Details

analyze8.0ms (0.2%)

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

Compiler

Compiled 29 to 19 computations (34.5% saved)

sample2.0s (50.7%)

Results

1.9s

8256×

body

256

valid

preprocess63.0ms (1.6%)

Algorithm

2×	egg-herbie

Rules

579×	`associate-/r*_binary64`
516×	`cancel-sign-sub-inv_binary64`
496×	`distribute-rgt-in_binary64`
478×	`distribute-lft-in_binary64`
434×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	40	26
2	200	17
3	1341	13
4	3774	13
5	6220	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 i (.f64 i (.f64 i i))) (.f64 (+.f64 (.f64 4 (.f64 i i)) -1) (.f64 4 (.f64 i i))))
(.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))))
(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))

Compiler

Compiled 27 to 18 computations (33.3% saved)

simplify47.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

579×	`associate-/r*_binary64`
516×	`cancel-sign-sub-inv_binary64`
496×	`distribute-rgt-in_binary64`
478×	`distribute-lft-in_binary64`
434×	`associate-/r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	40	26
2	200	17
3	1341	13
4	3774	13
5	6220	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 i (.f64 i (.f64 i i))) (.f64 (+.f64 (.f64 4 (.f64 i i)) -1) (.f64 4 (.f64 i i))))
(.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))))
(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))

eval1.0ms (0%)

Compiler: Compiled 35 to 23 computations (34.3% saved)

prune1.0ms (0%)

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

Click to see full alt table

Status	Error	Program
▶	43.6b	(/.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))
▶	0.3b	(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))

Compiler

Compiled 36 to 25 computations (30.6% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))
✓	1.0b	(/.f64 -1 (*.f64 i i))

Compiler

Compiled 29 to 17 computations (41.4% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite72.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

521×	`unpow-prod-down_binary64`
386×	`log-prod_binary64`
305×	`exp-prod_binary64`
256×	`prod-exp_binary64`
243×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	203	17
2	2514	17

