Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 5.4s

Alternatives: 9

Speedup: 1.0×

• 34.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (+ x (* (- y z) (- t x))))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (+ x (* (- y z) (- t x))))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (+ x (* (- y z) (- t x))))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \left(y - z\right) \cdot \left(t - x\right) \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 54.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+30}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+26}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+250} \lor \neg \left(z \leq 3 \cdot 10^{+258}\right):\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.6e+30)
   (* x z)
   (if (<= z 2.95e+26)
     (+ x (* y t))
     (if (or (<= z 2.7e+250) (not (<= z 3e+258)))
       (- x (* z t))
       (+ x (* x z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e+30) {
		tmp = x * z;
	} else if (z <= 2.95e+26) {
		tmp = x + (y * t);
	} else if ((z <= 2.7e+250) || !(z <= 3e+258)) {
		tmp = x - (z * t);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.6d+30)) then
        tmp = x * z
    else if (z <= 2.95d+26) then
        tmp = x + (y * t)
    else if ((z <= 2.7d+250) .or. (.not. (z <= 3d+258))) then
        tmp = x - (z * t)
    else
        tmp = x + (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e+30) {
		tmp = x * z;
	} else if (z <= 2.95e+26) {
		tmp = x + (y * t);
	} else if ((z <= 2.7e+250) || !(z <= 3e+258)) {
		tmp = x - (z * t);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.6e+30:
		tmp = x * z
	elif z <= 2.95e+26:
		tmp = x + (y * t)
	elif (z <= 2.7e+250) or not (z <= 3e+258):
		tmp = x - (z * t)
	else:
		tmp = x + (x * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.6e+30)
		tmp = Float64(x * z);
	elseif (z <= 2.95e+26)
		tmp = Float64(x + Float64(y * t));
	elseif ((z <= 2.7e+250) || !(z <= 3e+258))
		tmp = Float64(x - Float64(z * t));
	else
		tmp = Float64(x + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.6e+30)
		tmp = x * z;
	elseif (z <= 2.95e+26)
		tmp = x + (y * t);
	elseif ((z <= 2.7e+250) || ~((z <= 3e+258)))
		tmp = x - (z * t);
	else
		tmp = x + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.6e+30], N[(x * z), $MachinePrecision], If[LessEqual[z, 2.95e+26], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 2.7e+250], N[Not[LessEqual[z, 3e+258]], $MachinePrecision]], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.59999999999999986e30

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 74.0%

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

      1. mul-1-neg 74.0%

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

      2. distribute-rgt-neg-in 74.0%

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

      3. sub-neg 74.0%

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

      4. +-commutative 74.0%

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

      5. distribute-neg-in 74.0%

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

      6. remove-double-neg 74.0%

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

      7. sub-neg 74.0%

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

   5. Simplified 74.0%

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

      1. sub-neg 74.0%

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

      2. distribute-lft-in 72.0%

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

   7. Applied egg-rr 72.0%

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

   8. Taylor expanded in x around inf 48.1%

      \[\leadsto x + \color{blue}{x \cdot z} \]
   9. Step-by-step derivation

      1. *-commutative 48.1%

         \[\leadsto x + \color{blue}{z \cdot x} \]

   10. Simplified 48.1%

       \[\leadsto x + \color{blue}{z \cdot x} \]

   11. Taylor expanded in z around inf 48.1%

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

   if -1.59999999999999986e30 < z < 2.95000000000000015e26

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 87.9%

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

      1. *-commutative 87.9%

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

      2. *-commutative 87.9%

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

      3. associate-/l* 87.2%

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

      4. distribute-lft-out 87.2%

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

   5. Simplified 87.2%

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

   6. Taylor expanded in t around inf 58.1%

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

      1. associate-/l* 57.4%

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

   8. Simplified 57.4%

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

   9. Taylor expanded in y around inf 61.6%

      \[\leadsto x + \color{blue}{t \cdot y} \]

   if 2.95000000000000015e26 < z < 2.7e250 or 3e258 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 89.1%

