Details

analyze95.0ms (4.9%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
25%	25%	74.9%	0.1%	0%	0%	0%	5
28.6%	25%	62.4%	0.1%	12.5%	0%	0%	6
42.9%	37.5%	50%	0.1%	12.5%	0%	0%	7
55.6%	46.8%	37.5%	0.1%	15.6%	0%	0%	8
63.6%	53.1%	30.4%	0.1%	16.4%	0%	0%	9
73.9%	58.5%	20.7%	0.1%	20.7%	0%	0%	10
79.3%	62%	16.2%	0.1%	21.7%	0%	0%	11
85.7%	65%	10.8%	0.1%	24.1%	0%	0%	12

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample984.0ms (50.9%)

Results

932.0ms	8256×	body	256	valid
41.0ms	489×	body	256	infinite

Bogosity

preprocess57.0ms (2.9%)

Algorithm

2×	egg-herbie

Rules

513×	`fma-def_binary64`
355×	`fma-neg_binary64`
106×	`distribute-rgt-in_binary64`
92×	`cancel-sign-sub-inv_binary64`
84×	`unsub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	33	20
2	71	20
3	161	20
4	312	20
5	524	20
6	1006	20
7	1445	20
8	1896	20
9	2046	20
10	2048	20
11	2048	20
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

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

Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify54.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

388×	`fma-def_binary64`
286×	`fma-neg_binary64`
70×	`distribute-rgt-in_binary64`
68×	`cancel-sign-sub-inv_binary64`
67×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	18	10
2	43	10
3	102	10
4	207	10
5	294	10
6	501	10
7	871	10
8	1254	10
9	1451	10
10	1501	10

Stop Event

1×

saturated

Counts

1 → 3

Calls

Call 1

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

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

eval21.0ms (1.1%)

Compiler: Compiled 25 to 14 computations (44% saved)

prune1.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	1	2	3
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	3	4

Error

0.0b

Counts

4 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(.f64 (.f64 2 x) (-.f64 x y))
▶	0.0b	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))

Compiler

Compiled 20 to 13 computations (35% saved)

localize8.0ms (0.4%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 27 to 8 computations (70.4% saved)

series3.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

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

rewrite46.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

781×	`pow1_binary64`
729×	`add-log-exp_binary64`
729×	`log1p-expm1-u_binary64`
729×	`expm1-log1p-u_binary64`
713×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	143	7
2	2052	7

Stop Event

1×	node limit

Counts

1 → 51

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x x) (.f64 y (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x x) (.f64 (.f64 y (neg.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x x) (+.f64 (.f64 y (neg.f64 x)) (fma.f64 (neg.f64 y) x (.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 x) y (.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (-.f64 x y)) (fma.f64 (.f64 y (neg.f64 x)) 1 (.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 (cbrt.f64 (.f64 x y))) (pow.f64 (cbrt.f64 (.f64 x y)) 2) (.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 (sqrt.f64 (.f64 x y))) (sqrt.f64 (.f64 x y)) (.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (-.f64 x y)) (.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (-.f64 x y)) (+.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) (.f64 x (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 y (neg.f64 x)) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 x (-.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x (-.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 x (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 x (-.f64 x y))) (pow.f64 (cbrt.f64 (.f64 x (-.f64 x y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 x (-.f64 x y))) 2) (cbrt.f64 (.f64 x (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 x (-.f64 x y))) (sqrt.f64 (.f64 x (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 x y) 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (.f64 (.f64 x y) (.f64 x (+.f64 x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 x y) 2)) (/.f64 1 (.f64 x (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 x y) x)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 x (sqrt.f64 (.f64 x y))) (-.f64 x (sqrt.f64 (.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (.f64 (.f64 x y) (.f64 x (+.f64 x y)))) (-.f64 (pow.f64 x 6) (pow.f64 (.f64 x y) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (.f64 x (+.f64 x y)) (-.f64 (pow.f64 x 4) (pow.f64 (.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 x y) 3)) (+.f64 (pow.f64 x 4) (.f64 (.f64 x y) (.f64 x (+.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 x y) 2)) (.f64 x (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 x y) 3))) (neg.f64 (+.f64 (pow.f64 x 4) (.f64 (.f64 x y) (.f64 x (+.f64 x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 x y) 2))) (neg.f64 (.f64 x (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 (.f64 y (neg.f64 x)) 3)) (+.f64 (pow.f64 x 4) (-.f64 (.f64 (.f64 y (neg.f64 x)) (.f64 y (neg.f64 x))) (.f64 (.f64 x x) (.f64 y (neg.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 x (-.f64 x y)) 3) (pow.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) 3)) (+.f64 (pow.f64 (.f64 x (-.f64 x y)) 2) (-.f64 (.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y))) (.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (.f64 (.f64 y (neg.f64 x)) (.f64 y (neg.f64 x)))) (-.f64 (.f64 x x) (.f64 y (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (.f64 x (-.f64 x y)) 2) (.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y)))) (-.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x (-.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 x (-.f64 x y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 x (-.f64 x y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 x (-.f64 x y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 x (-.f64 x y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 x (-.f64 x y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 x (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 x (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 x (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (.f64 y (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (-.f64 x y) (fma.f64 (neg.f64 y) x (.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x x) (.f64 y (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (.f64 x (-.f64 x y))) 2) (cbrt.f64 (.f64 x (-.f64 x y))) (fma.f64 (neg.f64 y) x (.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (.f64 y (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 x (-.f64 x y))) (sqrt.f64 (.f64 x (-.f64 x y))) (fma.f64 (neg.f64 y) x (.f64 x y)))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (*.f64 y (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (*.f64 (*.f64 y (neg.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (+.f64 (*.f64 y (neg.f64 x)) (fma.f64 (neg.f64 y) x (*.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (-.f64 x y)) (fma.f64 (neg.f64 x) y (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (-.f64 x y)) (fma.f64 (*.f64 y (neg.f64 x)) 1 (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (-.f64 x y)) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 x y))) (pow.f64 (cbrt.f64 (*.f64 x y)) 2) (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (-.f64 x y)) (fma.f64 (neg.f64 (sqrt.f64 (*.f64 x y))) (sqrt.f64 (*.f64 x y)) (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (-.f64 x y)) (*.f64 (fma.f64 (neg.f64 y) x (*.f64 x y)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (-.f64 x y)) (+.f64 (fma.f64 (neg.f64 y) x (*.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (neg.f64 y) x (*.f64 x y)) (*.f64 x (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 y (neg.f64 x)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (-.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (-.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (-.f64 x y))) (pow.f64 (cbrt.f64 (*.f64 x (-.f64 x y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x (-.f64 x y))) 2) (cbrt.f64 (*.f64 x (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (-.f64 x y))) (sqrt.f64 (*.f64 x (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x 6) (pow.f64 (*.f64 x y) 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (*.f64 (*.f64 x y) (*.f64 x (+.f64 x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x 4) (pow.f64 (*.f64 x y) 2)) (/.f64 1 (*.f64 x (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 x y) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (sqrt.f64 (*.f64 x y))) (-.f64 x (sqrt.f64 (*.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (*.f64 (*.f64 x y) (*.f64 x (+.f64 x y)))) (-.f64 (pow.f64 x 6) (pow.f64 (*.f64 x y) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 x (+.f64 x y)) (-.f64 (pow.f64 x 4) (pow.f64 (*.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 6) (pow.f64 (*.f64 x y) 3)) (+.f64 (pow.f64 x 4) (*.f64 (*.f64 x y) (*.f64 x (+.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (pow.f64 (*.f64 x y) 2)) (*.f64 x (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 6) (pow.f64 (*.f64 x y) 3))) (neg.f64 (+.f64 (pow.f64 x 4) (*.f64 (*.f64 x y) (*.f64 x (+.f64 x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 4) (pow.f64 (*.f64 x y) 2))) (neg.f64 (*.f64 x (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 (*.f64 y (neg.f64 x)) 3)) (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (*.f64 y (neg.f64 x)) (*.f64 y (neg.f64 x))) (*.f64 (*.f64 x x) (*.f64 y (neg.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x (-.f64 x y)) 3) (pow.f64 (fma.f64 (neg.f64 y) x (*.f64 x y)) 3)) (+.f64 (pow.f64 (*.f64 x (-.f64 x y)) 2) (-.f64 (*.f64 (fma.f64 (neg.f64 y) x (*.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y))) (*.f64 (*.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (*.f64 (*.f64 y (neg.f64 x)) (*.f64 y (neg.f64 x)))) (-.f64 (*.f64 x x) (*.f64 y (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 x (-.f64 x y)) 2) (*.f64 (fma.f64 (neg.f64 y) x (*.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y)))) (-.f64 (*.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (-.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (-.f64 x y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (-.f64 x y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (-.f64 x y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (-.f64 x y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (-.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (-.f64 x y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (-.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (*.f64 y (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (-.f64 x y) (fma.f64 (neg.f64 y) x (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) (*.f64 y (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x (-.f64 x y))) 2) (cbrt.f64 (*.f64 x (-.f64 x y))) (fma.f64 (neg.f64 y) x (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (*.f64 y (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x (-.f64 x y))) (sqrt.f64 (*.f64 x (-.f64 x y))) (fma.f64 (neg.f64 y) x (*.f64 x y)))))))

