Details

analyze365.0ms (20.2%)

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
87.8%	12.1%	0.1%	13
89.3%	10.6%	0.1%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample875.0ms (48.4%)

Results

862.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 24 to 16 computations (33.3% saved)

preprocess16.0ms (0.9%)

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

Symmetry

(sort x y)

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify7.0ms (0.4%)

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

prune5.0ms (0.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

17.1b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 42 to 25 computations (40.5% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	16.3b	(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))

series5.0ms (0.3%)

Counts

1 → 24

Calls

6 calls:

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

rewrite48.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

517×	`log-prod_binary64`
482×	`prod-diff_binary64`
180×	`fma-def_binary64`
167×	`expm1-udef_binary64`
167×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	180	13
2	2662	13

Stop Event

1×	node limit

Counts

1 → 46

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

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

simplify12.0ms (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

70 → 50

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))

prune27.0ms (1.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	47	3	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	3	51

Error

Counts

51 → 3

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
	36.5b	(.f64 (/.f64 (sqrt.f64 (+.f64 x y)) x) (/.f64 (sqrt.f64 (+.f64 x y)) (.f64 y 2)))
	7.4b	(*.f64 (/.f64 (+.f64 x y) (+.f64 x x)) (/.f64 1 y))

Compiler

Compiled 820 to 437 computations (46.7% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.3%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	y	@	-inf	(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
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))
0.0ms	y	@	inf	(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
0.0ms	x	@	inf	(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))

rewrite44.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

903×	`prod-diff_binary64`
290×	`fma-def_binary64`
158×	`expm1-udef_binary64`
158×	`log1p-udef_binary64`
153×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	167	10
2	2523	10

Stop Event

1×	node limit

Counts

1 → 68

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

simplify11.0ms (0.6%)

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

92 → 72

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))

prune39.0ms (2.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	72	3	75

Error

Counts

75 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
▶	7.4b	(/.f64 (/.f64 (fma.f64 1/2 y (*.f64 1/2 x)) y) x)
	36.5b	(.f64 (/.f64 (sqrt.f64 (+.f64 x y)) x) (/.f64 (sqrt.f64 (+.f64 x y)) (.f64 y 2)))

Compiler

Compiled 1026 to 706 computations (31.2% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (fma.f64 1/2 y (*.f64 1/2 x)) y)
✓	6.8b	(/.f64 (/.f64 (fma.f64 1/2 y (*.f64 1/2 x)) y) x)

series8.0ms (0.4%)

Counts

2 → 48

Calls

12 calls:

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

rewrite53.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

475×	`log-prod_binary64`
235×	`pow2_binary64`
165×	`pow1/3_binary64`
162×	`expm1-udef_binary64`
162×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	25
1	174	23
2	2400	23

Stop Event

1×	node limit

Counts

2 → 85

Calls

Call 1

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

Outputs

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

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

simplify36.0ms (2%)

Algorithm

1×	egg-herbie

Rules

36×	`fma-def_binary64`
30×	`associate-/l*_binary64`
21×	`associate-/l/_binary64`
21×	`times-frac_binary64`
18×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	372
1	29	372
2	43	372
3	48	372
4	53	372
5	64	372
6	75	372
7	108	372
8	126	372
9	137	372
10	152	372
11	182	372
12	244	372
13	271	372
14	281	372

Stop Event

1×

saturated

Counts

133 → 94

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

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

prune43.0ms (2.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	94	3	97

Error

Counts

97 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
▶	7.3b	(/.f64 (fma.f64 1/2 (/.f64 x y) 1/2) x)
✓	7.4b	(/.f64 (/.f64 (fma.f64 1/2 y (*.f64 1/2 x)) y) x)

Compiler

Compiled 1410 to 792 computations (43.8% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/2 (/.f64 x y) 1/2)
✓	6.8b	(/.f64 (fma.f64 1/2 (/.f64 x y) 1/2) x)

series5.0ms (0.3%)

Counts

2 → 48

Calls

12 calls:

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

rewrite43.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

822×	`pow1_binary64`
764×	`log1p-expm1-u_binary64`
764×	`expm1-log1p-u_binary64`
77×	`add-sqr-sqrt_binary64`
75×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	151	19
2	2002	19

