Details

analyze111.0ms (2.3%)

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)

sample1.1s (22.4%)

Results

1.1s

8256×

body

256

valid

preprocess68.0ms (1.4%)

Algorithm

2×	egg-herbie

Rules

609×	`cancel-sign-sub-inv_binary64`
398×	`associate-*l/_binary64`
335×	`associate-l_binary64`
324×	`distribute-rgt-out--_binary64`
304×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	35	26
2	89	20
3	201	20
4	402	20
5	1096	20
6	5202	20
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

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

Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify76.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

921×	`fma-neg_binary64`
628×	`times-frac_binary64`
467×	`neg-mul-1_binary64`
305×	`*-commutative_binary64`
304×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	53	10
3	124	10
4	256	10
5	541	10
6	1084	10
7	4068	10
8	7900	10

Stop Event

1×	node limit

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

eval1.0ms (0%)

Compiler: Compiled 18 to 12 computations (33.3% saved)

prune2.0ms (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

0.0b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(-.f64 (/.f64 -1/2 x) (/.f64 -1/2 y))
▶	17.7b	(/.f64 (-.f64 x y) (.f64 (.f64 x 2) y))

Compiler

Compiled 20 to 14 computations (30% saved)

localize17.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 18 to 12 computations (33.3% saved)

series6.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite118.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

709×	`prod-diff_binary64`
570×	`unpow-prod-down_binary64`
410×	`log-prod_binary64`
269×	`fma-def_binary64`
233×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	168	10
2	2510	10

Stop Event

1×	node limit

Counts

1 → 152

Calls

Call 1

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

Outputs
((#(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 -1/2 x) (.f64 (/.f64 1/2 y) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 -1/2 x) (/.f64 1/2 y)) (fma.f64 (neg.f64 (/.f64 1 y)) -1/2 (/.f64 -1/2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 -1/2 x) (/.f64 1/2 y)) (fma.f64 (/.f64 1/2 y) 1 (/.f64 -1/2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 -1/2 x) (/.f64 1/2 y)) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 -1/2 y))) (cbrt.f64 (/.f64 1/4 (.f64 y y))) (/.f64 -1/2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 -1/2 x) (/.f64 1/2 y)) (+.f64 (/.f64 1/2 y) (/.f64 -1/2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 -1/2 x) (/.f64 1/2 y)) (fma.f64 -1 (/.f64 -1/2 y) (/.f64 -1/2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 -1/2 x) (/.f64 1/2 y)) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 1/4 (.f64 y 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Outputs

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(neg.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 (/.f64 -1/2 y) (/.f64 -1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (sqrt.f64 (/.f64 -1/2 x)) (sqrt.f64 (/.f64 -1/2 y))) (-.f64 (sqrt.f64 (/.f64 -1/2 x)) (sqrt.f64 (/.f64 -1/2 y))) (fma.f64 (neg.f64 (/.f64 1 y)) -1/2 (/.f64 -1/2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (sqrt.f64 (/.f64 -1/2 x)) (sqrt.f64 (/.f64 -1/2 y))) (-.f64 (sqrt.f64 (/.f64 -1/2 x)) (sqrt.f64 (/.f64 -1/2 y))) (fma.f64 (/.f64 1/2 y) 1 (/.f64 -1/2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (sqrt.f64 (/.f64 -1/2 x)) (sqrt.f64 (/.f64 -1/2 y))) (-.f64 (sqrt.f64 (/.f64 -1/2 x)) (sqrt.f64 (/.f64 -1/2 y))) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 -1/2 y))) (cbrt.f64 (/.f64 1/4 (*.f64 y y))) (/.f64 -1/2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (sqrt.f64 (/.f64 -1/2 x)) (sqrt.f64 (/.f64 -1/2 y))) (-.f64 (sqrt.f64 (/.f64 -1/2 x)) (sqrt.f64 (/.f64 -1/2 y))) (+.f64 (/.f64 1/2 y) (/.f64 -1/2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (/.f64 1/4 (*.f64 y y)))) (cbrt.f64 (/.f64 -1/2 y)) (/.f64 -1/2 x))))))

simplify59.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

141×	`fma-def_binary64`
102×	`fma-neg_binary64`
46×	`cancel-sign-sub-inv_binary64`
24×	`sub-neg_binary64`
21×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	204
1	27	204
2	43	204
3	62	204
4	91	204
5	140	204
6	229	204
7	322	204
8	400	204
9	513	204
10	567	204
11	573	204

