Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.4% → 93.1%

Time: 26.2s

Alternatives: 21

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{t - x}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-306} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- t x) (- z a))))))
   (if (or (<= t_1 -5e-306) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (+ t (/ (* x (- y a)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((t - x) / (z - a)));
	double tmp;
	if ((t_1 <= -5e-306) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = t + ((x * (y - a)) / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(t - x) / Float64(z - a))))
	tmp = 0.0
	if ((t_1 <= -5e-306) || !(t_1 <= 0.0))
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = Float64(t + Float64(Float64(x * Float64(y - a)) / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-306], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(t + N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.99999999999999998e-306 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 85.5%

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

      1. +-commutative 85.5%

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

      2. remove-double-neg 85.5%

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

      3. unsub-neg 85.5%

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

      4. *-commutative 85.5%

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

      5. associate-*l/ 75.3%

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

      6. associate-/l* 92.4%

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

      7. fma-neg 92.4%

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

      8. remove-double-neg 92.4%

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

   3. Simplified 92.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing

   if -4.99999999999999998e-306 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.0%

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

   3. Taylor expanded in z around inf 87.5%

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

      1. associate--l+ 87.5%

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

      2. associate-*r/ 87.5%

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

      3. associate-*r/ 87.5%

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

      4. mul-1-neg 87.5%

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

      5. div-sub 87.5%

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

      6. mul-1-neg 87.5%

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

      7. distribute-lft-out-- 87.5%

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

      8. associate-*r/ 87.5%

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

      9. mul-1-neg 87.5%

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

      10. unsub-neg 87.5%

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

      11. distribute-rgt-out-- 87.5%

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

   5. Simplified 87.5%

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

   6. Taylor expanded in t around 0 87.5%

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

      1. associate-*r/ 87.5%

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

      2. associate-*r* 87.5%

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

      3. mul-1-neg 87.5%

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

   8. Simplified 87.5%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{t - x}{z - a} \leq -5 \cdot 10^{-306} \lor \neg \left(x + \left(z - y\right) \cdot \frac{t - x}{z - a} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{t - x}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-249} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- t x) (- z a))))))
   (if (or (<= t_1 -5e-249) (not (<= t_1 0.0)))
     t_1
     (+ t (/ (* x (- y a)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((t - x) / (z - a)));
	double tmp;
	if ((t_1 <= -5e-249) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((x * (y - a)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - y) * ((t - x) / (z - a)))
    if ((t_1 <= (-5d-249)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t + ((x * (y - a)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((t - x) / (z - a)));
	double tmp;
	if ((t_1 <= -5e-249) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((x * (y - a)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - y) * ((t - x) / (z - a)))
	tmp = 0
	if (t_1 <= -5e-249) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t + ((x * (y - a)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(t - x) / Float64(z - a))))
	tmp = 0.0
	if ((t_1 <= -5e-249) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(x * Float64(y - a)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - y) * ((t - x) / (z - a)));
	tmp = 0.0;
	if ((t_1 <= -5e-249) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t + ((x * (y - a)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-249], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t + N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.9999999999999999e-249 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 87.2%

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

   if -4.9999999999999999e-249 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 8.4%

