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

Percentage Accurate: 84.2% → 96.6%

Time: 6.3s

Alternatives: 9

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: 84.2% 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: 96.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;\frac{x\_m \cdot \left(y - z\right)}{y} \leq -4 \cdot 10^{+165}:\\ \;\;\;\;\frac{y - z}{\frac{y}{x\_m}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\frac{y}{y - z}}\\ \end{array} \end{array} \]

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) -4e+165)
    (/ (- y z) (/ y x_m))
    (/ x_m (/ y (- y z))))))

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) <= -4e+165) {
		tmp = (y - z) / (y / x_m);
	} else {
		tmp = x_m / (y / (y - z));
	}
	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) <= (-4d+165)) then
        tmp = (y - z) / (y / x_m)
    else
        tmp = x_m / (y / (y - z))
    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) <= -4e+165) {
		tmp = (y - z) / (y / x_m);
	} else {
		tmp = x_m / (y / (y - z));
	}
	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) <= -4e+165:
		tmp = (y - z) / (y / x_m)
	else:
		tmp = x_m / (y / (y - z))
	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) <= -4e+165)
		tmp = Float64(Float64(y - z) / Float64(y / x_m));
	else
		tmp = Float64(x_m / Float64(y / Float64(y - z)));
	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) <= -4e+165)
		tmp = (y - z) / (y / x_m);
	else
		tmp = x_m / (y / (y - z));
	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], -4e+165], N[(N[(y - z), $MachinePrecision] / N[(y / x$95$m), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -3.9999999999999996e165

   1. Initial program 71.8%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/r* N/A

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

      5. clear-num N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 92.4

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

   4. Applied rewrites 92.4%

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

   if -3.9999999999999996e165 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 87.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/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-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 97.8

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

   4. Applied rewrites 97.8%

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

Alternative 2: 90.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := \frac{x\_m \cdot \left(y - z\right)}{y}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_0 \leq 0 \lor \neg \left(t\_0 \leq 10^{-159}\right):\\ \;\;\;\;\frac{x\_m}{y} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{1}\\ \end{array} \end{array} \end{array} \]

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 (or (<= t_0 0.0) (not (<= t_0 1e-159)))
      (* (/ x_m y) (- y z))
      (/ x_m 1.0)))))

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 <= 0.0) || !(t_0 <= 1e-159)) {
		tmp = (x_m / y) * (y - z);
	} else {
		tmp = x_m / 1.0;
	}
	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 <= 0.0d0) .or. (.not. (t_0 <= 1d-159))) then
        tmp = (x_m / y) * (y - z)
    else
        tmp = x_m / 1.0d0
    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 <= 0.0) || !(t_0 <= 1e-159)) {
		tmp = (x_m / y) * (y - z);
	} else {
		tmp = x_m / 1.0;
	}
	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 <= 0.0) or not (t_0 <= 1e-159):
		tmp = (x_m / y) * (y - z)
	else:
		tmp = x_m / 1.0
	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 <= 0.0) || !(t_0 <= 1e-159))
		tmp = Float64(Float64(x_m / y) * Float64(y - z));
	else
		tmp = Float64(x_m / 1.0);
	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 <= 0.0) || ~((t_0 <= 1e-159)))
		tmp = (x_m / y) * (y - z);
	else
		tmp = x_m / 1.0;
	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[Or[LessEqual[t$95$0, 0.0], N[Not[LessEqual[t$95$0, 1e-159]], $MachinePrecision]], N[(N[(x$95$m / y), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x$95$m / 1.0), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < 0.0 or 9.99999999999999989e-160 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 82.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/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. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 90.8

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

   4. Applied rewrites 90.8%

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

   if 0.0 < (/.f64 (*.f64 x (-.f64 y z)) y) < 9.99999999999999989e-160

   1. Initial program 99.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/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-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 93.5%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq 0 \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \leq 10^{-159}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;\frac{x\_m \cdot \left(y - z\right)}{y} \leq -4 \cdot 10^{+165}:\\ \;\;\;\;\frac{-x\_m}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\frac{y}{y - z}}\\ \end{array} \end{array} \]