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

      1. *-commutative 89.1%

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

      2. *-commutative 89.1%

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

      3. associate-/l* 89.0%

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

      4. distribute-lft-out 89.0%

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

   5. Simplified 89.0%

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

   6. Taylor expanded in t around inf 59.4%

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

      1. associate-/l* 51.5%

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

   8. Simplified 51.5%

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

   9. Taylor expanded in y around 0 66.3%

      \[\leadsto x + \color{blue}{-1 \cdot \left(t \cdot z\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 66.3%

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

       2. mul-1-neg 66.3%

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

   11. Simplified 66.3%

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

   if 2.7e250 < z < 3e258

   1. Initial program 99.7%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.7%

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

      1. mul-1-neg 99.7%

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

      2. distribute-rgt-neg-in 99.7%

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

      3. sub-neg 99.7%

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

      4. +-commutative 99.7%

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

      5. distribute-neg-in 99.7%

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

      6. remove-double-neg 99.7%

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

      7. sub-neg 99.7%

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

   5. Simplified 99.7%

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

      1. sub-neg 99.7%

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

      2. distribute-lft-in 100.0%

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

   7. Applied egg-rr 100.0%

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

   8. Taylor expanded in x around inf 92.4%

      \[\leadsto x + \color{blue}{x \cdot z} \]
   9. Step-by-step derivation

      1. *-commutative 92.4%

         \[\leadsto x + \color{blue}{z \cdot x} \]

   10. Simplified 92.4%

       \[\leadsto x + \color{blue}{z \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+30}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+26}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+250} \lor \neg \left(z \leq 3 \cdot 10^{+258}\right):\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+53} \lor \neg \left(z \leq 2.2 \cdot 10^{+44}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.2e+53) (not (<= z 2.2e+44)))
   (+ x (* z (- x t)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.2e+53) || !(z <= 2.2e+44)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5.2d+53)) .or. (.not. (z <= 2.2d+44))) then
        tmp = x + (z * (x - t))
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.2e+53) || !(z <= 2.2e+44)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.2e+53) or not (z <= 2.2e+44):
		tmp = x + (z * (x - t))
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.2e+53) || !(z <= 2.2e+44))
		tmp = Float64(x + Float64(z * Float64(x - t)));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.2e+53) || ~((z <= 2.2e+44)))
		tmp = x + (z * (x - t));
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.2e+53], N[Not[LessEqual[z, 2.2e+44]], $MachinePrecision]], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.19999999999999996e53 or 2.19999999999999996e44 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 85.7%

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

      1. mul-1-neg 85.7%

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

      2. distribute-rgt-neg-in 85.7%

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

      3. sub-neg 85.7%

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

      4. +-commutative 85.7%

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

      5. distribute-neg-in 85.7%

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

      6. remove-double-neg 85.7%

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

      7. sub-neg 85.7%

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

   5. Simplified 85.7%

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

   if -5.19999999999999996e53 < z < 2.19999999999999996e44

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 89.6%

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

      1. *-commutative 89.6%

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

   5. Simplified 89.6%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+53} \lor \neg \left(z \leq 2.2 \cdot 10^{+44}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+30} \lor \neg \left(z \leq 1.2 \cdot 10^{+55}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.25e+30) (not (<= z 1.2e+55)))
   (+ x (* z (- x t)))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.25e+30) || !(z <= 1.2e+55)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.25d+30)) .or. (.not. (z <= 1.2d+55))) then
        tmp = x + (z * (x - t))
    else
        tmp = x + ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.25e+30) || !(z <= 1.2e+55)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.25e+30) or not (z <= 1.2e+55):
		tmp = x + (z * (x - t))
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.25e+30) || !(z <= 1.2e+55))
		tmp = Float64(x + Float64(z * Float64(x - t)));
	else
		tmp = Float64(x + Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.25e+30) || ~((z <= 1.2e+55)))
		tmp = x + (z * (x - t));
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.25e+30], N[Not[LessEqual[z, 1.2e+55]], $MachinePrecision]], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25e30 or 1.2e55 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 83.7%

