Details

analyze9.0ms (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 (59.9%)

Results

1.2s

8256×

body

128

valid

preprocess32.0ms (1.6%)

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)

simplify23.0ms (1.2%)

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))))

prune5.0ms (0.2%)

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
	47.6b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
▶	5.3b	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))

Compiler

Compiled 107 to 74 computations (30.8% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(/.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))))
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 (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 expm1.f64 (log1p.f64 (pow.f64 i -2)))))) (#(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 +.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 expm1.f64 (log1p.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x 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)))))))))

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

simplify34.0ms (1.7%)

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))))

prune76.0ms (3.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	84	3	87

Error

Counts

87 → 3

Alt Table

Status	Error	Program
	34.9b	(+.f64 1/16 (/.f64 1/64 (*.f64 i i)))
▶	29.0b	(-.f64 (.f64 -4 (pow.f64 i 6)) (.f64 (*.f64 i i) (fma.f64 i i 1/4)))
✓	5.3b	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))

Compiler

Compiled 1102 to 875 computations (20.6% saved)

localize8.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 -4 (pow.f64 i 6)) (.f64 (*.f64 i i) (fma.f64 i i 1/4)))
✓	0.1b	(.f64 (.f64 i i) (fma.f64 i i 1/4))

series4.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	i	@	0	(.f64 (.f64 i i) (fma.f64 i i 1/4))
1.0ms	i	@	inf	(.f64 (.f64 i i) (fma.f64 i i 1/4))
1.0ms	i	@	-inf	(.f64 (.f64 i i) (fma.f64 i i 1/4))
1.0ms	i	@	inf	(-.f64 (.f64 -4 (pow.f64 i 6)) (.f64 (*.f64 i i) (fma.f64 i i 1/4)))
0.0ms	i	@	-inf	(-.f64 (.f64 -4 (pow.f64 i 6)) (.f64 (*.f64 i i) (fma.f64 i i 1/4)))

rewrite81.0ms (4%)

Algorithm

1×	batch-egg-rewrite

Rules

526×	`log-prod_binary64`
513×	`fma-def_binary64`
201×	`fma-neg_binary64`
199×	`expm1-udef_binary64`
199×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	252	31
2	3152	31

Stop Event

1×	node limit

Counts

2 → 201

Calls

Call 1

Inputs
(.f64 (.f64 i i) (fma.f64 i i 1/4))
(-.f64 (.f64 -4 (pow.f64 i 6)) (.f64 (*.f64 i i) (fma.f64 i i 1/4)))

Outputs
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Outputs

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simplify72.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

686×	`fma-def_binary64`
615×	`distribute-rgt-neg-in_binary64`
317×	`cancel-sign-sub-inv_binary64`
285×	`unswap-sqr_binary64`
277×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	303
1	48	294
2	107	294
3	325	294
4	1353	294
5	4382	294

Stop Event

1×	node limit

Counts

225 → 215

Calls

Call 1

Inputs
(*.f64 1/4 (pow.f64 i 2))
(+.f64 (*.f64 1/4 (pow.f64 i 2)) (pow.f64 i 4))
(+.f64 (*.f64 1/4 (pow.f64 i 2)) (pow.f64 i 4))
(+.f64 (*.f64 1/4 (pow.f64 i 2)) (pow.f64 i 4))
(pow.f64 i 4)
(+.f64 (*.f64 1/4 (pow.f64 i 2)) (pow.f64 i 4))
(+.f64 (*.f64 1/4 (pow.f64 i 2)) (pow.f64 i 4))
(+.f64 (*.f64 1/4 (pow.f64 i 2)) (pow.f64 i 4))
(pow.f64 i 4)
(+.f64 (*.f64 1/4 (pow.f64 i 2)) (pow.f64 i 4))
(+.f64 (*.f64 1/4 (pow.f64 i 2)) (pow.f64 i 4))
(+.f64 (*.f64 1/4 (pow.f64 i 2)) (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 (.f64 -1/4 (pow.f64 i 2)) (*.f64 -4 (pow.f64 i 6))))
(+.f64 (.f64 -1 (pow.f64 i 4)) (+.f64 (.f64 -1/4 (pow.f64 i 2)) (*.f64 -4 (pow.f64 i 6))))
(*.f64 -4 (pow.f64 i 6))
(+.f64 (.f64 -1 (pow.f64 i 4)) (.f64 -4 (pow.f64 i 6)))
(+.f64 (.f64 -1 (pow.f64 i 4)) (+.f64 (.f64 -1/4 (pow.f64 i 2)) (*.f64 -4 (pow.f64 i 6))))
(+.f64 (.f64 -1 (pow.f64 i 4)) (+.f64 (.f64 -1/4 (pow.f64 i 2)) (*.f64 -4 (pow.f64 i 6))))
(*.f64 -4 (pow.f64 i 6))
(+.f64 (.f64 -1 (pow.f64 i 4)) (.f64 -4 (pow.f64 i 6)))
(+.f64 (.f64 -1 (pow.f64 i 4)) (+.f64 (.f64 -1/4 (pow.f64 i 2)) (*.f64 -4 (pow.f64 i 6))))
(+.f64 (.f64 -1 (pow.f64 i 4)) (+.f64 (.f64 -1/4 (pow.f64 i 2)) (*.f64 -4 (pow.f64 i 6))))