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

   3. Taylor expanded in z around inf 82.2%

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

      1. associate--l+ 82.2%

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

      2. associate-*r/ 82.2%

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

      3. associate-*r/ 82.2%

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

      4. mul-1-neg 82.2%

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

      5. div-sub 82.2%

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

      6. mul-1-neg 82.2%

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

      7. distribute-lft-out-- 82.2%

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

      8. associate-*r/ 82.2%

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

      9. mul-1-neg 82.2%

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

      10. unsub-neg 82.2%

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

      11. distribute-rgt-out-- 82.2%

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

   5. Simplified 82.2%

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

   6. Taylor expanded in t around 0 82.2%

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

      1. associate-*r/ 82.2%

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

      2. associate-*r* 82.2%

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

      3. mul-1-neg 82.2%

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

   8. Simplified 82.2%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{t - x}{z - a} \leq -5 \cdot 10^{-249} \lor \neg \left(x + \left(z - y\right) \cdot \frac{t - x}{z - a} \leq 0\right):\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{t - x}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{t - x}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-249} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x - \frac{y - z}{\frac{a - z}{x - t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- t x) (- z a))))))
   (if (or (<= t_1 -5e-249) (not (<= t_1 0.0)))
     (- x (/ (- y z) (/ (- a z) (- x t))))
     (+ t (/ (* x (- y a)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((t - x) / (z - a)));
	double tmp;
	if ((t_1 <= -5e-249) || !(t_1 <= 0.0)) {
		tmp = x - ((y - z) / ((a - z) / (x - t)));
	} else {
		tmp = t + ((x * (y - a)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - y) * ((t - x) / (z - a)))
    if ((t_1 <= (-5d-249)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x - ((y - z) / ((a - z) / (x - t)))
    else
        tmp = t + ((x * (y - a)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((t - x) / (z - a)));
	double tmp;
	if ((t_1 <= -5e-249) || !(t_1 <= 0.0)) {
		tmp = x - ((y - z) / ((a - z) / (x - t)));
	} else {
		tmp = t + ((x * (y - a)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - y) * ((t - x) / (z - a)))
	tmp = 0
	if (t_1 <= -5e-249) or not (t_1 <= 0.0):
		tmp = x - ((y - z) / ((a - z) / (x - t)))
	else:
		tmp = t + ((x * (y - a)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(t - x) / Float64(z - a))))
	tmp = 0.0
	if ((t_1 <= -5e-249) || !(t_1 <= 0.0))
		tmp = Float64(x - Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(x - t))));
	else
		tmp = Float64(t + Float64(Float64(x * Float64(y - a)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - y) * ((t - x) / (z - a)));
	tmp = 0.0;
	if ((t_1 <= -5e-249) || ~((t_1 <= 0.0)))
		tmp = x - ((y - z) / ((a - z) / (x - t)));
	else
		tmp = t + ((x * (y - a)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-249], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.9999999999999999e-249 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 87.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 87.2%

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

      2. un-div-inv 87.6%

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

   4. Applied egg-rr 87.6%

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

   if -4.9999999999999999e-249 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 8.4%

