Details

analyze74.0ms (2.9%)

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
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 (44.2%)

Results

1.1s	8256×	body	256	valid
53.0ms	268×	body	256	invalid

preprocess68.0ms (2.7%)

Algorithm

2×	egg-herbie

Rules

1297×	`fma-neg_binary64`
333×	`cancel-sign-sub-inv_binary64`
300×	`fma-def_binary64`
262×	`sub-neg_binary64`
200×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	44	28
2	106	24
3	247	24
4	557	22
5	1221	22
6	2255	22
7	3430	22
8	3826	22
9	3844	22
10	3844	22
11	4502	22
12	4502	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 (.f64 x (+.f64 y -1)) (.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 -1/2 (fma.f64 y (+.f64 x -1) 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)

simplify31.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-neg_binary64`
578×	`fma-def_binary64`
222×	`cancel-sign-sub-inv_binary64`
114×	`sub-neg_binary64`
81×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	27	14
2	62	12
3	129	12
4	268	11
5	580	11
6	1075	11
7	1794	11
8	2581	11
9	2752	11
10	2779	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 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x)

eval1.0ms (0%)

Compiler: Compiled 21 to 15 computations (28.6% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 13 to 10 computations (23.1% saved)

localize17.0ms (0.6%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 38 to 26 computations (31.6% saved)

series4.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

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

rewrite68.0ms (2.6%)

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	2752	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 (fma.f64 (sqrt.f64 (+.f64 y -1)) (sqrt.f64 x) (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)) (fma.f64 x (+.f64 y -1) (neg.f64 (.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 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Outputs

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

simplify30.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

312×	`fma-def_binary64`
296×	`fma-neg_binary64`
67×	`cancel-sign-sub-inv_binary64`
47×	`sub-neg_binary64`
38×	`unsub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	233
1	52	233
2	139	215
3	273	215
4	639	215
5	1068	215
6	1274	215
7	1310	215
8	1313	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 (+.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 (+.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 (+.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 -1/2 y) (.f64 (-.f64 y 1) x))
(fma.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 -1/2 y) (.f64 (-.f64 y 1) x))
(fma.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 -1/2 y) (.f64 (-.f64 y 1) x))
(fma.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 -1/2 y) (.f64 (-.f64 y 1) x))
(fma.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 -1/2 y) (.f64 (-.f64 y 1) x))
(fma.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 -1/2 y) (.f64 (-.f64 y 1) x))
(fma.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 -1 x)
(neg.f64 x)
(+.f64 (.f64 y (-.f64 x 1/2)) (.f64 -1 x))
(fma.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 (-.f64 x 1/2)) (.f64 -1 x))
(fma.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 (-.f64 x 1/2)) (.f64 -1 x))
(fma.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 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 (+.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 -1 x) (.f64 y (-.f64 x 1/2)))
(fma.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 -1 x) (.f64 y (-.f64 x 1/2)))
(fma.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 -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 (+.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 -1 (.f64 y (+.f64 1/2 (.f64 -1 x)))) (.f64 -1 x))
(fma.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 -1 (.f64 y (+.f64 1/2 (.f64 -1 x)))) (.f64 -1 x))
(fma.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)

eval103.0ms (4%)

Compiler: Compiled 4061 to 2952 computations (27.3% saved)

prune30.0ms (1.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	183	6	189
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	184	6	190

Error

Counts

190 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	26.7b	(+.f64 (*.f64 -1/2 y) 918938533204673/1000000000000000)
▶	18.3b	(+.f64 (*.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)
▶	25.0b	(+.f64 (neg.f64 x) 918938533204673/1000000000000000)
▶	0b	(+.f64 (fma.f64 x (+.f64 y -1) (*.f64 y -1/2)) 918938533204673/1000000000000000)
▶	16.9b	(+.f64 (*.f64 (-.f64 y 1) x) 918938533204673/1000000000000000)
	0.0b	(+.f64 (-.f64 (*.f64 y (+.f64 -1/2 x)) x) 918938533204673/1000000000000000)

Compiler

Compiled 108 to 84 computations (22.2% saved)

localize14.0ms (0.6%)

Compiler: Compiled 31 to 21 computations (32.3% saved)

localize5.0ms (0.2%)

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

localize6.0ms (0.2%)

