Details

analyze73.0ms (2.8%)

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
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
50%	46.8%	3.2%	7
59.3%	37.5%	3.2%	8
67.1%	25.8%	7.1%	9
72.6%	20.3%	7.1%	10
76.9%	13.5%	9.7%	11
79.8%	10.5%	9.7%	12

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample1.1s (39.9%)

Results

1.0s	8256×	body	256	valid
30.0ms	259×	body	256	invalid

preprocess123.0ms (4.7%)

Algorithm

2×	egg-herbie

Rules

1297×	`fma-neg_binary64`
334×	`cancel-sign-sub-inv_binary64`
295×	`fma-def_binary64`
254×	`sub-neg_binary64`
198×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	44	28
2	106	24
3	245	24
4	555	22
5	1210	22
6	2256	22
7	3467	22
8	3857	22
9	3875	22
10	3875	22
11	4533	22
12	4533	22
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
(+.f64 (-.f64 (.f64 y (-.f64 x 1)) (.f64 x 1/2)) 918938533204673/1000000000000000)

Outputs
(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
(-.f64 (.f64 x (+.f64 y -1)) (-.f64 (.f64 y 1/2) 918938533204673/1000000000000000))
(+.f64 (fma.f64 x (+.f64 y -1) (*.f64 y -1/2)) 918938533204673/1000000000000000)
(fma.f64 x (-.f64 y 1) (fma.f64 y -1/2 918938533204673/1000000000000000))
(fma.f64 x (+.f64 y -1) (fma.f64 y -1/2 918938533204673/1000000000000000))
(fma.f64 y (+.f64 x -1/2) (-.f64 918938533204673/1000000000000000 x))
(-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x)
(+.f64 (-.f64 (.f64 y (-.f64 x 1)) (.f64 x 1/2)) 918938533204673/1000000000000000)
(+.f64 918938533204673/1000000000000000 (-.f64 (.f64 y (+.f64 x -1)) (.f64 x 1/2)))
(+.f64 918938533204673/1000000000000000 (fma.f64 y (+.f64 x -1) (*.f64 x -1/2)))
(fma.f64 y (+.f64 x -1) (fma.f64 x -1/2 918938533204673/1000000000000000))
(fma.f64 x (+.f64 y -1/2) (-.f64 918938533204673/1000000000000000 y))
(-.f64 918938533204673/1000000000000000 (fma.f64 x (-.f64 1/2 y) y))

Compiler

Compiled 15 to 12 computations (20% saved)

simplify56.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

706×	`fma-neg_binary64`
571×	`fma-def_binary64`
225×	`cancel-sign-sub-inv_binary64`
113×	`sub-neg_binary64`
83×	`associate--r+_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	27	14
2	62	12
3	131	12
4	270	11
5	576	11
6	1098	11
7	1824	11
8	2606	11
9	2777	11
10	2804	11

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)

Outputs
(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
(+.f64 (fma.f64 x (+.f64 y -1) (neg.f64 (*.f64 y 1/2))) 918938533204673/1000000000000000)
(+.f64 (fma.f64 x (+.f64 y -1) (*.f64 y -1/2)) 918938533204673/1000000000000000)
(fma.f64 x (+.f64 y -1) (fma.f64 y -1/2 918938533204673/1000000000000000))
(fma.f64 y (+.f64 x -1/2) (-.f64 918938533204673/1000000000000000 x))
(-.f64 918938533204673/1000000000000000 (fma.f64 y (-.f64 1/2 x) x))

eval1.0ms (0%)

Compiler: Compiled 21 to 15 computations (28.6% 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

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0b	(-.f64 918938533204673/1000000000000000 (fma.f64 y (-.f64 1/2 x) x))
▶	0.0b	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)

Compiler

Compiled 23 to 17 computations (26.1% saved)

localize15.0ms (0.6%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 38 to 26 computations (31.6% saved)

series4.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite77.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

459×	`log-prod_binary64`
426×	`fma-def_binary64`
366×	`prod-exp_binary64`
341×	`exp-prod_binary64`
313×	`pow-prod-down_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	208	11
2	2756	11

Stop Event

1×	node limit

Counts

1 → 175

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (+.f64 y -1)) (.f64 y -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (+.f64 y -1)) (.f64 (.f64 y -1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (+.f64 y -1)) (fma.f64 y -1/2 (fma.f64 y -1/2 (.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) (fma.f64 y -1/2 (.f64 y 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) (fma.f64 (.f64 y -1/2) 1 (.f64 y 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) (fma.f64 (neg.f64 (cbrt.f64 (.f64 y 1/2))) (cbrt.f64 (.f64 (.f64 y y) 1/4)) (.f64 y 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) (.f64 (fma.f64 y -1/2 (.f64 y 1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) (+.f64 (fma.f64 y -1/2 (.f64 y 1/2)) (fma.f64 y -1/2 (.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 y -1/2 (.f64 y 1/2)) (fma.f64 x (+.f64 y -1) (.f64 y -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 y -1/2) (.f64 x (+.f64 y -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))) (pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))) 2) (cbrt.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))) (sqrt.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 (.f64 x (+.f64 y -1)) 3) (.f64 1/8 (pow.f64 y 3))) (/.f64 1 (fma.f64 (.f64 y 1/2) (fma.f64 x (+.f64 y -1) (.f64 y 1/2)) (pow.f64 (.f64 x (+.f64 y -1)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 (.f64 x (+.f64 y -1)) 2) (.f64 (.f64 y y) 1/4)) (/.f64 1 (fma.f64 x (+.f64 y -1) (.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (sqrt.f64 (.f64 x (+.f64 y -1))) (sqrt.f64 (.f64 y 1/2))) (-.f64 (sqrt.f64 (.f64 x (+.f64 y -1))) (sqrt.f64 (.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (.f64 y 1/2) (fma.f64 x (+.f64 y -1) (.f64 y 1/2)) (pow.f64 (.f64 x (+.f64 y -1)) 2)) (-.f64 (pow.f64 (.f64 x (+.f64 y -1)) 3) (.f64 1/8 (pow.f64 y 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x (+.f64 y -1) (.f64 y 1/2)) (-.f64 (pow.f64 (.f64 x (+.f64 y -1)) 2) (.f64 (.f64 y y) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (.f64 x (+.f64 y -1)) 3) (.f64 1/8 (pow.f64 y 3))) (fma.f64 (.f64 y 1/2) (fma.f64 x (+.f64 y -1) (.f64 y 1/2)) (pow.f64 (.f64 x (+.f64 y -1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (.f64 x (+.f64 y -1)) 2) (.f64 (.f64 y y) 1/4)) (fma.f64 x (+.f64 y -1) (.f64 y 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (.f64 x (+.f64 y -1)) 3) (.f64 1/8 (pow.f64 y 3)))) (neg.f64 (fma.f64 (.f64 y 1/2) (fma.f64 x (+.f64 y -1) (.f64 y 1/2)) (pow.f64 (.f64 x (+.f64 y -1)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (.f64 x (+.f64 y -1)) 2) (.f64 (.f64 y y) 1/4))) (neg.f64 (fma.f64 x (+.f64 y -1) (.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 x (+.f64 y -1)) 3) (pow.f64 (.f64 y -1/2) 3)) (+.f64 (pow.f64 (.f64 x (+.f64 y -1)) 2) (-.f64 (pow.f64 (.f64 y -1/2) 2) (.f64 (.f64 x (+.f64 y -1)) (.f64 y -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) 3) (pow.f64 (fma.f64 y -1/2 (.f64 y 1/2)) 3)) (+.f64 (pow.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) 2) (-.f64 (pow.f64 (fma.f64 y -1/2 (.f64 y 1/2)) 2) (.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) (fma.f64 y -1/2 (.f64 y 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (.f64 x (+.f64 y -1)) 2) (pow.f64 (.f64 y -1/2) 2)) (-.f64 (.f64 x (+.f64 y -1)) (.f64 y -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) 2) (pow.f64 (fma.f64 y -1/2 (.f64 y 1/2)) 2)) (-.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) (fma.f64 y -1/2 (.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (.f64 y 1/2) (fma.f64 x (+.f64 y -1) (.f64 y 1/2)) (pow.f64 (.f64 x (+.f64 y -1)) 2)) (-.f64 (pow.f64 (.f64 x (+.f64 y -1)) 3) (.f64 1/8 (pow.f64 y 3)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 x (+.f64 y -1) (.f64 y 1/2)) (-.f64 (pow.f64 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1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (.f64 x (+.f64 y -1)))) (+.f64 1 (expm1.f64 (.f64 y 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 x (+.f64 y -1)))) (pow.f64 (exp.f64 y) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)))) (exp.f64 (fma.f64 y -1/2 (.f64 y 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (fma.f64 y -1/2 (.f64 y 1/2))) (+.f64 1 (expm1.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (pow.f64 (exp.f64 y) -1/2) (+.f64 1 (expm1.f64 (.f64 x (+.f64 y -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 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Outputs

