Details

analyze103.0ms (3.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
25%	74.9%	0.1%	6
40.6%	59.3%	0.1%	7
53.1%	46.8%	0.1%	8
66.3%	33.6%	0.1%	9
74.1%	25.8%	0.1%	10
82.1%	17.8%	0.1%	11
86.4%	13.5%	0.1%	12

Compiler

Compiled 14 to 10 computations (28.6% saved)

sample1.2s (37%)

Results

1.2s	8255×	body	256	valid
0.0ms	1×	body	2048	valid

preprocess86.0ms (2.7%)

Algorithm

2×	egg-herbie

Rules

1480×	`fma-neg_binary64`
549×	`fma-def_binary64`
512×	`div-sub_binary64`
496×	`associate-/r/_binary64`
386×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	28	32
2	43	28
3	65	28
4	95	28
5	165	28
6	292	28
7	557	28
8	1111	28
9	1847	28
10	3014	28
11	5206	28
12	6169	28
13	6347	28
14	6447	28
15	6447	28
16	7947	28
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

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

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify83.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1478×	`fma-neg_binary64`
995×	`div-sub_binary64`
845×	`associate-/l/_binary64`
519×	`fma-def_binary64`
403×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	18	16
2	28	14
3	41	14
4	60	14
5	96	14
6	172	14
7	254	14
8	492	14
9	1053	14
10	1774	14
11	3750	14
12	6240	14
13	6804	14
14	6970	14
15	7000	14
16	7006	14
17	7006	14
18	7629	14
19	7741	14
20	7741	14

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 23 to 16 computations (30.4% saved)

prune1.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

Counts

3 → 2

Alt Table

Click to see full alt table

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

Compiler

Compiled 25 to 18 computations (28% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 -1 (fma.f64 x -1/2 (/.f64 -1 y)))
	0.0b	(fma.f64 x -1/2 (/.f64 -1 y))
✓	0.0b	(fma.f64 x -1/2 (/.f64 -1 y))
✓	0.1b	(/.f64 -1 (fma.f64 x -1/2 (/.f64 -1 y)))

Compiler

Compiled 33 to 23 computations (30.3% saved)

series7.0ms (0.2%)

Counts

2 → 48

Calls

12 calls:

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

rewrite68.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

777×	`pow1_binary64`
714×	`add-log-exp_binary64`
714×	`log1p-expm1-u_binary64`
714×	`expm1-log1p-u_binary64`
700×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	166	19
2	1941	19

Stop Event

1×	node limit

Counts

2 → 42

Calls

Call 1

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

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

Outputs

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

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

simplify70.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-def_binary64`
679×	`fma-neg_binary64`
647×	`cancel-sign-sub-inv_binary64`
523×	`distribute-neg-frac_binary64`
414×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	750
1	143	706
2	428	702
3	1725	690
4	5269	690

Stop Event

1×	node limit

Counts

90 → 60

Calls

Call 1

Inputs
y
(+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x)))
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x))))
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (+.f64 (.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))) (.f64 -1/2 (.f64 (pow.f64 y 2) x)))))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
y
(+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x)))
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x))))
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (+.f64 (.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))) (.f64 -1/2 (.f64 (pow.f64 y 2) x)))))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(/.f64 -1 y)
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(*.f64 -1/2 x)
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(*.f64 -1/2 x)
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(/.f64 -1 y)
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(*.f64 -1/2 x)
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(*.f64 -1/2 x)
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))