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

      1. mul-1-neg 83.7%

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

      2. distribute-rgt-neg-in 83.7%

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

      3. sub-neg 83.7%

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

      4. +-commutative 83.7%

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

      5. distribute-neg-in 83.7%

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

      6. remove-double-neg 83.7%

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

      7. sub-neg 83.7%

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

   5. Simplified 83.7%

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

   if -1.25e30 < z < 1.2e55

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 70.4%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+30} \lor \neg \left(z \leq 1.2 \cdot 10^{+55}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-131} \lor \neg \left(t \leq 8.8 \cdot 10^{-144}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -7.5e-131) (not (<= t 8.8e-144)))
   (+ x (* (- y z) t))
   (+ x (* x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7.5e-131) || !(t <= 8.8e-144)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-7.5d-131)) .or. (.not. (t <= 8.8d-144))) then
        tmp = x + ((y - z) * t)
    else
        tmp = x + (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7.5e-131) || !(t <= 8.8e-144)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -7.5e-131) or not (t <= 8.8e-144):
		tmp = x + ((y - z) * t)
	else:
		tmp = x + (x * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -7.5e-131) || !(t <= 8.8e-144))
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = Float64(x + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -7.5e-131) || ~((t <= 8.8e-144)))
		tmp = x + ((y - z) * t);
	else
		tmp = x + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -7.5e-131], N[Not[LessEqual[t, 8.8e-144]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.49999999999999964e-131 or 8.80000000000000025e-144 < t

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 74.6%

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

   if -7.49999999999999964e-131 < t < 8.80000000000000025e-144

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 64.0%

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

      1. mul-1-neg 64.0%

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

      2. distribute-rgt-neg-in 64.0%

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

      3. sub-neg 64.0%

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

      4. +-commutative 64.0%

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

      5. distribute-neg-in 64.0%

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

      6. remove-double-neg 64.0%

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

      7. sub-neg 64.0%

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

   5. Simplified 64.0%

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

      1. sub-neg 64.0%

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

      2. distribute-lft-in 64.0%

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

   7. Applied egg-rr 64.0%

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

   8. Taylor expanded in x around inf 57.1%

      \[\leadsto x + \color{blue}{x \cdot z} \]
   9. Step-by-step derivation

      1. *-commutative 57.1%

         \[\leadsto x + \color{blue}{z \cdot x} \]

   10. Simplified 57.1%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-131} \lor \neg \left(t \leq 8.8 \cdot 10^{-144}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+29} \lor \neg \left(z \leq 2.1 \cdot 10^{+51}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.7e+29) (not (<= z 2.1e+51))) (* x z) (+ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e+29) || !(z <= 2.1e+51)) {
		tmp = x * z;
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.7d+29)) .or. (.not. (z <= 2.1d+51))) then
        tmp = x * z
    else
        tmp = x + (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e+29) || !(z <= 2.1e+51)) {
		tmp = x * z;
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.7e+29) or not (z <= 2.1e+51):
		tmp = x * z
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.7e+29) || !(z <= 2.1e+51))
		tmp = Float64(x * z);
	else
		tmp = Float64(x + Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.7e+29) || ~((z <= 2.1e+51)))
		tmp = x * z;
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.7e+29], N[Not[LessEqual[z, 2.1e+51]], $MachinePrecision]], N[(x * z), $MachinePrecision], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.69999999999999991e29 or 2.1000000000000001e51 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 84.2%

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

      1. mul-1-neg 84.2%

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

      2. distribute-rgt-neg-in 84.2%

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

      3. sub-neg 84.2%

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

      4. +-commutative 84.2%

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

      5. distribute-neg-in 84.2%

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

      6. remove-double-neg 84.2%

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

      7. sub-neg 84.2%

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

   5. Simplified 84.2%

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

      1. sub-neg 84.2%

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

      2. distribute-lft-in 83.3%

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

   7. Applied egg-rr 83.3%

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

   8. Taylor expanded in x around inf 42.7%

      \[\leadsto x + \color{blue}{x \cdot z} \]
   9. Step-by-step derivation

      1. *-commutative 42.7%

         \[\leadsto x + \color{blue}{z \cdot x} \]

   10. Simplified 42.7%

       \[\leadsto x + \color{blue}{z \cdot x} \]

