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

Percentage Accurate: 84.3% → 95.9%

Time: 6.5s

Alternatives: 7

Speedup: 0.8×

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: 84.3% 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: 95.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 1.4 \cdot 10^{-20}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x\_m}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{z}{y}\right) \cdot x\_m\\ \end{array} \end{array} \]

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 1.4e-20) (/ (* (- y z) x_m) 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 <= 1.4e-20) {
		tmp = ((y - z) * x_m) / 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 <= 1.4d-20) then
        tmp = ((y - z) * x_m) / 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 <= 1.4e-20) {
		tmp = ((y - z) * x_m) / 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 <= 1.4e-20:
		tmp = ((y - z) * x_m) / 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 (x_m <= 1.4e-20)
		tmp = Float64(Float64(Float64(y - z) * x_m) / 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 <= 1.4e-20)
		tmp = ((y - z) * x_m) / 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[x$95$m, 1.4e-20], N[(N[(N[(y - z), $MachinePrecision] * x$95$m), $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 x < 1.4000000000000001e-20

   1. Initial program 89.7%

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

   if 1.4000000000000001e-20 < x

   1. Initial program 81.0%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 99.9

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

   4. Applied rewrites 99.9%

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

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 99.9

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

   6. Applied rewrites 99.9%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.4 \cdot 10^{-20}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{z}{y}\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x\_m}{y} \leq -1 \cdot 10^{+92}:\\ \;\;\;\;\frac{-x\_m}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{z}{y}\right) \cdot x\_m\\ \end{array} \end{array} \]

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 (<= (/ (* (- y z) x_m) y) -1e+92)
    (* (/ (- x_m) y) z)
    (* (- 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 ((((y - z) * x_m) / y) <= -1e+92) {
		tmp = (-x_m / y) * z;
	} 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 ((((y - z) * x_m) / y) <= (-1d+92)) then
        tmp = (-x_m / y) * z
    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 ((((y - z) * x_m) / y) <= -1e+92) {
		tmp = (-x_m / y) * z;
	} 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 (((y - z) * x_m) / y) <= -1e+92:
		tmp = (-x_m / y) * z
	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(Float64(y - z) * x_m) / y) <= -1e+92)
		tmp = Float64(Float64(Float64(-x_m) / y) * z);
	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 ((((y - z) * x_m) / y) <= -1e+92)
		tmp = (-x_m / y) * z;
	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[(N[(y - z), $MachinePrecision] * x$95$m), $MachinePrecision] / y), $MachinePrecision], -1e+92], N[(N[((-x$95$m) / y), $MachinePrecision] * z), $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) < -1e92

   1. Initial program 80.8%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 67.8

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

   5. Applied rewrites 67.8%

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

   if -1e92 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 89.5%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 96.5

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

   4. Applied rewrites 96.5%

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

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 96.4

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

   6. Applied rewrites 96.4%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} \leq -1 \cdot 10^{+92}:\\ \;\;\;\;\frac{-x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{z}{y}\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-14}:\\ \;\;\;\;\frac{y - z}{y} \cdot x\_m\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-75}:\\ \;\;\;\;\frac{x\_m}{y} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{z}{y}\right) \cdot x\_m\\ \end{array} \end{array} \]

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 (<= y -5e-14)
    (* (/ (- y z) y) x_m)
    (if (<= y 1.8e-75) (* (/ x_m y) (- y z)) (* (- 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 (y <= -5e-14) {
		tmp = ((y - z) / y) * x_m;
	} else if (y <= 1.8e-75) {
		tmp = (x_m / y) * (y - z);
	} 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 (y <= (-5d-14)) then
        tmp = ((y - z) / y) * x_m
    else if (y <= 1.8d-75) then
        tmp = (x_m / y) * (y - z)
    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 (y <= -5e-14) {
		tmp = ((y - z) / y) * x_m;
	} else if (y <= 1.8e-75) {
		tmp = (x_m / y) * (y - z);
	} 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 y <= -5e-14:
		tmp = ((y - z) / y) * x_m
	elif y <= 1.8e-75:
		tmp = (x_m / y) * (y - z)
	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 (y <= -5e-14)
		tmp = Float64(Float64(Float64(y - z) / y) * x_m);
	elseif (y <= 1.8e-75)
		tmp = Float64(Float64(x_m / y) * Float64(y - z));
	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 (y <= -5e-14)
		tmp = ((y - z) / y) * x_m;
	elseif (y <= 1.8e-75)
		tmp = (x_m / y) * (y - z);
	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[y, -5e-14], N[(N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision] * x$95$m), $MachinePrecision], If[LessEqual[y, 1.8e-75], N[(N[(x$95$m / y), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision] * x$95$m), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -5.0000000000000002e-14

