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

Percentage Accurate: 84.5% → 97.5%

Time: 7.5s

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: 84.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (y - z)) / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := \frac{\left(y - z\right) \cdot x\_m}{y}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_0 \leq 0:\\ \;\;\;\;\frac{x\_m}{y} \cdot \left(y - z\right)\\ \mathbf{elif}\;t\_0 \leq 10^{+281}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{y} \cdot x\_m\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (let* ((t_0 (/ (* (- y z) x_m) y)))
   (*
    x_s
    (if (<= t_0 0.0)
      (* (/ x_m y) (- y z))
      (if (<= t_0 1e+281) t_0 (* (/ (- 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 t_0 = ((y - z) * x_m) / y;
	double tmp;
	if (t_0 <= 0.0) {
		tmp = (x_m / y) * (y - z);
	} else if (t_0 <= 1e+281) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = ((y - z) * x_m) / y
    if (t_0 <= 0.0d0) then
        tmp = (x_m / y) * (y - z)
    else if (t_0 <= 1d+281) then
        tmp = t_0
    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 t_0 = ((y - z) * x_m) / y;
	double tmp;
	if (t_0 <= 0.0) {
		tmp = (x_m / y) * (y - z);
	} else if (t_0 <= 1e+281) {
		tmp = t_0;
	} 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):
	t_0 = ((y - z) * x_m) / y
	tmp = 0
	if t_0 <= 0.0:
		tmp = (x_m / y) * (y - z)
	elif t_0 <= 1e+281:
		tmp = t_0
	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)
	t_0 = Float64(Float64(Float64(y - z) * x_m) / y)
	tmp = 0.0
	if (t_0 <= 0.0)
		tmp = Float64(Float64(x_m / y) * Float64(y - z));
	elseif (t_0 <= 1e+281)
		tmp = t_0;
	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)
	t_0 = ((y - z) * x_m) / y;
	tmp = 0.0;
	if (t_0 <= 0.0)
		tmp = (x_m / y) * (y - z);
	elseif (t_0 <= 1e+281)
		tmp = t_0;
	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_] := Block[{t$95$0 = N[(N[(N[(y - z), $MachinePrecision] * x$95$m), $MachinePrecision] / y), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$0, 0.0], N[(N[(x$95$m / y), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1e+281], t$95$0, N[(N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision] * x$95$m), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < 0.0

   1. Initial program 85.2%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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. *-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 86.3

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

   4. Applied rewrites 86.3%

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

   if 0.0 < (/.f64 (*.f64 x (-.f64 y z)) y) < 1e281

   1. Initial program 99.7%

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

   if 1e281 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 56.5%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 98.0

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

   4. Applied rewrites 98.0%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} \leq 0:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \leq 10^{+281}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := \frac{\left(y - z\right) \cdot x\_m}{y}\\ t_1 := \frac{x\_m}{y} \cdot \left(y - z\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_0 \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 4 \cdot 10^{-91}:\\ \;\;\;\;1 \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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 (/ (* (- y z) x_m) y)) (t_1 (* (/ x_m y) (- y z))))
   (* x_s (if (<= t_0 0.0) t_1 (if (<= t_0 4e-91) (* 1.0 x_m) t_1)))))

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 = ((y - z) * x_m) / y;
	double t_1 = (x_m / y) * (y - z);
	double tmp;
	if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 4e-91) {
		tmp = 1.0 * x_m;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = ((y - z) * x_m) / y
    t_1 = (x_m / y) * (y - z)
    if (t_0 <= 0.0d0) then
        tmp = t_1
    else if (t_0 <= 4d-91) then
        tmp = 1.0d0 * x_m
    else
        tmp = t_1
    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 = ((y - z) * x_m) / y;
	double t_1 = (x_m / y) * (y - z);
	double tmp;
	if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 4e-91) {
		tmp = 1.0 * x_m;
	} else {
		tmp = t_1;
	}
	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 = ((y - z) * x_m) / y
	t_1 = (x_m / y) * (y - z)
	tmp = 0
	if t_0 <= 0.0:
		tmp = t_1
	elif t_0 <= 4e-91:
		tmp = 1.0 * x_m
	else:
		tmp = t_1
	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(y - z) * x_m) / y)
	t_1 = Float64(Float64(x_m / y) * Float64(y - z))
	tmp = 0.0
	if (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 4e-91)
		tmp = Float64(1.0 * x_m);
	else
		tmp = t_1;
	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 = ((y - z) * x_m) / y;
	t_1 = (x_m / y) * (y - z);
	tmp = 0.0;
	if (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 4e-91)
		tmp = 1.0 * x_m;
	else
		tmp = t_1;
	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[(N[(y - z), $MachinePrecision] * x$95$m), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x$95$m / y), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$0, 0.0], t$95$1, If[LessEqual[t$95$0, 4e-91], N[(1.0 * x$95$m), $MachinePrecision], t$95$1]]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < 0.0 or 4.00000000000000009e-91 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 83.1%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 89.7

