Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C

Percentage Accurate: 94.2% → 95.5%

Time: 6.3s

Alternatives: 10

Speedup: 0.5×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- (/ y z) (/ t (- 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - 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 * ((y / z) - (t / (1.0d0 - z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y / z) - (t / (1.0 - z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 94.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- (/ y z) (/ t (- 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - 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 * ((y / z) - (t / (1.0d0 - z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y / z) - (t / (1.0 - z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 95.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+284}:\\ \;\;\;\;t_1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ y z) (/ t (- 1.0 z)))))
   (if (<= t_1 5e+284) (* t_1 x) (* y (/ x z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double tmp;
	if (t_1 <= 5e+284) {
		tmp = t_1 * x;
	} else {
		tmp = y * (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) :: t_1
    real(8) :: tmp
    t_1 = (y / z) - (t / (1.0d0 - z))
    if (t_1 <= 5d+284) then
        tmp = t_1 * x
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double tmp;
	if (t_1 <= 5e+284) {
		tmp = t_1 * x;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) - (t / (1.0 - z))
	tmp = 0
	if t_1 <= 5e+284:
		tmp = t_1 * x
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) - Float64(t / Float64(1.0 - z)))
	tmp = 0.0
	if (t_1 <= 5e+284)
		tmp = Float64(t_1 * x);
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) - (t / (1.0 - z));
	tmp = 0.0;
	if (t_1 <= 5e+284)
		tmp = t_1 * x;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+284], N[(t$95$1 * x), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 4.9999999999999999e284

   1. Initial program 97.0%

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

   if 4.9999999999999999e284 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

   1. Initial program 69.5%

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

   2. Taylor expanded in z around inf 67.3%

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

      1. *-commutative 67.3%

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

      2. associate-/l* 49.2%

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

      3. neg-mul-1 49.2%

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

   4. Simplified 49.2%

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

   5. Taylor expanded in y around inf 99.9%

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

      1. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq 5 \cdot 10^{+284}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1 - z}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 2: 64.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+94}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+122}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+203}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.5e+94)
   (* y (/ x z))
   (if (<= t 5.5e+122)
     (* (/ y z) x)
     (if (<= t 3.6e+203) (* x (- t)) (* x (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e+94) {
		tmp = y * (x / z);
	} else if (t <= 5.5e+122) {
		tmp = (y / z) * x;
	} else if (t <= 3.6e+203) {
		tmp = x * -t;
	} else {
		tmp = x * (t / 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 <= (-1.5d+94)) then
        tmp = y * (x / z)
    else if (t <= 5.5d+122) then
        tmp = (y / z) * x
    else if (t <= 3.6d+203) then
        tmp = x * -t
    else
        tmp = x * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e+94) {
		tmp = y * (x / z);
	} else if (t <= 5.5e+122) {
		tmp = (y / z) * x;
	} else if (t <= 3.6e+203) {
		tmp = x * -t;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.5e+94:
		tmp = y * (x / z)
	elif t <= 5.5e+122:
		tmp = (y / z) * x
	elif t <= 3.6e+203:
		tmp = x * -t
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.5e+94)
		tmp = Float64(y * Float64(x / z));
	elseif (t <= 5.5e+122)
		tmp = Float64(Float64(y / z) * x);
	elseif (t <= 3.6e+203)
		tmp = Float64(x * Float64(-t));
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.5e+94)
		tmp = y * (x / z);
	elseif (t <= 5.5e+122)
		tmp = (y / z) * x;
	elseif (t <= 3.6e+203)
		tmp = x * -t;
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.5e+94], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+122], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, 3.6e+203], N[(x * (-t)), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.5e94