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) -4e+165)
    (* (/ (- x_m) y) z)
    (/ x_m (/ y (- y z))))))

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) <= -4e+165) {
		tmp = (-x_m / y) * z;
	} else {
		tmp = x_m / (y / (y - z));
	}
	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) <= (-4d+165)) then
        tmp = (-x_m / y) * z
    else
        tmp = x_m / (y / (y - z))
    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) <= -4e+165) {
		tmp = (-x_m / y) * z;
	} else {
		tmp = x_m / (y / (y - z));
	}
	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) <= -4e+165:
		tmp = (-x_m / y) * z
	else:
		tmp = x_m / (y / (y - z))
	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) <= -4e+165)
		tmp = Float64(Float64(Float64(-x_m) / y) * z);
	else
		tmp = Float64(x_m / Float64(y / Float64(y - z)));
	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) <= -4e+165)
		tmp = (-x_m / y) * z;
	else
		tmp = x_m / (y / (y - z));
	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], -4e+165], N[(N[((-x$95$m) / y), $MachinePrecision] * z), $MachinePrecision], N[(x$95$m / N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -3.9999999999999996e165

   1. Initial program 71.8%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 52.2

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

   5. Applied rewrites 52.2%

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

   if -3.9999999999999996e165 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 87.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/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-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 97.8

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

   4. Applied rewrites 97.8%

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

Alternative 4: 96.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;\frac{x\_m \cdot \left(y - z\right)}{y} \leq -4 \cdot 10^{+165}:\\ \;\;\;\;\frac{-x\_m}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-z}{y}, x\_m, x\_m\right)\\ \end{array} \end{array} \]

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) -4e+165)
    (* (/ (- x_m) y) z)
    (fma (/ (- z) y) x_m 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) <= -4e+165) {
		tmp = (-x_m / y) * z;
	} else {
		tmp = fma((-z / y), x_m, 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) <= -4e+165)
		tmp = Float64(Float64(Float64(-x_m) / y) * z);
	else
		tmp = fma(Float64(Float64(-z) / y), x_m, x_m);
	end
	return Float64(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], -4e+165], N[(N[((-x$95$m) / y), $MachinePrecision] * z), $MachinePrecision], N[(N[((-z) / y), $MachinePrecision] * x$95$m + x$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -3.9999999999999996e165

   1. Initial program 71.8%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 52.2

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

   5. Applied rewrites 52.2%

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

   if -3.9999999999999996e165 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 87.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/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-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 97.8

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

   4. Applied rewrites 97.8%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/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--.f64 N/A

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

      5. sub-neg N/A

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

      6. lift-neg.f64 N/A

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

      7. +-commutative N/A

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

      8. distribute-rgt-in N/A

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

      9. clear-num N/A

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

      10. associate-/r/ N/A

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

      11. associate-*r* N/A

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

      12. lift-neg.f64 N/A

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

      13. distribute-lft-neg-in N/A

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

      14. div-inv N/A

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

      15. clear-num N/A

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

      16. associate-/r/ N/A

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

      17. associate-*r* N/A

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

      18. div-inv N/A

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

      19. *-inverses N/A

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

      20. *-lft-identity N/A

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

      21. lower-fma.f64 N/A

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

      22. distribute-neg-frac N/A

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

      23. lift-neg.f64 N/A

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

      24. lower-/.f64 97.5

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

   6. Applied rewrites 97.5%

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

Alternative 5: 96.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;\frac{x\_m \cdot \left(y - z\right)}{y} \leq -4 \cdot 10^{+165}:\\ \;\;\;\;\frac{-x\_m}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{y} \cdot x\_m\\ \end{array} \end{array} \]

