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

Percentage Accurate: 94.1% → 96.1%

Time: 12.5s

Alternatives: 14

Speedup: 0.5×

• 21.2% 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: 94.1% 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: 96.1% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ y z) (/ t (- 1.0 z)))))
   (if (<= t_1 (- INFINITY)) (* y (/ x z)) (* t_1 x))))

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 <= -((double) INFINITY)) {
		tmp = y * (x / z);
	} else {
		tmp = t_1 * x;
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (x / z);
	} else {
		tmp = t_1 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) - (t / (1.0 - z))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * (x / z)
	else:
		tmp = t_1 * x
	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 <= Float64(-Inf))
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(t_1 * x);
	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 <= -Inf)
		tmp = y * (x / z);
	else
		tmp = t_1 * x;
	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, (-Infinity)], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < -inf.0

   1. Initial program 72.4%

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

   2. Taylor expanded in y around inf 99.8%

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

      1. associate-*l/ 72.4%

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

   4. Simplified 72.4%

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

   5. Taylor expanded in y around 0 99.8%

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

      1. associate-*r/ 99.9%

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

   7. Simplified 99.9%

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

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

   1. Initial program 97.8%

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

4. Final simplification 97.9%

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

Alternative 2: 74.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+21}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ z y))))
   (if (<= z -5.4e+158)
     (* x (/ t z))
     (if (<= z -3.6e+102)
       t_1
       (if (<= z -6.2e+21)
         (* t (/ x z))
         (if (<= z 1.6e-17) (* x (- (/ y z) t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z / y);
	double tmp;
	if (z <= -5.4e+158) {
		tmp = x * (t / z);
	} else if (z <= -3.6e+102) {
		tmp = t_1;
	} else if (z <= -6.2e+21) {
		tmp = t * (x / z);
	} else if (z <= 1.6e-17) {
		tmp = x * ((y / z) - t);
	} 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) :: tmp
    t_1 = x / (z / y)
    if (z <= (-5.4d+158)) then
        tmp = x * (t / z)
    else if (z <= (-3.6d+102)) then
        tmp = t_1
    else if (z <= (-6.2d+21)) then
        tmp = t * (x / z)
    else if (z <= 1.6d-17) then
        tmp = x * ((y / z) - t)
    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 / (z / y);
	double tmp;
	if (z <= -5.4e+158) {
		tmp = x * (t / z);
	} else if (z <= -3.6e+102) {
		tmp = t_1;
	} else if (z <= -6.2e+21) {
		tmp = t * (x / z);
	} else if (z <= 1.6e-17) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z / y)
	tmp = 0
	if z <= -5.4e+158:
		tmp = x * (t / z)
	elif z <= -3.6e+102:
		tmp = t_1
	elif z <= -6.2e+21:
		tmp = t * (x / z)
	elif z <= 1.6e-17:
		tmp = x * ((y / z) - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z / y))
	tmp = 0.0
	if (z <= -5.4e+158)
		tmp = Float64(x * Float64(t / z));
	elseif (z <= -3.6e+102)
		tmp = t_1;
	elseif (z <= -6.2e+21)
		tmp = Float64(t * Float64(x / z));
	elseif (z <= 1.6e-17)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z / y);
	tmp = 0.0;
	if (z <= -5.4e+158)
		tmp = x * (t / z);
	elseif (z <= -3.6e+102)
		tmp = t_1;
	elseif (z <= -6.2e+21)
		tmp = t * (x / z);
	elseif (z <= 1.6e-17)
		tmp = x * ((y / z) - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4e+158], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.6e+102], t$95$1, If[LessEqual[z, -6.2e+21], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-17], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.39999999999999957e158

   1. Initial program 88.9%

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

   2. Taylor expanded in z around inf 77.7%

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

      1. *-commutative 77.7%

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

      2. associate-/l* 88.7%

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

      3. neg-mul-1 88.7%

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

   4. Simplified 88.7%

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

   5. Taylor expanded in y around 0 68.4%

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

      1. clear-num 68.4%

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

      2. associate-/r/ 68.4%

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

      3. clear-num 68.5%

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

   7. Applied egg-rr 68.5%

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

   if -5.39999999999999957e158 < z < -3.6000000000000002e102 or 1.6000000000000001e-17 < z

