Metrics for Diagrams.TwoD.Arc:arcBetween from diagrams-lib-1.3.0.3

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze2.0ms (0%)

Memory

3.6MiB live, 3.6MiB allocated; 0ms collecting garbage

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
75%	74.9%	25%	0.1%	0%	0%	0%	3
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	4
93.8%	93.7%	6.2%	0.1%	0%	0%	0%	5
96.9%	96.8%	3.1%	0.1%	0%	0%	0%	6
98.4%	98.3%	1.6%	0.1%	0%	0%	0%	7
99.2%	99.1%	0.8%	0.1%	0%	0%	0%	8
99.6%	99.5%	0.4%	0.1%	0%	0%	0%	9
99.8%	99.7%	0.2%	0.1%	0%	0%	0%	10
99.9%	99.8%	0.1%	0.1%	0%	0%	0%	11
100%	99.9%	0%	0.1%	0%	0%	0%	12

Compiler

Compiled 21 to 11 computations (47.6% saved)

sample1.2s (12.8%)

Memory

34.0MiB live, 1 251.2MiB allocated; 261ms collecting garbage

Samples

825.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 354.0ms

ival-mult!: 206.0ms (58.2% of total)

ival-sub!: 95.0ms (26.8% of total)

ival-div!: 33.0ms (9.3% of total)

ival-add!: 18.0ms (5.1% of total)

adjust: 1.0ms (0.3% of total)

Bogosity

preprocess76.0ms (0.8%)

Memory

-40.5MiB live, 24.0MiB allocated; 38ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	116
1	104	116
2	362	114
3	880	114
4	2892	114

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.0%	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)))

Symmetry

(abs x)

(abs y)

Compiler

Compiled 26 to 18 computations (30.8% saved)

series10.0ms (0.1%)

Memory

17.1MiB live, 17.1MiB allocated; 0ms collecting garbage

Counts

9 → 30

Calls

Call 1

Inputs
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)))
(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) y))
(*.f64 x x)
x
(.f64 (.f64 y #s(literal 4 binary64)) y)
(*.f64 y #s(literal 4 binary64))
y
#s(literal 4 binary64)
(+.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) y))

Outputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 -1))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (* 1/2 (/ (pow x 2) (pow y 2))) 1)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)))
#s(approx (- (* x x) (* (* y 4) y)) #s(hole binary64 (* -4 (pow y 2))))
#s(approx (- (* x x) (* (* y 4) y)) #s(hole binary64 (- (pow x 2) (* 4 (pow y 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (+ (* x x) (* (* y 4) y)) #s(hole binary64 (* 4 (pow y 2))))
#s(approx (+ (* x x) (* (* y 4) y)) #s(hole binary64 (+ (* 4 (pow y 2)) (pow x 2))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 1))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))))
#s(approx (- (* x x) (* (* y 4) y)) #s(hole binary64 (pow x 2)))
#s(approx (- (* x x) (* (* y 4) y)) #s(hole binary64 (* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))))
#s(approx (+ (* x x) (* (* y 4) y)) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) (* (* y 4) y)) #s(hole binary64 (* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (+ 1 (* -8 (/ (pow y 2) (pow x 2))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))))
#s(approx (- (* x x) (* (* y 4) y)) #s(hole binary64 (+ (* -4 (pow y 2)) (pow x 2))))
#s(approx (* (* y 4) y) #s(hole binary64 (* 4 (pow y 2))))
#s(approx (* y 4) #s(hole binary64 (* 4 y)))
#s(approx y #s(hole binary64 y))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))))
#s(approx (- (* x x) (* (* y 4) y)) #s(hole binary64 (* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))))
#s(approx (+ (* x x) (* (* y 4) y)) #s(hole binary64 (* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))))