   11. Taylor expanded in z around inf 42.7%

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

   if -1.69999999999999991e29 < z < 2.1000000000000001e51

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 87.5%

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

      1. *-commutative 87.5%

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

      2. *-commutative 87.5%

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

      3. associate-/l* 86.9%

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

      4. distribute-lft-out 86.9%

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

   5. Simplified 86.9%

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

   6. Taylor expanded in t around inf 58.0%

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

      1. associate-/l* 57.3%

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

   8. Simplified 57.3%

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

   9. Taylor expanded in y around inf 60.7%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+29} \lor \neg \left(z \leq 2.1 \cdot 10^{+51}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+31}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+52}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.65e+31) (* x z) (if (<= z 2.2e+52) (+ x (* y t)) (+ x (* x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.65e+31) {
		tmp = x * z;
	} else if (z <= 2.2e+52) {
		tmp = x + (y * t);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.65d+31)) then
        tmp = x * z
    else if (z <= 2.2d+52) then
        tmp = x + (y * t)
    else
        tmp = x + (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.65e+31) {
		tmp = x * z;
	} else if (z <= 2.2e+52) {
		tmp = x + (y * t);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.65e+31:
		tmp = x * z
	elif z <= 2.2e+52:
		tmp = x + (y * t)
	else:
		tmp = x + (x * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.65e+31)
		tmp = Float64(x * z);
	elseif (z <= 2.2e+52)
		tmp = Float64(x + Float64(y * t));
	else
		tmp = Float64(x + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.65e+31)
		tmp = x * z;
	elseif (z <= 2.2e+52)
		tmp = x + (y * t);
	else
		tmp = x + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.65e+31], N[(x * z), $MachinePrecision], If[LessEqual[z, 2.2e+52], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.64999999999999996e31

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 74.0%

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

      1. mul-1-neg 74.0%

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

      2. distribute-rgt-neg-in 74.0%

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

      3. sub-neg 74.0%

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

      4. +-commutative 74.0%

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

      5. distribute-neg-in 74.0%

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

      6. remove-double-neg 74.0%

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

      7. sub-neg 74.0%

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

   5. Simplified 74.0%

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

      1. sub-neg 74.0%

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

      2. distribute-lft-in 72.0%

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

   7. Applied egg-rr 72.0%

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

   8. Taylor expanded in x around inf 48.1%

      \[\leadsto x + \color{blue}{x \cdot z} \]
   9. Step-by-step derivation

      1. *-commutative 48.1%

         \[\leadsto x + \color{blue}{z \cdot x} \]

   10. Simplified 48.1%

       \[\leadsto x + \color{blue}{z \cdot x} \]

   11. Taylor expanded in z around inf 48.1%

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

   if -1.64999999999999996e31 < z < 2.2e52

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 87.5%

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

      1. *-commutative 87.5%

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

      2. *-commutative 87.5%

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

      3. associate-/l* 86.9%

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

      4. distribute-lft-out 86.9%

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

   5. Simplified 86.9%

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

   6. Taylor expanded in t around inf 58.0%

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

      1. associate-/l* 57.3%

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

   8. Simplified 57.3%

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

   9. Taylor expanded in y around inf 60.7%

      \[\leadsto x + \color{blue}{t \cdot y} \]

   if 2.2e52 < z

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 94.3%

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

      1. mul-1-neg 94.3%

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

      2. distribute-rgt-neg-in 94.3%

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

      3. sub-neg 94.3%

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

      4. +-commutative 94.3%

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

      5. distribute-neg-in 94.3%

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

      6. remove-double-neg 94.3%

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

      7. sub-neg 94.3%

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

   5. Simplified 94.3%

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

      1. sub-neg 94.3%

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

      2. distribute-lft-in 94.3%

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

   7. Applied egg-rr 94.3%

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

   8. Taylor expanded in x around inf 37.5%

      \[\leadsto x + \color{blue}{x \cdot z} \]
   9. Step-by-step derivation

      1. *-commutative 37.5%

         \[\leadsto x + \color{blue}{z \cdot x} \]