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

simplify44.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

292×	`fma-def_binary64`
290×	`fma-neg_binary64`
67×	`cancel-sign-sub-inv_binary64`
46×	`sub-neg_binary64`
39×	`unsub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	233
1	52	233
2	139	215
3	274	215
4	617	215
5	1040	215
6	1246	215
7	1282	215
8	1285	215

Stop Event

1×

saturated

Counts

199 → 189

Calls

Call 1

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

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

localize10.0ms (0.4%)

Compiler: Compiled 23 to 14 computations (39.1% saved)

eval85.0ms (3.2%)

Compiler: Compiled 4061 to 2957 computations (27.2% saved)

prune26.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	184	5	189
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	186	5	191

Error

Counts

191 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	21.9b	(+.f64 (*.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)
▶	21.7b	(+.f64 (neg.f64 x) 918938533204673/1000000000000000)
▶	15.9b	(+.f64 (-.f64 (*.f64 y x) x) 918938533204673/1000000000000000)
▶	0b	(+.f64 (-.f64 (*.f64 y (+.f64 -1/2 x)) x) 918938533204673/1000000000000000)
▶	28.1b	(+.f64 (*.f64 -1/2 y) 918938533204673/1000000000000000)

Compiler

Compiled 84 to 64 computations (23.8% saved)

localize14.0ms (0.5%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 30 to 19 computations (36.7% saved)

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite46.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

733×	`pow1_binary64`
685×	`add-log-exp_binary64`
685×	`log1p-expm1-u_binary64`
685×	`expm1-log1p-u_binary64`
672×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	136	7
2	1836	7

Stop Event

1×	node limit

Counts

1 → 24

Calls

Call 1

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

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

Outputs

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

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`distribute-rgt-out_binary64`
1×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	159
1	17	159
2	22	159

Stop Event

1×

saturated

Counts

48 → 30

Calls

Call 1

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

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

localize4.0ms (0.2%)

Compiler: Compiled 10 to 6 computations (40% saved)

localize6.0ms (0.2%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (-.f64 x 1/2))
✓	0.0b	(+.f64 (*.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)

Compiler

Compiled 21 to 14 computations (33.3% saved)

series3.0ms (0.1%)

Counts

2 → 36

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	y	@	inf	(+.f64 (*.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)
0.0ms	y	@	0	(+.f64 (*.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)
0.0ms	x	@	-inf	(+.f64 (*.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)
0.0ms	x	@	0	(+.f64 (*.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)
0.0ms	y	@	-inf	(+.f64 (*.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)

rewrite67.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

966×	`pow1_binary64`
905×	`add-log-exp_binary64`
905×	`log1p-expm1-u_binary64`
905×	`expm1-log1p-u_binary64`
94×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	184	15
2	2335	15

Stop Event

1×	node limit

Counts

2 → 51

Calls

Call 1

Inputs
(+.f64 (*.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)
(*.f64 y (-.f64 x 1/2))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (*.f64 y (+.f64 x -1/2)) 2) (fma.f64 y (+.f64 x -1/2) -918938533204673/1000000000000000)) (/.f64 844448027808355901771309036929/1000000000000000000000000000000 (fma.f64 y (+.f64 x -1/2) -918938533204673/1000000000000000)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)) (pow.f64 (cbrt.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)) 2) (cbrt.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)) (sqrt.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (pow.f64 (*.f64 y (+.f64 x -1/2)) 3)) (/.f64 1 (+.f64 (pow.f64 (*.f64 y (+.f64 x -1/2)) 2) (-.f64 844448027808355901771309036929/1000000000000000000000000000000 (*.f64 (+.f64 x -1/2) (*.f64 y 918938533204673/1000000000000000))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (*.f64 y (+.f64 x -1/2)) 2) -844448027808355901771309036929/1000000000000000000000000000000) (/.f64 1 (fma.f64 y (+.f64 x -1/2) -918938533204673/1000000000000000)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (*.f64 y (+.f64 x -1/2)) 2) (-.f64 844448027808355901771309036929/1000000000000000000000000000000 (*.f64 (+.f64 x -1/2) (*.f64 y 918938533204673/1000000000000000)))) (+.f64 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (pow.f64 (*.f64 y (+.f64 x -1/2)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 y (+.f64 x -1/2) -918938533204673/1000000000000000) (+.f64 (pow.f64 (*.f64 y (+.f64 x -1/2)) 2) -844448027808355901771309036929/1000000000000000000000000000000)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (pow.f64 (*.f64 y (+.f64 x -1/2)) 3)) (+.f64 (pow.f64 (*.f64 y (+.f64 x -1/2)) 2) (-.f64 844448027808355901771309036929/1000000000000000000000000000000 (*.f64 (+.f64 x -1/2) (*.f64 y 918938533204673/1000000000000000)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (pow.f64 (*.f64 y (+.f64 x -1/2)) 3)) (+.f64 844448027808355901771309036929/1000000000000000000000000000000 (-.f64 (pow.f64 (*.f64 y (+.f64 x -1/2)) 2) (*.f64 (+.f64 x -1/2) (*.f64 y 918938533204673/1000000000000000)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 y (+.f64 x -1/2)) 2) -844448027808355901771309036929/1000000000000000000000000000000) (fma.f64 y (+.f64 x -1/2) -918938533204673/1000000000000000))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (pow.f64 (*.f64 y (+.f64 x -1/2)) 3))) (neg.f64 (+.f64 (pow.f64 (*.f64 y (+.f64 x -1/2)) 2) (-.f64 844448027808355901771309036929/1000000000000000000000000000000 (*.f64 (+.f64 x -1/2) (*.f64 y 918938533204673/1000000000000000))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 y (+.f64 x -1/2)) 2) -844448027808355901771309036929/1000000000000000000000000000000)) (neg.f64 (fma.f64 y (+.f64 x -1/2) -918938533204673/1000000000000000)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 844448027808355901771309036929/1000000000000000000000000000000 (pow.f64 (*.f64 y (+.f64 x -1/2)) 2)) (-.f64 918938533204673/1000000000000000 (*.f64 y (+.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x -1/2) y 918938533204673/1000000000000000)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 y (+.f64 x -1/2)) 918938533204673/1000000000000000)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 y (+.f64 x -1/2))) 2) (cbrt.f64 (*.f64 y (+.f64 x -1/2))) 918938533204673/1000000000000000)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 y (+.f64 x -1/2))) (sqrt.f64 (*.f64 y (+.f64 x -1/2))) 918938533204673/1000000000000000)))))

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

simplify14.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

14×	`fma-def_binary64`
6×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`associate-+l+_binary64`
2×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	285
1	28	247
2	41	247
3	43	247

