Details

analyze9.0ms (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
0%	50%	50%	3
31.2%	18.7%	50%	4
40.6%	9.4%	50%	5
45.3%	4.7%	50%	6
47.6%	2.3%	50%	7
48.8%	1.2%	50%	8
49.4%	0.6%	50%	9
49.7%	0.3%	50%	10
49.8%	0.1%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 29 to 19 computations (34.5% saved)

sample1.1s (59.1%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 58 to 38 computations (34.5% saved)

preprocess31.0ms (1.7%)

Algorithm

2×	egg-herbie

Rules

554×	`associate-/r*_binary64`
513×	`distribute-rgt-in_binary64`
416×	`associate-/r/_binary64`
349×	`fma-def_binary64`
319×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	40	26
2	200	17
3	1316	13
4	3585	13
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))

Outputs
(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
(/.f64 (/.f64 (.f64 i (.f64 i (.f64 i i))) (.f64 4 (.f64 i i))) (+.f64 (.f64 4 (*.f64 i i)) -1))
(.f64 (/.f64 i (fma.f64 4 (.f64 i i) -1)) (/.f64 (pow.f64 i 3) (.f64 i (.f64 i 4))))
(.f64 (/.f64 i (fma.f64 (.f64 i i) 4 -1)) (/.f64 i 4))
(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify22.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

554×	`associate-/r*_binary64`
513×	`distribute-rgt-in_binary64`
416×	`associate-/r/_binary64`
349×	`fma-def_binary64`
319×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	40	26
2	200	17
3	1316	13
4	3585	13

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))

Outputs
(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
(/.f64 (/.f64 (.f64 i (.f64 i (.f64 i i))) (.f64 4 (.f64 i i))) (+.f64 (.f64 4 (*.f64 i i)) -1))
(.f64 (/.f64 i (fma.f64 4 (.f64 i i) -1)) (/.f64 (pow.f64 i 3) (.f64 i (.f64 i 4))))
(.f64 (/.f64 i (fma.f64 (.f64 i i) 4 -1)) (/.f64 i 4))
(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))

prune4.0ms (0.2%)

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

7.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	47.5b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
▶	7.9b	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))

Compiler

Compiled 107 to 74 computations (30.8% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
✓	12.2b	(/.f64 i (pow.f64 i 3))

series3.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	i	@	0	(/.f64 i (pow.f64 i 3))
1.0ms	i	@	0	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
1.0ms	i	@	inf	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
0.0ms	i	@	-inf	(/.f64 i (pow.f64 i 3))
0.0ms	i	@	-inf	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))

rewrite47.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

436×	`log-prod_binary64`
172×	`expm1-udef_binary64`
172×	`log1p-udef_binary64`
168×	`pow1/3_binary64`
150×	`pow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	215	14
2	2674	14

Stop Event

1×	node limit

Counts

2 → 68

Calls

Call 1

Inputs
(/.f64 i (pow.f64 i 3))
(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 i -2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 i -2))) (cbrt.f64 (exp.f64 (pow.f64 i -2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 i -2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 i -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 i (pow.f64 i -3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 i -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 i -2) (/.f64 i i))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 i -2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 i) i) (pow.f64 (/.f64 (cbrt.f64 i) i) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (/.f64 (cbrt.f64 i) i) 2) (/.f64 (cbrt.f64 i) i))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 i) 2) (.f64 (cbrt.f64 i) (pow.f64 i -3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 i) (/.f64 1 i))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 i) (/.f64 i (.f64 i i)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 i) (.f64 (sqrt.f64 i) (pow.f64 i -3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 i) (/.f64 1 (neg.f64 (pow.f64 i 3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 i -3) i)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 i) 2) i) (/.f64 (cbrt.f64 i) (.f64 i i)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 i) i) (/.f64 (sqrt.f64 i) (.f64 i i)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 i) (.f64 i i)) (/.f64 (sqrt.f64 i) i))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 i) 2) 1) (/.f64 (cbrt.f64 i) (pow.f64 i 3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 i) 1) (/.f64 (sqrt.f64 i) (pow.f64 i 3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 i) 2) (.f64 i i)) (/.f64 (cbrt.f64 i) i))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (pow.f64 i 3/2)) (/.f64 i (pow.f64 i 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 i) 2) (pow.f64 i 3/2)) (/.f64 (cbrt.f64 i) (pow.f64 i 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 i -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 i -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 i i) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cbrt.f64 i) i) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 i) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (pow.f64 i 6)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (.f64 i i) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 i (neg.f64 (pow.f64 i 3))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (pow.f64 i -2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 1 (pow.f64 i 6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 -2 (log.f64 i)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (*.f64 -2 (log.f64 i)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 i -2)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))) (cbrt.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/4 (/.f64 1 (-.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))) (pow.f64 (cbrt.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))) 2) (cbrt.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 (sqrt.f64 (-.f64 4 (pow.f64 i -2)))) (/.f64 1/2 (sqrt.f64 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1/4 (/.f64 1 (neg.f64 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (-.f64 4 (pow.f64 i -2))) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/4 (-.f64 64 (/.f64 1 (pow.f64 i 6)))) (fma.f64 (pow.f64 i -2) (+.f64 (pow.f64 i -2) 4) 16))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/4 (-.f64 16 (pow.f64 (pow.f64 i -2) 2))) (+.f64 (pow.f64 i -2) 4))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/2 (sqrt.f64 (-.f64 4 (pow.f64 i -2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 16 (/.f64 (pow.f64 i -2) 1/4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 16 (/.f64 (pow.f64 i -2) 1/4)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/16 (pow.f64 (-.f64 4 (pow.f64 i -2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 i -2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 i -2))) (cbrt.f64 (exp.f64 (pow.f64 i -2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 i -2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 i -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 i (pow.f64 i -3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 i -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 i -2) (/.f64 i i))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 i -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 i) i) (pow.f64 (/.f64 (cbrt.f64 i) i) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (cbrt.f64 i) i) 2) (/.f64 (cbrt.f64 i) i))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 i) 2) (*.f64 (cbrt.f64 i) (pow.f64 i -3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 i) (/.f64 1 i))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 i) (/.f64 i (*.f64 i i)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 i) (*.f64 (sqrt.f64 i) (pow.f64 i -3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 i) (/.f64 1 (neg.f64 (pow.f64 i 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 i -3) i)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 i) 2) i) (/.f64 (cbrt.f64 i) (*.f64 i i)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 i) i) (/.f64 (sqrt.f64 i) (*.f64 i i)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 i) (*.f64 i i)) (/.f64 (sqrt.f64 i) i))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 i) 2) 1) (/.f64 (cbrt.f64 i) (pow.f64 i 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 i) 1) (/.f64 (sqrt.f64 i) (pow.f64 i 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 i) 2) (*.f64 i i)) (/.f64 (cbrt.f64 i) i))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 i 3/2)) (/.f64 i (pow.f64 i 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 i) 2) (pow.f64 i 3/2)) (/.f64 (cbrt.f64 i) (pow.f64 i 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 i -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 i -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 i i) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cbrt.f64 i) i) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 i) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (pow.f64 i 6)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 i i) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 i (neg.f64 (pow.f64 i 3))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (pow.f64 i -2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 1 (pow.f64 i 6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 -2 (log.f64 i)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -2 (log.f64 i)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 i -2)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))) (cbrt.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (/.f64 1 (-.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))) (pow.f64 (cbrt.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))) 2) (cbrt.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (sqrt.f64 (-.f64 4 (pow.f64 i -2)))) (/.f64 1/2 (sqrt.f64 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/4 (/.f64 1 (neg.f64 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 4 (pow.f64 i -2))) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/4 (-.f64 64 (/.f64 1 (pow.f64 i 6)))) (fma.f64 (pow.f64 i -2) (+.f64 (pow.f64 i -2) 4) 16))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/4 (-.f64 16 (pow.f64 (pow.f64 i -2) 2))) (+.f64 (pow.f64 i -2) 4))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/2 (sqrt.f64 (-.f64 4 (pow.f64 i -2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 16 (/.f64 (pow.f64 i -2) 1/4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 16 (/.f64 (pow.f64 i -2) 1/4)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/16 (pow.f64 (-.f64 4 (pow.f64 i -2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))))

