Details

analyze13.0ms (0.2%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	50%	50%	0%	0%	0%	0
0%	0%	50%	50%	0%	0%	0%	1
0%	0%	50%	50%	0%	0%	0%	2
0%	0%	50%	50%	0%	0%	0%	3
62.5%	31.2%	18.7%	50%	0%	0%	0%	4
81.3%	40.6%	9.4%	50%	0%	0%	0%	5
90.6%	45.3%	4.7%	50%	0%	0%	0%	6
95.3%	47.6%	2.3%	50%	0%	0%	0%	7
97.7%	48.8%	1.2%	50%	0%	0%	0%	8
98.8%	49.4%	0.6%	50%	0%	0%	0%	9
99.4%	49.7%	0.3%	50%	0%	0%	0%	10
99.7%	49.8%	0.1%	50%	0%	0%	0%	11
99.9%	49.9%	0.1%	50%	0%	0%	0%	12

Compiler

Compiled 29 to 19 computations (34.5% saved)

sample2.2s (39.8%)

Results

2.2s

8256×

body

256

valid

Bogosity

preprocess57.0ms (1%)

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)

simplify46.0ms (0.8%)

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)

prune2.0ms (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

0.7b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	46.3b	(/.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))
▶	0.7b	(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))

Compiler

Compiled 36 to 25 computations (30.6% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 4 (/.f64 -1 (*.f64 i i)))
✓	0.5b	(/.f64 -1 (*.f64 i i))
✓	0.7b	(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))

Compiler

Compiled 29 to 17 computations (41.4% saved)

series4.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite80.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

518×	`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	30
1	203	25
2	2514	25

Stop Event

1×	node limit

Counts

3 → 154

Calls

Call 1

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

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

Outputs

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

simplify47.0ms (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`
412×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	369
1	94	366
2	221	366
3	664	366
4	3240	366

Stop Event

1×	node limit

Counts

190 → 174

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

localize33.0ms (0.6%)

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))
✓	17.0b	(/.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))
✓	42.2b	(/.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)))
0.0ms	i	@	inf	(.f64 (.f64 i i) (*.f64 i i))
0.0ms	i	@	0	(.f64 (.f64 i i) (*.f64 i i))
0.0ms	i	@	0	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))

rewrite91.0ms (1.6%)

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) 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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 (0.9%)

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)

eval174.0ms (3.1%)

Compiler: Compiled 7596 to 5437 computations (28.4% saved)

prune80.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	379	6	385
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	380	7	387

Error

Counts

387 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	17.5b	(/.f64 (.f64 1/4 (.f64 i i)) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
✓	0.7b	(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))
▶	0.8b	(/.f64 1/4 (+.f64 4 (*.f64 (/.f64 1 i) (/.f64 -1 i))))
▶	33.2b	(+.f64 1/16 (/.f64 (/.f64 1/64 i) i))
▶	31.8b	(.f64 (/.f64 (.f64 i i) (fma.f64 i (.f64 i 4) -1)) (/.f64 (.f64 i i) (.f64 i (.f64 i 4))))
▶	31.3b	(.f64 i (.f64 i -1/4))
	32.7b	1/16

Compiler

Compiled 138 to 98 computations (29% saved)

localize17.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 4 (*.f64 (/.f64 1 i) (/.f64 -1 i)))
✓	0.3b	(*.f64 (/.f64 1 i) (/.f64 -1 i))
✓	0.7b	(/.f64 1/4 (+.f64 4 (*.f64 (/.f64 1 i) (/.f64 -1 i))))

Compiler

Compiled 39 to 30 computations (23.1% saved)

series3.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite73.0ms (1.3%)

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	30
1	242	21
2	3065	21

Stop Event

1×	node limit

Counts

3 → 89

Calls

Call 1

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

Outputs

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

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

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

simplify42.0ms (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`
412×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	369
1	94	366
2	221	366
3	664	366
4	3240	366

Stop Event

1×	node limit

Counts

125 → 108

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

localize25.0ms (0.5%)

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

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1/16 (/.f64 (/.f64 1/64 i) i))
✓	0.1b	(/.f64 (/.f64 1/64 i) i)