Stop Event

1×

saturated

Counts

87 → 62

Calls

Call 1

Inputs
918938533204673/1000000000000000
(+.f64 918938533204673/1000000000000000 (*.f64 y (-.f64 x 1/2)))
(+.f64 918938533204673/1000000000000000 (*.f64 y (-.f64 x 1/2)))
(+.f64 918938533204673/1000000000000000 (*.f64 y (-.f64 x 1/2)))
(*.f64 y (-.f64 x 1/2))
(+.f64 918938533204673/1000000000000000 (*.f64 y (-.f64 x 1/2)))
(+.f64 918938533204673/1000000000000000 (*.f64 y (-.f64 x 1/2)))
(+.f64 918938533204673/1000000000000000 (*.f64 y (-.f64 x 1/2)))
(*.f64 y (-.f64 x 1/2))
(+.f64 918938533204673/1000000000000000 (*.f64 y (-.f64 x 1/2)))
(+.f64 918938533204673/1000000000000000 (*.f64 y (-.f64 x 1/2)))
(+.f64 918938533204673/1000000000000000 (*.f64 y (-.f64 x 1/2)))
(+.f64 918938533204673/1000000000000000 (*.f64 -1/2 y))
(+.f64 (.f64 -1/2 y) (+.f64 918938533204673/1000000000000000 (.f64 y x)))
(+.f64 (.f64 -1/2 y) (+.f64 918938533204673/1000000000000000 (.f64 y x)))
(+.f64 (.f64 -1/2 y) (+.f64 918938533204673/1000000000000000 (.f64 y x)))
(*.f64 y x)
(+.f64 (.f64 -1/2 y) (+.f64 918938533204673/1000000000000000 (.f64 y x)))
(+.f64 (.f64 -1/2 y) (+.f64 918938533204673/1000000000000000 (.f64 y x)))
(+.f64 (.f64 -1/2 y) (+.f64 918938533204673/1000000000000000 (.f64 y x)))
(*.f64 y x)
(+.f64 (.f64 -1/2 y) (+.f64 918938533204673/1000000000000000 (.f64 y x)))
(+.f64 (.f64 -1/2 y) (+.f64 918938533204673/1000000000000000 (.f64 y x)))
(+.f64 (.f64 -1/2 y) (+.f64 918938533204673/1000000000000000 (.f64 y x)))
(*.f64 -1/2 y)
(+.f64 (.f64 -1/2 y) (.f64 y x))
(+.f64 (.f64 -1/2 y) (.f64 y x))
(+.f64 (.f64 -1/2 y) (.f64 y x))
(*.f64 y x)
(+.f64 (.f64 -1/2 y) (.f64 y x))
(+.f64 (.f64 -1/2 y) (.f64 y x))
(+.f64 (.f64 -1/2 y) (.f64 y x))
(*.f64 y x)
(+.f64 (.f64 -1/2 y) (.f64 y x))
(+.f64 (.f64 -1/2 y) (.f64 y x))
(+.f64 (.f64 -1/2 y) (.f64 y x))

Outputs
918938533204673/1000000000000000
(+.f64 918938533204673/1000000000000000 (*.f64 y (-.f64 x 1/2)))
(+.f64 918938533204673/1000000000000000 (*.f64 y (+.f64 x -1/2)))
(fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)
(+.f64 918938533204673/1000000000000000 (*.f64 y (-.f64 x 1/2)))
(+.f64 918938533204673/1000000000000000 (*.f64 y (+.f64 x -1/2)))
(fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)
(+.f64 918938533204673/1000000000000000 (*.f64 y (-.f64 x 1/2)))
(+.f64 918938533204673/1000000000000000 (*.f64 y (+.f64 x -1/2)))
(fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)
(*.f64 y (-.f64 x 1/2))
(*.f64 y (+.f64 x -1/2))
(+.f64 918938533204673/1000000000000000 (*.f64 y (-.f64 x 1/2)))
(+.f64 918938533204673/1000000000000000 (*.f64 y (+.f64 x -1/2)))
(fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)
(+.f64 918938533204673/1000000000000000 (*.f64 y (-.f64 x 1/2)))
(+.f64 918938533204673/1000000000000000 (*.f64 y (+.f64 x -1/2)))
(fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)
(+.f64 918938533204673/1000000000000000 (*.f64 y (-.f64 x 1/2)))
(+.f64 918938533204673/1000000000000000 (*.f64 y (+.f64 x -1/2)))
(fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)
(*.f64 y (-.f64 x 1/2))
(*.f64 y (+.f64 x -1/2))
(+.f64 918938533204673/1000000000000000 (*.f64 y (-.f64 x 1/2)))
(+.f64 918938533204673/1000000000000000 (*.f64 y (+.f64 x -1/2)))
(fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)
(+.f64 918938533204673/1000000000000000 (*.f64 y (-.f64 x 1/2)))
(+.f64 918938533204673/1000000000000000 (*.f64 y (+.f64 x -1/2)))
(fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)
(+.f64 918938533204673/1000000000000000 (*.f64 y (-.f64 x 1/2)))
(+.f64 918938533204673/1000000000000000 (*.f64 y (+.f64 x -1/2)))
(fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)
(+.f64 918938533204673/1000000000000000 (*.f64 -1/2 y))
(+.f64 918938533204673/1000000000000000 (*.f64 y -1/2))
(fma.f64 y -1/2 918938533204673/1000000000000000)
(+.f64 (.f64 -1/2 y) (+.f64 918938533204673/1000000000000000 (.f64 y x)))
(+.f64 918938533204673/1000000000000000 (*.f64 y (+.f64 x -1/2)))
(fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)
(+.f64 (.f64 -1/2 y) (+.f64 918938533204673/1000000000000000 (.f64 y x)))
(+.f64 918938533204673/1000000000000000 (*.f64 y (+.f64 x -1/2)))
(fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)
(+.f64 (.f64 -1/2 y) (+.f64 918938533204673/1000000000000000 (.f64 y x)))
(+.f64 918938533204673/1000000000000000 (*.f64 y (+.f64 x -1/2)))
(fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)
(*.f64 y x)
(+.f64 (.f64 -1/2 y) (+.f64 918938533204673/1000000000000000 (.f64 y x)))
(+.f64 918938533204673/1000000000000000 (*.f64 y (+.f64 x -1/2)))
(fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)
(+.f64 (.f64 -1/2 y) (+.f64 918938533204673/1000000000000000 (.f64 y x)))
(+.f64 918938533204673/1000000000000000 (*.f64 y (+.f64 x -1/2)))
(fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)
(+.f64 (.f64 -1/2 y) (+.f64 918938533204673/1000000000000000 (.f64 y x)))
(+.f64 918938533204673/1000000000000000 (*.f64 y (+.f64 x -1/2)))
(fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)
(*.f64 y x)
(+.f64 (.f64 -1/2 y) (+.f64 918938533204673/1000000000000000 (.f64 y x)))
(+.f64 918938533204673/1000000000000000 (*.f64 y (+.f64 x -1/2)))
(fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)
(+.f64 (.f64 -1/2 y) (+.f64 918938533204673/1000000000000000 (.f64 y x)))
(+.f64 918938533204673/1000000000000000 (*.f64 y (+.f64 x -1/2)))
(fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)
(+.f64 (.f64 -1/2 y) (+.f64 918938533204673/1000000000000000 (.f64 y x)))
(+.f64 918938533204673/1000000000000000 (*.f64 y (+.f64 x -1/2)))
(fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000)
(*.f64 -1/2 y)
(*.f64 y -1/2)
(+.f64 (.f64 -1/2 y) (.f64 y x))
(*.f64 y (+.f64 x -1/2))
(+.f64 (.f64 -1/2 y) (.f64 y x))
(*.f64 y (+.f64 x -1/2))
(+.f64 (.f64 -1/2 y) (.f64 y x))
(*.f64 y (+.f64 x -1/2))
(*.f64 y x)
(+.f64 (.f64 -1/2 y) (.f64 y x))
(*.f64 y (+.f64 x -1/2))
(+.f64 (.f64 -1/2 y) (.f64 y x))
(*.f64 y (+.f64 x -1/2))
(+.f64 (.f64 -1/2 y) (.f64 y x))
(*.f64 y (+.f64 x -1/2))
(*.f64 y x)
(+.f64 (.f64 -1/2 y) (.f64 y x))
(*.f64 y (+.f64 x -1/2))
(+.f64 (.f64 -1/2 y) (.f64 y x))
(*.f64 y (+.f64 x -1/2))
(+.f64 (.f64 -1/2 y) (.f64 y x))
(*.f64 y (+.f64 x -1/2))

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 (*.f64 y x) x) 918938533204673/1000000000000000)
✓	0.0b	(-.f64 (*.f64 y x) x)

Compiler

Compiled 20 to 7 computations (65% saved)

series5.0ms (0.2%)

Counts

2 → 48

Calls

12 calls:

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

rewrite72.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

950×	`pow1_binary64`
890×	`add-log-exp_binary64`
890×	`log1p-expm1-u_binary64`
890×	`expm1-log1p-u_binary64`
87×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	164	17
2	2319	17