simplify27.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

691×	`cancel-sign-sub-inv_binary64`
657×	`fma-neg_binary64`
413×	`unswap-sqr_binary64`
410×	`fma-def_binary64`
352×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	270
1	90	267
2	211	267
3	639	267
4	2987	267

Stop Event

1×	node limit

Counts

92 → 85

Calls

Call 1

Inputs
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(*.f64 -1/4 (pow.f64 i 2))
(+.f64 (.f64 -1 (pow.f64 i 4)) (.f64 -1/4 (pow.f64 i 2)))
(+.f64 (.f64 -1 (pow.f64 i 4)) (+.f64 (.f64 -1/4 (pow.f64 i 2)) (*.f64 -4 (pow.f64 i 6))))
(+.f64 (.f64 -16 (pow.f64 i 8)) (+.f64 (.f64 -1 (pow.f64 i 4)) (+.f64 (.f64 -1/4 (pow.f64 i 2)) (.f64 -4 (pow.f64 i 6)))))
1/16
(+.f64 1/16 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))
(+.f64 (.f64 1/256 (/.f64 1 (pow.f64 i 4))) (+.f64 1/16 (.f64 1/64 (/.f64 1 (pow.f64 i 2)))))
(+.f64 (.f64 1/256 (/.f64 1 (pow.f64 i 4))) (+.f64 1/16 (+.f64 (.f64 1/1024 (/.f64 1 (pow.f64 i 6))) (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))))
1/16
(+.f64 1/16 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))
(+.f64 (.f64 1/256 (/.f64 1 (pow.f64 i 4))) (+.f64 1/16 (.f64 1/64 (/.f64 1 (pow.f64 i 2)))))
(+.f64 (.f64 1/256 (/.f64 1 (pow.f64 i 4))) (+.f64 1/16 (+.f64 (.f64 1/1024 (/.f64 1 (pow.f64 i 6))) (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))))