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 (<= (/ (* x_m (- y z)) y) -4e+165)
    (* (/ (- x_m) y) z)
    (* (/ (- y 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) <= -4e+165) {
		tmp = (-x_m / y) * z;
	} else {
		tmp = ((y - 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) <= (-4d+165)) then
        tmp = (-x_m / y) * z
    else
        tmp = ((y - 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) <= -4e+165) {
		tmp = (-x_m / y) * z;
	} else {
		tmp = ((y - 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) <= -4e+165:
		tmp = (-x_m / y) * z
	else:
		tmp = ((y - 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) <= -4e+165)
		tmp = Float64(Float64(Float64(-x_m) / y) * z);
	else
		tmp = Float64(Float64(Float64(y - 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) <= -4e+165)
		tmp = (-x_m / y) * z;
	else
		tmp = ((y - 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], -4e+165], N[(N[((-x$95$m) / y), $MachinePrecision] * z), $MachinePrecision], N[(N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision] * x$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -3.9999999999999996e165

   1. Initial program 71.8%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 52.2

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

   5. Applied rewrites 52.2%

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

   if -3.9999999999999996e165 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 87.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/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. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 97.4

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

   4. Applied rewrites 97.4%

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

Alternative 6: 70.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-48} \lor \neg \left(z \leq 3.8 \cdot 10^{+116}\right):\\ \;\;\;\;\frac{x\_m \cdot \left(-z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{1}\\ \end{array} \end{array} \]

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 -6.2e-48) (not (<= z 3.8e+116)))
    (/ (* x_m (- z)) y)
    (/ x_m 1.0))))

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 <= -6.2e-48) || !(z <= 3.8e+116)) {
		tmp = (x_m * -z) / y;
	} else {
		tmp = x_m / 1.0;
	}
	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 <= (-6.2d-48)) .or. (.not. (z <= 3.8d+116))) then
        tmp = (x_m * -z) / y
    else
        tmp = x_m / 1.0d0
    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 <= -6.2e-48) || !(z <= 3.8e+116)) {
		tmp = (x_m * -z) / y;
	} else {
		tmp = x_m / 1.0;
	}
	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 <= -6.2e-48) or not (z <= 3.8e+116):
		tmp = (x_m * -z) / y
	else:
		tmp = x_m / 1.0
	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 <= -6.2e-48) || !(z <= 3.8e+116))
		tmp = Float64(Float64(x_m * Float64(-z)) / y);
	else
		tmp = Float64(x_m / 1.0);
	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 <= -6.2e-48) || ~((z <= 3.8e+116)))
		tmp = (x_m * -z) / y;
	else
		tmp = x_m / 1.0;
	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, -6.2e-48], N[Not[LessEqual[z, 3.8e+116]], $MachinePrecision]], N[(N[(x$95$m * (-z)), $MachinePrecision] / y), $MachinePrecision], N[(x$95$m / 1.0), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -6.20000000000000033e-48 or 3.7999999999999999e116 < z

   1. Initial program 91.4%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 76.7

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

   5. Applied rewrites 76.7%

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

   if -6.20000000000000033e-48 < z < 3.7999999999999999e116

   1. Initial program 77.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/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-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 76.7%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-48} \lor \neg \left(z \leq 3.8 \cdot 10^{+116}\right):\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-48} \lor \neg \left(z \leq 3.8 \cdot 10^{+116}\right):\\ \;\;\;\;\frac{-x\_m}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{1}\\ \end{array} \end{array} \]

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 -6.2e-48) (not (<= z 3.8e+116)))
    (* (/ (- x_m) y) z)
    (/ x_m 1.0))))