Stop Event

1×	node limit

Counts

2 → 99

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (neg.f64 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (neg.f64 (pow.f64 i -2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (neg.f64 (pow.f64 i -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (neg.f64 (pow.f64 i -2))))) (log.f64 (sqrt.f64 (exp.f64 (neg.f64 (pow.f64 i -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (neg.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 (neg.f64 (pow.f64 i -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (neg.f64 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (neg.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 (neg.f64 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 -1) i) (/.f64 (sqrt.f64 -1) i))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 i -2) -1)))) (#(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) (pow.f64 (/.f64 1 i) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 i) (/.f64 -1 i))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (.f64 (cbrt.f64 i) i)) (pow.f64 (neg.f64 (pow.f64 (cbrt.f64 i) 2)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/3) (neg.f64 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (cbrt.f64 (neg.f64 (pow.f64 i -2)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (neg.f64 (pow.f64 i -2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 -1 1/3) (pow.f64 i -2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (neg.f64 (pow.f64 i -2)))) 2) 3) (cbrt.f64 (neg.f64 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 i -2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 i (neg.f64 i))) 2) -1) (cbrt.f64 (neg.f64 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (neg.f64 (.f64 (cbrt.f64 i) i)) -1) (pow.f64 (pow.f64 (cbrt.f64 i) 2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (pow.f64 i -4) -1) 1/3) (cbrt.f64 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (pow.f64 i -4) (cbrt.f64 (pow.f64 i -4))) 1/3) (cbrt.f64 (cbrt.f64 (neg.f64 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (neg.f64 (pow.f64 i -2)) 5/2) 1/3) (cbrt.f64 (/.f64 (sqrt.f64 -1) i)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (pow.f64 i -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 i -4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (neg.f64 (pow.f64 i -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 -1) i) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 i (neg.f64 i)) -1)))) (#(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 (exp.f64 1) (log.f64 (neg.f64 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (neg.f64 (pow.f64 i -2)))) 2)) (cbrt.f64 (log.f64 (neg.f64 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (neg.f64 (pow.f64 i -2))))) (sqrt.f64 (log.f64 (neg.f64 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (pow.f64 i -2))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 i -4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (neg.f64 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (neg.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 (neg.f64 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (neg.f64 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (neg.f64 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (neg.f64 (pow.f64 i -2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (neg.f64 (pow.f64 i -2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 -1) i)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 i (neg.f64 i))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 -1 (pow.f64 i -6))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (neg.f64 (pow.f64 i -2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (neg.f64 (pow.f64 i -2))) 3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (/.f64 -1 i)) (*.f64 (log.f64 i) 1)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/4 (/.f64 1 (fma.f64 -1 (pow.f64 i -2) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))) (pow.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))) 2) (cbrt.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 (sqrt.f64 (fma.f64 -1 (pow.f64 i -2) 4))) (/.f64 1/2 (sqrt.f64 (fma.f64 -1 (pow.f64 i -2) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1/4 (/.f64 1 (neg.f64 (fma.f64 -1 (pow.f64 i -2) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1/4 (pow.f64 (/.f64 1 (neg.f64 (fma.f64 -1 (pow.f64 i -2) 4))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (fma.f64 -1 (pow.f64 i -2) 4)) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -6) 64)) (-.f64 (+.f64 16 (pow.f64 i -4)) (.f64 -4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4))) (+.f64 4 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/3) (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -6) 64)) 1) (-.f64 (+.f64 16 (pow.f64 i -4)) (.f64 -4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4))) 1) (+.f64 4 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (pow.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (.f64 1/16 (pow.f64 (fma.f64 -1 (pow.f64 i -2) 4) -2)) 1/4) 1/3) (cbrt.f64 (/.f64 1 (fma.f64 -1 (pow.f64 i -2) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)) (cbrt.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)) 5/2) 1/3) (cbrt.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 -1 (pow.f64 i -2) 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 1/4) 3) (/.f64 1 (fma.f64 -1 (pow.f64 i -2) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))) 2) 3) (cbrt.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 -1 (pow.f64 i -2) 4) 4)) 2) -1) (cbrt.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/16 (pow.f64 (fma.f64 -1 (pow.f64 i -2) 4) -2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 -1 (pow.f64 i -2) 4))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (fma.f64 -1 (pow.f64 i -2) 4) 4) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (.f64 (fma.f64 -1 (pow.f64 i -2) 4) 4) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))) 2)) (cbrt.f64 (log.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))))) (sqrt.f64 (log.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 1/16 (pow.f64 (fma.f64 -1 (pow.f64 i -2) 4) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 -1 (pow.f64 i -2) 4)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (fma.f64 -1 (pow.f64 i -2) 4) 4)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (*.f64 (log.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))) 1) 1))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (neg.f64 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (neg.f64 (pow.f64 i -2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (neg.f64 (pow.f64 i -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (neg.f64 (pow.f64 i -2))))) (log.f64 (sqrt.f64 (exp.f64 (neg.f64 (pow.f64 i -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (neg.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 (neg.f64 (pow.f64 i -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (neg.f64 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (neg.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 (neg.f64 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 -1) i) (/.f64 (sqrt.f64 -1) i))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 i -2) -1)))) (#(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) (pow.f64 (/.f64 1 i) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 i) (/.f64 -1 i))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 (cbrt.f64 i) i)) (pow.f64 (neg.f64 (pow.f64 (cbrt.f64 i) 2)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (neg.f64 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (neg.f64 (pow.f64 i -2)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (neg.f64 (pow.f64 i -2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 -1 1/3) (pow.f64 i -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (neg.f64 (pow.f64 i -2)))) 2) 3) (cbrt.f64 (neg.f64 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 i -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 i (neg.f64 i))) 2) -1) (cbrt.f64 (neg.f64 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (neg.f64 (*.f64 (cbrt.f64 i) i)) -1) (pow.f64 (pow.f64 (cbrt.f64 i) 2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 i -4) -1) 1/3) (cbrt.f64 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 i -4) (cbrt.f64 (pow.f64 i -4))) 1/3) (cbrt.f64 (cbrt.f64 (neg.f64 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (neg.f64 (pow.f64 i -2)) 5/2) 1/3) (cbrt.f64 (/.f64 (sqrt.f64 -1) i)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (pow.f64 i -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 i -4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (neg.f64 (pow.f64 i -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 -1) i) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 i (neg.f64 i)) -1)))) (#(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 (exp.f64 1) (log.f64 (neg.f64 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (neg.f64 (pow.f64 i -2)))) 2)) (cbrt.f64 (log.f64 (neg.f64 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (neg.f64 (pow.f64 i -2))))) (sqrt.f64 (log.f64 (neg.f64 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (pow.f64 i -2))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 i -4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (neg.f64 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (neg.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 (neg.f64 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (neg.f64 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (neg.f64 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (neg.f64 (pow.f64 i -2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (neg.f64 (pow.f64 i -2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 -1) i)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 i (neg.f64 i))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 -1 (pow.f64 i -6))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (neg.f64 (pow.f64 i -2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (neg.f64 (pow.f64 i -2))) 3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (/.f64 -1 i)) (*.f64 (log.f64 i) 1)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (/.f64 1 (fma.f64 -1 (pow.f64 i -2) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))) (pow.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))) 2) (cbrt.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 -1 (pow.f64 i -2) 4))) (/.f64 1/2 (sqrt.f64 (fma.f64 -1 (pow.f64 i -2) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/4 (/.f64 1 (neg.f64 (fma.f64 -1 (pow.f64 i -2) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/4 (pow.f64 (/.f64 1 (neg.f64 (fma.f64 -1 (pow.f64 i -2) 4))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 -1 (pow.f64 i -2) 4)) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -6) 64)) (-.f64 (+.f64 16 (pow.f64 i -4)) (*.f64 -4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4))) (+.f64 4 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -6) 64)) 1) (-.f64 (+.f64 16 (pow.f64 i -4)) (*.f64 -4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4))) 1) (+.f64 4 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (*.f64 1/16 (pow.f64 (fma.f64 -1 (pow.f64 i -2) 4) -2)) 1/4) 1/3) (cbrt.f64 (/.f64 1 (fma.f64 -1 (pow.f64 i -2) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)) (cbrt.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)) 5/2) 1/3) (cbrt.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 -1 (pow.f64 i -2) 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 1/4) 3) (/.f64 1 (fma.f64 -1 (pow.f64 i -2) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))) 2) 3) (cbrt.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (fma.f64 -1 (pow.f64 i -2) 4) 4)) 2) -1) (cbrt.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/16 (pow.f64 (fma.f64 -1 (pow.f64 i -2) 4) -2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 -1 (pow.f64 i -2) 4))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (fma.f64 -1 (pow.f64 i -2) 4) 4) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 (fma.f64 -1 (pow.f64 i -2) 4) 4) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))) 2)) (cbrt.f64 (log.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))))) (sqrt.f64 (log.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/16 (pow.f64 (fma.f64 -1 (pow.f64 i -2) 4) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 1/2 (sqrt.f64 (fma.f64 -1 (pow.f64 i -2) 4)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (fma.f64 -1 (pow.f64 i -2) 4) 4)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 1/4 (fma.f64 -1 (pow.f64 i -2) 4))) 1) 1))))))