Outputs
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(*.f64 -1/4 (pow.f64 i 2))
(.f64 (.f64 i i) -1/4)
(.f64 i (.f64 i -1/4))
(+.f64 (.f64 -1 (pow.f64 i 4)) (.f64 -1/4 (pow.f64 i 2)))
(fma.f64 -1 (pow.f64 i 4) (.f64 (.f64 i i) -1/4))
(fma.f64 (*.f64 i i) -1/4 (neg.f64 (pow.f64 i 4)))
(.f64 (.f64 i i) (-.f64 -1/4 (*.f64 i i)))
(-.f64 (.f64 i (.f64 i -1/4)) (pow.f64 i 4))
(+.f64 (.f64 -1 (pow.f64 i 4)) (+.f64 (.f64 -1/4 (pow.f64 i 2)) (*.f64 -4 (pow.f64 i 6))))
(fma.f64 -1 (pow.f64 i 4) (fma.f64 -1/4 (.f64 i i) (.f64 -4 (pow.f64 i 6))))
(-.f64 (fma.f64 (.f64 i i) -1/4 (.f64 -4 (pow.f64 i 6))) (pow.f64 i 4))
(fma.f64 -4 (pow.f64 i 6) (.f64 (.f64 i i) (-.f64 -1/4 (*.f64 i i))))
(-.f64 (fma.f64 i (.f64 i -1/4) (.f64 -4 (pow.f64 i 6))) (pow.f64 i 4))
(-.f64 (.f64 -4 (pow.f64 i 6)) (.f64 (*.f64 i i) (fma.f64 i i 1/4)))
(+.f64 (.f64 -16 (pow.f64 i 8)) (+.f64 (.f64 -1 (pow.f64 i 4)) (+.f64 (.f64 -1/4 (pow.f64 i 2)) (.f64 -4 (pow.f64 i 6)))))
(fma.f64 -16 (pow.f64 i 8) (fma.f64 -1 (pow.f64 i 4) (fma.f64 -1/4 (.f64 i i) (.f64 -4 (pow.f64 i 6)))))
(fma.f64 -16 (pow.f64 i 8) (-.f64 (fma.f64 (.f64 i i) -1/4 (.f64 -4 (pow.f64 i 6))) (pow.f64 i 4)))
(-.f64 (fma.f64 -16 (pow.f64 i 8) (fma.f64 i (.f64 i -1/4) (.f64 -4 (pow.f64 i 6)))) (pow.f64 i 4))
(fma.f64 -4 (pow.f64 i 6) (fma.f64 -16 (pow.f64 i 8) (-.f64 (.f64 i (.f64 i -1/4)) (pow.f64 i 4))))
(fma.f64 i (.f64 i -1/4) (-.f64 (fma.f64 -4 (pow.f64 i 6) (.f64 -16 (pow.f64 i 8))) (pow.f64 i 4)))
1/16
(+.f64 1/16 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))
(+.f64 1/16 (/.f64 1/64 (*.f64 i i)))
(+.f64 (.f64 1/256 (/.f64 1 (pow.f64 i 4))) (+.f64 1/16 (.f64 1/64 (/.f64 1 (pow.f64 i 2)))))
(+.f64 (+.f64 1/16 (/.f64 1/64 (*.f64 i i))) (/.f64 1/256 (pow.f64 i 4)))
(+.f64 (/.f64 1/64 (*.f64 i i)) (+.f64 1/16 (/.f64 1/256 (pow.f64 i 4))))
(+.f64 1/16 (+.f64 (/.f64 1/64 (*.f64 i i)) (/.f64 1/256 (pow.f64 i 4))))
(+.f64 (.f64 1/256 (/.f64 1 (pow.f64 i 4))) (+.f64 1/16 (+.f64 (.f64 1/1024 (/.f64 1 (pow.f64 i 6))) (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))))
(+.f64 (/.f64 1/256 (pow.f64 i 4)) (+.f64 (+.f64 1/16 (/.f64 1/1024 (pow.f64 i 6))) (/.f64 1/64 (*.f64 i i))))
(+.f64 1/16 (+.f64 (+.f64 (/.f64 1/64 (*.f64 i i)) (/.f64 1/1024 (pow.f64 i 6))) (/.f64 1/256 (pow.f64 i 4))))
(+.f64 (+.f64 1/16 (/.f64 1/1024 (pow.f64 i 6))) (+.f64 (/.f64 1/64 (*.f64 i i)) (/.f64 1/256 (pow.f64 i 4))))
(+.f64 1/16 (+.f64 (/.f64 1/64 (*.f64 i i)) (+.f64 (/.f64 1/256 (pow.f64 i 4)) (/.f64 1/1024 (pow.f64 i 6)))))
(+.f64 (+.f64 1/16 (/.f64 1/64 (*.f64 i i))) (+.f64 (/.f64 1/256 (pow.f64 i 4)) (/.f64 1/1024 (pow.f64 i 6))))
1/16
(+.f64 1/16 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))
(+.f64 1/16 (/.f64 1/64 (*.f64 i i)))
(+.f64 (.f64 1/256 (/.f64 1 (pow.f64 i 4))) (+.f64 1/16 (.f64 1/64 (/.f64 1 (pow.f64 i 2)))))
(+.f64 (+.f64 1/16 (/.f64 1/64 (*.f64 i i))) (/.f64 1/256 (pow.f64 i 4)))
(+.f64 (/.f64 1/64 (*.f64 i i)) (+.f64 1/16 (/.f64 1/256 (pow.f64 i 4))))
(+.f64 1/16 (+.f64 (/.f64 1/64 (*.f64 i i)) (/.f64 1/256 (pow.f64 i 4))))
(+.f64 (.f64 1/256 (/.f64 1 (pow.f64 i 4))) (+.f64 1/16 (+.f64 (.f64 1/1024 (/.f64 1 (pow.f64 i 6))) (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))))
(+.f64 (/.f64 1/256 (pow.f64 i 4)) (+.f64 (+.f64 1/16 (/.f64 1/1024 (pow.f64 i 6))) (/.f64 1/64 (*.f64 i i))))
(+.f64 1/16 (+.f64 (+.f64 (/.f64 1/64 (*.f64 i i)) (/.f64 1/1024 (pow.f64 i 6))) (/.f64 1/256 (pow.f64 i 4))))
(+.f64 (+.f64 1/16 (/.f64 1/1024 (pow.f64 i 6))) (+.f64 (/.f64 1/64 (*.f64 i i)) (/.f64 1/256 (pow.f64 i 4))))
(+.f64 1/16 (+.f64 (/.f64 1/64 (*.f64 i i)) (+.f64 (/.f64 1/256 (pow.f64 i 4)) (/.f64 1/1024 (pow.f64 i 6)))))
(+.f64 (+.f64 1/16 (/.f64 1/64 (*.f64 i i))) (+.f64 (/.f64 1/256 (pow.f64 i 4)) (/.f64 1/1024 (pow.f64 i 6))))

prune135.0ms (7.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	85	2	87

Error

Counts

87 → 2

Alt Table

Status	Error	Program
	29.8b	(.f64 i (.f64 i -1/4))
▶	1.9b	(/.f64 1/4 (-.f64 4 (-.f64 (exp.f64 (log1p.f64 (pow.f64 i -2))) 1)))

Compiler

Compiled 1082 to 865 computations (20.1% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1/4 (-.f64 4 (-.f64 (exp.f64 (log1p.f64 (pow.f64 i -2))) 1)))
✓	1.1b	(-.f64 (exp.f64 (log1p.f64 (pow.f64 i -2))) 1)
✓	1.7b	(exp.f64 (log1p.f64 (pow.f64 i -2)))
✓	16.7b	(log1p.f64 (pow.f64 i -2))

series101.0ms (5.4%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
59.0ms	i	@	inf	(-.f64 (exp.f64 (log1p.f64 (pow.f64 i -2))) 1)
15.0ms	i	@	-inf	(-.f64 (exp.f64 (log1p.f64 (pow.f64 i -2))) 1)
11.0ms	i	@	0	(log1p.f64 (pow.f64 i -2))
7.0ms	i	@	0	(exp.f64 (log1p.f64 (pow.f64 i -2)))
2.0ms	i	@	inf	(exp.f64 (log1p.f64 (pow.f64 i -2)))

rewrite55.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

447×	`log-prod_binary64`
211×	`prod-diff_binary64`
198×	`log1p-udef_binary64`
197×	`expm1-udef_binary64`
156×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	270	27
2	3042	27

