Details

analyze62.0ms (1.5%)

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
36.4%	25%	43.7%	0.1%	31.2%	0%	0%	7
50%	31.2%	31.2%	0.1%	37.5%	0%	0%	8
62.5%	39%	23.4%	0.1%	37.5%	0%	0%	9
72.4%	42.9%	16.4%	0.1%	40.6%	0%	0%	10
79.6%	47.2%	12.1%	0.1%	40.6%	0%	0%	11
85.5%	49.4%	8.4%	0.1%	42.1%	0%	0%	12

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.1s (25.8%)

Results

1.1s	8256×	body	256	valid
26.0ms	207×	body	256	infinite

Bogosity

preprocess18.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

26×	`fma-def_binary64`
11×	`+-commutative_binary64`
6×	`associate-+r+_binary64`
6×	`associate-+l+_binary64`
4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	28	22
2	62	22
3	76	22
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

Outputs
(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(fma.f64 x (+.f64 x 2) (*.f64 y y))
(+.f64 (+.f64 (.f64 y 2) (.f64 y y)) (*.f64 x x))
(+.f64 (.f64 x x) (.f64 y (+.f64 2 y)))
(fma.f64 x x (*.f64 y (+.f64 2 y)))

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

14×	`fma-def_binary64`
6×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	17	11
2	34	11
3	42	11

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

Outputs
(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(fma.f64 x (+.f64 x 2) (*.f64 y y))

eval1.0ms (0%)

Compiler: Compiled 21 to 11 computations (47.6% 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

0.0b

Counts

3 → 2

Alt Table

Click to see full alt table

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

Compiler

Compiled 23 to 14 computations (39.1% saved)

localize12.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 32 to 14 computations (56.3% saved)

series4.0ms (0.1%)

Counts

2 → 36

Calls

9 calls:

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

rewrite79.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

577×	`fma-def_binary64`
467×	`log-prod_binary64`
356×	`pow-prod-down_binary64`
280×	`fma-neg_binary64`
262×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	203	18
2	2909	18

