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

Percentage Accurate: 94.6% → 96.5%

Time: 7.7s

Alternatives: 11

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: 94.6% 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: 96.5% accurate, 0.5× speedup

Math

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

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(Float64(y * 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[(N[(y * x), $MachinePrecision] / z), $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 57.7%

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

   2. Taylor expanded in y around inf 99.9%

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

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

   1. Initial program 97.5%

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

4. Final simplification 97.7%

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

Alternative 2: 73.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+225}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+61}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{+44} \lor \neg \left(z \leq 2.3 \cdot 10^{+85}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= z -1.7e+225)
     t_1
     (if (<= z -1.45e+61)
       (* (/ y z) x)
       (if (or (<= z -6.6e+44) (not (<= z 2.3e+85)))
         t_1
         (* x (- (/ y z) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (z <= -1.7e+225) {
		tmp = t_1;
	} else if (z <= -1.45e+61) {
		tmp = (y / z) * x;
	} else if ((z <= -6.6e+44) || !(z <= 2.3e+85)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (z <= (-1.7d+225)) then
        tmp = t_1
    else if (z <= (-1.45d+61)) then
        tmp = (y / z) * x
    else if ((z <= (-6.6d+44)) .or. (.not. (z <= 2.3d+85))) then
        tmp = t_1
    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 t_1 = x * (t / z);
	double tmp;
	if (z <= -1.7e+225) {
		tmp = t_1;
	} else if (z <= -1.45e+61) {
		tmp = (y / z) * x;
	} else if ((z <= -6.6e+44) || !(z <= 2.3e+85)) {
		tmp = t_1;
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if z <= -1.7e+225:
		tmp = t_1
	elif z <= -1.45e+61:
		tmp = (y / z) * x
	elif (z <= -6.6e+44) or not (z <= 2.3e+85):
		tmp = t_1
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (z <= -1.7e+225)
		tmp = t_1;
	elseif (z <= -1.45e+61)
		tmp = Float64(Float64(y / z) * x);
	elseif ((z <= -6.6e+44) || !(z <= 2.3e+85))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (z <= -1.7e+225)
		tmp = t_1;
	elseif (z <= -1.45e+61)
		tmp = (y / z) * x;
	elseif ((z <= -6.6e+44) || ~((z <= 2.3e+85)))
		tmp = t_1;
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+225], t$95$1, If[LessEqual[z, -1.45e+61], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[Or[LessEqual[z, -6.6e+44], N[Not[LessEqual[z, 2.3e+85]], $MachinePrecision]], t$95$1, N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.70000000000000009e225 or -1.45e61 < z < -6.60000000000000027e44 or 2.2999999999999999e85 < z

