Details

analyze8.0ms (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
31.2%	18.7%	50%	4
40.6%	9.4%	50%	5
45.3%	4.7%	50%	6
47.6%	2.3%	50%	7
48.8%	1.2%	50%	8
49.4%	0.6%	50%	9
49.7%	0.3%	50%	10
49.8%	0.1%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 29 to 19 computations (34.5% saved)

sample1.2s (62.5%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 58 to 38 computations (34.5% saved)

preprocess33.0ms (1.8%)

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 (1.1%)

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))))

prune7.0ms (0.4%)

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

5.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	5.4b	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
	46.1b	(/.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))))
✓	8.6b	(/.f64 i (pow.f64 i 3))

series3.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

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

rewrite43.0ms (2.3%)

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 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 +.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 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)))))))))

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 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 +.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 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)))))))))

simplify28.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

92 → 85

Calls

Call 1

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

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

prune57.0ms (3.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	84	3	87

Error

Counts

87 → 3

Alt Table

Status	Error	Program
	34.1b	(-.f64 (.f64 i (.f64 i -1/4)) (pow.f64 i 4))
	21.7b	(*.f64 (/.f64 1/4 (-.f64 16 (pow.f64 (pow.f64 i -2) 2))) (+.f64 (pow.f64 i -2) 4))
▶	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))

Compiler

Compiled 1118 to 895 computations (19.9% saved)

localize8.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))
✓	0.2b	(/.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	@	-inf	(/.f64 1/4 (-.f64 4 (/.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 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))
0.0ms	i	@	inf	(/.f64 1 (pow.f64 i 2))

rewrite41.0ms (2.2%)

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 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 +.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 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)))))))))

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 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 +.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 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)))))))))

simplify25.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	186
1	90	183
2	211	183
3	639	183
4	3051	183

Stop Event

1×	node limit

Counts

73 → 76

Calls

Call 1

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

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

prune47.0ms (2.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	76	3	79

Error

Counts

79 → 3

Alt Table

Status	Error	Program
	34.1b	(-.f64 (.f64 i (.f64 i -1/4)) (pow.f64 i 4))
▶	21.7b	(*.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4))) (+.f64 (pow.f64 i -2) 4))
✓	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))

Compiler

Compiled 939 to 793 computations (15.5% saved)

localize10.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.6b	(/.f64 1/4 (-.f64 16 (pow.f64 i -4)))
✓	20.8b	(*.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4))) (+.f64 (pow.f64 i -2) 4))

series4.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	i	@	0	(*.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4))) (+.f64 (pow.f64 i -2) 4))
1.0ms	i	@	0	(/.f64 1/4 (-.f64 16 (pow.f64 i -4)))
1.0ms	i	@	inf	(/.f64 1/4 (-.f64 16 (pow.f64 i -4)))
1.0ms	i	@	-inf	(/.f64 1/4 (-.f64 16 (pow.f64 i -4)))
1.0ms	i	@	inf	(*.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4))) (+.f64 (pow.f64 i -2) 4))

rewrite59.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

407×	`prod-diff_binary64`
240×	`log1p-udef_binary64`
144×	`add-sqr-sqrt_binary64`
142×	`add-log-exp_binary64`
142×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	29
1	309	29
2	3848	29

Stop Event

1×	node limit

Counts

2 → 72

Calls

Call 1

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

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (/.f64 1 (-.f64 16 (pow.f64 i -4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1/4 (-.f64 16 (pow.f64 i -4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4)))) (cbrt.f64 (/.f64 1/16 (pow.f64 (-.f64 16 (pow.f64 i -4)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1/16 (pow.f64 (-.f64 16 (pow.f64 i -4)) 2))) (cbrt.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (sqrt.f64 (-.f64 16 (pow.f64 i -4)))) (/.f64 1/2 (sqrt.f64 (-.f64 16 (pow.f64 i -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/4 (/.f64 1 (neg.f64 (-.f64 16 (pow.f64 i -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 16 (pow.f64 i -4))) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/4 (-.f64 4096 (pow.f64 i -12))) (+.f64 (+.f64 256 (pow.f64 i -8)) (*.f64 16 (pow.f64 i -4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/4 (-.f64 256 (pow.f64 i -8))) (+.f64 16 (pow.f64 i -4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/2 (sqrt.f64 (-.f64 16 (pow.f64 i -4)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 64 (/.f64 (pow.f64 i -4) 1/4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/16 (pow.f64 (-.f64 16 (pow.f64 i -4)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4)))))))))