simplify46.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

691×	`cancel-sign-sub-inv_binary64`
657×	`fma-neg_binary64`
472×	`distribute-lft-out_binary64`
413×	`unswap-sqr_binary64`
410×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	39	270
1	91	267
2	214	267
3	643	267
4	3200	267

Stop Event

1×	node limit

Counts

123 → 116

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

localize25.0ms (0.7%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 i i) (*.f64 i i))
✓	13.6b	(/.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))
✓	40.1b	(/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i)))

New

Error

Program

✓

0.2b

(*.f64 (*.f64 i i) (*.f64 i i))

✓

13.6b

(/.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))

✓

40.1b

(/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i)))

Compiler

Compiled 73 to 39 computations (46.6% saved)

series4.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	i	@	0	(/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i)))
1.0ms	i	@	inf	(/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i)))
0.0ms	i	@	inf	(.f64 (.f64 i i) (*.f64 i i))
0.0ms	i	@	0	(.f64 (.f64 i i) (*.f64 i i))
0.0ms	i	@	0	(/.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))

rewrite86.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

775×	`log-prod_binary64`
508×	`prod-diff_binary64`
288×	`fma-def_binary64`
260×	`log-div_binary64`
217×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	51
1	255	40
2	3965	40

Stop Event

1×	node limit

Counts

3 → 131

Calls

Call 1

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

Inputs

(/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i)))

(/.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 i i) (*.f64 i i))

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

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

simplify58.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

691×	`cancel-sign-sub-inv_binary64`
657×	`fma-neg_binary64`
473×	`distribute-lft-out_binary64`
413×	`unswap-sqr_binary64`
410×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	318
1	93	315
2	218	315
3	652	315
4	3251	315