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

   3. Taylor expanded in z around inf 82.2%

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

      1. associate--l+ 82.2%

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

      2. associate-*r/ 82.2%

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

      3. associate-*r/ 82.2%

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

      4. mul-1-neg 82.2%

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

      5. div-sub 82.2%

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

      6. mul-1-neg 82.2%

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

      7. distribute-lft-out-- 82.2%

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

      8. associate-*r/ 82.2%

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

      9. mul-1-neg 82.2%

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

      10. unsub-neg 82.2%

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

      11. distribute-rgt-out-- 82.2%

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

   5. Simplified 82.2%

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

   6. Taylor expanded in t around 0 82.2%

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

      1. associate-*r/ 82.2%

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

      2. associate-*r* 82.2%

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

      3. mul-1-neg 82.2%

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

   8. Simplified 82.2%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{t - x}{z - a} \leq -5 \cdot 10^{-249} \lor \neg \left(x + \left(z - y\right) \cdot \frac{t - x}{z - a} \leq 0\right):\\ \;\;\;\;x - \frac{y - z}{\frac{a - z}{x - t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 38.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a}\\ t_2 := x \cdot \left(\frac{z}{a} + 1\right)\\ \mathbf{if}\;a \leq -4.1 \cdot 10^{+160}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-181}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.48 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-138}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+176}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) a))) (t_2 (* x (+ (/ z a) 1.0))))
   (if (<= a -4.1e+160)
     t_2
     (if (<= a -5.8e-75)
       t_1
       (if (<= a -1.35e-181)
         t
         (if (<= a 1.48e-213)
           (* x (/ y z))
           (if (<= a 6.2e-138)
             t
             (if (<= a 2.9e+17)
               (* x (/ (- y a) z))
               (if (<= a 1.5e+176) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double t_2 = x * ((z / a) + 1.0);
	double tmp;
	if (a <= -4.1e+160) {
		tmp = t_2;
	} else if (a <= -5.8e-75) {
		tmp = t_1;
	} else if (a <= -1.35e-181) {
		tmp = t;
	} else if (a <= 1.48e-213) {
		tmp = x * (y / z);
	} else if (a <= 6.2e-138) {
		tmp = t;
	} else if (a <= 2.9e+17) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.5e+176) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((t - x) / a)
    t_2 = x * ((z / a) + 1.0d0)
    if (a <= (-4.1d+160)) then
        tmp = t_2
    else if (a <= (-5.8d-75)) then
        tmp = t_1
    else if (a <= (-1.35d-181)) then
        tmp = t
    else if (a <= 1.48d-213) then
        tmp = x * (y / z)
    else if (a <= 6.2d-138) then
        tmp = t
    else if (a <= 2.9d+17) then
        tmp = x * ((y - a) / z)
    else if (a <= 1.5d+176) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double t_2 = x * ((z / a) + 1.0);
	double tmp;
	if (a <= -4.1e+160) {
		tmp = t_2;
	} else if (a <= -5.8e-75) {
		tmp = t_1;
	} else if (a <= -1.35e-181) {
		tmp = t;
	} else if (a <= 1.48e-213) {
		tmp = x * (y / z);
	} else if (a <= 6.2e-138) {
		tmp = t;
	} else if (a <= 2.9e+17) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.5e+176) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / a)
	t_2 = x * ((z / a) + 1.0)
	tmp = 0
	if a <= -4.1e+160:
		tmp = t_2
	elif a <= -5.8e-75:
		tmp = t_1
	elif a <= -1.35e-181:
		tmp = t
	elif a <= 1.48e-213:
		tmp = x * (y / z)
	elif a <= 6.2e-138:
		tmp = t
	elif a <= 2.9e+17:
		tmp = x * ((y - a) / z)
	elif a <= 1.5e+176:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / a))
	t_2 = Float64(x * Float64(Float64(z / a) + 1.0))
	tmp = 0.0
	if (a <= -4.1e+160)
		tmp = t_2;
	elseif (a <= -5.8e-75)
		tmp = t_1;
	elseif (a <= -1.35e-181)
		tmp = t;
	elseif (a <= 1.48e-213)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 6.2e-138)
		tmp = t;
	elseif (a <= 2.9e+17)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 1.5e+176)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / a);
	t_2 = x * ((z / a) + 1.0);
	tmp = 0.0;
	if (a <= -4.1e+160)
		tmp = t_2;
	elseif (a <= -5.8e-75)
		tmp = t_1;
	elseif (a <= -1.35e-181)
		tmp = t;
	elseif (a <= 1.48e-213)
		tmp = x * (y / z);
	elseif (a <= 6.2e-138)
		tmp = t;
	elseif (a <= 2.9e+17)
		tmp = x * ((y - a) / z);
	elseif (a <= 1.5e+176)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(z / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.1e+160], t$95$2, If[LessEqual[a, -5.8e-75], t$95$1, If[LessEqual[a, -1.35e-181], t, If[LessEqual[a, 1.48e-213], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e-138], t, If[LessEqual[a, 2.9e+17], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e+176], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.09999999999999998e160 or 1.5e176 < a

   1. Initial program 91.2%

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

   3. Taylor expanded in x around -inf 72.8%

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

      1. mul-1-neg 72.8%

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

      2. *-commutative 72.8%

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

      3. distribute-rgt-neg-in 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in y around 0 67.5%

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

   7. Taylor expanded in z around 0 65.2%

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

   if -4.09999999999999998e160 < a < -5.8000000000000003e-75 or 2.9e17 < a < 1.5e176

   1. Initial program 87.2%

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

   3. Taylor expanded in z around 0 60.2%

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

   4. Taylor expanded in y around inf 47.4%

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

      1. div-sub 47.4%

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

   6. Simplified 47.4%

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

   if -5.8000000000000003e-75 < a < -1.35e-181 or 1.4800000000000001e-213 < a < 6.1999999999999996e-138

   1. Initial program 46.2%

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

   3. Taylor expanded in z around inf 54.6%

      \[\leadsto \color{blue}{t} \]

   if -1.35e-181 < a < 1.4800000000000001e-213

   1. Initial program 65.3%

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

   3. Taylor expanded in x around -inf 59.0%

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

      1. mul-1-neg 59.0%

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

      2. *-commutative 59.0%

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

      3. distribute-rgt-neg-in 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in z around -inf 50.7%

