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

Percentage Accurate: 85.0% → 97.0%

Time: 7.0s

Alternatives: 6

Speedup: 0.4×

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: 85.0% 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: 97.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := \frac{x\_m \cdot \left(y - z\right)}{y}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_0 \leq -2 \cdot 10^{+109}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{z}{y}\right) \cdot x\_m\\ \end{array} \end{array} \end{array} \]

FPCore

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 (/ (* x_m (- y z)) y)))
   (* x_s (if (<= t_0 -2e+109) t_0 (* (- 1.0 (/ z y)) x_m)))))

C

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 = (x_m * (y - z)) / y;
	double tmp;
	if (t_0 <= -2e+109) {
		tmp = t_0;
	} else {
		tmp = (1.0 - (z / y)) * x_m;
	}
	return x_s * tmp;
}

Fortran

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) :: tmp
    t_0 = (x_m * (y - z)) / y
    if (t_0 <= (-2d+109)) then
        tmp = t_0
    else
        tmp = (1.0d0 - (z / y)) * x_m
    end if
    code = x_s * tmp
end function

Java

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 = (x_m * (y - z)) / y;
	double tmp;
	if (t_0 <= -2e+109) {
		tmp = t_0;
	} else {
		tmp = (1.0 - (z / y)) * x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	t_0 = (x_m * (y - z)) / y
	tmp = 0
	if t_0 <= -2e+109:
		tmp = t_0
	else:
		tmp = (1.0 - (z / y)) * x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	t_0 = Float64(Float64(x_m * Float64(y - z)) / y)
	tmp = 0.0
	if (t_0 <= -2e+109)
		tmp = t_0;
	else
		tmp = Float64(Float64(1.0 - Float64(z / y)) * x_m);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	t_0 = (x_m * (y - z)) / y;
	tmp = 0.0;
	if (t_0 <= -2e+109)
		tmp = t_0;
	else
		tmp = (1.0 - (z / y)) * x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

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[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$0, -2e+109], t$95$0, N[(N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision] * x$95$m), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -1.99999999999999996e109

   1. Initial program 82.3%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   if -1.99999999999999996e109 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 86.5%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   4. Applied rewrites 96.8%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lower--.f64 N/A

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

      5. *-inverses N/A

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

      6. lower-/.f64 96.8

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

   6. Applied rewrites 96.8%

      \[\leadsto \color{blue}{\left(1 - \frac{z}{y}\right)} \cdot x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 96.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;\frac{x\_m \cdot \left(y - z\right)}{y} \leq -2 \cdot 10^{+109}:\\ \;\;\;\;\frac{x\_m \cdot \left(-z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{z}{y}\right) \cdot x\_m\\ \end{array} \end{array} \]

FPCore

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 (- y z)) y) -2e+109)
    (/ (* x_m (- z)) y)
    (* (- 1.0 (/ z y)) x_m))))

C

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 * (y - z)) / y) <= -2e+109) {
		tmp = (x_m * -z) / y;
	} else {
		tmp = (1.0 - (z / y)) * x_m;
	}
	return x_s * tmp;
}

Fortran

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) :: tmp
    if (((x_m * (y - z)) / y) <= (-2d+109)) then
        tmp = (x_m * -z) / y
    else
        tmp = (1.0d0 - (z / y)) * x_m
    end if
    code = x_s * tmp
end function

Java

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 tmp;
	if (((x_m * (y - z)) / y) <= -2e+109) {
		tmp = (x_m * -z) / y;
	} else {
		tmp = (1.0 - (z / y)) * x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if ((x_m * (y - z)) / y) <= -2e+109:
		tmp = (x_m * -z) / y
	else:
		tmp = (1.0 - (z / y)) * x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (Float64(Float64(x_m * Float64(y - z)) / y) <= -2e+109)
		tmp = Float64(Float64(x_m * Float64(-z)) / y);
	else
		tmp = Float64(Float64(1.0 - Float64(z / y)) * x_m);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (((x_m * (y - z)) / y) <= -2e+109)
		tmp = (x_m * -z) / y;
	else
		tmp = (1.0 - (z / y)) * x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

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[N[(N[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], -2e+109], N[(N[(x$95$m * (-z)), $MachinePrecision] / y), $MachinePrecision], N[(N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision] * x$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -1.99999999999999996e109

   1. Initial program 82.3%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 64.9

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

   5. Applied rewrites 64.9%

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

   if -1.99999999999999996e109 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 86.5%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   4. Applied rewrites 96.8%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lower--.f64 N/A