Stop Event

1×	node limit

Counts

2 → 167

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 x (+.f64 x 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (.f64 (.f64 x x) 4) (.f64 x (-.f64 2 x))) (/.f64 (pow.f64 x 4) (.f64 x (-.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 x (+.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x (+.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 x (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 x (+.f64 x 2))) (pow.f64 (cbrt.f64 (.f64 x (+.f64 x 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 x (+.f64 x 2))) 2) (cbrt.f64 (.f64 x (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 x (sqrt.f64 (+.f64 x x))) (hypot.f64 x (sqrt.f64 (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (/.f64 1 (-.f64 (fma.f64 (.f64 x x) 4 (pow.f64 x 4)) (.f64 2 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (.f64 (.f64 x x) 4) (pow.f64 x 4)) (/.f64 1 (.f64 x (-.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 x 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (fma.f64 (.f64 x x) 4 (pow.f64 x 4)) (.f64 2 (pow.f64 x 3))) (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (.f64 x (-.f64 2 x)) (-.f64 (.f64 (.f64 x x) 4) (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (-.f64 (fma.f64 (.f64 x x) 4 (pow.f64 x 4)) (.f64 2 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (-.f64 (.f64 (.f64 x x) 4) (.f64 2 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 x x) 4) (pow.f64 x 4)) (.f64 x (-.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6))) (neg.f64 (-.f64 (fma.f64 (.f64 x x) 4 (pow.f64 x 4)) (.f64 2 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) 4) (pow.f64 x 4))) (neg.f64 (.f64 x (-.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (.f64 (.f64 x x) 4)) (fma.f64 x x (neg.f64 (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x (+.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 x (+.f64 x 2)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 x (+.f64 x 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (sqrt.f64 (+.f64 x x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 x (+.f64 x 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (fma.f64 (.f64 x x) 4 (pow.f64 x 4)) (.f64 2 (pow.f64 x 3))) (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (.f64 x (-.f64 2 x)) (-.f64 (.f64 (.f64 x x) 4) (pow.f64 x 4))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 x (+.f64 x 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 x (+.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (+.f64 x x))) (pow.f64 (exp.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (expm1.f64 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (+.f64 x x))) (+.f64 1 (expm1.f64 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 x x))) (pow.f64 (exp.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (pow.f64 (exp.f64 x) x) (+.f64 1 (expm1.f64 (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 x x))) (+.f64 1 (expm1.f64 (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 x (+.f64 x 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 x (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 x (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 x (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 x (+.f64 x 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 x (+.f64 x 2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (hypot.f64 x (sqrt.f64 (+.f64 x x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (.f64 x (+.f64 x 2)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (.f64 x (+.f64 x 2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (.f64 x (+.f64 x 2))) 3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 2 (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 x (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x x) 1 (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x x) 1 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 x x) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x x) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (pow.f64 x 4)) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) 2) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 x x)) (pow.f64 (cbrt.f64 (+.f64 x x)) 2) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2) (cbrt.f64 (+.f64 x x)) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) 2) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 (+.f64 x x)) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 2 (sqrt.f64 x)) (sqrt.f64 x) (*.f64 x x))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (.f64 x (+.f64 x 2)) 2) (-.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) (/.f64 (pow.f64 y 4) (-.f64 (.f64 x (+.f64 x 2)) (.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2))) (pow.f64 (cbrt.f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2))) 2) (cbrt.f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 y (hypot.f64 x (sqrt.f64 (+.f64 x x)))) (hypot.f64 y (hypot.f64 x (sqrt.f64 (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (pow.f64 (.f64 x (+.f64 x 2)) 3) (pow.f64 y 6)) (/.f64 1 (fma.f64 (.f64 y y) (-.f64 (.f64 y y) (.f64 x (+.f64 x 2))) (pow.f64 (.f64 x (+.f64 x 2)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 (.f64 x (+.f64 x 2)) 2) (pow.f64 y 4)) (/.f64 1 (-.f64 (.f64 x (+.f64 x 2)) (.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (.f64 y y) (-.f64 (.f64 y y) (.f64 x (+.f64 x 2))) (pow.f64 (.f64 x (+.f64 x 2)) 2)) (+.f64 (pow.f64 (.f64 x (+.f64 x 2)) 3) (pow.f64 y 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) (-.f64 (pow.f64 (.f64 x (+.f64 x 2)) 2) (pow.f64 y 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 x (+.f64 x 2)) 3) (pow.f64 y 6)) (fma.f64 (.f64 y y) (-.f64 (.f64 y y) (.f64 x (+.f64 x 2))) (pow.f64 (.f64 x (+.f64 x 2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 x (+.f64 x 2)) 3) (pow.f64 y 6)) (+.f64 (pow.f64 y 4) (-.f64 (pow.f64 (.f64 x (+.f64 x 2)) 2) (.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (.f64 x (+.f64 x 2)) 2) (pow.f64 y 4)) (-.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (.f64 x (+.f64 x 2)) 3) (pow.f64 y 6))) (neg.f64 (fma.f64 (.f64 y y) (-.f64 (.f64 y y) (.f64 x (+.f64 x 2))) (pow.f64 (.f64 x (+.f64 x 2)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (.f64 x (+.f64 x 2)) 2) (pow.f64 y 4))) (neg.f64 (-.f64 (.f64 x (+.f64 x 2)) (.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 (pow.f64 (hypot.f64 x y) 2) 3)) (fma.f64 (.f64 x x) 4 (-.f64 (pow.f64 (pow.f64 (hypot.f64 x y) 2) 2) (.f64 (+.f64 x x) (pow.f64 (hypot.f64 x y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 x x) 4) (pow.f64 (pow.f64 (hypot.f64 x y) 2) 2)) 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(.f64 (+.f64 1 (expm1.f64 (.f64 x (+.f64 x 2)))) (+.f64 1 (expm1.f64 (.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 y y))) (pow.f64 (exp.f64 x) (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (pow.f64 (exp.f64 y) y) (+.f64 1 (expm1.f64 (.f64 x (+.f64 x 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 y y))) (+.f64 1 (expm1.f64 (.f64 x (+.f64 x 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (pow.f64 (hypot.f64 x y) 2)) (pow.f64 (exp.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (pow.f64 (hypot.f64 x y) 2)) (+.f64 1 (expm1.f64 (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (pow.f64 (exp.f64 1) (pow.f64 (hypot.f64 x y) 2)) (+.f64 1 (expm1.f64 (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2)) 3))))) (#(struct:change #<rule 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#<rule egg-rr> (2) ((x fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 2 (.f64 (pow.f64 (hypot.f64 x y) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (+.f64 x 2) (.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 x (.f64 (pow.f64 (hypot.f64 x y) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x x) 1 (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x x) 1 (.f64 (pow.f64 (hypot.f64 x y) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x x) 1 (fma.f64 x 2 (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x (+.f64 x 2)) 1 (.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y y (.f64 x (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 y y) 1 (.f64 x (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 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Outputs