simplify40.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

829×	`fma-def_binary64`
784×	`times-frac_binary64`
336×	`associate-/l*_binary64`
284×	`cancel-sign-sub-inv_binary64`
282×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	1045
1	388	815
2	1565	756

Stop Event

1×	node limit

Counts

75 → 70

Calls

Call 1

Inputs
(.f64 -1 (.f64 y x))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(.f64 -1 (.f64 y x))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(.f64 -1 (.f64 y x))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (.f64 x x) (.f64 y (neg.f64 x)))
(+.f64 (.f64 x x) (.f64 (*.f64 y (neg.f64 x)) 1))
(+.f64 (.f64 x x) (+.f64 (.f64 y (neg.f64 x)) (fma.f64 (neg.f64 y) x (*.f64 x y))))
(+.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y)))
(+.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 x) y (.f64 x y)))
(+.f64 (.f64 x (-.f64 x y)) (fma.f64 (.f64 y (neg.f64 x)) 1 (*.f64 x y)))
(+.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 (cbrt.f64 (.f64 x y))) (pow.f64 (cbrt.f64 (.f64 x y)) 2) (.f64 x y)))
(+.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 (sqrt.f64 (.f64 x y))) (sqrt.f64 (.f64 x y)) (.f64 x y)))
(+.f64 (.f64 x (-.f64 x y)) (.f64 (fma.f64 (neg.f64 y) x (*.f64 x y)) 1))
(+.f64 (.f64 x (-.f64 x y)) (+.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y))))
(+.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) (.f64 x (-.f64 x y)))
(+.f64 (.f64 y (neg.f64 x)) (.f64 x x))
(*.f64 x (-.f64 x y))
(.f64 (.f64 x (-.f64 x y)) 1)
(.f64 1 (.f64 x (-.f64 x y)))
(.f64 (cbrt.f64 (.f64 x (-.f64 x y))) (pow.f64 (cbrt.f64 (*.f64 x (-.f64 x y))) 2))
(.f64 (pow.f64 (cbrt.f64 (.f64 x (-.f64 x y))) 2) (cbrt.f64 (*.f64 x (-.f64 x y))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (-.f64 x y)))
(.f64 (sqrt.f64 (.f64 x (-.f64 x y))) (sqrt.f64 (*.f64 x (-.f64 x y))))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 x y)))
(.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 x y) 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (.f64 (.f64 x y) (*.f64 x (+.f64 x y))))))
(.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 x y) 2)) (/.f64 1 (*.f64 x (+.f64 x y))))
(*.f64 (-.f64 x y) x)
(.f64 (+.f64 x (sqrt.f64 (.f64 x y))) (-.f64 x (sqrt.f64 (*.f64 x y))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (.f64 (.f64 x y) (.f64 x (+.f64 x y)))) (-.f64 (pow.f64 x 6) (pow.f64 (.f64 x y) 3))))
(/.f64 1 (/.f64 (.f64 x (+.f64 x y)) (-.f64 (pow.f64 x 4) (pow.f64 (.f64 x y) 2))))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 x y) 3)) (+.f64 (pow.f64 x 4) (.f64 (.f64 x y) (.f64 x (+.f64 x y)))))
(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 x y) 2)) (.f64 x (+.f64 x y)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 x y) 3))) (neg.f64 (+.f64 (pow.f64 x 4) (.f64 (.f64 x y) (.f64 x (+.f64 x y))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 x y) 2))) (neg.f64 (.f64 x (+.f64 x y))))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 (.f64 y (neg.f64 x)) 3)) (+.f64 (pow.f64 x 4) (-.f64 (.f64 (.f64 y (neg.f64 x)) (.f64 y (neg.f64 x))) (.f64 (.f64 x x) (*.f64 y (neg.f64 x))))))
(/.f64 (+.f64 (pow.f64 (.f64 x (-.f64 x y)) 3) (pow.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) 3)) (+.f64 (pow.f64 (.f64 x (-.f64 x y)) 2) (-.f64 (.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y))) (.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y))))))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 (.f64 y (neg.f64 x)) (.f64 y (neg.f64 x)))) (-.f64 (.f64 x x) (*.f64 y (neg.f64 x))))
(/.f64 (-.f64 (pow.f64 (.f64 x (-.f64 x y)) 2) (.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y)))) (-.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y))))
(pow.f64 (*.f64 x (-.f64 x y)) 1)
(pow.f64 (pow.f64 (*.f64 x (-.f64 x y)) 3) 1/3)
(pow.f64 (cbrt.f64 (*.f64 x (-.f64 x y))) 3)
(pow.f64 (sqrt.f64 (*.f64 x (-.f64 x y))) 2)
(sqrt.f64 (pow.f64 (*.f64 x (-.f64 x y)) 2))
(log.f64 (pow.f64 (exp.f64 x) (-.f64 x y)))
(cbrt.f64 (pow.f64 (*.f64 x (-.f64 x y)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (-.f64 x y))))
(log1p.f64 (expm1.f64 (*.f64 x (-.f64 x y))))
(exp.f64 (log.f64 (*.f64 x (-.f64 x y))))
(fma.f64 x x (*.f64 y (neg.f64 x)))
(fma.f64 x (-.f64 x y) (fma.f64 (neg.f64 y) x (*.f64 x y)))
(fma.f64 1 (.f64 x x) (.f64 y (neg.f64 x)))
(fma.f64 1 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y)))
(fma.f64 (pow.f64 (cbrt.f64 (.f64 x (-.f64 x y))) 2) (cbrt.f64 (.f64 x (-.f64 x y))) (fma.f64 (neg.f64 y) x (*.f64 x y)))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (*.f64 y (neg.f64 x)))
(fma.f64 (sqrt.f64 (.f64 x (-.f64 x y))) (sqrt.f64 (.f64 x (-.f64 x y))) (fma.f64 (neg.f64 y) x (*.f64 x y)))

