Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3

Percentage Accurate: 83.7% → 96.0%

Time: 7.8s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (- y z)) y))

C

double code(double x, double y, double z) {
	return (x * (y - z)) / 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 = (x * (y - z)) / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 83.7% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (- y z)) y))

C

double code(double x, double y, double z) {
	return (x * (y - z)) / 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 = (x * (y - z)) / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+95}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8.5e+95) (* (- y z) (/ x y)) (- x (/ x (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.5e+95) {
		tmp = (y - z) * (x / y);
	} else {
		tmp = x - (x / (y / 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 (z <= (-8.5d+95)) then
        tmp = (y - z) * (x / y)
    else
        tmp = x - (x / (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.5e+95) {
		tmp = (y - z) * (x / y);
	} else {
		tmp = x - (x / (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -8.5e+95:
		tmp = (y - z) * (x / y)
	else:
		tmp = x - (x / (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8.5e+95)
		tmp = Float64(Float64(y - z) * Float64(x / y));
	else
		tmp = Float64(x - Float64(x / Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -8.5e+95)
		tmp = (y - z) * (x / y);
	else
		tmp = x - (x / (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8.5e+95], N[(N[(y - z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x - N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5000000000000002e95

   1. Initial program 74.8%

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

      1. *-commutative 74.8%

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

      2. associate-*r/ 96.0%

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

   3. Simplified 96.0%

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

   if -8.5000000000000002e95 < z

   1. Initial program 85.3%

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

      1. --rgt-identity 85.3%

         \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{y} - 0} \]

      2. associate-*l/ 81.5%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(y - z\right)} - 0 \]

      3. sub-neg 81.5%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(y + \left(-z\right)\right)} - 0 \]

      4. distribute-rgt-in 76.7%

         \[\leadsto \color{blue}{\left(y \cdot \frac{x}{y} + \left(-z\right) \cdot \frac{x}{y}\right)} - 0 \]

      5. *-commutative 76.7%

         \[\leadsto \left(\color{blue}{\frac{x}{y} \cdot y} + \left(-z\right) \cdot \frac{x}{y}\right) - 0 \]

      6. distribute-lft-neg-out 76.7%

         \[\leadsto \left(\frac{x}{y} \cdot y + \color{blue}{\left(-z \cdot \frac{x}{y}\right)}\right) - 0 \]

      7. unsub-neg 76.7%

         \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot y - z \cdot \frac{x}{y}\right)} - 0 \]

      8. associate--r+ 76.7%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot y - \left(z \cdot \frac{x}{y} + 0\right)} \]

      9. associate-*l/ 80.4%

         \[\leadsto \color{blue}{\frac{x \cdot y}{y}} - \left(z \cdot \frac{x}{y} + 0\right) \]

      10. associate-/l* 93.2%

          \[\leadsto \color{blue}{\frac{x}{\frac{y}{y}}} - \left(z \cdot \frac{x}{y} + 0\right) \]

      11. *-inverses 93.2%

          \[\leadsto \frac{x}{\color{blue}{1}} - \left(z \cdot \frac{x}{y} + 0\right) \]

      12. /-rgt-identity 93.2%

          \[\leadsto \color{blue}{x} - \left(z \cdot \frac{x}{y} + 0\right) \]

      13. +-rgt-identity 93.2%

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

      14. *-commutative 93.2%

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

      15. associate-/r/ 97.2%

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

   3. Simplified 97.2%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+95}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \end{array} \]

