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

Percentage Accurate: 99.9% → 100.0%

Time: 5.8s

Alternatives: 7

Speedup: 1.0×

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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. div-sub 99.9%

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

   2. associate-+r- 99.9%

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

   3. remove-double-neg 99.9%

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

   4. distribute-frac-neg 99.9%

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

   5. sub-neg 99.9%

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

   6. neg-mul-1 99.9%

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

   7. *-commutative 99.9%

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

   8. associate-/l* 99.9%

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

   9. *-rgt-identity 99.9%

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

   10. metadata-eval 99.9%

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

   11. distribute-lft-out-- 99.9%

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

   12. fma-neg 100.0%

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

   13. metadata-eval 100.0%

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

   14. metadata-eval 100.0%

       \[\leadsto \mathsf{fma}\left(x, 1 - \color{blue}{-0.5}, -\frac{y}{2}\right) \]

   15. metadata-eval 100.0%

       \[\leadsto \mathsf{fma}\left(x, \color{blue}{1.5}, -\frac{y}{2}\right) \]

   16. distribute-frac-neg 100.0%

       \[\leadsto \mathsf{fma}\left(x, 1.5, \color{blue}{\frac{-y}{2}}\right) \]

   17. neg-mul-1 100.0%

       \[\leadsto \mathsf{fma}\left(x, 1.5, \frac{\color{blue}{-1 \cdot y}}{2}\right) \]

   18. *-commutative 100.0%

       \[\leadsto \mathsf{fma}\left(x, 1.5, \frac{\color{blue}{y \cdot -1}}{2}\right) \]

   19. associate-/l* 100.0%

       \[\leadsto \mathsf{fma}\left(x, 1.5, \color{blue}{y \cdot \frac{-1}{2}}\right) \]

   20. metadata-eval 100.0%

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

3. Simplified 100.0%

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

Alternative 2: 76.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+60} \lor \neg \left(x \leq 7.6 \cdot 10^{+69}\right):\\ \;\;\;\;x \cdot 1.5\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.5e+60) (not (<= x 7.6e+69))) (* x 1.5) (+ x (* y -0.5))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.5e+60) || !(x <= 7.6e+69)) {
		tmp = x * 1.5;
	} else {
		tmp = x + (y * -0.5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.5d+60)) .or. (.not. (x <= 7.6d+69))) then
        tmp = x * 1.5d0
    else
        tmp = x + (y * (-0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.5e+60) || !(x <= 7.6e+69)) {
		tmp = x * 1.5;
	} else {
		tmp = x + (y * -0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.5e+60) or not (x <= 7.6e+69):
		tmp = x * 1.5
	else:
		tmp = x + (y * -0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.5e+60) || !(x <= 7.6e+69))
		tmp = Float64(x * 1.5);
	else
		tmp = Float64(x + Float64(y * -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.5e+60) || ~((x <= 7.6e+69)))
		tmp = x * 1.5;
	else
		tmp = x + (y * -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.5e+60], N[Not[LessEqual[x, 7.6e+69]], $MachinePrecision]], N[(x * 1.5), $MachinePrecision], N[(x + N[(y * -0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4999999999999999e60 or 7.60000000000000055e69 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 82.1%

      \[\leadsto \color{blue}{1.5 \cdot x} \]
   4. Step-by-step derivation

      1. *-commutative 82.1%

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

   5. Simplified 82.1%

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

   if -1.4999999999999999e60 < x < 7.60000000000000055e69

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 77.2%

      \[\leadsto x + \color{blue}{-0.5 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+60} \lor \neg \left(x \leq 7.6 \cdot 10^{+69}\right):\\ \;\;\;\;x \cdot 1.5\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot -0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+59} \lor \neg \left(x \leq 4 \cdot 10^{+69}\right):\\ \;\;\;\;x \cdot 1.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.4e+59) (not (<= x 4e+69))) (* x 1.5) (* y -0.5)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.4e+59) || !(x <= 4e+69)) {
		tmp = x * 1.5;
	} else {
		tmp = y * -0.5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-2.4d+59)) .or. (.not. (x <= 4d+69))) then
        tmp = x * 1.5d0
    else
        tmp = y * (-0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -2.4e+59) || !(x <= 4e+69)) {
		tmp = x * 1.5;
	} else {
		tmp = y * -0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.4e+59) or not (x <= 4e+69):
		tmp = x * 1.5
	else:
		tmp = y * -0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.4e+59) || !(x <= 4e+69))
		tmp = Float64(x * 1.5);
	else
		tmp = Float64(y * -0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2.4e+59) || ~((x <= 4e+69)))
		tmp = x * 1.5;
	else
		tmp = y * -0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.4e+59], N[Not[LessEqual[x, 4e+69]], $MachinePrecision]], N[(x * 1.5), $MachinePrecision], N[(y * -0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.4000000000000002e59 or 4.0000000000000003e69 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 82.1%

      \[\leadsto \color{blue}{1.5 \cdot x} \]
   4. Step-by-step derivation

      1. *-commutative 82.1%

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

   5. Simplified 82.1%

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

   if -2.4000000000000002e59 < x < 4.0000000000000003e69

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. remove-double-neg 99.9%

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

      4. unsub-neg 99.9%

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

      5. div-sub 99.9%

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

      6. associate-+r- 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+r- 99.9%

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

      9. neg-mul-1 99.9%

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

      10. *-commutative 99.9%

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

      11. associate-/l* 99.9%

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

      12. metadata-eval 99.9%

          \[\leadsto y \cdot \color{blue}{-0.5} + \left(x - \frac{-x}{2}\right) \]