Stop Event

1×

saturated

Counts

176 → 155

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

localize25.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	17.1b	(/.f64 (-.f64 x y) (.f64 (.f64 x 2) y))

Compiler

Compiled 25 to 13 computations (48% saved)

series9.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

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

rewrite460.0ms (9.4%)

Algorithm

1×	batch-egg-rewrite

Rules

847×	`prod-diff_binary64`
567×	`log-prod_binary64`
393×	`egg-rr`
254×	`pow2_binary64`
208×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	184	13
2	2863	13

Stop Event

1×	node limit

Counts

1 → 393

Calls

Call 1

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

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

simplify86.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

141×	`fma-def_binary64`
102×	`fma-neg_binary64`
46×	`cancel-sign-sub-inv_binary64`
24×	`sub-neg_binary64`
21×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	204
1	27	204
2	43	204
3	62	204
4	91	204
5	140	204
6	229	204
7	322	204
8	400	204
9	513	204
10	567	204
11	573	204

Stop Event

1×

saturated

Counts

417 → 397

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

eval700.0ms (14.3%)

Compiler: Compiled 23287 to 14094 computations (39.5% saved)

prune129.0ms (2.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	549	3	552
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	549	5	554

Error

Counts

554 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	35.8b	(/.f64 1/2 y)
▶	27.7b	(/.f64 -1/2 x)
✓	0.0b	(-.f64 (/.f64 -1/2 x) (/.f64 -1/2 y))
✓	17.7b	(/.f64 (-.f64 x y) (.f64 (.f64 x 2) y))
▶	10.9b	(/.f64 (/.f64 (-.f64 (.f64 -1/2 y) (.f64 -1/2 x)) x) y)

Compiler

Compiled 43 to 31 computations (27.9% saved)

localize3.0ms (0.1%)

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

localize3.0ms (0.1%)

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

localize59.0ms (1.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (.f64 -1/2 y) (.f64 -1/2 x)) x)
✓	10.2b	(/.f64 (/.f64 (-.f64 (.f64 -1/2 y) (.f64 -1/2 x)) x) y)

Compiler

Compiled 38 to 25 computations (34.2% saved)

series8.0ms (0.2%)

Counts

2 → 48

Calls

12 calls:

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

rewrite183.0ms (3.7%)

Algorithm

1×	batch-egg-rewrite

Rules

651×	`log-prod_binary64`
463×	`fma-def_binary64`
298×	`pow2_binary64`
239×	`fma-neg_binary64`
208×	`pow1/3_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	221	23
2	3470	19

Stop Event

1×	node limit

Counts

2 → 114

Calls

Call 1

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

Outputs

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

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

simplify164.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

1364×	`fma-neg_binary64`
613×	`div-sub_binary64`
516×	`fma-def_binary64`
281×	`associate-/l/_binary64`
210×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	372
1	35	372
2	56	372
3	78	372
4	121	372
5	222	372
6	438	372
7	682	372
8	930	372
9	1258	372
10	1499	372
11	2146	372
12	3652	372
13	5054	372
14	5412	372
15	5578	372
16	5640	372
17	5900	372
18	6076	372
19	6080	372

Stop Event

1×

saturated

Counts

162 → 122

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

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

eval87.0ms (1.8%)

Compiler: Compiled 1664 to 993 computations (40.3% saved)

prune170.0ms (3.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	0	0	0
Picked	1	0	1
Done	1	3	4
Total	123	4	127

Error

Counts

127 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	35.8b	(/.f64 1/2 y)
✓	27.7b	(/.f64 -1/2 x)
✓	0.0b	(-.f64 (/.f64 -1/2 x) (/.f64 -1/2 y))
▶	10.9b	(/.f64 (-.f64 (*.f64 -1/2 (/.f64 y x)) -1/2) y)