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	y	@	inf	((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (- (* x x) (* (* y 4) y)) (* x x) x (* (* y 4) y) (* y 4) y 4 (+ (* x x) (* (* y 4) y)))
2.0ms	x	@	0	((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (- (* x x) (* (* y 4) y)) (* x x) x (* (* y 4) y) (* y 4) y 4 (+ (* x x) (* (* y 4) y)))
2.0ms	x	@	inf	((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (- (* x x) (* (* y 4) y)) (* x x) x (* (* y 4) y) (* y 4) y 4 (+ (* x x) (* (* y 4) y)))
1.0ms	y	@	-inf	((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (- (* x x) (* (* y 4) y)) (* x x) x (* (* y 4) y) (* y 4) y 4 (+ (* x x) (* (* y 4) y)))
1.0ms	y	@	0	((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (- (* x x) (* (* y 4) y)) (* x x) x (* (* y 4) y) (* y 4) y 4 (+ (* x x) (* (* y 4) y)))

rewrite6.8s (75.1%)

Memory

-298.0MiB live, 723.4MiB allocated; 5.6s collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	158	969
0	168	917
1	437	885
2	1874	811
0	8426	807
0	36645	735

Stop Event

1×	iter-limit
1×	iter-limit
1×	node-limit
1×	iter-limit

Counts

39 → 169

Calls

Call 1

Inputs
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)))
(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) y))
(*.f64 x x)
x
(.f64 (.f64 y #s(literal 4 binary64)) y)
(*.f64 y #s(literal 4 binary64))
y
#s(literal 4 binary64)
(+.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) y))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 -1))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (* 1/2 (/ (pow x 2) (pow y 2))) 1)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)))
#s(approx (- (* x x) (* (* y 4) y)) #s(hole binary64 (* -4 (pow y 2))))
#s(approx (- (* x x) (* (* y 4) y)) #s(hole binary64 (- (pow x 2) (* 4 (pow y 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (+ (* x x) (* (* y 4) y)) #s(hole binary64 (* 4 (pow y 2))))
#s(approx (+ (* x x) (* (* y 4) y)) #s(hole binary64 (+ (* 4 (pow y 2)) (pow x 2))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 1))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))))
#s(approx (- (* x x) (* (* y 4) y)) #s(hole binary64 (pow x 2)))
#s(approx (- (* x x) (* (* y 4) y)) #s(hole binary64 (* (pow x 2) (+ 1 (* -4 (/ (pow y 2) (pow x 2)))))))
#s(approx (+ (* x x) (* (* y 4) y)) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) (* (* y 4) y)) #s(hole binary64 (* (pow x 2) (+ 1 (* 4 (/ (pow y 2) (pow x 2)))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (+ 1 (* -8 (/ (pow y 2) (pow x 2))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))))
#s(approx (- (* x x) (* (* y 4) y)) #s(hole binary64 (+ (* -4 (pow y 2)) (pow x 2))))
#s(approx (* (* y 4) y) #s(hole binary64 (* 4 (pow y 2))))
#s(approx (* y 4) #s(hole binary64 (* 4 y)))
#s(approx y #s(hole binary64 y))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))))
#s(approx (- (* x x) (* (* y 4) y)) #s(hole binary64 (* (pow y 2) (- (/ (pow x 2) (pow y 2)) 4))))
#s(approx (+ (* x x) (* (* y 4) y)) #s(hole binary64 (* (pow y 2) (+ 4 (/ (pow x 2) (pow y 2))))))

