Details

analyze7.0ms (0.1%)

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 (33.5%)

Results

1.9s

8256×

body

256

valid

preprocess106.0ms (1.8%)

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)

simplify64.0ms (1.1%)

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)

prune3.0ms (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

0.2b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	48.3b	(/.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))
▶	0.2b	(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))

Compiler

Compiled 36 to 25 computations (30.6% saved)

localize18.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))
✓	0.9b	(/.f64 -1 (*.f64 i i))

Compiler

Compiled 29 to 17 computations (41.4% saved)

series21.0ms (0.4%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
15.0ms	i	@	-inf	(/.f64 -1 (*.f64 i i))
2.0ms	i	@	0	(/.f64 -1 (*.f64 i i))
1.0ms	i	@	0	(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))
1.0ms	i	@	inf	(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))
1.0ms	i	@	inf	(/.f64 -1 (*.f64 i i))

rewrite81.0ms (1.4%)

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))))))

simplify74.0ms (1.3%)

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 (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1)
✓	0.1b	(.f64 (.f64 i i) (*.f64 i i))
✓	15.3b	(/.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))
✓	44.4b	(/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i)))

Compiler

Compiled 73 to 39 computations (46.6% saved)

series5.0ms (0.1%)

Counts

4 → 48

Calls

12 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)))
1.0ms	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))

rewrite127.0ms (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	61
1	255	48
2	3965	48

Stop Event

1×	node limit

Counts

4 → 190

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

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

simplify47.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

691×	`cancel-sign-sub-inv_binary64`
667×	`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	42	405
1	99	402
2	230	402
3	684	402
4	3301	402

Stop Event

1×	node limit

Counts

238 → 211

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)
-1
(-.f64 (*.f64 4 (pow.f64 i 2)) 1)
(-.f64 (*.f64 4 (pow.f64 i 2)) 1)
(-.f64 (*.f64 4 (pow.f64 i 2)) 1)
(*.f64 4 (pow.f64 i 2))
(-.f64 (*.f64 4 (pow.f64 i 2)) 1)
(-.f64 (*.f64 4 (pow.f64 i 2)) 1)
(-.f64 (*.f64 4 (pow.f64 i 2)) 1)
(*.f64 4 (pow.f64 i 2))
(-.f64 (*.f64 4 (pow.f64 i 2)) 1)
(-.f64 (*.f64 4 (pow.f64 i 2)) 1)
(-.f64 (*.f64 4 (pow.f64 i 2)) 1)

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

eval282.0ms (4.8%)

Compiler: Compiled 6749 to 4686 computations (30.6% saved)

prune63.0ms (1.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	321	6	327
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	322	7	329

Error

Counts

329 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	33.1b	(+.f64 1/16 (/.f64 (/.f64 1/64 i) i))
▶	0.3b	(/.f64 1/4 (+.f64 4 (*.f64 (/.f64 1 i) (/.f64 -1 i))))
▶	33.1b	(/.f64 (.f64 (.f64 i i) (.f64 (.f64 i i) (/.f64 1/4 (.f64 i i)))) (-.f64 (.f64 (.f64 2 i) (.f64 2 i)) 1))
	32.7b	1/16
▶	15.8b	(/.f64 (.f64 1/4 (.f64 i i)) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
✓	0.2b	(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))
▶	31.2b	(.f64 i (.f64 i -1/4))

Compiler

Compiled 144 to 102 computations (29.2% saved)

localize23.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1/4 (+.f64 4 (*.f64 (/.f64 1 i) (/.f64 -1 i))))
✓	0.3b	(*.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	@	-inf	(/.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	@	0	(/.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))

rewrite61.0ms (1.1%)

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	3066	14

Stop Event

1×	node limit

Counts

2 → 56

Calls

Call 1

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

Outputs

((#(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 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 (*.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 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 (/.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)))))))

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

simplify42.0ms (0.7%)

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

80 → 72

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)))))

localize5.0ms (0.1%)

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

localize225.0ms (3.9%)

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)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite78.0ms (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))))))))

simplify158.0ms (2.7%)

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))

localize432.0ms (7.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1)
✓	15.3b	(/.f64 (.f64 1/4 (.f64 i i)) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))

Compiler

Compiled 47 to 31 computations (34% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

0.0ms

(/.f64 (*.f64 1/4 (*.f64 i i)) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))

0.0ms

inf

(/.f64 (*.f64 1/4 (*.f64 i i)) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))

0.0ms

-inf

(/.f64 (*.f64 1/4 (*.f64 i i)) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))

rewrite70.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

616×	`log-prod_binary64`
448×	`prod-diff_binary64`
335×	`pow-prod-down_binary64`
282×	`pow2_binary64`
240×	`pow-unpow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	245	17
2	3259	17