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(hypot.f64 x (sqrt.f64 (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (/.f64 1 (-.f64 (fma.f64 (*.f64 x x) 4 (pow.f64 x 4)) (*.f64 2 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (*.f64 x x) 4) (pow.f64 x 4)) (/.f64 1 (*.f64 x (-.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (fma.f64 (*.f64 x x) 4 (pow.f64 x 4)) (*.f64 2 (pow.f64 x 3))) (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 x (-.f64 2 x)) (-.f64 (*.f64 (*.f64 x x) 4) (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (-.f64 (fma.f64 (*.f64 x x) 4 (pow.f64 x 4)) (*.f64 2 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 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(+.f64 x x)) (pow.f64 (cbrt.f64 (+.f64 x x)) 2) (*.f64 (pow.f64 (hypot.f64 x y) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2) (cbrt.f64 (+.f64 x x)) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2) (cbrt.f64 (+.f64 x x)) (*.f64 (pow.f64 (hypot.f64 x y) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) (fma.f64 x 2 (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (+.f64 x 2)) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 2) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 2) (*.f64 (pow.f64 (hypot.f64 x y) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 x (sqrt.f64 (+.f64 x x))) (hypot.f64 x (sqrt.f64 (+.f64 x x))) (*.f64 y y))))) (#(struct:change #<rule 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(#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 x y) (hypot.f64 x y) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (fma.f64 x 2 (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 y) 5) (cbrt.f64 y) (*.f64 x (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) (fma.f64 x 2 (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 (pow.f64 (hypot.f64 x y) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 2 (sqrt.f64 x)) (sqrt.f64 x) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 2 (sqrt.f64 x)) (sqrt.f64 x) (*.f64 (pow.f64 (hypot.f64 x y) 2) 1))))))

simplify191.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

1204×	`sqr-pow_binary64`
666×	`cube-prod_binary64`
661×	`fabs-mul_binary64`
514×	`pow-sqr_binary64`
511×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	346
1	28	304
2	55	289
3	88	289
4	190	289
5	496	289
6	1665	289
7	2348	289
8	2680	289
9	2940	289
10	3281	289
11	3787	289
12	4446	289
13	5240	289
14	6169	289
15	6690	289
16	7105	289
17	7498	289
18	7623	289
19	7669	289

Stop Event

1×	node limit

Counts

203 → 178

Calls

Call 1

Inputs
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 y 2)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 y 2)
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 y 2)
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))

Outputs
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 x 2))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 x 2))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 x 2))
(*.f64 x (+.f64 2 x))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (+.f64 x 2) (*.f64 y y))

Compiler

Compiled 19 to 9 computations (52.6% saved)

series2.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite56.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

742×	`pow1_binary64`
690×	`add-log-exp_binary64`
689×	`log1p-expm1-u_binary64`
689×	`expm1-log1p-u_binary64`
675×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	150	11
2	1860	11

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

Inputs
(fma.f64 x (+.f64 x 2) (*.f64 y y))

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

Outputs

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

simplify178.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

796×	`sqr-pow_binary64`
666×	`cube-prod_binary64`
663×	`fabs-mul_binary64`
514×	`pow-sqr_binary64`
505×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	262
1	34	214
2	59	214
3	87	214
4	192	214
5	511	214
6	1715	214
7	2370	214
8	2701	214
9	2961	214
10	3300	214
11	3806	214
12	4467	214
13	5261	214
14	6190	214
15	6711	214
16	7124	214
17	7517	214
18	7644	214
19	7690	214

Stop Event

1×	node limit

Counts

45 → 33

Calls

Call 1

Inputs
(pow.f64 y 2)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(*.f64 (+.f64 2 x) x)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))

Outputs
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(*.f64 (+.f64 2 x) x)
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))

eval58.0ms (1.4%)

Compiler: Compiled 3036 to 1583 computations (47.9% saved)

prune34.0ms (0.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	204	7	211
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	205	8	213

Error

Counts

213 → 8

Alt Table

Click to see full alt table

Status	Error	Program
▶	48.3b	(*.f64 x x)
✓	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
▶	33.4b	(*.f64 y y)
	20.3b	(+.f64 (.f64 x x) (.f64 y y))
▶	28.5b	(*.f64 (+.f64 2 x) x)
▶	14.0b	(+.f64 (.f64 2 x) (.f64 y y))
	13.9b	(fma.f64 y y (*.f64 2 x))
▶	0.0b	(+.f64 (.f64 (+.f64 x 2) x) (.f64 y y))

Compiler

Compiled 121 to 76 computations (37.2% saved)

localize22.0ms (0.5%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 25 to 13 computations (48% saved)

series6.0ms (0.1%)

Counts

2 → 36

Calls

9 calls:

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

rewrite81.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

972×	`pow1_binary64`
908×	`add-log-exp_binary64`
907×	`log1p-expm1-u_binary64`
907×	`expm1-log1p-u_binary64`
94×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	180	18
2	2476	18

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

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

Outputs

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

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

simplify182.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

796×	`sqr-pow_binary64`
666×	`cube-prod_binary64`
662×	`fabs-mul_binary64`
514×	`pow-sqr_binary64`
505×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	346
1	34	289
2	59	289
3	87	289
4	191	289
5	516	289
6	1699	289
7	2368	289
8	2699	289
9	2959	289
10	3298	289
11	3802	289
12	4463	289
13	5255	289
14	6186	289
15	6711	289
16	7126	289
17	7521	289
18	7646	289
19	7690	289