Compiler

Compiled 19 to 13 computations (31.6% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 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	@	0	(+.f64 1/16 (/.f64 (/.f64 1/64 i) i))
0.0ms	i	@	inf	(+.f64 1/16 (/.f64 (/.f64 1/64 i) i))
0.0ms	i	@	-inf	(/.f64 (/.f64 1/64 i) i)

rewrite61.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

866×	`pow1_binary64`
822×	`add-log-exp_binary64`
822×	`log1p-expm1-u_binary64`
822×	`expm1-log1p-u_binary64`
809×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	165	17
2	2191	17

Stop Event

1×	node limit

Counts

2 → 66

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (/.f64 1/64 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 (/.f64 1/64 i) i) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (/.f64 1/64 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 (cbrt.f64 (/.f64 1/64 i)) 2) (*.f64 (cbrt.f64 (/.f64 1/64 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 (/.f64 1/8 (sqrt.f64 i)) (*.f64 (/.f64 1/8 (sqrt.f64 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 (cbrt.f64 (/.f64 1/64 i)) 2) 1) (/.f64 (cbrt.f64 (/.f64 1/64 i)) i))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1/8 (sqrt.f64 i)) 1) (/.f64 (/.f64 1/8 (sqrt.f64 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 (cbrt.f64 (/.f64 1/64 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 (/.f64 1/8 (sqrt.f64 i)) (pow.f64 (cbrt.f64 i) 2)) (/.f64 (/.f64 1/8 (sqrt.f64 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 (cbrt.f64 (/.f64 1/64 i)) 2) (sqrt.f64 i)) (/.f64 (cbrt.f64 (/.f64 1/64 i)) (sqrt.f64 i)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 1/64 i) i) 1)))) (#(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 1/262144 (pow.f64 (*.f64 i i) 3)) 1/3)))) (#(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 (/.f64 1/64 i) i) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (/.f64 1/64 i) i)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 1/262144 (pow.f64 (*.f64 i i) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (/.f64 1/64 i) i)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (/.f64 1/64 i) i)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (/.f64 1/64 i) i)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 (/.f64 (/.f64 1/64 i) i) 1/16)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/256 (-.f64 1/16 (/.f64 (/.f64 1/64 i) i))) (/.f64 (pow.f64 (/.f64 (/.f64 1/64 i) i) 2) (-.f64 1/16 (/.f64 (/.f64 1/64 i) i))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 (/.f64 1/64 i) i) 1/16) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (/.f64 (/.f64 1/64 i) i) 1/16))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (/.f64 (/.f64 1/64 i) i) 1/16)) (pow.f64 (cbrt.f64 (+.f64 (/.f64 (/.f64 1/64 i) i) 1/16)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 (/.f64 1/64 i) i) 1/16)) 2) (cbrt.f64 (+.f64 (/.f64 (/.f64 1/64 i) i) 1/16)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (/.f64 (/.f64 1/64 i) i) 1/16)) (sqrt.f64 (+.f64 (/.f64 (/.f64 1/64 i) i) 1/16)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/4096 (/.f64 1/262144 (pow.f64 (*.f64 i i) 3))) (/.f64 1 (+.f64 1/256 (-.f64 (pow.f64 (/.f64 (/.f64 1/64 i) i) 2) (/.f64 1/1024 (*.f64 i i))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/256 (pow.f64 (/.f64 (/.f64 1/64 i) i) 2)) (/.f64 1 (-.f64 1/16 (/.f64 (/.f64 1/64 i) i))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1/256 (-.f64 (pow.f64 (/.f64 (/.f64 1/64 i) i) 2) (/.f64 1/1024 (*.f64 i i)))) (+.f64 1/4096 (/.f64 1/262144 (pow.f64 (*.f64 i i) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1/16 (/.f64 (/.f64 1/64 i) i)) (-.f64 1/256 (pow.f64 (/.f64 (/.f64 1/64 i) i) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/4096 (/.f64 1/262144 (pow.f64 (*.f64 i i) 3))) (+.f64 1/256 (-.f64 (pow.f64 (/.f64 (/.f64 1/64 i) i) 2) (/.f64 1/1024 (*.f64 i i)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/4096 (/.f64 1/262144 (pow.f64 (*.f64 i i) 3))) (+.f64 (pow.f64 (/.f64 (/.f64 1/64 i) i) 2) (-.f64 1/256 (/.f64 1/1024 (*.f64 i i)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/256 (pow.f64 (/.f64 (/.f64 1/64 i) i) 2)) (-.f64 1/16 (/.f64 (/.f64 1/64 i) i)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1/4096 (/.f64 1/262144 (pow.f64 (*.f64 i i) 3)))) (neg.f64 (+.f64 1/256 (-.f64 (pow.f64 (/.f64 (/.f64 1/64 i) i) 2) (/.f64 1/1024 (*.f64 i i))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/256 (pow.f64 (/.f64 (/.f64 1/64 i) i) 2))) (neg.f64 (-.f64 1/16 (/.f64 (/.f64 1/64 i) i))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (/.f64 (/.f64 1/64 i) i) 2) 1/256) (-.f64 (/.f64 (/.f64 1/64 i) i) 1/16))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (/.f64 (/.f64 1/64 i) i) 1/16) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (/.f64 (/.f64 1/64 i) i) 1/16) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (/.f64 (/.f64 1/64 i) i) 1/16)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (/.f64 (/.f64 1/64 i) i) 1/16)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (/.f64 (/.f64 1/64 i) i) 1/16) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (/.f64 (/.f64 1/64 i) i) 1/16)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (/.f64 (/.f64 1/64 i) i) 1/16) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (/.f64 (/.f64 1/64 i) i) 1/16)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (/.f64 (/.f64 1/64 i) i) 1/16)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (/.f64 (/.f64 1/64 i) i) 1/16)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1/64 i) (/.f64 1 i) 1/16)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 (/.f64 1/64 i) i) 1/16)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (/.f64 1/4 (pow.f64 (cbrt.f64 i) 2)) 2) (/.f64 1/4 (pow.f64 (cbrt.f64 i) 2)) 1/16)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1/8 i) (/.f64 1/8 i) 1/16)))))