Alternative 2: 70.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+27} \lor \neg \left(z \leq -1.9 \cdot 10^{-16} \lor \neg \left(z \leq -6.1 \cdot 10^{-71}\right) \land z \leq 2.5 \cdot 10^{+39}\right):\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2e+27)
         (not (or (<= z -1.9e-16) (and (not (<= z -6.1e-71)) (<= z 2.5e+39)))))
   (* x (/ (- z) y))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2e+27) || !((z <= -1.9e-16) || (!(z <= -6.1e-71) && (z <= 2.5e+39)))) {
		tmp = x * (-z / y);
	} else {
		tmp = x;
	}
	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 ((z <= (-2d+27)) .or. (.not. (z <= (-1.9d-16)) .or. (.not. (z <= (-6.1d-71))) .and. (z <= 2.5d+39))) then
        tmp = x * (-z / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2e+27) || !((z <= -1.9e-16) || (!(z <= -6.1e-71) && (z <= 2.5e+39)))) {
		tmp = x * (-z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2e+27) or not ((z <= -1.9e-16) or (not (z <= -6.1e-71) and (z <= 2.5e+39))):
		tmp = x * (-z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2e+27) || !((z <= -1.9e-16) || (!(z <= -6.1e-71) && (z <= 2.5e+39))))
		tmp = Float64(x * Float64(Float64(-z) / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2e+27) || ~(((z <= -1.9e-16) || (~((z <= -6.1e-71)) && (z <= 2.5e+39)))))
		tmp = x * (-z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2e+27], N[Not[Or[LessEqual[z, -1.9e-16], And[N[Not[LessEqual[z, -6.1e-71]], $MachinePrecision], LessEqual[z, 2.5e+39]]]], $MachinePrecision]], N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2e27 or -1.90000000000000006e-16 < z < -6.0999999999999998e-71 or 2.50000000000000008e39 < z

   1. Initial program 84.7%

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

      1. associate-*r/ 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in y around 0 68.7%

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

      1. neg-mul-1 68.7%

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

      2. distribute-neg-frac 68.7%

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

   6. Simplified 68.7%

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

   if -2e27 < z < -1.90000000000000006e-16 or -6.0999999999999998e-71 < z < 2.50000000000000008e39

   1. Initial program 81.3%

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

      1. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 82.8%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+27} \lor \neg \left(z \leq -1.9 \cdot 10^{-16} \lor \neg \left(z \leq -6.1 \cdot 10^{-71}\right) \land z \leq 2.5 \cdot 10^{+39}\right):\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 72.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+25} \lor \neg \left(z \leq -1.4 \cdot 10^{-15}\right) \land \left(z \leq -1.66 \cdot 10^{-71} \lor \neg \left(z \leq 1.25 \cdot 10^{+39}\right)\right):\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.5e+25)
         (and (not (<= z -1.4e-15))
              (or (<= z -1.66e-71) (not (<= z 1.25e+39)))))
   (* z (/ (- x) y))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.5e+25) || (!(z <= -1.4e-15) && ((z <= -1.66e-71) || !(z <= 1.25e+39)))) {
		tmp = z * (-x / y);
	} else {
		tmp = x;
	}
	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 ((z <= (-8.5d+25)) .or. (.not. (z <= (-1.4d-15))) .and. (z <= (-1.66d-71)) .or. (.not. (z <= 1.25d+39))) then
        tmp = z * (-x / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.5e+25) || (!(z <= -1.4e-15) && ((z <= -1.66e-71) || !(z <= 1.25e+39)))) {
		tmp = z * (-x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.5e+25) or (not (z <= -1.4e-15) and ((z <= -1.66e-71) or not (z <= 1.25e+39))):
		tmp = z * (-x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.5e+25) || (!(z <= -1.4e-15) && ((z <= -1.66e-71) || !(z <= 1.25e+39))))
		tmp = Float64(z * Float64(Float64(-x) / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -8.5e+25) || (~((z <= -1.4e-15)) && ((z <= -1.66e-71) || ~((z <= 1.25e+39)))))
		tmp = z * (-x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.5e+25], And[N[Not[LessEqual[z, -1.4e-15]], $MachinePrecision], Or[LessEqual[z, -1.66e-71], N[Not[LessEqual[z, 1.25e+39]], $MachinePrecision]]]], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -8.5000000000000007e25 or -1.40000000000000007e-15 < z < -1.6599999999999999e-71 or 1.25000000000000004e39 < z

   1. Initial program 84.7%

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

      1. associate-*r/ 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in y around 0 74.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 74.3%

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

      2. associate-*l/ 76.4%

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

      3. distribute-lft-neg-in 76.4%

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

      4. *-commutative 76.4%

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

      5. distribute-neg-frac 76.4%

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

   6. Simplified 76.4%

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

   if -8.5000000000000007e25 < z < -1.40000000000000007e-15 or -1.6599999999999999e-71 < z < 1.25000000000000004e39