Stop Event

1×	node limit

Counts

4 → 141

Calls

Call 1

Inputs
(log1p.f64 (pow.f64 i -2))
(exp.f64 (log1p.f64 (pow.f64 i -2)))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 i -2))) 1)
(/.f64 1/4 (-.f64 4 (-.f64 (exp.f64 (log1p.f64 (pow.f64 i -2))) 1)))

Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 i -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (pow.f64 i -2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 (pow.f64 i -2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (+.f64 (pow.f64 i -2) 1) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (+.f64 (pow.f64 i -2) 1))) (cbrt.f64 (exp.f64 (+.f64 (pow.f64 i -2) 1))))) (log.f64 (cbrt.f64 (exp.f64 (+.f64 (pow.f64 i -2) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (+.f64 (pow.f64 i -2) 1)))) (log.f64 (sqrt.f64 (exp.f64 (+.f64 (pow.f64 i -2) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (+.f64 (pow.f64 i -2) 1) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (pow.f64 i -2) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 (pow.f64 i -2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 (pow.f64 i -2) 1)) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 i -2) 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 (pow.f64 i -2) 1)) 2) (cbrt.f64 (+.f64 (pow.f64 i -2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 (pow.f64 i -2) 1)) 2) (.f64 (cbrt.f64 (+.f64 (pow.f64 i -2) 1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 1 (/.f64 1 i)) (hypot.f64 1 (/.f64 1 i)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 1 (/.f64 1 i)) (.f64 (hypot.f64 1 (/.f64 1 i)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 i -6)) (+.f64 1 (-.f64 (pow.f64 i -4) (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 i -4)) (-.f64 1 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (pow.f64 i -2) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log1p.f64 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (pow.f64 i -2) 1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (/.f64 1 i)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (pow.f64 i -2) 1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log1p.f64 (pow.f64 i -2)) 2))) (cbrt.f64 (log1p.f64 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log1p.f64 (pow.f64 i -2)))) (sqrt.f64 (log1p.f64 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (pow.f64 i -2) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (pow.f64 i -2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (pow.f64 i -2) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (pow.f64 i -2) 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 i -2) 1 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 i -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (+.f64 (pow.f64 i -2) 1) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 i -2)) (cbrt.f64 (pow.f64 i -4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 i -4)) (cbrt.f64 (pow.f64 i -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 i) (/.f64 1 i) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (expm1.f64 (.f64 3 (log1p.f64 (pow.f64 i -2)))) (/.f64 1 (+.f64 (pow.f64 (+.f64 (pow.f64 i -2) 1) 2) (+.f64 (+.f64 (pow.f64 i -2) 1) 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (expm1.f64 (.f64 2 (log1p.f64 (pow.f64 i -2)))) (/.f64 1 (+.f64 (+.f64 (pow.f64 i -2) 1) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (+.f64 (pow.f64 i -2) 1) 1) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (cbrt.f64 (+.f64 (+.f64 (pow.f64 i -2) 1) 1)) (cbrt.f64 (+.f64 (+.f64 (pow.f64 i -2) 1) 1))) (cbrt.f64 (+.f64 (+.f64 (pow.f64 i -2) 1) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (hypot.f64 1 (/.f64 1 i))) (hypot.f64 1 (hypot.f64 1 (/.f64 1 i))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (.f64 i i)) -2) (pow.f64 (cbrt.f64 i) -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (sqrt.f64 i) -2) (pow.f64 (sqrt.f64 i) -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (hypot.f64 1 (/.f64 1 i)) 1) (-.f64 (hypot.f64 1 (/.f64 1 i)) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (pow.f64 i -2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (pow.f64 i -2) 1)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (pow.f64 i -2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 i -2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 (pow.f64 i -2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 i -2))) (cbrt.f64 (exp.f64 (pow.f64 i -2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 i -2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 i -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 i -2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 i -2)) (cbrt.f64 (pow.f64 i -4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 i -4)) (cbrt.f64 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 i) (/.f64 1 i))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (expm1.f64 (.f64 3 (log1p.f64 (pow.f64 i -2)))) (/.f64 1 (+.f64 (pow.f64 (+.f64 (pow.f64 i -2) 1) 2) (+.f64 (+.f64 (pow.f64 i -2) 1) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (expm1.f64 (.f64 2 (log1p.f64 (pow.f64 i -2)))) (/.f64 1 (+.f64 (+.f64 (pow.f64 i -2) 1) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 i i)) -2) (pow.f64 (cbrt.f64 i) -2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 i) -2) (pow.f64 (sqrt.f64 i) -2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (hypot.f64 1 (/.f64 1 i)) 1) (-.f64 (hypot.f64 1 (/.f64 1 i)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 (pow.f64 i -2) 1) 2) (+.f64 (+.f64 (pow.f64 i -2) 1) 1)) (expm1.f64 (.f64 3 (log1p.f64 (pow.f64 i -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (+.f64 (pow.f64 i -2) 1) 1) (expm1.f64 (.f64 2 (log1p.f64 (pow.f64 i -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (expm1.f64 (.f64 3 (log1p.f64 (pow.f64 i -2)))) (+.f64 (pow.f64 (+.f64 (pow.f64 i -2) 1) 2) (+.f64 (+.f64 (pow.f64 i -2) 1) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (expm1.f64 (.f64 3 (log1p.f64 (pow.f64 i -2)))) (+.f64 (pow.f64 (+.f64 (pow.f64 i -2) 1) 2) (-.f64 1 (.f64 (+.f64 (pow.f64 i -2) 1) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (expm1.f64 (.f64 2 (log1p.f64 (pow.f64 i -2)))) (+.f64 (+.f64 (pow.f64 i -2) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (expm1.f64 (.f64 3 (log1p.f64 (pow.f64 i -2))))) (neg.f64 (+.f64 (pow.f64 (+.f64 (pow.f64 i -2) 1) 2) (+.f64 (+.f64 (pow.f64 i -2) 1) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (expm1.f64 (.f64 2 (log1p.f64 (pow.f64 i -2))))) (neg.f64 (+.f64 (+.f64 (pow.f64 i -2) 1) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 i -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 i -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 i i) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 i -2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 i) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 i -6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 i -4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 i -6))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 i -2) 1) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (pow.f64 i -2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 (pow.f64 i -2) 1)) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 i -2) 1)) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (pow.f64 i -2) 1)) 2) (cbrt.f64 (+.f64 (pow.f64 i -2) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (pow.f64 i -2) 1)) 2) (.f64 (cbrt.f64 (+.f64 (pow.f64 i -2) 1)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (/.f64 1 i)) (hypot.f64 1 (/.f64 1 i)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (/.f64 1 i)) (.f64 (hypot.f64 1 (/.f64 1 i)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 -2 (log.f64 i)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 -2 (log.f64 i)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 i -2)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))) (cbrt.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/4 (/.f64 1 (-.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))) (pow.f64 (cbrt.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))) 2) (cbrt.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 (sqrt.f64 (-.f64 4 (pow.f64 i -2)))) (/.f64 1/2 (sqrt.f64 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1/4 (/.f64 1 (neg.f64 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (-.f64 4 (pow.f64 i -2))) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/4 (-.f64 64 (pow.f64 i -6))) (+.f64 16 (fma.f64 (pow.f64 i -2) 4 (pow.f64 i -4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4))) (+.f64 (pow.f64 i -2) 4))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/2 (sqrt.f64 (-.f64 4 (pow.f64 i -2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 16 (/.f64 (pow.f64 i -2) 1/4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/16 (pow.f64 (-.f64 4 (pow.f64 i -2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))))