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

   7. Taylor expanded in y around inf 50.7%

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

      1. associate-/l* 54.5%

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

   9. Simplified 54.5%

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

   if 6.1999999999999996e-138 < a < 2.9e17

   1. Initial program 58.5%

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

   3. Taylor expanded in x around -inf 40.7%

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

      1. mul-1-neg 40.7%

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

      2. *-commutative 40.7%

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

      3. distribute-rgt-neg-in 40.7%

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

   5. Simplified 40.7%

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

   6. Taylor expanded in z around -inf 30.0%

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

      1. associate-/l* 39.0%

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

   8. Simplified 39.0%

      \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+160}:\\ \;\;\;\;x \cdot \left(\frac{z}{a} + 1\right)\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-75}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-181}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.48 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-138}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+176}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{z}{a} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -6.1 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-182}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-214}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{-139}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= a -6.1e+54)
     t_1
     (if (<= a -1.08e-74)
       (* y (/ (- t x) a))
       (if (<= a -5e-182)
         t
         (if (<= a 3.2e-214)
           (* y (/ (- x t) z))
           (if (<= a 1.16e-139)
             t
             (if (<= a 1.8e-15) (* x (/ (- y a) z)) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (a <= -6.1e+54) {
		tmp = t_1;
	} else if (a <= -1.08e-74) {
		tmp = y * ((t - x) / a);
	} else if (a <= -5e-182) {
		tmp = t;
	} else if (a <= 3.2e-214) {
		tmp = y * ((x - t) / z);
	} else if (a <= 1.16e-139) {
		tmp = t;
	} else if (a <= 1.8e-15) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t * (y / a))
    if (a <= (-6.1d+54)) then
        tmp = t_1
    else if (a <= (-1.08d-74)) then
        tmp = y * ((t - x) / a)
    else if (a <= (-5d-182)) then
        tmp = t
    else if (a <= 3.2d-214) then
        tmp = y * ((x - t) / z)
    else if (a <= 1.16d-139) then
        tmp = t
    else if (a <= 1.8d-15) then
        tmp = x * ((y - a) / 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 a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (a <= -6.1e+54) {
		tmp = t_1;
	} else if (a <= -1.08e-74) {
		tmp = y * ((t - x) / a);
	} else if (a <= -5e-182) {
		tmp = t;
	} else if (a <= 3.2e-214) {
		tmp = y * ((x - t) / z);
	} else if (a <= 1.16e-139) {
		tmp = t;
	} else if (a <= 1.8e-15) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if a <= -6.1e+54:
		tmp = t_1
	elif a <= -1.08e-74:
		tmp = y * ((t - x) / a)
	elif a <= -5e-182:
		tmp = t
	elif a <= 3.2e-214:
		tmp = y * ((x - t) / z)
	elif a <= 1.16e-139:
		tmp = t
	elif a <= 1.8e-15:
		tmp = x * ((y - a) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (a <= -6.1e+54)
		tmp = t_1;
	elseif (a <= -1.08e-74)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (a <= -5e-182)
		tmp = t;
	elseif (a <= 3.2e-214)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	elseif (a <= 1.16e-139)
		tmp = t;
	elseif (a <= 1.8e-15)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (a <= -6.1e+54)
		tmp = t_1;
	elseif (a <= -1.08e-74)
		tmp = y * ((t - x) / a);
	elseif (a <= -5e-182)
		tmp = t;
	elseif (a <= 3.2e-214)
		tmp = y * ((x - t) / z);
	elseif (a <= 1.16e-139)
		tmp = t;
	elseif (a <= 1.8e-15)
		tmp = x * ((y - a) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.1e+54], t$95$1, If[LessEqual[a, -1.08e-74], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5e-182], t, If[LessEqual[a, 3.2e-214], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.16e-139], t, If[LessEqual[a, 1.8e-15], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -6.0999999999999998e54 or 1.8000000000000001e-15 < a

   1. Initial program 89.9%

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

   3. Taylor expanded in z around 0 64.7%

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

      1. associate-/l* 72.0%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in t around inf 61.7%

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

      1. associate-/l* 62.9%

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

   8. Simplified 62.9%

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

   if -6.0999999999999998e54 < a < -1.0799999999999999e-74

   1. Initial program 82.4%

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

   3. Taylor expanded in z around 0 61.6%

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

   4. Taylor expanded in y around inf 56.8%

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

      1. div-sub 56.8%

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

   6. Simplified 56.8%

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

   if -1.0799999999999999e-74 < a < -5.00000000000000024e-182 or 3.20000000000000013e-214 < a < 1.15999999999999999e-139