Outputs
y
(+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x)))
(+.f64 y (.f64 -1/2 (.f64 (*.f64 y y) x)))
(fma.f64 -1/2 (.f64 y (.f64 y x)) y)
(fma.f64 x (.f64 y (.f64 y -1/2)) y)
(fma.f64 y (.f64 -1/2 (.f64 y x)) y)
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (+.f64 y (.f64 -1/2 (.f64 (*.f64 y y) x))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (fma.f64 -1/2 (.f64 y (.f64 y x)) y))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (fma.f64 x (.f64 y (.f64 y -1/2)) y))
(fma.f64 x (fma.f64 y (.f64 y -1/2) (.f64 x (*.f64 1/4 (pow.f64 y 3)))) y)
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (+.f64 (.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))) (.f64 -1/2 (.f64 (pow.f64 y 2) x)))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (+.f64 y (fma.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3)) (.f64 -1/2 (.f64 (.f64 y y) x)))))
(+.f64 (fma.f64 -1/2 (.f64 y (.f64 y x)) (.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3)))) (fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) y))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (fma.f64 (pow.f64 y 4) (.f64 -1/8 (pow.f64 x 3)) (fma.f64 x (.f64 y (*.f64 y -1/2)) y)))
(fma.f64 x (fma.f64 y (.f64 y -1/2) (.f64 x (.f64 1/4 (pow.f64 y 3)))) (fma.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3)) y))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (/.f64 2 x) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (*.f64 x x)))
(-.f64 (/.f64 2 x) (/.f64 (/.f64 4 (*.f64 x x)) y))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (-.f64 (/.f64 2 x) (/.f64 4 (.f64 y (.f64 x x)))))
(+.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (*.f64 x x))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 (/.f64 8 (.f64 y y)) (pow.f64 x 3)) (/.f64 -4 (.f64 y (*.f64 x x)))))
(+.f64 (/.f64 (/.f64 8 (.f64 y y)) (pow.f64 x 3)) (-.f64 (/.f64 2 x) (/.f64 (/.f64 4 (.f64 x x)) y)))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(-.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (+.f64 (/.f64 4 (.f64 y (.f64 x x))) (/.f64 16 (*.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (+.f64 (/.f64 4 (.f64 y (.f64 x x))) (/.f64 16 (*.f64 (pow.f64 y 3) (pow.f64 x 4))))))
(-.f64 (+.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (.f64 x x)))) (/.f64 16 (.f64 (pow.f64 y 3) (pow.f64 x 4))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 (/.f64 8 (.f64 y y)) (pow.f64 x 3)) (-.f64 (/.f64 (/.f64 -16 (pow.f64 y 3)) (pow.f64 x 4)) (/.f64 (/.f64 4 (.f64 x x)) y))))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (/.f64 2 x) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (*.f64 x x)))
(-.f64 (/.f64 2 x) (/.f64 (/.f64 4 (*.f64 x x)) y))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (-.f64 (/.f64 2 x) (/.f64 4 (.f64 y (.f64 x x)))))
(+.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (*.f64 x x))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 (/.f64 8 (.f64 y y)) (pow.f64 x 3)) (/.f64 -4 (.f64 y (*.f64 x x)))))
(+.f64 (/.f64 (/.f64 8 (.f64 y y)) (pow.f64 x 3)) (-.f64 (/.f64 2 x) (/.f64 (/.f64 4 (.f64 x x)) y)))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(-.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (+.f64 (/.f64 4 (.f64 y (.f64 x x))) (/.f64 16 (*.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (+.f64 (/.f64 4 (.f64 y (.f64 x x))) (/.f64 16 (*.f64 (pow.f64 y 3) (pow.f64 x 4))))))
(-.f64 (+.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (.f64 x x)))) (/.f64 16 (.f64 (pow.f64 y 3) (pow.f64 x 4))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 (/.f64 8 (.f64 y y)) (pow.f64 x 3)) (-.f64 (/.f64 (/.f64 -16 (pow.f64 y 3)) (pow.f64 x 4)) (/.f64 (/.f64 4 (.f64 x x)) y))))
y
(+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x)))
(+.f64 y (.f64 -1/2 (.f64 (*.f64 y y) x)))
(fma.f64 -1/2 (.f64 y (.f64 y x)) y)
(fma.f64 x (.f64 y (.f64 y -1/2)) y)
(fma.f64 y (.f64 -1/2 (.f64 y x)) y)
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (+.f64 y (.f64 -1/2 (.f64 (*.f64 y y) x))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (fma.f64 -1/2 (.f64 y (.f64 y x)) y))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (fma.f64 x (.f64 y (.f64 y -1/2)) y))
(fma.f64 x (fma.f64 y (.f64 y -1/2) (.f64 x (*.f64 1/4 (pow.f64 y 3)))) y)
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (+.f64 (.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))) (.f64 -1/2 (.f64 (pow.f64 y 2) x)))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (+.f64 y (fma.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3)) (.f64 -1/2 (.f64 (.f64 y y) x)))))
(+.f64 (fma.f64 -1/2 (.f64 y (.f64 y x)) (.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3)))) (fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) y))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (fma.f64 (pow.f64 y 4) (.f64 -1/8 (pow.f64 x 3)) (fma.f64 x (.f64 y (*.f64 y -1/2)) y)))
(fma.f64 x (fma.f64 y (.f64 y -1/2) (.f64 x (.f64 1/4 (pow.f64 y 3)))) (fma.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3)) y))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (/.f64 2 x) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (*.f64 x x)))
(-.f64 (/.f64 2 x) (/.f64 (/.f64 4 (*.f64 x x)) y))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (-.f64 (/.f64 2 x) (/.f64 4 (.f64 y (.f64 x x)))))
(+.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (*.f64 x x))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 (/.f64 8 (.f64 y y)) (pow.f64 x 3)) (/.f64 -4 (.f64 y (*.f64 x x)))))
(+.f64 (/.f64 (/.f64 8 (.f64 y y)) (pow.f64 x 3)) (-.f64 (/.f64 2 x) (/.f64 (/.f64 4 (.f64 x x)) y)))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(-.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (+.f64 (/.f64 4 (.f64 y (.f64 x x))) (/.f64 16 (*.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (+.f64 (/.f64 4 (.f64 y (.f64 x x))) (/.f64 16 (*.f64 (pow.f64 y 3) (pow.f64 x 4))))))
(-.f64 (+.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (.f64 x x)))) (/.f64 16 (.f64 (pow.f64 y 3) (pow.f64 x 4))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 (/.f64 8 (.f64 y y)) (pow.f64 x 3)) (-.f64 (/.f64 (/.f64 -16 (pow.f64 y 3)) (pow.f64 x 4)) (/.f64 (/.f64 4 (.f64 x x)) y))))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (/.f64 2 x) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (*.f64 x x)))
(-.f64 (/.f64 2 x) (/.f64 (/.f64 4 (*.f64 x x)) y))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (-.f64 (/.f64 2 x) (/.f64 4 (.f64 y (.f64 x x)))))
(+.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (*.f64 x x))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 (/.f64 8 (.f64 y y)) (pow.f64 x 3)) (/.f64 -4 (.f64 y (*.f64 x x)))))
(+.f64 (/.f64 (/.f64 8 (.f64 y y)) (pow.f64 x 3)) (-.f64 (/.f64 2 x) (/.f64 (/.f64 4 (.f64 x x)) y)))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(-.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (+.f64 (/.f64 4 (.f64 y (.f64 x x))) (/.f64 16 (*.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (+.f64 (/.f64 4 (.f64 y (.f64 x x))) (/.f64 16 (*.f64 (pow.f64 y 3) (pow.f64 x 4))))))
(-.f64 (+.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (.f64 x x)))) (/.f64 16 (.f64 (pow.f64 y 3) (pow.f64 x 4))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 (/.f64 8 (.f64 y y)) (pow.f64 x 3)) (-.f64 (/.f64 (/.f64 -16 (pow.f64 y 3)) (pow.f64 x 4)) (/.f64 (/.f64 4 (.f64 x x)) y))))
(/.f64 -1 y)
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(fma.f64 -1/2 x (/.f64 -1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(fma.f64 -1/2 x (/.f64 -1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(fma.f64 -1/2 x (/.f64 -1 y))
(*.f64 -1/2 x)
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(fma.f64 -1/2 x (/.f64 -1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(fma.f64 -1/2 x (/.f64 -1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(fma.f64 -1/2 x (/.f64 -1 y))
(*.f64 -1/2 x)
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(fma.f64 -1/2 x (/.f64 -1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(fma.f64 -1/2 x (/.f64 -1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(fma.f64 -1/2 x (/.f64 -1 y))
(/.f64 -1 y)
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(fma.f64 -1/2 x (/.f64 -1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(fma.f64 -1/2 x (/.f64 -1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(fma.f64 -1/2 x (/.f64 -1 y))
(*.f64 -1/2 x)
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(fma.f64 -1/2 x (/.f64 -1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(fma.f64 -1/2 x (/.f64 -1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(fma.f64 -1/2 x (/.f64 -1 y))
(*.f64 -1/2 x)
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(fma.f64 -1/2 x (/.f64 -1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(fma.f64 -1/2 x (/.f64 -1 y))
(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
(fma.f64 -1/2 x (/.f64 -1 y))