Stop Event

1×	node limit

Counts

90 → 67

Calls

Call 1

Inputs
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 y 2)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(*.f64 (+.f64 2 x) x)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))

Outputs
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(*.f64 (+.f64 2 x) x)
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 x (+.f64 2 x) (*.f64 y y))

localize3.0ms (0.1%)

Compiler: Compiled 6 to 3 computations (50% saved)

localize3.0ms (0.1%)

Compiler: Compiled 6 to 3 computations (50% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 2 x) x)

Compiler

Compiled 12 to 8 computations (33.3% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite50.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

583×	`pow1_binary64`
547×	`add-log-exp_binary64`
546×	`log1p-expm1-u_binary64`
546×	`expm1-log1p-u_binary64`
538×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	111	7
2	1433	7

Stop Event

1×	node limit

Counts

1 → 17

Calls

Call 1

Inputs
(*.f64 (+.f64 2 x) x)

Outputs

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

simplify184.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
560×	`cube-prod_binary64`
556×	`fabs-mul_binary64`
523×	`pow-sqr_binary64`
481×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	14	75
2	28	75
3	50	75
4	109	75
5	311	75
6	1042	75
7	2192	75
8	2539	75
9	2731	75
10	2941	75
11	3251	75
12	3660	75
13	4145	75
14	4717	75
15	5413	75
16	6261	75
17	6654	75
18	6942	75
19	7218	75
20	7290	75
21	7326	75

Stop Event

1×	node limit

Counts

29 → 22

Calls

Call 1

Inputs
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))

Outputs
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))

localize14.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 18 to 9 computations (50% saved)

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite80.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

747×	`pow1_binary64`
696×	`add-log-exp_binary64`
695×	`log1p-expm1-u_binary64`
695×	`expm1-log1p-u_binary64`
680×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	150	8
2	1954	8

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 2 x (*.f64 y y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (*.f64 2 x) 2) (-.f64 (*.f64 2 x) (*.f64 y y))) (/.f64 (pow.f64 y 4) (-.f64 (*.f64 2 x) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 2 x (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 2 x (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 2 x (*.f64 y y))) (pow.f64 (cbrt.f64 (fma.f64 2 x (*.f64 y y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 2 x (*.f64 y y))) 2) (cbrt.f64 (fma.f64 2 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 y (sqrt.f64 (*.f64 2 x))) (hypot.f64 y (sqrt.f64 (*.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 y 6)) (/.f64 1 (+.f64 (pow.f64 (*.f64 2 x) 2) (-.f64 (pow.f64 y 4) (*.f64 2 (*.f64 x (*.f64 y y)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (*.f64 2 x) 2) (pow.f64 y 4)) (/.f64 1 (-.f64 (*.f64 2 x) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (*.f64 2 x) 2) (-.f64 (pow.f64 y 4) (*.f64 2 (*.f64 x (*.f64 y y))))) (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 y 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (*.f64 2 x) (*.f64 y y)) (-.f64 (pow.f64 (*.f64 2 x) 2) (pow.f64 y 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 y 6)) (+.f64 (pow.f64 (*.f64 2 x) 2) (-.f64 (pow.f64 y 4) (*.f64 2 (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 y 6)) (+.f64 (pow.f64 y 4) (-.f64 (pow.f64 (*.f64 2 x) 2) (*.f64 2 (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 2 x) 2) (pow.f64 y 4)) (-.f64 (*.f64 2 x) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 y 6))) (neg.f64 (+.f64 (pow.f64 (*.f64 2 x) 2) (-.f64 (pow.f64 y 4) (*.f64 2 (*.f64 x (*.f64 y y)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 2 x) 2) (pow.f64 y 4))) (neg.f64 (-.f64 (*.f64 2 x) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 y 4) (pow.f64 (*.f64 2 x) 2)) (-.f64 (*.f64 y y) (*.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 2 x (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 2 x (*.f64 y y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 2 x (*.f64 y y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 y (sqrt.f64 (*.f64 2 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 2 x (*.f64 y y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 2 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 2 x (*.f64 y y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 2 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 2 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 2 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 x (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 2 (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y y (*.f64 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 2 x) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 y y) (*.f64 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 y 4)) (pow.f64 (cbrt.f64 y) 2) (*.f64 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 2 x)) 2) (cbrt.f64 (*.f64 2 x)) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 (*.f64 2 x)) (*.f64 y y))))))

simplify196.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

1366×	`sqr-pow_binary64`
695×	`pow-sqr_binary64`
617×	`cube-prod_binary64`
611×	`fabs-mul_binary64`
434×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	168
1	15	168
2	25	168
3	36	168
4	65	168
5	167	168
6	587	168
7	1453	168
8	1637	168
9	1821	168
10	2029	168
11	2324	168
12	2717	168
13	3202	168
14	3768	168
15	4456	168
16	5297	168
17	5691	168
18	5979	168
19	6255	168
20	6329	168
21	6363	168
22	7304	168