   1. Initial program 79.2%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 100.0

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

   4. Applied rewrites 100.0%

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

   if -5.0000000000000002e-14 < y < 1.8e-75

   1. Initial program 96.8%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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. 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 95.2

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

   4. Applied rewrites 95.2%

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

   if 1.8e-75 < y

   1. Initial program 78.0%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 99.8

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

   4. Applied rewrites 99.8%

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

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 99.8

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

   6. Applied rewrites 99.8%

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

Alternative 4: 96.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := \left(1 - \frac{z}{y}\right) \cdot x\_m\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+55}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-75}:\\ \;\;\;\;\frac{x\_m}{y} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \end{array} \]

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 (* (- 1.0 (/ z y)) x_m)))
   (*
    x_s
    (if (<= y -9e+55) t_0 (if (<= y 1.8e-75) (* (/ x_m y) (- y z)) t_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 = (1.0 - (z / y)) * x_m;
	double tmp;
	if (y <= -9e+55) {
		tmp = t_0;
	} else if (y <= 1.8e-75) {
		tmp = (x_m / y) * (y - z);
	} else {
		tmp = t_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 = (1.0d0 - (z / y)) * x_m
    if (y <= (-9d+55)) then
        tmp = t_0
    else if (y <= 1.8d-75) then
        tmp = (x_m / y) * (y - z)
    else
        tmp = t_0
    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 = (1.0 - (z / y)) * x_m;
	double tmp;
	if (y <= -9e+55) {
		tmp = t_0;
	} else if (y <= 1.8e-75) {
		tmp = (x_m / y) * (y - z);
	} else {
		tmp = t_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 = (1.0 - (z / y)) * x_m
	tmp = 0
	if y <= -9e+55:
		tmp = t_0
	elif y <= 1.8e-75:
		tmp = (x_m / y) * (y - z)
	else:
		tmp = t_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(1.0 - Float64(z / y)) * x_m)
	tmp = 0.0
	if (y <= -9e+55)
		tmp = t_0;
	elseif (y <= 1.8e-75)
		tmp = Float64(Float64(x_m / y) * Float64(y - z));
	else
		tmp = t_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 = (1.0 - (z / y)) * x_m;
	tmp = 0.0;
	if (y <= -9e+55)
		tmp = t_0;
	elseif (y <= 1.8e-75)
		tmp = (x_m / y) * (y - z);
	else
		tmp = t_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[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision] * x$95$m), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -9e+55], t$95$0, If[LessEqual[y, 1.8e-75], N[(N[(x$95$m / y), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision], t$95$0]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.99999999999999996e55 or 1.8e-75 < y

   1. Initial program 76.9%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 99.8

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

   4. Applied rewrites 99.8%

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

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 99.9

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

   6. Applied rewrites 99.9%

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

   if -8.99999999999999996e55 < y < 1.8e-75

   1. Initial program 96.4%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 95.7

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

   4. Applied rewrites 95.7%

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

Alternative 5: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+23}:\\ \;\;\;\;\frac{-x\_m}{y} \cdot z\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-71}:\\ \;\;\;\;1 \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-z\right) \cdot x\_m}{y}\\ \end{array} \end{array} \]

