Graphics.Rendering.Chart.Axis.Types:hBufferRect from Chart-1.5.3

Percentage Accurate: 99.9% → 100.0%

Time: 5.8s

Alternatives: 6

Speedup: 1.8×

Specification

Math

\[\begin{array}{l} \\ x + \frac{x - y}{2} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (/ (- x y) 2.0)))

C

double code(double x, double y) {
	return x + ((x - y) / 2.0);
}

Fortran

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

Java

public static double code(double x, double y) {
	return x + ((x - y) / 2.0);
}

Python

def code(x, y):
	return x + ((x - y) / 2.0)

Julia

function code(x, y)
	return Float64(x + Float64(Float64(x - y) / 2.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x + ((x - y) / 2.0);
end

Wolfram

code[x_, y_] := N[(x + N[(N[(x - y), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{x - y}{2} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (/ (- x y) 2.0)))

C

double code(double x, double y) {
	return x + ((x - y) / 2.0);
}

Fortran

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

Java

public static double code(double x, double y) {
	return x + ((x - y) / 2.0);
}

Python

def code(x, y):
	return x + ((x - y) / 2.0)

Julia

function code(x, y)
	return Float64(x + Float64(Float64(x - y) / 2.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x + ((x - y) / 2.0);
end

Wolfram

code[x_, y_] := N[(x + N[(N[(x - y), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, 1.5, -0.5 \cdot y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma x 1.5 (* -0.5 y)))

C

double code(double x, double y) {
	return fma(x, 1.5, (-0.5 * y));
}

Julia

function code(x, y)
	return fma(x, 1.5, Float64(-0.5 * y))
end

Wolfram

code[x_, y_] := N[(x * 1.5 + N[(-0.5 * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[x + \frac{x - y}{2} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \color{blue}{\frac{x - y}{2} + x} \]

   2. frac-2neg N/A

      \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(x - y\right)\right)}{\mathsf{neg}\left(2\right)}} + x \]

   3. div-inv N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \frac{1}{\mathsf{neg}\left(2\right)}} + x \]

   4. accelerator-lowering-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(\left(x - y\right)\right), \frac{1}{\mathsf{neg}\left(2\right)}, x\right)} \]

   5. neg-sub0 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{0 - \left(x - y\right)}, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

   6. sub-neg N/A

      \[\leadsto \mathsf{fma}\left(0 - \color{blue}{\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

   7. +-commutative N/A

      \[\leadsto \mathsf{fma}\left(0 - \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

   8. associate--r+ N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(0 - \left(\mathsf{neg}\left(y\right)\right)\right) - x}, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

   9. neg-sub0 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right)} - x, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

   10. remove-double-neg N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{y} - x, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

   11. --lowering--.f64 N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{y - x}, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

   12. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(y - x, \frac{1}{\color{blue}{-2}}, x\right) \]

   13. metadata-eval 99.8

       \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{-0.5}, x\right) \]

4. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, -0.5, x\right)} \]

5. Taylor expanded in y around 0

   \[\leadsto \color{blue}{x + \left(\frac{-1}{2} \cdot y + \frac{1}{2} \cdot x\right)} \]
6. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto x + \color{blue}{\left(\frac{1}{2} \cdot x + \frac{-1}{2} \cdot y\right)} \]

   2. associate-+r+ N/A

      \[\leadsto \color{blue}{\left(x + \frac{1}{2} \cdot x\right) + \frac{-1}{2} \cdot y} \]

   3. distribute-rgt1-in N/A

      \[\leadsto \color{blue}{\left(\frac{1}{2} + 1\right) \cdot x} + \frac{-1}{2} \cdot y \]

   4. metadata-eval N/A

      \[\leadsto \color{blue}{\frac{3}{2}} \cdot x + \frac{-1}{2} \cdot y \]

   5. *-commutative N/A

      \[\leadsto \color{blue}{x \cdot \frac{3}{2}} + \frac{-1}{2} \cdot y \]

   6. accelerator-lowering-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{3}{2}, \frac{-1}{2} \cdot y\right)} \]

   7. *-lowering-*.f64 100.0

      \[\leadsto \mathsf{fma}\left(x, 1.5, \color{blue}{-0.5 \cdot y}\right) \]

7. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, 1.5, -0.5 \cdot y\right)} \]
8. Add Preprocessing

Alternative 2: 75.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+56}:\\ \;\;\;\;\mathsf{fma}\left(y, -0.5, x\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-19}:\\ \;\;\;\;x \cdot 1.5\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, -0.5, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.2e+56)
   (fma y -0.5 x)
   (if (<= y 1.2e-19) (* x 1.5) (fma y -0.5 x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.2e+56) {
		tmp = fma(y, -0.5, x);
	} else if (y <= 1.2e-19) {
		tmp = x * 1.5;
	} else {
		tmp = fma(y, -0.5, x);
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.2e+56)
		tmp = fma(y, -0.5, x);
	elseif (y <= 1.2e-19)
		tmp = Float64(x * 1.5);
	else
		tmp = fma(y, -0.5, x);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.2e+56], N[(y * -0.5 + x), $MachinePrecision], If[LessEqual[y, 1.2e-19], N[(x * 1.5), $MachinePrecision], N[(y * -0.5 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.20000000000000003e56 or 1.20000000000000011e-19 < y