Stop Event

1×	node limit

Counts

59 → 39

Calls

Call 1

Inputs
(pow.f64 y 2)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(pow.f64 y 2)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(pow.f64 y 2)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (pow.f64 y 2))

Outputs
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))

eval68.0ms (1.6%)

Compiler: Compiled 1615 to 963 computations (40.4% saved)

prune41.0ms (1%)

Pruning

9 alts after pruning (4 fresh and 5 done)

	Pruned	Kept	Total
New	124	4	128
Fresh	2	0	2
Picked	0	1	1
Done	1	4	5
Total	127	9	136

Error

Counts

136 → 9

Alt Table

Click to see full alt table

Status	Error	Program
✓	33.4b	(*.f64 y y)
▶	20.3b	(+.f64 (.f64 x x) (.f64 y y))
▶	42.6b	(*.f64 2 x)
▶	13.9b	(fma.f64 y y (*.f64 2 x))
✓	28.5b	(*.f64 (+.f64 2 x) x)
✓	48.3b	(*.f64 x x)
✓	14.0b	(+.f64 (.f64 2 x) (.f64 y y))
▶	28.5b	(+.f64 (.f64 x x) (.f64 2 x))
✓	0.0b	(+.f64 (.f64 (+.f64 x 2) x) (.f64 y y))

Compiler

Compiled 68 to 44 computations (35.3% saved)

localize7.0ms (0.2%)

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

localize16.0ms (0.4%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 17 to 9 computations (47.1% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite73.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

683×	`pow1_binary64`
641×	`add-log-exp_binary64`
640×	`log1p-expm1-u_binary64`
640×	`expm1-log1p-u_binary64`
627×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	133	7
2	1793	7

Stop Event

1×	node limit

Counts

1 → 39

Calls

Call 1

Inputs
(+.f64 (.f64 x x) (.f64 2 x))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (+.f64 x 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x 4) (*.f64 x (-.f64 x 2))) (/.f64 (*.f64 (*.f64 x x) 4) (*.f64 x (-.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (+.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (+.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 2) (cbrt.f64 (*.f64 x (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x x)) (*.f64 (cbrt.f64 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 x (sqrt.f64 (*.f64 x 2))) (hypot.f64 x (sqrt.f64 (*.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 6) (*.f64 (pow.f64 x 3) 8)) (/.f64 1 (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 (pow.f64 x 3) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x 4) (*.f64 (*.f64 x x) 4)) (/.f64 1 (*.f64 x (-.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 (pow.f64 x 3) 2))) (+.f64 (pow.f64 x 6) (*.f64 (pow.f64 x 3) 8))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 x (-.f64 x 2)) (-.f64 (pow.f64 x 4) (*.f64 (*.f64 x x) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (*.f64 (pow.f64 x 3) 8)) (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 (pow.f64 x 3) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (*.f64 (pow.f64 x 3) 8)) (+.f64 (*.f64 (*.f64 x x) 4) (-.f64 (pow.f64 x 4) (*.f64 (pow.f64 x 3) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (*.f64 (*.f64 x x) 4)) (*.f64 x (-.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 6) (*.f64 (pow.f64 x 3) 8))) (neg.f64 (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (*.f64 x x) 4) (*.f64 (pow.f64 x 3) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 4) (*.f64 (*.f64 x x) 4))) (neg.f64 (*.f64 x (-.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x x) 4) (pow.f64 x 4)) (-.f64 (*.f64 x 2) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (+.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (sqrt.f64 (*.f64 x 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (*.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 2 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 x (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) (*.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x 2) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (*.f64 x x)) (*.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x 2)) 2) (cbrt.f64 (*.f64 x 2)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 2)) (sqrt.f64 (*.f64 x 2)) (*.f64 x x))))))

simplify180.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
560×	`cube-prod_binary64`
556×	`fabs-mul_binary64`
523×	`pow-sqr_binary64`
481×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	14	75
2	28	75
3	50	75
4	109	75
5	311	75
6	1042	75
7	2192	75
8	2539	75
9	2731	75
10	2941	75
11	3251	75
12	3660	75
13	4145	75
14	4717	75
15	5413	75
16	6261	75
17	6654	75
18	6942	75
19	7218	75
20	7290	75
21	7326	75