   1. Initial program 95.7%

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

   2. Taylor expanded in y around 0 66.3%

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

      1. associate-*r/ 66.3%

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

      2. mul-1-neg 66.3%

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

      3. *-commutative 66.3%

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

      4. distribute-rgt-neg-in 66.3%

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

      5. associate-*r/ 71.2%

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

      6. neg-mul-1 71.2%

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

      7. *-commutative 71.2%

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

      8. associate-*r/ 71.0%

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

      9. metadata-eval 71.0%

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

      10. associate-/r* 71.0%

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

      11. neg-mul-1 71.0%

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

      12. associate-*r/ 71.2%

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

      13. *-rgt-identity 71.2%

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

      14. neg-sub0 71.2%

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

      15. associate--r- 71.2%

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

      16. metadata-eval 71.2%

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

   4. Simplified 71.2%

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

   5. Taylor expanded in z around inf 71.2%

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

   if -1.70000000000000009e225 < z < -1.45e61

   1. Initial program 96.6%

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

   2. Taylor expanded in y around inf 52.3%

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

      1. associate-*l/ 63.3%

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

   4. Simplified 63.3%

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

   if -6.60000000000000027e44 < z < 2.2999999999999999e85

   1. Initial program 93.4%

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

   2. Taylor expanded in z around 0 90.8%

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

      1. associate-*l/ 85.2%

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

      2. associate-*r* 85.2%

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

      3. neg-mul-1 85.2%

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

      4. distribute-rgt-out 87.7%

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

      5. unsub-neg 87.7%

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

   4. Simplified 87.7%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+225}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+61}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{+44} \lor \neg \left(z \leq 2.3 \cdot 10^{+85}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 3: 93.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{elif}\;z \leq 0.052:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \left(t + z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.8e-11)
   (/ x (/ z (+ y t)))
   (if (<= z 0.052) (* x (- (/ y z) (+ t (* z t)))) (* x (/ (+ y t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.8e-11) {
		tmp = x / (z / (y + t));
	} else if (z <= 0.052) {
		tmp = x * ((y / z) - (t + (z * t)));
	} else {
		tmp = x * ((y + 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 (z <= (-1.8d-11)) then
        tmp = x / (z / (y + t))
    else if (z <= 0.052d0) then
        tmp = x * ((y / z) - (t + (z * t)))
    else
        tmp = x * ((y + t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.8e-11) {
		tmp = x / (z / (y + t));
	} else if (z <= 0.052) {
		tmp = x * ((y / z) - (t + (z * t)));
	} else {
		tmp = x * ((y + t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.8e-11:
		tmp = x / (z / (y + t))
	elif z <= 0.052:
		tmp = x * ((y / z) - (t + (z * t)))
	else:
		tmp = x * ((y + t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.8e-11)
		tmp = Float64(x / Float64(z / Float64(y + t)));
	elseif (z <= 0.052)
		tmp = Float64(x * Float64(Float64(y / z) - Float64(t + Float64(z * t))));
	else
		tmp = Float64(x * Float64(Float64(y + t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.8e-11)
		tmp = x / (z / (y + t));
	elseif (z <= 0.052)
		tmp = x * ((y / z) - (t + (z * t)));
	else
		tmp = x * ((y + t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.8e-11], N[(x / N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.052], N[(x * N[(N[(y / z), $MachinePrecision] - N[(t + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.79999999999999992e-11

   1. Initial program 97.1%

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

   2. Taylor expanded in z around inf 87.3%

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

      1. *-commutative 87.3%

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

      2. associate-/l* 95.7%

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

      3. neg-mul-1 95.7%

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

   4. Simplified 95.7%

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

   5. Taylor expanded in z around 0 95.7%

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

   if -1.79999999999999992e-11 < z < 0.0519999999999999976

   1. Initial program 92.0%

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

   2. Taylor expanded in z around 0 91.7%

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

      1. *-commutative 91.7%

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

   4. Simplified 91.7%

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

   if 0.0519999999999999976 < z

   1. Initial program 96.4%

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

   2. Taylor expanded in z around inf 94.0%

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

      1. cancel-sign-sub-inv 94.0%

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

      2. metadata-eval 94.0%

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

      3. *-lft-identity 94.0%

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

   4. Simplified 94.0%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{elif}\;z \leq 0.052:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \left(t + z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \]

Alternative 4: 64.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-x\right)\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+113}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- x))))
   (if (<= t -2.3e+253)
     t_1
     (if (<= t -8.6e+23)
       (* x (/ t z))
       (if (<= t 1.45e+113) (* (/ y z) x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * -x;
	double tmp;
	if (t <= -2.3e+253) {
		tmp = t_1;
	} else if (t <= -8.6e+23) {
		tmp = x * (t / z);
	} else if (t <= 1.45e+113) {
		tmp = (y / z) * x;
	} 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 = t * -x
    if (t <= (-2.3d+253)) then
        tmp = t_1
    else if (t <= (-8.6d+23)) then
        tmp = x * (t / z)
    else if (t <= 1.45d+113) then
        tmp = (y / z) * x
    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 = t * -x;
	double tmp;
	if (t <= -2.3e+253) {
		tmp = t_1;
	} else if (t <= -8.6e+23) {
		tmp = x * (t / z);
	} else if (t <= 1.45e+113) {
		tmp = (y / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * -x
	tmp = 0
	if t <= -2.3e+253:
		tmp = t_1
	elif t <= -8.6e+23:
		tmp = x * (t / z)
	elif t <= 1.45e+113:
		tmp = (y / z) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(-x))
	tmp = 0.0
	if (t <= -2.3e+253)
		tmp = t_1;
	elseif (t <= -8.6e+23)
		tmp = Float64(x * Float64(t / z));
	elseif (t <= 1.45e+113)
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * -x;
	tmp = 0.0;
	if (t <= -2.3e+253)
		tmp = t_1;
	elseif (t <= -8.6e+23)
		tmp = x * (t / z);
	elseif (t <= 1.45e+113)
		tmp = (y / z) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * (-x)), $MachinePrecision]}, If[LessEqual[t, -2.3e+253], t$95$1, If[LessEqual[t, -8.6e+23], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e+113], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.3e253 or 1.44999999999999992e113 < t