Outputs
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 x x) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))) (.f64 (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)))) (/.f64 (.f64 (.f64 x x) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))) (.f64 (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))))) (.f64 (/.f64 (.f64 (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)) (.f64 (.f64 y y) #s(literal 4 binary64))) (.f64 (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)))) (/.f64 (.f64 (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)) (.f64 (.f64 y y) #s(literal 4 binary64))) (.f64 (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)))))) (+.f64 (/.f64 (.f64 (.f64 x x) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))) (.f64 (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)))) (/.f64 (.f64 (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)) (.f64 (.f64 y y) #s(literal 4 binary64))) (.f64 (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (*.f64 x x))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 #s(literal -4 binary64) (.f64 y y)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))) (/.f64 (.f64 #s(literal -4 binary64) (.f64 y y)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)))) (.f64 (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal -4 binary64) (.f64 y y)) (.f64 x x))) (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal -4 binary64) (.f64 y y)) (.f64 x x))))) (fma.f64 (.f64 #s(literal -4 binary64) y) (/.f64 y (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))) (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal -4 binary64) (.f64 y y)) (*.f64 x x)))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 x x) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))) (/.f64 (.f64 x x) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)))) (.f64 (/.f64 (.f64 (.f64 y y) #s(literal 4 binary64)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))) (/.f64 (.f64 (.f64 y y) #s(literal 4 binary64)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))))) (fma.f64 x (/.f64 x (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))) (/.f64 (.f64 (.f64 y y) #s(literal 4 binary64)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 x x) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))) (.f64 (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)) (.f64 (.f64 y y) #s(literal 4 binary64))) (.f64 (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 x x) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))) (.f64 (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)))) (/.f64 (.f64 (.f64 x x) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))) (.f64 (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)))) (fma.f64 (/.f64 (.f64 (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)) (.f64 (.f64 y y) #s(literal 4 binary64))) (.f64 (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)))) (/.f64 (.f64 (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)) (.f64 (.f64 y y) #s(literal 4 binary64))) (.f64 (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)))) (.f64 (/.f64 (.f64 (.f64 x x) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))) (.f64 (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)))) (/.f64 (.f64 (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)) (.f64 (.f64 y y) #s(literal 4 binary64))) (.f64 (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (*.f64 x x))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal -4 binary64) (.f64 y y)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal -4 binary64) (.f64 y y)) (.f64 x x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal -4 binary64) (.f64 y y)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))) (/.f64 (.f64 #s(literal -4 binary64) (.f64 y y)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))) (fma.f64 (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal -4 binary64) (.f64 y y)) (.f64 x