (sqrt.f64 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (log.f64 base)) (atan2.f64 im re))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (neg.f64 (log.f64 base))) (neg.f64 (atan2.f64 im re)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (atan2.f64 im re) (log.f64 base))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (atan2.f64 im re)) 2) (/.f64 (log.f64 base) (cbrt.f64 (atan2.f64 im re))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (log.f64 base) (sqrt.f64 (atan2.f64 im re))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (atan2.f64 im re)) (neg.f64 (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (atan2.f64 im re) 1) (log.f64 base))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (atan2.f64 im re)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) 2)) (cbrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (atan2.f64 im re) (pow.f64 (cbrt.f64 (log.f64 base)) 2)) (cbrt.f64 (log.f64 base)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (atan2.f64 im re) 3) (pow.f64 (log.f64 base) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (atan2.f64 im re)) (log.f64 (log.f64 base))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 base) (/.f64 1 (atan2.f64 im re)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log.f64 base)) 2) (*.f64 (cbrt.f64 (log.f64 base)) (/.f64 1 (atan2.f64 im re))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) (pow.f64 (cbrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) 2) (cbrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log.f64 base)) (*.f64 (sqrt.f64 (log.f64 base)) (/.f64 1 (atan2.f64 im re))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) (sqrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (log.f64 base)) (/.f64 1 (neg.f64 (atan2.f64 im re))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (atan2.f64 im re)) (log.f64 base))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (log.f64 base)) 2) 1) (/.f64 (cbrt.f64 (log.f64 base)) (atan2.f64 im re)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (log.f64 base)) 1) (/.f64 (sqrt.f64 (log.f64 base)) (atan2.f64 im re)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (atan2.f64 im re)) 2)) (/.f64 (log.f64 base) (cbrt.f64 (atan2.f64 im re))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (log.f64 base)) 2) (pow.f64 (cbrt.f64 (atan2.f64 im re)) 2)) (cbrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (log.f64 base)) (pow.f64 (cbrt.f64 (atan2.f64 im re)) 2)) (/.f64 (sqrt.f64 (log.f64 base)) (cbrt.f64 (atan2.f64 im re))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (atan2.f64 im re))) (/.f64 (log.f64 base) (sqrt.f64 (atan2.f64 im re))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (log.f64 base)) 2) (sqrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (log.f64 base)) (sqrt.f64 (atan2.f64 im re))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (log.f64 base) (neg.f64 (atan2.f64 im re))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 base (/.f64 1 (atan2.f64 im re))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (log.f64 base) 3) (pow.f64 (atan2.f64 im re) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))))))

simplify33.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

493×	`distribute-rgt-in_binary64`
360×	`fma-def_binary64`
350×	`distribute-lft-in_binary64`
289×	`div-sub_binary64`
215×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	428
1	40	428
2	65	396
3	133	396
4	381	396
5	1215	396
6	3534	396

Stop Event

1×	node limit

Counts

120 → 81

Calls

Call 1

Inputs
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(*.f64 -1 (/.f64 (log.f64 (/.f64 1 base)) (atan2.f64 im re)))
(*.f64 -1 (/.f64 (log.f64 (/.f64 1 base)) (atan2.f64 im re)))
(*.f64 -1 (/.f64 (log.f64 (/.f64 1 base)) (atan2.f64 im re)))
(*.f64 -1 (/.f64 (log.f64 (/.f64 1 base)) (atan2.f64 im re)))
(/.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))) (atan2.f64 im re))
(/.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))) (atan2.f64 im re))
(/.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))) (atan2.f64 im re))
(/.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))) (atan2.f64 im re))

