Details

analyze6.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
0%	50%	50%	3
37.5%	12.5%	50%	4
43.7%	6.2%	50%	5
46.9%	3.1%	50%	6
48.4%	1.6%	50%	7
49.2%	0.8%	50%	8
49.6%	0.4%	50%	9
49.8%	0.2%	50%	10
49.9%	0.1%	50%	11
49.9%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 29 to 19 computations (34.5% saved)

sample1.0s (67.4%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 58 to 38 computations (34.5% saved)

preprocess30.0ms (1.9%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify20.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

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

prune4.0ms (0.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

3.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	3.8b	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
	47.9b	(/.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 107 to 74 computations (30.8% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
✓	11.3b	(/.f64 i (pow.f64 i 3))

series4.0ms (0.3%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	i	@	0	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
1.0ms	i	@	0	(/.f64 i (pow.f64 i 3))
1.0ms	i	@	inf	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
0.0ms	i	@	-inf	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
0.0ms	i	@	-inf	(/.f64 i (pow.f64 i 3))

rewrite48.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 68

Calls

Call 1

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

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

Outputs

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

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

simplify34.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

438×	`associate-l_binary64`
438×	`fma-neg_binary64`
413×	`unswap-sqr_binary64`
320×	`cancel-sign-sub-inv_binary64`
291×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	273
1	104	271
2	285	267
3	1068	267
4	4284	267

Stop Event

1×	node limit

Counts

92 → 85

Calls

Call 1

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

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

prune49.0ms (3.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

Counts

87 → 2

Alt Table

Status	Error	Program
	33.1b	(-.f64 (.f64 i (.f64 i -1/4)) (pow.f64 i 4))
▶	0.1b	(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))

Compiler

Compiled 1083 to 866 computations (20% saved)

localize7.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))
✓	0.4b	(/.f64 1 (pow.f64 i 2))

series2.0ms (0.1%)

Counts

2 → 12

Calls

6 calls:

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

rewrite40.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

386×	`log-prod_binary64`
246×	`pow2_binary64`
171×	`expm1-udef_binary64`
171×	`log1p-udef_binary64`
168×	`pow1/3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	225	14
2	2594	14

Stop Event

1×	node limit

Counts

2 → 61

Calls

Call 1

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

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

Outputs

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

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

simplify33.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

448×	`associate-l_binary64`
438×	`fma-neg_binary64`
413×	`unswap-sqr_binary64`
320×	`cancel-sign-sub-inv_binary64`
291×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	189
1	104	187
2	285	183
3	1067	183
4	4298	183

Stop Event

1×	node limit

Counts

73 → 76

Calls

Call 1

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

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

prune45.0ms (2.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	76	2	78

Error

Counts

78 → 2

Alt Table

Status	Error	Program
▶	33.1b	(-.f64 (.f64 i (.f64 i -1/4)) (pow.f64 i 4))
✓	0.1b	(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))

Compiler

Compiled 908 to 772 computations (15% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite45.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

811×	`log1p-expm1-u_binary64`
811×	`expm1-log1p-u_binary64`
87×	`add-sqr-sqrt_binary64`
85×	`add-log-exp_binary64`
84×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	180	13
2	2261	13

