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

Percentage Accurate: 85.1% → 96.4%
Time: 8.5s
Alternatives: 6
Speedup: 1.0×

Specification

?
\[\begin{array}{l} \\ \frac{x \cdot \left(y - z\right)}{y} \end{array} \]
(FPCore (x y z) :precision binary64 (/ (* x (- y z)) y))
double code(double x, double y, double z) {
	return (x * (y - z)) / y;
}
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
public static double code(double x, double y, double z) {
	return (x * (y - z)) / y;
}
def code(x, y, z):
	return (x * (y - z)) / y
function code(x, y, z)
	return Float64(Float64(x * Float64(y - z)) / y)
end
function tmp = code(x, y, z)
	tmp = (x * (y - z)) / y;
end
code[x_, y_, z_] := N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]
\begin{array}{l}

\\
\frac{x \cdot \left(y - z\right)}{y}
\end{array}

Sampling outcomes in binary64 precision:

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Accuracy vs Speed?

Herbie found 6 alternatives:

AlternativeAccuracySpeedup
The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Initial Program: 85.1% accurate, 1.0× speedup?

\[\begin{array}{l} \\ \frac{x \cdot \left(y - z\right)}{y} \end{array} \]
(FPCore (x y z) :precision binary64 (/ (* x (- y z)) y))
double code(double x, double y, double z) {
	return (x * (y - z)) / y;
}
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
public static double code(double x, double y, double z) {
	return (x * (y - z)) / y;
}
def code(x, y, z):
	return (x * (y - z)) / y
function code(x, y, z)
	return Float64(Float64(x * Float64(y - z)) / y)
end
function tmp = code(x, y, z)
	tmp = (x * (y - z)) / y;
end
code[x_, y_, z_] := N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]
\begin{array}{l}

\\
\frac{x \cdot \left(y - z\right)}{y}
\end{array}

Alternative 1: 96.4% accurate, 0.7× speedup?

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 1.35 \cdot 10^{-230}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot x\_m, \frac{-1}{y}, x\_m\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{y} \cdot x\_m\\ \end{array} \end{array} \]
x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= x_m 1.35e-230)
    (fma (* z x_m) (/ -1.0 y) x_m)
    (* (/ (- y z) y) x_m))))
x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (x_m <= 1.35e-230) {
		tmp = fma((z * x_m), (-1.0 / y), x_m);
	} else {
		tmp = ((y - z) / y) * x_m;
	}
	return x_s * tmp;
}
x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (x_m <= 1.35e-230)
		tmp = fma(Float64(z * x_m), Float64(-1.0 / y), x_m);
	else
		tmp = Float64(Float64(Float64(y - z) / y) * x_m);
	end
	return Float64(x_s * tmp)
end
x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[x$95$m, 1.35e-230], N[(N[(z * x$95$m), $MachinePrecision] * N[(-1.0 / y), $MachinePrecision] + x$95$m), $MachinePrecision], N[(N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision] * x$95$m), $MachinePrecision]]), $MachinePrecision]
\begin{array}{l}
x\_m = \left|x\right|
\\
x\_s = \mathsf{copysign}\left(1, x\right)

\\
x\_s \cdot \begin{array}{l}
\mathbf{if}\;x\_m \leq 1.35 \cdot 10^{-230}:\\
\;\;\;\;\mathsf{fma}\left(z \cdot x\_m, \frac{-1}{y}, x\_m\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{y - z}{y} \cdot x\_m\\


\end{array}
\end{array}
Derivation
  1. Split input into 2 regimes
  2. if x < 1.35000000000000006e-230

    1. Initial program 90.3%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
    2. Add Preprocessing
    3. Step-by-step derivation
      1. lift-/.f64N/A

        \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{y}} \]
      2. lift-*.f64N/A

        \[\leadsto \frac{\color{blue}{x \cdot \left(y - z\right)}}{y} \]
      3. associate-/l*N/A