Stop Event

1×	node limit

Counts

167 → 148

Calls

Call 1

Inputs
(*.f64 1/4 (pow.f64 i 2))
(*.f64 1/4 (pow.f64 i 2))
(*.f64 1/4 (pow.f64 i 2))
(*.f64 1/4 (pow.f64 i 2))
(*.f64 1/4 (pow.f64 i 2))
(*.f64 1/4 (pow.f64 i 2))
(*.f64 1/4 (pow.f64 i 2))
(*.f64 1/4 (pow.f64 i 2))
(*.f64 1/4 (pow.f64 i 2))
(*.f64 1/4 (pow.f64 i 2))
(*.f64 1/4 (pow.f64 i 2))
(*.f64 1/4 (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))))))
(pow.f64 i 4)
(pow.f64 i 4)
(pow.f64 i 4)
(pow.f64 i 4)
(pow.f64 i 4)
(pow.f64 i 4)
(pow.f64 i 4)
(pow.f64 i 4)
(pow.f64 i 4)
(pow.f64 i 4)
(pow.f64 i 4)
(pow.f64 i 4)

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

eval112.0ms (2.9%)

Compiler: Compiled 5022 to 3769 computations (25% saved)

prune34.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	259	5	264
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	260	6	266

Error

Counts

266 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	32.2b	(.f64 (.f64 i i) (-.f64 -1/4 (*.f64 i i)))
▶	32.5b	(.f64 i (.f64 i -1/4))
▶	31.6b	(+.f64 1/16 (/.f64 (/.f64 1/64 i) i))
▶	0.4b	(/.f64 1/4 (+.f64 4 (*.f64 (/.f64 1 i) (/.f64 -1 i))))
✓	0.3b	(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))
	31.4b	1/16

Compiler

Compiled 48 to 35 computations (27.1% saved)

localize6.0ms (0.1%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 i i) (-.f64 -1/4 (*.f64 i i)))

Compiler

Compiled 20 to 8 computations (60% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite54.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

711×	`pow1_binary64`
669×	`add-log-exp_binary64`
669×	`log1p-expm1-u_binary64`
669×	`expm1-log1p-u_binary64`
656×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	137	13
2	1814	13

Stop Event

1×	node limit

Counts

1 → 19

Calls

Call 1

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

Outputs

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

simplify85.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

777×	`fma-neg_binary64`
648×	`distribute-rgt-neg-in_binary64`
529×	`distribute-lft-neg-in_binary64`
514×	`fma-def_binary64`
379×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	145
1	23	136
2	51	136
3	146	136
4	503	136
5	1930	136
6	4416	136
7	6515	136
8	7548	136

Stop Event

1×	node limit

Counts

31 → 25

Calls

Call 1

Inputs
(*.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 -1/4 (pow.f64 i 2)))
(+.f64 (.f64 -1 (pow.f64 i 4)) (.f64 -1/4 (pow.f64 i 2)))
(*.f64 -1 (pow.f64 i 4))
(+.f64 (.f64 -1 (pow.f64 i 4)) (.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 -1/4 (pow.f64 i 2)))
(*.f64 -1 (pow.f64 i 4))
(+.f64 (.f64 -1 (pow.f64 i 4)) (.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 -1/4 (pow.f64 i 2)))

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

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 1/64 i) i)

Compiler

Compiled 19 to 13 computations (31.6% saved)

series3.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	i	@	inf	(/.f64 (/.f64 1/64 i) i)
1.0ms	i	@	0	(/.f64 (/.f64 1/64 i) i)
0.0ms	i	@	-inf	(/.f64 (/.f64 1/64 i) i)

rewrite52.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

578×	`pow1_binary64`
546×	`add-log-exp_binary64`
546×	`log1p-expm1-u_binary64`
546×	`expm1-log1p-u_binary64`
536×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	113	7
2	1481	7