x))) (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal -4 binary64) (.f64 y y)) (.f64 x x))) (.f64 (/.f64 (.f64 #s(literal -4 binary64) (.f64 y y)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))) (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal -4 binary64) (.f64 y y)) (*.f64 x x)))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x x) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 (.f64 y y) #s(literal 4 binary64)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 x x) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))) (/.f64 (.f64 x x) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))) (fma.f64 (/.f64 (.f64 (.f64 y y) #s(literal 4 binary64)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))) (/.f64 (.f64 (.f64 y y) #s(literal 4 binary64)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))) (.f64 (/.f64 (.f64 x x) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))) (/.f64 (.f64 (.f64 y y) #s(literal 4 binary64)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (*.f64 x x)))))))
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#s(approx (* x x) (*.f64 x x))
#s(approx x x)
#s(approx (+ (* x x) (* (* y 4) y)) (.f64 (.f64 y y) #s(literal 4 binary64)))
#s(approx (+ (* x x) (* (* y 4) y)) (fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 #s(literal -8 binary64) y) (/.f64 y (.f64 x x)) #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 #s(literal -4 binary64) (fma.f64 (.f64 #s(literal -8 binary64) (.f64 y y)) (/.f64 (.f64 y y) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (.f64 y (+.f64 y y)) (.f64 x x))) #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 #s(literal 16 binary64) (.f64 (.f64 y y) (.f64 y y))) (/.f64 (.f64 #s(literal -8 binary64) (.f64 y y)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (fma.f64 #s(literal -4 binary64) (fma.f64 (.f64 #s(literal -8 binary64) (.f64 y y)) (/.f64 (.f64 y y) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (.f64 y (+.f64 y y)) (*.f64 x x))) #s(literal 1 binary64))))
#s(approx (- (* x x) (* (* y 4) y)) (*.f64 x x))
#s(approx (- (* x x) (* (* y 4) y)) (fma.f64 (.f64 #s(literal -4 binary64) (.f64 y y)) #s(literal 1 binary64) (*.f64 x x)))
#s(approx (+ (* x x) (* (* y 4) y)) (*.f64 x x))
#s(approx (+ (* x x) (* (* y 4) y)) (fma.f64 (.f64 (.f64 y y) #s(literal 4 binary64)) #s(literal 1 binary64) (*.f64 x x)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 #s(literal -8 binary64) y) (/.f64 y (.f64 x x)) #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 (fma.f64 (/.f64 (.f64 y y) (.f64 (.f64 x x) (.f64 x x))) #s(literal 32 binary64) (/.f64 #s(literal -8 binary64) (.f64 x x))) y) y #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 (fma.f64 (.f64 (fma.f64 (/.f64 (.f64 y y) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) #s(literal -128 binary64) (/.f64 #s(literal 32 binary64) (.f64 (.f64 x x) (.f64 x x)))) y) y (/.f64 #s(literal -8 binary64) (.f64 x x))) y) y #s(literal 1 binary64)))
#s(approx (- (* x x) (* (* y 4) y)) (fma.f64 (.f64 #s(literal -4 binary64) y) y (.f64 x x)))
#s(approx (* (* y 4) y) (.f64 (.f64 y y) #s(literal 4 binary64)))
#s(approx (* y 4) (*.f64 #s(literal 4 binary64) y))
#s(approx y y)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) (/.f64 (.f64 x x) (.f64 (.f64 y y) (.f64 y y)))) #s(literal -1/4 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (*.f64 x x) #s(literal -1 binary64))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) (/.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 (.f64 y y) y) (.f64 (.f64 y y) y)))) #s(literal 1/16 binary64) (fma.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) (/.f64 (.f64 x x) (.f64 (.f64 y y) (.f64 y y)))) #s(literal -1/4 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64)))))
#s(approx (- (* x x) (* (* y 4) y)) (.f64 (-.f64 (.f64 x (/.f64 x (.f64 y y))) #s(literal 4 binary64)) (.f64 y y)))
#s(approx (+ (* x x) (* (* y 4) y)) (.f64 (.f64 (fma.f64 x (/.f64 x (*.f64 y y)) #s(literal 4 binary64)) y) y))