Outputs
(*.f64 1/4 (pow.f64 i 2))
(.f64 1/4 (.f64 i i))
(.f64 i (.f64 1/4 i))
(+.f64 (*.f64 1/4 (pow.f64 i 2)) (pow.f64 i 4))
(fma.f64 1/4 (*.f64 i i) (pow.f64 i 4))
(.f64 i (.f64 i (fma.f64 i i 1/4)))
(*.f64 i (fma.f64 1/4 i (pow.f64 i 3)))
(.f64 (.f64 i i) (fma.f64 i i 1/4))
(+.f64 (*.f64 1/4 (pow.f64 i 2)) (pow.f64 i 4))
(fma.f64 1/4 (*.f64 i i) (pow.f64 i 4))
(.f64 i (.f64 i (fma.f64 i i 1/4)))
(*.f64 i (fma.f64 1/4 i (pow.f64 i 3)))
(.f64 (.f64 i i) (fma.f64 i i 1/4))
(+.f64 (*.f64 1/4 (pow.f64 i 2)) (pow.f64 i 4))
(fma.f64 1/4 (*.f64 i i) (pow.f64 i 4))
(.f64 i (.f64 i (fma.f64 i i 1/4)))
(*.f64 i (fma.f64 1/4 i (pow.f64 i 3)))
(.f64 (.f64 i i) (fma.f64 i i 1/4))
(pow.f64 i 4)
(+.f64 (*.f64 1/4 (pow.f64 i 2)) (pow.f64 i 4))
(fma.f64 1/4 (*.f64 i i) (pow.f64 i 4))
(.f64 i (.f64 i (fma.f64 i i 1/4)))
(*.f64 i (fma.f64 1/4 i (pow.f64 i 3)))
(.f64 (.f64 i i) (fma.f64 i i 1/4))
(+.f64 (*.f64 1/4 (pow.f64 i 2)) (pow.f64 i 4))
(fma.f64 1/4 (*.f64 i i) (pow.f64 i 4))
(.f64 i (.f64 i (fma.f64 i i 1/4)))
(*.f64 i (fma.f64 1/4 i (pow.f64 i 3)))
(.f64 (.f64 i i) (fma.f64 i i 1/4))
(+.f64 (*.f64 1/4 (pow.f64 i 2)) (pow.f64 i 4))
(fma.f64 1/4 (*.f64 i i) (pow.f64 i 4))
(.f64 i (.f64 i (fma.f64 i i 1/4)))
(*.f64 i (fma.f64 1/4 i (pow.f64 i 3)))
(.f64 (.f64 i i) (fma.f64 i i 1/4))
(pow.f64 i 4)
(+.f64 (*.f64 1/4 (pow.f64 i 2)) (pow.f64 i 4))
(fma.f64 1/4 (*.f64 i i) (pow.f64 i 4))
(.f64 i (.f64 i (fma.f64 i i 1/4)))
(*.f64 i (fma.f64 1/4 i (pow.f64 i 3)))
(.f64 (.f64 i i) (fma.f64 i i 1/4))
(+.f64 (*.f64 1/4 (pow.f64 i 2)) (pow.f64 i 4))
(fma.f64 1/4 (*.f64 i i) (pow.f64 i 4))
(.f64 i (.f64 i (fma.f64 i i 1/4)))
(*.f64 i (fma.f64 1/4 i (pow.f64 i 3)))
(.f64 (.f64 i i) (fma.f64 i i 1/4))
(+.f64 (*.f64 1/4 (pow.f64 i 2)) (pow.f64 i 4))
(fma.f64 1/4 (*.f64 i i) (pow.f64 i 4))
(.f64 i (.f64 i (fma.f64 i i 1/4)))
(*.f64 i (fma.f64 1/4 i (pow.f64 i 3)))
(.f64 (.f64 i i) (fma.f64 i i 1/4))
(*.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 (.f64 i i) -1/4) (pow.f64 i 4))
(+.f64 (.f64 -1 (pow.f64 i 4)) (+.f64 (.f64 -1/4 (pow.f64 i 2)) (*.f64 -4 (pow.f64 i 6))))
(fma.f64 -1 (pow.f64 i 4) (fma.f64 -1/4 (.f64 i i) (.f64 -4 (pow.f64 i 6))))
(-.f64 (fma.f64 (.f64 i i) -1/4 (.f64 -4 (pow.f64 i 6))) (pow.f64 i 4))
(-.f64 (fma.f64 -4 (pow.f64 i 6) (.f64 (.f64 i i) -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 -4 (pow.f64 i 6)) (.f64 i (fma.f64 1/4 i (pow.f64 i 3))))
