Details

analyze305.0ms (17.2%)

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)

sample927.0ms (52.4%)

Results

910.0ms	8256×	body	256	valid
6.0ms	84×	body	256	infinite

Bogosity

preprocess44.0ms (2.5%)

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 (0.7%)

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

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)

prune2.0ms (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
▶	0b	(fma.f64 x x (+.f64 y y))
▶	0.0b	(+.f64 (+.f64 (*.f64 x x) y) y)

Compiler

Compiled 17 to 9 computations (47.1% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 19 to 5 computations (73.7% saved)

series2.0ms (0.1%)

Counts

2 → 48

Calls

12 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	x	@	0	(+.f64 (+.f64 (*.f64 x x) y) y)
0.0ms	y	@	0	(+.f64 (*.f64 x x) y)
0.0ms	y	@	-inf	(+.f64 (*.f64 x x) y)

rewrite62.0ms (3.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1934×	`add-sqr-sqrt`
1914×	`*-un-lft-identity`
1796×	`add-cube-cbrt`
1780×	`add-cbrt-cube`
174×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	24
1	162	24
2	2376	24

Stop Event

1×	node limit

Counts

2 → 75

Calls

Call 1

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

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

Outputs

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

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

simplify89.0ms (5%)

Algorithm

1×	egg-herbie

Rules

1460×	`associate-+l-`
1030×	`fma-def`
848×	`distribute-lft-in`
770×	`distribute-rgt-in`
636×	`unswap-sqr`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	175	2527
1	418	2413
2	1670	2343
3	7448	2343

Stop Event

1×	node limit

Counts

123 → 95

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

eval18.0ms (1%)

Compiler: Compiled 1273 to 469 computations (63.2% saved)

prune13.0ms (0.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	93	4	97

Error

Counts

97 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0b	(fma.f64 x x (+.f64 y y))
✓	0.0b	(+.f64 (+.f64 (*.f64 x x) y) y)
▶	35.2b	(+.f64 (*.f64 x x) y)
▶	21.1b	(+.f64 y y)

Compiler

Compiled 29 to 16 computations (44.8% saved)

localize3.0ms (0.2%)

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

localize7.0ms (0.4%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 12 to 4 computations (66.7% saved)

eval6.0ms (0.4%)

Compiler: Compiled 415 to 169 computations (59.3% saved)

prune7.0ms (0.4%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	39	2	41
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	39	6	45

Error

Counts

45 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0b	(fma.f64 x x (+.f64 y y))
✓	0.0b	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	35.2b	(+.f64 (*.f64 x x) y)
✓	21.1b	(+.f64 y y)
▶	41.7b	(*.f64 x x)
	55.2b	y

Compiler

Compiled 37 to 21 computations (43.2% saved)

localize3.0ms (0.1%)

Compiler: Compiled 6 to 3 computations (50% 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
✓	0b	(fma.f64 x x (+.f64 y y))
✓	0.0b	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	35.2b	(+.f64 (*.f64 x x) y)
✓	21.1b	(+.f64 y y)
✓	41.7b	(*.f64 x x)
	55.2b	y

Compiler

Compiled 37 to 21 computations (43.2% 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
✓	0b	(fma.f64 x x (+.f64 y y))
✓	0.0b	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	35.2b	(+.f64 (*.f64 x x) y)
✓	21.1b	(+.f64 y y)
✓	41.7b	(*.f64 x x)
	55.2b	y

Compiler

Compiled 37 to 21 computations (43.2% saved)

regimes19.0ms (1.1%)

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 (+.f64 y y))

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 47 to 19 computations (59.6% saved)

regimes19.0ms (1.1%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

4 calls:

6.0ms	(+.f64 (+.f64 (*.f64 x x) y) y)
5.0ms	x
4.0ms	y
3.0ms	(*.f64 x x)

Results

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

Compiler

Compiled 41 to 18 computations (56.1% saved)

regimes36.0ms (2.1%)

Counts

4 → 3

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)

Calls

3 calls:

15.0ms	y
13.0ms	x
8.0ms	(*.f64 x x)

Results

Error	Segments	Branch
8.6b	3	`x`
16.2b	3	`y`
8.6b	2	`(*.f64 x x)`

Compiler

Compiled 25 to 12 computations (52% saved)

bsearch25.0ms (1.4%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
15.0ms	2.36419583307657e-26	2.1487771395336507e-23
10.0ms	-1.5048017302616266e-27	-2.913112708475959e-28

Results

22.0ms

224×

body

256

valid

Compiler

Compiled 210 to 135 computations (35.7% saved)

regimes36.0ms (2%)

Counts

3 → 3

Calls

Call 1

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

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

Calls

3 calls:

18.0ms	y
10.0ms	x
7.0ms	(*.f64 x x)