   1. Initial program 98.3%

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

   2. Taylor expanded in y around inf 61.2%

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

      1. associate-*l/ 66.2%

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

   4. Simplified 66.2%

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

   5. Taylor expanded in y around 0 61.2%

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

      1. associate-*r/ 58.7%

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

      2. *-commutative 58.7%

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

      3. associate-/r/ 66.3%

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

   7. Simplified 66.3%

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

   if -3.6000000000000002e102 < z < -6.2e21

   1. Initial program 99.4%

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

   2. Taylor expanded in z around inf 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-/l* 99.8%

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

      3. neg-mul-1 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in y around 0 71.9%

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

      1. associate-*r/ 72.1%

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

   8. Simplified 72.1%

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

   if -6.2e21 < z < 1.6000000000000001e-17

   1. Initial program 95.7%

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

   2. Taylor expanded in z around 0 92.0%

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

      1. associate-*l/ 89.2%

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

      2. associate-*r* 89.2%

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

      3. neg-mul-1 89.2%

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

      4. distribute-rgt-out 93.8%

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

      5. unsub-neg 93.8%

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

   4. Simplified 93.8%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+102}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+21}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]

Alternative 3: 65.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-x\right)\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{+165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+73}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 1.48 \cdot 10^{+175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+194}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- x))))
   (if (<= t -5.2e+165)
     t_1
     (if (<= t 8.5e+73)
       (* (/ y z) x)
       (if (<= t 1.48e+175)
         t_1
         (if (<= t 3.9e+194) (* y (/ x z)) (* x (/ t z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * -x;
	double tmp;
	if (t <= -5.2e+165) {
		tmp = t_1;
	} else if (t <= 8.5e+73) {
		tmp = (y / z) * x;
	} else if (t <= 1.48e+175) {
		tmp = t_1;
	} else if (t <= 3.9e+194) {
		tmp = y * (x / z);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * -x
    if (t <= (-5.2d+165)) then
        tmp = t_1
    else if (t <= 8.5d+73) then
        tmp = (y / z) * x
    else if (t <= 1.48d+175) then
        tmp = t_1
    else if (t <= 3.9d+194) then
        tmp = y * (x / z)
    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 t_1 = t * -x;
	double tmp;
	if (t <= -5.2e+165) {
		tmp = t_1;
	} else if (t <= 8.5e+73) {
		tmp = (y / z) * x;
	} else if (t <= 1.48e+175) {
		tmp = t_1;
	} else if (t <= 3.9e+194) {
		tmp = y * (x / z);
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * -x
	tmp = 0
	if t <= -5.2e+165:
		tmp = t_1
	elif t <= 8.5e+73:
		tmp = (y / z) * x
	elif t <= 1.48e+175:
		tmp = t_1
	elif t <= 3.9e+194:
		tmp = y * (x / z)
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(-x))
	tmp = 0.0
	if (t <= -5.2e+165)
		tmp = t_1;
	elseif (t <= 8.5e+73)
		tmp = Float64(Float64(y / z) * x);
	elseif (t <= 1.48e+175)
		tmp = t_1;
	elseif (t <= 3.9e+194)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * -x;
	tmp = 0.0;
	if (t <= -5.2e+165)
		tmp = t_1;
	elseif (t <= 8.5e+73)
		tmp = (y / z) * x;
	elseif (t <= 1.48e+175)
		tmp = t_1;
	elseif (t <= 3.9e+194)
		tmp = y * (x / z);
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * (-x)), $MachinePrecision]}, If[LessEqual[t, -5.2e+165], t$95$1, If[LessEqual[t, 8.5e+73], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, 1.48e+175], t$95$1, If[LessEqual[t, 3.9e+194], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.2000000000000002e165 or 8.4999999999999998e73 < t < 1.4800000000000001e175