simplify32.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

836×	`fma-def_binary64`
547×	`times-frac_binary64`
435×	`associate-/r*_binary64`
299×	`fma-neg_binary64`
165×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	63	372
1	151	369
2	366	369
3	1155	369
4	4147	369

Stop Event

1×	node limit

Counts

96 → 101

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 4))
(+.f64 (.f64 -4 (pow.f64 i 8)) (.f64 -1/4 (pow.f64 i 4)))
(+.f64 (.f64 -4 (pow.f64 i 8)) (+.f64 (.f64 -1/4 (pow.f64 i 4)) (*.f64 -64 (pow.f64 i 12))))
(+.f64 (.f64 -1024 (pow.f64 i 16)) (+.f64 (.f64 -4 (pow.f64 i 8)) (+.f64 (.f64 -1/4 (pow.f64 i 4)) (.f64 -64 (pow.f64 i 12)))))
1/64
(+.f64 1/64 (*.f64 1/1024 (/.f64 1 (pow.f64 i 4))))
(+.f64 1/64 (+.f64 (.f64 1/1024 (/.f64 1 (pow.f64 i 4))) (.f64 1/16384 (/.f64 1 (pow.f64 i 8)))))
(+.f64 (.f64 1/262144 (/.f64 1 (pow.f64 i 12))) (+.f64 1/64 (+.f64 (.f64 1/1024 (/.f64 1 (pow.f64 i 4))) (*.f64 1/16384 (/.f64 1 (pow.f64 i 8))))))
1/64
(+.f64 1/64 (*.f64 1/1024 (/.f64 1 (pow.f64 i 4))))
(+.f64 1/64 (+.f64 (.f64 1/1024 (/.f64 1 (pow.f64 i 4))) (.f64 1/16384 (/.f64 1 (pow.f64 i 8)))))
(+.f64 (.f64 1/262144 (/.f64 1 (pow.f64 i 12))) (+.f64 1/64 (+.f64 (.f64 1/1024 (/.f64 1 (pow.f64 i 4))) (*.f64 1/16384 (/.f64 1 (pow.f64 i 8))))))