Stop Event

1×	node limit

Counts

2 → 79

Calls

Call 1

Inputs
(-.f64 (*.f64 y x) x)
(+.f64 (-.f64 (*.f64 y x) x) 918938533204673/1000000000000000)

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 y x) (-.f64 x 918938533204673/1000000000000000))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 y x (neg.f64 (-.f64 x 918938533204673/1000000000000000))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (-.f64 (*.f64 y x) x) 2) (-.f64 (*.f64 y x) (+.f64 x 918938533204673/1000000000000000))) (/.f64 844448027808355901771309036929/1000000000000000000000000000000 (-.f64 (*.f64 y x) (+.f64 x 918938533204673/1000000000000000))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 918938533204673/1000000000000000 (*.f64 y x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 y x (neg.f64 (-.f64 x 918938533204673/1000000000000000))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 y x (neg.f64 (-.f64 x 918938533204673/1000000000000000))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 y x (neg.f64 (-.f64 x 918938533204673/1000000000000000)))) (pow.f64 (cbrt.f64 (fma.f64 y x (neg.f64 (-.f64 x 918938533204673/1000000000000000)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 y x (neg.f64 (-.f64 x 918938533204673/1000000000000000)))) 2) (cbrt.f64 (fma.f64 y x (neg.f64 (-.f64 x 918938533204673/1000000000000000)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 y x (neg.f64 (-.f64 x 918938533204673/1000000000000000)))) (sqrt.f64 (fma.f64 y x (neg.f64 (-.f64 x 918938533204673/1000000000000000)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (pow.f64 (-.f64 (*.f64 y x) x) 3)) (/.f64 1 (+.f64 (pow.f64 (-.f64 (*.f64 y x) x) 2) (-.f64 844448027808355901771309036929/1000000000000000000000000000000 (*.f64 (-.f64 (*.f64 y x) x) 918938533204673/1000000000000000)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (-.f64 (*.f64 y x) x) 2) -844448027808355901771309036929/1000000000000000000000000000000) (/.f64 1 (-.f64 (*.f64 y x) (+.f64 x 918938533204673/1000000000000000))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (-.f64 (*.f64 y x) x) 2) (-.f64 844448027808355901771309036929/1000000000000000000000000000000 (*.f64 (-.f64 (*.f64 y x) x) 918938533204673/1000000000000000))) (+.f64 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (pow.f64 (-.f64 (*.f64 y x) x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (*.f64 y x) (+.f64 x 918938533204673/1000000000000000)) (+.f64 (pow.f64 (-.f64 (*.f64 y x) x) 2) -844448027808355901771309036929/1000000000000000000000000000000)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (pow.f64 (-.f64 (*.f64 y x) x) 3)) (+.f64 (pow.f64 (-.f64 (*.f64 y x) x) 2) (-.f64 844448027808355901771309036929/1000000000000000000000000000000 (*.f64 (-.f64 (*.f64 y x) x) 918938533204673/1000000000000000))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (pow.f64 (-.f64 (*.f64 y x) x) 3)) (+.f64 844448027808355901771309036929/1000000000000000000000000000000 (-.f64 (pow.f64 (-.f64 (*.f64 y x) x) 2) (*.f64 (-.f64 (*.f64 y x) x) 918938533204673/1000000000000000))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (-.f64 (*.f64 y x) x) 2) -844448027808355901771309036929/1000000000000000000000000000000) (-.f64 (*.f64 y x) (+.f64 x 918938533204673/1000000000000000)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 775995832041789488711238455368417219672369217/1000000000000000000000000000000000000000000000 (pow.f64 (-.f64 (*.f64 y x) x) 3))) (neg.f64 (+.f64 (pow.f64 (-.f64 (*.f64 y x) x) 2) (-.f64 844448027808355901771309036929/1000000000000000000000000000000 (*.f64 (-.f64 (*.f64 y x) x) 918938533204673/1000000000000000)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (-.f64 (*.f64 y x) x) 2) -844448027808355901771309036929/1000000000000000000000000000000)) (neg.f64 (-.f64 (*.f64 y x) (+.f64 x 918938533204673/1000000000000000))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 y x) 3) (pow.f64 (-.f64 x 918938533204673/1000000000000000) 3)) (+.f64 (pow.f64 (*.f64 y x) 2) (+.f64 (*.f64 (-.f64 x 918938533204673/1000000000000000) (-.f64 x 918938533204673/1000000000000000)) (*.f64 (*.f64 y x) (-.f64 x 918938533204673/1000000000000000)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 y x) 2) (*.f64 (-.f64 x 918938533204673/1000000000000000) (-.f64 x 918938533204673/1000000000000000))) (+.f64 (*.f64 y x) (-.f64 x 918938533204673/1000000000000000)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 844448027808355901771309036929/1000000000000000000000000000000 (pow.f64 (-.f64 (*.f64 y x) x) 2)) (-.f64 918938533204673/1000000000000000 (-.f64 (*.f64 y x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 y x (neg.f64 (-.f64 x 918938533204673/1000000000000000))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 y x (neg.f64 (-.f64 x 918938533204673/1000000000000000))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 y x (neg.f64 (-.f64 x 918938533204673/1000000000000000)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 y x (neg.f64 (-.f64 x 918938533204673/1000000000000000)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 y x (neg.f64 (-.f64 x 918938533204673/1000000000000000))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 y x (neg.f64 (-.f64 x 918938533204673/1000000000000000)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 y x (neg.f64 (-.f64 x 918938533204673/1000000000000000))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 y x (neg.f64 (-.f64 x 918938533204673/1000000000000000))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 y x (neg.f64 (-.f64 x 918938533204673/1000000000000000)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 y x (neg.f64 (-.f64 x 918938533204673/1000000000000000)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 y x (neg.f64 (-.f64 x 918938533204673/1000000000000000)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y x (neg.f64 (-.f64 x 918938533204673/1000000000000000)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x y (neg.f64 (-.f64 x 918938533204673/1000000000000000)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 y x) (neg.f64 (-.f64 x 918938533204673/1000000000000000)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (-.f64 (*.f64 y x) x) 918938533204673/1000000000000000)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (-.f64 (*.f64 y x) x)) 2) (cbrt.f64 (-.f64 (*.f64 y x) x)) 918938533204673/1000000000000000)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 y x)) 2) (cbrt.f64 (*.f64 y x)) (neg.f64 (-.f64 x 918938533204673/1000000000000000)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 (*.f64 y x) x)) (sqrt.f64 (-.f64 (*.f64 y x) x)) 918938533204673/1000000000000000)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 y x)) (sqrt.f64 (*.f64 y x)) (neg.f64 (-.f64 x 918938533204673/1000000000000000)))))))

simplify45.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

158×	`fma-def_binary64`
145×	`fma-neg_binary64`
47×	`cancel-sign-sub-inv_binary64`
30×	`sub-neg_binary64`
27×	`associate--r+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	365
1	48	329
2	93	329
3	191	329
4	358	329
5	580	329
6	708	329
7	768	329
8	802	329
9	808	329