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

localize10.0ms (0.4%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 21 to 14 computations (33.3% saved)

series2.0ms (0.1%)

Counts

1 → 21

Calls

6 calls:

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

rewrite51.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

888×	`pow1_binary64`
830×	`add-log-exp_binary64`
829×	`log1p-expm1-u_binary64`
829×	`expm1-log1p-u_binary64`
816×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	8
1	176	8
2	2225	8

Stop Event

1×	node limit

Counts

1 → 32

Calls

Call 1

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

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

Outputs

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

simplify25.0ms (1%)

Algorithm

1×	egg-herbie

Rules

203×	`fma-def_binary64`
183×	`fma-neg_binary64`
59×	`cancel-sign-sub-inv_binary64`
32×	`sub-neg_binary64`
31×	`associate--r+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	179
1	28	147
2	46	147
3	66	147
4	100	147
5	160	147
6	318	147
7	537	147
8	748	147
9	845	147
10	880	147
11	882	147

Stop Event

1×

saturated

Counts

53 → 42

Calls

Call 1

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

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

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series5.0ms (0.2%)

Counts

2 → 36

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	y	@	-inf	(+.f64 (*.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)
1.0ms	y	@	0	(+.f64 (*.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)
1.0ms	x	@	-inf	(+.f64 (*.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)
0.0ms	y	@	inf	(+.f64 (*.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)
0.0ms	x	@	inf	(+.f64 (*.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)

rewrite51.0ms (2%)

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	2334	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 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 (cbrt.f64 (pow.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 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 expm1.f64 (log1p.f64 (fma.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 (+.f64 x -1/2)) y))))) (#(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 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))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.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))

eval36.0ms (1.4%)

Compiler: Compiled 1237 to 927 computations (25.1% saved)

prune22.0ms (0.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	0	1	1
Picked	0	1	1
Done	2	2	4
Total	101	9	110

Error

Counts

110 → 9

Alt Table

Click to see full alt table

Status	Error	Program
✓	18.3b	(+.f64 (*.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)
▶	54.1b	(*.f64 x y)
✓	26.7b	(+.f64 (*.f64 -1/2 y) 918938533204673/1000000000000000)
▶	36.5b	(-.f64 (*.f64 x y) x)
	43.3b	918938533204673/1000000000000000
▶	25.0b	(-.f64 918938533204673/1000000000000000 x)
✓	0b	(+.f64 (fma.f64 x (+.f64 y -1) (*.f64 y -1/2)) 918938533204673/1000000000000000)
▶	37.5b	(*.f64 y (+.f64 x -1/2))
▶	0.0b	(+.f64 (-.f64 (*.f64 y (+.f64 -1/2 x)) x) 918938533204673/1000000000000000)

Compiler

Compiled 101 to 73 computations (27.7% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 30 to 19 computations (36.7% saved)

series4.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

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

rewrite58.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

975×	`pow1_binary64`
911×	`add-log-exp_binary64`
911×	`log1p-expm1-u_binary64`
911×	`expm1-log1p-u_binary64`
89×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	167	17
2	2424	17

Stop Event

1×	node limit

Counts

2 → 63

Calls

Call 1

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

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

simplify33.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

262×	`fma-def_binary64`
226×	`fma-neg_binary64`
61×	`cancel-sign-sub-inv_binary64`
49×	`distribute-rgt-in_binary64`
37×	`associate--r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	374
1	52	374
2	97	374
3	179	374
4	369	374
5	707	374
6	1024	374
7	1174	374
8	1186	374

Stop Event

1×

saturated

Counts

111 → 80

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

localize3.0ms (0.1%)

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

localize3.0ms (0.1%)

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

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 13 to 8 computations (38.5% saved)

series2.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite44.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

725×	`pow1_binary64`
677×	`add-log-exp_binary64`
677×	`log1p-expm1-u_binary64`
677×	`expm1-log1p-u_binary64`
664×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	136	7
2	1819	7

Stop Event

1×	node limit

Counts

1 → 24

Calls

Call 1

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

Outputs

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

simplify9.0ms (0.4%)

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))

localize5.0ms (0.2%)

Compiler: Compiled 12 to 4 computations (66.7% saved)

eval34.0ms (1.3%)

Compiler: Compiled 1442 to 931 computations (35.4% saved)

prune22.0ms (0.8%)

