From Rump in a 1983 paper

Average Accuracy: 18.8% → 100.0%

Time: 3.2s

Precision: binary64

Cost: 1600

\[x = 10864 \land y = 18817\]

Math

\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right) \]

↓

\[\begin{array}{l} t_0 := 3 \cdot \left(x \cdot x\right)\\ \left(t_0 - y \cdot y\right) \cdot \left(t_0 + y \cdot y\right) + \left(y \cdot y\right) \cdot 2 \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (+ (- (* 9.0 (pow x 4.0)) (pow y 4.0)) (* 2.0 (* y y))))

↓

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* 3.0 (* x x))))
   (+ (* (- t_0 (* y y)) (+ t_0 (* y y))) (* (* y y) 2.0))))

C

double code(double x, double y) {
	return ((9.0 * pow(x, 4.0)) - pow(y, 4.0)) + (2.0 * (y * y));
}

↓

double code(double x, double y) {
	double t_0 = 3.0 * (x * x);
	return ((t_0 - (y * y)) * (t_0 + (y * y))) + ((y * y) * 2.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((9.0d0 * (x ** 4.0d0)) - (y ** 4.0d0)) + (2.0d0 * (y * y))
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    t_0 = 3.0d0 * (x * x)
    code = ((t_0 - (y * y)) * (t_0 + (y * y))) + ((y * y) * 2.0d0)
end function

Java

public static double code(double x, double y) {
	return ((9.0 * Math.pow(x, 4.0)) - Math.pow(y, 4.0)) + (2.0 * (y * y));
}

↓

public static double code(double x, double y) {
	double t_0 = 3.0 * (x * x);
	return ((t_0 - (y * y)) * (t_0 + (y * y))) + ((y * y) * 2.0);
}

Python

def code(x, y):
	return ((9.0 * math.pow(x, 4.0)) - math.pow(y, 4.0)) + (2.0 * (y * y))

↓

def code(x, y):
	t_0 = 3.0 * (x * x)
	return ((t_0 - (y * y)) * (t_0 + (y * y))) + ((y * y) * 2.0)

Julia

function code(x, y)
	return Float64(Float64(Float64(9.0 * (x ^ 4.0)) - (y ^ 4.0)) + Float64(2.0 * Float64(y * y)))
end

↓

function code(x, y)
	t_0 = Float64(3.0 * Float64(x * x))
	return Float64(Float64(Float64(t_0 - Float64(y * y)) * Float64(t_0 + Float64(y * y))) + Float64(Float64(y * y) * 2.0))
end

MATLAB

function tmp = code(x, y)
	tmp = ((9.0 * (x ^ 4.0)) - (y ^ 4.0)) + (2.0 * (y * y));
end

↓

function tmp = code(x, y)
	t_0 = 3.0 * (x * x);
	tmp = ((t_0 - (y * y)) * (t_0 + (y * y))) + ((y * y) * 2.0);
end

Wolfram

code[x_, y_] := N[(N[(N[(9.0 * N[Power[x, 4.0], $MachinePrecision]), $MachinePrecision] - N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := Block[{t$95$0 = N[(3.0 * N[(x * x), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(t$95$0 - N[(y * y), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * y), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 18.8%

   \[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right) \]

2. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\left(3 \cdot \left(x \cdot x\right) - y \cdot y\right) \cdot \left(3 \cdot \left(x \cdot x\right) + y \cdot y\right)} + 2 \cdot \left(y \cdot y\right) \]
   Proof