   1. Initial program 90.7%

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

   2. Taylor expanded in z around inf 52.9%

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

      1. *-commutative 52.9%

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

      2. associate-/l* 55.1%

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

      3. neg-mul-1 55.1%

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

   4. Simplified 55.1%

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

   5. Taylor expanded in y around inf 50.3%

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

      1. associate-*r/ 52.7%

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

   7. Simplified 52.7%

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

   if -1.5e94 < t < 5.4999999999999998e122

   1. Initial program 95.3%

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

   2. Taylor expanded in y around inf 76.8%

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

      1. associate-*l/ 79.0%

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

   4. Simplified 79.0%

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

   if 5.4999999999999998e122 < t < 3.59999999999999982e203

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 89.0%

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

      1. mul-1-neg 89.0%

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

      2. associate-/l* 82.8%

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

      3. associate-/r/ 88.9%

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

      4. distribute-rgt-neg-in 88.9%

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

   4. Simplified 88.9%

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

   5. Taylor expanded in z around 0 71.5%

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

      1. mul-1-neg 71.5%

         \[\leadsto \color{blue}{-t \cdot x} \]

      2. distribute-lft-neg-out 71.5%

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

      3. *-commutative 71.5%

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

   7. Simplified 71.5%

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

   if 3.59999999999999982e203 < t

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 69.0%

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

      1. sub-neg 69.0%

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

      2. remove-double-neg 69.0%

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

      3. neg-mul-1 69.0%

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

      4. distribute-neg-in 69.0%

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

      5. neg-mul-1 69.0%

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

      6. sub-neg 69.0%

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

      7. distribute-lft-neg-in 69.0%

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

      8. distribute-neg-frac 69.0%

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

      9. associate-/l* 55.3%

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

      10. associate-/r/ 78.9%

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

      11. distribute-lft-neg-in 78.9%

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

   4. Simplified 78.9%

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

   5. Taylor expanded in y around 0 72.2%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+94}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+122}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+203}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 3: 73.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+206}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.2e+29)
   (* x (* y (/ 1.0 z)))
   (if (<= z 5e+53)
     (* x (- (/ y z) t))
     (if (<= z 3.8e+206) (/ x (/ z t)) (* (/ y z) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.2e+29) {
		tmp = x * (y * (1.0 / z));
	} else if (z <= 5e+53) {
		tmp = x * ((y / z) - t);
	} else if (z <= 3.8e+206) {
		tmp = x / (z / t);
	} else {
		tmp = (y / z) * 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 <= (-6.2d+29)) then
        tmp = x * (y * (1.0d0 / z))
    else if (z <= 5d+53) then
        tmp = x * ((y / z) - t)
    else if (z <= 3.8d+206) then
        tmp = x / (z / t)
    else
        tmp = (y / z) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.2e+29) {
		tmp = x * (y * (1.0 / z));
	} else if (z <= 5e+53) {
		tmp = x * ((y / z) - t);
	} else if (z <= 3.8e+206) {
		tmp = x / (z / t);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.2e+29:
		tmp = x * (y * (1.0 / z))
	elif z <= 5e+53:
		tmp = x * ((y / z) - t)
	elif z <= 3.8e+206:
		tmp = x / (z / t)
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.2e+29)
		tmp = Float64(x * Float64(y * Float64(1.0 / z)));
	elseif (z <= 5e+53)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	elseif (z <= 3.8e+206)
		tmp = Float64(x / Float64(z / t));
	else
		tmp = Float64(Float64(y / z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.2e+29)
		tmp = x * (y * (1.0 / z));
	elseif (z <= 5e+53)
		tmp = x * ((y / z) - t);
	elseif (z <= 3.8e+206)
		tmp = x / (z / t);
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.2e+29], N[(x * N[(y * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+53], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+206], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.1999999999999998e29

   1. Initial program 97.6%

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

   2. Taylor expanded in y around inf 68.6%

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

      1. div-inv 68.7%

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

      2. *-commutative 68.7%

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

      3. associate-*l* 70.7%

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

   4. Applied egg-rr 70.7%

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

   if -6.1999999999999998e29 < z < 5.0000000000000004e53

   1. Initial program 94.2%

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

   2. Taylor expanded in z around 0 86.9%

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

      1. associate-*l/ 85.1%

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

      2. associate-*r* 85.1%

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

      3. neg-mul-1 85.1%

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

      4. distribute-rgt-out 88.4%

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

      5. unsub-neg 88.4%

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

   4. Simplified 88.4%

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

   if 5.0000000000000004e53 < z < 3.7999999999999999e206

   1. Initial program 96.9%

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

   2. Taylor expanded in z around inf 92.2%

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

      1. *-commutative 92.2%

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

      2. associate-/l* 96.9%

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

      3. neg-mul-1 96.9%

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

   4. Simplified 96.9%

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

   5. Taylor expanded in y around 0 63.6%

      \[\leadsto \frac{x}{\color{blue}{\frac{z}{t}}} \]

   if 3.7999999999999999e206 < z

   1. Initial program 95.5%

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

   2. Taylor expanded in y around inf 72.8%

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

      1. associate-*l/ 77.2%

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

   4. Simplified 77.2%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+206}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]