simplify39.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

527×	`fma-def_binary64`
506×	`associate-/r*_binary64`
459×	`associate-l_binary64`
361×	`associate-r_binary64`
156×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	73	656
1	199	650
2	489	650
3	1358	551

Stop Event

1×	node limit

Counts

189 → 174

Calls

Call 1

Inputs
(*.f64 -2 (log.f64 i))
(+.f64 (pow.f64 i 2) (*.f64 -2 (log.f64 i)))
(+.f64 (.f64 -1/2 (pow.f64 i 4)) (+.f64 (pow.f64 i 2) (.f64 -2 (log.f64 i))))
(+.f64 (.f64 -1/2 (pow.f64 i 4)) (+.f64 (pow.f64 i 2) (+.f64 (.f64 1/3 (pow.f64 i 6)) (*.f64 -2 (log.f64 i)))))
(/.f64 1 (pow.f64 i 2))
(-.f64 (/.f64 1 (pow.f64 i 2)) (*.f64 1/2 (/.f64 1 (pow.f64 i 4))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 i 2)) (.f64 1/3 (/.f64 1 (pow.f64 i 6)))) (.f64 1/2 (/.f64 1 (pow.f64 i 4))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 i 2)) (.f64 1/3 (/.f64 1 (pow.f64 i 6)))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 i 8))) (*.f64 1/2 (/.f64 1 (pow.f64 i 4)))))
(/.f64 1 (pow.f64 i 2))
(-.f64 (/.f64 1 (pow.f64 i 2)) (*.f64 1/2 (/.f64 1 (pow.f64 i 4))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 i 2)) (.f64 1/3 (/.f64 1 (pow.f64 i 6)))) (.f64 1/2 (/.f64 1 (pow.f64 i 4))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 i 2)) (.f64 1/3 (/.f64 1 (pow.f64 i 6)))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 i 8))) (*.f64 1/2 (/.f64 1 (pow.f64 i 4)))))
(/.f64 1 (pow.f64 i 2))
(+.f64 1 (/.f64 1 (pow.f64 i 2)))
(+.f64 1 (/.f64 1 (pow.f64 i 2)))
(+.f64 1 (/.f64 1 (pow.f64 i 2)))
1
(+.f64 1 (/.f64 1 (pow.f64 i 2)))
(+.f64 1 (/.f64 1 (pow.f64 i 2)))
(+.f64 1 (/.f64 1 (pow.f64 i 2)))
1
(+.f64 1 (/.f64 1 (pow.f64 i 2)))
(+.f64 1 (/.f64 1 (pow.f64 i 2)))
(+.f64 1 (/.f64 1 (pow.f64 i 2)))
(-.f64 (pow.f64 i -2) 1)
(pow.f64 i -2)
(pow.f64 i -2)
(pow.f64 i -2)
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1/4 (-.f64 5 (pow.f64 i -2)))
(+.f64 (.f64 1/4 (/.f64 1 (pow.f64 (-.f64 5 (pow.f64 i -2)) 2))) (.f64 1/4 (/.f64 1 (-.f64 5 (pow.f64 i -2)))))
(+.f64 (.f64 1/4 (/.f64 1 (pow.f64 (-.f64 5 (pow.f64 i -2)) 2))) (+.f64 (.f64 1/4 (/.f64 1 (-.f64 5 (pow.f64 i -2)))) (*.f64 1/4 (/.f64 1 (pow.f64 (-.f64 5 (pow.f64 i -2)) 3)))))
(+.f64 (.f64 1/4 (/.f64 1 (pow.f64 (-.f64 5 (pow.f64 i -2)) 2))) (+.f64 (.f64 1/4 (/.f64 1 (-.f64 5 (pow.f64 i -2)))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 (-.f64 5 (pow.f64 i -2)) 3))) (.f64 1/4 (/.f64 1 (pow.f64 (-.f64 5 (pow.f64 i -2)) 4))))))
1/16
(+.f64 1/16 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))
(+.f64 (.f64 1/256 (/.f64 1 (pow.f64 i 4))) (+.f64 1/16 (.f64 1/64 (/.f64 1 (pow.f64 i 2)))))
(+.f64 (.f64 1/256 (/.f64 1 (pow.f64 i 4))) (+.f64 1/16 (+.f64 (.f64 1/1024 (/.f64 1 (pow.f64 i 6))) (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))))
1/16
(+.f64 1/16 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))
(+.f64 (.f64 1/256 (/.f64 1 (pow.f64 i 4))) (+.f64 1/16 (.f64 1/64 (/.f64 1 (pow.f64 i 2)))))
(+.f64 (.f64 1/256 (/.f64 1 (pow.f64 i 4))) (+.f64 1/16 (+.f64 (.f64 1/1024 (/.f64 1 (pow.f64 i 6))) (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))))

