Details

analyze8.0ms (0.5%)

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)

sample1.1s (67.3%)

Results

1.1s

8256×

body

128

valid

preprocess32.0ms (1.9%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify20.0ms (1.2%)

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))))

eval1.0ms (0.1%)

Compiler: Compiled 35 to 24 computations (31.4% saved)

prune3.0ms (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

4.1b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
	45.1b	(/.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))
▶	4.1b	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))

Compiler

Compiled 72 to 50 computations (30.6% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
✓	10.0b	(/.f64 i (pow.f64 i 3))

series13.0ms (0.8%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
10.0ms	i	@	inf	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
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 i (pow.f64 i 3))

rewrite44.0ms (2.6%)

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

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 log1p.f64 (expm1.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 expm1.f64 (log1p.f64 (pow.f64 i -2)))))))

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

simplify28.0ms (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))))

eval30.0ms (1.8%)

Compiler: Compiled 1046 to 835 computations (20.2% saved)

prune141.0ms (8.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Error

Counts

87 → 2

Alt Table

Click to see full alt table

Status	Error	Program
✓	4.1b	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
▶	33.0b	(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)))

Compiler

Compiled 50 to 38 computations (24% saved)

localize14.0ms (0.8%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8)))
✓	0.0b	(*.f64 -16 (pow.f64 i 8))

series4.0ms (0.2%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	i	@	0	(*.f64 -16 (pow.f64 i 8))
1.0ms	i	@	inf	(*.f64 -16 (pow.f64 i 8))
1.0ms	i	@	-inf	(fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8)))
1.0ms	i	@	inf	(fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8)))
1.0ms	i	@	0	(fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8)))

rewrite37.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

788×	`log1p-expm1-u_binary64`
788×	`expm1-log1p-u_binary64`
100×	`add-sqr-sqrt_binary64`
99×	`add-log-exp_binary64`
97×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	215	21
2	2271	21

Stop Event

1×	node limit

Counts

2 → 36

Calls

Call 1

Inputs
(*.f64 -16 (pow.f64 i 8))
(fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 -16 (pow.f64 i 8)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 -16 (pow.f64 i 8)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 -16 (pow.f64 i 8)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 -16 (pow.f64 i 8))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 -16) (pow.f64 i 4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 i 16) 256))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -16) (pow.f64 i 8)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 -16 (pow.f64 i 8)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 -16 (pow.f64 i 8)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 -16 (pow.f64 i 8))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 -16 (pow.f64 i 8))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 -16 (pow.f64 i 8))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 -16 (pow.f64 i 8))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 -16 (pow.f64 i 8)) (.f64 -4 (pow.f64 i 6)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 -4 (pow.f64 i 6)) (.f64 -16 (pow.f64 i 8)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 -4 (pow.f64 i 6)) 1) (.f64 -16 (pow.f64 i 8)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 -4 (pow.f64 i 6) (.f64 -16 (pow.f64 i 8))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 -4 (pow.f64 i 6) (.f64 -16 (pow.f64 i 8))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 -4 (pow.f64 i 6) (.f64 -16 (pow.f64 i 8))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 -4 (pow.f64 i 6) (.f64 -16 (pow.f64 i 8)))) (cbrt.f64 (pow.f64 (fma.f64 -4 (pow.f64 i 6) (.f64 -16 (pow.f64 i 8))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (fma.f64 -4 (pow.f64 i 6) (.f64 -16 (pow.f64 i 8))) 2)) (cbrt.f64 (fma.f64 -4 (pow.f64 i 6) (.f64 -16 (pow.f64 i 8)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 -4 (pow.f64 i 6) (.f64 -16 (pow.f64 i 8)))) (sqrt.f64 (fma.f64 -4 (pow.f64 i 6) (.f64 -16 (pow.f64 i 8)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 -4 (pow.f64 i 6)) 3) (pow.f64 (.f64 -16 (pow.f64 i 8)) 3)) (+.f64 (.f64 (.f64 -4 (pow.f64 i 6)) (.f64 -4 (pow.f64 i 6))) (-.f64 (.f64 (pow.f64 i 16) 256) (.f64 (.f64 -4 (pow.f64 i 6)) (.f64 -16 (pow.f64 i 8))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 -4 (pow.f64 i 6)) (.f64 -4 (pow.f64 i 6))) (.f64 (pow.f64 i 16) 256)) (-.f64 (.f64 -4 (pow.f64 i 6)) (.f64 -16 (pow.f64 i 8))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 -4 (pow.f64 i 6) (.f64 -16 (pow.f64 i 8))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 -4 (pow.f64 i 6) (.f64 -16 (pow.f64 i 8))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 -4 (pow.f64 i 6) (.f64 -16 (pow.f64 i 8)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 -4 (pow.f64 i 6) (.f64 -16 (pow.f64 i 8)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 -4 (pow.f64 i 6) (.f64 -16 (pow.f64 i 8))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 -4 (pow.f64 i 6) (.f64 -16 (pow.f64 i 8)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 -4 (pow.f64 i 6) (.f64 -16 (pow.f64 i 8))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 -4 (pow.f64 i 6) (.f64 -16 (pow.f64 i 8))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 -4 (pow.f64 i 6) (.f64 -16 (pow.f64 i 8)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 -4 (pow.f64 i 6) (.f64 -16 (pow.f64 i 8)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 -4 (pow.f64 i 6) (.f64 -16 (pow.f64 i 8)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8)))))))))