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 83.6%

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

   3. Taylor expanded in z around 0 59.7%

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

   if -5.2000000000000002e165 < t < 8.4999999999999998e73

   1. Initial program 95.4%

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

   2. Taylor expanded in y around inf 76.0%

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

      1. associate-*l/ 76.5%

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

   4. Simplified 76.5%

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

   if 1.4800000000000001e175 < t < 3.90000000000000016e194

   1. Initial program 54.1%

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

   2. Taylor expanded in y around inf 99.2%

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

      1. associate-*l/ 54.1%

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

   4. Simplified 54.1%

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

   5. Taylor expanded in y around 0 99.2%

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

      1. associate-*r/ 98.4%

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

   7. Simplified 98.4%

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

   if 3.90000000000000016e194 < t

   1. Initial program 96.9%

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

   2. Taylor expanded in z around inf 55.9%

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

      1. *-commutative 55.9%

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

      2. associate-/l* 73.0%

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

      3. neg-mul-1 73.0%

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

   4. Simplified 73.0%

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

   5. Taylor expanded in y around 0 67.3%

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

      1. clear-num 67.3%

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

      2. associate-/r/ 67.3%

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

      3. clear-num 67.2%

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

   7. Applied egg-rr 67.2%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+165}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+73}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 1.48 \cdot 10^{+175}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+194}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 4: 65.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-x\right)\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+75}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+194}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- x))))
   (if (<= t -8.5e+161)
     t_1
     (if (<= t 6.2e+75)
       (* (/ y z) x)
       (if (<= t 1.3e+178)
         t_1
         (if (<= t 2.35e+194) (* y (/ x z)) (/ x (/ z t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * -x;
	double tmp;
	if (t <= -8.5e+161) {
		tmp = t_1;
	} else if (t <= 6.2e+75) {
		tmp = (y / z) * x;
	} else if (t <= 1.3e+178) {
		tmp = t_1;
	} else if (t <= 2.35e+194) {
		tmp = y * (x / z);
	} else {
		tmp = x / (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) :: t_1
    real(8) :: tmp
    t_1 = t * -x
    if (t <= (-8.5d+161)) then
        tmp = t_1
    else if (t <= 6.2d+75) then
        tmp = (y / z) * x
    else if (t <= 1.3d+178) then
        tmp = t_1
    else if (t <= 2.35d+194) then
        tmp = y * (x / z)
    else
        tmp = x / (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * -x;
	double tmp;
	if (t <= -8.5e+161) {
		tmp = t_1;
	} else if (t <= 6.2e+75) {
		tmp = (y / z) * x;
	} else if (t <= 1.3e+178) {
		tmp = t_1;
	} else if (t <= 2.35e+194) {
		tmp = y * (x / z);
	} else {
		tmp = x / (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * -x
	tmp = 0
	if t <= -8.5e+161:
		tmp = t_1
	elif t <= 6.2e+75:
		tmp = (y / z) * x
	elif t <= 1.3e+178:
		tmp = t_1
	elif t <= 2.35e+194:
		tmp = y * (x / z)
	else:
		tmp = x / (z / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(-x))
	tmp = 0.0
	if (t <= -8.5e+161)
		tmp = t_1;
	elseif (t <= 6.2e+75)
		tmp = Float64(Float64(y / z) * x);
	elseif (t <= 1.3e+178)
		tmp = t_1;
	elseif (t <= 2.35e+194)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(x / Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * -x;
	tmp = 0.0;
	if (t <= -8.5e+161)
		tmp = t_1;
	elseif (t <= 6.2e+75)
		tmp = (y / z) * x;
	elseif (t <= 1.3e+178)
		tmp = t_1;
	elseif (t <= 2.35e+194)
		tmp = y * (x / z);
	else
		tmp = x / (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * (-x)), $MachinePrecision]}, If[LessEqual[t, -8.5e+161], t$95$1, If[LessEqual[t, 6.2e+75], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, 1.3e+178], t$95$1, If[LessEqual[t, 2.35e+194], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.50000000000000007e161 or 6.2000000000000002e75 < t < 1.3e178

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 83.6%

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

   3. Taylor expanded in z around 0 59.7%

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

   if -8.50000000000000007e161 < t < 6.2000000000000002e75

   1. Initial program 95.4%

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

   2. Taylor expanded in y around inf 76.0%

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

      1. associate-*l/ 76.5%

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

   4. Simplified 76.5%

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

   if 1.3e178 < t < 2.34999999999999986e194

   1. Initial program 54.1%

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

   2. Taylor expanded in y around inf 99.2%

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

      1. associate-*l/ 54.1%

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

   4. Simplified 54.1%

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

   5. Taylor expanded in y around 0 99.2%

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

      1. associate-*r/ 98.4%

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

   7. Simplified 98.4%

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

   if 2.34999999999999986e194 < t

   1. Initial program 96.9%

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

   2. Taylor expanded in z around inf 55.9%

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

      1. *-commutative 55.9%

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

      2. associate-/l* 73.0%

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

      3. neg-mul-1 73.0%

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

   4. Simplified 73.0%

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

   5. Taylor expanded in y around 0 67.3%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+161}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+75}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+178}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+194}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \]

