Details

analyze277.0ms (3.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
25%	74.9%	0.1%	7
31.2%	68.7%	0.1%	8
56.2%	43.7%	0.1%	9
60.9%	39%	0.1%	10
76.5%	23.4%	0.1%	11
79.2%	20.7%	0.1%	12

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample2.0s (22.8%)

Results

2.0s	8256×	body	256	valid
0.0ms	1×	body	256	invalid

preprocess34.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

12×	`associate-/r*_binary64`
5×	`*-commutative_binary64`
4×	`associate-l_binary64`
4×	`associate-/l/_binary64`
2×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	24	26
2	39	26
3	49	26
4	49	26
0	2	2
1	2	2

Stop Event

1×	unsound
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1
0

Call 2

Inputs
(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))
(/.f64 (+.f64 y x) (.f64 (.f64 y 2) x))

Outputs
(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))
(/.f64 (+.f64 x y) (.f64 x (.f64 y 2)))
(/.f64 (+.f64 y x) (.f64 (.f64 y 2) x))
(/.f64 (+.f64 x y) (.f64 x (.f64 y 2)))

Symmetry

(sort x y)

Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify15.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

13×	`associate-/r*_binary64`
5×	`*-commutative_binary64`
4×	`associate-/l/_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	15	13
2	29	13
3	43	13
4	45	13

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))

Outputs
(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))
(/.f64 (+.f64 x y) (.f64 y (.f64 x 2)))
(/.f64 (/.f64 (+.f64 x y) x) (*.f64 y 2))

eval3.0ms (0%)

Compiler: Compiled 20 to 11 computations (45% saved)

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	17.1b	(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))
▶	7.3b	(/.f64 (/.f64 (+.f64 x y) x) (*.f64 y 2))

Compiler

Compiled 22 to 14 computations (36.4% saved)

localize21.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	16.4b	(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))

Compiler

Compiled 25 to 13 computations (48% saved)

series45.0ms (0.5%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
37.0ms	x	@	0	(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))
2.0ms	y	@	-inf	(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))
2.0ms	x	@	-inf	(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))
2.0ms	x	@	inf	(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))
1.0ms	y	@	inf	(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))

rewrite80.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

517×	`log-prod_binary64`
482×	`prod-diff_binary64`
321×	`pow-prod-down_binary64`
243×	`pow2_binary64`
180×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	180	13
2	2668	13

Stop Event

1×	node limit

Counts

1 → 54

Calls

Call 1

Inputs
(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))

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

Outputs

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

simplify80.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`associate-*r/_binary64`
1×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	204
1	21	204
2	28	204

Stop Event

1×

saturated

Counts

78 → 58

Calls

Call 1

Inputs
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))

Outputs
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))

localize16.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x y) x)
✓	6.9b	(/.f64 (/.f64 (+.f64 x y) x) (*.f64 y 2))

Compiler

Compiled 25 to 10 computations (60% saved)

series6.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/.f64 (+.f64 x y) x)
1.0ms	x	@	-inf	(/.f64 (+.f64 x y) x)
1.0ms	y	@	-inf	(/.f64 (+.f64 x y) x)
1.0ms	y	@	0	(/.f64 (+.f64 x y) x)
1.0ms	x	@	0	(/.f64 (/.f64 (+.f64 x y) x) (*.f64 y 2))

rewrite99.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

544×	`log-prod_binary64`
500×	`prod-diff_binary64`
348×	`pow-prod-down_binary64`
257×	`pow2_binary64`
199×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	186	20
2	2938	20

Stop Event

1×	node limit

Counts

2 → 95

Calls

Call 1

Inputs
(/.f64 (/.f64 (+.f64 x y) x) (*.f64 y 2))
(/.f64 (+.f64 x y) x)

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

Outputs

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

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

simplify22.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`associate-*r/_binary64`
1×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	345
1	24	345
2	31	345