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 -16 (pow.f64 i 8)) (*.f64 -4 (pow.f64 i 6)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 -4 (pow.f64 i 6)) (*.f64 -16 (pow.f64 i 8)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 -4 (pow.f64 i 6)) 1) (*.f64 -16 (pow.f64 i 8)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8)))) (cbrt.f64 (pow.f64 (fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8))) 2)) (cbrt.f64 (fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8)))) (sqrt.f64 (fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 -4 (pow.f64 i 6)) 3) (pow.f64 (*.f64 -16 (pow.f64 i 8)) 3)) (+.f64 (*.f64 (*.f64 -4 (pow.f64 i 6)) (*.f64 -4 (pow.f64 i 6))) (-.f64 (*.f64 (pow.f64 i 16) 256) (*.f64 (*.f64 -4 (pow.f64 i 6)) (*.f64 -16 (pow.f64 i 8))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 -4 (pow.f64 i 6)) (*.f64 -4 (pow.f64 i 6))) (*.f64 (pow.f64 i 16) 256)) (-.f64 (*.f64 -4 (pow.f64 i 6)) (*.f64 -16 (pow.f64 i 8))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8)))))))))

simplify66.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

485×	`sqr-pow_binary64`
462×	`fma-def_binary64`
430×	`*-commutative_binary64`
396×	`associate-l_binary64`
339×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	147
1	24	147
2	47	147
3	118	147
4	359	147
5	1328	147
6	2549	147
7	2889	147
8	3044	147
9	3240	147
10	3503	147
11	3842	147
12	4313	147
13	4843	147

Stop Event

1×	node limit

Counts

48 → 39

Calls

Call 1

Inputs
(*.f64 -4 (pow.f64 i 6))
(+.f64 (.f64 -16 (pow.f64 i 8)) (.f64 -4 (pow.f64 i 6)))
(+.f64 (.f64 -16 (pow.f64 i 8)) (.f64 -4 (pow.f64 i 6)))
(+.f64 (.f64 -16 (pow.f64 i 8)) (.f64 -4 (pow.f64 i 6)))
(*.f64 -16 (pow.f64 i 8))
(+.f64 (.f64 -16 (pow.f64 i 8)) (.f64 -4 (pow.f64 i 6)))
(+.f64 (.f64 -16 (pow.f64 i 8)) (.f64 -4 (pow.f64 i 6)))
(+.f64 (.f64 -16 (pow.f64 i 8)) (.f64 -4 (pow.f64 i 6)))
(*.f64 -16 (pow.f64 i 8))
(+.f64 (.f64 -16 (pow.f64 i 8)) (.f64 -4 (pow.f64 i 6)))
(+.f64 (.f64 -16 (pow.f64 i 8)) (.f64 -4 (pow.f64 i 6)))
(+.f64 (.f64 -16 (pow.f64 i 8)) (.f64 -4 (pow.f64 i 6)))