Pruning

10 alts after pruning (3 fresh and 7 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	0	1	1
Picked	0	1	1
Done	1	6	7
Total	109	10	119

Error

Counts

119 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	18.3b	(+.f64 (*.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)
✓	54.1b	(*.f64 x y)
✓	0.0b	(+.f64 (-.f64 (*.f64 y (+.f64 -1/2 x)) x) 918938533204673/1000000000000000)
▶	0b	(+.f64 (fma.f64 (+.f64 -1/2 x) y (neg.f64 x)) 918938533204673/1000000000000000)
✓	26.7b	(+.f64 (*.f64 -1/2 y) 918938533204673/1000000000000000)
✓	36.5b	(-.f64 (*.f64 x y) x)
▶	45.9b	(*.f64 y -1/2)
	43.3b	918938533204673/1000000000000000
✓	25.0b	(-.f64 918938533204673/1000000000000000 x)
✓	37.5b	(*.f64 y (+.f64 x -1/2))

Compiler

Compiled 70 to 52 computations (25.7% saved)

localize3.0ms (0.1%)

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

localize13.0ms (0.5%)

Compiler: Compiled 27 to 15 computations (44.4% saved)

eval0.0ms (0%)

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

prune4.0ms (0.2%)

Pruning

10 alts after pruning (1 fresh and 9 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	8	8
Total	10	10

Error

Counts

10 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	18.3b	(+.f64 (*.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)
✓	54.1b	(*.f64 x y)
✓	0.0b	(+.f64 (-.f64 (*.f64 y (+.f64 -1/2 x)) x) 918938533204673/1000000000000000)
✓	0b	(+.f64 (fma.f64 (+.f64 -1/2 x) y (neg.f64 x)) 918938533204673/1000000000000000)
✓	26.7b	(+.f64 (*.f64 -1/2 y) 918938533204673/1000000000000000)
✓	36.5b	(-.f64 (*.f64 x y) x)
✓	45.9b	(*.f64 y -1/2)
	43.3b	918938533204673/1000000000000000
✓	25.0b	(-.f64 918938533204673/1000000000000000 x)
✓	37.5b	(*.f64 y (+.f64 x -1/2))

Compiler

Compiled 70 to 52 computations (25.7% saved)

regimes15.0ms (0.6%)

Counts

10 → 1

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	y
6.0ms	x

Results

Error	Segments	Branch
0b	1	`x`
0b	1	`y`

Compiler

Compiled 58 to 37 computations (36.2% saved)

regimes15.0ms (0.6%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	x
6.0ms	y

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`y`

Compiler

Compiled 49 to 31 computations (36.7% saved)

regimes39.0ms (1.5%)

Counts

8 → 3

Calls

Call 1

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

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

Calls

2 calls:

21.0ms	x
16.0ms	y

Results

Error	Segments	Branch
0.9b	3	`x`
0.4b	3	`y`

Compiler

Compiled 40 to 25 computations (37.5% saved)

bsearch40.0ms (1.6%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
19.0ms	1.5671491280380653e-11	2.3583391504686918e-9
21.0ms	-8.329993913024635e-13	-1.8490581912368364e-18

Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes33.0ms (1.3%)

Counts

7 → 3

Calls

Call 1

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

16.0ms	y
15.0ms	x

Results

Error	Segments	Branch
1.2b	3	`x`
0.8b	3	`y`

Compiler

Compiled 33 to 20 computations (39.4% saved)

bsearch40.0ms (1.6%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
20.0ms	2.3583391504686918e-9	32075.51690087317
20.0ms	-6.343413215155137	-8.329993913024635e-13

Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes42.0ms (1.6%)

Counts

4 → 4

Calls

Call 1

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

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

Calls

2 calls:

25.0ms	x
16.0ms	y

Results

Error	Segments	Branch
18.8b	7	`x`
7.7b	4	`y`

Compiler

Compiled 18 to 12 computations (33.3% saved)

bsearch109.0ms (4.3%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
20.0ms	2.3583391504686918e-9	32075.51690087317
20.0ms	-6.343413215155137	-8.329993913024635e-13
70.0ms	-1.4583477100170303e+131	-1.4153491649223465e+128