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

Inputs
(/.f64 (/.f64 1/64 i) i)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 1/64 (*.f64 i i))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/64 (*.f64 (/.f64 1 i) (/.f64 1 i)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/64 (/.f64 (/.f64 1 i) i))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/64 (/.f64 1 (*.f64 i i)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/64 i) (/.f64 1 i))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/64 (*.f64 i i)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1/64 (*.f64 i i)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/4 (pow.f64 (cbrt.f64 i) 2)) (pow.f64 (/.f64 1/4 (pow.f64 (cbrt.f64 i) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 1/4 (pow.f64 (cbrt.f64 i) 2)) 2) (/.f64 1/4 (pow.f64 (cbrt.f64 i) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 1/4 (cbrt.f64 i)) 2) (*.f64 (/.f64 1/4 (cbrt.f64 i)) (/.f64 1 i)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/8 i) (/.f64 1/8 i))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 1/64 i)) (*.f64 (sqrt.f64 (/.f64 1/64 i)) (/.f64 1 i)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1/64 i) (/.f64 1 (neg.f64 i)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 i) (/.f64 1/64 i))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (/.f64 1/4 (cbrt.f64 i)) 2) 1) (/.f64 (/.f64 1/4 (cbrt.f64 i)) i))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (/.f64 1/64 i)) 1) (/.f64 (sqrt.f64 (/.f64 1/64 i)) i))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/64 (pow.f64 (cbrt.f64 i) 2)) (/.f64 (/.f64 1 i) (cbrt.f64 i)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 i) 2)) (/.f64 (/.f64 1/64 i) (cbrt.f64 i)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (/.f64 1/4 (cbrt.f64 i)) 2) (pow.f64 (cbrt.f64 i) 2)) (/.f64 1/4 (pow.f64 (cbrt.f64 i) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (/.f64 1/64 i)) (pow.f64 (cbrt.f64 i) 2)) (/.f64 (sqrt.f64 (/.f64 1/64 i)) (cbrt.f64 i)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/64 (sqrt.f64 i)) (/.f64 (/.f64 1 i) (sqrt.f64 i)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 i)) (/.f64 (/.f64 1/64 i) (sqrt.f64 i)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (/.f64 1/4 (cbrt.f64 i)) 2) (sqrt.f64 i)) (/.f64 (/.f64 1/4 (cbrt.f64 i)) (sqrt.f64 i)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/64 (*.f64 i i)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1/64 (*.f64 i i)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/4 (pow.f64 (cbrt.f64 i) 2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/8 i) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 i (*.f64 i 64)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (/.f64 1/64 i) (neg.f64 i)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 1/64 (*.f64 i i)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/64 (*.f64 i i))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1/64 (*.f64 i i)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/64 (*.f64 i i))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/64 (*.f64 i i))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/64 (*.f64 i i))))))))

simplify180.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

1140×	`associate-/r*_binary64`
1082×	`sqr-pow_binary64`
560×	`cube-prod_binary64`
554×	`fabs-mul_binary64`
523×	`pow-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	11	84
2	20	84
3	35	84
4	75	84
5	224	84
6	834	84
7	2042	84
8	2208	84
9	2392	84
10	2600	84
11	2899	84
12	3292	84
13	3771	84
14	4337	84
15	5023	84
16	5856	84
17	6246	84
18	6538	84
19	6816	84
20	6890	84
21	6926	84

Stop Event

1×	node limit

Counts

47 → 37

Calls

Call 1

Inputs
(/.f64 1/64 (pow.f64 i 2))
(/.f64 1/64 (pow.f64 i 2))
(/.f64 1/64 (pow.f64 i 2))
(/.f64 1/64 (pow.f64 i 2))
(/.f64 1/64 (pow.f64 i 2))
(/.f64 1/64 (pow.f64 i 2))
(/.f64 1/64 (pow.f64 i 2))
(/.f64 1/64 (pow.f64 i 2))
(/.f64 1/64 (pow.f64 i 2))
(/.f64 1/64 (pow.f64 i 2))
(/.f64 1/64 (pow.f64 i 2))
(/.f64 1/64 (pow.f64 i 2))

Outputs
(/.f64 1/64 (pow.f64 i 2))
(/.f64 1/64 (*.f64 i i))
(/.f64 1/64 (pow.f64 i 2))
(/.f64 1/64 (*.f64 i i))
(/.f64 1/64 (pow.f64 i 2))
(/.f64 1/64 (*.f64 i i))
(/.f64 1/64 (pow.f64 i 2))
(/.f64 1/64 (*.f64 i i))
(/.f64 1/64 (pow.f64 i 2))
(/.f64 1/64 (*.f64 i i))
(/.f64 1/64 (pow.f64 i 2))
(/.f64 1/64 (*.f64 i i))
(/.f64 1/64 (pow.f64 i 2))
(/.f64 1/64 (*.f64 i i))
(/.f64 1/64 (pow.f64 i 2))
(/.f64 1/64 (*.f64 i i))
(/.f64 1/64 (pow.f64 i 2))
(/.f64 1/64 (*.f64 i i))
(/.f64 1/64 (pow.f64 i 2))
(/.f64 1/64 (*.f64 i i))
(/.f64 1/64 (pow.f64 i 2))
(/.f64 1/64 (*.f64 i i))
(/.f64 1/64 (pow.f64 i 2))
(/.f64 1/64 (*.f64 i i))

localize21.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 1 i) (/.f64 -1 i))
✓	0.3b	(/.f64 1/4 (+.f64 4 (*.f64 (/.f64 1 i) (/.f64 -1 i))))