Stop Event

1×

saturated

Counts

143 → 103

Calls

Call 1

Inputs
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 y x)
(+.f64 1 (/.f64 y x))
(+.f64 1 (/.f64 y x))
(+.f64 1 (/.f64 y x))
1
(+.f64 (/.f64 y x) 1)
(+.f64 (/.f64 y x) 1)
(+.f64 (/.f64 y x) 1)
1
(+.f64 (/.f64 y x) 1)
(+.f64 (/.f64 y x) 1)
(+.f64 (/.f64 y x) 1)
1
(+.f64 (/.f64 y x) 1)
(+.f64 (/.f64 y x) 1)
(+.f64 (/.f64 y x) 1)
(/.f64 y x)
(+.f64 1 (/.f64 y x))
(+.f64 1 (/.f64 y x))
(+.f64 1 (/.f64 y x))
(/.f64 y x)
(+.f64 1 (/.f64 y x))
(+.f64 1 (/.f64 y x))
(+.f64 1 (/.f64 y x))

Outputs
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 y x)
(+.f64 1 (/.f64 y x))
(+.f64 1 (/.f64 y x))
(+.f64 1 (/.f64 y x))
1
(+.f64 (/.f64 y x) 1)
(+.f64 1 (/.f64 y x))
(+.f64 (/.f64 y x) 1)
(+.f64 1 (/.f64 y x))
(+.f64 (/.f64 y x) 1)
(+.f64 1 (/.f64 y x))
1
(+.f64 (/.f64 y x) 1)
(+.f64 1 (/.f64 y x))
(+.f64 (/.f64 y x) 1)
(+.f64 1 (/.f64 y x))
(+.f64 (/.f64 y x) 1)
(+.f64 1 (/.f64 y x))
1
(+.f64 (/.f64 y x) 1)
(+.f64 1 (/.f64 y x))
(+.f64 (/.f64 y x) 1)
(+.f64 1 (/.f64 y x))
(+.f64 (/.f64 y x) 1)
(+.f64 1 (/.f64 y x))
(/.f64 y x)
(+.f64 1 (/.f64 y x))
(+.f64 1 (/.f64 y x))
(+.f64 1 (/.f64 y x))
(/.f64 y x)
(+.f64 1 (/.f64 y x))
(+.f64 1 (/.f64 y x))
(+.f64 1 (/.f64 y x))

eval85.0ms (1%)

Compiler: Compiled 2289 to 957 computations (58.2% saved)

prune78.0ms (0.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	154	7	161
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	155	8	163

Error

Counts

163 → 8

Alt Table

Click to see full alt table

Status	Error	Program
✓	17.1b	(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))
▶	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
▶	7.3b	(/.f64 (+.f64 (/.f64 y x) 1) (*.f64 y 2))
▶	29.7b	(/.f64 1/2 y)
▶	33.5b	(/.f64 1/2 x)
	18.1b	(*.f64 (/.f64 (sqrt.f64 (/.f64 (+.f64 x y) x)) y) (/.f64 (sqrt.f64 (/.f64 (+.f64 x y) x)) 2))
▶	7.4b	(*.f64 (/.f64 (+.f64 x y) x) (/.f64 1/2 y))
	18.1b	(/.f64 (pow.f64 (sqrt.f64 (/.f64 (+.f64 x y) x)) 2) (*.f64 y 2))

Compiler

Compiled 159 to 105 computations (34% saved)

localize96.0ms (1.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))

Compiler

Compiled 18 to 12 computations (33.3% saved)

series5.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	y	@	0	(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
1.0ms	x	@	0	(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
1.0ms	y	@	inf	(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
1.0ms	y	@	-inf	(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
1.0ms	x	@	inf	(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))

rewrite90.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

903×	`prod-diff_binary64`
555×	`unpow-prod-down_binary64`
401×	`log-prod_binary64`
290×	`fma-def_binary64`
230×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	167	10
2	2527	10