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 41 to 22 computations (46.3% saved)

series6.0ms (0.2%)

Counts

2 → 48

Calls

12 calls:

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

rewrite171.0ms (5.4%)

Algorithm

1×	batch-egg-rewrite

Rules

460×	`log-prod_binary64`
347×	`exp-prod_binary64`
283×	`pow-prod-down_binary64`
265×	`prod-diff_binary64`
245×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	198	18
2	2644	18

Stop Event

1×	node limit

Counts

2 → 104

Calls

Call 1

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

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

Outputs

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

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

simplify56.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

782×	`fma-def_binary64`
675×	`fma-neg_binary64`
643×	`cancel-sign-sub-inv_binary64`
528×	`distribute-neg-frac_binary64`
414×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	714
1	142	706
2	429	702
3	1713	690
4	5233	690

Stop Event

1×	node limit

Counts

152 → 118

Calls

Call 1

Inputs
y
(+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x)))
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x))))
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (+.f64 (.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))) (.f64 -1/2 (.f64 (pow.f64 y 2) x)))))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
y
(+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x)))
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x))))
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (+.f64 (.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))) (.f64 -1/2 (.f64 (pow.f64 y 2) x)))))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))

Outputs
y
(+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x)))
(+.f64 y (.f64 -1/2 (.f64 (*.f64 y y) x)))
(fma.f64 -1/2 (.f64 y (.f64 y x)) y)
(fma.f64 x (.f64 y (.f64 y -1/2)) y)
(fma.f64 (.f64 y y) (.f64 -1/2 x) y)
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (+.f64 y (.f64 -1/2 (.f64 (*.f64 y y) x))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (fma.f64 -1/2 (.f64 y (.f64 y x)) y))
(fma.f64 -1/2 (.f64 y (.f64 y x)) (fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) y))
(fma.f64 x (fma.f64 y (.f64 y -1/2) (.f64 x (*.f64 1/4 (pow.f64 y 3)))) y)
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (+.f64 (.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))) (.f64 -1/2 (.f64 (pow.f64 y 2) x)))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (+.f64 y (fma.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3)) (.f64 -1/2 (.f64 (.f64 y y) x)))))
(+.f64 (fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (fma.f64 -1/2 (.f64 y (.f64 y x)) y)) (.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (fma.f64 (pow.f64 y 4) (.f64 -1/8 (pow.f64 x 3)) (fma.f64 x (.f64 y (*.f64 y -1/2)) y)))
(fma.f64 x (fma.f64 y (.f64 y -1/2) (.f64 x (.f64 1/4 (pow.f64 y 3)))) (fma.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3)) y))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (/.f64 2 x) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (*.f64 x x)))
(-.f64 (/.f64 2 x) (/.f64 (/.f64 (/.f64 4 x) x) y))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(+.f64 (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3))) (-.f64 (/.f64 2 x) (/.f64 4 (.f64 y (.f64 x x)))))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (/.f64 4 (.f64 y (.f64 x x)))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (/.f64 (/.f64 -4 y) (*.f64 x x))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 (/.f64 8 (pow.f64 x 3)) (.f64 y y)) (/.f64 -4 (.f64 y (*.f64 x x)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(-.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (+.f64 (/.f64 4 (.f64 y (.f64 x x))) (/.f64 16 (*.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(+.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (-.f64 (/.f64 2 x) (+.f64 (/.f64 4 (.f64 y (.f64 x x))) (/.f64 16 (*.f64 (pow.f64 y 3) (pow.f64 x 4))))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3))))) (-.f64 (/.f64 (/.f64 -4 y) (.f64 x x)) (/.f64 16 (.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 (/.f64 8 (pow.f64 x 3)) (.f64 y y)) (+.f64 (/.f64 -4 (.f64 y (*.f64 x x))) (/.f64 (/.f64 -16 (pow.f64 x 4)) (pow.f64 y 3)))))
(+.f64 (/.f64 (/.f64 8 (pow.f64 x 3)) (*.f64 y y)) (-.f64 (/.f64 2 x) (-.f64 (/.f64 (/.f64 (/.f64 4 x) x) y) (/.f64 (/.f64 -16 (pow.f64 x 4)) (pow.f64 y 3)))))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (/.f64 2 x) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (*.f64 x x)))
(-.f64 (/.f64 2 x) (/.f64 (/.f64 (/.f64 4 x) x) y))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(+.f64 (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3))) (-.f64 (/.f64 2 x) (/.f64 4 (.f64 y (.f64 x x)))))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (/.f64 4 (.f64 y (.f64 x x)))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (/.f64 (/.f64 -4 y) (*.f64 x x))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 (/.f64 8 (pow.f64 x 3)) (.f64 y y)) (/.f64 -4 (.f64 y (*.f64 x x)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(-.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (+.f64 (/.f64 4 (.f64 y (.f64 x x))) (/.f64 16 (*.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(+.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (-.f64 (/.f64 2 x) (+.f64 (/.f64 4 (.f64 y (.f64 x x))) (/.f64 16 (*.f64 (pow.f64 y 3) (pow.f64 x 4))))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3))))) (-.f64 (/.f64 (/.f64 -4 y) (.f64 x x)) (/.f64 16 (.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 (/.f64 8 (pow.f64 x 3)) (.f64 y y)) (+.f64 (/.f64 -4 (.f64 y (*.f64 x x))) (/.f64 (/.f64 -16 (pow.f64 x 4)) (pow.f64 y 3)))))
(+.f64 (/.f64 (/.f64 8 (pow.f64 x 3)) (*.f64 y y)) (-.f64 (/.f64 2 x) (-.f64 (/.f64 (/.f64 (/.f64 4 x) x) y) (/.f64 (/.f64 -16 (pow.f64 x 4)) (pow.f64 y 3)))))