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

      5. *-inverses N/A

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

      6. lower-/.f64 96.8

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

   6. Applied rewrites 96.8%

      \[\leadsto \color{blue}{\left(1 - \frac{z}{y}\right)} \cdot x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2800000000 \lor \neg \left(z \leq 12000000\right):\\ \;\;\;\;\frac{-x\_m}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\_m\\ \end{array} \end{array} \]

FPCore

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 (or (<= z -2800000000.0) (not (<= z 12000000.0)))
    (* (/ (- x_m) y) z)
    (* 1.0 x_m))))

C

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 ((z <= -2800000000.0) || !(z <= 12000000.0)) {
		tmp = (-x_m / y) * z;
	} else {
		tmp = 1.0 * x_m;
	}
	return x_s * tmp;
}

Fortran

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) :: tmp
    if ((z <= (-2800000000.0d0)) .or. (.not. (z <= 12000000.0d0))) then
        tmp = (-x_m / y) * z
    else
        tmp = 1.0d0 * x_m
    end if
    code = x_s * tmp
end function

Java

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 tmp;
	if ((z <= -2800000000.0) || !(z <= 12000000.0)) {
		tmp = (-x_m / y) * z;
	} else {
		tmp = 1.0 * x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if (z <= -2800000000.0) or not (z <= 12000000.0):
		tmp = (-x_m / y) * z
	else:
		tmp = 1.0 * x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if ((z <= -2800000000.0) || !(z <= 12000000.0))
		tmp = Float64(Float64(Float64(-x_m) / y) * z);
	else
		tmp = Float64(1.0 * x_m);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if ((z <= -2800000000.0) || ~((z <= 12000000.0)))
		tmp = (-x_m / y) * z;
	else
		tmp = 1.0 * x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

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[Or[LessEqual[z, -2800000000.0], N[Not[LessEqual[z, 12000000.0]], $MachinePrecision]], N[(N[((-x$95$m) / y), $MachinePrecision] * z), $MachinePrecision], N[(1.0 * x$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -2.8e9 or 1.2e7 < z

   1. Initial program 90.2%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{y}} \cdot z \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{y}} \cdot z \]

      6. mul-1-neg N/A

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

      7. lower-neg.f64 83.3

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

   5. Applied rewrites 83.3%

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

   if -2.8e9 < z < 1.2e7

   1. Initial program 80.5%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 74.3%

      \[\leadsto \color{blue}{1} \cdot x \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2800000000 \lor \neg \left(z \leq 12000000\right):\\ \;\;\;\;\frac{-x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2800000000:\\ \;\;\;\;\frac{-x\_m}{y} \cdot z\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-56}:\\ \;\;\;\;1 \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m \cdot \left(-z\right)}{y}\\ \end{array} \end{array} \]

FPCore

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 (<= z -2800000000.0)
    (* (/ (- x_m) y) z)
    (if (<= z 3.4e-56) (* 1.0 x_m) (/ (* x_m (- z)) y)))))

C

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 (z <= -2800000000.0) {
		tmp = (-x_m / y) * z;
	} else if (z <= 3.4e-56) {
		tmp = 1.0 * x_m;
	} else {
		tmp = (x_m * -z) / y;
	}
	return x_s * tmp;
}

Fortran

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) :: tmp
    if (z <= (-2800000000.0d0)) then
        tmp = (-x_m / y) * z
    else if (z <= 3.4d-56) then
        tmp = 1.0d0 * x_m
    else
        tmp = (x_m * -z) / y
    end if
    code = x_s * tmp
end function

Java

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 tmp;
	if (z <= -2800000000.0) {
		tmp = (-x_m / y) * z;
	} else if (z <= 3.4e-56) {
		tmp = 1.0 * x_m;
	} else {
		tmp = (x_m * -z) / y;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if z <= -2800000000.0:
		tmp = (-x_m / y) * z
	elif z <= 3.4e-56:
		tmp = 1.0 * x_m
	else:
		tmp = (x_m * -z) / y
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (z <= -2800000000.0)
		tmp = Float64(Float64(Float64(-x_m) / y) * z);
	elseif (z <= 3.4e-56)
		tmp = Float64(1.0 * x_m);
	else
		tmp = Float64(Float64(x_m * Float64(-z)) / y);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (z <= -2800000000.0)
		tmp = (-x_m / y) * z;
	elseif (z <= 3.4e-56)
		tmp = 1.0 * x_m;
	else
		tmp = (x_m * -z) / y;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