eval13.0ms (0.1%)

Memory: 19.0MiB live, 19.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 2 123 to 596 computations (71.9% saved)

prune4.0ms (0%)

Memory

6.8MiB live, 6.8MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	158	3	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	3	162

Accuracy

99.3%

Counts

162 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	47.5%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64)))
▶	48.5%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
▶	52.3%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

Status

Accuracy

Program

▶

47.5%

#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 y y)) (*.f64 x x) #s(literal -1 binary64)))

▶

48.5%

#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))

▶

52.3%

#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

Compiler

Compiled 47 to 38 computations (19.1% saved)

series112.0ms (1.2%)

Memory

-55.6MiB live, 9.9MiB allocated; 40ms collecting garbage

Counts

12 → 24

Calls

Call 1

Inputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64))
(/.f64 #s(literal 1/2 binary64) (*.f64 y y))
#s(literal 1/2 binary64)
(*.f64 y y)
y
(*.f64 x x)
x

Outputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 -1))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (* 1/2 (/ (pow x 2) (pow y 2))) 1)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)))
#s(approx (+ (* (/ 1/2 (* y y)) (* x x)) -1) #s(hole binary64 -1))
#s(approx (+ (* (/ 1/2 (* y y)) (* x x)) -1) #s(hole binary64 (- (* 1/2 (/ (pow x 2) (pow y 2))) 1)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 1))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))))
#s(approx (+ (* (/ 1/2 (* y y)) (* x x)) -1) #s(hole binary64 (* 1/2 (/ (pow x 2) (pow y 2)))))
#s(approx (+ (* (/ 1/2 (* y y)) (* x x)) -1) #s(hole binary64 (* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (+ 1 (* -8 (/ (pow y 2) (pow x 2))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))))
#s(approx (+ (* (/ 1/2 (* y y)) (* x x)) -1) #s(hole binary64 (/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))))
#s(approx (/ 1/2 (* y y)) #s(hole binary64 (/ 1/2 (pow y 2))))
#s(approx (* y y) #s(hole binary64 (pow y 2)))
#s(approx y #s(hole binary64 y))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))))

