Details

analyze44.0ms (2.5%)

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
30.8%	25%	56.2%	0.1%	18.7%	0%	0%	6
48%	37.5%	40.6%	0.1%	21.9%	0%	0%	7
60%	46.8%	31.2%	0.1%	21.9%	0%	0%	8
71.4%	54.6%	21.9%	0.1%	23.4%	0%	0%	9
78.6%	60.1%	16.4%	0.1%	23.4%	0%	0%	10
85.1%	64.4%	11.3%	0.1%	24.2%	0%	0%	11
88.9%	67.3%	8.4%	0.1%	24.2%	0%	0%	12

Compiler

Compiled 10 to 6 computations (40% saved)

sample975.0ms (54.4%)

Results

957.0ms	8256×	body	256	valid
8.0ms	106×	body	256	infinite

Bogosity

preprocess10.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

16×	`fma-def`
12×	`+-commutative`
4×	`*-commutative`
4×	`associate-+l+`
4×	`count-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	21	30
2	28	30
3	32	30
4	34	30
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 x) y) y)
(+.f64 (+.f64 (*.f64 y y) x) x)

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify12.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

8×	`fma-def`
6×	`+-commutative`
2×	`*-commutative`
2×	`associate-+l+`
2×	`count-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	17	15
3	19	15
4	20	15

Stop Event

1×

saturated

Counts

1 → 3

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 21 to 9 computations (57.1% 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

Counts

4 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0%	(fma.f64 x x (+.f64 y y))
▶	0.01%	(+.f64 (+.f64 (*.f64 x x) y) y)

Compiler

Compiled 17 to 9 computations (47.1% saved)

localize41.0ms (2.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.01%	(+.f64 (*.f64 x x) y)

Compiler

Compiled 19 to 5 computations (73.7% saved)

series1.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite52.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1408×	`add-sqr-sqrt`
1388×	`*-un-lft-identity`
1300×	`add-cube-cbrt`
1288×	`add-cbrt-cube`
1278×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	131	9
2	1775	9

Stop Event

1×	node limit

Counts

1 → 34

Calls

Call 1

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

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

Outputs

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

simplify62.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

998×	`associate-+r+`
994×	`associate-r`
858×	`associate-l`
714×	`associate-+l+`
494×	`distribute-lft-neg-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	90	940
1	216	890
2	719	890
3	3691	890

Stop Event

1×	node limit

Counts

58 → 43

Calls

Call 1

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

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

localize5.0ms (0.3%)

Compiler: Compiled 13 to 4 computations (69.2% saved)

eval9.0ms (0.5%)

Compiler: Compiled 548 to 241 computations (56% saved)

prune6.0ms (0.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	41	2	43
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	41	4	45

Error

Counts

45 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0%	(fma.f64 x x (+.f64 y y))
✓	0.01%	(+.f64 (+.f64 (*.f64 x x) y) y)
▶	56.88%	(+.f64 (*.f64 x x) y)
▶	29.54%	(+.f64 y y)

Compiler

Compiled 29 to 16 computations (44.8% saved)

localize3.0ms (0.1%)

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

localize8.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.01%	(+.f64 (*.f64 x x) y)

Compiler

Compiled 12 to 4 computations (66.7% saved)

eval7.0ms (0.4%)

Compiler: Compiled 462 to 198 computations (57.1% saved)

prune8.0ms (0.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	40	3	43
Fresh	0	0	0
Picked	0	1	1
Done	1	2	3
Total	41	6	47

Error

Counts

47 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	56.87%	(fma.f64 x x y)
✓	0.01%	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	56.88%	(+.f64 (*.f64 x x) y)
✓	29.54%	(+.f64 y y)
▶	67.41%	(*.f64 x x)
	85.9%	y

Compiler

Compiled 35 to 20 computations (42.9% saved)

localize3.0ms (0.1%)

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

localize3.0ms (0.2%)

Compiler: Compiled 8 to 3 computations (62.5% saved)

eval0.0ms (0%)

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

prune2.0ms (0.1%)

Pruning

6 alts after pruning (1 fresh and 5 done)

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

Error

Counts

6 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	56.87%	(fma.f64 x x y)
✓	0.01%	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	56.88%	(+.f64 (*.f64 x x) y)
✓	29.54%	(+.f64 y y)
✓	67.41%	(*.f64 x x)
	85.9%	y

Compiler

Compiled 35 to 20 computations (42.9% saved)

eval0.0ms (0%)

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

prune2.0ms (0.1%)

Pruning

6 alts after pruning (1 fresh and 5 done)

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

Error

Counts

6 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	56.87%	(fma.f64 x x y)
✓	0.01%	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	56.88%	(+.f64 (*.f64 x x) y)
✓	29.54%	(+.f64 y y)
✓	67.41%	(*.f64 x x)
	85.9%	y

Compiler

Compiled 35 to 20 computations (42.9% saved)

regimes20.0ms (1.1%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

4 calls:

6.0ms	x
5.0ms	y
5.0ms	(+.f64 (+.f64 (*.f64 x x) y) y)
4.0ms	(*.f64 x x)

Results

Error	Segments	Branch
0%	1	`x`
0%	1	`y`
0%	1	`(+.f64 (+.f64 (*.f64 x x) y) y)`
0%	1	`(*.f64 x x)`

Compiler

Compiled 51 to 20 computations (60.8% saved)

regimes52.0ms (2.9%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

4 calls:

38.0ms	y
5.0ms	x
5.0ms	(+.f64 (+.f64 (*.f64 x x) y) y)
3.0ms	(*.f64 x x)

Results

Error	Segments	Branch
0.01%	1	`x`
0.01%	1	`y`
0.01%	1	`(+.f64 (+.f64 (*.f64 x x) y) y)`
0.01%	1	`(*.f64 x x)`

Compiler

Compiled 45 to 19 computations (57.8% saved)

regimes110.0ms (6.1%)

Counts

4 → 5

Calls

Call 1

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

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

Calls

3 calls:

79.0ms	x
19.0ms	y
11.0ms	(*.f64 x x)

Results

Error	Segments	Branch
10.98%	5	`x`
20.87%	5	`y`
11.86%	4	`(*.f64 x x)`

Compiler

Compiled 25 to 12 computations (52% saved)

bsearch76.0ms (4.3%)

Algorithm

4×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough
1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
15.0ms	5.893597492378287e+65	6.007071999960102e+76
9.0ms	33099.44336282797	517419.9446496124
38.0ms	1.1381071325581678e-60	9.873433259408258e-57
14.0ms	-0.007305616121391193	-2.0189645115477693e-5

Results

71.0ms

512×

body

256

valid

Compiler

Compiled 462 to 297 computations (35.7% saved)

regimes92.0ms (5.1%)

Counts

3 → 5

Calls

Call 1

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

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

Calls

3 calls:

33.0ms	(*.f64 x x)
29.0ms	y
28.0ms	x

Results

Error	Segments	Branch
11.93%	5	`x`
22.24%	5	`y`
12.74%	4	`(*.f64 x x)`

Compiler

Compiled 20 to 11 computations (45% saved)

bsearch55.0ms (3.1%)

Algorithm

4×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough
1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
17.0ms	5.893597492378287e+65	6.007071999960102e+76
14.0ms	33099.44336282797	517419.9446496124
9.0ms	3.1133699444773885e-56	1.5718237898599212e-55
15.0ms	-0.007305616121391193	-2.0189645115477693e-5

Results

45.0ms

480×

body

256

valid

Compiler

Compiled 374 to 249 computations (33.4% saved)

regimes24.0ms (1.3%)

Accuracy

Total -23.0b remaining (-59.5%)

Threshold costs -23b (-59.5%)

Counts

2 → 3

Calls

Call 1

Inputs
y
(*.f64 x x)

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

Calls

3 calls:

10.0ms	y
9.0ms	x
4.0ms	(*.f64 x x)

Results

Error	Segments	Branch
60.46%	3	`x`
63.84%	3	`y`
60.55%	2	`(*.f64 x x)`

Compiler

Compiled 17 to 10 computations (41.2% saved)

bsearch41.0ms (2.3%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
13.0ms	1.405043950325218e-115	8.145769960468221e-111
28.0ms	-7.843072153484458e-61	-2.05230996913513e-68

Results

38.0ms

272×

body

256

valid

Compiler

Compiled 184 to 128 computations (30.4% saved)

simplify12.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

16×	`not-or`
14×	`if-if-or-not`
12×	`if-not`
10×	`not-not`
4×	`+-commutative`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	222
1	53	222
2	59	216
3	70	208
4	78	208
5	86	208
6	88	208
7	90	208

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(fma.f64 x x (+.f64 y y))
(+.f64 (+.f64 (*.f64 x x) y) y)
(if (<=.f64 x -8264141345021879/73786976294838206464) (+.f64 (.f64 x x) y) (if (<=.f64 x 7950811791502729/883423532389192164791648750371459257913741948437809479060803100646309888) (+.f64 y y) (if (<=.f64 x 130000) (+.f64 (.f64 x x) y) (if (<=.f64 x 600000000000000042022284152290696487454451377086439361183251169280) (+.f64 y y) (+.f64 (*.f64 x x) y)))))
(if (<=.f64 x -7526271582073497/147573952589676412928) (.f64 x x) (if (<=.f64 x 8558165470020299/55213970774324510299478046898216203619608871777363092441300193790394368) (+.f64 y y) (if (<=.f64 x 180000) (.f64 x x) (if (<=.f64 x 600000000000000042022284152290696487454451377086439361183251169280) (+.f64 y y) (*.f64 x x)))))
(if (<=.f64 x -3853560729817883/29642774844752946028434172162224104410437116074403984394101141506025761187823616) (.f64 x x) (if (<=.f64 x 4982140856623339/21661481985318866090456360813617841433097164651373566993519371723551728967231450179999800047688590453885868835635965404913860608) y (.f64 x x)))
y