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

   4. Applied rewrites 89.7%

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

   if 0.0 < (/.f64 (*.f64 x (-.f64 y z)) y) < 4.00000000000000009e-91

   1. Initial program 99.7%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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. *-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. Taylor expanded in z around 0

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

   7. Applied rewrites 72.2%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} \leq 0:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \leq 4 \cdot 10^{-91}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{-43}:\\ \;\;\;\;1 \cdot x\_m\\ \mathbf{elif}\;y \leq 31000000000:\\ \;\;\;\;\left(-z\right) \cdot \frac{x\_m}{y}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= y -7.6e-43)
    (* 1.0 x_m)
    (if (<= y 31000000000.0) (* (- z) (/ x_m y)) (* 1.0 x_m)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -7.6e-43) {
		tmp = 1.0 * x_m;
	} else if (y <= 31000000000.0) {
		tmp = -z * (x_m / y);
	} else {
		tmp = 1.0 * x_m;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-7.6d-43)) then
        tmp = 1.0d0 * x_m
    else if (y <= 31000000000.0d0) then
        tmp = -z * (x_m / y)
    else
        tmp = 1.0d0 * x_m
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -7.6e-43) {
		tmp = 1.0 * x_m;
	} else if (y <= 31000000000.0) {
		tmp = -z * (x_m / y);
	} else {
		tmp = 1.0 * x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if y <= -7.6e-43:
		tmp = 1.0 * x_m
	elif y <= 31000000000.0:
		tmp = -z * (x_m / y)
	else:
		tmp = 1.0 * x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (y <= -7.6e-43)
		tmp = Float64(1.0 * x_m);
	elseif (y <= 31000000000.0)
		tmp = Float64(Float64(-z) * Float64(x_m / y));
	else
		tmp = Float64(1.0 * x_m);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (y <= -7.6e-43)
		tmp = 1.0 * x_m;
	elseif (y <= 31000000000.0)
		tmp = -z * (x_m / y);
	else
		tmp = 1.0 * x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[y, -7.6e-43], N[(1.0 * x$95$m), $MachinePrecision], If[LessEqual[y, 31000000000.0], N[((-z) * N[(x$95$m / y), $MachinePrecision]), $MachinePrecision], N[(1.0 * x$95$m), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -7.59999999999999939e-43 or 3.1e10 < y

   1. Initial program 75.2%

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

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 82.0%

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

   if -7.59999999999999939e-43 < y < 3.1e10

   1. Initial program 94.2%

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

   3. Taylor expanded in z around inf

      \[\leadsto \frac{x \cdot \color{blue}{\left(-1 \cdot z\right)}}{y} \]
   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 77.6