Alternative 4: 93.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.0)))
   (* x (/ (+ y t) z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = x * ((y + t) / z);
	} 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 <= (-1.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * ((y + t) / z)
    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 <= -1.0) || !(z <= 1.0)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.0):
		tmp = x * ((y + t) / z)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1.0))
		tmp = Float64(x * Float64(Float64(y + t) / z));
	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 <= -1.0) || ~((z <= 1.0)))
		tmp = x * ((y + t) / z);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 97.3%

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

   2. Taylor expanded in z around inf 89.4%

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

      1. sub-neg 89.4%

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

      2. remove-double-neg 89.4%

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

      3. neg-mul-1 89.4%

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

      4. distribute-neg-in 89.4%

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

      5. neg-mul-1 89.4%

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

      6. sub-neg 89.4%

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

      7. distribute-lft-neg-in 89.4%

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

      8. distribute-neg-frac 89.4%

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

      9. associate-/l* 79.7%

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

      10. associate-/r/ 95.6%

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

      11. distribute-lft-neg-in 95.6%

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

   4. Simplified 95.6%

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

   if -1 < z < 1

   1. Initial program 93.6%

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

   2. Taylor expanded in z around 0 91.8%

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

      1. associate-*l/ 89.0%

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

      2. associate-*r* 89.0%

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

      3. neg-mul-1 89.0%

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

      4. distribute-rgt-out 92.7%

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

      5. unsub-neg 92.7%

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

   4. Simplified 92.7%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 5: 93.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.0)
   (* x (/ (+ y t) z))
   (if (<= z 1.0) (* x (- (/ y z) t)) (/ x (/ z (+ y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * ((y + t) / z);
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x / (z / (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 <= (-1.0d0)) then
        tmp = x * ((y + t) / z)
    else if (z <= 1.0d0) then
        tmp = x * ((y / z) - t)
    else
        tmp = x / (z / (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 <= -1.0) {
		tmp = x * ((y + t) / z);
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x / (z / (y + t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.0:
		tmp = x * ((y + t) / z)
	elif z <= 1.0:
		tmp = x * ((y / z) - t)
	else:
		tmp = x / (z / (y + t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(x * Float64(Float64(y + t) / z));
	elseif (z <= 1.0)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(x / Float64(z / Float64(y + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = x * ((y + t) / z);
	elseif (z <= 1.0)
		tmp = x * ((y / z) - t);
	else
		tmp = x / (z / (y + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.0], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1