   [Start] 18.8	\[ \left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right) \]
   add-sqr-sqrt [=>] 18.8	\[ \left(\color{blue}{\sqrt{9 \cdot {x}^{4}} \cdot \sqrt{9 \cdot {x}^{4}}} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right) \]
   sqr-pow [=>] 18.8	\[ \left(\sqrt{9 \cdot {x}^{4}} \cdot \sqrt{9 \cdot {x}^{4}} - \color{blue}{{y}^{\left(\frac{4}{2}\right)} \cdot {y}^{\left(\frac{4}{2}\right)}}\right) + 2 \cdot \left(y \cdot y\right) \]
   difference-of-squares [=>] 100.0	\[ \color{blue}{\left(\sqrt{9 \cdot {x}^{4}} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left(\sqrt{9 \cdot {x}^{4}} - {y}^{\left(\frac{4}{2}\right)}\right)} + 2 \cdot \left(y \cdot y\right) \]
   *-commutative [=>] 100.0	\[ \color{blue}{\left(\sqrt{9 \cdot {x}^{4}} - {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left(\sqrt{9 \cdot {x}^{4}} + {y}^{\left(\frac{4}{2}\right)}\right)} + 2 \cdot \left(y \cdot y\right) \]
   sqrt-prod [=>] 100.0	\[ \left(\color{blue}{\sqrt{9} \cdot \sqrt{{x}^{4}}} - {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left(\sqrt{9 \cdot {x}^{4}} + {y}^{\left(\frac{4}{2}\right)}\right) + 2 \cdot \left(y \cdot y\right) \]
   metadata-eval [=>] 100.0	\[ \left(\color{blue}{3} \cdot \sqrt{{x}^{4}} - {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left(\sqrt{9 \cdot {x}^{4}} + {y}^{\left(\frac{4}{2}\right)}\right) + 2 \cdot \left(y \cdot y\right) \]
   sqrt-pow1 [=>] 100.0	\[ \left(3 \cdot \color{blue}{{x}^{\left(\frac{4}{2}\right)}} - {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left(\sqrt{9 \cdot {x}^{4}} + {y}^{\left(\frac{4}{2}\right)}\right) + 2 \cdot \left(y \cdot y\right) \]
   metadata-eval [=>] 100.0	\[ \left(3 \cdot {x}^{\color{blue}{2}} - {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left(\sqrt{9 \cdot {x}^{4}} + {y}^{\left(\frac{4}{2}\right)}\right) + 2 \cdot \left(y \cdot y\right) \]
   unpow2 [=>] 100.0	\[ \left(3 \cdot \color{blue}{\left(x \cdot x\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left(\sqrt{9 \cdot {x}^{4}} + {y}^{\left(\frac{4}{2}\right)}\right) + 2 \cdot \left(y \cdot y\right) \]
   metadata-eval [=>] 100.0	\[ \left(3 \cdot \left(x \cdot x\right) - {y}^{\color{blue}{2}}\right) \cdot \left(\sqrt{9 \cdot {x}^{4}} + {y}^{\left(\frac{4}{2}\right)}\right) + 2 \cdot \left(y \cdot y\right) \]
   unpow2 [=>] 100.0	\[ \left(3 \cdot \left(x \cdot x\right) - \color{blue}{y \cdot y}\right) \cdot \left(\sqrt{9 \cdot {x}^{4}} + {y}^{\left(\frac{4}{2}\right)}\right) + 2 \cdot \left(y \cdot y\right) \]
   sqrt-prod [=>] 100.0	\[ \left(3 \cdot \left(x \cdot x\right) - y \cdot y\right) \cdot \left(\color{blue}{\sqrt{9} \cdot \sqrt{{x}^{4}}} + {y}^{\left(\frac{4}{2}\right)}\right) + 2 \cdot \left(y \cdot y\right) \]
   metadata-eval [=>] 100.0	\[ \left(3 \cdot \left(x \cdot x\right) - y \cdot y\right) \cdot \left(\color{blue}{3} \cdot \sqrt{{x}^{4}} + {y}^{\left(\frac{4}{2}\right)}\right) + 2 \cdot \left(y \cdot y\right) \]
   sqrt-pow1 [=>] 100.0	\[ \left(3 \cdot \left(x \cdot x\right) - y \cdot y\right) \cdot \left(3 \cdot \color{blue}{{x}^{\left(\frac{4}{2}\right)}} + {y}^{\left(\frac{4}{2}\right)}\right) + 2 \cdot \left(y \cdot y\right) \]
   metadata-eval [=>] 100.0	\[ \left(3 \cdot \left(x \cdot x\right) - y \cdot y\right) \cdot \left(3 \cdot {x}^{\color{blue}{2}} + {y}^{\left(\frac{4}{2}\right)}\right) + 2 \cdot \left(y \cdot y\right) \]
   unpow2 [=>] 100.0	\[ \left(3 \cdot \left(x \cdot x\right) - y \cdot y\right) \cdot \left(3 \cdot \color{blue}{\left(x \cdot x\right)} + {y}^{\left(\frac{4}{2}\right)}\right) + 2 \cdot \left(y \cdot y\right) \]
   metadata-eval [=>] 100.0	\[ \left(3 \cdot \left(x \cdot x\right) - y \cdot y\right) \cdot \left(3 \cdot \left(x \cdot x\right) + {y}^{\color{blue}{2}}\right) + 2 \cdot \left(y \cdot y\right) \]
   unpow2 [=>] 100.0	\[ \left(3 \cdot \left(x \cdot x\right) - y \cdot y\right) \cdot \left(3 \cdot \left(x \cdot x\right) + \color{blue}{y \cdot y}\right) + 2 \cdot \left(y \cdot y\right) \]

3. Final simplification 100.0%

   \[\leadsto \left(3 \cdot \left(x \cdot x\right) - y \cdot y\right) \cdot \left(3 \cdot \left(x \cdot x\right) + y \cdot y\right) + \left(y \cdot y\right) \cdot 2 \]

Reproduce

herbie shell --seed 2023126 
(FPCore (x y)
  :name "From Rump in a 1983 paper"
  :precision binary64
  :pre (and (== x 10864.0) (== y 18817.0))
  (+ (- (* 9.0 (pow x 4.0)) (pow y 4.0)) (* 2.0 (* y y))))