Outputs
(.f64 -1 (.f64 y x))
(*.f64 y (neg.f64 x))
(*.f64 x (neg.f64 y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(.f64 -1 (.f64 y x))
(*.f64 y (neg.f64 x))
(*.f64 x (neg.f64 y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(.f64 -1 (.f64 y x))
(*.f64 y (neg.f64 x))
(*.f64 x (neg.f64 y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(+.f64 (.f64 x x) (.f64 y (neg.f64 x)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(+.f64 (.f64 x x) (.f64 (*.f64 y (neg.f64 x)) 1))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(+.f64 (.f64 x x) (+.f64 (.f64 y (neg.f64 x)) (fma.f64 (neg.f64 y) x (*.f64 x y))))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(+.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(+.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 x) y (.f64 x y)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(+.f64 (.f64 x (-.f64 x y)) (fma.f64 (.f64 y (neg.f64 x)) 1 (*.f64 x y)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(+.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 (cbrt.f64 (.f64 x y))) (pow.f64 (cbrt.f64 (.f64 x y)) 2) (.f64 x y)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(+.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 (sqrt.f64 (.f64 x y))) (sqrt.f64 (.f64 x y)) (.f64 x y)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(+.f64 (.f64 x (-.f64 x y)) (.f64 (fma.f64 (neg.f64 y) x (*.f64 x y)) 1))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(+.f64 (.f64 x (-.f64 x y)) (+.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y))))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(+.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) (.f64 x (-.f64 x y)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(+.f64 (.f64 y (neg.f64 x)) (.f64 x x))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(*.f64 x (-.f64 x y))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(.f64 (.f64 x (-.f64 x y)) 1)
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(.f64 1 (.f64 x (-.f64 x y)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(.f64 (cbrt.f64 (.f64 x (-.f64 x y))) (pow.f64 (cbrt.f64 (*.f64 x (-.f64 x y))) 2))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(.f64 (pow.f64 (cbrt.f64 (.f64 x (-.f64 x y))) 2) (cbrt.f64 (*.f64 x (-.f64 x y))))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (-.f64 x y)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(.f64 (sqrt.f64 (.f64 x (-.f64 x y))) (sqrt.f64 (*.f64 x (-.f64 x y))))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 x y)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 x y) 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (.f64 (.f64 x y) (*.f64 x (+.f64 x y))))))
(/.f64 (.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) 1) (+.f64 (pow.f64 x 4) (.f64 x (.f64 y (*.f64 x (+.f64 y x))))))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) (fma.f64 (.f64 y x) (*.f64 x (+.f64 y x)) (pow.f64 x 4)))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) (fma.f64 y (.f64 x (*.f64 x (+.f64 y x))) (pow.f64 x 4)))
(.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 x y) 2)) (/.f64 1 (*.f64 x (+.f64 x y))))
(.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 y x) 2)) (/.f64 1 (*.f64 x (+.f64 y x))))
(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 y x) 2)) (.f64 x (+.f64 y x)))
(*.f64 (-.f64 x y) x)
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(.f64 (+.f64 x (sqrt.f64 (.f64 x y))) (-.f64 x (sqrt.f64 (*.f64 x y))))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (.f64 (.f64 x y) (.f64 x (+.f64 x y)))) (-.f64 (pow.f64 x 6) (pow.f64 (.f64 x y) 3))))
(/.f64 (.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) 1) (+.f64 (pow.f64 x 4) (.f64 x (.f64 y (*.f64 x (+.f64 y x))))))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) (fma.f64 (.f64 y x) (*.f64 x (+.f64 y x)) (pow.f64 x 4)))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) (fma.f64 y (.f64 x (*.f64 x (+.f64 y x))) (pow.f64 x 4)))
(/.f64 1 (/.f64 (.f64 x (+.f64 x y)) (-.f64 (pow.f64 x 4) (pow.f64 (.f64 x y) 2))))
(.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 y x) 2)) (/.f64 1 (*.f64 x (+.f64 y x))))
(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 y x) 2)) (.f64 x (+.f64 y x)))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 x y) 3)) (+.f64 (pow.f64 x 4) (.f64 (.f64 x y) (.f64 x (+.f64 x y)))))
(/.f64 (.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) 1) (+.f64 (pow.f64 x 4) (.f64 x (.f64 y (*.f64 x (+.f64 y x))))))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) (fma.f64 (.f64 y x) (*.f64 x (+.f64 y x)) (pow.f64 x 4)))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) (fma.f64 y (.f64 x (*.f64 x (+.f64 y x))) (pow.f64 x 4)))
(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 x y) 2)) (.f64 x (+.f64 x y)))
(.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 y x) 2)) (/.f64 1 (*.f64 x (+.f64 y x))))