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 -4 (pow.f64 i 6) (.f64 -1/4 (.f64 i i))) (pow.f64 i 4))
(-.f64 (fma.f64 -1/4 (.f64 i i) (.f64 -4 (pow.f64 i 6))) (pow.f64 i 4))
(-.f64 (.f64 (.f64 i i) (fma.f64 (pow.f64 i 4) -4 -1/4)) (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 -4 (pow.f64 i 6) (.f64 -1/4 (.f64 i i))) (pow.f64 i 4)))
(-.f64 (fma.f64 -16 (pow.f64 i 8) (fma.f64 -1/4 (.f64 i i) (.f64 -4 (pow.f64 i 6)))) (pow.f64 i 4))
(fma.f64 -4 (pow.f64 i 6) (fma.f64 i (-.f64 (.f64 -1/4 i) (pow.f64 i 3)) (.f64 -16 (pow.f64 i 8))))
(fma.f64 -4 (pow.f64 i 6) (-.f64 (.f64 -16 (pow.f64 i 8)) (.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 (.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 1/256 (pow.f64 i 4)) (+.f64 (+.f64 1/16 (/.f64 1/64 (*.f64 i i))) (/.f64 1/1024 (pow.f64 i 6))))
(+.f64 (/.f64 1/64 (*.f64 i i)) (+.f64 1/16 (+.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 1/256 (pow.f64 i 4)) (+.f64 (+.f64 1/16 (/.f64 1/64 (*.f64 i i))) (/.f64 1/1024 (pow.f64 i 6))))
(+.f64 (/.f64 1/64 (*.f64 i i)) (+.f64 1/16 (+.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)))))
(*.f64 -1/4 (pow.f64 i 4))
(+.f64 (.f64 -4 (pow.f64 i 8)) (.f64 -1/4 (pow.f64 i 4)))
(fma.f64 -4 (pow.f64 i 8) (*.f64 -1/4 (pow.f64 i 4)))
(fma.f64 -1/4 (pow.f64 i 4) (*.f64 -4 (pow.f64 i 8)))
(*.f64 (pow.f64 i 4) (fma.f64 (pow.f64 i 4) -4 -1/4))
(+.f64 (.f64 -4 (pow.f64 i 8)) (+.f64 (.f64 -1/4 (pow.f64 i 4)) (*.f64 -64 (pow.f64 i 12))))
(fma.f64 -4 (pow.f64 i 8) (fma.f64 -1/4 (pow.f64 i 4) (*.f64 -64 (pow.f64 i 12))))
(fma.f64 -4 (pow.f64 i 8) (fma.f64 -64 (pow.f64 i 12) (*.f64 -1/4 (pow.f64 i 4))))
(fma.f64 -1/4 (pow.f64 i 4) (fma.f64 -4 (pow.f64 i 8) (*.f64 -64 (pow.f64 i 12))))
(+.f64 (.f64 -1024 (pow.f64 i 16)) (+.f64 (.f64 -4 (pow.f64 i 8)) (+.f64 (.f64 -1/4 (pow.f64 i 4)) (.f64 -64 (pow.f64 i 12)))))
(fma.f64 -1024 (pow.f64 i 16) (fma.f64 -4 (pow.f64 i 8) (fma.f64 -1/4 (pow.f64 i 4) (*.f64 -64 (pow.f64 i 12)))))
(fma.f64 -1024 (pow.f64 i 16) (fma.f64 -4 (pow.f64 i 8) (fma.f64 -64 (pow.f64 i 12) (*.f64 -1/4 (pow.f64 i 4)))))
(fma.f64 -4 (pow.f64 i 8) (fma.f64 -1024 (pow.f64 i 16) (fma.f64 -1/4 (pow.f64 i 4) (*.f64 -64 (pow.f64 i 12)))))
(fma.f64 (pow.f64 i 4) (fma.f64 (pow.f64 i 4) -4 -1/4) (fma.f64 -64 (pow.f64 i 12) (*.f64 -1024 (pow.f64 i 16))))
1/64
(+.f64 1/64 (*.f64 1/1024 (/.f64 1 (pow.f64 i 4))))
(+.f64 1/64 (/.f64 1/1024 (pow.f64 i 4)))
(+.f64 1/64 (+.f64 (.f64 1/1024 (/.f64 1 (pow.f64 i 4))) (.f64 1/16384 (/.f64 1 (pow.f64 i 8)))))
(+.f64 1/64 (+.f64 (/.f64 1/1024 (pow.f64 i 4)) (/.f64 1/16384 (pow.f64 i 8))))
(+.f64 (.f64 1/262144 (/.f64 1 (pow.f64 i 12))) (+.f64 1/64 (+.f64 (.f64 1/1024 (/.f64 1 (pow.f64 i 4))) (*.f64 1/16384 (/.f64 1 (pow.f64 i 8))))))
(+.f64 (+.f64 1/64 (+.f64 (/.f64 1/1024 (pow.f64 i 4)) (/.f64 1/16384 (pow.f64 i 8)))) (/.f64 1/262144 (pow.f64 i 12)))
(+.f64 (+.f64 1/64 (/.f64 1/1024 (pow.f64 i 4))) (+.f64 (/.f64 1/16384 (pow.f64 i 8)) (/.f64 1/262144 (pow.f64 i 12))))
(+.f64 1/64 (+.f64 (/.f64 1/1024 (pow.f64 i 4)) (+.f64 (/.f64 1/16384 (pow.f64 i 8)) (/.f64 1/262144 (pow.f64 i 12)))))
1/64
(+.f64 1/64 (*.f64 1/1024 (/.f64 1 (pow.f64 i 4))))
(+.f64 1/64 (/.f64 1/1024 (pow.f64 i 4)))
(+.f64 1/64 (+.f64 (.f64 1/1024 (/.f64 1 (pow.f64 i 4))) (.f64 1/16384 (/.f64 1 (pow.f64 i 8)))))
(+.f64 1/64 (+.f64 (/.f64 1/1024 (pow.f64 i 4)) (/.f64 1/16384 (pow.f64 i 8))))
(+.f64 (.f64 1/262144 (/.f64 1 (pow.f64 i 12))) (+.f64 1/64 (+.f64 (.f64 1/1024 (/.f64 1 (pow.f64 i 4))) (*.f64 1/16384 (/.f64 1 (pow.f64 i 8))))))
(+.f64 (+.f64 1/64 (+.f64 (/.f64 1/1024 (pow.f64 i 4)) (/.f64 1/16384 (pow.f64 i 8)))) (/.f64 1/262144 (pow.f64 i 12)))
(+.f64 (+.f64 1/64 (/.f64 1/1024 (pow.f64 i 4))) (+.f64 (/.f64 1/16384 (pow.f64 i 8)) (/.f64 1/262144 (pow.f64 i 12))))
(+.f64 1/64 (+.f64 (/.f64 1/1024 (pow.f64 i 4)) (+.f64 (/.f64 1/16384 (pow.f64 i 8)) (/.f64 1/262144 (pow.f64 i 12)))))