y
(+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x)))
(+.f64 y (.f64 -1/2 (.f64 (*.f64 y y) x)))
(fma.f64 -1/2 (.f64 y (.f64 y x)) y)
(fma.f64 x (.f64 y (.f64 y -1/2)) y)
(fma.f64 (.f64 y y) (.f64 -1/2 x) y)
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (+.f64 y (.f64 -1/2 (.f64 (*.f64 y y) x))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (fma.f64 -1/2 (.f64 y (.f64 y x)) y))
(fma.f64 -1/2 (.f64 y (.f64 y x)) (fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) y))
(fma.f64 x (fma.f64 y (.f64 y -1/2) (.f64 x (*.f64 1/4 (pow.f64 y 3)))) y)
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (+.f64 (.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))) (.f64 -1/2 (.f64 (pow.f64 y 2) x)))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (+.f64 y (fma.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3)) (.f64 -1/2 (.f64 (.f64 y y) x)))))
(+.f64 (fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (fma.f64 -1/2 (.f64 y (.f64 y x)) y)) (.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (fma.f64 (pow.f64 y 4) (.f64 -1/8 (pow.f64 x 3)) (fma.f64 x (.f64 y (*.f64 y -1/2)) y)))
(fma.f64 x (fma.f64 y (.f64 y -1/2) (.f64 x (.f64 1/4 (pow.f64 y 3)))) (fma.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3)) y))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (/.f64 2 x) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (*.f64 x x)))
(-.f64 (/.f64 2 x) (/.f64 (/.f64 (/.f64 4 x) x) y))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(+.f64 (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3))) (-.f64 (/.f64 2 x) (/.f64 4 (.f64 y (.f64 x x)))))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (/.f64 4 (.f64 y (.f64 x x)))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (/.f64 (/.f64 -4 y) (*.f64 x x))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 (/.f64 8 (pow.f64 x 3)) (.f64 y y)) (/.f64 -4 (.f64 y (*.f64 x x)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(-.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (+.f64 (/.f64 4 (.f64 y (.f64 x x))) (/.f64 16 (*.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(+.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (-.f64 (/.f64 2 x) (+.f64 (/.f64 4 (.f64 y (.f64 x x))) (/.f64 16 (*.f64 (pow.f64 y 3) (pow.f64 x 4))))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3))))) (-.f64 (/.f64 (/.f64 -4 y) (.f64 x x)) (/.f64 16 (.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 (/.f64 8 (pow.f64 x 3)) (.f64 y y)) (+.f64 (/.f64 -4 (.f64 y (*.f64 x x))) (/.f64 (/.f64 -16 (pow.f64 x 4)) (pow.f64 y 3)))))
(+.f64 (/.f64 (/.f64 8 (pow.f64 x 3)) (*.f64 y y)) (-.f64 (/.f64 2 x) (-.f64 (/.f64 (/.f64 (/.f64 4 x) x) y) (/.f64 (/.f64 -16 (pow.f64 x 4)) (pow.f64 y 3)))))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (/.f64 2 x) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (*.f64 x x)))
(-.f64 (/.f64 2 x) (/.f64 (/.f64 (/.f64 4 x) x) y))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(+.f64 (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3))) (-.f64 (/.f64 2 x) (/.f64 4 (.f64 y (.f64 x x)))))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (/.f64 4 (.f64 y (.f64 x x)))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (/.f64 (/.f64 -4 y) (*.f64 x x))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 (/.f64 8 (pow.f64 x 3)) (.f64 y y)) (/.f64 -4 (.f64 y (*.f64 x x)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(-.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (+.f64 (/.f64 4 (.f64 y (.f64 x x))) (/.f64 16 (*.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(+.f64 (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3)))) (-.f64 (/.f64 2 x) (+.f64 (/.f64 4 (.f64 y (.f64 x x))) (/.f64 16 (*.f64 (pow.f64 y 3) (pow.f64 x 4))))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 y (.f64 y (pow.f64 x 3))))) (-.f64 (/.f64 (/.f64 -4 y) (.f64 x x)) (/.f64 16 (.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 (/.f64 8 (pow.f64 x 3)) (.f64 y y)) (+.f64 (/.f64 -4 (.f64 y (*.f64 x x))) (/.f64 (/.f64 -16 (pow.f64 x 4)) (pow.f64 y 3)))))
(+.f64 (/.f64 (/.f64 8 (pow.f64 x 3)) (*.f64 y y)) (-.f64 (/.f64 2 x) (-.f64 (/.f64 (/.f64 (/.f64 4 x) x) y) (/.f64 (/.f64 -16 (pow.f64 x 4)) (pow.f64 y 3)))))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 1/2 y) x)
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 1/2 y) x)
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 1/2 y) x)
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 1/2 y) x)
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 1/2 y) x)
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 1/2 y) x)
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 1/2 y) x)
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 1/2 y) x)
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 1/2 y) x)
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 1/2 y) x)
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 1/2 y) x)
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 1/2 y) x)
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 1/2 y) x)
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 1/2 y) x)
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 1/2 y) x)
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 1/2 y) x)
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 1/2 y) x)
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 1/2 y) x)
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 1/2 y) x)
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 1/2 y) x)
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 1/2 y) x)
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 1/2 y) x)
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 1/2 y) x)
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 1/2 y) x)
(.f64 y (.f64 x 1/2))
(.f64 x (.f64 y 1/2))