   1. Initial program 99.9%

      \[x + \frac{x - y}{2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{x - y}{2} + x} \]

      2. frac-2neg N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(x - y\right)\right)}{\mathsf{neg}\left(2\right)}} + x \]

      3. div-inv N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \frac{1}{\mathsf{neg}\left(2\right)}} + x \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(\left(x - y\right)\right), \frac{1}{\mathsf{neg}\left(2\right)}, x\right)} \]

      5. neg-sub0 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{0 - \left(x - y\right)}, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(0 - \color{blue}{\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(0 - \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

      8. associate--r+ N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(0 - \left(\mathsf{neg}\left(y\right)\right)\right) - x}, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right)} - x, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{y} - x, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{y - x}, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(y - x, \frac{1}{\color{blue}{-2}}, x\right) \]

      13. metadata-eval 99.9

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{-0.5}, x\right) \]

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, -0.5, x\right)} \]

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{y}, \frac{-1}{2}, x\right) \]
   6. Step-by-step derivation

   7. Simplified 81.6%

      \[\leadsto \mathsf{fma}\left(\color{blue}{y}, -0.5, x\right) \]

   if -3.20000000000000003e56 < y < 1.20000000000000011e-19

   1. Initial program 99.7%

      \[x + \frac{x - y}{2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{3}{2} \cdot x} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{x \cdot \frac{3}{2}} \]

      2. *-lowering-*.f64 81.9

         \[\leadsto \color{blue}{x \cdot 1.5} \]

   5. Simplified 81.9%

      \[\leadsto \color{blue}{x \cdot 1.5} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 73.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+70}:\\ \;\;\;\;-0.5 \cdot y\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-18}:\\ \;\;\;\;x \cdot 1.5\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -8.6e+70) (* -0.5 y) (if (<= y 1.75e-18) (* x 1.5) (* -0.5 y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -8.6e+70) {
		tmp = -0.5 * y;
	} else if (y <= 1.75e-18) {
		tmp = x * 1.5;
	} else {
		tmp = -0.5 * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-8.6d+70)) then
        tmp = (-0.5d0) * y
    else if (y <= 1.75d-18) then
        tmp = x * 1.5d0
    else
        tmp = (-0.5d0) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -8.6e+70) {
		tmp = -0.5 * y;
	} else if (y <= 1.75e-18) {
		tmp = x * 1.5;
	} else {
		tmp = -0.5 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -8.6e+70:
		tmp = -0.5 * y
	elif y <= 1.75e-18:
		tmp = x * 1.5
	else:
		tmp = -0.5 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -8.6e+70)
		tmp = Float64(-0.5 * y);
	elseif (y <= 1.75e-18)
		tmp = Float64(x * 1.5);
	else
		tmp = Float64(-0.5 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -8.6e+70)
		tmp = -0.5 * y;
	elseif (y <= 1.75e-18)
		tmp = x * 1.5;
	else
		tmp = -0.5 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -8.6e+70], N[(-0.5 * y), $MachinePrecision], If[LessEqual[y, 1.75e-18], N[(x * 1.5), $MachinePrecision], N[(-0.5 * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.6000000000000002e70 or 1.7499999999999999e-18 < y

   1. Initial program 99.9%

      \[x + \frac{x - y}{2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot y} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 80.0

         \[\leadsto \color{blue}{-0.5 \cdot y} \]

   5. Simplified 80.0%

      \[\leadsto \color{blue}{-0.5 \cdot y} \]

   if -8.6000000000000002e70 < y < 1.7499999999999999e-18

   1. Initial program 99.7%

      \[x + \frac{x - y}{2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{3}{2} \cdot x} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{x \cdot \frac{3}{2}} \]

      2. *-lowering-*.f64 80.3

         \[\leadsto \color{blue}{x \cdot 1.5} \]

   5. Simplified 80.3%

      \[\leadsto \color{blue}{x \cdot 1.5} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 99.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - x, -0.5, x\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma (- y x) -0.5 x))

C

double code(double x, double y) {
	return fma((y - x), -0.5, x);
}

Julia

function code(x, y)
	return fma(Float64(y - x), -0.5, x)
end

Wolfram

code[x_, y_] := N[(N[(y - x), $MachinePrecision] * -0.5 + x), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[x + \frac{x - y}{2} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \color{blue}{\frac{x - y}{2} + x} \]

   2. frac-2neg N/A

      \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(x - y\right)\right)}{\mathsf{neg}\left(2\right)}} + x \]