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) -1 (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) 1 (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ 1/2 (* y y)) (* x x)) -1) (/ 1/2 (* y y)) 1/2 (* y y) y (* x x) x)
1.0ms	y	@	0	((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) -1 (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) 1 (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ 1/2 (* y y)) (* x x)) -1) (/ 1/2 (* y y)) 1/2 (* y y) y (* x x) x)
1.0ms	y	@	inf	((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) -1 (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) 1 (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ 1/2 (* y y)) (* x x)) -1) (/ 1/2 (* y y)) 1/2 (* y y) y (* x x) x)
1.0ms	x	@	-inf	((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) -1 (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) 1 (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ 1/2 (* y y)) (* x x)) -1) (/ 1/2 (* y y)) 1/2 (* y y) y (* x x) x)
1.0ms	y	@	-inf	((/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) -1 (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) 1 (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (+ (* (/ 1/2 (* y y)) (* x x)) -1) (/ 1/2 (* y y)) 1/2 (* y y) y (* x x) x)

rewrite437.0ms (4.9%)

Memory

33.2MiB live, 348.3MiB allocated; 50ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	151	915
0	157	853
1	439	805
2	2119	744
0	8132	744
0	28656	678

Stop Event

1×	iter-limit
1×	iter-limit
1×	node-limit
1×	iter-limit

Counts

36 → 429

Calls

Call 1

Inputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64))
(/.f64 #s(literal 1/2 binary64) (*.f64 y y))
#s(literal 1/2 binary64)
(*.f64 y y)
y
(*.f64 x x)
x
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 -1))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (* 1/2 (/ (pow x 2) (pow y 2))) 1)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))) 1)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (* (pow x 2) (+ (* (pow x 2) (- (* 1/32 (/ (pow x 2) (pow y 6))) (* 1/8 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))) 1)))
#s(approx (+ (* (/ 1/2 (* y y)) (* x x)) -1) #s(hole binary64 -1))
#s(approx (+ (* (/ 1/2 (* y y)) (* x x)) -1) #s(hole binary64 (- (* 1/2 (/ (pow x 2) (pow y 2))) 1)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 1))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (+ 1 (* -4 (/ (pow y 2) (pow x 2)))) (* 4 (/ (pow y 2) (pow x 2))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (+ 1 (+ (* -4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* -4 (/ (pow y 2) (pow x 2))))) (* 4 (/ (pow y 2) (pow x 2))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (+ 1 (+ (* -4 (/ (pow y 2) (pow x 2))) (* 16 (/ (* (pow y 4) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 6))))) (+ (* 4 (/ (* (pow y 2) (- (* -4 (pow y 2)) (* 4 (pow y 2)))) (pow x 4))) (* 4 (/ (pow y 2) (pow x 2)))))))
#s(approx (+ (* (/ 1/2 (* y y)) (* x x)) -1) #s(hole binary64 (* 1/2 (/ (pow x 2) (pow y 2)))))
#s(approx (+ (* (/ 1/2 (* y y)) (* x x)) -1) #s(hole binary64 (* (pow x 2) (- (* 1/2 (/ 1 (pow y 2))) (/ 1 (pow x 2))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (+ 1 (* -8 (/ (pow y 2) (pow x 2))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (+ 1 (* (pow y 2) (- (* 32 (/ (pow y 2) (pow x 4))) (* 8 (/ 1 (pow x 2))))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (+ 1 (* (pow y 2) (- (* (pow y 2) (+ (* -128 (/ (pow y 2) (pow x 6))) (* 32 (/ 1 (pow x 4))))) (* 8 (/ 1 (pow x 2))))))))
#s(approx (+ (* (/ 1/2 (* y y)) (* x x)) -1) #s(hole binary64 (/ (+ (* -1 (pow y 2)) (* 1/2 (pow x 2))) (pow y 2))))
#s(approx (/ 1/2 (* y y)) #s(hole binary64 (/ 1/2 (pow y 2))))
#s(approx (* y y) #s(hole binary64 (pow y 2)))
#s(approx y #s(hole binary64 y))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (* 1/4 (/ (pow x 2) (pow y 2))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (+ (* -1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (* -1/4 (/ (pow x 2) (pow y 2)))))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(hole binary64 (- (+ (* 1/16 (/ (* (pow x 4) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 6))) (* 1/4 (/ (pow x 2) (pow y 2)))) (+ 1 (+ (* -1/4 (/ (pow x 2) (pow y 2))) (* 1/4 (/ (* (pow x 2) (- (* 1/4 (pow x 2)) (* -1/4 (pow x 2)))) (pow y 4))))))))

Outputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) x) x #s(literal -1 binary64)))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 (neg.f64 y) y) (.f64 y y)) (.f64 (.f64 y y) (.f64 y y))) (/.f64 (.f64 (.f64 (neg.f64 y) y) (.f64 y y)) (.f64 (.f64 y y) (.f64 y y)))) (.f64 (/.f64 (.f64 (.f64 y y) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (.f64 (.f64 y y) (.f64 y y))) (/.f64 (.f64 (.f64 y y) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (.f64 (.f64 y y) (.f64 y y))))) (-.f64 (/.f64 (.f64 (.f64 (neg.f64 y) y) (.f64 y y)) (.f64 (.f64 y y) (.f64 y y))) (/.f64 (.f64 (.f64 y y) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (.f64 (.f64 y y) (*.f64 y y)))))
(/.f64 (-.f64 (.f64 (fma.f64 (.f64 x x) (/.f64 #s(literal 1/4 binary64) (.f64 y y)) #s(literal -1 binary64)) (fma.f64 (.f64 x x) (/.f64 #s(literal 1/4 binary64) (.f64 y y)) #s(literal -1 binary64))) (.f64 (.f64 (.f64 x x) (/.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 (.f64 x x) (/.f64 #s(literal 1/4 binary64) (.f64 y y))))) (-.f64 (fma.f64 (.f64 x x) (/.f64 #s(literal 1/4 binary64) (.f64 y y)) #s(literal -1 binary64)) (.f64 (.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 y y)))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) (/.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 (.f64 x x) (/.f64 #s(literal 1/4 binary64) (.f64 y y)))) (.f64 (fma.f64 (.f64 x x) (/.f64 #s(literal 1/4 binary64) (.f64 y y)) #s(literal -1 binary64)) (fma.f64 (.f64 x x) (/.f64 #s(literal 1/4 binary64) (.f64 y y)) #s(literal -1 binary64)))) (-.f64 (.f64 (.f64 x x) (/.f64 #s(literal 1/4 binary64) (.f64 y y))) (fma.f64 (.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 y y)) #s(literal -1 binary64))))
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(fabs.f64 (*.f64 (fabs.f64 x) x))
(fabs.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 (neg.f64 (fabs.f64 x))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (fabs.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x x)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
x
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) x) x #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (.f64 y y) (.f64 y y))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 y y))) x) x #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 (fma.f64 (.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (.f64 (.f64 y y) y) (.f64 (.f64 y y) y))) #s(literal 1/32 binary64) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 y y) (.f64 y y)))) x) x (/.f64 #s(literal 1/2 binary64) (.f64 y y))) x) x #s(literal -1 binary64)))
#s(approx (+ (* (/ 1/2 (* y y)) (* x x)) -1) #s(literal -1 binary64))
#s(approx (+ (* (/ 1/2 (* y y)) (* x x)) -1) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) x) x #s(literal -1 binary64)))
#s(approx (* x x) (*.f64 x x))
#s(approx x x)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 y y) (/.f64 #s(literal -8 binary64) (.f64 x x)) #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 #s(literal -8 binary64) (.f64 y (/.f64 y (.f64 x x))) (fma.f64 (.f64 (.f64 #s(literal 8 binary64) (.f64 y y)) (/.f64 (.f64 y y) (.f64 (.f64 x x) (*.f64 x x)))) #s(literal 4 binary64) #s(literal 1 binary64))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (-.f64 (fma.f64 (.f64 (.f64 #s(literal -8 binary64) (.f64 y y)) (/.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))) #s(literal 16 binary64) (fma.f64 (.f64 #s(literal -4 binary64) (.f64 y y)) (/.f64 (.f64 #s(literal -8 binary64) (.f64 y y)) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 y y) (/.f64 #s(literal -8 binary64) (*.f64 x x))))) #s(literal -1 binary64)))
#s(approx (+ (* (/ 1/2 (* y y)) (* x x)) -1) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 y y)) x) x))
#s(approx (+ (* (/ 1/2 (* y y)) (* x x)) -1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (/.f64 #s(literal 1 binary64) (.f64 x x))) x) x))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 y y) (/.f64 #s(literal -8 binary64) (.f64 x x)) #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 (fma.f64 (/.f64 (.f64 y y) (.f64 (.f64 x x) (.f64 x x))) #s(literal 32 binary64) (/.f64 #s(literal -8 binary64) (.f64 x x))) y) y #s(literal 1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 (fma.f64 (.f64 (fma.f64 (/.f64 (.f64 y y) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) #s(literal -128 binary64) (/.f64 #s(literal 32 binary64) (.f64 (.f64 x x) (.f64 x x)))) y) y (/.f64 #s(literal -8 binary64) (.f64 x x))) y) y #s(literal 1 binary64)))
#s(approx (+ (* (/ 1/2 (* y y)) (* x x)) -1) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) x) x #s(literal -1 binary64)))
#s(approx (/ 1/2 (* y y)) (/.f64 #s(literal 1/2 binary64) (*.f64 y y)))
#s(approx (* y y) (*.f64 y y))
#s(approx y y)
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) x) x #s(literal -1 binary64)))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 #s(literal -1/4 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x x) (.f64 (.f64 y y) (.f64 y y)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 y y)) x) x #s(literal -1 binary64))))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) (/.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 (.f64 y y) y) (.f64 (.f64 y y) y)))) #s(literal 1/16 binary64) (fma.f64 (.f64 #s(literal -1/4 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x x) (.f64 (.f64 y y) (.f64 y y)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) x) x #s(literal -1 binary64)))))