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 <= -6.2e-48) || !(z <= 3.8e+116)) {
		tmp = (-x_m / y) * z;
	} else {
		tmp = x_m / 1.0;
	}
	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 <= (-6.2d-48)) .or. (.not. (z <= 3.8d+116))) then
        tmp = (-x_m / y) * z
    else
        tmp = x_m / 1.0d0
    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 <= -6.2e-48) || !(z <= 3.8e+116)) {
		tmp = (-x_m / y) * z;
	} else {
		tmp = x_m / 1.0;
	}
	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 <= -6.2e-48) or not (z <= 3.8e+116):
		tmp = (-x_m / y) * z
	else:
		tmp = x_m / 1.0
	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 <= -6.2e-48) || !(z <= 3.8e+116))
		tmp = Float64(Float64(Float64(-x_m) / y) * z);
	else
		tmp = Float64(x_m / 1.0);
	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 <= -6.2e-48) || ~((z <= 3.8e+116)))
		tmp = (-x_m / y) * z;
	else
		tmp = x_m / 1.0;
	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, -6.2e-48], N[Not[LessEqual[z, 3.8e+116]], $MachinePrecision]], N[(N[((-x$95$m) / y), $MachinePrecision] * z), $MachinePrecision], N[(x$95$m / 1.0), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -6.20000000000000033e-48 or 3.7999999999999999e116 < z

   1. Initial program 91.4%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 75.4

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

   5. Applied rewrites 75.4%

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

   if -6.20000000000000033e-48 < z < 3.7999999999999999e116

   1. Initial program 77.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/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-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 76.7%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-48} \lor \neg \left(z \leq 3.8 \cdot 10^{+116}\right):\\ \;\;\;\;\frac{-x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-48}:\\ \;\;\;\;\frac{-x\_m}{y} \cdot z\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+116}:\\ \;\;\;\;\frac{x\_m}{1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{y} \cdot x\_m\\ \end{array} \end{array} \]

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 -6.2e-48)
    (* (/ (- x_m) y) z)
    (if (<= z 3.8e+116) (/ x_m 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 (z <= -6.2e-48) {
		tmp = (-x_m / y) * z;
	} else if (z <= 3.8e+116) {
		tmp = x_m / 1.0;
	} 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 <= (-6.2d-48)) then
        tmp = (-x_m / y) * z
    else if (z <= 3.8d+116) then
        tmp = x_m / 1.0d0
    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 <= -6.2e-48) {
		tmp = (-x_m / y) * z;
	} else if (z <= 3.8e+116) {
		tmp = x_m / 1.0;
	} 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 <= -6.2e-48:
		tmp = (-x_m / y) * z
	elif z <= 3.8e+116:
		tmp = x_m / 1.0
	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 <= -6.2e-48)
		tmp = Float64(Float64(Float64(-x_m) / y) * z);
	elseif (z <= 3.8e+116)
		tmp = Float64(x_m / 1.0);
	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 <= -6.2e-48)
		tmp = (-x_m / y) * z;
	elseif (z <= 3.8e+116)
		tmp = x_m / 1.0;
	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, -6.2e-48], N[(N[((-x$95$m) / y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 3.8e+116], N[(x$95$m / 1.0), $MachinePrecision], N[(N[((-z) / y), $MachinePrecision] * x$95$m), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -6.20000000000000033e-48

   1. Initial program 93.7%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 75.6

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

   5. Applied rewrites 75.6%

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

   if -6.20000000000000033e-48 < z < 3.7999999999999999e116

   1. Initial program 77.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/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-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 76.7%

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

   if 3.7999999999999999e116 < z

   1. Initial program 85.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/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. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 91.3

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

   4. Applied rewrites 91.3%

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

   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 76.2

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

   7. Applied rewrites 76.2%

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

Alternative 9: 50.7% accurate, 1.7× speedup

Math

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

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 (/ x_m 1.0)))

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 * (x_m / 1.0);
}

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 * (x_m / 1.0d0)
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 * (x_m / 1.0);
}

Python

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

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	return Float64(x_s * Float64(x_m / 1.0))
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 * (x_m / 1.0);
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[(x$95$m / 1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 83.7%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/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-num N/A

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

   5. un-div-inv N/A

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

   6. lower-/.f64 N/A

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

   7. lower-/.f64 97.3

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

4. Applied rewrites 97.3%

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

5. Taylor expanded in y around inf

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

7. Applied rewrites 53.1%

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

Developer Target 1: 96.2% 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 2024323 
(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))