   3. div-inv N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \frac{1}{\mathsf{neg}\left(2\right)}} + x \]

   4. accelerator-lowering-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(\left(x - y\right)\right), \frac{1}{\mathsf{neg}\left(2\right)}, x\right)} \]

   5. neg-sub0 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{0 - \left(x - y\right)}, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

   6. sub-neg N/A

      \[\leadsto \mathsf{fma}\left(0 - \color{blue}{\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

   7. +-commutative N/A

      \[\leadsto \mathsf{fma}\left(0 - \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

   8. associate--r+ N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(0 - \left(\mathsf{neg}\left(y\right)\right)\right) - x}, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

   9. neg-sub0 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right)} - x, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

   10. remove-double-neg N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{y} - x, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

   11. --lowering--.f64 N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{y - x}, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

   12. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(y - x, \frac{1}{\color{blue}{-2}}, x\right) \]

   13. metadata-eval 99.8

       \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{-0.5}, x\right) \]

4. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, -0.5, x\right)} \]
5. Add Preprocessing

Alternative 5: 51.6% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ -0.5 \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* -0.5 y))

C

double code(double x, double y) {
	return -0.5 * y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (-0.5d0) * y
end function

Java

public static double code(double x, double y) {
	return -0.5 * y;
}

Python

def code(x, y):
	return -0.5 * y

Julia

function code(x, y)
	return Float64(-0.5 * y)
end

MATLAB

function tmp = code(x, y)
	tmp = -0.5 * y;
end

Wolfram

code[x_, y_] := N[(-0.5 * y), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[x + \frac{x - y}{2} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{-1}{2} \cdot y} \]
4. Step-by-step derivation

   1. *-lowering-*.f64 49.3

      \[\leadsto \color{blue}{-0.5 \cdot y} \]

5. Simplified 49.3%

   \[\leadsto \color{blue}{-0.5 \cdot y} \]
6. Add Preprocessing

Alternative 6: 11.5% accurate, 18.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 x)

C

double code(double x, double y) {
	return x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x
end function

Java

public static double code(double x, double y) {
	return x;
}

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

function tmp = code(x, y)
	tmp = x;
end

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 99.8%

   \[x + \frac{x - y}{2} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \color{blue}{\frac{x - y}{2} + x} \]

   2. frac-2neg N/A

      \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left(x - y\right)\right)}{\mathsf{neg}\left(2\right)}} + x \]

   3. div-inv N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \frac{1}{\mathsf{neg}\left(2\right)}} + x \]

   4. accelerator-lowering-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(\left(x - y\right)\right), \frac{1}{\mathsf{neg}\left(2\right)}, x\right)} \]

   5. neg-sub0 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{0 - \left(x - y\right)}, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

   6. sub-neg N/A

      \[\leadsto \mathsf{fma}\left(0 - \color{blue}{\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

   7. +-commutative N/A

      \[\leadsto \mathsf{fma}\left(0 - \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

   8. associate--r+ N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(0 - \left(\mathsf{neg}\left(y\right)\right)\right) - x}, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

   9. neg-sub0 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right)} - x, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

   10. remove-double-neg N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{y} - x, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

   11. --lowering--.f64 N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{y - x}, \frac{1}{\mathsf{neg}\left(2\right)}, x\right) \]

   12. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(y - x, \frac{1}{\color{blue}{-2}}, x\right) \]

   13. metadata-eval 99.8

       \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{-0.5}, x\right) \]

4. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, -0.5, x\right)} \]

5. Taylor expanded in y around inf

   \[\leadsto \mathsf{fma}\left(\color{blue}{y}, \frac{-1}{2}, x\right) \]
6. Step-by-step derivation

7. Simplified 57.8%

   \[\leadsto \mathsf{fma}\left(\color{blue}{y}, -0.5, x\right) \]

8. Taylor expanded in y around 0

   \[\leadsto \color{blue}{x} \]
9. Step-by-step derivation

10. Simplified 11.9%

    \[\leadsto \color{blue}{x} \]
11. Add Preprocessing

Developer Target 1: 99.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ 1.5 \cdot x - 0.5 \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (* 1.5 x) (* 0.5 y)))

C

double code(double x, double y) {
	return (1.5 * x) - (0.5 * y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.5d0 * x) - (0.5d0 * y)
end function

Java

public static double code(double x, double y) {
	return (1.5 * x) - (0.5 * y);
}

Python

def code(x, y):
	return (1.5 * x) - (0.5 * y)

Julia

function code(x, y)
	return Float64(Float64(1.5 * x) - Float64(0.5 * y))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.5 * x) - (0.5 * y);
end

Wolfram

code[x_, y_] := N[(N[(1.5 * x), $MachinePrecision] - N[(0.5 * y), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024204 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Axis.Types:hBufferRect from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (- (* 3/2 x) (* 1/2 y)))

  (+ x (/ (- x y) 2.0)))