Stop Event

1×	node limit

Counts

51 → 44

Calls

Call 1

Inputs
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))

Outputs
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 17 to 5 computations (70.6% saved)

series2.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite58.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

650×	`pow1_binary64`
606×	`add-log-exp_binary64`
606×	`log1p-expm1-u_binary64`
606×	`expm1-log1p-u_binary64`
589×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	129	7
2	1751	7

Stop Event

1×	node limit

Counts

1 → 33

Calls

Call 1

Inputs
(+.f64 (.f64 x x) (.f64 y y))

Outputs

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

simplify181.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

1204×	`sqr-pow_binary64`
754×	`cube-prod_binary64`
743×	`fabs-mul_binary64`
514×	`pow-sqr_binary64`
346×	`unpow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	204
1	16	168
2	29	168
3	47	168
4	99	168
5	295	168
6	1113	168
7	1389	168
8	1679	168
9	1930	168
10	2269	168
11	2762	168
12	3421	168
13	4211	168
14	5133	168
15	5654	168
16	6071	168
17	6462	168
18	6583	168
19	6627	168
20	7796	168

Stop Event

1×	node limit

Counts

57 → 38

Calls

Call 1

Inputs
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))

Outputs
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (.f64 y y) (.f64 x x))
(fma.f64 y y (*.f64 x x))

localize12.0ms (0.3%)

Compiler: Compiled 14 to 8 computations (42.9% saved)

eval40.0ms (1%)

Compiler: Compiled 921 to 561 computations (39.1% saved)

prune27.0ms (0.6%)

Pruning

9 alts after pruning (0 fresh and 9 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	0	0
Picked	0	1	1
Done	0	8	8
Total	82	9	91

Error

Counts

91 → 9

Alt Table

Click to see full alt table

Status	Error	Program
✓	33.4b	(*.f64 y y)
✓	20.3b	(+.f64 (.f64 x x) (.f64 y y))
✓	42.6b	(*.f64 2 x)
✓	13.9b	(fma.f64 y y (*.f64 2 x))
✓	28.5b	(*.f64 (+.f64 2 x) x)
✓	48.3b	(*.f64 x x)
✓	14.0b	(+.f64 (.f64 2 x) (.f64 y y))
✓	28.5b	(+.f64 (.f64 x x) (.f64 2 x))
✓	0.0b	(+.f64 (.f64 (+.f64 x 2) x) (.f64 y y))

Compiler

Compiled 68 to 44 computations (35.3% saved)

regimes101.0ms (2.4%)

Counts

13 → 1

Calls

Call 1

Inputs
(*.f64 2 x)
(*.f64 x x)
(*.f64 y y)
(*.f64 (+.f64 2 x) x)
(+.f64 (.f64 x x) (.f64 y y))
(+.f64 (.f64 x x) (.f64 2 x))
(+.f64 (.f64 x x) (.f64 y y))
(+.f64 (.f64 2 x) (.f64 y y))
(+.f64 (.f64 (+.f64 x 2) x) (.f64 y y))
(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(fma.f64 y y (*.f64 2 x))
(fma.f64 x (+.f64 x 2) (*.f64 y y))

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

Calls

6 calls:

18.0ms	(+.f64 (.f64 x 2) (.f64 x x))
17.0ms	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
16.0ms	(+.f64 (.f64 x 2) (.f64 x x))
16.0ms	x
16.0ms	y

Results

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

Compiler

Compiled 126 to 60 computations (52.4% saved)

regimes96.0ms (2.3%)

Counts

8 → 3

Calls

Call 1

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

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

Calls

3 calls:

44.0ms	y
32.0ms	x
15.0ms	(*.f64 y y)

Results

Error	Segments	Branch
1.0b	3	`x`
3.4b	3	`y`
3.4b	2	`(*.f64 y y)`

Compiler

Compiled 55 to 23 computations (58.2% saved)

bsearch62.0ms (1.5%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
25.0ms	0.560253368179771	19726369.203731786
37.0ms	-236919.7790335652	-52.12352284226094

Compiler

Compiled 18 to 12 computations (33.3% saved)

regimes51.0ms (1.2%)

Counts

7 → 3

Calls

Call 1

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

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

Calls

3 calls:

24.0ms	x
14.0ms	y
11.0ms	(*.f64 y y)

Results

Error	Segments	Branch
17.5b	5	`x`
3.4b	3	`y`
3.4b	2	`(*.f64 y y)`

Compiler

Compiled 48 to 20 computations (58.3% saved)

bsearch152.0ms (3.6%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
18.0ms	4.4759096644063214e-73	6.615614923203447e-63
134.0ms	-1.4973113209662152e-83	-7.86529606470995e-84

Compiler

Compiled 18 to 12 computations (33.3% saved)

regimes155.0ms (3.7%)