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

   5. Applied rewrites 77.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 77.9

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

   7. Applied rewrites 77.9%

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

Alternative 4: 71.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{-43}:\\ \;\;\;\;1 \cdot x\_m\\ \mathbf{elif}\;y \leq 31000000000:\\ \;\;\;\;\frac{-z}{y} \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= y -7.6e-43)
    (* 1.0 x_m)
    (if (<= y 31000000000.0) (* (/ (- z) y) x_m) (* 1.0 x_m)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -7.6e-43) {
		tmp = 1.0 * x_m;
	} else if (y <= 31000000000.0) {
		tmp = (-z / y) * x_m;
	} else {
		tmp = 1.0 * x_m;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-7.6d-43)) then
        tmp = 1.0d0 * x_m
    else if (y <= 31000000000.0d0) then
        tmp = (-z / y) * x_m
    else
        tmp = 1.0d0 * x_m
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -7.6e-43) {
		tmp = 1.0 * x_m;
	} else if (y <= 31000000000.0) {
		tmp = (-z / y) * x_m;
	} else {
		tmp = 1.0 * x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if y <= -7.6e-43:
		tmp = 1.0 * x_m
	elif y <= 31000000000.0:
		tmp = (-z / y) * x_m
	else:
		tmp = 1.0 * x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (y <= -7.6e-43)
		tmp = Float64(1.0 * x_m);
	elseif (y <= 31000000000.0)
		tmp = Float64(Float64(Float64(-z) / y) * x_m);
	else
		tmp = Float64(1.0 * x_m);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (y <= -7.6e-43)
		tmp = 1.0 * x_m;
	elseif (y <= 31000000000.0)
		tmp = (-z / y) * x_m;
	else
		tmp = 1.0 * x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[y, -7.6e-43], N[(1.0 * x$95$m), $MachinePrecision], If[LessEqual[y, 31000000000.0], N[(N[((-z) / y), $MachinePrecision] * x$95$m), $MachinePrecision], N[(1.0 * x$95$m), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -7.59999999999999939e-43 or 3.1e10 < y

   1. Initial program 75.2%

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

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 82.0%

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

   if -7.59999999999999939e-43 < y < 3.1e10

   1. Initial program 94.2%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 71.3

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

   5. Applied rewrites 71.3%

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

Alternative 5: 96.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 8 \cdot 10^{-222}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-1}{y}, z \cdot x\_m, x\_m\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{y} \cdot x\_m\\ \end{array} \end{array} \]

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 8e-222) (fma (/ -1.0 y) (* z x_m) x_m) (* (/ (- 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 <= 8e-222) {
		tmp = fma((-1.0 / y), (z * x_m), x_m);
	} 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 (x_m <= 8e-222)
		tmp = fma(Float64(-1.0 / y), Float64(z * x_m), x_m);
	else
		tmp = Float64(Float64(Float64(y - z) / y) * 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[x$95$m, 8e-222], N[(N[(-1.0 / y), $MachinePrecision] * N[(z * x$95$m), $MachinePrecision] + x$95$m), $MachinePrecision], N[(N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision] * x$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 8.00000000000000038e-222

   1. Initial program 85.2%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 93.6

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

   4. Applied rewrites 93.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      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. lift--.f64 N/A

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

      7. sub-neg N/A

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

      8. lift-neg.f64 N/A

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

      9. +-commutative N/A

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

      10. distribute-rgt-in N/A

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

      11. lift-neg.f64 N/A

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

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

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

      13. clear-num N/A

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

      14. lift-/.f64 N/A

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

      15. div-inv N/A

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

      16. *-lft-identity N/A

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

      17. lift-/.f64 N/A

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

      18. div-inv N/A

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

      19. times-frac N/A

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

      20. unpow-1 N/A

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

      21. lift-pow.f64 N/A

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

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

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

      23. div-inv N/A

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

      24. remove-double-div N/A

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

      25. clear-num N/A

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

   6. Applied rewrites 94.8%

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

   if 8.00000000000000038e-222 < x

   1. Initial program 83.8%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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. 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 98.1

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

   4. Applied rewrites 98.1%

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

Alternative 6: 95.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{+58}:\\ \;\;\;\;\frac{y - z}{y} \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{y} \cdot \left(y - z\right)\\ \end{array} \end{array} \]

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 (<= z 2e+58) (* (/ (- 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 (z <= 2e+58) {
		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 (z <= 2d+58) 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 (z <= 2e+58) {
		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 z <= 2e+58:
		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 (z <= 2e+58)
		tmp = Float64(Float64(Float64(y - z) / y) * x_m);
	else
		tmp = Float64(Float64(x_m / 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 (z <= 2e+58)
		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[z, 2e+58], N[(N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision] * x$95$m), $MachinePrecision], N[(N[(x$95$m / y), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < 1.99999999999999989e58

   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. 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 97.6

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

   4. Applied rewrites 97.6%

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

   if 1.99999999999999989e58 < z

   1. Initial program 92.4%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 98.0

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

   4. Applied rewrites 98.0%

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

Alternative 7: 51.1% 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 84.6%

   \[\frac{x \cdot \left(y - z\right)}{y} \]
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 95.5

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

4. Applied rewrites 95.5%

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

5. Taylor expanded in z around 0

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

7. Applied rewrites 51.7%

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

Developer Target 1: 96.1% 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 2024254 
(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))