        \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]
      4. clear-numN/A

        \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{y}{y - z}}} \]
      5. un-div-invN/A

        \[\leadsto \color{blue}{\frac{x}{\frac{y}{y - z}}} \]
      6. lower-/.f64N/A

        \[\leadsto \color{blue}{\frac{x}{\frac{y}{y - z}}} \]
      7. lower-/.f6484.1

        \[\leadsto \frac{x}{\color{blue}{\frac{y}{y - z}}} \]
    4. Applied rewrites84.1%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{y - z}}} \]
    5. Step-by-step derivation
      1. lift-/.f64N/A

        \[\leadsto \color{blue}{\frac{x}{\frac{y}{y - z}}} \]
      2. lift-/.f64N/A

        \[\leadsto \frac{x}{\color{blue}{\frac{y}{y - z}}} \]
      3. associate-/r/N/A

        \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(y - z\right)} \]
      4. lift--.f64N/A

        \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(y - z\right)} \]
      5. sub-negN/A

        \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(y + \left(\mathsf{neg}\left(z\right)\right)\right)} \]
      6. lift-neg.f64N/A

        \[\leadsto \frac{x}{y} \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right) \]
      7. +-commutativeN/A

        \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) + y\right)} \]
      8. distribute-lft-inN/A

        \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(\mathsf{neg}\left(z\right)\right) + \frac{x}{y} \cdot y} \]
      9. *-commutativeN/A

        \[\leadsto \frac{x}{y} \cdot \left(\mathsf{neg}\left(z\right)\right) + \color{blue}{y \cdot \frac{x}{y}} \]
      10. clear-numN/A

        \[\leadsto \frac{x}{y} \cdot \left(\mathsf{neg}\left(z\right)\right) + y \cdot \color{blue}{\frac{1}{\frac{y}{x}}} \]
      11. associate-/r/N/A

        \[\leadsto \frac{x}{y} \cdot \left(\mathsf{neg}\left(z\right)\right) + y \cdot \color{blue}{\left(\frac{1}{y} \cdot x\right)} \]
      12. associate-*r*N/A

        \[\leadsto \frac{x}{y} \cdot \left(\mathsf{neg}\left(z\right)\right) + \color{blue}{\left(y \cdot \frac{1}{y}\right) \cdot x} \]
      13. div-invN/A

        \[\leadsto \frac{x}{y} \cdot \left(\mathsf{neg}\left(z\right)\right) + \color{blue}{\frac{y}{y}} \cdot x \]
      14. *-inversesN/A

        \[\leadsto \frac{x}{y} \cdot \left(\mathsf{neg}\left(z\right)\right) + \color{blue}{1} \cdot x \]
      15. *-lft-identityN/A

        \[\leadsto \frac{x}{y} \cdot \left(\mathsf{neg}\left(z\right)\right) + \color{blue}{x} \]
      16. lower-fma.f64N/A

        \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{y}, \mathsf{neg}\left(z\right), x\right)} \]
      17. lower-/.f6491.0

        \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{x}{y}}, -z, x\right) \]
    6. Applied rewrites91.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{y}, -z, x\right)} \]
    7. Step-by-step derivation
      1. lift-fma.f64N/A

        \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(\mathsf{neg}\left(z\right)\right) + x} \]
      2. lift-/.f64N/A

        \[\leadsto \color{blue}{\frac{x}{y}} \cdot \left(\mathsf{neg}\left(z\right)\right) + x \]
      3. associate-*l/N/A

        \[\leadsto \color{blue}{\frac{x \cdot \left(\mathsf{neg}\left(z\right)\right)}{y}} + x \]
      4. frac-2negN/A

        \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(x \cdot \left(\mathsf{neg}\left(z\right)\right)\right)}{\mathsf{neg}\left(y\right)}} + x \]
      5. div-invN/A

        \[\leadsto \color{blue}{\left(\mathsf{neg}\left(x \cdot \left(\mathsf{neg}\left(z\right)\right)\right)\right) \cdot \frac{1}{\mathsf{neg}\left(y\right)}} + x \]
      6. lower-fma.f64N/A

        \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(x \cdot \left(\mathsf{neg}\left(z\right)\right)\right), \frac{1}{\mathsf{neg}\left(y\right)}, x\right)} \]
      7. *-commutativeN/A