Outputs
(*.f64 -2 (log.f64 i))
(+.f64 (pow.f64 i 2) (*.f64 -2 (log.f64 i)))
(+.f64 (.f64 -2 (log.f64 i)) (.f64 i i))
(fma.f64 -2 (log.f64 i) (*.f64 i i))
(+.f64 (.f64 -1/2 (pow.f64 i 4)) (+.f64 (pow.f64 i 2) (.f64 -2 (log.f64 i))))
(fma.f64 -1/2 (pow.f64 i 4) (+.f64 (.f64 -2 (log.f64 i)) (.f64 i i)))
(fma.f64 -1/2 (pow.f64 i 4) (fma.f64 -2 (log.f64 i) (*.f64 i i)))
(fma.f64 -2 (log.f64 i) (fma.f64 -1/2 (pow.f64 i 4) (*.f64 i i)))
(+.f64 (.f64 -1/2 (pow.f64 i 4)) (+.f64 (pow.f64 i 2) (+.f64 (.f64 1/3 (pow.f64 i 6)) (*.f64 -2 (log.f64 i)))))
(fma.f64 -1/2 (pow.f64 i 4) (+.f64 (.f64 i i) (fma.f64 1/3 (pow.f64 i 6) (.f64 -2 (log.f64 i)))))
(fma.f64 -1/2 (pow.f64 i 4) (fma.f64 i i (fma.f64 -2 (log.f64 i) (*.f64 1/3 (pow.f64 i 6)))))
(fma.f64 i i (fma.f64 -1/2 (pow.f64 i 4) (fma.f64 -2 (log.f64 i) (*.f64 1/3 (pow.f64 i 6)))))
(fma.f64 -2 (log.f64 i) (fma.f64 i i (fma.f64 -1/2 (pow.f64 i 4) (*.f64 1/3 (pow.f64 i 6)))))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(pow.f64 i -2)
(-.f64 (/.f64 1 (pow.f64 i 2)) (*.f64 1/2 (/.f64 1 (pow.f64 i 4))))
(-.f64 (/.f64 1 (*.f64 i i)) (/.f64 1/2 (pow.f64 i 4)))
(+.f64 (/.f64 1 (*.f64 i i)) (/.f64 -1/2 (pow.f64 i 4)))
(+.f64 (pow.f64 i -2) (/.f64 -1/2 (pow.f64 i 4)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 i 2)) (.f64 1/3 (/.f64 1 (pow.f64 i 6)))) (.f64 1/2 (/.f64 1 (pow.f64 i 4))))
(+.f64 (/.f64 1 (*.f64 i i)) (-.f64 (/.f64 1/3 (pow.f64 i 6)) (/.f64 1/2 (pow.f64 i 4))))
(+.f64 (/.f64 1/3 (pow.f64 i 6)) (+.f64 (/.f64 1 (*.f64 i i)) (/.f64 -1/2 (pow.f64 i 4))))
(+.f64 (pow.f64 i -2) (+.f64 (/.f64 1/3 (pow.f64 i 6)) (/.f64 -1/2 (pow.f64 i 4))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 i 2)) (.f64 1/3 (/.f64 1 (pow.f64 i 6)))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 i 8))) (*.f64 1/2 (/.f64 1 (pow.f64 i 4)))))
(-.f64 (+.f64 (/.f64 1 (*.f64 i i)) (/.f64 1/3 (pow.f64 i 6))) (+.f64 (/.f64 1/2 (pow.f64 i 4)) (/.f64 1/4 (pow.f64 i 8))))
(+.f64 (/.f64 1 (*.f64 i i)) (-.f64 (/.f64 1/3 (pow.f64 i 6)) (+.f64 (/.f64 1/2 (pow.f64 i 4)) (/.f64 1/4 (pow.f64 i 8)))))
(+.f64 (/.f64 1 (*.f64 i i)) (+.f64 (/.f64 1/3 (pow.f64 i 6)) (+.f64 (/.f64 -1/2 (pow.f64 i 4)) (/.f64 -1/4 (pow.f64 i 8)))))
(+.f64 (+.f64 (pow.f64 i -2) (/.f64 1/3 (pow.f64 i 6))) (+.f64 (/.f64 -1/2 (pow.f64 i 4)) (/.f64 -1/4 (pow.f64 i 8))))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(pow.f64 i -2)
(-.f64 (/.f64 1 (pow.f64 i 2)) (*.f64 1/2 (/.f64 1 (pow.f64 i 4))))
(-.f64 (/.f64 1 (*.f64 i i)) (/.f64 1/2 (pow.f64 i 4)))
(+.f64 (/.f64 1 (*.f64 i i)) (/.f64 -1/2 (pow.f64 i 4)))
(+.f64 (pow.f64 i -2) (/.f64 -1/2 (pow.f64 i 4)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 i 2)) (.f64 1/3 (/.f64 1 (pow.f64 i 6)))) (.f64 1/2 (/.f64 1 (pow.f64 i 4))))
(+.f64 (/.f64 1 (*.f64 i i)) (-.f64 (/.f64 1/3 (pow.f64 i 6)) (/.f64 1/2 (pow.f64 i 4))))
(+.f64 (/.f64 1/3 (pow.f64 i 6)) (+.f64 (/.f64 1 (*.f64 i i)) (/.f64 -1/2 (pow.f64 i 4))))
(+.f64 (pow.f64 i -2) (+.f64 (/.f64 1/3 (pow.f64 i 6)) (/.f64 -1/2 (pow.f64 i 4))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 i 2)) (.f64 1/3 (/.f64 1 (pow.f64 i 6)))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 i 8))) (*.f64 1/2 (/.f64 1 (pow.f64 i 4)))))
(-.f64 (+.f64 (/.f64 1 (*.f64 i i)) (/.f64 1/3 (pow.f64 i 6))) (+.f64 (/.f64 1/2 (pow.f64 i 4)) (/.f64 1/4 (pow.f64 i 8))))
(+.f64 (/.f64 1 (*.f64 i i)) (-.f64 (/.f64 1/3 (pow.f64 i 6)) (+.f64 (/.f64 1/2 (pow.f64 i 4)) (/.f64 1/4 (pow.f64 i 8)))))
(+.f64 (/.f64 1 (*.f64 i i)) (+.f64 (/.f64 1/3 (pow.f64 i 6)) (+.f64 (/.f64 -1/2 (pow.f64 i 4)) (/.f64 -1/4 (pow.f64 i 8)))))
(+.f64 (+.f64 (pow.f64 i -2) (/.f64 1/3 (pow.f64 i 6))) (+.f64 (/.f64 -1/2 (pow.f64 i 4)) (/.f64 -1/4 (pow.f64 i 8))))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(pow.f64 i -2)
(+.f64 1 (/.f64 1 (pow.f64 i 2)))
(+.f64 1 (/.f64 1 (*.f64 i i)))
(+.f64 1 (pow.f64 i -2))
(+.f64 1 (/.f64 1 (pow.f64 i 2)))
(+.f64 1 (/.f64 1 (*.f64 i i)))
(+.f64 1 (pow.f64 i -2))
(+.f64 1 (/.f64 1 (pow.f64 i 2)))
(+.f64 1 (/.f64 1 (*.f64 i i)))
(+.f64 1 (pow.f64 i -2))
1
(+.f64 1 (/.f64 1 (pow.f64 i 2)))
(+.f64 1 (/.f64 1 (*.f64 i i)))
(+.f64 1 (pow.f64 i -2))
(+.f64 1 (/.f64 1 (pow.f64 i 2)))
(+.f64 1 (/.f64 1 (*.f64 i i)))
(+.f64 1 (pow.f64 i -2))
(+.f64 1 (/.f64 1 (pow.f64 i 2)))
(+.f64 1 (/.f64 1 (*.f64 i i)))
(+.f64 1 (pow.f64 i -2))
1
(+.f64 1 (/.f64 1 (pow.f64 i 2)))
(+.f64 1 (/.f64 1 (*.f64 i i)))
(+.f64 1 (pow.f64 i -2))
(+.f64 1 (/.f64 1 (pow.f64 i 2)))
(+.f64 1 (/.f64 1 (*.f64 i i)))
(+.f64 1 (pow.f64 i -2))
(+.f64 1 (/.f64 1 (pow.f64 i 2)))
(+.f64 1 (/.f64 1 (*.f64 i i)))
