Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1

Percentage Accurate: 100.0% → 100.0%

Time: 3.5s

Alternatives: 5

Speedup: N/A×

Specification

Math

\[\begin{array}{l} \\ \left(\frac{x}{2} + y \cdot x\right) + z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (+ (/ x 2.0) (* y x)) z))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\frac{x}{2} + y \cdot x\right) + z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (+ (/ x 2.0) (* y x)) z))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ z + x \cdot \left(y - -0.5\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(\frac{x}{2} + y \cdot x\right) + z \]
2. Step-by-step derivation

   1. +-commutative 100.0%

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

   2. remove-double-neg 100.0%

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

   3. distribute-neg-in 100.0%

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

   4. distribute-frac-neg 100.0%

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

   5. distribute-rgt-neg-out 100.0%

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

   6. unsub-neg 100.0%

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

   7. distribute-rgt-neg-out 100.0%

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

   8. unsub-neg 100.0%

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

   9. neg-mul-1 100.0%

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

   10. associate-/l* 99.9%

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

   11. associate-/r/ 100.0%

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

   12. distribute-rgt-out-- 100.0%

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

   13. metadata-eval 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{z - x \cdot \left(-0.5 - y\right)} \]
4. Add Preprocessing

5. Final simplification 100.0%

   \[\leadsto z + x \cdot \left(y - -0.5\right) \]
6. Add Preprocessing

Alternative 2: 98.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -14500000 \lor \neg \left(y \leq 10^{-9}\right):\\ \;\;\;\;z + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -14500000.0) (not (<= y 1e-9))) (+ z (* x y)) (- z (* x -0.5))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -14500000.0) || !(y <= 1e-9)) {
		tmp = z + (x * y);
	} else {
		tmp = z - (x * -0.5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-14500000.0d0)) .or. (.not. (y <= 1d-9))) then
        tmp = z + (x * y)
    else
        tmp = z - (x * (-0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -14500000.0) || !(y <= 1e-9)) {
		tmp = z + (x * y);
	} else {
		tmp = z - (x * -0.5);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -14500000.0) or not (y <= 1e-9):
		tmp = z + (x * y)
	else:
		tmp = z - (x * -0.5)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -14500000.0) || !(y <= 1e-9))
		tmp = Float64(z + Float64(x * y));
	else
		tmp = Float64(z - Float64(x * -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -14500000.0) || ~((y <= 1e-9)))
		tmp = z + (x * y);
	else
		tmp = z - (x * -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -14500000.0], N[Not[LessEqual[y, 1e-9]], $MachinePrecision]], N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(z - N[(x * -0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.45e7 or 1.00000000000000006e-9 < y

   1. Initial program 100.0%

      \[\left(\frac{x}{2} + y \cdot x\right) + z \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. distribute-rgt-neg-out 100.0%

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

      6. unsub-neg 100.0%

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

      7. distribute-rgt-neg-out 100.0%

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

      8. unsub-neg 100.0%

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

      9. neg-mul-1 100.0%

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

      10. associate-/l* 100.0%

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

      11. associate-/r/ 100.0%

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

      12. distribute-rgt-out-- 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{z - x \cdot \left(-0.5 - y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 98.8%

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

      1. associate-*r* 98.8%

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

      2. *-commutative 98.8%

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

      3. mul-1-neg 98.8%

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

   7. Simplified 98.8%

      \[\leadsto z - \color{blue}{y \cdot \left(-x\right)} \]
   8. Step-by-step derivation

      1. sub-neg 98.8%

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

      2. +-commutative 98.8%

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

      3. distribute-rgt-neg-out 98.8%

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

      4. remove-double-neg 98.8%

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

   9. Applied egg-rr 98.8%

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

   if -1.45e7 < y < 1.00000000000000006e-9

   1. Initial program 100.0%

      \[\left(\frac{x}{2} + y \cdot x\right) + z \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. distribute-rgt-neg-out 100.0%

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

      6. unsub-neg 100.0%

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

      7. distribute-rgt-neg-out 100.0%

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

      8. unsub-neg 100.0%

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

      9. neg-mul-1 100.0%

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

      10. associate-/l* 99.9%

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

      11. associate-/r/ 100.0%

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

      12. distribute-rgt-out-- 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{z - x \cdot \left(-0.5 - y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 99.4%

      \[\leadsto z - \color{blue}{-0.5 \cdot x} \]
   6. Step-by-step derivation

      1. *-commutative 99.4%

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

   7. Simplified 99.4%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -14500000 \lor \neg \left(y \leq 10^{-9}\right):\\ \;\;\;\;z + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+27} \lor \neg \left(y \leq 9.5 \cdot 10^{+117}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.7e+27) (not (<= y 9.5e+117))) (* x y) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.7e+27) || !(y <= 9.5e+117)) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-3.7d+27)) .or. (.not. (y <= 9.5d+117))) then
        tmp = x * y
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.7e+27) || !(y <= 9.5e+117)) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.7e+27) or not (y <= 9.5e+117):
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.7e+27) || !(y <= 9.5e+117))
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.7e+27) || ~((y <= 9.5e+117)))
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.7e+27], N[Not[LessEqual[y, 9.5e+117]], $MachinePrecision]], N[(x * y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -3.70000000000000002e27 or 9.50000000000000041e117 < y