Alternative 5: 65.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-x\right)\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+75}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+193}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- x))))
   (if (<= t -1.5e+162)
     t_1
     (if (<= t 2e+75)
       (/ x (/ z y))
       (if (<= t 8.5e+178)
         t_1
         (if (<= t 6.6e+193) (* y (/ x z)) (/ x (/ z t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * -x;
	double tmp;
	if (t <= -1.5e+162) {
		tmp = t_1;
	} else if (t <= 2e+75) {
		tmp = x / (z / y);
	} else if (t <= 8.5e+178) {
		tmp = t_1;
	} else if (t <= 6.6e+193) {
		tmp = y * (x / z);
	} else {
		tmp = x / (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) :: t_1
    real(8) :: tmp
    t_1 = t * -x
    if (t <= (-1.5d+162)) then
        tmp = t_1
    else if (t <= 2d+75) then
        tmp = x / (z / y)
    else if (t <= 8.5d+178) then
        tmp = t_1
    else if (t <= 6.6d+193) then
        tmp = y * (x / z)
    else
        tmp = x / (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * -x;
	double tmp;
	if (t <= -1.5e+162) {
		tmp = t_1;
	} else if (t <= 2e+75) {
		tmp = x / (z / y);
	} else if (t <= 8.5e+178) {
		tmp = t_1;
	} else if (t <= 6.6e+193) {
		tmp = y * (x / z);
	} else {
		tmp = x / (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * -x
	tmp = 0
	if t <= -1.5e+162:
		tmp = t_1
	elif t <= 2e+75:
		tmp = x / (z / y)
	elif t <= 8.5e+178:
		tmp = t_1
	elif t <= 6.6e+193:
		tmp = y * (x / z)
	else:
		tmp = x / (z / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(-x))
	tmp = 0.0
	if (t <= -1.5e+162)
		tmp = t_1;
	elseif (t <= 2e+75)
		tmp = Float64(x / Float64(z / y));
	elseif (t <= 8.5e+178)
		tmp = t_1;
	elseif (t <= 6.6e+193)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(x / Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * -x;
	tmp = 0.0;
	if (t <= -1.5e+162)
		tmp = t_1;
	elseif (t <= 2e+75)
		tmp = x / (z / y);
	elseif (t <= 8.5e+178)
		tmp = t_1;
	elseif (t <= 6.6e+193)
		tmp = y * (x / z);
	else
		tmp = x / (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * (-x)), $MachinePrecision]}, If[LessEqual[t, -1.5e+162], t$95$1, If[LessEqual[t, 2e+75], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+178], t$95$1, If[LessEqual[t, 6.6e+193], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.4999999999999999e162 or 1.99999999999999985e75 < t < 8.49999999999999991e178

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 83.6%

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

   3. Taylor expanded in z around 0 59.7%

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

   if -1.4999999999999999e162 < t < 1.99999999999999985e75

   1. Initial program 95.4%

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

   2. Taylor expanded in y around inf 76.0%

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

      1. associate-*l/ 76.5%

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

   4. Simplified 76.5%

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

   5. Taylor expanded in y around 0 76.0%

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

      1. associate-*r/ 73.2%

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

      2. *-commutative 73.2%

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

      3. associate-/r/ 76.8%

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

   7. Simplified 76.8%

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

   if 8.49999999999999991e178 < t < 6.6e193

   1. Initial program 54.1%

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

   2. Taylor expanded in y around inf 99.2%

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

      1. associate-*l/ 54.1%

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

   4. Simplified 54.1%

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

   5. Taylor expanded in y around 0 99.2%

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

      1. associate-*r/ 98.4%

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

   7. Simplified 98.4%

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

   if 6.6e193 < t

   1. Initial program 96.9%

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

   2. Taylor expanded in z around inf 55.9%

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

      1. *-commutative 55.9%

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

      2. associate-/l* 73.0%

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

      3. neg-mul-1 73.0%

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

   4. Simplified 73.0%

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

   5. Taylor expanded in y around 0 67.3%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+162}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+75}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+178}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+193}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \]