Stop Event

1×	node limit

Counts

1 → 61

Calls

Call 1

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

Outputs

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

simplify43.0ms (0.7%)

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	38	186
1	90	183
2	211	183
3	637	183
4	3179	183

Stop Event

1×	node limit

Counts

73 → 76

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))))))

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

localize51.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1)
✓	0.8b	(/.f64 1/4 (*.f64 i i))
✓	15.3b	(/.f64 (.f64 (.f64 i i) (.f64 (.f64 i i) (/.f64 1/4 (.f64 i i)))) (-.f64 (.f64 (.f64 2 i) (.f64 2 i)) 1))
✓	32.1b	(.f64 (.f64 i i) (/.f64 1/4 (*.f64 i i)))

Compiler

Compiled 77 to 40 computations (48.1% saved)

series3.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	i	@	-inf	(/.f64 1/4 (*.f64 i i))
0.0ms	i	@	-inf	(/.f64 (.f64 (.f64 i i) (.f64 (.f64 i i) (/.f64 1/4 (.f64 i i)))) (-.f64 (.f64 (.f64 2 i) (.f64 2 i)) 1))
0.0ms	i	@	0	(.f64 (.f64 i i) (/.f64 1/4 (*.f64 i i)))
0.0ms	i	@	inf	(/.f64 (.f64 (.f64 i i) (.f64 (.f64 i i) (/.f64 1/4 (.f64 i i)))) (-.f64 (.f64 (.f64 2 i) (.f64 2 i)) 1))
0.0ms	i	@	0	(/.f64 (.f64 (.f64 i i) (.f64 (.f64 i i) (/.f64 1/4 (.f64 i i)))) (-.f64 (.f64 (.f64 2 i) (.f64 2 i)) 1))

rewrite108.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

825×	`log-prod_binary64`
457×	`prod-diff_binary64`
262×	`fma-def_binary64`
239×	`log1p-udef_binary64`
238×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	51
1	299	40
2	4240	40

Stop Event

1×	node limit

Counts

3 → 118

Calls

Call 1

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

Outputs

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

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

simplify65.0ms (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	40	282
1	92	279
2	215	279
3	645	279
4	3176	279

Stop Event

1×	node limit

Counts

154 → 136

Calls

Call 1

Inputs
1/4
1/4
1/4
1/4
1/4
1/4
1/4
1/4
1/4
1/4
1/4
1/4
(*.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 (.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 1/4 (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))

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

eval235.0ms (4%)

Compiler: Compiled 8434 to 5552 computations (34.2% saved)

prune91.0ms (1.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	443	4	447
Fresh	1	0	1
Picked	1	0	1
Done	2	3	5
Total	447	7	454

Error

Counts

454 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	33.1b	(+.f64 1/16 (/.f64 (/.f64 1/64 i) i))
▶	33.1b	(/.f64 (.f64 (.f64 i i) (.f64 (.f64 i i) (/.f64 1/4 (.f64 i i)))) (+.f64 (.f64 i (*.f64 i 4)) -1))
▶	0.2b	(/.f64 1/4 (+.f64 4 (/.f64 (/.f64 1 i) (neg.f64 i))))
	32.7b	1/16
▶	15.8b	(/.f64 (.f64 1/4 (.f64 i i)) (+.f64 (.f64 i (.f64 i 4)) -1))
✓	0.2b	(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))
✓	31.2b	(.f64 i (.f64 i -1/4))

Compiler

Compiled 73 to 51 computations (30.1% saved)

localize15.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 1 i) (neg.f64 i))
✓	0.2b	(/.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))

rewrite82.0ms (1.4%)

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)))))))

simplify44.0ms (0.8%)

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))

localize86.0ms (1.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 i (.f64 i 4)) -1)
✓	15.3b	(/.f64 (.f64 1/4 (.f64 i i)) (+.f64 (.f64 i (.f64 i 4)) -1))

Compiler

Compiled 41 to 25 computations (39% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite78.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

599×	`log-prod_binary64`
331×	`pow-prod-down_binary64`
293×	`pow2_binary64`
227×	`prod-diff_binary64`
210×	`pow-unpow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	240	25
2	3089	25

Stop Event

1×	node limit

Counts

2 → 114

Calls

Call 1

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

Outputs

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

simplify46.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

691×	`cancel-sign-sub-inv_binary64`
667×	`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	40	273
1	96	270
2	223	270
3	663	270
4	3258	270