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[z, -2800000000.0], N[(N[((-x$95$m) / y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 3.4e-56], N[(1.0 * x$95$m), $MachinePrecision], N[(N[(x$95$m * (-z)), $MachinePrecision] / y), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -2.8e9

   1. Initial program 93.8%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{y}} \cdot z \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{y}} \cdot z \]

      6. mul-1-neg N/A

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

      7. lower-neg.f64 89.5

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

   5. Applied rewrites 89.5%

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

   if -2.8e9 < z < 3.39999999999999982e-56

   1. Initial program 79.4%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 77.6%

      \[\leadsto \color{blue}{1} \cdot x \]

   if 3.39999999999999982e-56 < z

   1. Initial program 87.0%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 74.4

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

   5. Applied rewrites 74.4%

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

Alternative 5: 72.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2800000000:\\ \;\;\;\;\frac{-x\_m}{y} \cdot z\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-56}:\\ \;\;\;\;1 \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{y} \cdot x\_m\\ \end{array} \end{array} \]

FPCore

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 (<= z -2800000000.0)
    (* (/ (- x_m) y) z)
    (if (<= z 3.4e-56) (* 1.0 x_m) (* (/ (- z) y) x_m)))))

C

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 (z <= -2800000000.0) {
		tmp = (-x_m / y) * z;
	} else if (z <= 3.4e-56) {
		tmp = 1.0 * x_m;
	} else {
		tmp = (-z / y) * x_m;
	}
	return x_s * tmp;
}

Fortran

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) :: tmp
    if (z <= (-2800000000.0d0)) then
        tmp = (-x_m / y) * z
    else if (z <= 3.4d-56) then
        tmp = 1.0d0 * x_m
    else
        tmp = (-z / y) * x_m
    end if
    code = x_s * tmp
end function

Java

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 tmp;
	if (z <= -2800000000.0) {
		tmp = (-x_m / y) * z;
	} else if (z <= 3.4e-56) {
		tmp = 1.0 * x_m;
	} else {
		tmp = (-z / y) * x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if z <= -2800000000.0:
		tmp = (-x_m / y) * z
	elif z <= 3.4e-56:
		tmp = 1.0 * x_m
	else:
		tmp = (-z / y) * x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (z <= -2800000000.0)
		tmp = Float64(Float64(Float64(-x_m) / y) * z);
	elseif (z <= 3.4e-56)
		tmp = Float64(1.0 * x_m);
	else
		tmp = Float64(Float64(Float64(-z) / y) * x_m);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (z <= -2800000000.0)
		tmp = (-x_m / y) * z;
	elseif (z <= 3.4e-56)
		tmp = 1.0 * x_m;
	else
		tmp = (-z / y) * x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

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[z, -2800000000.0], N[(N[((-x$95$m) / y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 3.4e-56], N[(1.0 * x$95$m), $MachinePrecision], N[(N[((-z) / y), $MachinePrecision] * x$95$m), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -2.8e9

   1. Initial program 93.8%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{y}} \cdot z \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{y}} \cdot z \]

      6. mul-1-neg N/A

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

      7. lower-neg.f64 89.5

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

   5. Applied rewrites 89.5%

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

   if -2.8e9 < z < 3.39999999999999982e-56

   1. Initial program 79.4%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 77.6%

      \[\leadsto \color{blue}{1} \cdot x \]

   if 3.39999999999999982e-56 < z

   1. Initial program 87.0%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   4. Applied rewrites 96.3%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 73.4

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

   7. Applied rewrites 73.4%

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

Alternative 6: 51.6% accurate, 3.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \left(1 \cdot x\_m\right) \end{array} \]

FPCore

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 (* 1.0 x_m)))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	return x_s * (1.0 * x_m);
}

Fortran

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
    code = x_s * (1.0d0 * x_m)
end function

Java

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) {
	return x_s * (1.0 * x_m);
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	return x_s * (1.0 * x_m)

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	return Float64(x_s * Float64(1.0 * x_m))
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z)
	tmp = x_s * (1.0 * x_m);
end

Wolfram

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 * N[(1.0 * x$95$m), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 85.2%

   \[\frac{x \cdot \left(y - z\right)}{y} \]
2. Add Preprocessing

4. Applied rewrites 96.9%

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

5. Taylor expanded in y around inf

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

7. Applied rewrites 45.2%

   \[\leadsto \color{blue}{1} \cdot x \]
8. Add Preprocessing

Developer Target 1: 96.3% accurate, 0.5× 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 2024338 
(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))