Outputs
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(*.f64 -1 (/.f64 (atan2.f64 im re) (log.f64 (/.f64 1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(/.f64 (atan2.f64 im re) (log.f64 base))
(*.f64 -1 (/.f64 (log.f64 (/.f64 1 base)) (atan2.f64 im re)))
(neg.f64 (/.f64 (neg.f64 (log.f64 base)) (atan2.f64 im re)))
(/.f64 (neg.f64 (neg.f64 (log.f64 base))) (atan2.f64 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(*.f64 -1 (/.f64 (log.f64 (/.f64 1 base)) (atan2.f64 im re)))
(neg.f64 (/.f64 (neg.f64 (log.f64 base)) (atan2.f64 im re)))
(/.f64 (neg.f64 (neg.f64 (log.f64 base))) (atan2.f64 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(*.f64 -1 (/.f64 (log.f64 (/.f64 1 base)) (atan2.f64 im re)))
(neg.f64 (/.f64 (neg.f64 (log.f64 base)) (atan2.f64 im re)))
(/.f64 (neg.f64 (neg.f64 (log.f64 base))) (atan2.f64 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(*.f64 -1 (/.f64 (log.f64 (/.f64 1 base)) (atan2.f64 im re)))
(neg.f64 (/.f64 (neg.f64 (log.f64 base)) (atan2.f64 im re)))
(/.f64 (neg.f64 (neg.f64 (log.f64 base))) (atan2.f64 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))) (atan2.f64 im re))
(neg.f64 (/.f64 (neg.f64 (log.f64 base)) (atan2.f64 im re)))
(/.f64 (neg.f64 (neg.f64 (log.f64 base))) (atan2.f64 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))) (atan2.f64 im re))
(neg.f64 (/.f64 (neg.f64 (log.f64 base)) (atan2.f64 im re)))
(/.f64 (neg.f64 (neg.f64 (log.f64 base))) (atan2.f64 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))) (atan2.f64 im re))
(neg.f64 (/.f64 (neg.f64 (log.f64 base)) (atan2.f64 im re)))
(/.f64 (neg.f64 (neg.f64 (log.f64 base))) (atan2.f64 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))
(/.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 base))) (atan2.f64 im re))
(neg.f64 (/.f64 (neg.f64 (log.f64 base)) (atan2.f64 im re)))
(/.f64 (neg.f64 (neg.f64 (log.f64 base))) (atan2.f64 im re))
(/.f64 (log.f64 base) (atan2.f64 im re))

prune50.0ms (0.9%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	80	11	91

Error

Counts

91 → 11

Alt Table

Status	Error	Program
	30.6b	(pow.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3) 1/3)
✓	0.7b	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
	33.3b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))))
	31.5b	(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
	1.3b	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (pow.f64 (/.f64 1 (cbrt.f64 (log.f64 base))) 3) 3)))
	10.0b	(pow.f64 (log.f64 (pow.f64 base (/.f64 1 (atan2.f64 im re)))) -1)
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	0.8b	(/.f64 (/.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (log.f64 base) 2))) (cbrt.f64 (log.f64 base)))
	5.5b	(cbrt.f64 (/.f64 (pow.f64 (atan2.f64 im re) 3) (pow.f64 (log.f64 base) 3)))
✓	0.7b	(pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) -1)
	0.9b	(.f64 (atan2.f64 im re) (.f64 (/.f64 1 (cbrt.f64 (log.f64 base))) (pow.f64 (pow.f64 (log.f64 base) -2) 1/3)))

Compiler

Compiled 1194 to 495 computations (58.5% saved)

regimes387.0ms (7.1%)

Accuracy

Total 0.3b remaining (89.1%)

Threshold costs 0.3b (89.1%)

Counts

71 → 1

Compiler

Compiled 5381 to 3866 computations (28.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (atan2.f64 im re) (log.f64 base))

Outputs
(/.f64 (atan2.f64 im re) (log.f64 base))

end159.0ms (2.9%)

Stop Event

1×

fuel

Compiler

Compiled 191 to 137 computations (28.3% saved)

Details

analyze571.0ms (10.4%)

sample1.9s (34.1%)

preprocess53.0ms (1%)

simplify21.0ms (0.4%)

prune14.0ms (0.3%)

localize5.0ms (0.1%)

series341.0ms (6.2%)

rewrite37.0ms (0.7%)

simplify29.0ms (0.5%)

prune30.0ms (0.5%)

localize6.0ms (0.1%)

series363.0ms (6.6%)

rewrite39.0ms (0.7%)

simplify38.0ms (0.7%)

prune43.0ms (0.8%)

localize10.0ms (0.2%)

series424.0ms (7.8%)

rewrite47.0ms (0.9%)

simplify40.0ms (0.7%)

prune97.0ms (1.8%)

localize6.0ms (0.1%)

series715.0ms (13.1%)

rewrite42.0ms (0.8%)

simplify33.0ms (0.6%)

prune50.0ms (0.9%)

regimes387.0ms (7.1%)

simplify2.0ms (0%)

end159.0ms (2.9%)

Profiling