   1. Initial program 95.6%

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

   2. Taylor expanded in y around 0 84.6%

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

      1. associate-*r/ 84.6%

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

      2. mul-1-neg 84.6%

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

      3. *-commutative 84.6%

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

      4. distribute-rgt-neg-in 84.6%

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

      5. associate-*r/ 86.0%

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

      6. neg-mul-1 86.0%

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

      7. *-commutative 86.0%

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

      8. associate-*r/ 85.9%

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

      9. metadata-eval 85.9%

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

      10. associate-/r* 85.9%

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

      11. neg-mul-1 85.9%

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

      12. associate-*r/ 86.0%

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

      13. *-rgt-identity 86.0%

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

      14. neg-sub0 86.0%

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

      15. associate--r- 86.0%

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

      16. metadata-eval 86.0%

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

   4. Simplified 86.0%

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

   5. Taylor expanded in z around 0 58.2%

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

      1. mul-1-neg 58.2%

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

   7. Simplified 58.2%

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

   if -2.3e253 < t < -8.5999999999999997e23

   1. Initial program 91.5%

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

   2. Taylor expanded in y around 0 60.0%

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

      1. associate-*r/ 60.0%

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

      2. mul-1-neg 60.0%

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

      3. *-commutative 60.0%

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

      4. distribute-rgt-neg-in 60.0%

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

      5. associate-*r/ 70.5%

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

      6. neg-mul-1 70.5%

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

      7. *-commutative 70.5%

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

      8. associate-*r/ 70.4%

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

      9. metadata-eval 70.4%

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

      10. associate-/r* 70.4%

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

      11. neg-mul-1 70.4%

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

      12. associate-*r/ 70.5%

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

      13. *-rgt-identity 70.5%

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

      14. neg-sub0 70.5%

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

      15. associate--r- 70.5%

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

      16. metadata-eval 70.5%

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

   4. Simplified 70.5%

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

   5. Taylor expanded in z around inf 55.2%

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

   if -8.5999999999999997e23 < t < 1.44999999999999992e113

   1. Initial program 94.7%

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

   2. Taylor expanded in y around inf 78.6%

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

      1. associate-*l/ 81.5%

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

   4. Simplified 81.5%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+253}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+113}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]