   1. Initial program 100.0%

      \[\left(\frac{x}{2} + y \cdot x\right) + z \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. distribute-rgt-neg-out 100.0%

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

      6. unsub-neg 100.0%

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

      7. distribute-rgt-neg-out 100.0%

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

      8. unsub-neg 100.0%

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

      9. neg-mul-1 100.0%

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

      10. associate-/l* 100.0%

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

      11. associate-/r/ 100.0%

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

      12. distribute-rgt-out-- 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{z - x \cdot \left(-0.5 - y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

      3. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 78.8%

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

   if -3.70000000000000002e27 < y < 9.50000000000000041e117

   1. Initial program 100.0%

      \[\left(\frac{x}{2} + y \cdot x\right) + z \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. distribute-rgt-neg-out 100.0%

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

      6. unsub-neg 100.0%

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

      7. distribute-rgt-neg-out 100.0%

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

      8. unsub-neg 100.0%

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

      9. neg-mul-1 100.0%

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

      10. associate-/l* 99.9%

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

      11. associate-/r/ 100.0%

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

      12. distribute-rgt-out-- 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{z - x \cdot \left(-0.5 - y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 64.8%

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

      1. associate-*r* 64.8%

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

      2. *-commutative 64.8%

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

      3. mul-1-neg 64.8%

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

   7. Simplified 64.8%

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

   8. Taylor expanded in z around inf 58.1%

      \[\leadsto \color{blue}{z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+27} \lor \neg \left(y \leq 9.5 \cdot 10^{+117}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ z + x \cdot y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ z (* x y)))

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return z + (x * y)

Julia

function code(x, y, z)
	return Float64(z + Float64(x * y))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(\frac{x}{2} + y \cdot x\right) + z \]
2. Step-by-step derivation

   1. +-commutative 100.0%

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

   2. remove-double-neg 100.0%

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

   3. distribute-neg-in 100.0%

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

   4. distribute-frac-neg 100.0%

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

   5. distribute-rgt-neg-out 100.0%

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

   6. unsub-neg 100.0%

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

   7. distribute-rgt-neg-out 100.0%

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

   8. unsub-neg 100.0%

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

   9. neg-mul-1 100.0%

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

   10. associate-/l* 99.9%

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

   11. associate-/r/ 100.0%

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

   12. distribute-rgt-out-- 100.0%

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

   13. metadata-eval 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{z - x \cdot \left(-0.5 - y\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around inf 79.9%

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

   1. associate-*r* 79.9%

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

   2. *-commutative 79.9%

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

   3. mul-1-neg 79.9%

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

7. Simplified 79.9%

   \[\leadsto z - \color{blue}{y \cdot \left(-x\right)} \]
8. Step-by-step derivation

   1. sub-neg 79.9%

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

   2. +-commutative 79.9%

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

   3. distribute-rgt-neg-out 79.9%

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

   4. remove-double-neg 79.9%

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

9. Applied egg-rr 79.9%

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

10. Final simplification 79.9%

    \[\leadsto z + x \cdot y \]
11. Add Preprocessing

Alternative 5: 40.3% accurate, 9.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 z)

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return z

Julia

function code(x, y, z)
	return z
end

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 100.0%

   \[\left(\frac{x}{2} + y \cdot x\right) + z \]
2. Step-by-step derivation

   1. +-commutative 100.0%

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

   2. remove-double-neg 100.0%

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

   3. distribute-neg-in 100.0%

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

   4. distribute-frac-neg 100.0%

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

   5. distribute-rgt-neg-out 100.0%

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

   6. unsub-neg 100.0%

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

   7. distribute-rgt-neg-out 100.0%

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

   8. unsub-neg 100.0%

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

   9. neg-mul-1 100.0%

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

   10. associate-/l* 99.9%

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

   11. associate-/r/ 100.0%

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

   12. distribute-rgt-out-- 100.0%

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

   13. metadata-eval 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{z - x \cdot \left(-0.5 - y\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around inf 79.9%

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

   1. associate-*r* 79.9%

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

   2. *-commutative 79.9%

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

   3. mul-1-neg 79.9%

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

7. Simplified 79.9%

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

8. Taylor expanded in z around inf 43.1%

   \[\leadsto \color{blue}{z} \]

9. Final simplification 43.1%

   \[\leadsto z \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024010 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2.0) (* y x)) z))