Details

analyze286.0ms (14.9%)

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)

sample943.0ms (49.3%)

Results

927.0ms

8256×

body

128

valid

preprocess41.0ms (2.1%)

Algorithm

2×	egg-herbie

Rules

403×	`associate-*l/_binary64`
286×	`fma-def_binary64`
238×	`unsub-neg_binary64`
226×	`associate-*r/_binary64`
224×	`associate-l_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	1086	20
6	4649	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 x) (/.f64 -1/2 y))

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify28.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

921×	`fma-neg_binary64`
613×	`times-frac_binary64`
288×	`associate-/l*_binary64`
236×	`associate-/r/_binary64`
226×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	53	10
3	123	10
4	253	10
5	551	10
6	1090	10
7	3999	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 (0.1%)

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))
	17.3b	(/.f64 (-.f64 x y) (.f64 (.f64 x 2) y))

Compiler

Compiled 40 to 28 computations (30% saved)

localize12.0ms (0.6%)

Local error

Found 1 expressions with local error:

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

series3.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

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

rewrite57.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

709×	`prod-diff_binary64`
269×	`fma-def_binary64`
160×	`expm1-udef_binary64`
160×	`log1p-udef_binary64`
148×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	168	10
2	2506	10

Stop Event

1×	node limit

Counts

1 → 136

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

simplify28.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

141×	`fma-def_binary64`
102×	`fma-neg_binary64`
48×	`cancel-sign-sub-inv_binary64`
25×	`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	402	204
9	514	204
10	568	204
11	574	204

Stop Event

1×

saturated

Counts

160 → 140

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

eval55.0ms (2.9%)

Compiler: Compiled 2520 to 1842 computations (26.9% saved)

prune229.0ms (12%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	140	2	142

Error

Counts

142 → 2

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(-.f64 (/.f64 -1/2 x) (/.f64 -1/2 y))
▶	7.1b	(/.f64 (/.f64 (fma.f64 -1/2 y (*.f64 (neg.f64 x) -1/2)) x) y)

Compiler

Compiled 35 to 25 computations (28.6% saved)

localize7.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (fma.f64 -1/2 y (*.f64 (neg.f64 x) -1/2)) x)
✓	6.6b	(/.f64 (/.f64 (fma.f64 -1/2 y (*.f64 (neg.f64 x) -1/2)) x) y)

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 (neg.f64 x) -1/2)) x) y)
1.0ms	y	@	0	(/.f64 (/.f64 (fma.f64 -1/2 y (*.f64 (neg.f64 x) -1/2)) x) y)
1.0ms	x	@	-inf	(/.f64 (/.f64 (fma.f64 -1/2 y (*.f64 (neg.f64 x) -1/2)) x) y)
1.0ms	x	@	inf	(/.f64 (/.f64 (fma.f64 -1/2 y (*.f64 (neg.f64 x) -1/2)) x) y)
1.0ms	y	@	inf	(/.f64 (/.f64 (fma.f64 -1/2 y (*.f64 (neg.f64 x) -1/2)) x) y)

rewrite57.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

916×	`log1p-expm1-u_binary64`
916×	`expm1-log1p-u_binary64`
101×	`add-sqr-sqrt_binary64`
97×	`*-un-lft-identity_binary64`
97×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	29
1	198	23
2	2802	23

Stop Event

1×	node limit

Counts

2 → 81

Calls

Call 1

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

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

Outputs

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

simplify58.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1290×	`fma-neg_binary64`
565×	`div-sub_binary64`
516×	`fma-def_binary64`
216×	`times-frac_binary64`
196×	`associate-/l*_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	436	372
7	680	372
8	930	372
9	1256	372
10	1503	372
11	2158	372
12	3633	372
13	4781	372

Stop Event

1×	node limit

Counts

129 → 90

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

eval22.0ms (1.2%)

Compiler: Compiled 1294 to 713 computations (44.9% saved)

prune46.0ms (2.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	90	2	92

Error

Counts

92 → 2

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(-.f64 (/.f64 -1/2 x) (/.f64 -1/2 y))
✓	7.1b	(/.f64 (/.f64 (fma.f64 -1/2 y (*.f64 (neg.f64 x) -1/2)) x) y)

Compiler

Compiled 22 to 16 computations (27.3% saved)

regimes13.0ms (0.7%)

Accuracy

Total -24.4b remaining (-311772.1%)

Threshold costs -24.4b (-311772.1%)

Counts

3 → 1

Calls

Call 1

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

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

Results

Time	Error	Segments	Branch
4.0ms	0.0b	1	`x`
4.0ms	0.0b	1	`y`
3.0ms	0.0b	1	`(/.f64 (-.f64 x y) (.f64 (.f64 x 2) y))`

Compiler

Compiled 46 to 30 computations (34.8% saved)

simplify2.0ms (0.1%)

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	7	10
1	9	10
2	17	10
3	19	10
4	20	10

Stop Event

1×

saturated

Calls

Call 1

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

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

end14.0ms (0.7%)

Stop Event

1×

done

Compiler

Compiled 18 to 14 computations (22.2% 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	402	204
9	514	204
10	568	204
11	574	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	402	204
9	514	204
10	568	204
11	574	204

Details

analyze286.0ms (14.9%)

sample943.0ms (49.3%)

preprocess41.0ms (2.1%)

simplify28.0ms (1.5%)

eval1.0ms (0%)

prune2.0ms (0.1%)

localize12.0ms (0.6%)

series3.0ms (0.2%)

rewrite57.0ms (3%)

simplify28.0ms (1.5%)

eval55.0ms (2.9%)

prune229.0ms (12%)

localize7.0ms (0.4%)

series8.0ms (0.4%)

rewrite57.0ms (3%)

simplify58.0ms (3%)

eval22.0ms (1.2%)

prune46.0ms (2.4%)

regimes13.0ms (0.7%)

simplify2.0ms (0.1%)

end14.0ms (0.7%)

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	402	204
9	514	204
10	568	204
11	574	204