Stop Event

1×	node limit

Counts

1 → 89

Calls

Call 1

Inputs
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))

Outputs

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

simplify64.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`associate-*r/_binary64`
1×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	204
1	21	204
2	28	204

Stop Event

1×

saturated

Counts

113 → 93

Calls

Call 1

Inputs
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))

Outputs
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))

localize8.0ms (0.1%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

localize8.0ms (0.1%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

localize21.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (+.f64 x y) x)
✓	6.9b	(*.f64 (/.f64 (+.f64 x y) x) (/.f64 1/2 y))

Compiler

Compiled 25 to 10 computations (60% saved)

series3.0ms (0%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(*.f64 (/.f64 (+.f64 x y) x) (/.f64 1/2 y))
0.0ms	x	@	inf	(*.f64 (/.f64 (+.f64 x y) x) (/.f64 1/2 y))
0.0ms	x	@	-inf	(*.f64 (/.f64 (+.f64 x y) x) (/.f64 1/2 y))
0.0ms	y	@	-inf	(*.f64 (/.f64 (+.f64 x y) x) (/.f64 1/2 y))
0.0ms	y	@	0	(*.f64 (/.f64 (+.f64 x y) x) (/.f64 1/2 y))

rewrite96.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

496×	`log-prod_binary64`
482×	`prod-diff_binary64`
363×	`pow-prod-down_binary64`
257×	`pow2_binary64`
209×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	189	13
2	2860	13

Stop Event

1×	node limit

Counts

1 → 64

Calls

Call 1

Inputs
(*.f64 (/.f64 (+.f64 x y) x) (/.f64 1/2 y))

Outputs

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

simplify25.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`associate-*r/_binary64`
1×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	204
1	21	204
2	28	204

Stop Event

1×

saturated

Counts

88 → 68

Calls

Call 1

Inputs
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))

Outputs
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))

localize21.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	6.9b	(/.f64 (+.f64 (/.f64 y x) 1) (*.f64 y 2))

Compiler

Compiled 26 to 14 computations (46.2% saved)

series9.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	y	@	-inf	(/.f64 (+.f64 (/.f64 y x) 1) (*.f64 y 2))
1.0ms	y	@	0	(/.f64 (+.f64 (/.f64 y x) 1) (*.f64 y 2))
1.0ms	y	@	inf	(/.f64 (+.f64 (/.f64 y x) 1) (*.f64 y 2))
1.0ms	x	@	-inf	(/.f64 (+.f64 (/.f64 y x) 1) (*.f64 y 2))
1.0ms	x	@	0	(/.f64 (+.f64 (/.f64 y x) 1) (*.f64 y 2))

rewrite101.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

501×	`log-prod_binary64`
386×	`exp-prod_binary64`
277×	`prod-diff_binary64`
271×	`pow-prod-down_binary64`
251×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	197	13
2	2753	13

Stop Event

1×	node limit

Counts

1 → 54

Calls

Call 1

Inputs
(/.f64 (+.f64 (/.f64 y x) 1) (*.f64 y 2))

Outputs

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

simplify44.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`associate-*r/_binary64`
1×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	204
1	21	204
2	28	204

Stop Event

1×

saturated

Counts

78 → 58

Calls

Call 1

Inputs
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))

Outputs
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))

eval195.0ms (2.2%)

Compiler: Compiled 3548 to 2118 computations (40.3% saved)

prune144.0ms (1.6%)

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	261	1	262
Fresh	2	0	2
Picked	0	1	1
Done	0	5	5
Total	263	7	270

Error

Counts

270 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	17.1b	(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))
✓	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
✓	7.3b	(/.f64 (+.f64 (/.f64 y x) 1) (*.f64 y 2))
✓	29.7b	(/.f64 1/2 y)
✓	33.5b	(/.f64 1/2 x)
✓	7.4b	(*.f64 (/.f64 (+.f64 x y) x) (/.f64 1/2 y))
▶	32.3b	(/.f64 (-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))