   1. Initial program 97.8%

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

   2. Taylor expanded in z around inf 89.4%

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

      1. sub-neg 89.4%

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

      2. remove-double-neg 89.4%

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

      3. neg-mul-1 89.4%

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

      4. distribute-neg-in 89.4%

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

      5. neg-mul-1 89.4%

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

      6. sub-neg 89.4%

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

      7. distribute-lft-neg-in 89.4%

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

      8. distribute-neg-frac 89.4%

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

      9. associate-/l* 77.1%

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

      10. associate-/r/ 94.8%

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

      11. distribute-lft-neg-in 94.8%

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

   4. Simplified 94.8%

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

   if -1 < z < 1

   1. Initial program 93.6%

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

   2. Taylor expanded in z around 0 91.8%

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

      1. associate-*l/ 89.0%

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

      2. associate-*r* 89.0%

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

      3. neg-mul-1 89.0%

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

      4. distribute-rgt-out 92.7%

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

      5. unsub-neg 92.7%

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

   4. Simplified 92.7%

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

   if 1 < z

   1. Initial program 96.9%

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

   2. Taylor expanded in z around inf 89.4%

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

      1. *-commutative 89.4%

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

      2. associate-/l* 96.2%

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

      3. neg-mul-1 96.2%

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

   4. Simplified 96.2%

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

   5. Taylor expanded in z around 0 96.2%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \end{array} \]

Alternative 6: 93.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02:\\ \;\;\;\;x \cdot \left(\left(y + t\right) \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.02)
   (* x (* (+ y t) (/ 1.0 z)))
   (if (<= z 1.0) (* x (- (/ y z) t)) (/ x (/ z (+ y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.02) {
		tmp = x * ((y + t) * (1.0 / z));
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x / (z / (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 <= (-1.02d0)) then
        tmp = x * ((y + t) * (1.0d0 / z))
    else if (z <= 1.0d0) then
        tmp = x * ((y / z) - t)
    else
        tmp = x / (z / (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 <= -1.02) {
		tmp = x * ((y + t) * (1.0 / z));
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x / (z / (y + t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.02:
		tmp = x * ((y + t) * (1.0 / z))
	elif z <= 1.0:
		tmp = x * ((y / z) - t)
	else:
		tmp = x / (z / (y + t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.02)
		tmp = Float64(x * Float64(Float64(y + t) * Float64(1.0 / z)));
	elseif (z <= 1.0)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(x / Float64(z / Float64(y + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.02)
		tmp = x * ((y + t) * (1.0 / z));
	elseif (z <= 1.0)
		tmp = x * ((y / z) - t);
	else
		tmp = x / (z / (y + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.02], N[(x * N[(N[(y + t), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.02

   1. Initial program 97.8%

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

   2. Taylor expanded in z around inf 89.4%

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

      1. sub-neg 89.4%

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

      2. remove-double-neg 89.4%

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

      3. neg-mul-1 89.4%

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

      4. distribute-neg-in 89.4%

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

      5. neg-mul-1 89.4%

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

      6. sub-neg 89.4%

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

      7. distribute-lft-neg-in 89.4%

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

      8. distribute-neg-frac 89.4%

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

      9. associate-/l* 77.1%

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

      10. associate-/r/ 94.8%

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

      11. distribute-lft-neg-in 94.8%

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

   4. Simplified 94.8%

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

      1. div-inv 94.9%

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

   6. Applied egg-rr 94.9%

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

   if -1.02 < z < 1

   1. Initial program 93.6%

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

   2. Taylor expanded in z around 0 91.8%

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

      1. associate-*l/ 89.0%

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

      2. associate-*r* 89.0%

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

      3. neg-mul-1 89.0%

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

      4. distribute-rgt-out 92.7%

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

      5. unsub-neg 92.7%

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

   4. Simplified 92.7%

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

   if 1 < z

   1. Initial program 96.9%

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

   2. Taylor expanded in z around inf 89.4%

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

      1. *-commutative 89.4%

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

      2. associate-/l* 96.2%

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

      3. neg-mul-1 96.2%

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

   4. Simplified 96.2%

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

   5. Taylor expanded in z around 0 96.2%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02:\\ \;\;\;\;x \cdot \left(\left(y + t\right) \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \end{array} \]

Alternative 7: 63.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.3 \cdot 10^{+122}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+202}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.3e+122)
   (* y (/ x z))
   (if (<= t 7e+202) (* x (- t)) (* x (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.3e+122) {
		tmp = y * (x / z);
	} else if (t <= 7e+202) {
		tmp = x * -t;
	} else {
		tmp = x * (t / 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 <= 1.3d+122) then
        tmp = y * (x / z)
    else if (t <= 7d+202) then
        tmp = x * -t
    else
        tmp = x * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.3e+122) {
		tmp = y * (x / z);
	} else if (t <= 7e+202) {
		tmp = x * -t;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.3e+122:
		tmp = y * (x / z)
	elif t <= 7e+202:
		tmp = x * -t
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.3e+122)
		tmp = Float64(y * Float64(x / z));
	elseif (t <= 7e+202)
		tmp = Float64(x * Float64(-t));
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.3e+122)
		tmp = y * (x / z);
	elseif (t <= 7e+202)
		tmp = x * -t;
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.3e+122], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+202], N[(x * (-t)), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 1.30000000000000004e122