Compiler

Compiled 114 to 86 computations (24.6% saved)

regimes35.0ms (1.3%)

Counts

3 → 3

Calls

Call 1

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

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

Calls

2 calls:

23.0ms	x
10.0ms	y

Results

Error	Segments	Branch
18.8b	7	`x`
8.9b	3	`y`

Compiler

Compiled 15 to 11 computations (26.7% saved)

bsearch40.0ms (1.6%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
20.0ms	2.3583391504686918e-9	32075.51690087317
20.0ms	-40462471414959.77	-83314956.79552375

Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes8.0ms (0.3%)

Accuracy

Total -18.3b remaining (-73.1%)

Threshold costs -18.3b (-73.1%)

Counts

2 → 1

Calls

Call 1

Inputs
918938533204673/1000000000000000
(-.f64 918938533204673/1000000000000000 x)

Outputs
(-.f64 918938533204673/1000000000000000 x)

Calls

2 calls:

3.0ms	x
3.0ms	y

Results

Error	Segments	Branch
25.0b	1	`x`
25.0b	1	`y`

Compiler

Compiled 12 to 9 computations (25% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
6×	`*-commutative_binary64`
4×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	155
1	60	155
2	64	155
3	65	155

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (fma.f64 (+.f64 -1/2 x) y (neg.f64 x)) 918938533204673/1000000000000000)
(+.f64 (-.f64 (*.f64 y (+.f64 -1/2 x)) x) 918938533204673/1000000000000000)
(if (<=.f64 y -65997011148394848/79228162514264337593543950336) (+.f64 (.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000) (if (<=.f64 y 1241623458002874880/79228162514264337593543950336) (-.f64 918938533204673/1000000000000000 x) (+.f64 (.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)))
(if (<=.f64 y -7142048348007439/1125899906842624) (.f64 y (+.f64 x -1/2)) (if (<=.f64 y 5702114180819263/2417851639229258349412352) (-.f64 918938533204673/1000000000000000 x) (.f64 y (+.f64 x -1/2))))
(if (<=.f64 y -141999999999999991435516304062343822230317878239793038052981651877846380550295320270508502617009272176191570847491843500776882176) (.f64 y -1/2) (if (<=.f64 y -7142048348007439/1125899906842624) (.f64 x y) (if (<=.f64 y 5702114180819263/2417851639229258349412352) (-.f64 918938533204673/1000000000000000 x) (*.f64 y -1/2))))
(if (<=.f64 y -5179196341114851/128) (.f64 y -1/2) (if (<=.f64 y 5702114180819263/2417851639229258349412352) (-.f64 918938533204673/1000000000000000 x) (.f64 y -1/2)))
(-.f64 918938533204673/1000000000000000 x)
918938533204673/1000000000000000

Outputs
(+.f64 (fma.f64 (+.f64 -1/2 x) y (neg.f64 x)) 918938533204673/1000000000000000)
(+.f64 (-.f64 (*.f64 y (+.f64 -1/2 x)) x) 918938533204673/1000000000000000)
(+.f64 918938533204673/1000000000000000 (-.f64 (*.f64 y (+.f64 -1/2 x)) x))
(if (<=.f64 y -65997011148394848/79228162514264337593543950336) (+.f64 (.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000) (if (<=.f64 y 1241623458002874880/79228162514264337593543950336) (-.f64 918938533204673/1000000000000000 x) (+.f64 (.f64 y (-.f64 x 1/2)) 918938533204673/1000000000000000)))
(if (<=.f64 y -2062406598387339/2475880078570760549798248448) (+.f64 918938533204673/1000000000000000 (.f64 y (+.f64 -1/2 x))) (if (<=.f64 y 2425045816411865/154742504910672534362390528) (-.f64 918938533204673/1000000000000000 x) (+.f64 918938533204673/1000000000000000 (.f64 y (+.f64 -1/2 x)))))
(if (<=.f64 y -7142048348007439/1125899906842624) (.f64 y (+.f64 x -1/2)) (if (<=.f64 y 5702114180819263/2417851639229258349412352) (-.f64 918938533204673/1000000000000000 x) (.f64 y (+.f64 x -1/2))))
(if (<=.f64 y -7142048348007439/1125899906842624) (.f64 y (+.f64 -1/2 x)) (if (<=.f64 y 5702114180819263/2417851639229258349412352) (-.f64 918938533204673/1000000000000000 x) (.f64 y (+.f64 -1/2 x))))
(if (<=.f64 y -141999999999999991435516304062343822230317878239793038052981651877846380550295320270508502617009272176191570847491843500776882176) (.f64 y -1/2) (if (<=.f64 y -7142048348007439/1125899906842624) (.f64 x y) (if (<=.f64 y 5702114180819263/2417851639229258349412352) (-.f64 918938533204673/1000000000000000 x) (*.f64 y -1/2))))
(if (<=.f64 y -141999999999999991435516304062343822230317878239793038052981651877846380550295320270508502617009272176191570847491843500776882176) (.f64 -1/2 y) (if (<=.f64 y -7142048348007439/1125899906842624) (.f64 x y) (if (<=.f64 y 5702114180819263/2417851639229258349412352) (-.f64 918938533204673/1000000000000000 x) (*.f64 -1/2 y))))
(if (<=.f64 y -5179196341114851/128) (.f64 y -1/2) (if (<=.f64 y 5702114180819263/2417851639229258349412352) (-.f64 918938533204673/1000000000000000 x) (.f64 y -1/2)))
(if (<=.f64 y -5179196341114851/128) (.f64 -1/2 y) (if (<=.f64 y 5702114180819263/2417851639229258349412352) (-.f64 918938533204673/1000000000000000 x) (.f64 -1/2 y)))
(-.f64 918938533204673/1000000000000000 x)
918938533204673/1000000000000000