Compiler

Compiled 73 to 52 computations (28.8% saved)

localize83.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1/4 (*.f64 x x))
✓	0.7b	(/.f64 1/4 (*.f64 y y))
✓	4.2b	(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
✓	29.8b	(/.f64 (-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))

Compiler

Compiled 65 to 35 computations (46.2% saved)

series17.0ms (0.2%)

Counts

4 → 72

Calls

18 calls:

Time	Variable		Point	Expression
2.0ms	y	@	0	(/.f64 (-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
2.0ms	x	@	0	(/.f64 (-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
1.0ms	y	@	inf	(/.f64 (-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
1.0ms	x	@	inf	(/.f64 (-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
1.0ms	y	@	-inf	(/.f64 (-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))

rewrite211.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

674×	`fma-def_binary64`
374×	`fma-neg_binary64`
302×	`expm1-udef_binary64`
302×	`log1p-udef_binary64`
183×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	58
1	347	37
2	5705	37

Stop Event

1×	node limit

Counts

4 → 295

Calls

Call 1

Inputs
(/.f64 (-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
(/.f64 1/4 (*.f64 y y))
(/.f64 1/4 (*.f64 x x))

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

simplify115.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

795×	`fma-def_binary64`
549×	`distribute-neg-frac_binary64`
505×	`associate-*l/_binary64`
462×	`associate-/l*_binary64`
422×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	702
1	52	702
2	89	702
3	167	702
4	430	702
5	1527	702
6	5162	702
7	7007	702

Stop Event

1×	node limit

Counts

367 → 306

Calls

Call 1

Inputs
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/4 (pow.f64 y 2))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(/.f64 -1/4 (pow.f64 x 2))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(/.f64 -1/4 (pow.f64 x 2))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(/.f64 -1/4 (pow.f64 x 2))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(/.f64 1/4 (pow.f64 y 2))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(/.f64 1/4 (pow.f64 y 2))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (pow.f64 x 2))
(/.f64 1/4 (pow.f64 x 2))
(/.f64 1/4 (pow.f64 x 2))
(/.f64 1/4 (pow.f64 x 2))
(/.f64 1/4 (pow.f64 x 2))
(/.f64 1/4 (pow.f64 x 2))
(/.f64 1/4 (pow.f64 x 2))
(/.f64 1/4 (pow.f64 x 2))
(/.f64 1/4 (pow.f64 x 2))
(/.f64 1/4 (pow.f64 x 2))
(/.f64 1/4 (pow.f64 x 2))
(/.f64 1/4 (pow.f64 x 2))