Alternative 5: 64.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-x\right)\\ \mathbf{if}\;t \leq -6 \cdot 10^{+253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 1.92 \cdot 10^{+118}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- x))))
   (if (<= t -6e+253)
     t_1
     (if (<= t -1.85e+24)
       (/ x (/ z t))
       (if (<= t 1.92e+118) (* (/ y z) x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * -x;
	double tmp;
	if (t <= -6e+253) {
		tmp = t_1;
	} else if (t <= -1.85e+24) {
		tmp = x / (z / t);
	} else if (t <= 1.92e+118) {
		tmp = (y / z) * x;
	} 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 = t * -x
    if (t <= (-6d+253)) then
        tmp = t_1
    else if (t <= (-1.85d+24)) then
        tmp = x / (z / t)
    else if (t <= 1.92d+118) then
        tmp = (y / z) * x
    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 = t * -x;
	double tmp;
	if (t <= -6e+253) {
		tmp = t_1;
	} else if (t <= -1.85e+24) {
		tmp = x / (z / t);
	} else if (t <= 1.92e+118) {
		tmp = (y / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * -x
	tmp = 0
	if t <= -6e+253:
		tmp = t_1
	elif t <= -1.85e+24:
		tmp = x / (z / t)
	elif t <= 1.92e+118:
		tmp = (y / z) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(-x))
	tmp = 0.0
	if (t <= -6e+253)
		tmp = t_1;
	elseif (t <= -1.85e+24)
		tmp = Float64(x / Float64(z / t));
	elseif (t <= 1.92e+118)
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * -x;
	tmp = 0.0;
	if (t <= -6e+253)
		tmp = t_1;
	elseif (t <= -1.85e+24)
		tmp = x / (z / t);
	elseif (t <= 1.92e+118)
		tmp = (y / z) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * (-x)), $MachinePrecision]}, If[LessEqual[t, -6e+253], t$95$1, If[LessEqual[t, -1.85e+24], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.92e+118], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.9999999999999996e253 or 1.9199999999999999e118 < t

   1. Initial program 95.6%

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

   2. Taylor expanded in y around 0 84.6%

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

      1. associate-*r/ 84.6%

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

      2. mul-1-neg 84.6%

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

      3. *-commutative 84.6%

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

      4. distribute-rgt-neg-in 84.6%

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

      5. associate-*r/ 86.0%

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

      6. neg-mul-1 86.0%

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

      7. *-commutative 86.0%

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

      8. associate-*r/ 85.9%

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

      9. metadata-eval 85.9%

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

      10. associate-/r* 85.9%

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

      11. neg-mul-1 85.9%

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

      12. associate-*r/ 86.0%

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

      13. *-rgt-identity 86.0%

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

      14. neg-sub0 86.0%

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

      15. associate--r- 86.0%

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

      16. metadata-eval 86.0%

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

   4. Simplified 86.0%

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

   5. Taylor expanded in z around 0 58.2%

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

      1. mul-1-neg 58.2%

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

   7. Simplified 58.2%

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

   if -5.9999999999999996e253 < t < -1.85e24

   1. Initial program 91.5%

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

   2. Taylor expanded in z around inf 58.2%

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

      1. *-commutative 58.2%

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

      2. associate-/l* 69.6%

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

      3. neg-mul-1 69.6%

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

   4. Simplified 69.6%

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

   5. Taylor expanded in y around 0 55.2%

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

   if -1.85e24 < t < 1.9199999999999999e118

   1. Initial program 94.7%

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

   2. Taylor expanded in y around inf 78.6%

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

      1. associate-*l/ 81.5%

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

   4. Simplified 81.5%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+253}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 1.92 \cdot 10^{+118}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]

Alternative 6: 64.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-x\right)\\ \mathbf{if}\;t \leq -5.1 \cdot 10^{+253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+168}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- x))))
   (if (<= t -5.1e+253)
     t_1
     (if (<= t -1.85e+24)
       (/ x (/ z t))
       (if (<= t 6.5e+168) (/ y (/ z x)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * -x;
	double tmp;
	if (t <= -5.1e+253) {
		tmp = t_1;
	} else if (t <= -1.85e+24) {
		tmp = x / (z / t);
	} else if (t <= 6.5e+168) {
		tmp = y / (z / x);
	} 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 = t * -x
    if (t <= (-5.1d+253)) then
        tmp = t_1
    else if (t <= (-1.85d+24)) then
        tmp = x / (z / t)
    else if (t <= 6.5d+168) then
        tmp = y / (z / x)
    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 = t * -x;
	double tmp;
	if (t <= -5.1e+253) {
		tmp = t_1;
	} else if (t <= -1.85e+24) {
		tmp = x / (z / t);
	} else if (t <= 6.5e+168) {
		tmp = y / (z / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * -x
	tmp = 0
	if t <= -5.1e+253:
		tmp = t_1
	elif t <= -1.85e+24:
		tmp = x / (z / t)
	elif t <= 6.5e+168:
		tmp = y / (z / x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(-x))
	tmp = 0.0
	if (t <= -5.1e+253)
		tmp = t_1;
	elseif (t <= -1.85e+24)
		tmp = Float64(x / Float64(z / t));
	elseif (t <= 6.5e+168)
		tmp = Float64(y / Float64(z / x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * -x;
	tmp = 0.0;
	if (t <= -5.1e+253)
		tmp = t_1;
	elseif (t <= -1.85e+24)
		tmp = x / (z / t);
	elseif (t <= 6.5e+168)
		tmp = y / (z / x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * (-x)), $MachinePrecision]}, If[LessEqual[t, -5.1e+253], t$95$1, If[LessEqual[t, -1.85e+24], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e+168], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.09999999999999994e253 or 6.49999999999999999e168 < t