   1. Initial program 46.2%

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

   3. Taylor expanded in z around inf 54.6%

      \[\leadsto \color{blue}{t} \]

   if -5.00000000000000024e-182 < a < 3.20000000000000013e-214

   1. Initial program 65.3%

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

   3. Taylor expanded in z around inf 86.7%

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

      1. associate--l+ 86.7%

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

      2. associate-*r/ 86.7%

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

      3. associate-*r/ 86.7%

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

      4. mul-1-neg 86.7%

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

      5. div-sub 86.7%

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

      6. mul-1-neg 86.7%

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

      7. distribute-lft-out-- 86.7%

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

      8. associate-*r/ 86.7%

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

      9. mul-1-neg 86.7%

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

      10. unsub-neg 86.7%

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

      11. distribute-rgt-out-- 86.7%

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

   5. Simplified 86.7%

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

   6. Taylor expanded in y around -inf 57.6%

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

      1. mul-1-neg 57.6%

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

      2. associate-/l* 58.3%

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

   8. Simplified 58.3%

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

   if 1.15999999999999999e-139 < a < 1.8000000000000001e-15

   1. Initial program 55.9%

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

   3. Taylor expanded in x around -inf 39.0%

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

      1. mul-1-neg 39.0%

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

      2. *-commutative 39.0%

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

      3. distribute-rgt-neg-in 39.0%

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

   5. Simplified 39.0%

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

   6. Taylor expanded in z around -inf 30.4%

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

      1. associate-/l* 40.8%

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

   8. Simplified 40.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.1 \cdot 10^{+54}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-182}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-214}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{-139}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 47.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -1.28 \cdot 10^{-189}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-212}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-136}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 10^{-13}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.3e+41)
   (* x (- 1.0 (/ y a)))
   (if (<= a -6.4e-76)
     (* y (/ (- t x) a))
     (if (<= a -1.28e-189)
       t
       (if (<= a 1.1e-212)
         (* y (/ (- x t) z))
         (if (<= a 1.45e-136)
           t
           (if (<= a 1e-13) (* x (/ (- y a) z)) (+ x (* t (/ y a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.3e+41) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= -6.4e-76) {
		tmp = y * ((t - x) / a);
	} else if (a <= -1.28e-189) {
		tmp = t;
	} else if (a <= 1.1e-212) {
		tmp = y * ((x - t) / z);
	} else if (a <= 1.45e-136) {
		tmp = t;
	} else if (a <= 1e-13) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.3d+41)) then
        tmp = x * (1.0d0 - (y / a))
    else if (a <= (-6.4d-76)) then
        tmp = y * ((t - x) / a)
    else if (a <= (-1.28d-189)) then
        tmp = t
    else if (a <= 1.1d-212) then
        tmp = y * ((x - t) / z)
    else if (a <= 1.45d-136) then
        tmp = t
    else if (a <= 1d-13) then
        tmp = x * ((y - a) / z)
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.3e+41) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= -6.4e-76) {
		tmp = y * ((t - x) / a);
	} else if (a <= -1.28e-189) {
		tmp = t;
	} else if (a <= 1.1e-212) {
		tmp = y * ((x - t) / z);
	} else if (a <= 1.45e-136) {
		tmp = t;
	} else if (a <= 1e-13) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.3e+41:
		tmp = x * (1.0 - (y / a))
	elif a <= -6.4e-76:
		tmp = y * ((t - x) / a)
	elif a <= -1.28e-189:
		tmp = t
	elif a <= 1.1e-212:
		tmp = y * ((x - t) / z)
	elif a <= 1.45e-136:
		tmp = t
	elif a <= 1e-13:
		tmp = x * ((y - a) / z)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.3e+41)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (a <= -6.4e-76)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (a <= -1.28e-189)
		tmp = t;
	elseif (a <= 1.1e-212)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	elseif (a <= 1.45e-136)
		tmp = t;
	elseif (a <= 1e-13)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.3e+41)
		tmp = x * (1.0 - (y / a));
	elseif (a <= -6.4e-76)
		tmp = y * ((t - x) / a);
	elseif (a <= -1.28e-189)
		tmp = t;
	elseif (a <= 1.1e-212)
		tmp = y * ((x - t) / z);
	elseif (a <= 1.45e-136)
		tmp = t;
	elseif (a <= 1e-13)
		tmp = x * ((y - a) / z);
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.3e+41], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.4e-76], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.28e-189], t, If[LessEqual[a, 1.1e-212], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.45e-136], t, If[LessEqual[a, 1e-13], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.3e41