(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 y x) 2)) (.f64 x (+.f64 y x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 x y) 3))) (neg.f64 (+.f64 (pow.f64 x 4) (.f64 (.f64 x y) (.f64 x (+.f64 x y))))))
(/.f64 (.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) 1) (+.f64 (pow.f64 x 4) (.f64 x (.f64 y (*.f64 x (+.f64 y x))))))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) (fma.f64 (.f64 y x) (*.f64 x (+.f64 y x)) (pow.f64 x 4)))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) (fma.f64 y (.f64 x (*.f64 x (+.f64 y x))) (pow.f64 x 4)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 x y) 2))) (neg.f64 (.f64 x (+.f64 x y))))
(.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 y x) 2)) (/.f64 1 (*.f64 x (+.f64 y x))))
(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 y x) 2)) (.f64 x (+.f64 y x)))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 (.f64 y (neg.f64 x)) 3)) (+.f64 (pow.f64 x 4) (-.f64 (.f64 (.f64 y (neg.f64 x)) (.f64 y (neg.f64 x))) (.f64 (.f64 x x) (*.f64 y (neg.f64 x))))))
(/.f64 (.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) 1) (+.f64 (pow.f64 x 4) (.f64 x (.f64 y (*.f64 x (+.f64 y x))))))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) (fma.f64 (.f64 y x) (*.f64 x (+.f64 y x)) (pow.f64 x 4)))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 (.f64 y x) 3)) (fma.f64 y (.f64 x (*.f64 x (+.f64 y x))) (pow.f64 x 4)))
(/.f64 (+.f64 (pow.f64 (.f64 x (-.f64 x y)) 3) (pow.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) 3)) (+.f64 (pow.f64 (.f64 x (-.f64 x y)) 2) (-.f64 (.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y))) (.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (*.f64 x y))))))
(/.f64 (+.f64 (pow.f64 (.f64 x (-.f64 x y)) 3) (pow.f64 (fma.f64 (neg.f64 x) y (.f64 y x)) 3)) (+.f64 (pow.f64 (.f64 x (-.f64 x y)) 2) (.f64 (fma.f64 (neg.f64 x) y (.f64 y x)) (-.f64 (fma.f64 (neg.f64 x) y (.f64 y x)) (*.f64 x (-.f64 x y))))))
(/.f64 (+.f64 (pow.f64 (.f64 x (-.f64 x y)) 3) (pow.f64 (.f64 0 (.f64 y x)) 3)) (fma.f64 (.f64 0 (.f64 y x)) (-.f64 (.f64 0 (.f64 y x)) (.f64 x (-.f64 x y))) (pow.f64 (*.f64 x (-.f64 x y)) 2)))
(/.f64 (+.f64 0 (pow.f64 (.f64 x (-.f64 x y)) 3)) (pow.f64 (.f64 x (-.f64 x y)) 2))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 (.f64 y (neg.f64 x)) (.f64 y (neg.f64 x)))) (-.f64 (.f64 x x) (*.f64 y (neg.f64 x))))
(.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 y x) 2)) (/.f64 1 (*.f64 x (+.f64 y x))))
(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 y x) 2)) (.f64 x (+.f64 y x)))
(/.f64 (-.f64 (pow.f64 (.f64 x (-.f64 x y)) 2) (.f64 (fma.f64 (neg.f64 y) x (.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y)))) (-.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y))))
(/.f64 (-.f64 (pow.f64 (.f64 x (-.f64 x y)) 2) (.f64 (fma.f64 (neg.f64 x) y (.f64 y x)) (fma.f64 (neg.f64 x) y (.f64 y x)))) (-.f64 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 x) y (.f64 y x))))
(/.f64 (+.f64 (pow.f64 (.f64 x (-.f64 x y)) 2) (.f64 (.f64 0 (.f64 y x)) (.f64 0 (.f64 y x)))) (fma.f64 x (-.f64 x y) (.f64 0 (.f64 y x))))
(/.f64 (pow.f64 (.f64 x (-.f64 x y)) 2) (.f64 x (-.f64 x y)))
(pow.f64 (*.f64 x (-.f64 x y)) 1)
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(pow.f64 (pow.f64 (*.f64 x (-.f64 x y)) 3) 1/3)
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(pow.f64 (cbrt.f64 (*.f64 x (-.f64 x y))) 3)
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(pow.f64 (sqrt.f64 (*.f64 x (-.f64 x y))) 2)
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(sqrt.f64 (pow.f64 (*.f64 x (-.f64 x y)) 2))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(log.f64 (pow.f64 (exp.f64 x) (-.f64 x y)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(cbrt.f64 (pow.f64 (*.f64 x (-.f64 x y)) 3))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(expm1.f64 (log1p.f64 (*.f64 x (-.f64 x y))))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(log1p.f64 (expm1.f64 (*.f64 x (-.f64 x y))))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(exp.f64 (log.f64 (*.f64 x (-.f64 x y))))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(fma.f64 x x (*.f64 y (neg.f64 x)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(fma.f64 x (-.f64 x y) (fma.f64 (neg.f64 y) x (*.f64 x y)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(fma.f64 1 (.f64 x x) (.f64 y (neg.f64 x)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(fma.f64 1 (.f64 x (-.f64 x y)) (fma.f64 (neg.f64 y) x (.f64 x y)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(fma.f64 (pow.f64 (cbrt.f64 (.f64 x (-.f64 x y))) 2) (cbrt.f64 (.f64 x (-.f64 x y))) (fma.f64 (neg.f64 y) x (*.f64 x y)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (*.f64 y (neg.f64 x)))
(-.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (pow.f64 x 4))) (.f64 y x))
(fma.f64 (sqrt.f64 (.f64 x (-.f64 x y))) (sqrt.f64 (.f64 x (-.f64 x y))) (fma.f64 (neg.f64 y) x (*.f64 x y)))
(fma.f64 y (neg.f64 x) (*.f64 x x))
(*.f64 x (-.f64 x y))