   10. Simplified 37.5%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+31}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+52}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 37.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-5} \lor \neg \left(z \leq 0.215\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1e-5) (not (<= z 0.215))) (* x z) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1e-5) || !(z <= 0.215)) {
		tmp = x * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1d-5)) .or. (.not. (z <= 0.215d0))) then
        tmp = x * z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1e-5) || !(z <= 0.215)) {
		tmp = x * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1e-5) or not (z <= 0.215):
		tmp = x * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1e-5) || !(z <= 0.215))
		tmp = Float64(x * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1e-5) || ~((z <= 0.215)))
		tmp = x * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1e-5], N[Not[LessEqual[z, 0.215]], $MachinePrecision]], N[(x * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.00000000000000008e-5 or 0.214999999999999997 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 75.7%

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

      1. mul-1-neg 75.7%

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

      2. distribute-rgt-neg-in 75.7%

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

      3. sub-neg 75.7%

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

      4. +-commutative 75.7%

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

      5. distribute-neg-in 75.7%

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

      6. remove-double-neg 75.7%

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

      7. sub-neg 75.7%

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

   5. Simplified 75.7%

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

      1. sub-neg 75.7%

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

      2. distribute-lft-in 74.9%

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

   7. Applied egg-rr 74.9%

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

   8. Taylor expanded in x around inf 36.9%

      \[\leadsto x + \color{blue}{x \cdot z} \]
   9. Step-by-step derivation

      1. *-commutative 36.9%

         \[\leadsto x + \color{blue}{z \cdot x} \]

   10. Simplified 36.9%

       \[\leadsto x + \color{blue}{z \cdot x} \]

   11. Taylor expanded in z around inf 36.6%

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

   if -1.00000000000000008e-5 < z < 0.214999999999999997

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 38.2%

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

      1. mul-1-neg 38.2%

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

      2. distribute-rgt-neg-in 38.2%

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

      3. sub-neg 38.2%

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

      4. +-commutative 38.2%

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

      5. distribute-neg-in 38.2%

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

      6. remove-double-neg 38.2%

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

      7. sub-neg 38.2%

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

   5. Simplified 38.2%

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

      1. sub-neg 38.2%

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

      2. distribute-lft-in 38.2%

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

   7. Applied egg-rr 38.2%

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

   8. Taylor expanded in x around inf 32.5%

      \[\leadsto x + \color{blue}{x \cdot z} \]
   9. Step-by-step derivation

      1. *-commutative 32.5%

         \[\leadsto x + \color{blue}{z \cdot x} \]

   10. Simplified 32.5%

       \[\leadsto x + \color{blue}{z \cdot x} \]

   11. Taylor expanded in z around 0 32.2%

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

4. Final simplification 34.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-5} \lor \neg \left(z \leq 0.215\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 17.7% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 x)

C

double code(double x, double y, double z, double t) {
	return x;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x
end function

Java

public static double code(double x, double y, double z, double t) {
	return x;
}

Python

def code(x, y, z, t):
	return x

Julia

function code(x, y, z, t)
	return x
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 100.0%

   \[x + \left(y - z\right) \cdot \left(t - x\right) \]
2. Add Preprocessing

3. Taylor expanded in y around 0 56.2%

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

   1. mul-1-neg 56.2%

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

   2. distribute-rgt-neg-in 56.2%

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

   3. sub-neg 56.2%

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

   4. +-commutative 56.2%

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

   5. distribute-neg-in 56.2%

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

   6. remove-double-neg 56.2%

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

   7. sub-neg 56.2%

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

5. Simplified 56.2%

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

   1. sub-neg 56.2%

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

   2. distribute-lft-in 55.8%

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

7. Applied egg-rr 55.8%

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

8. Taylor expanded in x around inf 34.6%

   \[\leadsto x + \color{blue}{x \cdot z} \]
9. Step-by-step derivation

   1. *-commutative 34.6%

      \[\leadsto x + \color{blue}{z \cdot x} \]

10. Simplified 34.6%

    \[\leadsto x + \color{blue}{z \cdot x} \]

11. Taylor expanded in z around 0 18.0%

    \[\leadsto \color{blue}{x} \]
12. Add Preprocessing

Developer target: 96.1% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ x (+ (* t (- y z)) (* (- x) (- y z)))))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024103 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :alt
  (+ x (+ (* t (- y z)) (* (- x) (- y z))))

  (+ x (* (- y z) (- t x))))