eval203.0ms (6.4%)

Compiler: Compiled 2907 to 2026 computations (30.3% saved)

prune33.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	175	3	178
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	176	4	180

Error

Counts

180 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
▶	14.6b	(-.f64 x y)
▶	25.0b	(-.f64 x (/.f64 2 x))
▶	0.0b	(-.f64 x (/.f64 -1 (-.f64 (*.f64 -1/2 x) (/.f64 1 y))))

Compiler

Compiled 38 to 27 computations (28.9% saved)

localize130.0ms (4.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 -1 (-.f64 (*.f64 -1/2 x) (/.f64 1 y)))
	0.0b	(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
✓	0.0b	(-.f64 (*.f64 -1/2 x) (/.f64 1 y))
✓	0.1b	(/.f64 -1 (-.f64 (*.f64 -1/2 x) (/.f64 1 y)))

Compiler

Compiled 40 to 29 computations (27.5% saved)

series5.0ms (0.2%)

Counts

2 → 30

Calls

12 calls:

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

rewrite89.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

609×	`prod-diff_binary64`
450×	`log-prod_binary64`
350×	`exp-prod_binary64`
262×	`pow2_binary64`
249×	`pow-prod-down_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	211	19
2	2636	19

Stop Event

1×	node limit

Counts

2 → 166

Calls

Call 1

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

Outputs

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

simplify96.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

782×	`fma-def_binary64`
675×	`fma-neg_binary64`
643×	`cancel-sign-sub-inv_binary64`
527×	`distribute-neg-frac_binary64`
414×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	570
1	139	562
2	419	558
3	1715	546
4	5230	546

Stop Event

1×	node limit

Counts

196 → 182

Calls

Call 1

Inputs
y
(+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x)))
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x))))
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (+.f64 (.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))) (.f64 -1/2 (.f64 (pow.f64 y 2) x)))))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
y
(+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x)))
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x))))
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (+.f64 (.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))) (.f64 -1/2 (.f64 (pow.f64 y 2) x)))))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(/.f64 -1 y)
(*.f64 -1/2 x)
(*.f64 -1/2 x)
(/.f64 -1 y)
(*.f64 -1/2 x)
(*.f64 -1/2 x)