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 18 to 9 computations (50% saved)

series4.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

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

rewrite63.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

824×	`pow1_binary64`
767×	`add-log-exp_binary64`
766×	`log1p-expm1-u_binary64`
766×	`expm1-log1p-u_binary64`
751×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	153	10
2	2049	10

Stop Event

1×	node limit

Counts

1 → 19

Calls

Call 1

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

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

Outputs

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

simplify49.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

739×	`log-prod_binary64`
681×	`associate-l_binary64`
654×	`associate-r_binary64`
262×	`fma-neg_binary64`
174×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	68	590
1	199	555
2	712	450
3	4806	450

Stop Event

1×	node limit

Counts

43 → 32

Calls

Call 1

Inputs
(.f64 -2 (.f64 y x))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(*.f64 2 (pow.f64 x 2))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(*.f64 2 (pow.f64 x 2))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(*.f64 2 (pow.f64 x 2))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(.f64 -2 (.f64 y x))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(.f64 -2 (.f64 y x))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(+.f64 (.f64 x (.f64 2 x)) (.f64 (neg.f64 y) (.f64 2 x)))
(+.f64 (.f64 (.f64 2 x) x) (.f64 (.f64 2 x) (neg.f64 y)))
(-.f64 (+.f64 1 (.f64 x (.f64 2 (-.f64 x y)))) 1)
(/.f64 (.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)) (.f64 2 x)) (fma.f64 x x (*.f64 y (+.f64 x y))))
(/.f64 (.f64 (-.f64 (.f64 x x) (.f64 y y)) (.f64 2 x)) (+.f64 x y))
(/.f64 (.f64 (.f64 2 x) (-.f64 (pow.f64 x 3) (pow.f64 y 3))) (fma.f64 x x (*.f64 y (+.f64 x y))))
(/.f64 (.f64 (.f64 2 x) (-.f64 (.f64 x x) (.f64 y y))) (+.f64 x y))
(pow.f64 (.f64 x (.f64 2 (-.f64 x y))) 1)
(pow.f64 (pow.f64 (.f64 x (.f64 2 (-.f64 x y))) 3) 1/3)
(pow.f64 (cbrt.f64 (.f64 x (.f64 2 (-.f64 x y)))) 3)
(pow.f64 (sqrt.f64 (.f64 x (.f64 2 (-.f64 x y)))) 2)
(sqrt.f64 (pow.f64 (.f64 x (.f64 2 (-.f64 x y))) 2))
(log.f64 (pow.f64 (exp.f64 (-.f64 x y)) (*.f64 2 x)))
(cbrt.f64 (pow.f64 (.f64 x (.f64 2 (-.f64 x y))) 3))
(cbrt.f64 (.f64 (pow.f64 (.f64 2 x) 3) (pow.f64 (-.f64 x y) 3)))
(cbrt.f64 (.f64 (pow.f64 (-.f64 x y) 3) (pow.f64 (.f64 2 x) 3)))
(expm1.f64 (log1p.f64 (.f64 x (.f64 2 (-.f64 x y)))))
(log1p.f64 (expm1.f64 (.f64 x (.f64 2 (-.f64 x y)))))
(exp.f64 (log.f64 (.f64 x (.f64 2 (-.f64 x y)))))