(+.f64 1 (pow.f64 i -2))
(-.f64 (pow.f64 i -2) 1)
(+.f64 (pow.f64 i -2) -1)
(pow.f64 i -2)
(/.f64 1 (*.f64 i i))
(pow.f64 i -2)
(/.f64 1 (*.f64 i i))
(pow.f64 i -2)
(/.f64 1 (*.f64 i i))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(pow.f64 i -2)
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(pow.f64 i -2)
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(pow.f64 i -2)
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(pow.f64 i -2)
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(pow.f64 i -2)
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(pow.f64 i -2)
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(pow.f64 i -2)
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(pow.f64 i -2)
(/.f64 1/4 (-.f64 5 (pow.f64 i -2)))
(+.f64 (.f64 1/4 (/.f64 1 (pow.f64 (-.f64 5 (pow.f64 i -2)) 2))) (.f64 1/4 (/.f64 1 (-.f64 5 (pow.f64 i -2)))))
(+.f64 (/.f64 1/4 (pow.f64 (-.f64 5 (pow.f64 i -2)) 2)) (/.f64 1/4 (-.f64 5 (pow.f64 i -2))))
(+.f64 (.f64 1/4 (/.f64 1 (pow.f64 (-.f64 5 (pow.f64 i -2)) 2))) (+.f64 (.f64 1/4 (/.f64 1 (-.f64 5 (pow.f64 i -2)))) (*.f64 1/4 (/.f64 1 (pow.f64 (-.f64 5 (pow.f64 i -2)) 3)))))
(+.f64 (/.f64 1/4 (pow.f64 (-.f64 5 (pow.f64 i -2)) 2)) (+.f64 (/.f64 1/4 (-.f64 5 (pow.f64 i -2))) (/.f64 1/4 (pow.f64 (-.f64 5 (pow.f64 i -2)) 3))))
(+.f64 (.f64 1/4 (/.f64 1 (pow.f64 (-.f64 5 (pow.f64 i -2)) 2))) (+.f64 (.f64 1/4 (/.f64 1 (-.f64 5 (pow.f64 i -2)))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 (-.f64 5 (pow.f64 i -2)) 3))) (.f64 1/4 (/.f64 1 (pow.f64 (-.f64 5 (pow.f64 i -2)) 4))))))
(+.f64 (+.f64 (/.f64 1/4 (pow.f64 (-.f64 5 (pow.f64 i -2)) 2)) (/.f64 1/4 (-.f64 5 (pow.f64 i -2)))) (+.f64 (/.f64 1/4 (pow.f64 (-.f64 5 (pow.f64 i -2)) 3)) (/.f64 1/4 (pow.f64 (-.f64 5 (pow.f64 i -2)) 4))))
(+.f64 (/.f64 1/4 (pow.f64 (-.f64 5 (pow.f64 i -2)) 2)) (+.f64 (/.f64 1/4 (-.f64 5 (pow.f64 i -2))) (+.f64 (/.f64 1/4 (pow.f64 (-.f64 5 (pow.f64 i -2)) 3)) (/.f64 1/4 (pow.f64 (-.f64 5 (pow.f64 i -2)) 4)))))
(+.f64 (/.f64 1/4 (pow.f64 (-.f64 5 (pow.f64 i -2)) 2)) (+.f64 (/.f64 1/4 (pow.f64 (-.f64 5 (pow.f64 i -2)) 3)) (+.f64 (/.f64 1/4 (-.f64 5 (pow.f64 i -2))) (/.f64 1/4 (pow.f64 (-.f64 5 (pow.f64 i -2)) 4)))))
(+.f64 (/.f64 1/4 (pow.f64 (-.f64 5 (pow.f64 i -2)) 2)) (+.f64 (/.f64 1/4 (-.f64 5 (pow.f64 i -2))) (*.f64 (/.f64 1 (pow.f64 (-.f64 5 (pow.f64 i -2)) 3)) (+.f64 1/4 (/.f64 1/4 (-.f64 5 (pow.f64 i -2)))))))
1/16
(+.f64 1/16 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))
(+.f64 1/16 (/.f64 1/64 (*.f64 i i)))
(fma.f64 (pow.f64 i -2) 1/64 1/16)
(+.f64 (.f64 1/256 (/.f64 1 (pow.f64 i 4))) (+.f64 1/16 (.f64 1/64 (/.f64 1 (pow.f64 i 2)))))
(+.f64 (+.f64 1/16 (/.f64 1/64 (*.f64 i i))) (/.f64 1/256 (pow.f64 i 4)))
(+.f64 (/.f64 1/64 (*.f64 i i)) (+.f64 1/16 (/.f64 1/256 (pow.f64 i 4))))
(+.f64 1/16 (fma.f64 (pow.f64 i -2) 1/64 (/.f64 1/256 (pow.f64 i 4))))
(+.f64 (.f64 1/256 (/.f64 1 (pow.f64 i 4))) (+.f64 1/16 (+.f64 (.f64 1/1024 (/.f64 1 (pow.f64 i 6))) (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))))
(+.f64 (/.f64 1/256 (pow.f64 i 4)) (+.f64 1/16 (+.f64 (/.f64 1/64 (*.f64 i i)) (/.f64 1/1024 (pow.f64 i 6)))))
(+.f64 (/.f64 1/256 (pow.f64 i 4)) (+.f64 (+.f64 1/16 (/.f64 1/64 (*.f64 i i))) (/.f64 1/1024 (pow.f64 i 6))))
(+.f64 (/.f64 1/64 (*.f64 i i)) (+.f64 (/.f64 1/1024 (pow.f64 i 6)) (+.f64 1/16 (/.f64 1/256 (pow.f64 i 4)))))
(+.f64 1/16 (+.f64 (/.f64 1/256 (pow.f64 i 4)) (fma.f64 (pow.f64 i -2) 1/64 (/.f64 1/1024 (pow.f64 i 6)))))
1/16
(+.f64 1/16 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))
(+.f64 1/16 (/.f64 1/64 (*.f64 i i)))
(fma.f64 (pow.f64 i -2) 1/64 1/16)
(+.f64 (.f64 1/256 (/.f64 1 (pow.f64 i 4))) (+.f64 1/16 (.f64 1/64 (/.f64 1 (pow.f64 i 2)))))
(+.f64 (+.f64 1/16 (/.f64 1/64 (*.f64 i i))) (/.f64 1/256 (pow.f64 i 4)))
(+.f64 (/.f64 1/64 (*.f64 i i)) (+.f64 1/16 (/.f64 1/256 (pow.f64 i 4))))
(+.f64 1/16 (fma.f64 (pow.f64 i -2) 1/64 (/.f64 1/256 (pow.f64 i 4))))
(+.f64 (.f64 1/256 (/.f64 1 (pow.f64 i 4))) (+.f64 1/16 (+.f64 (.f64 1/1024 (/.f64 1 (pow.f64 i 6))) (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))))
(+.f64 (/.f64 1/256 (pow.f64 i 4)) (+.f64 1/16 (+.f64 (/.f64 1/64 (*.f64 i i)) (/.f64 1/1024 (pow.f64 i 6)))))
(+.f64 (/.f64 1/256 (pow.f64 i 4)) (+.f64 (+.f64 1/16 (/.f64 1/64 (*.f64 i i))) (/.f64 1/1024 (pow.f64 i 6))))
(+.f64 (/.f64 1/64 (*.f64 i i)) (+.f64 (/.f64 1/1024 (pow.f64 i 6)) (+.f64 1/16 (/.f64 1/256 (pow.f64 i 4)))))
(+.f64 1/16 (+.f64 (/.f64 1/256 (pow.f64 i 4)) (fma.f64 (pow.f64 i -2) 1/64 (/.f64 1/1024 (pow.f64 i 6)))))