simplify110.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1115×	`associate-/r/_binary64`
627×	`*-commutative_binary64`
565×	`sqr-pow_binary64`
434×	`unswap-sqr_binary64`
336×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	183
1	20	183
2	32	183
3	55	183
4	127	183
5	424	183
6	2000	183
7	3631	183
8	3877	183
9	4174	183
10	4490	183
11	4868	183
12	5332	183
13	6565	183
14	7544	183

Stop Event

1×	node limit

Counts

90 → 71

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))
(/.f64 1/64 (pow.f64 i 2))
(+.f64 1/16 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))
(+.f64 1/16 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))
(+.f64 1/16 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))
1/16
(+.f64 1/16 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))
(+.f64 1/16 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))
(+.f64 1/16 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))
1/16
(+.f64 1/16 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))
(+.f64 1/16 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))
(+.f64 1/16 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))

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

localize46.0ms (0.8%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1)
✓	0.0b	(.f64 1/4 (.f64 i i))
✓	17.0b	(/.f64 (.f64 1/4 (.f64 i i)) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))

Compiler

Compiled 47 to 31 computations (34% 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 (.f64 2 i) (*.f64 2 i)) 1))
0.0ms	i	@	inf	(/.f64 (.f64 1/4 (.f64 i i)) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
0.0ms	i	@	-inf	(/.f64 (.f64 1/4 (.f64 i i)) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
0.0ms	i	@	inf	(.f64 1/4 (.f64 i i))
0.0ms	i	@	0	(.f64 1/4 (.f64 i i))

rewrite81.0ms (1.5%)

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	26
1	245	24
2	3259	24

Stop Event

1×	node limit

Counts

2 → 78

Calls

Call 1

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

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))))))

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

simplify75.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	270
1	93	267
2	218	267
3	654	267
4	3212	267

Stop Event

1×	node limit

Counts

102 → 95

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

localize23.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (/.f64 (.f64 i i) (fma.f64 i (.f64 i 4) -1)) (/.f64 (.f64 i i) (.f64 i (.f64 i 4))))
✓	17.0b	(/.f64 (.f64 i i) (fma.f64 i (.f64 i 4) -1))
✓	31.0b	(/.f64 (.f64 i i) (.f64 i (*.f64 i 4)))

Compiler

Compiled 60 to 32 computations (46.7% saved)

series5.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite158.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

616×	`log-prod_binary64`
404×	`pow-prod-down_binary64`
292×	`pow2_binary64`
281×	`pow-unpow_binary64`
207×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	56
1	242	32
2	3682	32

Stop Event

1×	node limit

Counts

3 → 128

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x . 1/4)))))

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

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

simplify52.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

779×	`times-frac_binary64`
752×	`fma-def_binary64`
605×	`distribute-rgt-neg-in_binary64`
555×	`distribute-lft-neg-in_binary64`
546×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	58	380
1	152	377
2	369	377
3	1083	377
4	4966	377