        \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot x}\right), \frac{1}{\mathsf{neg}\left(y\right)}, x\right) \]
      8. distribute-lft-neg-inN/A

        \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) \cdot x}, \frac{1}{\mathsf{neg}\left(y\right)}, x\right) \]
      9. lift-neg.f64N/A

        \[\leadsto \mathsf{fma}\left(\left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right) \cdot x, \frac{1}{\mathsf{neg}\left(y\right)}, x\right) \]
      10. remove-double-negN/A

        \[\leadsto \mathsf{fma}\left(\color{blue}{z} \cdot x, \frac{1}{\mathsf{neg}\left(y\right)}, x\right) \]
      11. lower-*.f64N/A

        \[\leadsto \mathsf{fma}\left(\color{blue}{z \cdot x}, \frac{1}{\mathsf{neg}\left(y\right)}, x\right) \]
      12. neg-mul-1N/A

        \[\leadsto \mathsf{fma}\left(z \cdot x, \frac{1}{\color{blue}{-1 \cdot y}}, x\right) \]
      13. associate-/r*N/A

        \[\leadsto \mathsf{fma}\left(z \cdot x, \color{blue}{\frac{\frac{1}{-1}}{y}}, x\right) \]
      14. metadata-evalN/A

        \[\leadsto \mathsf{fma}\left(z \cdot x, \frac{\color{blue}{-1}}{y}, x\right) \]
      15. lower-/.f6497.3

        \[\leadsto \mathsf{fma}\left(z \cdot x, \color{blue}{\frac{-1}{y}}, x\right) \]
    8. Applied rewrites97.3%

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

    if 1.35000000000000006e-230 < x

    1. Initial program 84.2%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
    2. Add Preprocessing
    3. Step-by-step derivation
      1. lift-/.f64N/A

        \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{y}} \]
      2. lift-*.f64N/A

        \[\leadsto \frac{\color{blue}{x \cdot \left(y - z\right)}}{y} \]
      3. associate-/l*N/A

        \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]
      4. *-commutativeN/A

        \[\leadsto \color{blue}{\frac{y - z}{y} \cdot x} \]
      5. lower-*.f64N/A

        \[\leadsto \color{blue}{\frac{y - z}{y} \cdot x} \]
      6. lower-/.f6499.9

        \[\leadsto \color{blue}{\frac{y - z}{y}} \cdot x \]
    4. Applied rewrites99.9%

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

Alternative 2: 91.7% accurate, 0.3× speedup?

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := \frac{\left(y - z\right) \cdot x\_m}{y}\\ t_1 := \frac{x\_m}{y} \cdot \left(y - z\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_0 \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-128}:\\ \;\;\;\;1 \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]
x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (let* ((t_0 (/ (* (- y z) x_m) y)) (t_1 (* (/ x_m y) (- y z))))
   (* x_s (if (<= t_0 0.0) t_1 (if (<= t_0 5e-128) (* 1.0 x_m) t_1)))))
x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double t_0 = ((y - z) * x_m) / y;
	double t_1 = (x_m / y) * (y - z);
	double tmp;
	if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 5e-128) {
		tmp = 1.0 * x_m;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}
x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ((y - z) * x_m) / y
    t_1 = (x_m / y) * (y - z)
    if (t_0 <= 0.0d0) then
        tmp = t_1
    else if (t_0 <= 5d-128) then
        tmp = 1.0d0 * x_m
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function
x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double t_0 = ((y - z) * x_m) / y;
	double t_1 = (x_m / y) * (y - z);
	double tmp;
	if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 5e-128) {
		tmp = 1.0 * x_m;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}
x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	t_0 = ((y - z) * x_m) / y
	t_1 = (x_m / y) * (y - z)
	tmp = 0
	if t_0 <= 0.0:
		tmp = t_1
	elif t_0 <= 5e-128:
		tmp = 1.0 * x_m
	else:
		tmp = t_1
	return x_s * tmp
x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	t_0 = Float64(Float64(Float64(y - z) * x_m) / y)
	t_1 = Float64(Float64(x_m / y) * Float64(y - z))
	tmp = 0.0
	if (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 5e-128)
		tmp = Float64(1.0 * x_m);
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end
x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	t_0 = ((y - z) * x_m) / y;
	t_1 = (x_m / y) * (y - z);
	tmp = 0.0;
	if (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 5e-128)
		tmp = 1.0 * x_m;
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end
x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y - z), $MachinePrecision] * x$95$m), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x$95$m / y), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$0, 0.0], t$95$1, If[LessEqual[t$95$0, 5e-128], N[(1.0 * x$95$m), $MachinePrecision], t$95$1]]), $MachinePrecision]]]
\begin{array}{l}
x\_m = \left|x\right|
\\
x\_s = \mathsf{copysign}\left(1, x\right)