Stop Event

1×	node limit

Counts

138 → 133

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))))))
-1
(-.f64 (*.f64 4 (pow.f64 i 2)) 1)
(-.f64 (*.f64 4 (pow.f64 i 2)) 1)
(-.f64 (*.f64 4 (pow.f64 i 2)) 1)
(*.f64 4 (pow.f64 i 2))
(-.f64 (*.f64 4 (pow.f64 i 2)) 1)
(-.f64 (*.f64 4 (pow.f64 i 2)) 1)
(-.f64 (*.f64 4 (pow.f64 i 2)) 1)
(*.f64 4 (pow.f64 i 2))
(-.f64 (*.f64 4 (pow.f64 i 2)) 1)
(-.f64 (*.f64 4 (pow.f64 i 2)) 1)
(-.f64 (*.f64 4 (pow.f64 i 2)) 1)

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

localize49.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (.f64 i (.f64 i 4)) -1)
	0.8b	(/.f64 1/4 (*.f64 i i))
✓	15.3b	(/.f64 (.f64 (.f64 i i) (.f64 (.f64 i i) (/.f64 1/4 (.f64 i i)))) (+.f64 (.f64 i (*.f64 i 4)) -1))
	32.1b	(.f64 (.f64 i i) (/.f64 1/4 (*.f64 i i)))

Compiler

Compiled 71 to 34 computations (52.1% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

0.0ms

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

0.0ms

-inf

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

0.0ms

inf

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

rewrite126.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

803×	`log-prod_binary64`
255×	`pow1/3_binary64`
248×	`expm1-udef_binary64`
248×	`log1p-udef_binary64`
236×	`prod-diff_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	29
1	294	23
2	4058	23

Stop Event

1×	node limit

Counts

1 → 58

Calls

Call 1

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

Outputs

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

simplify41.0ms (0.7%)

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	38	186
1	90	183
2	211	183
3	637	183
4	3179	183

Stop Event

1×	node limit

Counts

70 → 73

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))))))

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

eval262.0ms (4.5%)

Compiler: Compiled 7649 to 5179 computations (32.3% saved)

prune76.0ms (1.3%)

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	396	1	397
Fresh	1	0	1
Picked	0	1	1
Done	0	5	5
Total	397	7	404

Error

Counts

404 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	33.1b	(+.f64 1/16 (/.f64 (/.f64 1/64 i) i))
✓	33.1b	(/.f64 (.f64 (.f64 i i) (.f64 (.f64 i i) (/.f64 1/4 (.f64 i i)))) (+.f64 (.f64 i (*.f64 i 4)) -1))
	32.7b	1/16
✓	31.2b	(.f64 i (.f64 i -1/4))
✓	0.2b	(/.f64 1/4 (+.f64 4 (/.f64 (/.f64 1 i) (neg.f64 i))))
✓	15.8b	(/.f64 (.f64 1/4 (.f64 i i)) (+.f64 (.f64 i (.f64 i 4)) -1))
✓	0.2b	(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))

Compiler

Compiled 73 to 51 computations (30.1% saved)

eval0.0ms (0%)

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

prune4.0ms (0.1%)

Pruning

7 alts after pruning (1 fresh and 6 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	6	6
Total	7	7

Error

Counts

7 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	33.1b	(+.f64 1/16 (/.f64 (/.f64 1/64 i) i))
✓	33.1b	(/.f64 (.f64 (.f64 i i) (.f64 (.f64 i i) (/.f64 1/4 (.f64 i i)))) (+.f64 (.f64 i (*.f64 i 4)) -1))
	32.7b	1/16
✓	31.2b	(.f64 i (.f64 i -1/4))
✓	0.2b	(/.f64 1/4 (+.f64 4 (/.f64 (/.f64 1 i) (neg.f64 i))))
✓	15.8b	(/.f64 (.f64 1/4 (.f64 i i)) (+.f64 (.f64 i (.f64 i 4)) -1))
✓	0.2b	(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))

Compiler

Compiled 73 to 51 computations (30.1% saved)

regimes25.0ms (0.4%)

Counts

13 → 1

Calls

Call 1

Inputs
1/16
1/16
1/16
(.f64 i (.f64 i -1/4))
(+.f64 1/16 (/.f64 (/.f64 1/64 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 1/4 (.f64 i i)) (+.f64 (.f64 i (.f64 i 4)) -1))
(/.f64 (.f64 1/4 (.f64 i i)) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
(/.f64 (.f64 (.f64 i i) (.f64 (.f64 i i) (/.f64 1/4 (.f64 i i)))) (+.f64 (.f64 i (*.f64 i 4)) -1))
(/.f64 (.f64 (.f64 i i) (.f64 (.f64 i i) (/.f64 1/4 (.f64 i i)))) (-.f64 (.f64 (.f64 2 i) (.f64 2 i)) 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))