Compiler

Compiled 39 to 30 computations (23.1% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	i	@	0	(/.f64 1/4 (+.f64 4 (*.f64 (/.f64 1 i) (/.f64 -1 i))))
0.0ms	i	@	0	(*.f64 (/.f64 1 i) (/.f64 -1 i))
0.0ms	i	@	-inf	(/.f64 1/4 (+.f64 4 (*.f64 (/.f64 1 i) (/.f64 -1 i))))
0.0ms	i	@	inf	(/.f64 1/4 (+.f64 4 (*.f64 (/.f64 1 i) (/.f64 -1 i))))
0.0ms	i	@	inf	(*.f64 (/.f64 1 i) (/.f64 -1 i))

rewrite71.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

967×	`pow1_binary64`
911×	`add-log-exp_binary64`
909×	`log1p-expm1-u_binary64`
909×	`expm1-log1p-u_binary64`
110×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	242	14
2	3065	14

Stop Event

1×	node limit

Counts

2 → 56

Calls

Call 1

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

Outputs

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

simplify44.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

691×	`cancel-sign-sub-inv_binary64`
657×	`fma-neg_binary64`
472×	`distribute-lft-out_binary64`
413×	`unswap-sqr_binary64`
410×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	39	270
1	91	267
2	214	267
3	648	267
4	3214	267

Stop Event

1×	node limit

Counts

80 → 72

Calls

Call 1

Inputs
(*.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))))))
(/.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))

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

eval36.0ms (0.9%)

Compiler: Compiled 1532 to 1132 computations (26.1% saved)

prune29.0ms (0.7%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	1	0	1
Picked	1	0	1
Done	0	4	4
Total	134	6	140

Error

Counts

140 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	32.2b	(.f64 (.f64 i i) (-.f64 -1/4 (*.f64 i i)))
✓	32.5b	(.f64 i (.f64 i -1/4))
✓	31.6b	(+.f64 1/16 (/.f64 (/.f64 1/64 i) i))
▶	0.3b	(/.f64 1/4 (+.f64 4 (/.f64 (/.f64 1 i) (neg.f64 i))))
✓	0.3b	(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))
	31.4b	1/16

Compiler

Compiled 47 to 34 computations (27.7% saved)

localize13.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 1 i) (neg.f64 i))
✓	0.3b	(/.f64 1/4 (+.f64 4 (/.f64 (/.f64 1 i) (neg.f64 i))))

Compiler

Compiled 34 to 22 computations (35.3% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	i	@	0	(/.f64 1/4 (+.f64 4 (/.f64 (/.f64 1 i) (neg.f64 i))))
0.0ms	i	@	-inf	(/.f64 1/4 (+.f64 4 (/.f64 (/.f64 1 i) (neg.f64 i))))
0.0ms	i	@	inf	(/.f64 1/4 (+.f64 4 (/.f64 (/.f64 1 i) (neg.f64 i))))
0.0ms	i	@	-inf	(/.f64 (/.f64 1 i) (neg.f64 i))
0.0ms	i	@	0	(/.f64 (/.f64 1 i) (neg.f64 i))

rewrite58.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

942×	`pow1_binary64`
890×	`add-log-exp_binary64`
889×	`log1p-expm1-u_binary64`
889×	`expm1-log1p-u_binary64`
107×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	228	14
2	3130	14

Stop Event

1×	node limit

Counts

2 → 57

Calls

Call 1

Inputs
(/.f64 1/4 (+.f64 4 (/.f64 (/.f64 1 i) (neg.f64 i))))
(/.f64 (/.f64 1 i) (neg.f64 i))