Counts

4 → 4

Calls

Call 1

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

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

Calls

3 calls:

122.0ms	(*.f64 y y)
21.0ms	x
11.0ms	y

Results

Error	Segments	Branch
19.8b	5	`x`
8.0b	3	`y`
7.6b	4	`(*.f64 y y)`

Compiler

Compiled 27 to 16 computations (40.7% saved)

bsearch51.0ms (1.2%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
17.0ms	1.6788593480545286e-20	2.317010805193136e-19
17.0ms	7.251660243094325e-77	4.085984765152896e-71
17.0ms	2.003376732392591e-145	1.6778939283058932e-144

Compiler

Compiled 18 to 12 computations (33.3% saved)

regimes44.0ms (1%)

Counts

3 → 3

Calls

Call 1

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

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

Calls

3 calls:

24.0ms	x
10.0ms	y
8.0ms	(*.f64 y y)

Results

Error	Segments	Branch
19.5b	7	`x`
16.9b	3	`y`
16.9b	2	`(*.f64 y y)`

Compiler

Compiled 22 to 13 computations (40.9% saved)

bsearch38.0ms (0.9%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
19.0ms	4.4759096644063214e-73	6.615614923203447e-63
19.0ms	-1.4973113209662152e-83	-7.86529606470995e-84

Compiler

Compiled 18 to 12 computations (33.3% saved)

regimes19.0ms (0.4%)

Accuracy

Total -32.1b remaining (-109.2%)

Threshold costs -32.1b (-109.2%)

Counts

2 → 3

Calls

Call 1

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

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

Calls

2 calls:

11.0ms	x
6.0ms	y

Results

Error	Segments	Branch
29.4b	3	`x`
39.2b	2	`y`

Compiler

Compiled 14 to 9 computations (35.7% saved)

bsearch39.0ms (0.9%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
20.0ms	0.560253368179771	19726369.203731786
19.0ms	-52.12352284226094	-0.016199218932530204

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	195
1	50	195

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(+.f64 (.f64 (+.f64 x 2) x) (.f64 y y))
(if (<=.f64 x -1017562702724709/4294967296) (+.f64 (.f64 x x) (.f64 y y)) (if (<=.f64 x 1261578430083741/2251799813685248) (+.f64 (.f64 2 x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))))
(if (<=.f64 y -2046872045005727/136703170298938245273281389194851335334573089430825777276610662900622062449960995201469573563940864) (+.f64 (.f64 x x) (.f64 y y)) (if (<=.f64 y 1780779104144315/3978585891278293137243057985174566720803649206378781739523711815145275976100267004264448) (.f64 (+.f64 2 x) x) (+.f64 (.f64 x x) (*.f64 y y))))
(if (<=.f64 (.f64 y y) 2816568505321219/14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203637047296) (.f64 (+.f64 2 x) x) (if (<=.f64 (.f64 y y) 590875712133505/8148143905337944345073782753637512644205873574663745002544561797417525199053346824733589504) (.f64 y y) (if (<=.f64 (.f64 y y) 5578967116048229/332306998946228968225951765070086144) (.f64 (+.f64 2 x) x) (*.f64 y y))))
(if (<=.f64 y -2046872045005727/136703170298938245273281389194851335334573089430825777276610662900622062449960995201469573563940864) (.f64 y y) (if (<=.f64 y 1780779104144315/3978585891278293137243057985174566720803649206378781739523711815145275976100267004264448) (.f64 2 x) (*.f64 y y)))
(if (<=.f64 x -1833933422262843/35184372088832) (.f64 x x) (if (<=.f64 x 1261578430083741/2251799813685248) (.f64 2 x) (*.f64 x x)))
(*.f64 2 x)