   1. Initial program 98.0%

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

   2. Taylor expanded in y around 0 89.3%

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

      1. associate-*r/ 89.3%

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

      2. mul-1-neg 89.3%

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

      3. *-commutative 89.3%

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

      4. distribute-rgt-neg-in 89.3%

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

      5. associate-*r/ 91.3%

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

      6. neg-mul-1 91.3%

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

      7. *-commutative 91.3%

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

      8. associate-*r/ 91.3%

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

      9. metadata-eval 91.3%

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

      10. associate-/r* 91.3%

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

      11. neg-mul-1 91.3%

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

      12. associate-*r/ 91.3%

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

      13. *-rgt-identity 91.3%

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

      14. neg-sub0 91.3%

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

      15. associate--r- 91.3%

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

      16. metadata-eval 91.3%

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

   4. Simplified 91.3%

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

   5. Taylor expanded in z around 0 64.7%

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

      1. mul-1-neg 64.7%

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

   7. Simplified 64.7%

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

   if -5.09999999999999994e253 < t < -1.85e24

   1. Initial program 91.5%

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

   2. Taylor expanded in z around inf 58.2%

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

      1. *-commutative 58.2%

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

      2. associate-/l* 69.6%

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

      3. neg-mul-1 69.6%

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

   4. Simplified 69.6%

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

   5. Taylor expanded in y around 0 55.2%

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

   if -1.85e24 < t < 6.49999999999999999e168

   1. Initial program 94.1%

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

      1. clear-num 93.6%

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

      2. frac-sub 78.7%

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

      3. *-un-lft-identity 78.7%

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

   3. Applied egg-rr 78.7%

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

   4. Taylor expanded in z around 0 74.3%

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

      1. associate-/l* 77.4%

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

   6. Simplified 77.4%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{+253}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+168}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]

Alternative 7: 75.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+23} \lor \neg \left(t \leq 4.3 \cdot 10^{+109}\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8.5e+23) (not (<= t 4.3e+109)))
   (* x (/ t (+ z -1.0)))
   (* (/ y z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.5e+23) || !(t <= 4.3e+109)) {
		tmp = x * (t / (z + -1.0));
	} 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 ((t <= (-8.5d+23)) .or. (.not. (t <= 4.3d+109))) then
        tmp = x * (t / (z + (-1.0d0)))
    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 ((t <= -8.5e+23) || !(t <= 4.3e+109)) {
		tmp = x * (t / (z + -1.0));
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8.5e+23) or not (t <= 4.3e+109):
		tmp = x * (t / (z + -1.0))
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8.5e+23) || !(t <= 4.3e+109))
		tmp = Float64(x * Float64(t / Float64(z + -1.0)));
	else
		tmp = Float64(Float64(y / z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -8.5e+23) || ~((t <= 4.3e+109)))
		tmp = x * (t / (z + -1.0));
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8.5e+23], N[Not[LessEqual[t, 4.3e+109]], $MachinePrecision]], N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.5000000000000001e23 or 4.3000000000000001e109 < t