Outputs

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

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

simplify43.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

691×	`cancel-sign-sub-inv_binary64`
657×	`fma-neg_binary64`
472×	`distribute-lft-out_binary64`
413×	`unswap-sqr_binary64`
410×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	39	270
1	91	267
2	214	267
3	648	267
4	3214	267

Stop Event

1×	node limit

Counts

81 → 74

Calls

Call 1

Inputs
(*.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))))))
(/.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))

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

eval22.0ms (0.6%)

Compiler: Compiled 898 to 742 computations (17.4% saved)

prune11.0ms (0.3%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	1	1
Picked	0	1	1
Done	0	4	4
Total	74	6	80

Error

Counts

80 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	32.2b	(.f64 (.f64 i i) (-.f64 -1/4 (*.f64 i i)))
✓	32.5b	(.f64 i (.f64 i -1/4))
✓	31.6b	(+.f64 1/16 (/.f64 (/.f64 1/64 i) i))
✓	0.3b	(/.f64 1/4 (+.f64 4 (/.f64 (/.f64 1 i) (neg.f64 i))))
✓	0.3b	(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))
	31.4b	1/16

Compiler

Compiled 47 to 34 computations (27.7% saved)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune3.0ms (0.1%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	5	5
Total	6	6

Error

Counts

6 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	32.2b	(.f64 (.f64 i i) (-.f64 -1/4 (*.f64 i i)))
✓	32.5b	(.f64 i (.f64 i -1/4))
✓	31.6b	(+.f64 1/16 (/.f64 (/.f64 1/64 i) i))
✓	0.3b	(/.f64 1/4 (+.f64 4 (/.f64 (/.f64 1 i) (neg.f64 i))))
✓	0.3b	(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))
	31.4b	1/16

Compiler

Compiled 47 to 34 computations (27.7% saved)

regimes56.0ms (1.5%)

Counts

9 → 1

Calls

Call 1

Inputs
1/16
1/16
(.f64 i (.f64 i -1/4))
(+.f64 1/16 (/.f64 (/.f64 1/64 i) i))
(.f64 (.f64 i i) (-.f64 -1/4 (*.f64 i i)))
(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))
(/.f64 1/4 (+.f64 4 (/.f64 (/.f64 1 i) (neg.f64 i))))
(/.f64 1/4 (+.f64 4 (*.f64 (/.f64 1 i) (/.f64 -1 i))))
(/.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 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))

Calls

3 calls:

44.0ms

(/.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))

6.0ms

4.0ms

(/.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))

Results

Error	Segments	Branch
0.3b	1	`i`
0.3b	1	`(/.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))`
0.3b	1	`(/.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))`

Compiler

Compiled 133 to 88 computations (33.8% saved)

regimes17.0ms (0.4%)

Counts

5 → 2

Calls

Call 1

Inputs
1/16
1/16
(.f64 i (.f64 i -1/4))
(+.f64 1/16 (/.f64 (/.f64 1/64 i) i))
(.f64 (.f64 i i) (-.f64 -1/4 (*.f64 i i)))

Outputs
(.f64 (.f64 i i) (-.f64 -1/4 (*.f64 i i)))
(+.f64 1/16 (/.f64 (/.f64 1/64 i) i))

Calls

1 calls:

16.0ms

Results

Error	Segments	Branch
0.2b	2	`i`

Compiler

Compiled 26 to 16 computations (38.5% saved)

bsearch27.0ms (0.7%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
27.0ms	0.00012387664648386409	104.65918454657539

Compiler

Compiled 30 to 20 computations (33.3% saved)

regimes9.0ms (0.2%)

Counts

4 → 2

Calls

Call 1

Inputs
1/16
1/16
(.f64 i (.f64 i -1/4))
(+.f64 1/16 (/.f64 (/.f64 1/64 i) i))

Outputs
(.f64 i (.f64 i -1/4))
(+.f64 1/16 (/.f64 (/.f64 1/64 i) i))

Calls

1 calls:

8.0ms

Results

Error	Segments	Branch
0.6b	2	`i`

Compiler

Compiled 17 to 12 computations (29.4% saved)

bsearch26.0ms (0.7%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
25.0ms	0.00012387664648386409	104.65918454657539

Compiler

Compiled 30 to 20 computations (33.3% saved)

regimes29.0ms (0.7%)

Counts

3 → 2

Calls

Call 1

Inputs
1/16
1/16
(.f64 i (.f64 i -1/4))

Outputs
(.f64 i (.f64 i -1/4))
1/16

Calls

1 calls:

27.0ms

Results

Error	Segments	Branch
0.9b	2	`i`

Compiler

Compiled 10 to 7 computations (30% saved)

bsearch25.0ms (0.7%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
25.0ms	0.00012387664648386409	104.65918454657539

Compiler

Compiled 30 to 20 computations (33.3% saved)

regimes4.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0.0b (-0%)

Counts

2 → 1

Calls

Call 1

Inputs
1/16
1/16

Outputs
1/16

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
31.4b	1	`i`

Compiler

Compiled 5 to 4 computations (20% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	80
1	35	80
2	42	80
3	46	80
4	48	80

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))
(if (<=.f64 i 2285120794397233/18446744073709551616) (.f64 (.f64 i i) (-.f64 -1/4 (*.f64 i i))) (+.f64 1/16 (/.f64 (/.f64 1/64 i) i)))
(if (<=.f64 i 2285120794397233/18446744073709551616) (.f64 i (.f64 i -1/4)) (+.f64 1/16 (/.f64 (/.f64 1/64 i) i)))
(if (<=.f64 i 2285120794397233/18446744073709551616) (.f64 i (.f64 i -1/4)) 1/16)
1/16

Outputs
(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))
(if (<=.f64 i 2285120794397233/18446744073709551616) (.f64 (.f64 i i) (-.f64 -1/4 (*.f64 i i))) (+.f64 1/16 (/.f64 (/.f64 1/64 i) i)))
(if (<=.f64 i 2285120794397233/18446744073709551616) (.f64 i (.f64 i -1/4)) (+.f64 1/16 (/.f64 (/.f64 1/64 i) i)))
(if (<=.f64 i 2285120794397233/18446744073709551616) (.f64 i (.f64 i -1/4)) 1/16)
1/16

Compiler

Compiled 61 to 43 computations (29.5% saved)

soundness311.0ms (8.1%)

Algorithm

3×	egg-herbie

Rules

691×	`cancel-sign-sub-inv_binary64`
691×	`cancel-sign-sub-inv_binary64`
657×	`fma-neg_binary64`
657×	`fma-neg_binary64`
579×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	40	26
2	200	17
3	1341	13
4	3774	13
5	6220	13
0	39	270
1	91	267
2	214	267
3	643	267
4	3200	267
0	40	318
1	93	315
2	218	315
3	652	315
4	3251	315

Stop Event

1×	node limit
1×	node limit
1×	node limit

Compiler

Compiled 774 to 504 computations (34.9% saved)

end71.0ms (1.8%)

Compiler: Compiled 57 to 38 computations (33.3% saved)

Details

analyze8.0ms (0.2%)

sample2.0s (50.7%)

preprocess63.0ms (1.6%)

simplify47.0ms (1.2%)

eval1.0ms (0%)

prune1.0ms (0%)

localize10.0ms (0.3%)

series3.0ms (0.1%)

rewrite72.0ms (1.9%)

simplify46.0ms (1.2%)

localize25.0ms (0.7%)

series4.0ms (0.1%)

rewrite86.0ms (2.2%)

simplify58.0ms (1.5%)

eval112.0ms (2.9%)

prune34.0ms (0.9%)

localize6.0ms (0.1%)

localize7.0ms (0.2%)

series2.0ms (0%)

rewrite54.0ms (1.4%)

simplify85.0ms (2.2%)

localize8.0ms (0.2%)

series3.0ms (0.1%)

rewrite52.0ms (1.3%)

simplify180.0ms (4.7%)

localize21.0ms (0.5%)

series2.0ms (0%)

rewrite71.0ms (1.8%)

simplify44.0ms (1.1%)

eval36.0ms (0.9%)

prune29.0ms (0.7%)

localize13.0ms (0.3%)

series2.0ms (0%)

rewrite58.0ms (1.5%)

simplify43.0ms (1.1%)

eval22.0ms (0.6%)

prune11.0ms (0.3%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes56.0ms (1.5%)

regimes17.0ms (0.4%)

bsearch27.0ms (0.7%)

regimes9.0ms (0.2%)

bsearch26.0ms (0.7%)

regimes29.0ms (0.7%)

bsearch25.0ms (0.7%)

regimes4.0ms (0.1%)

simplify7.0ms (0.2%)

soundness311.0ms (8.1%)

end71.0ms (1.8%)

Profiling