Stop Event

1×

saturated

Counts

127 → 93

Calls

Call 1

Inputs
(*.f64 -1 x)
(+.f64 (.f64 y x) (.f64 -1 x))
(+.f64 (.f64 y x) (.f64 -1 x))
(+.f64 (.f64 y x) (.f64 -1 x))
(*.f64 y x)
(+.f64 (.f64 y x) (.f64 -1 x))
(+.f64 (.f64 y x) (.f64 -1 x))
(+.f64 (.f64 y x) (.f64 -1 x))
(*.f64 y x)
(+.f64 (.f64 y x) (.f64 -1 x))
(+.f64 (.f64 y x) (.f64 -1 x))
(+.f64 (.f64 y x) (.f64 -1 x))
(*.f64 (-.f64 y 1) x)
(*.f64 (-.f64 y 1) x)
(*.f64 (-.f64 y 1) x)
(*.f64 (-.f64 y 1) x)
(*.f64 (-.f64 y 1) x)
(*.f64 (-.f64 y 1) x)
(*.f64 (-.f64 y 1) x)
(*.f64 (-.f64 y 1) x)
(.f64 -1 (.f64 (+.f64 1 (*.f64 -1 y)) x))
(.f64 -1 (.f64 (+.f64 1 (*.f64 -1 y)) x))
(.f64 -1 (.f64 (+.f64 1 (*.f64 -1 y)) x))
(.f64 -1 (.f64 (+.f64 1 (*.f64 -1 y)) x))
(-.f64 918938533204673/1000000000000000 x)
(-.f64 (+.f64 918938533204673/1000000000000000 (*.f64 y x)) x)
(-.f64 (+.f64 918938533204673/1000000000000000 (*.f64 y x)) x)
(-.f64 (+.f64 918938533204673/1000000000000000 (*.f64 y x)) x)
(*.f64 y x)
(-.f64 (+.f64 918938533204673/1000000000000000 (*.f64 y x)) x)
(-.f64 (+.f64 918938533204673/1000000000000000 (*.f64 y x)) x)
(-.f64 (+.f64 918938533204673/1000000000000000 (*.f64 y x)) x)
(*.f64 y x)
(-.f64 (+.f64 918938533204673/1000000000000000 (*.f64 y x)) x)
(-.f64 (+.f64 918938533204673/1000000000000000 (*.f64 y x)) x)
(-.f64 (+.f64 918938533204673/1000000000000000 (*.f64 y x)) x)
918938533204673/1000000000000000
(+.f64 (*.f64 (-.f64 y 1) x) 918938533204673/1000000000000000)
(+.f64 (*.f64 (-.f64 y 1) x) 918938533204673/1000000000000000)
(+.f64 (*.f64 (-.f64 y 1) x) 918938533204673/1000000000000000)
(*.f64 (-.f64 y 1) x)
(+.f64 918938533204673/1000000000000000 (*.f64 (-.f64 y 1) x))
(+.f64 918938533204673/1000000000000000 (*.f64 (-.f64 y 1) x))
(+.f64 918938533204673/1000000000000000 (*.f64 (-.f64 y 1) x))
(.f64 -1 (.f64 (+.f64 1 (*.f64 -1 y)) x))
(+.f64 918938533204673/1000000000000000 (.f64 -1 (.f64 (+.f64 1 (*.f64 -1 y)) x)))
(+.f64 918938533204673/1000000000000000 (.f64 -1 (.f64 (+.f64 1 (*.f64 -1 y)) x)))
(+.f64 918938533204673/1000000000000000 (.f64 -1 (.f64 (+.f64 1 (*.f64 -1 y)) x)))

Outputs
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (.f64 y x) (.f64 -1 x))
(*.f64 x (+.f64 y -1))
(*.f64 x (+.f64 -1 y))
(-.f64 (*.f64 x y) x)
(+.f64 (.f64 y x) (.f64 -1 x))
(*.f64 x (+.f64 y -1))
(*.f64 x (+.f64 -1 y))
(-.f64 (*.f64 x y) x)
(+.f64 (.f64 y x) (.f64 -1 x))
(*.f64 x (+.f64 y -1))
(*.f64 x (+.f64 -1 y))
(-.f64 (*.f64 x y) x)
(*.f64 y x)
(*.f64 x y)
(+.f64 (.f64 y x) (.f64 -1 x))
(*.f64 x (+.f64 y -1))
(*.f64 x (+.f64 -1 y))
(-.f64 (*.f64 x y) x)
(+.f64 (.f64 y x) (.f64 -1 x))
(*.f64 x (+.f64 y -1))
(*.f64 x (+.f64 -1 y))
(-.f64 (*.f64 x y) x)
(+.f64 (.f64 y x) (.f64 -1 x))
(*.f64 x (+.f64 y -1))
(*.f64 x (+.f64 -1 y))
(-.f64 (*.f64 x y) x)
(*.f64 y x)
(*.f64 x y)
(+.f64 (.f64 y x) (.f64 -1 x))
(*.f64 x (+.f64 y -1))
(*.f64 x (+.f64 -1 y))
(-.f64 (*.f64 x y) x)
(+.f64 (.f64 y x) (.f64 -1 x))
(*.f64 x (+.f64 y -1))
(*.f64 x (+.f64 -1 y))
(-.f64 (*.f64 x y) x)
(+.f64 (.f64 y x) (.f64 -1 x))
(*.f64 x (+.f64 y -1))
(*.f64 x (+.f64 -1 y))
(-.f64 (*.f64 x y) x)
(*.f64 (-.f64 y 1) x)
(*.f64 x (+.f64 y -1))
(*.f64 x (+.f64 -1 y))
(-.f64 (*.f64 x y) x)
(*.f64 (-.f64 y 1) x)
(*.f64 x (+.f64 y -1))
(*.f64 x (+.f64 -1 y))
(-.f64 (*.f64 x y) x)
(*.f64 (-.f64 y 1) x)
(*.f64 x (+.f64 y -1))
(*.f64 x (+.f64 -1 y))
(-.f64 (*.f64 x y) x)
(*.f64 (-.f64 y 1) x)
(*.f64 x (+.f64 y -1))
(*.f64 x (+.f64 -1 y))
(-.f64 (*.f64 x y) x)
(*.f64 (-.f64 y 1) x)
(*.f64 x (+.f64 y -1))
(*.f64 x (+.f64 -1 y))
(-.f64 (*.f64 x y) x)
(*.f64 (-.f64 y 1) x)
(*.f64 x (+.f64 y -1))
(*.f64 x (+.f64 -1 y))
(-.f64 (*.f64 x y) x)
(*.f64 (-.f64 y 1) x)
(*.f64 x (+.f64 y -1))
(*.f64 x (+.f64 -1 y))
(-.f64 (*.f64 x y) x)
(*.f64 (-.f64 y 1) x)
(*.f64 x (+.f64 y -1))
(*.f64 x (+.f64 -1 y))
(-.f64 (*.f64 x y) x)
(.f64 -1 (.f64 (+.f64 1 (*.f64 -1 y)) x))
(*.f64 x (+.f64 y -1))
(*.f64 x (+.f64 -1 y))
(-.f64 (*.f64 x y) x)
(.f64 -1 (.f64 (+.f64 1 (*.f64 -1 y)) x))
(*.f64 x (+.f64 y -1))
(*.f64 x (+.f64 -1 y))
(-.f64 (*.f64 x y) x)
(.f64 -1 (.f64 (+.f64 1 (*.f64 -1 y)) x))
(*.f64 x (+.f64 y -1))
(*.f64 x (+.f64 -1 y))
(-.f64 (*.f64 x y) x)
(.f64 -1 (.f64 (+.f64 1 (*.f64 -1 y)) x))
(*.f64 x (+.f64 y -1))
(*.f64 x (+.f64 -1 y))
(-.f64 (*.f64 x y) x)
(-.f64 918938533204673/1000000000000000 x)
(-.f64 (+.f64 918938533204673/1000000000000000 (*.f64 y x)) x)
(+.f64 918938533204673/1000000000000000 (-.f64 (*.f64 x y) x))
(-.f64 (fma.f64 x y 918938533204673/1000000000000000) x)
(fma.f64 x y (-.f64 918938533204673/1000000000000000 x))
(-.f64 (+.f64 918938533204673/1000000000000000 (*.f64 y x)) x)
(+.f64 918938533204673/1000000000000000 (-.f64 (*.f64 x y) x))
(-.f64 (fma.f64 x y 918938533204673/1000000000000000) x)
(fma.f64 x y (-.f64 918938533204673/1000000000000000 x))
(-.f64 (+.f64 918938533204673/1000000000000000 (*.f64 y x)) x)
(+.f64 918938533204673/1000000000000000 (-.f64 (*.f64 x y) x))
(-.f64 (fma.f64 x y 918938533204673/1000000000000000) x)
(fma.f64 x y (-.f64 918938533204673/1000000000000000 x))
(*.f64 y x)
(*.f64 x y)
(-.f64 (+.f64 918938533204673/1000000000000000 (*.f64 y x)) x)
(+.f64 918938533204673/1000000000000000 (-.f64 (*.f64 x y) x))
(-.f64 (fma.f64 x y 918938533204673/1000000000000000) x)
(fma.f64 x y (-.f64 918938533204673/1000000000000000 x))
(-.f64 (+.f64 918938533204673/1000000000000000 (*.f64 y x)) x)
(+.f64 918938533204673/1000000000000000 (-.f64 (*.f64 x y) x))
(-.f64 (fma.f64 x y 918938533204673/1000000000000000) x)
(fma.f64 x y (-.f64 918938533204673/1000000000000000 x))
(-.f64 (+.f64 918938533204673/1000000000000000 (*.f64 y x)) x)
(+.f64 918938533204673/1000000000000000 (-.f64 (*.f64 x y) x))
(-.f64 (fma.f64 x y 918938533204673/1000000000000000) x)
(fma.f64 x y (-.f64 918938533204673/1000000000000000 x))
(*.f64 y x)
(*.f64 x y)
(-.f64 (+.f64 918938533204673/1000000000000000 (*.f64 y x)) x)
(+.f64 918938533204673/1000000000000000 (-.f64 (*.f64 x y) x))
(-.f64 (fma.f64 x y 918938533204673/1000000000000000) x)
(fma.f64 x y (-.f64 918938533204673/1000000000000000 x))
(-.f64 (+.f64 918938533204673/1000000000000000 (*.f64 y x)) x)
(+.f64 918938533204673/1000000000000000 (-.f64 (*.f64 x y) x))
(-.f64 (fma.f64 x y 918938533204673/1000000000000000) x)
(fma.f64 x y (-.f64 918938533204673/1000000000000000 x))
(-.f64 (+.f64 918938533204673/1000000000000000 (*.f64 y x)) x)
(+.f64 918938533204673/1000000000000000 (-.f64 (*.f64 x y) x))
(-.f64 (fma.f64 x y 918938533204673/1000000000000000) x)
(fma.f64 x y (-.f64 918938533204673/1000000000000000 x))
918938533204673/1000000000000000
(+.f64 (*.f64 (-.f64 y 1) x) 918938533204673/1000000000000000)
(+.f64 918938533204673/1000000000000000 (-.f64 (*.f64 x y) x))
(-.f64 (fma.f64 x y 918938533204673/1000000000000000) x)
(fma.f64 x y (-.f64 918938533204673/1000000000000000 x))
(+.f64 (*.f64 (-.f64 y 1) x) 918938533204673/1000000000000000)
(+.f64 918938533204673/1000000000000000 (-.f64 (*.f64 x y) x))
(-.f64 (fma.f64 x y 918938533204673/1000000000000000) x)
(fma.f64 x y (-.f64 918938533204673/1000000000000000 x))
(+.f64 (*.f64 (-.f64 y 1) x) 918938533204673/1000000000000000)
(+.f64 918938533204673/1000000000000000 (-.f64 (*.f64 x y) x))
(-.f64 (fma.f64 x y 918938533204673/1000000000000000) x)
(fma.f64 x y (-.f64 918938533204673/1000000000000000 x))
(*.f64 (-.f64 y 1) x)
(*.f64 x (+.f64 y -1))
(*.f64 x (+.f64 -1 y))
(-.f64 (*.f64 x y) x)
(+.f64 918938533204673/1000000000000000 (*.f64 (-.f64 y 1) x))
(+.f64 918938533204673/1000000000000000 (-.f64 (*.f64 x y) x))
(-.f64 (fma.f64 x y 918938533204673/1000000000000000) x)
(fma.f64 x y (-.f64 918938533204673/1000000000000000 x))
(+.f64 918938533204673/1000000000000000 (*.f64 (-.f64 y 1) x))
(+.f64 918938533204673/1000000000000000 (-.f64 (*.f64 x y) x))
(-.f64 (fma.f64 x y 918938533204673/1000000000000000) x)
(fma.f64 x y (-.f64 918938533204673/1000000000000000 x))
(+.f64 918938533204673/1000000000000000 (*.f64 (-.f64 y 1) x))
(+.f64 918938533204673/1000000000000000 (-.f64 (*.f64 x y) x))
(-.f64 (fma.f64 x y 918938533204673/1000000000000000) x)
(fma.f64 x y (-.f64 918938533204673/1000000000000000 x))
(.f64 -1 (.f64 (+.f64 1 (*.f64 -1 y)) x))
(*.f64 x (+.f64 y -1))
(*.f64 x (+.f64 -1 y))
(-.f64 (*.f64 x y) x)
(+.f64 918938533204673/1000000000000000 (.f64 -1 (.f64 (+.f64 1 (*.f64 -1 y)) x)))
(+.f64 918938533204673/1000000000000000 (-.f64 (*.f64 x y) x))
(-.f64 (fma.f64 x y 918938533204673/1000000000000000) x)
(fma.f64 x y (-.f64 918938533204673/1000000000000000 x))
(+.f64 918938533204673/1000000000000000 (.f64 -1 (.f64 (+.f64 1 (*.f64 -1 y)) x)))
(+.f64 918938533204673/1000000000000000 (-.f64 (*.f64 x y) x))
(-.f64 (fma.f64 x y 918938533204673/1000000000000000) x)
(fma.f64 x y (-.f64 918938533204673/1000000000000000 x))
(+.f64 918938533204673/1000000000000000 (.f64 -1 (.f64 (+.f64 1 (*.f64 -1 y)) x)))
(+.f64 918938533204673/1000000000000000 (-.f64 (*.f64 x y) x))
(-.f64 (fma.f64 x y 918938533204673/1000000000000000) x)
(fma.f64 x y (-.f64 918938533204673/1000000000000000 x))