   1. Initial program 94.4%

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

   2. Taylor expanded in z around inf 70.1%

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

      1. *-commutative 70.1%

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

      2. associate-/l* 70.4%

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

      3. neg-mul-1 70.4%

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

   4. Simplified 70.4%

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

   5. Taylor expanded in y around inf 71.7%

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

      1. associate-*r/ 67.6%

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

   7. Simplified 67.6%

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

   if 1.30000000000000004e122 < t < 6.99999999999999975e202

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 89.0%

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

      1. mul-1-neg 89.0%

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

      2. associate-/l* 82.8%

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

      3. associate-/r/ 88.9%

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

      4. distribute-rgt-neg-in 88.9%

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

   4. Simplified 88.9%

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

   5. Taylor expanded in z around 0 71.5%

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

      1. mul-1-neg 71.5%

         \[\leadsto \color{blue}{-t \cdot x} \]

      2. distribute-lft-neg-out 71.5%

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

      3. *-commutative 71.5%

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

   7. Simplified 71.5%

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

   if 6.99999999999999975e202 < t

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 69.0%

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

      1. sub-neg 69.0%

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

      2. remove-double-neg 69.0%

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

      3. neg-mul-1 69.0%

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

      4. distribute-neg-in 69.0%

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

      5. neg-mul-1 69.0%

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

      6. sub-neg 69.0%

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

      7. distribute-lft-neg-in 69.0%

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

      8. distribute-neg-frac 69.0%

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

      9. associate-/l* 55.3%

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

      10. associate-/r/ 78.9%

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

      11. distribute-lft-neg-in 78.9%

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

   4. Simplified 78.9%

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

   5. Taylor expanded in y around 0 72.2%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.3 \cdot 10^{+122}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+202}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 8: 64.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.3 \cdot 10^{+120}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+203}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.3e+120)
   (/ x (/ z y))
   (if (<= t 5.8e+203) (* x (- t)) (* x (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.3e+120) {
		tmp = x / (z / y);
	} else if (t <= 5.8e+203) {
		tmp = x * -t;
	} else {
		tmp = x * (t / 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 <= 1.3d+120) then
        tmp = x / (z / y)
    else if (t <= 5.8d+203) then
        tmp = x * -t
    else
        tmp = x * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.3e+120) {
		tmp = x / (z / y);
	} else if (t <= 5.8e+203) {
		tmp = x * -t;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.3e+120:
		tmp = x / (z / y)
	elif t <= 5.8e+203:
		tmp = x * -t
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.3e+120)
		tmp = Float64(x / Float64(z / y));
	elseif (t <= 5.8e+203)
		tmp = Float64(x * Float64(-t));
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.3e+120)
		tmp = x / (z / y);
	elseif (t <= 5.8e+203)
		tmp = x * -t;
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.3e+120], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e+203], N[(x * (-t)), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 1.2999999999999999e120

   1. Initial program 94.4%

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

   2. Taylor expanded in z around inf 70.1%

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

      1. *-commutative 70.1%

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

      2. associate-/l* 70.4%

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

      3. neg-mul-1 70.4%

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

   4. Simplified 70.4%

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

   5. Taylor expanded in y around inf 72.0%

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

   if 1.2999999999999999e120 < t < 5.80000000000000021e203

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 89.0%

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

      1. mul-1-neg 89.0%

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

      2. associate-/l* 82.8%

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

      3. associate-/r/ 88.9%

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

      4. distribute-rgt-neg-in 88.9%

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

   4. Simplified 88.9%

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

   5. Taylor expanded in z around 0 71.5%

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

      1. mul-1-neg 71.5%

         \[\leadsto \color{blue}{-t \cdot x} \]