\\
\begin{array}{l}
t_0 := \frac{\left(y - z\right) \cdot x\_m}{y}\\
t_1 := \frac{x\_m}{y} \cdot \left(y - z\right)\\
x\_s \cdot \begin{array}{l}
\mathbf{if}\;t\_0 \leq 0:\\
\;\;\;\;t\_1\\

\mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-128}:\\
\;\;\;\;1 \cdot x\_m\\

\mathbf{else}:\\
\;\;\;\;t\_1\\


\end{array}
\end{array}
\end{array}
Derivation
  1. Split input into 2 regimes
  2. if (/.f64 (*.f64 x (-.f64 y z)) y) < 0.0 or 5.0000000000000001e-128 < (/.f64 (*.f64 x (-.f64 y z)) y)

    1. Initial program 82.8%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
    2. Add Preprocessing
    3. Step-by-step derivation
      1. lift-/.f64N/A

        \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{y}} \]
      2. lift-*.f64N/A

        \[\leadsto \frac{\color{blue}{x \cdot \left(y - z\right)}}{y} \]
      3. *-commutativeN/A

        \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot x}}{y} \]
      4. associate-/l*N/A

        \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{x}{y}} \]
      5. *-commutativeN/A

        \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(y - z\right)} \]
      6. lower-*.f64N/A

        \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(y - z\right)} \]
      7. lower-/.f6491.8

        \[\leadsto \color{blue}{\frac{x}{y}} \cdot \left(y - z\right) \]
    4. Applied rewrites91.8%

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

    if 0.0 < (/.f64 (*.f64 x (-.f64 y z)) y) < 5.0000000000000001e-128

    1. Initial program 98.7%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
    2. Add Preprocessing
    3. Step-by-step derivation
      1. lift-/.f64N/A

        \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{y}} \]
      2. lift-*.f64N/A

        \[\leadsto \frac{\color{blue}{x \cdot \left(y - z\right)}}{y} \]
      3. associate-/l*N/A

        \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]
      4. *-commutativeN/A

        \[\leadsto \color{blue}{\frac{y - z}{y} \cdot x} \]
      5. lower-*.f64N/A

        \[\leadsto \color{blue}{\frac{y - z}{y} \cdot x} \]
      6. lower-/.f6499.9

        \[\leadsto \color{blue}{\frac{y - z}{y}} \cdot x \]
    4. Applied rewrites99.9%

      \[\leadsto \color{blue}{\frac{y - z}{y} \cdot x} \]
    5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \cdot x \]
    6. Step-by-step derivation
      1. Applied rewrites90.7%

        \[\leadsto \color{blue}{1} \cdot x \]
    7. Recombined 2 regimes into one program.
    8. Final simplification91.7%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} \leq 0:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \leq 5 \cdot 10^{-128}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \end{array} \]
    9. Add Preprocessing

    Developer Target 1: 95.8% accurate, 0.5× speedup?

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

    Reproduce

    ?
    herbie shell --seed 2024230 
    (FPCore (x y z)
      :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
      :precision binary64
    
      :alt
      (! :herbie-platform default (if (< z -206020233192173900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- x (/ (* z x) y)) (if (< z 1693976601382852600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ x (/ y (- y z))) (* (- y z) (/ x y)))))
    
      (/ (* x (- y z)) y))