Stop Event

1×	node limit

Counts

164 → 157

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

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

eval537.0ms (9.7%)

Compiler: Compiled 7938 to 5533 computations (30.3% saved)

prune128.0ms (2.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	490	4	494
Fresh	1	0	1
Picked	1	0	1
Done	2	3	5
Total	494	7	501

Error

Counts

501 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	17.5b	(/.f64 (.f64 (.f64 i i) 1/4) (fma.f64 i (*.f64 i 4) -1))
▶	17.5b	(/.f64 (.f64 1/4 (.f64 i i)) (+.f64 (.f64 i (.f64 i 4)) -1))
▶	0.7b	(/.f64 1/4 (+.f64 4 (/.f64 (/.f64 1 i) (neg.f64 i))))
✓	0.7b	(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))
✓	33.2b	(+.f64 1/16 (/.f64 (/.f64 1/64 i) i))
✓	31.3b	(.f64 i (.f64 i -1/4))
	32.7b	1/16

Compiler

Compiled 64 to 48 computations (25% saved)

localize26.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 4 (/.f64 (/.f64 1 i) (neg.f64 i)))
✓	0.1b	(/.f64 (/.f64 1 i) (neg.f64 i))
✓	0.7b	(/.f64 1/4 (+.f64 4 (/.f64 (/.f64 1 i) (neg.f64 i))))

Compiler

Compiled 34 to 22 computations (35.3% saved)

series5.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite113.0ms (2%)

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	36
1	228	21
2	3130	21

Stop Event

1×	node limit

Counts

3 → 90

Calls

Call 1

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

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

simplify59.0ms (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`
412×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	369
1	94	366
2	221	366
3	664	366
4	3240	366

Stop Event

1×	node limit

Counts

126 → 110

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

localize29.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 i (.f64 i 4)) -1)
	0.0b	(.f64 1/4 (.f64 i i))
✓	17.0b	(/.f64 (.f64 1/4 (.f64 i i)) (+.f64 (.f64 i (.f64 i 4)) -1))

Compiler

Compiled 41 to 25 computations (39% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite96.0ms (1.7%)

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

((#(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)))))

simplify55.0ms (1%)

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)

localize25.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 i i) 1/4)
✓	17.0b	(/.f64 (.f64 (.f64 i i) 1/4) (fma.f64 i (*.f64 i 4) -1))

Compiler

Compiled 34 to 20 computations (41.2% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite83.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

487×	`log-prod_binary64`
371×	`exp-prod_binary64`
322×	`prod-exp_binary64`
264×	`pow-prod-down_binary64`
250×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	208	24
2	2524	24

Stop Event

1×	node limit

Counts

2 → 80

Calls

Call 1

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

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

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

simplify55.0ms (1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	270
1	93	267
2	218	267
3	654	267
4	3212	267

Stop Event

1×	node limit

Counts

104 → 97

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

eval258.0ms (4.7%)

Compiler: Compiled 5592 to 4153 computations (25.7% saved)

prune83.0ms (1.5%)

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	359	0	359
Fresh	0	1	1
Picked	0	1	1
Done	0	5	5
Total	359	7	366

Error

Counts

366 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	17.5b	(/.f64 (.f64 (.f64 i i) 1/4) (fma.f64 i (*.f64 i 4) -1))
✓	17.5b	(/.f64 (.f64 1/4 (.f64 i i)) (+.f64 (.f64 i (.f64 i 4)) -1))
✓	0.7b	(/.f64 1/4 (+.f64 4 (/.f64 (/.f64 1 i) (neg.f64 i))))
✓	0.7b	(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))
✓	33.2b	(+.f64 1/16 (/.f64 (/.f64 1/64 i) i))
✓	31.3b	(.f64 i (.f64 i -1/4))
	32.7b	1/16

Compiler

Compiled 64 to 48 computations (25% saved)

eval0.0ms (0%)

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

prune7.0ms (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
✓	17.5b	(/.f64 (.f64 (.f64 i i) 1/4) (fma.f64 i (*.f64 i 4) -1))
✓	17.5b	(/.f64 (.f64 1/4 (.f64 i i)) (+.f64 (.f64 i (.f64 i 4)) -1))
✓	0.7b	(/.f64 1/4 (+.f64 4 (/.f64 (/.f64 1 i) (neg.f64 i))))
✓	0.7b	(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))
✓	33.2b	(+.f64 1/16 (/.f64 (/.f64 1/64 i) i))
✓	31.3b	(.f64 i (.f64 i -1/4))
	32.7b	1/16