eval53.0ms (2%)

Compiler: Compiled 2362 to 1428 computations (39.5% saved)

prune36.0ms (1.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	180	5	185
Fresh	0	0	0
Picked	0	1	1
Done	2	2	4
Total	182	8	190

Error

Counts

190 → 8

Alt Table

Click to see full alt table

Status	Error	Program
▶	6.5b	(+.f64 (-.f64 (*.f64 y -1/2) x) 918938533204673/1000000000000000)
✓	15.9b	(+.f64 (-.f64 (*.f64 y x) x) 918938533204673/1000000000000000)
▶	41.0b	(*.f64 y (-.f64 x 1/2))
✓	0b	(+.f64 (-.f64 (*.f64 y (+.f64 -1/2 x)) x) 918938533204673/1000000000000000)
	43.2b	918938533204673/1000000000000000
▶	56.7b	(*.f64 y x)
▶	21.7b	(-.f64 918938533204673/1000000000000000 x)
✓	28.1b	(+.f64 (*.f64 -1/2 y) 918938533204673/1000000000000000)

Compiler

Compiled 56 to 42 computations (25% saved)

localize3.0ms (0.1%)

Compiler: Compiled 7 to 3 computations (57.1% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 13 to 8 computations (38.5% saved)

localize8.0ms (0.3%)

Compiler: Compiled 21 to 14 computations (33.3% saved)

localize3.0ms (0.1%)

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

eval6.0ms (0.2%)

Compiler: Compiled 175 to 121 computations (30.9% saved)

prune7.0ms (0.3%)

Pruning

9 alts after pruning (2 fresh and 7 done)

	Pruned	Kept	Total
New	20	1	21
Fresh	0	1	1
Picked	0	1	1
Done	0	6	6
Total	20	9	29

Error

Counts

29 → 9

Alt Table

Click to see full alt table

Status	Error	Program
✓	6.5b	(+.f64 (-.f64 (*.f64 y -1/2) x) 918938533204673/1000000000000000)
✓	15.9b	(+.f64 (-.f64 (*.f64 y x) x) 918938533204673/1000000000000000)
✓	41.0b	(*.f64 y (-.f64 x 1/2))
✓	0b	(+.f64 (-.f64 (*.f64 y (+.f64 -1/2 x)) x) 918938533204673/1000000000000000)
▶	47.3b	(*.f64 y -1/2)
	43.2b	918938533204673/1000000000000000
✓	56.7b	(*.f64 y x)
✓	21.7b	(-.f64 918938533204673/1000000000000000 x)
✓	28.1b	(+.f64 (*.f64 -1/2 y) 918938533204673/1000000000000000)

Compiler

Compiled 61 to 46 computations (24.6% saved)

localize3.0ms (0.1%)

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

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune5.0ms (0.2%)

Pruning

9 alts after pruning (1 fresh and 8 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	7	7
Total	9	9