Compiler

Compiled 30 to 23 computations (23.3% saved)

localize23.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	10.2b	(/.f64 (-.f64 (*.f64 -1/2 (/.f64 y x)) -1/2) y)

Compiler

Compiled 29 to 15 computations (48.3% saved)

series11.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	y	@	inf	(/.f64 (-.f64 (*.f64 -1/2 (/.f64 y x)) -1/2) y)
1.0ms	y	@	0	(/.f64 (-.f64 (*.f64 -1/2 (/.f64 y x)) -1/2) y)
1.0ms	y	@	-inf	(/.f64 (-.f64 (*.f64 -1/2 (/.f64 y x)) -1/2) y)
1.0ms	x	@	0	(/.f64 (-.f64 (*.f64 -1/2 (/.f64 y x)) -1/2) y)
1.0ms	x	@	-inf	(/.f64 (-.f64 (*.f64 -1/2 (/.f64 y x)) -1/2) y)

rewrite194.0ms (4%)

Algorithm

1×	batch-egg-rewrite

Rules

501×	`log-prod_binary64`
387×	`exp-prod_binary64`
274×	`pow-prod-down_binary64`
256×	`pow2_binary64`
179×	`pow1/3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	189	11
2	2722	11

Stop Event

1×	node limit

Counts

1 → 122

Calls

Call 1

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

Outputs

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

simplify50.0ms (1%)

Algorithm

1×	egg-herbie

Rules

141×	`fma-def_binary64`
102×	`fma-neg_binary64`
46×	`cancel-sign-sub-inv_binary64`
24×	`sub-neg_binary64`
21×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	204
1	27	204
2	43	204
3	62	204
4	91	204
5	140	204
6	229	204
7	322	204
8	400	204
9	513	204
10	567	204
11	573	204

Stop Event

1×

saturated

Counts

146 → 126

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

eval218.0ms (4.4%)

Compiler: Compiled 3176 to 2232 computations (29.7% saved)

prune180.0ms (3.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	126	4	130

Error

Counts

130 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	35.8b	(/.f64 1/2 y)
✓	27.7b	(/.f64 -1/2 x)
✓	0.0b	(-.f64 (/.f64 -1/2 x) (/.f64 -1/2 y))
✓	10.9b	(/.f64 (-.f64 (*.f64 -1/2 (/.f64 y x)) -1/2) y)

Compiler

Compiled 30 to 23 computations (23.3% saved)

regimes32.0ms (0.7%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

13.0ms	y
9.0ms	(/.f64 (-.f64 x y) (.f64 (.f64 x 2) 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 61 to 40 computations (34.4% saved)

regimes65.0ms (1.3%)

Accuracy

Total -47.2b remaining (-323.8%)

Threshold costs -47.2b (-323.8%)

Counts

2 → 3

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)

Calls

2 calls:

46.0ms	x
18.0ms	y

Results

Error	Segments	Branch
14.6b	3	`x`
15.2b	3	`y`

Compiler

Compiled 14 to 10 computations (28.6% saved)

bsearch66.0ms (1.4%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
31.0ms	1.179548848031843e-100	3.006575250170564e-93
35.0ms	-3.031556045393247e+153	-1.452538236956163e+153

Compiler

Compiled 16 to 11 computations (31.3% saved)

simplify27.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	38
1	18	38
2	25	38
3	27	38
4	28	38

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs

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

(if (<=.f64 x -3031556045393246959181170228926240470292734190045564845464069748756651076149127327825110509975246384621653430105748871069980906149274411567473409591869440) (/.f64 1/2 y) (if (<=.f64 x 4647659101910065/39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816) (/.f64 -1/2 x) (/.f64 1/2 y)))

(/.f64 1/2 y)