   1. Initial program 93.9%

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

   2. Taylor expanded in y around 0 74.6%

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

      1. associate-*r/ 74.6%

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

      2. mul-1-neg 74.6%

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

      3. *-commutative 74.6%

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

      4. distribute-rgt-neg-in 74.6%

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

      5. associate-*r/ 79.7%

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

      6. neg-mul-1 79.7%

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

      7. *-commutative 79.7%

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

      8. associate-*r/ 79.6%

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

      9. metadata-eval 79.6%

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

      10. associate-/r* 79.6%

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

      11. neg-mul-1 79.6%

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

      12. associate-*r/ 79.7%

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

      13. *-rgt-identity 79.7%

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

      14. neg-sub0 79.7%

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

      15. associate--r- 79.7%

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

      16. metadata-eval 79.7%

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

   4. Simplified 79.7%

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

   if -8.5000000000000001e23 < t < 4.3000000000000001e109

   1. Initial program 94.7%

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

   2. Taylor expanded in y around inf 78.6%

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

      1. associate-*l/ 81.5%

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

   4. Simplified 81.5%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+23} \lor \neg \left(t \leq 4.3 \cdot 10^{+109}\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]

Alternative 8: 93.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.052\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 0.052)))
   (* 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 <= 0.052)) {
		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 <= 0.052d0))) 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 <= 0.052)) {
		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 <= 0.052):
		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 <= 0.052))
		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 <= 0.052)))
		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, 0.052]], $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 0.0519999999999999976 < z

   1. Initial program 96.9%

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

   2. Taylor expanded in z around inf 95.1%

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

      1. cancel-sign-sub-inv 95.1%

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

      2. metadata-eval 95.1%

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

      3. *-lft-identity 95.1%

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

   4. Simplified 95.1%

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

   if -1 < z < 0.0519999999999999976

   1. Initial program 92.2%

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

   2. Taylor expanded in z around 0 96.0%

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

      1. associate-*l/ 89.3%

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

      2. associate-*r* 89.3%

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

      3. neg-mul-1 89.3%

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

      4. distribute-rgt-out 91.6%

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

      5. unsub-neg 91.6%

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

   4. Simplified 91.6%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.052\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 9: 93.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{elif}\;z \leq 0.052:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.8e-11)
   (/ x (/ z (+ y t)))
   (if (<= z 0.052) (* x (- (/ y z) t)) (* x (/ (+ y t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.8e-11) {
		tmp = x / (z / (y + t));
	} else if (z <= 0.052) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x * ((y + 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 (z <= (-1.8d-11)) then
        tmp = x / (z / (y + t))
    else if (z <= 0.052d0) then
        tmp = x * ((y / z) - t)
    else
        tmp = x * ((y + t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.8e-11) {
		tmp = x / (z / (y + t));
	} else if (z <= 0.052) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x * ((y + t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.8e-11:
		tmp = x / (z / (y + t))
	elif z <= 0.052:
		tmp = x * ((y / z) - t)
	else:
		tmp = x * ((y + t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.8e-11)
		tmp = Float64(x / Float64(z / Float64(y + t)));
	elseif (z <= 0.052)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(x * Float64(Float64(y + t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.8e-11)
		tmp = x / (z / (y + t));
	elseif (z <= 0.052)
		tmp = x * ((y / z) - t);
	else
		tmp = x * ((y + t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.8e-11], N[(x / N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.052], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.79999999999999992e-11

   1. Initial program 97.1%

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

   2. Taylor expanded in z around inf 87.3%

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

      1. *-commutative 87.3%

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

      2. associate-/l* 95.7%

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

      3. neg-mul-1 95.7%

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

   4. Simplified 95.7%

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

   5. Taylor expanded in z around 0 95.7%

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

   if -1.79999999999999992e-11 < z < 0.0519999999999999976

   1. Initial program 92.0%

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

   2. Taylor expanded in z around 0 95.9%

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

      1. associate-*l/ 89.1%

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

      2. associate-*r* 89.1%

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

      3. neg-mul-1 89.1%

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

      4. distribute-rgt-out 91.4%

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

      5. unsub-neg 91.4%

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

   4. Simplified 91.4%

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

   if 0.0519999999999999976 < z

   1. Initial program 96.4%

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

   2. Taylor expanded in z around inf 94.0%

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

      1. cancel-sign-sub-inv 94.0%

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

      2. metadata-eval 94.0%

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

      3. *-lft-identity 94.0%

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

   4. Simplified 94.0%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{elif}\;z \leq 0.052:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \]