Alternative 6: 65.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-x\right)\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{+162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+75}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+193}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- x))))
   (if (<= t -6.8e+162)
     t_1
     (if (<= t 6.2e+75)
       (/ x (/ z y))
       (if (<= t 1.95e+175)
         t_1
         (if (<= t 6.6e+193) (/ y (/ z x)) (/ x (/ z t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * -x;
	double tmp;
	if (t <= -6.8e+162) {
		tmp = t_1;
	} else if (t <= 6.2e+75) {
		tmp = x / (z / y);
	} else if (t <= 1.95e+175) {
		tmp = t_1;
	} else if (t <= 6.6e+193) {
		tmp = y / (z / x);
	} else {
		tmp = x / (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) :: t_1
    real(8) :: tmp
    t_1 = t * -x
    if (t <= (-6.8d+162)) then
        tmp = t_1
    else if (t <= 6.2d+75) then
        tmp = x / (z / y)
    else if (t <= 1.95d+175) then
        tmp = t_1
    else if (t <= 6.6d+193) then
        tmp = y / (z / x)
    else
        tmp = x / (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * -x;
	double tmp;
	if (t <= -6.8e+162) {
		tmp = t_1;
	} else if (t <= 6.2e+75) {
		tmp = x / (z / y);
	} else if (t <= 1.95e+175) {
		tmp = t_1;
	} else if (t <= 6.6e+193) {
		tmp = y / (z / x);
	} else {
		tmp = x / (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * -x
	tmp = 0
	if t <= -6.8e+162:
		tmp = t_1
	elif t <= 6.2e+75:
		tmp = x / (z / y)
	elif t <= 1.95e+175:
		tmp = t_1
	elif t <= 6.6e+193:
		tmp = y / (z / x)
	else:
		tmp = x / (z / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(-x))
	tmp = 0.0
	if (t <= -6.8e+162)
		tmp = t_1;
	elseif (t <= 6.2e+75)
		tmp = Float64(x / Float64(z / y));
	elseif (t <= 1.95e+175)
		tmp = t_1;
	elseif (t <= 6.6e+193)
		tmp = Float64(y / Float64(z / x));
	else
		tmp = Float64(x / Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * -x;
	tmp = 0.0;
	if (t <= -6.8e+162)
		tmp = t_1;
	elseif (t <= 6.2e+75)
		tmp = x / (z / y);
	elseif (t <= 1.95e+175)
		tmp = t_1;
	elseif (t <= 6.6e+193)
		tmp = y / (z / x);
	else
		tmp = x / (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * (-x)), $MachinePrecision]}, If[LessEqual[t, -6.8e+162], t$95$1, If[LessEqual[t, 6.2e+75], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e+175], t$95$1, If[LessEqual[t, 6.6e+193], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.80000000000000006e162 or 6.2000000000000002e75 < t < 1.94999999999999986e175

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 83.6%

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

   3. Taylor expanded in z around 0 59.7%

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

   if -6.80000000000000006e162 < t < 6.2000000000000002e75

   1. Initial program 95.4%

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

   2. Taylor expanded in y around inf 76.0%

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

      1. associate-*l/ 76.5%

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

   4. Simplified 76.5%

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

   5. Taylor expanded in y around 0 76.0%

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

      1. associate-*r/ 73.2%

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

      2. *-commutative 73.2%

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

      3. associate-/r/ 76.8%

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

   7. Simplified 76.8%

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

   if 1.94999999999999986e175 < t < 6.6e193

   1. Initial program 54.1%

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

   2. Taylor expanded in y around inf 99.2%

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

      1. associate-*l/ 54.1%

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

   4. Simplified 54.1%

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

      1. associate-*l/ 99.2%

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

      2. div-inv 100.0%

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

      3. associate-*r* 99.2%

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

      4. div-inv 98.4%

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

      5. clear-num 99.2%

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

      6. un-div-inv 99.2%

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

   6. Applied egg-rr 99.2%

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

   if 6.6e193 < t

   1. Initial program 96.9%

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

   2. Taylor expanded in z around inf 55.9%

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

      1. *-commutative 55.9%

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

      2. associate-/l* 73.0%

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

      3. neg-mul-1 73.0%

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

   4. Simplified 73.0%

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

   5. Taylor expanded in y around 0 67.3%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+162}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+75}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+175}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+193}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \]