Error

Counts

9 → 9

Alt Table

Click to see full alt table

Status	Error	Program
✓	6.5b	(+.f64 (-.f64 (*.f64 y -1/2) x) 918938533204673/1000000000000000)
✓	15.9b	(+.f64 (-.f64 (*.f64 y x) x) 918938533204673/1000000000000000)
✓	41.0b	(*.f64 y (-.f64 x 1/2))
✓	0b	(+.f64 (-.f64 (*.f64 y (+.f64 -1/2 x)) x) 918938533204673/1000000000000000)
✓	47.3b	(*.f64 y -1/2)
	43.2b	918938533204673/1000000000000000
✓	56.7b	(*.f64 y x)
✓	21.7b	(-.f64 918938533204673/1000000000000000 x)
✓	28.1b	(+.f64 (*.f64 -1/2 y) 918938533204673/1000000000000000)

Compiler

Compiled 61 to 46 computations (24.6% saved)

regimes48.0ms (1.8%)

Counts

13 → 1

Calls

Call 1

Inputs
918938533204673/1000000000000000
(*.f64 y -1/2)
(*.f64 y x)
(-.f64 918938533204673/1000000000000000 x)
(+.f64 (neg.f64 x) 918938533204673/1000000000000000)
(*.f64 y (-.f64 x 1/2))
(+.f64 (*.f64 -1/2 y) 918938533204673/1000000000000000)
(+.f64 (-.f64 (*.f64 y -1/2) x) 918938533204673/1000000000000000)
(+.f64 (*.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)
(+.f64 (-.f64 (*.f64 y x) x) 918938533204673/1000000000000000)
(+.f64 (-.f64 (*.f64 y (+.f64 -1/2 x)) x) 918938533204673/1000000000000000)
(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
(-.f64 918938533204673/1000000000000000 (fma.f64 y (-.f64 1/2 x) x))

Outputs
(+.f64 (-.f64 (*.f64 y (+.f64 -1/2 x)) x) 918938533204673/1000000000000000)

Calls

6 calls:

9.0ms	(-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2))
8.0ms	x
8.0ms	(-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2))
7.0ms	y
7.0ms	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)

Results

Error	Segments	Branch
0b	1	`x`
0b	1	`y`
0b	1	`(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)`
0b	1	`(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)`
0b	1	`(-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2))`
0b	1	`(-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2))`

Compiler

Compiled 129 to 90 computations (30.2% saved)

regimes37.0ms (1.4%)

Counts

10 → 3

Calls

Call 1

Inputs
918938533204673/1000000000000000
(*.f64 y -1/2)
(*.f64 y x)
(-.f64 918938533204673/1000000000000000 x)
(+.f64 (neg.f64 x) 918938533204673/1000000000000000)
(*.f64 y (-.f64 x 1/2))
(+.f64 (*.f64 -1/2 y) 918938533204673/1000000000000000)
(+.f64 (-.f64 (*.f64 y -1/2) x) 918938533204673/1000000000000000)
(+.f64 (*.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)
(+.f64 (-.f64 (*.f64 y x) x) 918938533204673/1000000000000000)

Outputs
(+.f64 (-.f64 (*.f64 y x) x) 918938533204673/1000000000000000)
(+.f64 (*.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)
(+.f64 (-.f64 (*.f64 y x) x) 918938533204673/1000000000000000)

Calls

2 calls:

17.0ms	x
17.0ms	y

Results

Error	Segments	Branch
0.3b	3	`x`
0.3b	3	`y`

Compiler

Compiled 53 to 35 computations (34% saved)

bsearch36.0ms (1.4%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
18.0ms	257609935.23354307	13830742593123.436
18.0ms	-3.3314034762393124e-16	-1.1507319004679778e-24

Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes26.0ms (1%)

Counts

9 → 3

Calls

Call 1

Inputs
918938533204673/1000000000000000
(*.f64 y -1/2)
(*.f64 y x)
(-.f64 918938533204673/1000000000000000 x)
(+.f64 (neg.f64 x) 918938533204673/1000000000000000)
(*.f64 y (-.f64 x 1/2))
(+.f64 (*.f64 -1/2 y) 918938533204673/1000000000000000)
(+.f64 (-.f64 (*.f64 y -1/2) x) 918938533204673/1000000000000000)
(+.f64 (*.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)

Outputs
(+.f64 (*.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)
(+.f64 (-.f64 (*.f64 y -1/2) x) 918938533204673/1000000000000000)
(+.f64 (*.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)

Calls

2 calls:

16.0ms	y
6.0ms	x

Results

Error	Segments	Branch
6.5b	1	`x`
0.5b	3	`y`

Compiler

Compiled 46 to 32 computations (30.4% saved)

bsearch38.0ms (1.4%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
18.0ms	3.487064303855046e-12	1.1438132165957093e-11
19.0ms	-6893.50182897125	-1896.4048845480497

Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes25.0ms (0.9%)

Counts

8 → 3

Calls

Call 1

Inputs
918938533204673/1000000000000000
(*.f64 y -1/2)
(*.f64 y x)
(-.f64 918938533204673/1000000000000000 x)
(+.f64 (neg.f64 x) 918938533204673/1000000000000000)
(*.f64 y (-.f64 x 1/2))
(+.f64 (*.f64 -1/2 y) 918938533204673/1000000000000000)
(+.f64 (-.f64 (*.f64 y -1/2) x) 918938533204673/1000000000000000)

Outputs
(*.f64 y (-.f64 x 1/2))
(+.f64 (-.f64 (*.f64 y -1/2) x) 918938533204673/1000000000000000)
(*.f64 y (-.f64 x 1/2))

Calls

2 calls:

16.0ms	y
6.0ms	x

Results

Error	Segments	Branch
6.5b	1	`x`
0.6b	3	`y`

Compiler

Compiled 39 to 27 computations (30.8% saved)

bsearch36.0ms (1.4%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
18.0ms	1.1438132165957093e-11	3741593014.199811
18.0ms	-1.5408773491812858e+27	-2.010348297099022e+22

Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes32.0ms (1.2%)

Counts

7 → 3

Calls

Call 1

Inputs
918938533204673/1000000000000000
(*.f64 y -1/2)
(*.f64 y x)
(-.f64 918938533204673/1000000000000000 x)
(+.f64 (neg.f64 x) 918938533204673/1000000000000000)
(*.f64 y (-.f64 x 1/2))
(+.f64 (*.f64 -1/2 y) 918938533204673/1000000000000000)

Outputs
(*.f64 y (-.f64 x 1/2))
(-.f64 918938533204673/1000000000000000 x)
(*.f64 y (-.f64 x 1/2))

Calls

2 calls:

15.0ms	x
14.0ms	y

Results

Error	Segments	Branch
6.6b	3	`x`
0.9b	3	`y`

Compiler

Compiled 32 to 22 computations (31.3% saved)

bsearch36.0ms (1.4%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
18.0ms	1.1438132165957093e-11	3741593014.199811
18.0ms	-1896.4048845480497	-1.845721660222086e-5

Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes49.0ms (1.9%)

Counts

5 → 3

Calls

Call 1

Inputs
918938533204673/1000000000000000
(*.f64 y -1/2)
(*.f64 y x)
(-.f64 918938533204673/1000000000000000 x)
(+.f64 (neg.f64 x) 918938533204673/1000000000000000)

Outputs
(*.f64 y -1/2)
(-.f64 918938533204673/1000000000000000 x)
(*.f64 y -1/2)

Calls

2 calls:

34.0ms	x
14.0ms	y

Results

Error	Segments	Branch
18.8b	5	`x`
6.9b	3	`y`

Compiler

Compiled 22 to 15 computations (31.8% saved)

bsearch42.0ms (1.6%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
18.0ms	1.1438132165957093e-11	3741593014.199811
24.0ms	-1896.4048845480497	-1.845721660222086e-5

Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes32.0ms (1.2%)

Accuracy

Total -34.2b remaining (-120.2%)

Threshold costs -34.2b (-120.2%)

Counts

3 → 3

Calls

Call 1

Inputs
918938533204673/1000000000000000
(*.f64 y -1/2)
(*.f64 y x)

Outputs
(*.f64 y -1/2)
918938533204673/1000000000000000
(*.f64 y -1/2)

Calls

2 calls:

21.0ms	x
10.0ms	y

Results

Error	Segments	Branch
35.1b	6	`x`
28.5b	3	`y`

Compiler

Compiled 15 to 10 computations (33.3% saved)

bsearch36.0ms (1.3%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
18.0ms	1.1438132165957093e-11	3741593014.199811
18.0ms	-1.845721660222086e-5	-4.480195591696182e-12