Stop Event

1×	node limit

Counts

1 → 40

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 i (*.f64 i -1/4)) (neg.f64 (pow.f64 i 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 i (*.f64 i -1/4)) (*.f64 (neg.f64 (pow.f64 i 4)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 i (*.f64 i -1/4) (neg.f64 (pow.f64 i 4))) (fma.f64 (neg.f64 (pow.f64 i 4)) 1 (pow.f64 i 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 i (*.f64 i -1/4) (neg.f64 (pow.f64 i 4))) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 i 4))) (cbrt.f64 (pow.f64 i 8)) (pow.f64 i 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 i (*.f64 i -1/4) (neg.f64 (pow.f64 i 4))) (fma.f64 (neg.f64 (*.f64 i i)) (*.f64 i i) (pow.f64 i 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (pow.f64 i 4)) (*.f64 i (*.f64 i -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 i (*.f64 i -1/4) (neg.f64 (pow.f64 i 4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 i (*.f64 i -1/4) (neg.f64 (pow.f64 i 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 i (*.f64 i -1/4) (neg.f64 (pow.f64 i 4)))) (pow.f64 (cbrt.f64 (fma.f64 i (*.f64 i -1/4) (neg.f64 (pow.f64 i 4)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 i (*.f64 i -1/4) (neg.f64 (pow.f64 i 4)))) 2) (cbrt.f64 (fma.f64 i (*.f64 i -1/4) (neg.f64 (pow.f64 i 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 i (*.f64 i -1/4) (neg.f64 (pow.f64 i 4)))) (sqrt.f64 (fma.f64 i (*.f64 i -1/4) (neg.f64 (pow.f64 i 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (pow.f64 (*.f64 i i) 3) -1/64) (pow.f64 i 12)) (/.f64 1 (+.f64 (*.f64 (pow.f64 i 4) 1/16) (*.f64 (pow.f64 i 4) (fma.f64 i (*.f64 i -1/4) (pow.f64 i 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (pow.f64 i 4) 1/16) (pow.f64 i 8)) (/.f64 1 (fma.f64 i (*.f64 i -1/4) (pow.f64 i 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 i (sqrt.f64 -1/4)) (*.f64 i i)) (-.f64 (*.f64 i (sqrt.f64 -1/4)) (*.f64 i i)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 (pow.f64 i 4) 1/16) (*.f64 (pow.f64 i 4) (fma.f64 i (*.f64 i -1/4) (pow.f64 i 4)))) (-.f64 (*.f64 (pow.f64 (*.f64 i i) 3) -1/64) (pow.f64 i 12))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 i (*.f64 i -1/4) (pow.f64 i 4)) (-.f64 (*.f64 (pow.f64 i 4) 1/16) (pow.f64 i 8))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (pow.f64 (*.f64 i i) 3) -1/64) (pow.f64 i 12)) (+.f64 (*.f64 (pow.f64 i 4) 1/16) (*.f64 (pow.f64 i 4) (fma.f64 i (*.f64 i -1/4) (pow.f64 i 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (pow.f64 i 4) 1/16) (pow.f64 i 8)) (fma.f64 i (*.f64 i -1/4) (pow.f64 i 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 (pow.f64 (*.f64 i i) 3) -1/64) (pow.f64 i 12))) (neg.f64 (+.f64 (*.f64 (pow.f64 i 4) 1/16) (*.f64 (pow.f64 i 4) (fma.f64 i (*.f64 i -1/4) (pow.f64 i 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 (pow.f64 i 4) 1/16) (pow.f64 i 8))) (neg.f64 (fma.f64 i (*.f64 i -1/4) (pow.f64 i 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 (*.f64 i i) 3) -1/64) (pow.f64 (neg.f64 (pow.f64 i 4)) 3)) (+.f64 (*.f64 (pow.f64 i 4) 1/16) (-.f64 (*.f64 (neg.f64 (pow.f64 i 4)) (neg.f64 (pow.f64 i 4))) (*.f64 (*.f64 i (*.f64 i -1/4)) (neg.f64 (pow.f64 i 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (pow.f64 i 4) 1/16) (*.f64 (neg.f64 (pow.f64 i 4)) (neg.f64 (pow.f64 i 4)))) (-.f64 (*.f64 i (*.f64 i -1/4)) (neg.f64 (pow.f64 i 4))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 i (*.f64 i -1/4) (neg.f64 (pow.f64 i 4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 i (*.f64 i -1/4) (neg.f64 (pow.f64 i 4))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 i (*.f64 i -1/4) (neg.f64 (pow.f64 i 4)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 i (*.f64 i -1/4) (neg.f64 (pow.f64 i 4)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 i (*.f64 i -1/4) (neg.f64 (pow.f64 i 4))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 i (*.f64 i -1/4) (neg.f64 (pow.f64 i 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 i (*.f64 i -1/4) (neg.f64 (pow.f64 i 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 i (*.f64 i -1/4) (neg.f64 (pow.f64 i 4))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 i (*.f64 i -1/4) (neg.f64 (pow.f64 i 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 i (*.f64 i -1/4) (neg.f64 (pow.f64 i 4)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 i (*.f64 i -1/4) (neg.f64 (pow.f64 i 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 i -1/4) i (neg.f64 (pow.f64 i 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 i (*.f64 i -1/4)) (neg.f64 (pow.f64 i 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 i i) -1/4 (neg.f64 (pow.f64 i 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 i 4) 1/16)) (cbrt.f64 (*.f64 i (*.f64 i -1/4))) (neg.f64 (pow.f64 i 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 i (sqrt.f64 -1/4)) (*.f64 i (sqrt.f64 -1/4)) (neg.f64 (pow.f64 i 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 i (*.f64 i -1/4) (neg.f64 (pow.f64 i 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 i (*.f64 i -1/4) (neg.f64 (pow.f64 i 4)))))))))

simplify30.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1054×	`fma-neg_binary64`
490×	`distribute-rgt-neg-in_binary64`
462×	`fma-def_binary64`
380×	`cancel-sign-sub-inv_binary64`
242×	`unswap-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	154
1	31	136
2	80	136
3	259	136
4	911	136
5	2330	136
6	4019	136

Stop Event

1×	node limit

Counts

52 → 46

Calls

Call 1

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

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

prune25.0ms (1.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	46	2	48

Error

Counts

48 → 2

Alt Table

Status	Error	Program
✓	33.1b	(-.f64 (.f64 i (.f64 i -1/4)) (pow.f64 i 4))
✓	0.1b	(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))

Compiler

Compiled 741 to 536 computations (27.7% saved)

regimes23.0ms (1.5%)

Accuracy

Total 0.4b remaining (97.7%)

Threshold costs 0.4b (97.7%)

Counts

16 → 1

Compiler

Compiled 179 to 128 computations (28.5% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	14	13
2	20	13
3	22	13
4	23	13

Stop Event

1×

saturated

Calls

Call 1

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

Outputs
(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))

end48.0ms (3.1%)

Stop Event

1×

done

Compiler

Compiled 40 to 34 computations (15% saved)

Details

analyze6.0ms (0.4%)

sample1.0s (67.4%)

preprocess30.0ms (1.9%)

simplify20.0ms (1.3%)

prune4.0ms (0.3%)

localize5.0ms (0.3%)

series4.0ms (0.3%)

rewrite48.0ms (3.1%)

simplify34.0ms (2.2%)

prune49.0ms (3.1%)

localize7.0ms (0.5%)

series2.0ms (0.1%)

rewrite40.0ms (2.6%)

simplify33.0ms (2.1%)

prune45.0ms (2.9%)

localize5.0ms (0.3%)

series2.0ms (0.1%)

rewrite45.0ms (2.9%)

simplify30.0ms (1.9%)

prune25.0ms (1.6%)

regimes23.0ms (1.5%)

simplify3.0ms (0.2%)

end48.0ms (3.1%)

Profiling