Outputs
(*.f64 -4 (pow.f64 i 6))
(+.f64 (.f64 -16 (pow.f64 i 8)) (.f64 -4 (pow.f64 i 6)))
(fma.f64 -16 (pow.f64 i 8) (*.f64 -4 (pow.f64 i 6)))
(fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8)))
(.f64 (pow.f64 i 6) (fma.f64 i (.f64 i -16) -4))
(+.f64 (.f64 -16 (pow.f64 i 8)) (.f64 -4 (pow.f64 i 6)))
(fma.f64 -16 (pow.f64 i 8) (*.f64 -4 (pow.f64 i 6)))
(fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8)))
(.f64 (pow.f64 i 6) (fma.f64 i (.f64 i -16) -4))
(+.f64 (.f64 -16 (pow.f64 i 8)) (.f64 -4 (pow.f64 i 6)))
(fma.f64 -16 (pow.f64 i 8) (*.f64 -4 (pow.f64 i 6)))
(fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8)))
(.f64 (pow.f64 i 6) (fma.f64 i (.f64 i -16) -4))
(*.f64 -16 (pow.f64 i 8))
(+.f64 (.f64 -16 (pow.f64 i 8)) (.f64 -4 (pow.f64 i 6)))
(fma.f64 -16 (pow.f64 i 8) (*.f64 -4 (pow.f64 i 6)))
(fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8)))
(.f64 (pow.f64 i 6) (fma.f64 i (.f64 i -16) -4))
(+.f64 (.f64 -16 (pow.f64 i 8)) (.f64 -4 (pow.f64 i 6)))
(fma.f64 -16 (pow.f64 i 8) (*.f64 -4 (pow.f64 i 6)))
(fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8)))
(.f64 (pow.f64 i 6) (fma.f64 i (.f64 i -16) -4))
(+.f64 (.f64 -16 (pow.f64 i 8)) (.f64 -4 (pow.f64 i 6)))
(fma.f64 -16 (pow.f64 i 8) (*.f64 -4 (pow.f64 i 6)))
(fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8)))
(.f64 (pow.f64 i 6) (fma.f64 i (.f64 i -16) -4))
(*.f64 -16 (pow.f64 i 8))
(+.f64 (.f64 -16 (pow.f64 i 8)) (.f64 -4 (pow.f64 i 6)))
(fma.f64 -16 (pow.f64 i 8) (*.f64 -4 (pow.f64 i 6)))
(fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8)))
(.f64 (pow.f64 i 6) (fma.f64 i (.f64 i -16) -4))
(+.f64 (.f64 -16 (pow.f64 i 8)) (.f64 -4 (pow.f64 i 6)))
(fma.f64 -16 (pow.f64 i 8) (*.f64 -4 (pow.f64 i 6)))
(fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8)))
(.f64 (pow.f64 i 6) (fma.f64 i (.f64 i -16) -4))
(+.f64 (.f64 -16 (pow.f64 i 8)) (.f64 -4 (pow.f64 i 6)))
(fma.f64 -16 (pow.f64 i 8) (*.f64 -4 (pow.f64 i 6)))
(fma.f64 -4 (pow.f64 i 6) (*.f64 -16 (pow.f64 i 8)))
(.f64 (pow.f64 i 6) (fma.f64 i (.f64 i -16) -4))

eval22.0ms (1.3%)

Compiler: Compiled 912 to 704 computations (22.8% saved)

prune29.0ms (1.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	39	0	39
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	39	2	41

Error

Counts

41 → 2

Alt Table

Click to see full alt table

Status	Error	Program
✓	4.1b	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
✓	33.0b	(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)))

Compiler

Compiled 30 to 23 computations (23.3% saved)

regimes14.0ms (0.8%)

Accuracy

Total -53.1b remaining (-∞%)

Threshold costs -53.1b (-∞%)

Counts

3 → 2

Calls

Call 1

Inputs

(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)))

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

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

Results

Time	Error	Segments	Branch
8.0ms	0b	2	`i`
5.0ms	0b	2	`(/.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 82 to 56 computations (31.7% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Point		Range
0.0ms	-0.0	∈ [	-0.0	,	0.06249999999999999	]

Compiler

Compiled 30 to 20 computations (33.3% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
6×	`*-commutative_binary64`
6×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	82
1	46	82
2	55	82
3	61	82
4	65	82
5	66	82

Stop Event

1×

saturated

Calls

Call 1

Inputs

(if (<=.f64 (/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1)) 0) (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))) (/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3)))))

Outputs

(if (<=.f64 (/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1)) 0) (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))) (/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3)))))

(if (<=.f64 (/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 i 2) (*.f64 i 2))) (+.f64 (*.f64 (*.f64 i 2) (*.f64 i 2)) -1)) 0) (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))) (/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3)))))

end38.0ms (2.2%)

Stop Event

1×

done

Compiler

Compiled 114 to 82 computations (28.1% saved)

Details

analyze8.0ms (0.5%)

sample1.1s (67.3%)

preprocess32.0ms (1.9%)

simplify20.0ms (1.2%)

eval1.0ms (0.1%)

prune3.0ms (0.2%)

localize5.0ms (0.3%)

series13.0ms (0.8%)

rewrite44.0ms (2.6%)

simplify28.0ms (1.7%)

eval30.0ms (1.8%)

prune141.0ms (8.4%)

localize14.0ms (0.8%)

series4.0ms (0.2%)

rewrite37.0ms (2.2%)

simplify66.0ms (3.9%)

eval22.0ms (1.3%)

prune29.0ms (1.7%)

regimes14.0ms (0.8%)

bsearch0.0ms (0%)

simplify4.0ms (0.2%)

end38.0ms (2.2%)

Profiling