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify12.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	209
1	66	209
2	74	209
3	76	209
4	77	209

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(+.f64 (-.f64 (*.f64 y (+.f64 -1/2 x)) x) 918938533204673/1000000000000000)
(if (<=.f64 x -6756888986011479/20282409603651670423947251286016) (+.f64 (-.f64 (.f64 y x) x) 918938533204673/1000000000000000) (if (<=.f64 x 8643955054318325/33554432) (+.f64 (.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000) (+.f64 (-.f64 (*.f64 y x) x) 918938533204673/1000000000000000)))
(if (<=.f64 y -1894871354262253/274877906944) (+.f64 (.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000) (if (<=.f64 y 4316776521304963/1237940039285380274899124224) (+.f64 (-.f64 (.f64 y -1/2) x) 918938533204673/1000000000000000) (+.f64 (*.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)))
(if (<=.f64 y -1540877349181285813400371200) (.f64 y (-.f64 x 1/2)) (if (<=.f64 y 1769965222859537/154742504910672534362390528) (+.f64 (-.f64 (.f64 y -1/2) x) 918938533204673/1000000000000000) (*.f64 y (-.f64 x 1/2))))
(if (<=.f64 y -4170238443063567/2199023255552) (.f64 y (-.f64 x 1/2)) (if (<=.f64 y 1769965222859537/154742504910672534362390528) (-.f64 918938533204673/1000000000000000 x) (.f64 y (-.f64 x 1/2))))
(if (<=.f64 y -4170238443063567/2199023255552) (.f64 y -1/2) (if (<=.f64 y 1769965222859537/154742504910672534362390528) (-.f64 918938533204673/1000000000000000 x) (.f64 y -1/2)))
(if (<=.f64 y -5447608815587059/295147905179352825856) (.f64 y -1/2) (if (<=.f64 y 1769965222859537/154742504910672534362390528) 918938533204673/1000000000000000 (.f64 y -1/2)))
918938533204673/1000000000000000

Outputs
(+.f64 (-.f64 (*.f64 y (+.f64 -1/2 x)) x) 918938533204673/1000000000000000)
(if (<=.f64 x -6756888986011479/20282409603651670423947251286016) (+.f64 (-.f64 (.f64 y x) x) 918938533204673/1000000000000000) (if (<=.f64 x 8643955054318325/33554432) (+.f64 (.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000) (+.f64 (-.f64 (*.f64 y x) x) 918938533204673/1000000000000000)))
(if (<=.f64 x -6756888986011479/20282409603651670423947251286016) (+.f64 918938533204673/1000000000000000 (-.f64 (.f64 y x) x)) (if (<=.f64 x 8643955054318325/33554432) (+.f64 918938533204673/1000000000000000 (.f64 y (+.f64 -1/2 x))) (+.f64 918938533204673/1000000000000000 (-.f64 (*.f64 y x) x))))
(if (<=.f64 y -1894871354262253/274877906944) (+.f64 (.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000) (if (<=.f64 y 4316776521304963/1237940039285380274899124224) (+.f64 (-.f64 (.f64 y -1/2) x) 918938533204673/1000000000000000) (+.f64 (*.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)))
(if (<=.f64 y -1894871354262253/274877906944) (+.f64 918938533204673/1000000000000000 (.f64 y (+.f64 -1/2 x))) (if (<=.f64 y 4316776521304963/1237940039285380274899124224) (+.f64 918938533204673/1000000000000000 (-.f64 (.f64 y -1/2) x)) (+.f64 918938533204673/1000000000000000 (*.f64 y (+.f64 -1/2 x)))))
(if (<=.f64 y -1540877349181285813400371200) (.f64 y (-.f64 x 1/2)) (if (<=.f64 y 1769965222859537/154742504910672534362390528) (+.f64 (-.f64 (.f64 y -1/2) x) 918938533204673/1000000000000000) (*.f64 y (-.f64 x 1/2))))
(if (<=.f64 y -1540877349181285813400371200) (.f64 y (+.f64 -1/2 x)) (if (<=.f64 y 1769965222859537/154742504910672534362390528) (+.f64 918938533204673/1000000000000000 (-.f64 (.f64 y -1/2) x)) (*.f64 y (+.f64 -1/2 x))))
(if (<=.f64 y -4170238443063567/2199023255552) (.f64 y (-.f64 x 1/2)) (if (<=.f64 y 1769965222859537/154742504910672534362390528) (-.f64 918938533204673/1000000000000000 x) (.f64 y (-.f64 x 1/2))))
(if (<=.f64 y -4170238443063567/2199023255552) (.f64 y (+.f64 -1/2 x)) (if (<=.f64 y 1769965222859537/154742504910672534362390528) (-.f64 918938533204673/1000000000000000 x) (.f64 y (+.f64 -1/2 x))))
(if (<=.f64 y -4170238443063567/2199023255552) (.f64 y -1/2) (if (<=.f64 y 1769965222859537/154742504910672534362390528) (-.f64 918938533204673/1000000000000000 x) (.f64 y -1/2)))
(if (<=.f64 y -5447608815587059/295147905179352825856) (.f64 y -1/2) (if (<=.f64 y 1769965222859537/154742504910672534362390528) 918938533204673/1000000000000000 (.f64 y -1/2)))
918938533204673/1000000000000000

Compiler

Compiled 162 to 115 computations (29% saved)

soundness75.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

292×	`fma-def_binary64`
290×	`fma-neg_binary64`
67×	`cancel-sign-sub-inv_binary64`
46×	`sub-neg_binary64`
39×	`unsub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	233
1	52	233
2	139	215
3	274	215
4	617	215
5	1040	215
6	1246	215
7	1282	215
8	1285	215

Stop Event

1×

saturated

Compiler

Compiled 171 to 118 computations (31% saved)

end79.0ms (3%)

Compiler: Compiled 148 to 101 computations (31.8% saved)

Iter	Nodes	Cost
0	21	365
1	48	329
2	93	329
3	191	329
4	358	329
5	580	329
6	708	329
7	768	329
8	802	329
9	808	329

Iter	Nodes	Cost
0	21	365
1	48	329
2	93	329
3	191	329
4	358	329
5	580	329
6	708	329
7	768	329
8	802	329
9	808	329

Details

analyze73.0ms (2.8%)

sample1.1s (39.9%)

preprocess123.0ms (4.7%)

simplify56.0ms (2.1%)

eval1.0ms (0%)

prune2.0ms (0.1%)

localize15.0ms (0.6%)

series4.0ms (0.1%)

rewrite77.0ms (2.9%)

simplify44.0ms (1.7%)

localize10.0ms (0.4%)

eval85.0ms (3.2%)

prune26.0ms (1%)

localize14.0ms (0.5%)

series3.0ms (0.1%)

rewrite46.0ms (1.7%)

simplify9.0ms (0.3%)

localize4.0ms (0.2%)

localize6.0ms (0.2%)

localize8.0ms (0.3%)

series3.0ms (0.1%)

rewrite67.0ms (2.5%)

simplify14.0ms (0.5%)

localize6.0ms (0.2%)

series5.0ms (0.2%)

rewrite72.0ms (2.7%)

simplify45.0ms (1.7%)

eval53.0ms (2%)

prune36.0ms (1.4%)

localize3.0ms (0.1%)

localize6.0ms (0.2%)

localize8.0ms (0.3%)

localize3.0ms (0.1%)

eval6.0ms (0.2%)

prune7.0ms (0.3%)

localize3.0ms (0.1%)

eval0.0ms (0%)

prune5.0ms (0.2%)

regimes48.0ms (1.8%)

regimes37.0ms (1.4%)

bsearch36.0ms (1.4%)

regimes26.0ms (1%)

bsearch38.0ms (1.4%)

regimes25.0ms (0.9%)

bsearch36.0ms (1.4%)

regimes32.0ms (1.2%)

bsearch36.0ms (1.4%)

regimes49.0ms (1.9%)

bsearch42.0ms (1.6%)

regimes32.0ms (1.2%)

bsearch36.0ms (1.3%)

simplify12.0ms (0.5%)

soundness75.0ms (2.8%)

end79.0ms (3%)

Profiling

Iter	Nodes	Cost
0	21	365
1	48	329
2	93	329
3	191	329
4	358	329
5	580	329
6	708	329
7	768	329
8	802	329
9	808	329