Outputs
(.f64 -2 (.f64 y x))
(.f64 x (.f64 -2 y))
(.f64 y (.f64 -2 x))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(*.f64 2 (pow.f64 x 2))
(.f64 x (.f64 x 2))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(*.f64 2 (pow.f64 x 2))
(.f64 x (.f64 x 2))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(*.f64 2 (pow.f64 x 2))
(.f64 x (.f64 x 2))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(.f64 -2 (.f64 y x))
(.f64 x (.f64 -2 y))
(.f64 y (.f64 -2 x))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(.f64 -2 (.f64 y x))
(.f64 x (.f64 -2 y))
(.f64 y (.f64 -2 x))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -2 (*.f64 y x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(+.f64 (.f64 x (.f64 2 x)) (.f64 (neg.f64 y) (.f64 2 x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(+.f64 (.f64 (.f64 2 x) x) (.f64 (.f64 2 x) (neg.f64 y)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(-.f64 (+.f64 1 (.f64 x (.f64 2 (-.f64 x y)))) 1)
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(/.f64 (.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)) (.f64 2 x)) (fma.f64 x x (*.f64 y (+.f64 x y))))
(/.f64 (.f64 x 2) (/.f64 (fma.f64 x x (.f64 y (+.f64 y x))) (-.f64 (pow.f64 x 3) (pow.f64 y 3))))
(.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)) (/.f64 (.f64 x 2) (fma.f64 y (+.f64 y x) (*.f64 x x))))
(.f64 (.f64 x 2) (/.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)) (fma.f64 y (+.f64 y x) (*.f64 x x))))
(/.f64 (.f64 (-.f64 (.f64 x x) (.f64 y y)) (.f64 2 x)) (+.f64 x y))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(/.f64 (.f64 (.f64 2 x) (-.f64 (pow.f64 x 3) (pow.f64 y 3))) (fma.f64 x x (*.f64 y (+.f64 x y))))
(/.f64 (.f64 x 2) (/.f64 (fma.f64 x x (.f64 y (+.f64 y x))) (-.f64 (pow.f64 x 3) (pow.f64 y 3))))
(.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)) (/.f64 (.f64 x 2) (fma.f64 y (+.f64 y x) (*.f64 x x))))
(.f64 (.f64 x 2) (/.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)) (fma.f64 y (+.f64 y x) (*.f64 x x))))
(/.f64 (.f64 (.f64 2 x) (-.f64 (.f64 x x) (.f64 y y))) (+.f64 x y))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(pow.f64 (.f64 x (.f64 2 (-.f64 x y))) 1)
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(pow.f64 (pow.f64 (.f64 x (.f64 2 (-.f64 x y))) 3) 1/3)
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(pow.f64 (cbrt.f64 (.f64 x (.f64 2 (-.f64 x y)))) 3)
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(pow.f64 (sqrt.f64 (.f64 x (.f64 2 (-.f64 x y)))) 2)
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(sqrt.f64 (pow.f64 (.f64 x (.f64 2 (-.f64 x y))) 2))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(log.f64 (pow.f64 (exp.f64 (-.f64 x y)) (*.f64 2 x)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(cbrt.f64 (pow.f64 (.f64 x (.f64 2 (-.f64 x y))) 3))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(cbrt.f64 (.f64 (pow.f64 (.f64 2 x) 3) (pow.f64 (-.f64 x y) 3)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(cbrt.f64 (.f64 (pow.f64 (-.f64 x y) 3) (pow.f64 (.f64 2 x) 3)))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(expm1.f64 (log1p.f64 (.f64 x (.f64 2 (-.f64 x y)))))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(log1p.f64 (expm1.f64 (.f64 x (.f64 2 (-.f64 x y)))))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))
(exp.f64 (log.f64 (.f64 x (.f64 2 (-.f64 x y)))))
(fma.f64 2 (.f64 x x) (.f64 -2 (*.f64 y x)))
(.f64 x (+.f64 (.f64 -2 y) (*.f64 x 2)))
(.f64 x (.f64 2 (-.f64 x y)))
(.f64 2 (.f64 x (-.f64 x y)))

eval25.0ms (1.3%)

Compiler: Compiled 1585 to 667 computations (57.9% saved)

prune26.0ms (1.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	99	3	102
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	99	5	104

Error

Counts

104 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(.f64 (.f64 2 x) (-.f64 x y))
▶	21.4b	(.f64 y (.f64 -2 x))
▶	34.2b	(.f64 x (.f64 x 2))
▶	0.0b	(.f64 2 (fma.f64 y (neg.f64 x) (.f64 x x)))
✓	0.0b	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))

Compiler

Compiled 45 to 30 computations (33.3% saved)

localize8.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y (neg.f64 x) (*.f64 x x))

Compiler

Compiled 26 to 8 computations (69.2% saved)

series2.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite88.0ms (4.6%)

Algorithm

1×	batch-egg-rewrite

Rules

486×	`pow1_binary64`
466×	`add-sqr-sqrt_binary64`
459×	`*-un-lft-identity_binary64`
448×	`add-log-exp_binary64`
447×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	122	8
2	1508	8

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

Inputs
(fma.f64 y (neg.f64 x) (*.f64 x x))

Outputs

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

simplify38.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

461×	`associate-l_binary64`
379×	`associate-r_binary64`
355×	`fma-neg_binary64`
346×	`log-prod_binary64`
319×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	57	430
1	158	370
2	657	330
3	3944	330

Stop Event

1×	node limit

Counts

45 → 37

Calls

Call 1

Inputs
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(.f64 -1 (.f64 y x))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(.f64 -1 (.f64 y x))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(.f64 -1 (.f64 y x))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (.f64 x x) (.f64 y x))
(+.f64 (.f64 y x) (.f64 x x))
(+.f64 (.f64 (.f64 y x) 1) (*.f64 x x))
(-.f64 (+.f64 1 (fma.f64 y x (*.f64 x x))) 1)
(.f64 (fma.f64 y x (.f64 x x)) 1)
(.f64 1 (fma.f64 y x (.f64 x x)))
(.f64 (cbrt.f64 (fma.f64 y x (.f64 x x))) (pow.f64 (cbrt.f64 (fma.f64 y x (*.f64 x x))) 2))
(.f64 (pow.f64 (cbrt.f64 (fma.f64 y x (.f64 x x))) 2) (cbrt.f64 (fma.f64 y x (*.f64 x x))))
(.f64 (sqrt.f64 (fma.f64 y x (.f64 x x))) (sqrt.f64 (fma.f64 y x (*.f64 x x))))
(/.f64 (+.f64 (pow.f64 (.f64 y x) 3) (pow.f64 (.f64 x x) 3)) (+.f64 (.f64 (.f64 y x) (.f64 y x)) (-.f64 (pow.f64 x 4) (.f64 (.f64 y x) (.f64 x x)))))
(/.f64 (-.f64 (.f64 (.f64 y x) (.f64 y x)) (pow.f64 x 4)) (-.f64 (.f64 y x) (*.f64 x x)))
(pow.f64 (fma.f64 y x (*.f64 x x)) 1)
(pow.f64 (pow.f64 (fma.f64 y x (*.f64 x x)) 3) 1/3)
(pow.f64 (cbrt.f64 (fma.f64 y x (*.f64 x x))) 3)
(pow.f64 (sqrt.f64 (fma.f64 y x (*.f64 x x))) 2)
(sqrt.f64 (pow.f64 (fma.f64 y x (*.f64 x x)) 2))
(log.f64 (exp.f64 (fma.f64 y x (*.f64 x x))))
(cbrt.f64 (pow.f64 (fma.f64 y x (*.f64 x x)) 3))
(expm1.f64 (log1p.f64 (fma.f64 y x (*.f64 x x))))
(log1p.f64 (expm1.f64 (fma.f64 y x (*.f64 x x))))
(exp.f64 (log.f64 (fma.f64 y x (*.f64 x x))))