Outputs
y
(+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x)))
(+.f64 y (.f64 -1/2 (.f64 (*.f64 y y) x)))
(fma.f64 -1/2 (.f64 (.f64 y y) x) y)
(fma.f64 -1/2 (.f64 y (.f64 y x)) y)
(fma.f64 (.f64 y y) (.f64 -1/2 x) y)
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (+.f64 y (.f64 -1/2 (.f64 (*.f64 y y) x))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (fma.f64 -1/2 (.f64 (.f64 y y) x) y))
(fma.f64 -1/2 (.f64 y (.f64 y x)) (fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) y))
(fma.f64 x (fma.f64 y (.f64 y -1/2) (.f64 x (*.f64 1/4 (pow.f64 y 3)))) y)
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (+.f64 (.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))) (.f64 -1/2 (.f64 (pow.f64 y 2) x)))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (+.f64 y (fma.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3)) (.f64 -1/2 (.f64 (.f64 y y) x)))))
(+.f64 (fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (fma.f64 -1/2 (.f64 (.f64 y y) x) y)) (.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (fma.f64 -1/2 (.f64 y (.f64 y x)) (fma.f64 -1/8 (*.f64 (pow.f64 y 4) (pow.f64 x 3)) y)))
(fma.f64 x (fma.f64 y (.f64 y -1/2) (.f64 x (.f64 1/4 (pow.f64 y 3)))) (fma.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3)) y))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (/.f64 2 x) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (*.f64 x x)))
(+.f64 (/.f64 2 x) (/.f64 -4 (.f64 y (.f64 x x))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3))) (/.f64 4 (.f64 y (.f64 x x)))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3))) (/.f64 (/.f64 -4 y) (*.f64 x x))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 (/.f64 8 (pow.f64 x 3)) (.f64 y y))) (/.f64 -4 (.f64 y (*.f64 x x))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(+.f64 (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3))) (-.f64 (/.f64 2 x) (+.f64 (/.f64 4 (.f64 y (.f64 x x))) (/.f64 16 (*.f64 (pow.f64 y 3) (pow.f64 x 4))))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (-.f64 (/.f64 (/.f64 -4 y) (.f64 x x)) (/.f64 16 (.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 (/.f64 8 (pow.f64 x 3)) (.f64 y y))) (+.f64 (/.f64 -4 (.f64 y (.f64 x x))) (/.f64 -16 (.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (/.f64 2 x) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (*.f64 x x)))
(+.f64 (/.f64 2 x) (/.f64 -4 (.f64 y (.f64 x x))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3))) (/.f64 4 (.f64 y (.f64 x x)))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3))) (/.f64 (/.f64 -4 y) (*.f64 x x))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 (/.f64 8 (pow.f64 x 3)) (.f64 y y))) (/.f64 -4 (.f64 y (*.f64 x x))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(+.f64 (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3))) (-.f64 (/.f64 2 x) (+.f64 (/.f64 4 (.f64 y (.f64 x x))) (/.f64 16 (*.f64 (pow.f64 y 3) (pow.f64 x 4))))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (-.f64 (/.f64 (/.f64 -4 y) (.f64 x x)) (/.f64 16 (.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 (/.f64 8 (pow.f64 x 3)) (.f64 y y))) (+.f64 (/.f64 -4 (.f64 y (.f64 x x))) (/.f64 -16 (.f64 (pow.f64 y 3) (pow.f64 x 4)))))
y
(+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x)))
(+.f64 y (.f64 -1/2 (.f64 (*.f64 y y) x)))
(fma.f64 -1/2 (.f64 (.f64 y y) x) y)
(fma.f64 -1/2 (.f64 y (.f64 y x)) y)
(fma.f64 (.f64 y y) (.f64 -1/2 x) y)
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (.f64 -1/2 (.f64 (pow.f64 y 2) x))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (+.f64 y (.f64 -1/2 (.f64 (*.f64 y y) x))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (fma.f64 -1/2 (.f64 (.f64 y y) x) y))
(fma.f64 -1/2 (.f64 y (.f64 y x)) (fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) y))
(fma.f64 x (fma.f64 y (.f64 y -1/2) (.f64 x (*.f64 1/4 (pow.f64 y 3)))) y)
(+.f64 (.f64 1/4 (.f64 (pow.f64 y 3) (pow.f64 x 2))) (+.f64 y (+.f64 (.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))) (.f64 -1/2 (.f64 (pow.f64 y 2) x)))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (+.f64 y (fma.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3)) (.f64 -1/2 (.f64 (.f64 y y) x)))))
(+.f64 (fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (fma.f64 -1/2 (.f64 (.f64 y y) x) y)) (.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3))))
(fma.f64 1/4 (.f64 (pow.f64 y 3) (.f64 x x)) (fma.f64 -1/2 (.f64 y (.f64 y x)) (fma.f64 -1/8 (*.f64 (pow.f64 y 4) (pow.f64 x 3)) y)))
(fma.f64 x (fma.f64 y (.f64 y -1/2) (.f64 x (.f64 1/4 (pow.f64 y 3)))) (fma.f64 -1/8 (.f64 (pow.f64 y 4) (pow.f64 x 3)) y))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (/.f64 2 x) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (*.f64 x x)))
(+.f64 (/.f64 2 x) (/.f64 -4 (.f64 y (.f64 x x))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3))) (/.f64 4 (.f64 y (.f64 x x)))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3))) (/.f64 (/.f64 -4 y) (*.f64 x x))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 (/.f64 8 (pow.f64 x 3)) (.f64 y y))) (/.f64 -4 (.f64 y (*.f64 x x))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(+.f64 (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3))) (-.f64 (/.f64 2 x) (+.f64 (/.f64 4 (.f64 y (.f64 x x))) (/.f64 16 (*.f64 (pow.f64 y 3) (pow.f64 x 4))))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (-.f64 (/.f64 (/.f64 -4 y) (.f64 x x)) (/.f64 16 (.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 (/.f64 8 (pow.f64 x 3)) (.f64 y y))) (+.f64 (/.f64 -4 (.f64 y (.f64 x x))) (/.f64 -16 (.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(/.f64 2 x)
(-.f64 (.f64 2 (/.f64 1 x)) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (/.f64 2 x) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (/.f64 (/.f64 -4 y) (*.f64 x x)))
(+.f64 (/.f64 2 x) (/.f64 -4 (.f64 y (.f64 x x))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2)))))
(-.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (/.f64 4 (.f64 y (.f64 x x))))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3))) (/.f64 4 (.f64 y (.f64 x x)))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3))) (/.f64 (/.f64 -4 y) (*.f64 x x))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 (/.f64 8 (pow.f64 x 3)) (.f64 y y))) (/.f64 -4 (.f64 y (*.f64 x x))))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (.f64 (pow.f64 y 2) (pow.f64 x 3)))) (.f64 2 (/.f64 1 x))) (+.f64 (.f64 16 (/.f64 1 (.f64 (pow.f64 y 3) (pow.f64 x 4)))) (.f64 4 (/.f64 1 (*.f64 y (pow.f64 x 2))))))
(+.f64 (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3))) (-.f64 (/.f64 2 x) (+.f64 (/.f64 4 (.f64 y (.f64 x x))) (/.f64 16 (*.f64 (pow.f64 y 3) (pow.f64 x 4))))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 8 (.f64 (.f64 y y) (pow.f64 x 3)))) (-.f64 (/.f64 (/.f64 -4 y) (.f64 x x)) (/.f64 16 (.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(+.f64 (+.f64 (/.f64 2 x) (/.f64 (/.f64 8 (pow.f64 x 3)) (.f64 y y))) (+.f64 (/.f64 -4 (.f64 y (.f64 x x))) (/.f64 -16 (.f64 (pow.f64 y 3) (pow.f64 x 4)))))
(/.f64 -1 y)
(*.f64 -1/2 x)
(*.f64 -1/2 x)
(/.f64 -1 y)
(*.f64 -1/2 x)
(*.f64 -1/2 x)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 12 to 8 computations (33.3% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite66.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