      2. distribute-lft-neg-out 71.5%

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

      3. *-commutative 71.5%

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

   7. Simplified 71.5%

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

   if 5.80000000000000021e203 < t

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 69.0%

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

      1. sub-neg 69.0%

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

      2. remove-double-neg 69.0%

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

      3. neg-mul-1 69.0%

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

      4. distribute-neg-in 69.0%

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

      5. neg-mul-1 69.0%

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

      6. sub-neg 69.0%

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

      7. distribute-lft-neg-in 69.0%

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

      8. distribute-neg-frac 69.0%

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

      9. associate-/l* 55.3%

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

      10. associate-/r/ 78.9%

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

      11. distribute-lft-neg-in 78.9%

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

   4. Simplified 78.9%

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

   5. Taylor expanded in y around 0 72.2%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.3 \cdot 10^{+120}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+203}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 9: 62.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 3.8 \cdot 10^{+122}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 3.8e+122) (* y (/ x z)) (* x (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 3.8e+122) {
		tmp = y * (x / z);
	} else {
		tmp = x * -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 (t <= 3.8d+122) then
        tmp = y * (x / z)
    else
        tmp = x * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 3.8e+122) {
		tmp = y * (x / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 3.8e+122:
		tmp = y * (x / z)
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 3.8e+122)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(x * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 3.8e+122)
		tmp = y * (x / z);
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 3.8e+122], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 3.7999999999999998e122

   1. Initial program 94.4%

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

   2. Taylor expanded in z around inf 70.1%

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

      1. *-commutative 70.1%

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

      2. associate-/l* 70.4%

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

      3. neg-mul-1 70.4%

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

   4. Simplified 70.4%

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

   5. Taylor expanded in y around inf 71.7%

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

      1. associate-*r/ 67.6%

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

   7. Simplified 67.6%

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

   if 3.7999999999999998e122 < t

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 85.1%

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

      1. mul-1-neg 85.1%

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

      2. associate-/l* 74.3%

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

      3. associate-/r/ 89.2%

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

      4. distribute-rgt-neg-in 89.2%

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

   4. Simplified 89.2%

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

   5. Taylor expanded in z around 0 44.1%

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

      1. mul-1-neg 44.1%

         \[\leadsto \color{blue}{-t \cdot x} \]

      2. distribute-lft-neg-out 44.1%

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

      3. *-commutative 44.1%

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

   7. Simplified 44.1%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.8 \cdot 10^{+122}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]

Alternative 10: 23.0% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.4%

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

2. Taylor expanded in y around 0 45.3%

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

   1. mul-1-neg 45.3%

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

   2. associate-/l* 44.1%

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

   3. associate-/r/ 46.4%

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

   4. distribute-rgt-neg-in 46.4%

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

4. Simplified 46.4%

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

5. Taylor expanded in z around 0 25.6%

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

   1. mul-1-neg 25.6%

      \[\leadsto \color{blue}{-t \cdot x} \]

   2. distribute-lft-neg-out 25.6%

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

   3. *-commutative 25.6%

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

7. Simplified 25.6%

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

8. Final simplification 25.6%

   \[\leadsto x \cdot \left(-t\right) \]

Developer target: 94.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ t_2 := x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{if}\;t_2 < -7.623226303312042 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 < 1.4133944927702302 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))))
        (t_2 (* x (- (/ y z) (/ t (- 1.0 z))))))
   (if (< t_2 -7.623226303312042e-196)
     t_1
     (if (< t_2 1.4133944927702302e-211)
       (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z))))
       t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y / z) - (t * (1.0d0 / (1.0d0 - z))))
    t_2 = x * ((y / z) - (t / (1.0d0 - z)))
    if (t_2 < (-7.623226303312042d-196)) then
        tmp = t_1
    else if (t_2 < 1.4133944927702302d-211) then
        tmp = ((y * x) / z) + -((t * x) / (1.0d0 - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))))
	t_2 = x * ((y / z) - (t / (1.0 - z)))
	tmp = 0
	if t_2 < -7.623226303312042e-196:
		tmp = t_1
	elif t_2 < 1.4133944927702302e-211:
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - Float64(t * Float64(1.0 / Float64(1.0 - z)))))
	t_2 = Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
	tmp = 0.0
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = Float64(Float64(Float64(y * x) / z) + Float64(-Float64(Float64(t * x) / Float64(1.0 - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	t_2 = x * ((y / z) - (t / (1.0 - z)));
	tmp = 0.0;
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t * N[(1.0 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -7.623226303312042e-196], t$95$1, If[Less[t$95$2, 1.4133944927702302e-211], N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] + (-N[(N[(t * x), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2023199 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :herbie-target
  (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) -7.623226303312042e-196) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))) (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) 1.4133944927702302e-211) (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z)))) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z)))))))

  (* x (- (/ y z) (/ t (- 1.0 z)))))