   1. Initial program 81.3%

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

      1. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 82.8%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+25} \lor \neg \left(z \leq -1.4 \cdot 10^{-15}\right) \land \left(z \leq -1.66 \cdot 10^{-71} \lor \neg \left(z \leq 1.25 \cdot 10^{+39}\right)\right):\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 72.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \frac{-x}{y}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+22}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-71}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (/ (- x) y))))
   (if (<= z -5.2e+22)
     t_0
     (if (<= z -1.75e-15)
       x
       (if (<= z -6.1e-71) t_0 (if (<= z 1.75e+40) x (/ (* z (- x)) y)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-x / y);
	double tmp;
	if (z <= -5.2e+22) {
		tmp = t_0;
	} else if (z <= -1.75e-15) {
		tmp = x;
	} else if (z <= -6.1e-71) {
		tmp = t_0;
	} else if (z <= 1.75e+40) {
		tmp = x;
	} else {
		tmp = (z * -x) / y;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = z * (-x / y)
    if (z <= (-5.2d+22)) then
        tmp = t_0
    else if (z <= (-1.75d-15)) then
        tmp = x
    else if (z <= (-6.1d-71)) then
        tmp = t_0
    else if (z <= 1.75d+40) then
        tmp = x
    else
        tmp = (z * -x) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (-x / y);
	double tmp;
	if (z <= -5.2e+22) {
		tmp = t_0;
	} else if (z <= -1.75e-15) {
		tmp = x;
	} else if (z <= -6.1e-71) {
		tmp = t_0;
	} else if (z <= 1.75e+40) {
		tmp = x;
	} else {
		tmp = (z * -x) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-x / y)
	tmp = 0
	if z <= -5.2e+22:
		tmp = t_0
	elif z <= -1.75e-15:
		tmp = x
	elif z <= -6.1e-71:
		tmp = t_0
	elif z <= 1.75e+40:
		tmp = x
	else:
		tmp = (z * -x) / y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(Float64(-x) / y))
	tmp = 0.0
	if (z <= -5.2e+22)
		tmp = t_0;
	elseif (z <= -1.75e-15)
		tmp = x;
	elseif (z <= -6.1e-71)
		tmp = t_0;
	elseif (z <= 1.75e+40)
		tmp = x;
	else
		tmp = Float64(Float64(z * Float64(-x)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-x / y);
	tmp = 0.0;
	if (z <= -5.2e+22)
		tmp = t_0;
	elseif (z <= -1.75e-15)
		tmp = x;
	elseif (z <= -6.1e-71)
		tmp = t_0;
	elseif (z <= 1.75e+40)
		tmp = x;
	else
		tmp = (z * -x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+22], t$95$0, If[LessEqual[z, -1.75e-15], x, If[LessEqual[z, -6.1e-71], t$95$0, If[LessEqual[z, 1.75e+40], x, N[(N[(z * (-x)), $MachinePrecision] / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.2e22 or -1.75e-15 < z < -6.0999999999999998e-71

   1. Initial program 80.1%

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

      1. associate-*r/ 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in y around 0 71.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 71.0%

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

      2. associate-*l/ 75.1%

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

      3. distribute-lft-neg-in 75.1%

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

      4. *-commutative 75.1%

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

      5. distribute-neg-frac 75.1%

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

   6. Simplified 75.1%

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

   if -5.2e22 < z < -1.75e-15 or -6.0999999999999998e-71 < z < 1.75e40

   1. Initial program 81.3%

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

      1. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 82.8%

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

   if 1.75e40 < z

   1. Initial program 91.3%

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

      1. associate-*r/ 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in y around 0 78.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{y}} \]
   5. Step-by-step derivation

      1. associate-*r/ 78.9%

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

      2. mul-1-neg 78.9%

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

      3. distribute-rgt-neg-out 78.9%

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

   6. Simplified 78.9%

      \[\leadsto \color{blue}{\frac{x \cdot \left(-z\right)}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+22}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-71}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \end{array} \]