Outputs
(+.f64 (.f64 (+.f64 x 2) x) (.f64 y y))
(+.f64 (.f64 y y) (.f64 x (+.f64 x 2)))
(if (<=.f64 x -1017562702724709/4294967296) (+.f64 (.f64 x x) (.f64 y y)) (if (<=.f64 x 1261578430083741/2251799813685248) (+.f64 (.f64 2 x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))))
(if (<=.f64 x -1017562702724709/4294967296) (+.f64 (.f64 y y) (.f64 x x)) (if (<=.f64 x 1261578430083741/2251799813685248) (+.f64 (.f64 y y) (.f64 x 2)) (+.f64 (.f64 y y) (.f64 x x))))
(if (<=.f64 y -2046872045005727/136703170298938245273281389194851335334573089430825777276610662900622062449960995201469573563940864) (+.f64 (.f64 x x) (.f64 y y)) (if (<=.f64 y 1780779104144315/3978585891278293137243057985174566720803649206378781739523711815145275976100267004264448) (.f64 (+.f64 2 x) x) (+.f64 (.f64 x x) (*.f64 y y))))
(if (<=.f64 y -2046872045005727/136703170298938245273281389194851335334573089430825777276610662900622062449960995201469573563940864) (+.f64 (.f64 y y) (.f64 x x)) (if (<=.f64 y 1780779104144315/3978585891278293137243057985174566720803649206378781739523711815145275976100267004264448) (.f64 x (+.f64 x 2)) (+.f64 (.f64 y y) (*.f64 x x))))
(if (<=.f64 (.f64 y y) 2816568505321219/14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203637047296) (.f64 (+.f64 2 x) x) (if (<=.f64 (.f64 y y) 590875712133505/8148143905337944345073782753637512644205873574663745002544561797417525199053346824733589504) (.f64 y y) (if (<=.f64 (.f64 y y) 5578967116048229/332306998946228968225951765070086144) (.f64 (+.f64 2 x) x) (*.f64 y y))))
(if (<=.f64 (.f64 y y) 2816568505321219/14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203637047296) (.f64 x (+.f64 x 2)) (if (<=.f64 (.f64 y y) 590875712133505/8148143905337944345073782753637512644205873574663745002544561797417525199053346824733589504) (.f64 y y) (if (<=.f64 (.f64 y y) 5578967116048229/332306998946228968225951765070086144) (.f64 x (+.f64 x 2)) (*.f64 y y))))
(if (<=.f64 y -2046872045005727/136703170298938245273281389194851335334573089430825777276610662900622062449960995201469573563940864) (.f64 y y) (if (<=.f64 y 1780779104144315/3978585891278293137243057985174566720803649206378781739523711815145275976100267004264448) (.f64 2 x) (*.f64 y y)))
(if (<=.f64 y -2046872045005727/136703170298938245273281389194851335334573089430825777276610662900622062449960995201469573563940864) (.f64 y y) (if (<=.f64 y 1780779104144315/3978585891278293137243057985174566720803649206378781739523711815145275976100267004264448) (.f64 x 2) (*.f64 y y)))
(if (<=.f64 x -1833933422262843/35184372088832) (.f64 x x) (if (<=.f64 x 1261578430083741/2251799813685248) (.f64 2 x) (*.f64 x x)))
(if (<=.f64 x -1833933422262843/35184372088832) (.f64 x x) (if (<=.f64 x 1261578430083741/2251799813685248) (.f64 x 2) (*.f64 x x)))
(*.f64 2 x)
(*.f64 x 2)

Compiler

Compiled 150 to 79 computations (47.3% saved)

soundness0.0ms (0%)

end59.0ms (1.4%)

Compiler: Compiled 138 to 60 computations (56.5% saved)

Details

analyze62.0ms (1.5%)

sample1.1s (25.8%)

preprocess18.0ms (0.4%)

simplify8.0ms (0.2%)

eval1.0ms (0%)

prune1.0ms (0%)

localize12.0ms (0.3%)

series4.0ms (0.1%)

rewrite79.0ms (1.9%)

simplify191.0ms (4.5%)

localize8.0ms (0.2%)

series2.0ms (0.1%)

rewrite56.0ms (1.3%)

simplify178.0ms (4.2%)

eval58.0ms (1.4%)

prune34.0ms (0.8%)

localize22.0ms (0.5%)

series6.0ms (0.1%)

rewrite81.0ms (1.9%)

simplify182.0ms (4.3%)

localize3.0ms (0.1%)

localize3.0ms (0.1%)

localize5.0ms (0.1%)

series1.0ms (0%)

rewrite50.0ms (1.2%)

simplify184.0ms (4.3%)

localize14.0ms (0.3%)

series3.0ms (0.1%)

rewrite80.0ms (1.9%)

simplify196.0ms (4.6%)

eval68.0ms (1.6%)

prune41.0ms (1%)

localize7.0ms (0.2%)

localize16.0ms (0.4%)

series2.0ms (0%)

rewrite73.0ms (1.7%)

simplify180.0ms (4.3%)

localize7.0ms (0.2%)

series2.0ms (0%)

rewrite58.0ms (1.4%)

simplify181.0ms (4.3%)

localize12.0ms (0.3%)

eval40.0ms (1%)

prune27.0ms (0.6%)

regimes101.0ms (2.4%)

regimes96.0ms (2.3%)

bsearch62.0ms (1.5%)

regimes51.0ms (1.2%)

bsearch152.0ms (3.6%)

regimes155.0ms (3.7%)

bsearch51.0ms (1.2%)

regimes44.0ms (1%)

bsearch38.0ms (0.9%)

regimes19.0ms (0.4%)

bsearch39.0ms (0.9%)

simplify10.0ms (0.2%)

soundness0.0ms (0%)

end59.0ms (1.4%)

Profiling