668×	`pow1_binary64`
629×	`add-log-exp_binary64`
628×	`log1p-expm1-u_binary64`
628×	`expm1-log1p-u_binary64`
617×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	119	7
2	1680	7

Stop Event

1×	node limit

Counts

1 → 36

Calls

Call 1

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

Outputs

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

simplify20.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

66×	`fma-neg_binary64`
65×	`fma-def_binary64`
30×	`associate-/r*_binary64`
26×	`cancel-sign-sub-inv_binary64`
23×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	69
1	19	69
2	30	69
3	47	69
4	63	69
5	88	69
6	135	69
7	187	69
8	243	69
9	326	69
10	462	69
11	487	69
12	505	69

Stop Event

1×

saturated

Counts

48 → 39

Calls

Call 1

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

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

localize3.0ms (0.1%)

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

eval113.0ms (3.6%)

Compiler: Compiled 4243 to 3032 computations (28.5% saved)

prune45.0ms (1.4%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	219	2	221
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	219	6	225

Error

Counts

225 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	57.1b	(/.f64 -2 x)
✓	14.6b	(-.f64 x y)
✓	0.0b	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
	24.0b	x
✓	25.0b	(-.f64 x (/.f64 2 x))
✓	0.0b	(-.f64 x (/.f64 -1 (-.f64 (*.f64 -1/2 x) (/.f64 1 y))))

Compiler

Compiled 46 to 33 computations (28.3% 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)

prune124.0ms (3.9%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	4	4
Total	6	6

Error

Counts

6 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	57.1b	(/.f64 -2 x)
✓	14.6b	(-.f64 x y)
✓	0.0b	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
	24.0b	x
✓	25.0b	(-.f64 x (/.f64 2 x))
✓	0.0b	(-.f64 x (/.f64 -1 (-.f64 (*.f64 -1/2 x) (/.f64 1 y))))

Compiler

Compiled 46 to 33 computations (28.3% saved)

eval0.0ms (0%)

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

prune3.0ms (0.1%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	5	5
Total	6	6

Error

Counts

6 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	57.1b	(/.f64 -2 x)
✓	14.6b	(-.f64 x y)
✓	0.0b	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
	24.0b	x
✓	25.0b	(-.f64 x (/.f64 2 x))
✓	0.0b	(-.f64 x (/.f64 -1 (-.f64 (*.f64 -1/2 x) (/.f64 1 y))))

Compiler

Compiled 46 to 33 computations (28.3% saved)

regimes19.0ms (0.6%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

7.0ms	y
5.0ms	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
5.0ms	x

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`y`
0.0b	1	`(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))`

Compiler

Compiled 55 to 36 computations (34.5% saved)

regimes12.0ms (0.4%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	x
4.0ms	y

Results

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

Compiler

Compiled 31 to 20 computations (35.5% saved)

regimes37.0ms (1.2%)

Counts

4 → 3

Calls

Call 1

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

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

Calls

2 calls:

25.0ms	x
10.0ms	y

Results

Error	Segments	Branch
6.5b	3	`x`
6.2b	3	`y`

Compiler

Compiled 20 to 12 computations (40% saved)

bsearch111.0ms (3.5%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
21.0ms	3.0641046635522495e+180	9.52972057665123e+188
90.0ms	-7.745885359542814e+110	-6.592358200700884e+109

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes41.0ms (1.3%)

Accuracy

Total -56.3b remaining (-831.7%)

Threshold costs -56.3b (-831.7%)

Counts

3 → 3

Calls

Call 1

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

Outputs
x
(-.f64 x y)
x

Calls

2 calls:

10.0ms	x
8.0ms	y

Results

Error	Segments	Branch
6.8b	3	`x`
11.2b	2	`y`

Compiler

Compiled 15 to 9 computations (40% saved)

bsearch82.0ms (2.6%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
61.0ms	9.356096739143766e-18	8.575298000149808e-17
21.0ms	-29.310736809011996	-1.0681707529120498e-5

Compiler

Compiled 18 to 13 computations (27.8% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	81
1	48	81
2	71	81
3	81	81
4	86	81

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
(-.f64 x (/.f64 -1 (-.f64 (*.f64 -1/2 x) (/.f64 1 y))))
(if (<=.f64 y -774588535954281385205370372632015327213058025448713697172543494535012923679124629398869758820858431605284274176) (-.f64 x (/.f64 2 x)) (if (<=.f64 y 3064104663552249450531346332927901268999518447583000512662013843714473735431855832979102875526831343124332993315637970515149356268999887780765250530949994569856313349264116398686208) (-.f64 x y) (-.f64 x (/.f64 2 x))))
(if (<=.f64 x -8250238960688819/281474976710656) x (if (<=.f64 x 6072453963350515/649037107316853453566312041152512) (-.f64 x y) x))
x

Outputs
(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
(-.f64 x (/.f64 -1 (-.f64 (*.f64 -1/2 x) (/.f64 1 y))))
(-.f64 x (/.f64 -1 (-.f64 (*.f64 x -1/2) (/.f64 1 y))))
(+.f64 x (/.f64 1 (+.f64 (*.f64 x -1/2) (/.f64 -1 y))))
(if (<=.f64 y -774588535954281385205370372632015327213058025448713697172543494535012923679124629398869758820858431605284274176) (-.f64 x (/.f64 2 x)) (if (<=.f64 y 3064104663552249450531346332927901268999518447583000512662013843714473735431855832979102875526831343124332993315637970515149356268999887780765250530949994569856313349264116398686208) (-.f64 x y) (-.f64 x (/.f64 2 x))))
(if (<=.f64 y -774588535954281385205370372632015327213058025448713697172543494535012923679124629398869758820858431605284274176) (+.f64 x (/.f64 -2 x)) (if (<=.f64 y 3064104663552249450531346332927901268999518447583000512662013843714473735431855832979102875526831343124332993315637970515149356268999887780765250530949994569856313349264116398686208) (-.f64 x y) (+.f64 x (/.f64 -2 x))))
(if (<=.f64 x -8250238960688819/281474976710656) x (if (<=.f64 x 6072453963350515/649037107316853453566312041152512) (-.f64 x y) x))
x

end49.0ms (1.6%)

Stop Event

1×

fuel

Compiler

Compiled 126 to 81 computations (35.7% saved)

Iter	Nodes	Cost
0	9	69
1	19	69
2	30	69
3	47	69
4	63	69
5	88	69
6	135	69
7	187	69
8	243	69
9	326	69
10	462	69
11	487	69
12	505	69

Iter	Nodes	Cost
0	9	69
1	19	69
2	30	69
3	47	69
4	63	69
5	88	69
6	135	69
7	187	69
8	243	69
9	326	69
10	462	69
11	487	69
12	505	69

Details

analyze103.0ms (3.3%)

sample1.2s (37%)

preprocess86.0ms (2.7%)

simplify83.0ms (2.6%)

eval1.0ms (0%)

prune1.0ms (0%)

localize15.0ms (0.5%)

series7.0ms (0.2%)

rewrite68.0ms (2.2%)

simplify70.0ms (2.2%)

localize16.0ms (0.5%)

series6.0ms (0.2%)

rewrite171.0ms (5.4%)

simplify56.0ms (1.8%)

eval203.0ms (6.4%)

prune33.0ms (1%)

localize130.0ms (4.1%)

series5.0ms (0.2%)

rewrite89.0ms (2.8%)

simplify96.0ms (3.1%)

localize6.0ms (0.2%)

series2.0ms (0.1%)

rewrite66.0ms (2.1%)

simplify20.0ms (0.6%)

localize3.0ms (0.1%)

eval113.0ms (3.6%)

prune45.0ms (1.4%)

localize3.0ms (0.1%)

eval0.0ms (0%)

prune124.0ms (3.9%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes19.0ms (0.6%)

regimes12.0ms (0.4%)

regimes37.0ms (1.2%)

bsearch111.0ms (3.5%)

regimes41.0ms (1.3%)

bsearch82.0ms (2.6%)

simplify5.0ms (0.2%)

end49.0ms (1.6%)

Profiling

Iter	Nodes	Cost
0	9	69
1	19	69
2	30	69
3	47	69
4	63	69
5	88	69
6	135	69
7	187	69
8	243	69
9	326	69
10	462	69
11	487	69
12	505	69