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

Calls

3 calls:

9.0ms

7.0ms

(/.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))

5.0ms

(/.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
0.2b	1	`i`
0.2b	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))`
0.2b	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 197 to 126 computations (36% saved)

regimes11.0ms (0.2%)

Counts

5 → 2

Calls

Call 1

Inputs
1/16
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:

9.0ms

Results

Error	Segments	Branch
0.7b	2	`i`

Compiler

Compiled 18 to 13 computations (27.8% saved)

bsearch27.0ms (0.5%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
27.0ms	0.03030671184898758	2.9636758141648327

Compiler

Compiled 30 to 20 computations (33.3% saved)

regimes44.0ms (0.8%)

Counts

4 → 2

Calls

Call 1

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

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

Calls

1 calls:

8.0ms

Results

Error	Segments	Branch
0.9b	2	`i`

Compiler

Compiled 11 to 8 computations (27.3% saved)

bsearch34.0ms (0.6%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
34.0ms	0.03030671184898758	2.9636758141648327

Compiler

Compiled 30 to 20 computations (33.3% saved)

regimes5.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0.0b (-0%)

Counts

3 → 1

Calls

Call 1

Inputs
1/16
1/16
1/16

Outputs
1/16

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
32.7b	1	`i`

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	51
1	26	51

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))
(if (<=.f64 i 4367657478077615/144115188075855872) (.f64 i (.f64 i -1/4)) (+.f64 1/16 (/.f64 (/.f64 1/64 i) i)))
(if (<=.f64 i 4367657478077615/144115188075855872) (.f64 i (.f64 i -1/4)) 1/16)
1/16

Outputs
(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))
(if (<=.f64 i 4367657478077615/144115188075855872) (.f64 i (.f64 i -1/4)) (+.f64 1/16 (/.f64 (/.f64 1/64 i) i)))
(if (<=.f64 i 4367657478077615/144115188075855872) (.f64 i (.f64 i -1/4)) 1/16)
1/16

Compiler

Compiled 40 to 30 computations (25% saved)

soundness156.0ms (2.7%)

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

Compiler

Compiled 627 to 388 computations (38.1% saved)

end33.0ms (0.6%)

Compiler: Compiled 37 to 27 computations (27% saved)

Details

analyze7.0ms (0.1%)

sample2.0s (33.5%)

preprocess106.0ms (1.8%)

simplify64.0ms (1.1%)

eval1.0ms (0%)

prune3.0ms (0%)

localize18.0ms (0.3%)

series21.0ms (0.4%)

rewrite81.0ms (1.4%)

simplify74.0ms (1.3%)

localize25.0ms (0.4%)

series5.0ms (0.1%)

rewrite127.0ms (2.2%)

simplify47.0ms (0.8%)

eval282.0ms (4.8%)

prune63.0ms (1.1%)

localize23.0ms (0.4%)

series2.0ms (0%)

rewrite61.0ms (1.1%)

simplify42.0ms (0.7%)

localize5.0ms (0.1%)

localize225.0ms (3.9%)

series1.0ms (0%)

rewrite78.0ms (1.3%)

simplify158.0ms (2.7%)

localize432.0ms (7.4%)

series1.0ms (0%)

rewrite70.0ms (1.2%)

simplify43.0ms (0.7%)

localize51.0ms (0.9%)

series3.0ms (0.1%)

rewrite108.0ms (1.9%)

simplify65.0ms (1.1%)

eval235.0ms (4%)

prune91.0ms (1.6%)

localize15.0ms (0.3%)

series2.0ms (0%)

rewrite82.0ms (1.4%)

simplify44.0ms (0.8%)

localize86.0ms (1.5%)

series2.0ms (0%)

rewrite78.0ms (1.3%)

simplify46.0ms (0.8%)

localize49.0ms (0.8%)

series1.0ms (0%)

rewrite126.0ms (2.2%)

simplify41.0ms (0.7%)

eval262.0ms (4.5%)

prune76.0ms (1.3%)

eval0.0ms (0%)

prune4.0ms (0.1%)

regimes25.0ms (0.4%)

regimes11.0ms (0.2%)

bsearch27.0ms (0.5%)

regimes44.0ms (0.8%)

bsearch34.0ms (0.6%)

regimes5.0ms (0.1%)

simplify7.0ms (0.1%)

soundness156.0ms (2.7%)

end33.0ms (0.6%)

Profiling