Results

Error	Segments	Branch
9.2b	3	`x`
17.0b	3	`y`
9.2b	2	`(*.f64 x x)`

Compiler

Compiled 20 to 11 computations (45% saved)

bsearch24.0ms (1.4%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
9.0ms	2.2021848469101585e-11	2.192022407559541e-10
15.0ms	-1.2589036270523814e+36	-5.76237540805569e+25

Results

21.0ms

256×

body

256

valid

Compiler

Compiled 206 to 137 computations (33.5% saved)

regimes18.0ms (1%)

Accuracy

Total -24.3b remaining (-65%)

Threshold costs -24.3b (-65%)

Counts

2 → 3

Calls

Call 1

Inputs
y
(*.f64 x x)

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

Calls

3 calls:

9.0ms	x
6.0ms	(*.f64 x x)
3.0ms	y

Results

Error	Segments	Branch
37.3b	3	`x`
41.7b	1	`y`
37.7b	2	`(*.f64 x x)`

Compiler

Compiled 17 to 10 computations (41.2% saved)

bsearch23.0ms (1.3%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
11.0ms	4.0183252663229593e-135	2.674787248768316e-133
12.0ms	-2.6392900567131974e-68	-3.1106594364914707e-71

Results

21.0ms

240×

body

256

valid

Compiler

Compiled 164 to 114 computations (30.5% saved)

simplify6.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

6×	`if-if-or-not`
4×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	152
1	44	152

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 -2285826382849389/2787593149816327892691964784081045188247552) (+.f64 (.f64 x x) y) (if (<=.f64 x 3920052866929211/43556142965880123323311949751266331066368) (+.f64 y y) (+.f64 (.f64 x x) y)))
(if (<=.f64 x -234999999999999988004290560) (.f64 x x) (if (<=.f64 x 7118155225890937/77371252455336267181195264) (+.f64 y y) (.f64 x x)))
(if (<=.f64 x -1958210243363535/62165404551223330269422781018352605012557018849668464680057997111644937126566671941632) (.f64 x x) (if (<=.f64 x 4500912085857195/51146728248377216718956089012931236753385031969422887335676427626502090568823039920051095192592252455482604439493126109519019633529459266458258243584) 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 -2285826382849389/2787593149816327892691964784081045188247552) (+.f64 (.f64 x x) y) (if (<=.f64 x 3920052866929211/43556142965880123323311949751266331066368) (+.f64 y y) (+.f64 (.f64 x x) y)))
(if (or (<=.f64 x -2285826382849389/2787593149816327892691964784081045188247552) (not (<=.f64 x 3920052866929211/43556142965880123323311949751266331066368))) (+.f64 y (*.f64 x x)) (+.f64 y y))
(if (<=.f64 x -234999999999999988004290560) (.f64 x x) (if (<=.f64 x 7118155225890937/77371252455336267181195264) (+.f64 y y) (.f64 x x)))
(if (or (<=.f64 x -234999999999999988004290560) (not (<=.f64 x 7118155225890937/77371252455336267181195264))) (*.f64 x x) (+.f64 y y))
(if (<=.f64 x -1958210243363535/62165404551223330269422781018352605012557018849668464680057997111644937126566671941632) (.f64 x x) (if (<=.f64 x 4500912085857195/51146728248377216718956089012931236753385031969422887335676427626502090568823039920051095192592252455482604439493126109519019633529459266458258243584) y (.f64 x x)))
y

Compiler

Compiled 73 to 43 computations (41.1% 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)

end34.0ms (1.9%)

Compiler: Compiled 63 to 27 computations (57.1% saved)

Details

analyze305.0ms (17.2%)

sample927.0ms (52.4%)

preprocess44.0ms (2.5%)

simplify12.0ms (0.7%)

eval1.0ms (0%)

prune2.0ms (0.1%)

localize6.0ms (0.3%)

series2.0ms (0.1%)

rewrite62.0ms (3.5%)

simplify89.0ms (5%)

localize5.0ms (0.3%)

eval18.0ms (1%)

prune13.0ms (0.7%)

localize3.0ms (0.2%)

localize7.0ms (0.4%)

eval6.0ms (0.4%)

prune7.0ms (0.4%)

localize3.0ms (0.1%)

eval0.0ms (0%)

prune2.0ms (0.1%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes19.0ms (1.1%)

regimes19.0ms (1.1%)

regimes36.0ms (2.1%)

bsearch25.0ms (1.4%)

regimes36.0ms (2%)

bsearch24.0ms (1.4%)

regimes18.0ms (1%)

bsearch23.0ms (1.3%)

simplify6.0ms (0.4%)

soundness13.0ms (0.7%)

end34.0ms (1.9%)

Profiling