Outputs
(fma.f64 x x (+.f64 y y))
(+.f64 (+.f64 (*.f64 x x) y) y)
(+.f64 y (+.f64 y (*.f64 x x)))
(if (<=.f64 x -8264141345021879/73786976294838206464) (+.f64 (.f64 x x) y) (if (<=.f64 x 7950811791502729/883423532389192164791648750371459257913741948437809479060803100646309888) (+.f64 y y) (if (<=.f64 x 130000) (+.f64 (.f64 x x) y) (if (<=.f64 x 600000000000000042022284152290696487454451377086439361183251169280) (+.f64 y y) (+.f64 (*.f64 x x) y)))))
(if (<=.f64 x -8264141345021879/73786976294838206464) (+.f64 y (.f64 x x)) (if (<=.f64 x 7950811791502729/883423532389192164791648750371459257913741948437809479060803100646309888) (+.f64 y y) (if (or (<=.f64 x 130000) (not (<=.f64 x 600000000000000042022284152290696487454451377086439361183251169280))) (+.f64 y (.f64 x x)) (+.f64 y y))))
(if (or (<=.f64 x -8264141345021879/73786976294838206464) (not (or (<=.f64 x 7950811791502729/883423532389192164791648750371459257913741948437809479060803100646309888) (not (or (<=.f64 x 130000) (not (<=.f64 x 600000000000000042022284152290696487454451377086439361183251169280))))))) (+.f64 y (*.f64 x x)) (+.f64 y y))
(if (or (<=.f64 x -8264141345021879/73786976294838206464) (not (or (<=.f64 x 7950811791502729/883423532389192164791648750371459257913741948437809479060803100646309888) (and (not (<=.f64 x 130000)) (<=.f64 x 600000000000000042022284152290696487454451377086439361183251169280))))) (+.f64 y (*.f64 x x)) (+.f64 y y))
(if (or (<=.f64 x -8264141345021879/73786976294838206464) (and (not (<=.f64 x 7950811791502729/883423532389192164791648750371459257913741948437809479060803100646309888)) (or (<=.f64 x 130000) (not (<=.f64 x 600000000000000042022284152290696487454451377086439361183251169280))))) (+.f64 y (*.f64 x x)) (+.f64 y y))
(if (<=.f64 x -7526271582073497/147573952589676412928) (.f64 x x) (if (<=.f64 x 8558165470020299/55213970774324510299478046898216203619608871777363092441300193790394368) (+.f64 y y) (if (<=.f64 x 180000) (.f64 x x) (if (<=.f64 x 600000000000000042022284152290696487454451377086439361183251169280) (+.f64 y y) (*.f64 x x)))))
(if (<=.f64 x -7526271582073497/147573952589676412928) (.f64 x x) (if (or (<=.f64 x 8558165470020299/55213970774324510299478046898216203619608871777363092441300193790394368) (and (not (<=.f64 x 180000)) (<=.f64 x 600000000000000042022284152290696487454451377086439361183251169280))) (+.f64 y y) (.f64 x x)))
(if (<=.f64 x -3853560729817883/29642774844752946028434172162224104410437116074403984394101141506025761187823616) (.f64 x x) (if (<=.f64 x 4982140856623339/21661481985318866090456360813617841433097164651373566993519371723551728967231450179999800047688590453885868835635965404913860608) y (.f64 x x)))
y

Compiler

Compiled 93 to 56 computations (39.8% saved)

soundness13.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

8×	`fma-def`
6×	`+-commutative`
2×	`*-commutative`
2×	`associate-+l+`
2×	`count-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	17	15
3	19	15
4	20	15

Stop Event

1×

saturated

Compiler

Compiled 22 to 8 computations (63.6% saved)

end41.0ms (2.3%)

Compiler: Compiled 83 to 40 computations (51.8% saved)

Details

analyze44.0ms (2.5%)

sample975.0ms (54.4%)

preprocess10.0ms (0.6%)

simplify12.0ms (0.6%)

eval1.0ms (0%)

prune1.0ms (0.1%)

localize41.0ms (2.3%)

series1.0ms (0.1%)

rewrite52.0ms (2.9%)

simplify62.0ms (3.5%)

localize5.0ms (0.3%)

eval9.0ms (0.5%)

prune6.0ms (0.4%)

localize3.0ms (0.1%)

localize8.0ms (0.4%)

eval7.0ms (0.4%)

prune8.0ms (0.5%)

localize3.0ms (0.1%)

localize3.0ms (0.2%)

eval0.0ms (0%)

prune2.0ms (0.1%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes20.0ms (1.1%)

regimes52.0ms (2.9%)

regimes110.0ms (6.1%)

bsearch76.0ms (4.3%)

regimes92.0ms (5.1%)

bsearch55.0ms (3.1%)

regimes24.0ms (1.3%)

bsearch41.0ms (2.3%)

simplify12.0ms (0.7%)

soundness13.0ms (0.7%)

end41.0ms (2.3%)

Profiling