Alternative 5: 95.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+99}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.05e+99) (* (- y z) (/ x y)) (* x (/ (- y z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.05e+99) {
		tmp = (y - z) * (x / y);
	} else {
		tmp = x * ((y - z) / y);
	}
	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 (z <= (-1.05d+99)) then
        tmp = (y - z) * (x / y)
    else
        tmp = x * ((y - z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.05e+99) {
		tmp = (y - z) * (x / y);
	} else {
		tmp = x * ((y - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.05e+99:
		tmp = (y - z) * (x / y)
	else:
		tmp = x * ((y - z) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.05e+99)
		tmp = Float64(Float64(y - z) * Float64(x / y));
	else
		tmp = Float64(x * Float64(Float64(y - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.05e+99)
		tmp = (y - z) * (x / y);
	else
		tmp = x * ((y - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.05e+99], N[(N[(y - z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05000000000000005e99

   1. Initial program 74.4%

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

      1. *-commutative 74.4%

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

      2. associate-*r/ 96.0%

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

   3. Simplified 96.0%

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

   if -1.05000000000000005e99 < z

   1. Initial program 85.4%

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

      1. associate-*r/ 97.1%

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

   3. Simplified 97.1%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+99}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \end{array} \]

Alternative 6: 51.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.2 \cdot 10^{-97}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x 4.2e-97) x (* y (/ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 4.2e-97) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	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 (x <= 4.2d-97) then
        tmp = x
    else
        tmp = y * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 4.2e-97) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 4.2e-97:
		tmp = x
	else:
		tmp = y * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 4.2e-97)
		tmp = x;
	else
		tmp = Float64(y * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 4.2e-97)
		tmp = x;
	else
		tmp = y * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 4.2e-97], x, N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.2000000000000002e-97

   1. Initial program 88.2%

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

      1. associate-*r/ 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in y around inf 51.9%

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

   if 4.2000000000000002e-97 < x

   1. Initial program 74.3%

      \[\frac{x \cdot \left(y - z\right)}{y} \]

   2. Taylor expanded in y around inf 32.1%

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

      1. associate-/l* 51.0%

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

      2. associate-/r/ 56.9%

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

   4. Applied egg-rr 56.9%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.2 \cdot 10^{-97}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \]

Alternative 7: 96.3% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (* x (/ (- y z) y)))

C

double code(double x, double y, double z) {
	return x * ((y - z) / 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 = x * ((y - z) / y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.0%

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

   1. associate-*r/ 94.4%

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

3. Simplified 94.4%

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

4. Final simplification 94.4%

   \[\leadsto x \cdot \frac{y - z}{y} \]

Alternative 8: 51.0% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 83.0%

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

   1. associate-*r/ 94.4%

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

3. Simplified 94.4%

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

4. Taylor expanded in y around inf 51.6%

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

5. Final simplification 51.6%

   \[\leadsto x \]

Developer target: 96.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z < -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z < 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (< z -2.060202331921739e+104)
   (- x (/ (* z x) y))
   (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z < -2.060202331921739e+104) {
		tmp = x - ((z * x) / y);
	} else if (z < 1.6939766013828526e+213) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (y - z) * (x / y);
	}
	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 (z < (-2.060202331921739d+104)) then
        tmp = x - ((z * x) / y)
    else if (z < 1.6939766013828526d+213) then
        tmp = x / (y / (y - z))
    else
        tmp = (y - z) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z < -2.060202331921739e+104) {
		tmp = x - ((z * x) / y);
	} else if (z < 1.6939766013828526e+213) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (y - z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z < -2.060202331921739e+104:
		tmp = x - ((z * x) / y)
	elif z < 1.6939766013828526e+213:
		tmp = x / (y / (y - z))
	else:
		tmp = (y - z) * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z < -2.060202331921739e+104)
		tmp = Float64(x - Float64(Float64(z * x) / y));
	elseif (z < 1.6939766013828526e+213)
		tmp = Float64(x / Float64(y / Float64(y - z)));
	else
		tmp = Float64(Float64(y - z) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z < -2.060202331921739e+104)
		tmp = x - ((z * x) / y);
	elseif (z < 1.6939766013828526e+213)
		tmp = x / (y / (y - z));
	else
		tmp = (y - z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Less[z, -2.060202331921739e+104], N[(x - N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[Less[z, 1.6939766013828526e+213], N[(x / N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2023287 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< z -2.060202331921739e+104) (- x (/ (* z x) y)) (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

  (/ (* x (- y z)) y))