(+.f64 (.f64 -1 (pow.f64 i 4)) (+.f64 (.f64 -1/4 (pow.f64 i 2)) (*.f64 -4 (pow.f64 i 6))))
(fma.f64 -1 (pow.f64 i 4) (fma.f64 -1/4 (.f64 i i) (.f64 -4 (pow.f64 i 6))))
(-.f64 (fma.f64 (.f64 i i) -1/4 (.f64 -4 (pow.f64 i 6))) (pow.f64 i 4))
(-.f64 (fma.f64 -4 (pow.f64 i 6) (.f64 (.f64 i i) -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 -4 (pow.f64 i 6)) (.f64 i (fma.f64 1/4 i (pow.f64 i 3))))
(*.f64 -4 (pow.f64 i 6))
(+.f64 (.f64 -1 (pow.f64 i 4)) (.f64 -4 (pow.f64 i 6)))
(fma.f64 -1 (pow.f64 i 4) (*.f64 -4 (pow.f64 i 6)))
(-.f64 (*.f64 -4 (pow.f64 i 6)) (pow.f64 i 4))
(+.f64 (.f64 -1 (pow.f64 i 4)) (+.f64 (.f64 -1/4 (pow.f64 i 2)) (*.f64 -4 (pow.f64 i 6))))
(fma.f64 -1 (pow.f64 i 4) (fma.f64 -1/4 (.f64 i i) (.f64 -4 (pow.f64 i 6))))
(-.f64 (fma.f64 (.f64 i i) -1/4 (.f64 -4 (pow.f64 i 6))) (pow.f64 i 4))
(-.f64 (fma.f64 -4 (pow.f64 i 6) (.f64 (.f64 i i) -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 -4 (pow.f64 i 6)) (.f64 i (fma.f64 1/4 i (pow.f64 i 3))))
(+.f64 (.f64 -1 (pow.f64 i 4)) (+.f64 (.f64 -1/4 (pow.f64 i 2)) (*.f64 -4 (pow.f64 i 6))))
(fma.f64 -1 (pow.f64 i 4) (fma.f64 -1/4 (.f64 i i) (.f64 -4 (pow.f64 i 6))))
(-.f64 (fma.f64 (.f64 i i) -1/4 (.f64 -4 (pow.f64 i 6))) (pow.f64 i 4))
(-.f64 (fma.f64 -4 (pow.f64 i 6) (.f64 (.f64 i i) -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 -4 (pow.f64 i 6)) (.f64 i (fma.f64 1/4 i (pow.f64 i 3))))
(*.f64 -4 (pow.f64 i 6))
(+.f64 (.f64 -1 (pow.f64 i 4)) (.f64 -4 (pow.f64 i 6)))
(fma.f64 -1 (pow.f64 i 4) (*.f64 -4 (pow.f64 i 6)))
(-.f64 (*.f64 -4 (pow.f64 i 6)) (pow.f64 i 4))
(+.f64 (.f64 -1 (pow.f64 i 4)) (+.f64 (.f64 -1/4 (pow.f64 i 2)) (*.f64 -4 (pow.f64 i 6))))
(fma.f64 -1 (pow.f64 i 4) (fma.f64 -1/4 (.f64 i i) (.f64 -4 (pow.f64 i 6))))
(-.f64 (fma.f64 (.f64 i i) -1/4 (.f64 -4 (pow.f64 i 6))) (pow.f64 i 4))
(-.f64 (fma.f64 -4 (pow.f64 i 6) (.f64 (.f64 i i) -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 -4 (pow.f64 i 6)) (.f64 i (fma.f64 1/4 i (pow.f64 i 3))))
(+.f64 (.f64 -1 (pow.f64 i 4)) (+.f64 (.f64 -1/4 (pow.f64 i 2)) (*.f64 -4 (pow.f64 i 6))))
(fma.f64 -1 (pow.f64 i 4) (fma.f64 -1/4 (.f64 i i) (.f64 -4 (pow.f64 i 6))))
(-.f64 (fma.f64 (.f64 i i) -1/4 (.f64 -4 (pow.f64 i 6))) (pow.f64 i 4))
(-.f64 (fma.f64 -4 (pow.f64 i 6) (.f64 (.f64 i i) -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 -4 (pow.f64 i 6)) (.f64 i (fma.f64 1/4 i (pow.f64 i 3))))