Outputs
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (neg.f64 (.f64 x y)) (.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (neg.f64 (.f64 x y)) (.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (neg.f64 (.f64 x y)) (.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(.f64 -1 (.f64 y x))
(neg.f64 (*.f64 x y))
(*.f64 y (neg.f64 x))
(*.f64 x (neg.f64 y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (neg.f64 (.f64 x y)) (.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (neg.f64 (.f64 x y)) (.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (neg.f64 (.f64 x y)) (.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(.f64 -1 (.f64 y x))
(neg.f64 (*.f64 x y))
(*.f64 y (neg.f64 x))
(*.f64 x (neg.f64 y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (neg.f64 (.f64 x y)) (.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (neg.f64 (.f64 x y)) (.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (neg.f64 (.f64 x y)) (.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(.f64 -1 (.f64 y x))
(neg.f64 (*.f64 x y))
(*.f64 y (neg.f64 x))
(*.f64 x (neg.f64 y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (neg.f64 (.f64 x y)) (.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (neg.f64 (.f64 x y)) (.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (neg.f64 (.f64 x y)) (.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (neg.f64 (.f64 x y)) (.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (neg.f64 (.f64 x y)) (.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (neg.f64 (.f64 x y)) (.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (neg.f64 (.f64 x y)) (.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (neg.f64 (.f64 x y)) (.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(+.f64 (pow.f64 x 2) (.f64 -1 (.f64 y x)))
(+.f64 (neg.f64 (.f64 x y)) (.f64 x x))
(*.f64 x (+.f64 (neg.f64 y) x))
(*.f64 x (-.f64 x y))
(+.f64 (.f64 x x) (.f64 y x))
(*.f64 x (+.f64 y x))
(*.f64 x (+.f64 x y))
(+.f64 (.f64 y x) (.f64 x x))
(*.f64 x (+.f64 y x))
(*.f64 x (+.f64 x y))
(+.f64 (.f64 (.f64 y x) 1) (*.f64 x x))
(*.f64 x (+.f64 y x))
(*.f64 x (+.f64 x y))
(-.f64 (+.f64 1 (fma.f64 y x (*.f64 x x))) 1)
(*.f64 x (+.f64 y x))
(*.f64 x (+.f64 x y))
(.f64 (fma.f64 y x (.f64 x x)) 1)
(*.f64 x (+.f64 y x))
(*.f64 x (+.f64 x y))
(.f64 1 (fma.f64 y x (.f64 x x)))
(*.f64 x (+.f64 y x))
(*.f64 x (+.f64 x y))
(.f64 (cbrt.f64 (fma.f64 y x (.f64 x x))) (pow.f64 (cbrt.f64 (fma.f64 y x (*.f64 x x))) 2))
(*.f64 x (+.f64 y x))
(*.f64 x (+.f64 x y))
(.f64 (pow.f64 (cbrt.f64 (fma.f64 y x (.f64 x x))) 2) (cbrt.f64 (fma.f64 y x (*.f64 x x))))
(*.f64 x (+.f64 y x))
(*.f64 x (+.f64 x y))
(.f64 (sqrt.f64 (fma.f64 y x (.f64 x x))) (sqrt.f64 (fma.f64 y x (*.f64 x x))))
(*.f64 x (+.f64 y x))
(*.f64 x (+.f64 x y))
(/.f64 (+.f64 (pow.f64 (.f64 y x) 3) (pow.f64 (.f64 x x) 3)) (+.f64 (.f64 (.f64 y x) (.f64 y x)) (-.f64 (pow.f64 x 4) (.f64 (.f64 y x) (.f64 x x)))))
(/.f64 (+.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 x x) 3)) (fma.f64 (.f64 x y) (.f64 x y) (-.f64 (pow.f64 x 4) (.f64 y (.f64 x (*.f64 x x))))))
(/.f64 (+.f64 (pow.f64 (.f64 x y) 3) (pow.f64 x 6)) (-.f64 (fma.f64 y (.f64 y (.f64 x x)) (pow.f64 x 4)) (.f64 y (pow.f64 x 3))))
(/.f64 (+.f64 (pow.f64 (.f64 x y) 3) (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (.f64 (.f64 x y) (.f64 x (-.f64 y x)))))
(/.f64 (+.f64 (pow.f64 (.f64 x y) 3) (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (.f64 x (.f64 (.f64 x y) (-.f64 y x)))))
(/.f64 (-.f64 (.f64 (.f64 y x) (.f64 y x)) (pow.f64 x 4)) (-.f64 (.f64 y x) (*.f64 x x)))
(*.f64 x (+.f64 y x))
(*.f64 x (+.f64 x y))
(pow.f64 (fma.f64 y x (*.f64 x x)) 1)
(*.f64 x (+.f64 y x))
(*.f64 x (+.f64 x y))
(pow.f64 (pow.f64 (fma.f64 y x (*.f64 x x)) 3) 1/3)
(*.f64 x (+.f64 y x))
(*.f64 x (+.f64 x y))
(pow.f64 (cbrt.f64 (fma.f64 y x (*.f64 x x))) 3)
(*.f64 x (+.f64 y x))
(*.f64 x (+.f64 x y))
(pow.f64 (sqrt.f64 (fma.f64 y x (*.f64 x x))) 2)
(*.f64 x (+.f64 y x))
(*.f64 x (+.f64 x y))
(sqrt.f64 (pow.f64 (fma.f64 y x (*.f64 x x)) 2))
(*.f64 x (+.f64 y x))
(*.f64 x (+.f64 x y))
(log.f64 (exp.f64 (fma.f64 y x (*.f64 x x))))
(*.f64 x (+.f64 y x))
(*.f64 x (+.f64 x y))
(cbrt.f64 (pow.f64 (fma.f64 y x (*.f64 x x)) 3))
(*.f64 x (+.f64 y x))
(*.f64 x (+.f64 x y))
(expm1.f64 (log1p.f64 (fma.f64 y x (*.f64 x x))))
(*.f64 x (+.f64 y x))
(*.f64 x (+.f64 x y))
(log1p.f64 (expm1.f64 (fma.f64 y x (*.f64 x x))))
(*.f64 x (+.f64 y x))
(*.f64 x (+.f64 x y))
(exp.f64 (log.f64 (fma.f64 y x (*.f64 x x))))
(*.f64 x (+.f64 y x))
(*.f64 x (+.f64 x y))

localize5.0ms (0.2%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

localize10.0ms (0.5%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

eval7.0ms (0.4%)