Outputs
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 x)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/2 y)
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(+.f64 (.f64 1/2 (/.f64 1 y)) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (*.f64 y y))
(/.f64 (/.f64 1/4 y) y)
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
(+.f64 (/.f64 1/4 (.f64 y y)) (/.f64 -1/4 (.f64 x x)))
(+.f64 (/.f64 (/.f64 1/4 y) y) (/.f64 -1/4 (*.f64 x x)))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
(+.f64 (/.f64 1/4 (.f64 y y)) (/.f64 -1/4 (.f64 x x)))
(+.f64 (/.f64 (/.f64 1/4 y) y) (/.f64 -1/4 (*.f64 x x)))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
(+.f64 (/.f64 1/4 (.f64 y y)) (/.f64 -1/4 (.f64 x x)))
(+.f64 (/.f64 (/.f64 1/4 y) y) (/.f64 -1/4 (*.f64 x x)))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
(+.f64 (/.f64 1/4 (.f64 y y)) (/.f64 -1/4 (.f64 x x)))
(+.f64 (/.f64 (/.f64 1/4 y) y) (/.f64 -1/4 (*.f64 x x)))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
(+.f64 (/.f64 1/4 (.f64 y y)) (/.f64 -1/4 (.f64 x x)))
(+.f64 (/.f64 (/.f64 1/4 y) y) (/.f64 -1/4 (*.f64 x x)))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
(+.f64 (/.f64 1/4 (.f64 y y)) (/.f64 -1/4 (.f64 x x)))
(+.f64 (/.f64 (/.f64 1/4 y) y) (/.f64 -1/4 (*.f64 x x)))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
(+.f64 (/.f64 1/4 (.f64 y y)) (/.f64 -1/4 (.f64 x x)))
(+.f64 (/.f64 (/.f64 1/4 y) y) (/.f64 -1/4 (*.f64 x x)))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
(+.f64 (/.f64 1/4 (.f64 y y)) (/.f64 -1/4 (.f64 x x)))
(+.f64 (/.f64 (/.f64 1/4 y) y) (/.f64 -1/4 (*.f64 x x)))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
(+.f64 (/.f64 1/4 (.f64 y y)) (/.f64 -1/4 (.f64 x x)))
(+.f64 (/.f64 (/.f64 1/4 y) y) (/.f64 -1/4 (*.f64 x x)))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
(+.f64 (/.f64 1/4 (.f64 y y)) (/.f64 -1/4 (.f64 x x)))
(+.f64 (/.f64 (/.f64 1/4 y) y) (/.f64 -1/4 (*.f64 x x)))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
(+.f64 (/.f64 1/4 (.f64 y y)) (/.f64 -1/4 (.f64 x x)))
(+.f64 (/.f64 (/.f64 1/4 y) y) (/.f64 -1/4 (*.f64 x x)))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
(+.f64 (/.f64 1/4 (.f64 y y)) (/.f64 -1/4 (.f64 x x)))
(+.f64 (/.f64 (/.f64 1/4 y) y) (/.f64 -1/4 (*.f64 x x)))
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (*.f64 y y))
(/.f64 (/.f64 1/4 y) y)
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
(+.f64 (/.f64 1/4 (.f64 y y)) (/.f64 -1/4 (.f64 x x)))
(+.f64 (/.f64 (/.f64 1/4 y) y) (/.f64 -1/4 (*.f64 x x)))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
(+.f64 (/.f64 1/4 (.f64 y y)) (/.f64 -1/4 (.f64 x x)))
(+.f64 (/.f64 (/.f64 1/4 y) y) (/.f64 -1/4 (*.f64 x x)))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
(+.f64 (/.f64 1/4 (.f64 y y)) (/.f64 -1/4 (.f64 x x)))
(+.f64 (/.f64 (/.f64 1/4 y) y) (/.f64 -1/4 (*.f64 x x)))
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (*.f64 y y))
(/.f64 (/.f64 1/4 y) y)
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
(+.f64 (/.f64 1/4 (.f64 y y)) (/.f64 -1/4 (.f64 x x)))
(+.f64 (/.f64 (/.f64 1/4 y) y) (/.f64 -1/4 (*.f64 x x)))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
(+.f64 (/.f64 1/4 (.f64 y y)) (/.f64 -1/4 (.f64 x x)))
(+.f64 (/.f64 (/.f64 1/4 y) y) (/.f64 -1/4 (*.f64 x x)))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 y 2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x)))
(+.f64 (/.f64 1/4 (.f64 y y)) (/.f64 -1/4 (.f64 x x)))
(+.f64 (/.f64 (/.f64 1/4 y) y) (/.f64 -1/4 (*.f64 x x)))
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (*.f64 y y))
(/.f64 (/.f64 1/4 y) y)
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (*.f64 y y))
(/.f64 (/.f64 1/4 y) y)
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (*.f64 y y))
(/.f64 (/.f64 1/4 y) y)
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (*.f64 y y))
(/.f64 (/.f64 1/4 y) y)
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (*.f64 y y))
(/.f64 (/.f64 1/4 y) y)
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (*.f64 y y))
(/.f64 (/.f64 1/4 y) y)
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (*.f64 y y))
(/.f64 (/.f64 1/4 y) y)
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (*.f64 y y))
(/.f64 (/.f64 1/4 y) y)
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (*.f64 y y))
(/.f64 (/.f64 1/4 y) y)
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (*.f64 y y))
(/.f64 (/.f64 1/4 y) y)
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (*.f64 y y))
(/.f64 (/.f64 1/4 y) y)
(/.f64 1/4 (pow.f64 y 2))
(/.f64 1/4 (*.f64 y y))
(/.f64 (/.f64 1/4 y) y)
(/.f64 1/4 (pow.f64 x 2))
(/.f64 1/4 (*.f64 x x))
(/.f64 1/4 (pow.f64 x 2))
(/.f64 1/4 (*.f64 x x))
(/.f64 1/4 (pow.f64 x 2))
(/.f64 1/4 (*.f64 x x))
(/.f64 1/4 (pow.f64 x 2))
(/.f64 1/4 (*.f64 x x))
(/.f64 1/4 (pow.f64 x 2))
(/.f64 1/4 (*.f64 x x))
(/.f64 1/4 (pow.f64 x 2))
(/.f64 1/4 (*.f64 x x))
(/.f64 1/4 (pow.f64 x 2))
(/.f64 1/4 (*.f64 x x))
(/.f64 1/4 (pow.f64 x 2))
(/.f64 1/4 (*.f64 x x))
(/.f64 1/4 (pow.f64 x 2))
(/.f64 1/4 (*.f64 x x))
(/.f64 1/4 (pow.f64 x 2))
(/.f64 1/4 (*.f64 x x))
(/.f64 1/4 (pow.f64 x 2))
(/.f64 1/4 (*.f64 x x))
(/.f64 1/4 (pow.f64 x 2))
(/.f64 1/4 (*.f64 x x))