Alternative 7: 74.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-33} \lor \neg \left(t \leq 430\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.2e-33) (not (<= t 430.0)))
   (* x (/ t (+ z -1.0)))
   (/ x (/ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.2e-33) || !(t <= 430.0)) {
		tmp = x * (t / (z + -1.0));
	} else {
		tmp = x / (z / y);
	}
	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 <= (-3.2d-33)) .or. (.not. (t <= 430.0d0))) then
        tmp = x * (t / (z + (-1.0d0)))
    else
        tmp = x / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.2e-33) || !(t <= 430.0)) {
		tmp = x * (t / (z + -1.0));
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.2e-33) or not (t <= 430.0):
		tmp = x * (t / (z + -1.0))
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.2e-33) || !(t <= 430.0))
		tmp = Float64(x * Float64(t / Float64(z + -1.0)));
	else
		tmp = Float64(x / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.2e-33) || ~((t <= 430.0)))
		tmp = x * (t / (z + -1.0));
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.2e-33], N[Not[LessEqual[t, 430.0]], $MachinePrecision]], N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.19999999999999977e-33 or 430 < t

   1. Initial program 97.6%

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

   2. Taylor expanded in y around 0 65.6%

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

      1. associate-*r/ 65.6%

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

      2. associate-*r* 65.6%

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

      3. neg-mul-1 65.6%

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

      4. associate-*l/ 72.9%

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

      5. *-commutative 72.9%

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

      6. neg-mul-1 72.9%

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

      7. *-commutative 72.9%

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

      8. associate-*r/ 72.8%

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

      9. metadata-eval 72.8%

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

      10. associate-/r* 72.8%

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

      11. neg-mul-1 72.8%

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

      12. associate-*r/ 72.9%

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

      13. *-rgt-identity 72.9%

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

      14. neg-sub0 72.9%

          \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      15. associate--r- 72.9%

          \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      16. metadata-eval 72.9%

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

   4. Simplified 72.9%

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

   if -3.19999999999999977e-33 < t < 430

   1. Initial program 94.6%

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

   2. Taylor expanded in y around inf 85.0%

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

      1. associate-*l/ 85.6%

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

   4. Simplified 85.6%

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

   5. Taylor expanded in y around 0 85.0%

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

      1. associate-*r/ 81.9%

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

      2. *-commutative 81.9%

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

      3. associate-/r/ 86.0%

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

   7. Simplified 86.0%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-33} \lor \neg \left(t \leq 430\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]

Alternative 8: 89.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.3) (not (<= z 1.0)))
   (* (/ x z) (+ y t))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.3) || !(z <= 1.0)) {
		tmp = (x / z) * (y + 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 <= (-1.3d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = (x / z) * (y + 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 <= -1.3) || !(z <= 1.0)) {
		tmp = (x / z) * (y + t);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.3) or not (z <= 1.0):
		tmp = (x / z) * (y + t)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.3) || !(z <= 1.0))
		tmp = Float64(Float64(x / z) * Float64(y + 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 <= -1.3) || ~((z <= 1.0)))
		tmp = (x / z) * (y + t);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.3], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] * N[(y + t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.30000000000000004 or 1 < z

   1. Initial program 96.5%

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

   2. Taylor expanded in z around inf 87.6%

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

      1. *-commutative 87.6%

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

      2. associate-/l* 96.6%

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

      3. associate-/r/ 88.3%

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

      4. cancel-sign-sub-inv 88.3%

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

      5. metadata-eval 88.3%

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

      6. *-lft-identity 88.3%

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

   4. Simplified 88.3%

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

   if -1.30000000000000004 < z < 1

   1. Initial program 95.7%

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

   2. Taylor expanded in z around 0 92.6%

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

      1. associate-*l/ 89.9%

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

      2. associate-*r* 89.9%

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

      3. neg-mul-1 89.9%

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

      4. distribute-rgt-out 94.5%

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

      5. unsub-neg 94.5%

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

   4. Simplified 94.5%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 9: 92.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.6 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.6e-17)))
   (* 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 <= 1.6e-17)) {
		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 <= 1.6d-17))) 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 <= 1.6e-17)) {
		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 <= 1.6e-17):
		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 <= 1.6e-17))
		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 <= 1.6e-17)))
		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, 1.6e-17]], $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 1.6000000000000001e-17 < z