prune71.0ms (3.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	101	3	104

Error

Counts

104 → 3

Alt Table

Status	Error	Program
▶	34.1b	(-.f64 (.f64 i (.f64 i -1/4)) (pow.f64 i 4))
✓	21.7b	(*.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4))) (+.f64 (pow.f64 i -2) 4))
✓	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))

Compiler

Compiled 1928 to 1629 computations (15.5% 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	@	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))

rewrite46.0ms (2.5%)

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 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 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 expm1.f64 (log1p.f64 (fma.f64 i (*.f64 i -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)))))))))

simplify29.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

777×	`fma-neg_binary64`
514×	`fma-def_binary64`
386×	`associate-l_binary64`
342×	`unswap-sqr_binary64`
327×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	145
1	23	136
2	51	136
3	142	136
4	492	136
5	1882	136
6	4349	136

Stop Event

1×	node limit

Counts

52 → 46

Calls

Call 1

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

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

prune26.0ms (1.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	46	3	49

Error

Counts

49 → 3

Alt Table

Status	Error	Program
✓	34.1b	(-.f64 (.f64 i (.f64 i -1/4)) (pow.f64 i 4))
✓	21.7b	(*.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4))) (+.f64 (pow.f64 i -2) 4))
✓	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))

Compiler

Compiled 756 to 549 computations (27.4% saved)

regimes25.0ms (1.3%)

Accuracy

Total 0.3b remaining (99.2%)

Threshold costs 0.3b (99.2%)

Counts

17 → 1

Compiler

Compiled 203 to 150 computations (26.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	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))))

end59.0ms (3.2%)

Stop Event

1×

done

Compiler

Compiled 54 to 46 computations (14.8% saved)

Details

analyze8.0ms (0.4%)

sample1.2s (62.5%)

preprocess33.0ms (1.8%)

simplify20.0ms (1.1%)

prune7.0ms (0.4%)

localize5.0ms (0.3%)

series3.0ms (0.2%)

rewrite43.0ms (2.3%)

simplify28.0ms (1.5%)

prune57.0ms (3.1%)

localize8.0ms (0.4%)

series2.0ms (0.1%)

rewrite41.0ms (2.2%)

simplify25.0ms (1.4%)

prune47.0ms (2.5%)

localize10.0ms (0.5%)

series4.0ms (0.2%)

rewrite59.0ms (3.2%)

simplify32.0ms (1.7%)

prune71.0ms (3.8%)

localize5.0ms (0.3%)

series2.0ms (0.1%)

rewrite46.0ms (2.5%)

simplify29.0ms (1.5%)

prune26.0ms (1.4%)

regimes25.0ms (1.3%)

simplify2.0ms (0.1%)

end59.0ms (3.2%)

Profiling