eval66.0ms (0.7%)

Memory: -23.6MiB live, 81.2MiB allocated; 20ms collecting garbage
Compiler: Compiled 4 010 to 1 492 computations (62.8% saved)

prune7.0ms (0.1%)

Memory

12.8MiB live, 12.8MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	412	0	412
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	412	3	415

Accuracy

99.3%

Counts

415 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	47.5%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64)))
✓	48.5%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
✓	52.3%	#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

Status

Accuracy

Program

✓

47.5%

#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 y y)) (*.f64 x x) #s(literal -1 binary64)))

✓

48.5%

#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))

✓

52.3%

#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

Compiler

Compiled 98 to 63 computations (35.7% saved)

regimes9.0ms (0.1%)

Memory

14.6MiB live, 14.6MiB allocated; 0ms collecting garbage

Counts

4 → 3

Calls

Call 1

Inputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x x) #s(literal -1 binary64)))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)))

Outputs

#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)) (+.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) y)))

#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))

Calls

5 calls:

2.0ms	y
2.0ms	x
2.0ms	(.f64 (.f64 y #s(literal 4 binary64)) y)
1.0ms	(*.f64 x x)
1.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)))

Results

Accuracy	Segments	Branch
81.0%	3	`(.f64 (.f64 y #s(literal 4 binary64)) y)`
82.3%	3	`(*.f64 x x)`
76.6%	2	`(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)))`
82.3%	3	`x`
81.0%	3	`y`

Compiler

Compiled 21 to 21 computations (0% saved)

regimes7.0ms (0.1%)

Memory

10.6MiB live, 10.6MiB allocated; 0ms collecting garbage

Counts

3 → 2

Calls

Call 1

Inputs

#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))

#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 y y)) (*.f64 x x) #s(literal -1 binary64)))

Outputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal 1 binary64))

Calls

5 calls:

1.0ms	x
1.0ms	y
1.0ms	(.f64 (.f64 y #s(literal 4 binary64)) y)
1.0ms	(*.f64 x x)
1.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)))

Results

Accuracy	Segments	Branch
76.5%	2	`(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)))`
75.6%	2	`(.f64 (.f64 y #s(literal 4 binary64)) y)`
75.6%	2	`y`
74.7%	2	`(*.f64 x x)`
74.7%	2	`x`

Compiler

Compiled 21 to 21 computations (0% saved)

regimes39.0ms (0.4%)

Memory

-38.1MiB live, 9.1MiB allocated; 4ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

Outputs
#s(approx (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) #s(literal -1 binary64))

Calls

5 calls:

35.0ms	(.f64 (.f64 y #s(literal 4 binary64)) y)
1.0ms	x
1.0ms	y
1.0ms	(*.f64 x x)
1.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)))

Results

Accuracy	Segments	Branch
52.3%	1	`(*.f64 x x)`
52.3%	1	`x`
52.3%	1	`(.f64 (.f64 y #s(literal 4 binary64)) y)`
52.3%	1	`y`
52.3%	1	`(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)) (+.f64 (.f64 x x) (.f64 (.f64 y #s(literal 4 binary64)) y)))`

Compiler

Compiled 21 to 21 computations (0% saved)

bsearch17.0ms (0.2%)

Memory

20.7MiB live, 20.7MiB allocated; 0ms collecting garbage

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
6.0ms	2.6758493220837316e+104	5.5074705260620573e+104
9.0ms	1.721601338187524e-168	2.512509462623053e-165

Samples

8.0ms

208×

valid

Compiler

Compiled 373 to 300 computations (19.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-mult!: 3.0ms (71.9% of total)

ival-div!: 1.0ms (24% of total)

ival-sub!: 0.0ms (0% of total)

adjust: 0.0ms (0% of total)

ival-add!: 0.0ms (0% of total)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9999999999997852	1.0

Compiler

Compiled 16 to 14 computations (12.5% saved)

derivations220.0ms (2.4%)

Memory

-25.1MiB live, 72.0MiB allocated; 18ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 45 to 29 computations (35.6% saved)

preprocess69.0ms (0.8%)

Memory

15.1MiB live, 61.2MiB allocated; 4ms collecting garbage

Remove

(abs y)

(abs x)

Compiler

Compiled 522 to 330 computations (36.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze2.0ms (0%)

sample1.2s (12.8%)

preprocess76.0ms (0.8%)

series10.0ms (0.1%)

rewrite6.8s (75.1%)

eval13.0ms (0.1%)

prune4.0ms (0%)

series112.0ms (1.2%)

rewrite437.0ms (4.9%)

eval66.0ms (0.7%)

prune7.0ms (0.1%)

regimes9.0ms (0.1%)

regimes7.0ms (0.1%)

regimes39.0ms (0.4%)

bsearch17.0ms (0.2%)

bsearch0.0ms (0%)

derivations220.0ms (2.4%)

preprocess69.0ms (0.8%)

end0.0ms (0%)

Profiling