   1. Initial program 96.6%

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

   2. Taylor expanded in z around inf 87.8%

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

      1. associate-/l* 86.4%

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

      2. associate-/r/ 96.6%

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

      3. cancel-sign-sub-inv 96.6%

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

      4. metadata-eval 96.6%

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

      5. *-lft-identity 96.6%

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

   4. Simplified 96.6%

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

   if -1 < z < 1.6000000000000001e-17

   1. Initial program 95.6%

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

   2. Taylor expanded in z around 0 92.5%

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

      1. associate-*l/ 89.7%

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

      2. associate-*r* 89.7%

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

      3. neg-mul-1 89.7%

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

      4. distribute-rgt-out 94.4%

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

      5. unsub-neg 94.4%

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

   4. Simplified 94.4%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.6 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 10: 92.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.0)
   (* x (/ (+ y t) z))
   (if (<= z 1.6e-17) (* 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 <= 1.6e-17) {
		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 <= 1.6d-17) 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 <= 1.6e-17) {
		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 <= 1.6e-17:
		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 <= 1.6e-17)
		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 <= 1.6e-17)
		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, 1.6e-17], 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 94.8%

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

   2. Taylor expanded in z around inf 85.0%

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

      1. associate-/l* 88.4%

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

      2. associate-/r/ 94.8%

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

      3. cancel-sign-sub-inv 94.8%

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

      4. metadata-eval 94.8%

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

      5. *-lft-identity 94.8%

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

   4. Simplified 94.8%

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

   if -1 < z < 1.6000000000000001e-17

   1. Initial program 95.6%

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

   2. Taylor expanded in z around 0 92.5%

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

      1. associate-*l/ 89.7%

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

      2. associate-*r* 89.7%

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

      3. neg-mul-1 89.7%

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

      4. distribute-rgt-out 94.4%

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

      5. unsub-neg 94.4%

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

   4. Simplified 94.4%

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

   if 1.6000000000000001e-17 < z

   1. Initial program 98.1%

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

   2. Taylor expanded in z around inf 90.2%

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

      1. *-commutative 90.2%

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

      2. associate-/l* 98.2%

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

      3. neg-mul-1 98.2%

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

   4. Simplified 98.2%

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

   5. Taylor expanded in z around 0 98.2%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \end{array} \]

Alternative 11: 42.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.4 \cdot 10^{+28}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.4e+28))) (* t (/ x z)) (* t (- x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.4e+28)) {
		tmp = t * (x / z);
	} else {
		tmp = 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 <= (-1.0d0)) .or. (.not. (z <= 1.4d+28))) then
        tmp = t * (x / z)
    else
        tmp = 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 <= -1.0) || !(z <= 1.4e+28)) {
		tmp = t * (x / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.4e+28):
		tmp = t * (x / z)
	else:
		tmp = t * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1.4e+28))
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(t * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 1.4e+28)))
		tmp = t * (x / z);
	else
		tmp = t * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.4e+28]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(t * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1.4000000000000001e28 < z

   1. Initial program 96.4%

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

   2. Taylor expanded in z around inf 87.2%

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

      1. *-commutative 87.2%

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

      2. associate-/l* 96.5%

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

      3. neg-mul-1 96.5%

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

   4. Simplified 96.5%

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

   5. Taylor expanded in z around 0 96.5%

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

   6. Taylor expanded in y around 0 50.0%

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

      1. associate-*r/ 52.4%

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

   8. Simplified 52.4%

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

   if -1 < z < 1.4000000000000001e28

   1. Initial program 95.8%

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

   2. Taylor expanded in y around 0 40.0%

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

   3. Taylor expanded in z around 0 38.9%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.4 \cdot 10^{+28}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]