Alternative 10: 44.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-11} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.8e-11) (not (<= z 1.0))) (* x (/ t z)) (* t (- x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.8e-11) || !(z <= 1.0)) {
		tmp = x * (t / 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 <= (-1.8d-11)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * (t / 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 <= -1.8e-11) || !(z <= 1.0)) {
		tmp = x * (t / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.8e-11) or not (z <= 1.0):
		tmp = x * (t / z)
	else:
		tmp = t * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.8e-11) || !(z <= 1.0))
		tmp = Float64(x * Float64(t / 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 <= -1.8e-11) || ~((z <= 1.0)))
		tmp = x * (t / z);
	else
		tmp = t * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.8e-11], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(t * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.79999999999999992e-11 or 1 < z

   1. Initial program 96.8%

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

   2. Taylor expanded in y around 0 53.3%

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

      1. associate-*r/ 53.3%

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

      2. mul-1-neg 53.3%

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

      3. *-commutative 53.3%

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

      4. distribute-rgt-neg-in 53.3%

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

      5. associate-*r/ 56.3%

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

      6. neg-mul-1 56.3%

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

      7. *-commutative 56.3%

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

      8. associate-*r/ 56.2%

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

      9. metadata-eval 56.2%

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

      10. associate-/r* 56.2%

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

      11. neg-mul-1 56.2%

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

      12. associate-*r/ 56.3%

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

      13. *-rgt-identity 56.3%

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

      14. neg-sub0 56.3%

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

      15. associate--r- 56.3%

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

      16. metadata-eval 56.3%

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

   4. Simplified 56.3%

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

   5. Taylor expanded in z around inf 54.5%

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

   if -1.79999999999999992e-11 < z < 1

   1. Initial program 92.2%

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

   2. Taylor expanded in y around 0 42.0%

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

      1. associate-*r/ 42.0%

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

      2. mul-1-neg 42.0%

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

      3. *-commutative 42.0%

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

      4. distribute-rgt-neg-in 42.0%

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

      5. associate-*r/ 41.9%

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

      6. neg-mul-1 41.9%

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

      7. *-commutative 41.9%

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

      8. associate-*r/ 41.9%

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

      9. metadata-eval 41.9%

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

      10. associate-/r* 41.9%

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

      11. neg-mul-1 41.9%

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

      12. associate-*r/ 41.9%

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

      13. *-rgt-identity 41.9%

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

      14. neg-sub0 41.9%

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

      15. associate--r- 41.9%

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

      16. metadata-eval 41.9%

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

   4. Simplified 41.9%

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

   5. Taylor expanded in z around 0 41.3%

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

      1. mul-1-neg 41.3%

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

   7. Simplified 41.3%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-11} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]

Alternative 11: 23.3% 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 94.4%

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

2. Taylor expanded in y around 0 47.3%

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

   1. associate-*r/ 47.3%

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

   2. mul-1-neg 47.3%

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

   3. *-commutative 47.3%

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

   4. distribute-rgt-neg-in 47.3%

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

   5. associate-*r/ 48.8%

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

   6. neg-mul-1 48.8%

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

   7. *-commutative 48.8%

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

   8. associate-*r/ 48.7%

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

   9. metadata-eval 48.7%

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

   10. associate-/r* 48.7%

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

   11. neg-mul-1 48.7%

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

   12. associate-*r/ 48.8%

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

   13. *-rgt-identity 48.8%

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

   14. neg-sub0 48.8%

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

   15. associate--r- 48.8%

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

   16. metadata-eval 48.8%

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

4. Simplified 48.8%

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

5. Taylor expanded in z around 0 27.4%

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

   1. mul-1-neg 27.4%

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

7. Simplified 27.4%

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

8. Final simplification 27.4%

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

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 2023192 
(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)))))