Compiler

Compiled 64 to 48 computations (25% saved)

regimes38.0ms (0.7%)

Counts

12 → 1

Calls

Call 1

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

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

Calls

3 calls:

14.0ms

9.0ms

(/.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))

8.0ms

(/.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
0.7b	1	`i`
0.7b	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))`
0.7b	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 184 to 120 computations (34.8% saved)

regimes19.0ms (0.3%)

Counts

4 → 2

Calls

Call 1

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

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

Calls

1 calls:

17.0ms

Results

Error	Segments	Branch
0.9b	2	`i`

Compiler

Compiled 17 to 12 computations (29.4% saved)

bsearch44.0ms (0.8%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
43.0ms	0.47298990335889374	27.14319977486631

Compiler

Compiled 30 to 20 computations (33.3% saved)

regimes17.0ms (0.3%)

Counts

3 → 2

Calls

Call 1

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

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

Calls

1 calls:

15.0ms

Results

Error	Segments	Branch
1.0b	2	`i`

Compiler

Compiled 10 to 7 computations (30% saved)

bsearch37.0ms (0.7%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
36.0ms	0.47298990335889374	27.14319977486631

Compiler

Compiled 30 to 20 computations (33.3% saved)

regimes4.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

2 → 1

Calls

Call 1

Inputs
1/16
1/16

Outputs
1/16

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
32.7b	1	`i`

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (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 8520628610068483/18014398509481984) (.f64 i (.f64 i -1/4)) (+.f64 1/16 (/.f64 (/.f64 1/64 i) i)))
(if (<=.f64 i 8520628610068483/18014398509481984) (.f64 i (.f64 i -1/4)) 1/16)
1/16

Outputs
(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))
(if (<=.f64 i 8520628610068483/18014398509481984) (.f64 i (.f64 i -1/4)) (+.f64 1/16 (/.f64 (/.f64 1/64 i) i)))
(if (<=.f64 i 8520628610068483/18014398509481984) (.f64 i (.f64 i -1/4)) 1/16)
1/16

Compiler

Compiled 40 to 30 computations (25% saved)

soundness96.0ms (1.7%)

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)

end35.0ms (0.6%)

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

Details

analyze13.0ms (0.2%)

sample2.2s (39.8%)

preprocess57.0ms (1%)

simplify46.0ms (0.8%)

eval1.0ms (0%)

prune2.0ms (0%)

localize11.0ms (0.2%)

series4.0ms (0.1%)

rewrite80.0ms (1.5%)

simplify47.0ms (0.8%)

localize33.0ms (0.6%)

series5.0ms (0.1%)

rewrite91.0ms (1.6%)

simplify47.0ms (0.9%)

eval174.0ms (3.1%)

prune80.0ms (1.4%)

localize17.0ms (0.3%)

series3.0ms (0.1%)

rewrite73.0ms (1.3%)

simplify42.0ms (0.8%)

localize25.0ms (0.5%)

localize8.0ms (0.1%)

series2.0ms (0%)

rewrite61.0ms (1.1%)

simplify110.0ms (2%)

localize46.0ms (0.8%)

series2.0ms (0%)

rewrite81.0ms (1.5%)

simplify75.0ms (1.4%)

localize23.0ms (0.4%)

series5.0ms (0.1%)

rewrite158.0ms (2.9%)

simplify52.0ms (0.9%)

eval537.0ms (9.7%)

prune128.0ms (2.3%)

localize26.0ms (0.5%)

series5.0ms (0.1%)

rewrite113.0ms (2%)

simplify59.0ms (1.1%)

localize29.0ms (0.5%)

series3.0ms (0.1%)

rewrite96.0ms (1.7%)

simplify55.0ms (1%)

localize25.0ms (0.4%)

series3.0ms (0.1%)

rewrite83.0ms (1.5%)

simplify55.0ms (1%)

eval258.0ms (4.7%)

prune83.0ms (1.5%)

eval0.0ms (0%)

prune7.0ms (0.1%)

regimes38.0ms (0.7%)

regimes19.0ms (0.3%)

bsearch44.0ms (0.8%)

regimes17.0ms (0.3%)

bsearch37.0ms (0.7%)

regimes4.0ms (0.1%)

simplify5.0ms (0.1%)

soundness96.0ms (1.7%)

end35.0ms (0.6%)

Profiling