Alternative 12: 61.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+156}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3e+156)
   (* t (- x))
   (if (<= t 4.6e-44) (* y (/ x z)) (* t (/ x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3e+156) {
		tmp = t * -x;
	} else if (t <= 4.6e-44) {
		tmp = y * (x / z);
	} else {
		tmp = t * (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 <= (-3d+156)) then
        tmp = t * -x
    else if (t <= 4.6d-44) then
        tmp = y * (x / z)
    else
        tmp = t * (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 <= -3e+156) {
		tmp = t * -x;
	} else if (t <= 4.6e-44) {
		tmp = y * (x / z);
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3e+156:
		tmp = t * -x
	elif t <= 4.6e-44:
		tmp = y * (x / z)
	else:
		tmp = t * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3e+156)
		tmp = Float64(t * Float64(-x));
	elseif (t <= 4.6e-44)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(t * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3e+156)
		tmp = t * -x;
	elseif (t <= 4.6e-44)
		tmp = y * (x / z);
	else
		tmp = t * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3e+156], N[(t * (-x)), $MachinePrecision], If[LessEqual[t, 4.6e-44], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3e156

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 80.7%

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

   3. Taylor expanded in z around 0 59.4%

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

   if -3e156 < t < 4.59999999999999996e-44

   1. Initial program 95.5%

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

   2. Taylor expanded in y around inf 77.8%

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

      1. associate-*l/ 78.4%

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

   4. Simplified 78.4%

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

   5. Taylor expanded in y around 0 77.8%

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

      1. associate-*r/ 77.1%

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

   7. Simplified 77.1%

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

   if 4.59999999999999996e-44 < t

   1. Initial program 95.3%

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

   2. Taylor expanded in z around inf 57.2%

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

      1. *-commutative 57.2%

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

      2. associate-/l* 64.8%

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

      3. neg-mul-1 64.8%

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

   4. Simplified 64.8%

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

   5. Taylor expanded in z around 0 64.8%

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

   6. Taylor expanded in y around 0 45.3%

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

      1. associate-*r/ 46.7%

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

   8. Simplified 46.7%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+156}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]

Alternative 13: 63.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+165}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.5e+165)
   (* t (- x))
   (if (<= t 4.6e-44) (* y (/ x z)) (* x (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.5e+165) {
		tmp = t * -x;
	} else if (t <= 4.6e-44) {
		tmp = y * (x / z);
	} 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 <= (-4.5d+165)) then
        tmp = t * -x
    else if (t <= 4.6d-44) then
        tmp = y * (x / z)
    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 <= -4.5e+165) {
		tmp = t * -x;
	} else if (t <= 4.6e-44) {
		tmp = y * (x / z);
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.5e+165:
		tmp = t * -x
	elif t <= 4.6e-44:
		tmp = y * (x / z)
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.5e+165)
		tmp = Float64(t * Float64(-x));
	elseif (t <= 4.6e-44)
		tmp = Float64(y * Float64(x / z));
	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 <= -4.5e+165)
		tmp = t * -x;
	elseif (t <= 4.6e-44)
		tmp = y * (x / z);
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.5e+165], N[(t * (-x)), $MachinePrecision], If[LessEqual[t, 4.6e-44], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.4999999999999996e165

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 80.7%

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

   3. Taylor expanded in z around 0 59.4%

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

   if -4.4999999999999996e165 < t < 4.59999999999999996e-44

   1. Initial program 95.5%

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

   2. Taylor expanded in y around inf 77.8%

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

      1. associate-*l/ 78.4%

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

   4. Simplified 78.4%

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

   5. Taylor expanded in y around 0 77.8%

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

      1. associate-*r/ 77.1%

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

   7. Simplified 77.1%

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

   if 4.59999999999999996e-44 < t

   1. Initial program 95.3%

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

   2. Taylor expanded in z around inf 57.2%

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

      1. *-commutative 57.2%

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

      2. associate-/l* 64.8%

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

      3. neg-mul-1 64.8%

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

   4. Simplified 64.8%

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

   5. Taylor expanded in y around 0 53.7%

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

      1. clear-num 53.6%

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

      2. associate-/r/ 53.7%

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

      3. clear-num 53.7%

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

   7. Applied egg-rr 53.7%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+165}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 14: 23.6% accurate, 2.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 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 = t * -x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

2. Taylor expanded in y around 0 44.7%

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

3. Taylor expanded in z around 0 27.1%

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

4. Final simplification 27.1%

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

Developer target: 94.6% 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 2023274 
(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)))))