Outputs
(-.f64 (/.f64 -1/2 x) (/.f64 -1/2 y))
(+.f64 (/.f64 -1/2 x) (/.f64 1/2 y))
(if (<=.f64 x -3031556045393246959181170228926240470292734190045564845464069748756651076149127327825110509975246384621653430105748871069980906149274411567473409591869440) (/.f64 1/2 y) (if (<=.f64 x 4647659101910065/39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816) (/.f64 -1/2 x) (/.f64 1/2 y)))
(/.f64 1/2 y)

Compiler

Compiled 33 to 25 computations (24.2% saved)

soundness184.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

921×	`fma-neg_binary64`
628×	`times-frac_binary64`
467×	`neg-mul-1_binary64`
305×	`*-commutative_binary64`
304×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	53	10
3	124	10
4	256	10
5	541	10
6	1084	10
7	4068	10
8	7900	10

Stop Event

1×	node limit

Compiler

Compiled 303 to 219 computations (27.7% saved)

end203.0ms (4.2%)

Compiler: Compiled 29 to 21 computations (27.6% saved)

Iter	Nodes	Cost
0	13	204
1	27	204
2	43	204
3	62	204
4	91	204
5	140	204
6	229	204
7	322	204
8	400	204
9	513	204
10	567	204
11	573	204

Iter	Nodes	Cost
0	13	204
1	27	204
2	43	204
3	62	204
4	91	204
5	140	204
6	229	204
7	322	204
8	400	204
9	513	204
10	567	204
11	573	204

Iter	Nodes	Cost
0	13	204
1	27	204
2	43	204
3	62	204
4	91	204
5	140	204
6	229	204
7	322	204
8	400	204
9	513	204
10	567	204
11	573	204

Iter	Nodes	Cost
0	13	204
1	27	204
2	43	204
3	62	204
4	91	204
5	140	204
6	229	204
7	322	204
8	400	204
9	513	204
10	567	204
11	573	204

Iter	Nodes	Cost
0	13	204
1	27	204
2	43	204
3	62	204
4	91	204
5	140	204
6	229	204
7	322	204
8	400	204
9	513	204
10	567	204
11	573	204

Iter	Nodes	Cost
0	13	204
1	27	204
2	43	204
3	62	204
4	91	204
5	140	204
6	229	204
7	322	204
8	400	204
9	513	204
10	567	204
11	573	204

Details

analyze111.0ms (2.3%)

sample1.1s (22.4%)

preprocess68.0ms (1.4%)

simplify76.0ms (1.6%)

eval1.0ms (0%)

prune2.0ms (0%)

localize17.0ms (0.3%)

series6.0ms (0.1%)

rewrite118.0ms (2.4%)

simplify59.0ms (1.2%)

localize25.0ms (0.5%)

series9.0ms (0.2%)

rewrite460.0ms (9.4%)

simplify86.0ms (1.8%)

eval700.0ms (14.3%)

prune129.0ms (2.6%)

localize3.0ms (0.1%)

localize3.0ms (0.1%)

localize59.0ms (1.2%)

series8.0ms (0.2%)

rewrite183.0ms (3.7%)

simplify164.0ms (3.3%)

eval87.0ms (1.8%)

prune170.0ms (3.5%)

localize23.0ms (0.5%)

series11.0ms (0.2%)

rewrite194.0ms (4%)

simplify50.0ms (1%)

eval218.0ms (4.4%)

prune180.0ms (3.7%)

regimes32.0ms (0.7%)

regimes65.0ms (1.3%)

bsearch66.0ms (1.4%)

simplify27.0ms (0.5%)

soundness184.0ms (3.8%)

end203.0ms (4.2%)

Profiling

Iter	Nodes	Cost
0	13	204
1	27	204
2	43	204
3	62	204
4	91	204
5	140	204
6	229	204
7	322	204
8	400	204
9	513	204
10	567	204
11	573	204

Iter	Nodes	Cost
0	13	204
1	27	204
2	43	204
3	62	204
4	91	204
5	140	204
6	229	204
7	322	204
8	400	204
9	513	204
10	567	204
11	573	204

Iter	Nodes	Cost
0	13	204
1	27	204
2	43	204
3	62	204
4	91	204
5	140	204
6	229	204
7	322	204
8	400	204
9	513	204
10	567	204
11	573	204