Stop Event

1×	node limit

Counts

2 → 56

Calls

Call 1

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

Outputs

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

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

simplify36.0ms (2%)

Algorithm

1×	egg-herbie

Rules

36×	`fma-def_binary64`
29×	`associate-/l*_binary64`
21×	`associate-/l/_binary64`
21×	`times-frac_binary64`
18×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	372
1	29	372
2	43	372
3	48	372
4	53	372
5	64	372
6	75	372
7	108	372
8	126	372
9	137	372
10	152	372
11	182	372
12	244	372
13	270	372
14	280	372

Stop Event

1×

saturated

Counts

104 → 63

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

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

prune31.0ms (1.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	63	3	66

Error

Counts

66 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 1/2 x))
✓	7.3b	(/.f64 (fma.f64 1/2 (/.f64 x y) 1/2) x)
✓	7.4b	(/.f64 (/.f64 (fma.f64 1/2 y (*.f64 1/2 x)) y) x)

Compiler

Compiled 845 to 528 computations (37.5% saved)

regimes26.0ms (1.5%)

Accuracy

Total 0.0b remaining (70.6%)

Threshold costs 0.0b (70.6%)

Counts

12 → 1

Compiler

Compiled 142 to 85 computations (40.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	8	10

Stop Event

1×

saturated

Calls

Call 1

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

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

end46.0ms (2.5%)

Stop Event

1×

done

Remove

(sort x y)

Compiler

Compiled 67 to 50 computations (25.4% saved)

Iter	Nodes	Cost
0	16	372
1	29	372
2	43	372
3	48	372
4	53	372
5	64	372
6	75	372
7	108	372
8	126	372
9	137	372
10	152	372
11	182	372
12	244	372
13	271	372
14	281	372

Iter	Nodes	Cost
0	16	372
1	29	372
2	43	372
3	48	372
4	53	372
5	64	372
6	75	372
7	108	372
8	126	372
9	137	372
10	152	372
11	182	372
12	244	372
13	270	372
14	280	372

Iter	Nodes	Cost
0	16	372
1	29	372
2	43	372
3	48	372
4	53	372
5	64	372
6	75	372
7	108	372
8	126	372
9	137	372
10	152	372
11	182	372
12	244	372
13	271	372
14	281	372

Iter	Nodes	Cost
0	16	372
1	29	372
2	43	372
3	48	372
4	53	372
5	64	372
6	75	372
7	108	372
8	126	372
9	137	372
10	152	372
11	182	372
12	244	372
13	270	372
14	280	372

Details

analyze365.0ms (20.2%)

sample875.0ms (48.4%)

preprocess16.0ms (0.9%)

simplify7.0ms (0.4%)

prune5.0ms (0.3%)

localize5.0ms (0.3%)

series5.0ms (0.3%)

rewrite48.0ms (2.7%)

simplify12.0ms (0.7%)

prune27.0ms (1.5%)

localize4.0ms (0.2%)

series6.0ms (0.3%)

rewrite44.0ms (2.4%)

simplify11.0ms (0.6%)

prune39.0ms (2.1%)

localize6.0ms (0.3%)

series8.0ms (0.4%)

rewrite53.0ms (2.9%)

simplify36.0ms (2%)

prune43.0ms (2.4%)

localize6.0ms (0.3%)

series5.0ms (0.3%)

rewrite43.0ms (2.4%)

simplify36.0ms (2%)

prune31.0ms (1.7%)

regimes26.0ms (1.5%)

simplify2.0ms (0.1%)

end46.0ms (2.5%)

Profiling

Iter	Nodes	Cost
0	16	372
1	29	372
2	43	372
3	48	372
4	53	372
5	64	372
6	75	372
7	108	372
8	126	372
9	137	372
10	152	372
11	182	372
12	244	372
13	271	372
14	281	372

Iter	Nodes	Cost
0	16	372
1	29	372
2	43	372
3	48	372
4	53	372
5	64	372
6	75	372
7	108	372
8	126	372
9	137	372
10	152	372
11	182	372
12	244	372
13	270	372
14	280	372