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 -1.35e+23)
    (* (/ (- x_m) y) z)
    (if (<= z 1.12e-71) (* 1.0 x_m) (/ (* (- z) x_m) 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 <= -1.35e+23) {
		tmp = (-x_m / y) * z;
	} else if (z <= 1.12e-71) {
		tmp = 1.0 * x_m;
	} else {
		tmp = (-z * x_m) / 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 <= (-1.35d+23)) then
        tmp = (-x_m / y) * z
    else if (z <= 1.12d-71) then
        tmp = 1.0d0 * x_m
    else
        tmp = (-z * x_m) / 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 <= -1.35e+23) {
		tmp = (-x_m / y) * z;
	} else if (z <= 1.12e-71) {
		tmp = 1.0 * x_m;
	} else {
		tmp = (-z * x_m) / 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 <= -1.35e+23:
		tmp = (-x_m / y) * z
	elif z <= 1.12e-71:
		tmp = 1.0 * x_m
	else:
		tmp = (-z * x_m) / 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 <= -1.35e+23)
		tmp = Float64(Float64(Float64(-x_m) / y) * z);
	elseif (z <= 1.12e-71)
		tmp = Float64(1.0 * x_m);
	else
		tmp = Float64(Float64(Float64(-z) * x_m) / 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 <= -1.35e+23)
		tmp = (-x_m / y) * z;
	elseif (z <= 1.12e-71)
		tmp = 1.0 * x_m;
	else
		tmp = (-z * x_m) / 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, -1.35e+23], N[(N[((-x$95$m) / y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 1.12e-71], N[(1.0 * x$95$m), $MachinePrecision], N[(N[((-z) * x$95$m), $MachinePrecision] / y), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -1.3499999999999999e23

   1. Initial program 91.0%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 87.1

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

   5. Applied rewrites 87.1%

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

   if -1.3499999999999999e23 < z < 1.1199999999999999e-71

   1. Initial program 86.6%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 100.0

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

   4. Applied rewrites 100.0%

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

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 100.0

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

   6. Applied rewrites 100.0%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 81.2%

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

   if 1.1199999999999999e-71 < z

   1. Initial program 86.0%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 71.0

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

   5. Applied rewrites 71.0%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+23}:\\ \;\;\;\;\frac{-x}{y} \cdot z\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-71}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-z\right) \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := \frac{-x\_m}{y} \cdot z\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+23}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-71}:\\ \;\;\;\;1 \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \end{array} \]

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)))
   (* x_s (if (<= z -1.35e+23) t_0 (if (<= z 1.12e-71) (* 1.0 x_m) t_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;
	double tmp;
	if (z <= -1.35e+23) {
		tmp = t_0;
	} else if (z <= 1.12e-71) {
		tmp = 1.0 * x_m;
	} else {
		tmp = t_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
    if (z <= (-1.35d+23)) then
        tmp = t_0
    else if (z <= 1.12d-71) then
        tmp = 1.0d0 * x_m
    else
        tmp = t_0
    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;
	double tmp;
	if (z <= -1.35e+23) {
		tmp = t_0;
	} else if (z <= 1.12e-71) {
		tmp = 1.0 * x_m;
	} else {
		tmp = t_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
	tmp = 0
	if z <= -1.35e+23:
		tmp = t_0
	elif z <= 1.12e-71:
		tmp = 1.0 * x_m
	else:
		tmp = t_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(Float64(-x_m) / y) * z)
	tmp = 0.0
	if (z <= -1.35e+23)
		tmp = t_0;
	elseif (z <= 1.12e-71)
		tmp = Float64(1.0 * x_m);
	else
		tmp = t_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;
	tmp = 0.0;
	if (z <= -1.35e+23)
		tmp = t_0;
	elseif (z <= 1.12e-71)
		tmp = 1.0 * x_m;
	else
		tmp = t_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) / y), $MachinePrecision] * z), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -1.35e+23], t$95$0, If[LessEqual[z, 1.12e-71], N[(1.0 * x$95$m), $MachinePrecision], t$95$0]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3499999999999999e23 or 1.1199999999999999e-71 < z

   1. Initial program 88.0%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 77.1

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

   5. Applied rewrites 77.1%

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

   if -1.3499999999999999e23 < z < 1.1199999999999999e-71

   1. Initial program 86.6%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 100.0

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

   4. Applied rewrites 100.0%

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

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 100.0

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

   6. Applied rewrites 100.0%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 81.2%

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

Alternative 7: 50.6% 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 87.3%

   \[\frac{x \cdot \left(y - z\right)}{y} \]
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 92.5

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

4. Applied rewrites 92.5%

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

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

   5. lower--.f64 N/A

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

   6. lower-/.f64 92.5

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

6. Applied rewrites 92.5%

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

7. Taylor expanded in y around inf

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

9. Applied rewrites 49.2%

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

Developer Target 1: 96.0% 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 2024295 
(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))