end74.0ms (2.9%)

Stop Event

1×

fuel

Compiler

Compiled 236 to 168 computations (28.8% saved)

Iter	Nodes	Cost
0	14	179
1	28	147
2	46	147
3	66	147
4	100	147
5	160	147
6	318	147
7	537	147
8	748	147
9	845	147
10	880	147
11	882	147

Iter	Nodes	Cost
0	14	179
1	28	147
2	46	147
3	66	147
4	100	147
5	160	147
6	318	147
7	537	147
8	748	147
9	845	147
10	880	147
11	882	147

Details

analyze74.0ms (2.9%)

sample1.1s (44.2%)

preprocess68.0ms (2.7%)

simplify31.0ms (1.2%)

eval1.0ms (0%)

prune1.0ms (0%)

localize17.0ms (0.6%)

series4.0ms (0.2%)

rewrite68.0ms (2.6%)

simplify30.0ms (1.2%)

eval103.0ms (4%)

prune30.0ms (1.2%)

localize14.0ms (0.6%)

localize5.0ms (0.2%)

localize6.0ms (0.2%)

localize10.0ms (0.4%)

series2.0ms (0.1%)

rewrite51.0ms (2%)

simplify25.0ms (1%)

localize10.0ms (0.4%)

series5.0ms (0.2%)

rewrite51.0ms (2%)

simplify14.0ms (0.5%)

eval36.0ms (1.4%)

prune22.0ms (0.9%)

localize14.0ms (0.5%)

series4.0ms (0.1%)

rewrite58.0ms (2.3%)

simplify33.0ms (1.3%)

localize3.0ms (0.1%)

localize3.0ms (0.1%)

localize7.0ms (0.3%)

series2.0ms (0.1%)

rewrite44.0ms (1.7%)

simplify9.0ms (0.4%)

localize5.0ms (0.2%)

eval34.0ms (1.3%)

prune22.0ms (0.8%)

localize3.0ms (0.1%)

localize13.0ms (0.5%)

eval0.0ms (0%)

prune4.0ms (0.2%)

regimes15.0ms (0.6%)

regimes15.0ms (0.6%)

regimes39.0ms (1.5%)

bsearch40.0ms (1.6%)

regimes33.0ms (1.3%)

bsearch40.0ms (1.6%)

regimes42.0ms (1.6%)

bsearch109.0ms (4.3%)

regimes35.0ms (1.3%)

bsearch40.0ms (1.6%)

regimes8.0ms (0.3%)

simplify6.0ms (0.2%)

end74.0ms (2.9%)

Profiling

Iter	Nodes	Cost
0	14	179
1	28	147
2	46	147
3	66	147
4	100	147
5	160	147
6	318	147
7	537	147
8	748	147
9	845	147
10	880	147
11	882	147