prune143.0ms (7.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	174	2	176

Error

Counts

176 → 2

Alt Table

Status	Error	Program
▶	29.8b	(.f64 i (.f64 i -1/4))
✓	1.9b	(/.f64 1/4 (-.f64 4 (-.f64 (exp.f64 (log1p.f64 (pow.f64 i -2))) 1)))

Compiler

Compiled 2820 to 2503 computations (11.2% saved)

localize4.0ms (0.2%)

prune1.0ms (0.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Error

Counts

2 → 2

Alt Table

Status	Error	Program
✓	29.8b	(.f64 i (.f64 i -1/4))
✓	1.9b	(/.f64 1/4 (-.f64 4 (-.f64 (exp.f64 (log1p.f64 (pow.f64 i -2))) 1)))

Compiler

Compiled 18 to 15 computations (16.7% saved)

regimes55.0ms (2.9%)

Accuracy

Total 0.3b remaining (91.7%)

Threshold costs 0.3b (91.7%)

Counts

48 → 1

Compiler

Compiled 508 to 421 computations (17.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	13	13
2	19	13
3	21	13
4	22	13

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

Outputs
(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))

end65.0ms (3.5%)

Stop Event

1×

done

Compiler

Compiled 38 to 31 computations (18.4% saved)

Details

analyze9.0ms (0.5%)

sample1.1s (59.1%)

preprocess31.0ms (1.7%)

simplify22.0ms (1.2%)

prune4.0ms (0.2%)

localize5.0ms (0.3%)

series3.0ms (0.2%)

rewrite47.0ms (2.5%)

simplify27.0ms (1.5%)

prune135.0ms (7.3%)

localize8.0ms (0.4%)

series101.0ms (5.4%)

rewrite55.0ms (3%)

simplify39.0ms (2.1%)

prune143.0ms (7.7%)

localize4.0ms (0.2%)

prune1.0ms (0.1%)

regimes55.0ms (2.9%)

simplify2.0ms (0.1%)

end65.0ms (3.5%)

Profiling