      13. *-rgt-identity 99.9%

          \[\leadsto y \cdot -0.5 + \left(\color{blue}{x \cdot 1} - \frac{-x}{2}\right) \]

      14. metadata-eval 99.9%

          \[\leadsto y \cdot -0.5 + \left(x \cdot \color{blue}{\left(--1\right)} - \frac{-x}{2}\right) \]

      15. neg-mul-1 99.9%

          \[\leadsto y \cdot -0.5 + \left(x \cdot \left(--1\right) - \frac{\color{blue}{-1 \cdot x}}{2}\right) \]

      16. *-commutative 99.9%

          \[\leadsto y \cdot -0.5 + \left(x \cdot \left(--1\right) - \frac{\color{blue}{x \cdot -1}}{2}\right) \]

      17. associate-/l* 99.9%

          \[\leadsto y \cdot -0.5 + \left(x \cdot \left(--1\right) - \color{blue}{x \cdot \frac{-1}{2}}\right) \]

      18. distribute-lft-out-- 99.9%

          \[\leadsto y \cdot -0.5 + \color{blue}{x \cdot \left(\left(--1\right) - \frac{-1}{2}\right)} \]

      19. metadata-eval 99.9%

          \[\leadsto y \cdot -0.5 + x \cdot \left(\color{blue}{1} - \frac{-1}{2}\right) \]

      20. metadata-eval 99.9%

          \[\leadsto y \cdot -0.5 + x \cdot \left(1 - \color{blue}{-0.5}\right) \]

      21. metadata-eval 99.9%

          \[\leadsto y \cdot -0.5 + x \cdot \color{blue}{1.5} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{y \cdot -0.5 + x \cdot 1.5} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 99.9%

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

   6. Taylor expanded in x around 0 72.9%

      \[\leadsto y \cdot \color{blue}{-0.5} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+59} \lor \neg \left(x \leq 4 \cdot 10^{+69}\right):\\ \;\;\;\;x \cdot 1.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. sub-neg 99.9%

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

   2. +-commutative 99.9%

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

   3. remove-double-neg 99.9%

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

   4. unsub-neg 99.9%

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

   5. div-sub 99.9%

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

   6. associate-+r- 99.9%

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

   7. +-commutative 99.9%

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

   8. associate-+r- 99.9%

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

   9. neg-mul-1 99.9%

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

   10. *-commutative 99.9%

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

   11. associate-/l* 99.9%

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

   12. metadata-eval 99.9%

       \[\leadsto y \cdot \color{blue}{-0.5} + \left(x - \frac{-x}{2}\right) \]

   13. *-rgt-identity 99.9%

       \[\leadsto y \cdot -0.5 + \left(\color{blue}{x \cdot 1} - \frac{-x}{2}\right) \]

   14. metadata-eval 99.9%

       \[\leadsto y \cdot -0.5 + \left(x \cdot \color{blue}{\left(--1\right)} - \frac{-x}{2}\right) \]

   15. neg-mul-1 99.9%

       \[\leadsto y \cdot -0.5 + \left(x \cdot \left(--1\right) - \frac{\color{blue}{-1 \cdot x}}{2}\right) \]

   16. *-commutative 99.9%

       \[\leadsto y \cdot -0.5 + \left(x \cdot \left(--1\right) - \frac{\color{blue}{x \cdot -1}}{2}\right) \]

   17. associate-/l* 99.9%

       \[\leadsto y \cdot -0.5 + \left(x \cdot \left(--1\right) - \color{blue}{x \cdot \frac{-1}{2}}\right) \]

   18. distribute-lft-out-- 99.9%

       \[\leadsto y \cdot -0.5 + \color{blue}{x \cdot \left(\left(--1\right) - \frac{-1}{2}\right)} \]

   19. metadata-eval 99.9%

       \[\leadsto y \cdot -0.5 + x \cdot \left(\color{blue}{1} - \frac{-1}{2}\right) \]

   20. metadata-eval 99.9%

       \[\leadsto y \cdot -0.5 + x \cdot \left(1 - \color{blue}{-0.5}\right) \]

   21. metadata-eval 99.9%

       \[\leadsto y \cdot -0.5 + x \cdot \color{blue}{1.5} \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{y \cdot -0.5 + x \cdot 1.5} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 5: 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]

Derivation

1. Initial program 99.9%

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

Alternative 6: 50.8% accurate, 2.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around inf 52.4%

   \[\leadsto \color{blue}{1.5 \cdot x} \]
4. Step-by-step derivation

   1. *-commutative 52.4%

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

5. Simplified 52.4%

   \[\leadsto \color{blue}{x \cdot 1.5} \]
6. Add Preprocessing

Alternative 7: 11.7% accurate, 7.0× 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 99.9%

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

3. Taylor expanded in x around 0 57.3%

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

4. Taylor expanded in x around inf 12.1%

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

Developer Target 1: 99.9% accurate, 1.0× 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 2024145 
(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)))