Compiler: Compiled 473 to 215 computations (54.5% saved)

prune7.0ms (0.4%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	37	0	37
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	37	5	42

Error

Counts

42 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(.f64 (.f64 2 x) (-.f64 x y))
✓	21.4b	(.f64 y (.f64 -2 x))
✓	34.2b	(.f64 x (.f64 x 2))
✓	0.0b	(.f64 2 (fma.f64 y (neg.f64 x) (.f64 x x)))
✓	0.0b	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))

Compiler

Compiled 45 to 30 computations (33.3% saved)

regimes19.0ms (1%)

Counts

5 → 1

Calls

Call 1

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

Outputs
(.f64 2 (fma.f64 y (neg.f64 x) (.f64 x x)))

Calls

4 calls:

5.0ms	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
4.0ms	y
4.0ms	x
4.0ms	(-.f64 (.f64 x x) (.f64 x y))

Results

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

Compiler

Compiled 63 to 37 computations (41.3% saved)

regimes50.0ms (2.6%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

4 calls:

6.0ms	x
4.0ms	y
4.0ms	(-.f64 (.f64 x x) (.f64 x y))
4.0ms	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))

Results

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

Compiler

Compiled 54 to 33 computations (38.9% saved)

regimes10.0ms (0.5%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	x
3.0ms	y

Results

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

Compiler

Compiled 25 to 16 computations (36% saved)

regimes27.0ms (1.4%)

Accuracy

Total -45.4b remaining (-523.8%)

Threshold costs -45.4b (-523.8%)

Counts

2 → 3

Calls

Call 1

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

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

Calls

2 calls:

14.0ms	x
12.0ms	y

Results

Error	Segments	Branch
10.2b	5	`x`
8.7b	3	`y`

Compiler

Compiled 18 to 12 computations (33.3% saved)

bsearch27.0ms (1.4%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
10.0ms	7.259366161858974e-97	3.652481897290837e-96
16.0ms	-8.16804084750239e-58	-8.587333453036596e-65

Results

24.0ms

240×

body

256

valid

Compiler

Compiled 256 to 191 computations (25.4% saved)

simplify5.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	76
1	45	76
2	57	76
3	62	76
4	64	76

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(.f64 2 (fma.f64 y (neg.f64 x) (.f64 x x)))
(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
(.f64 (.f64 2 x) (-.f64 x y))
(if (<=.f64 y -2894802230932905/115792089237316195423570985008687907853269984665640564039457584007913129639936) (.f64 y (.f64 -2 x)) (if (<=.f64 y 4208588308330709/1202453802380202612679414065556140558016349465041059773802132977424491020858679523053413887173001575952350707712) (.f64 x (.f64 x 2)) (.f64 y (.f64 -2 x))))
(.f64 x (.f64 x 2))

Outputs
(.f64 2 (fma.f64 y (neg.f64 x) (.f64 x x)))
(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
(.f64 2 (-.f64 (.f64 x x) (*.f64 y x)))
(.f64 (.f64 2 x) (-.f64 x y))
(if (<=.f64 y -2894802230932905/115792089237316195423570985008687907853269984665640564039457584007913129639936) (.f64 y (.f64 -2 x)) (if (<=.f64 y 4208588308330709/1202453802380202612679414065556140558016349465041059773802132977424491020858679523053413887173001575952350707712) (.f64 x (.f64 x 2)) (.f64 y (.f64 -2 x))))
(if (<=.f64 y -2894802230932905/115792089237316195423570985008687907853269984665640564039457584007913129639936) (.f64 y (.f64 x -2)) (if (<=.f64 y 4208588308330709/1202453802380202612679414065556140558016349465041059773802132977424491020858679523053413887173001575952350707712) (.f64 x (.f64 2 x)) (.f64 y (.f64 x -2))))
(.f64 x (.f64 x 2))
(.f64 x (.f64 2 x))

Compiler

Compiled 63 to 42 computations (33.3% saved)

soundness89.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

829×	`fma-def_binary64`
784×	`times-frac_binary64`
336×	`associate-/l*_binary64`
284×	`cancel-sign-sub-inv_binary64`
282×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	1045
1	388	815
2	1565	756

Stop Event

1×	node limit

Compiler

Compiled 60 to 39 computations (35% saved)

end60.0ms (3.1%)

Compiler: Compiled 55 to 33 computations (40% saved)

Details

analyze95.0ms (4.9%)

sample984.0ms (50.9%)

preprocess57.0ms (2.9%)

simplify54.0ms (2.8%)

eval21.0ms (1.1%)

prune1.0ms (0.1%)

localize8.0ms (0.4%)

series3.0ms (0.2%)

rewrite46.0ms (2.4%)

simplify40.0ms (2.1%)

localize6.0ms (0.3%)

series4.0ms (0.2%)

rewrite63.0ms (3.2%)

simplify49.0ms (2.5%)

eval25.0ms (1.3%)

prune26.0ms (1.4%)

localize8.0ms (0.4%)

series2.0ms (0.1%)

rewrite88.0ms (4.6%)

simplify38.0ms (1.9%)

localize5.0ms (0.2%)

localize10.0ms (0.5%)

eval7.0ms (0.4%)

prune7.0ms (0.4%)

regimes19.0ms (1%)

regimes50.0ms (2.6%)

regimes10.0ms (0.5%)

regimes27.0ms (1.4%)

bsearch27.0ms (1.4%)

simplify5.0ms (0.3%)

soundness89.0ms (4.6%)

end60.0ms (3.1%)

Profiling