eval4.3s (48.4%)

Compiler: Compiled 7684 to 5642 computations (26.6% saved)

prune124.0ms (1.4%)

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	306	0	306
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	306	7	313

Error

Counts

313 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	17.1b	(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))
✓	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
✓	7.3b	(/.f64 (+.f64 (/.f64 y x) 1) (*.f64 y 2))
✓	29.7b	(/.f64 1/2 y)
✓	33.5b	(/.f64 1/2 x)
✓	7.4b	(*.f64 (/.f64 (+.f64 x y) x) (/.f64 1/2 y))
✓	32.3b	(/.f64 (-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))

Compiler

Compiled 73 to 52 computations (28.8% saved)

regimes23.0ms (0.3%)

Counts

10 → 1

Calls

Call 1

Inputs
(/.f64 1/2 y)
(/.f64 1/2 x)
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
(/.f64 (+.f64 (/.f64 y x) 1) (*.f64 y 2))
(*.f64 (/.f64 (+.f64 x y) x) (/.f64 1/2 y))
(/.f64 (/.f64 (+.f64 x y) x) (*.f64 y 2))
(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))
(/.f64 (-.f64 (/.f64 1/4 (.f64 y y)) (/.f64 1/4 (.f64 x x))) (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
(/.f64 (pow.f64 (sqrt.f64 (/.f64 (+.f64 x y) x)) 2) (*.f64 y 2))
(*.f64 (/.f64 (sqrt.f64 (/.f64 (+.f64 x y) x)) y) (/.f64 (sqrt.f64 (/.f64 (+.f64 x y) x)) 2))

Outputs
(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))

Calls

3 calls:

8.0ms	(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))
6.0ms	y
6.0ms	x

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`y`
0.0b	1	`(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))`

Compiler

Compiled 116 to 63 computations (45.7% saved)

regimes46.0ms (0.5%)

Accuracy

Total -52.4b remaining (-562%)

Threshold costs -52.4b (-562%)

Counts

2 → 4

Calls

Call 1

Inputs
(/.f64 1/2 y)
(/.f64 1/2 x)

Outputs
(/.f64 1/2 y)
(/.f64 1/2 x)
(/.f64 1/2 y)
(/.f64 1/2 x)