prune186.0ms (9.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	215	3	218

Error

Counts

218 → 3

Alt Table

Status	Error	Program
▶	34.9b	(+.f64 1/16 (/.f64 1/64 (*.f64 i i)))
✓	29.0b	(-.f64 (.f64 -4 (pow.f64 i 6)) (.f64 (*.f64 i i) (fma.f64 i i 1/4)))
✓	5.3b	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))

Compiler

Compiled 6733 to 3961 computations (41.2% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1/64 (*.f64 i i))

series1.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite31.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

495×	`pow1_binary64`
469×	`add-log-exp_binary64`
469×	`log1p-expm1-u_binary64`
469×	`expm1-log1p-u_binary64`
459×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	110	7
2	1323	7

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

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

Outputs

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

simplify57.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

608×	`sqr-pow_binary64`
434×	`unswap-sqr_binary64`
335×	`associate-/l/_binary64`
281×	`cube-prod_binary64`
274×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	11	84
2	20	84
3	35	84
4	75	84
5	209	84
6	754	84
7	1961	84
8	2127	84
9	2311	84
10	2519	84
11	2810	84
12	3203	84
13	3681	84
14	4244	84
15	4932	84

Stop Event

1×	node limit

Counts

33 → 23

Calls

Call 1

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

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

prune13.0ms (0.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	23	3	26

Error

Counts

26 → 3

Alt Table

Status	Error	Program
✓	34.9b	(+.f64 1/16 (/.f64 1/64 (*.f64 i i)))
✓	29.0b	(-.f64 (.f64 -4 (pow.f64 i 6)) (.f64 (*.f64 i i) (fma.f64 i i 1/4)))
✓	5.3b	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))

Compiler

Compiled 249 to 210 computations (15.7% saved)

regimes57.0ms (2.8%)

Accuracy

Total 0.3b remaining (97.8%)

Threshold costs 0.3b (97.8%)

Counts

45 → 1

Compiler

Compiled 489 to 384 computations (21.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`/-rgt-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	16	13
2	19	13
3	21	13
4	22	13

Stop Event

1×

saturated

Calls

Call 1

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

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

end62.0ms (3.1%)

Stop Event

1×

done

Compiler

Compiled 53 to 40 computations (24.5% saved)

Details

analyze9.0ms (0.4%)

sample1.2s (59.9%)

preprocess32.0ms (1.6%)

simplify23.0ms (1.2%)

prune5.0ms (0.2%)

localize5.0ms (0.3%)

series3.0ms (0.2%)

rewrite48.0ms (2.3%)

simplify34.0ms (1.7%)

prune76.0ms (3.7%)

localize8.0ms (0.4%)

series4.0ms (0.2%)

rewrite81.0ms (4%)

simplify72.0ms (3.5%)

prune186.0ms (9.1%)

localize4.0ms (0.2%)

series1.0ms (0.1%)

rewrite31.0ms (1.5%)

simplify57.0ms (2.8%)

prune13.0ms (0.6%)

regimes57.0ms (2.8%)

simplify2.0ms (0.1%)

end62.0ms (3.1%)

Profiling