Calls

2 calls:

34.0ms	y
11.0ms	x

Results

Error	Segments	Branch
9.3b	4	`x`
10.1b	2	`y`

Compiler

Compiled 14 to 10 computations (28.6% saved)

bsearch55.0ms (0.6%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
18.0ms	-3.515213645947372e-196	-2.8744446548670264e-202
19.0ms	-3.439993204440938e-109	-1.341707184037203e-109
18.0ms	-1.2855552766150297e-85	-7.243602304809988e-91

Compiler

Compiled 16 to 11 computations (31.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	48
1	18	48

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs

(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))

(if (<=.f64 x -8997861473679517/69992023193056381579920071267763883691301421788582797965624659405118495974380029543152421664737722368) (/.f64 1/2 y) (if (<=.f64 x -7276889729259443/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192) (/.f64 1/2 x) (if (<=.f64 x -3698100300132105/10520271803096747014481979765760257331100679605646347718996561806137464308594161644227333072555176902453965937712356435426038864500367607726255629541303761699910447342256889196383327515768645434542586503471562752) (/.f64 1/2 y) (/.f64 1/2 x))))

(/.f64 1/2 y)

Outputs

(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))

(if (<=.f64 x -8997861473679517/69992023193056381579920071267763883691301421788582797965624659405118495974380029543152421664737722368) (/.f64 1/2 y) (if (<=.f64 x -7276889729259443/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192) (/.f64 1/2 x) (if (<=.f64 x -3698100300132105/10520271803096747014481979765760257331100679605646347718996561806137464308594161644227333072555176902453965937712356435426038864500367607726255629541303761699910447342256889196383327515768645434542586503471562752) (/.f64 1/2 y) (/.f64 1/2 x))))

(/.f64 1/2 y)

Compiler

Compiled 40 to 30 computations (25% saved)

soundness60.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

13×	`associate-/r*_binary64`
5×	`*-commutative_binary64`
4×	`fma-def_binary64`
4×	`associate-/l/_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	15	13
2	29	13
3	43	13
4	45	13
0	15	345
1	24	345
2	31	345

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 101 to 75 computations (25.7% saved)

end30.0ms (0.3%)

Remove: (sort x y)
Compiler: Compiled 54 to 40 computations (25.9% saved)

Details

analyze277.0ms (3.1%)

sample2.0s (22.8%)

preprocess34.0ms (0.4%)

simplify15.0ms (0.2%)

eval3.0ms (0%)

prune3.0ms (0%)

localize21.0ms (0.2%)

series45.0ms (0.5%)

rewrite80.0ms (0.9%)

simplify80.0ms (0.9%)

localize16.0ms (0.2%)

series6.0ms (0.1%)

rewrite99.0ms (1.1%)

simplify22.0ms (0.3%)

eval85.0ms (1%)

prune78.0ms (0.9%)

localize96.0ms (1.1%)

series5.0ms (0.1%)

rewrite90.0ms (1%)

simplify64.0ms (0.7%)

localize8.0ms (0.1%)

localize8.0ms (0.1%)

localize21.0ms (0.2%)

series3.0ms (0%)

rewrite96.0ms (1.1%)

simplify25.0ms (0.3%)

localize21.0ms (0.2%)

series9.0ms (0.1%)

rewrite101.0ms (1.1%)

simplify44.0ms (0.5%)

eval195.0ms (2.2%)

prune144.0ms (1.6%)

localize83.0ms (0.9%)

series17.0ms (0.2%)

rewrite211.0ms (2.4%)

simplify115.0ms (1.3%)

eval4.3s (48.4%)

prune124.0ms (1.4%)

regimes23.0ms (0.3%)

regimes46.0ms (0.5%)

bsearch55.0ms (0.6%)

simplify4.0ms (0%)

soundness60.0ms (0.7%)

end30.0ms (0.3%)

Profiling