   1. Initial program 86.5%

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

   3. Taylor expanded in z around 0 60.4%

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

   4. Taylor expanded in x around inf 59.9%

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

      1. mul-1-neg 59.9%

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

   6. Simplified 59.9%

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

   if -1.3e41 < a < -6.3999999999999995e-76

   1. Initial program 80.3%

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

   3. Taylor expanded in z around 0 57.0%

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

   4. Taylor expanded in y around inf 57.0%

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

      1. div-sub 57.0%

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

   6. Simplified 57.0%

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

   if -6.3999999999999995e-76 < a < -1.28e-189 or 1.10000000000000002e-212 < a < 1.44999999999999997e-136

   1. Initial program 46.2%

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

   3. Taylor expanded in z around inf 54.6%

      \[\leadsto \color{blue}{t} \]

   if -1.28e-189 < a < 1.10000000000000002e-212

   1. Initial program 65.3%

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

   3. Taylor expanded in z around inf 86.7%

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

      1. associate--l+ 86.7%

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

      2. associate-*r/ 86.7%

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

      3. associate-*r/ 86.7%

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

      4. mul-1-neg 86.7%

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

      5. div-sub 86.7%

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

      6. mul-1-neg 86.7%

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

      7. distribute-lft-out-- 86.7%

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

      8. associate-*r/ 86.7%

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

      9. mul-1-neg 86.7%

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

      10. unsub-neg 86.7%

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

      11. distribute-rgt-out-- 86.7%

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

   5. Simplified 86.7%

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

   6. Taylor expanded in y around -inf 57.6%

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

      1. mul-1-neg 57.6%

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

      2. associate-/l* 58.3%

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

   8. Simplified 58.3%

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

   if 1.44999999999999997e-136 < a < 1e-13

   1. Initial program 55.9%

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

   3. Taylor expanded in x around -inf 39.0%

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

      1. mul-1-neg 39.0%

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

      2. *-commutative 39.0%

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

      3. distribute-rgt-neg-in 39.0%

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

   5. Simplified 39.0%

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

   6. Taylor expanded in z around -inf 30.4%

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

      1. associate-/l* 40.8%

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

   8. Simplified 40.8%

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

   if 1e-13 < a

   1. Initial program 93.3%

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

   3. Taylor expanded in z around 0 69.9%

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

      1. associate-/l* 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in t around inf 64.5%

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

      1. associate-/l* 66.1%

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

   8. Simplified 66.1%

      \[\leadsto x + \color{blue}{t \cdot \frac{y}{a}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -1.28 \cdot 10^{-189}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-212}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-136}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 10^{-13}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;x \leq -6 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq -1.76 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 10^{+200}:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= x -6e+107)
     (* x (- 1.0 (/ y a)))
     (if (<= x -1.76e-50)
       t_1
       (if (<= x 4.1e-43)
         t_2
         (if (<= x 7.5e+55)
           t_1
           (if (<= x 2.9e+68)
             t_2
             (if (<= x 1e+200) (- x (* y (/ x a))) (* (- y a) (/ x z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (x <= -6e+107) {
		tmp = x * (1.0 - (y / a));
	} else if (x <= -1.76e-50) {
		tmp = t_1;
	} else if (x <= 4.1e-43) {
		tmp = t_2;
	} else if (x <= 7.5e+55) {
		tmp = t_1;
	} else if (x <= 2.9e+68) {
		tmp = t_2;
	} else if (x <= 1e+200) {
		tmp = x - (y * (x / a));
	} else {
		tmp = (y - a) * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    t_2 = t * ((y - z) / (a - z))
    if (x <= (-6d+107)) then
        tmp = x * (1.0d0 - (y / a))
    else if (x <= (-1.76d-50)) then
        tmp = t_1
    else if (x <= 4.1d-43) then
        tmp = t_2
    else if (x <= 7.5d+55) then
        tmp = t_1
    else if (x <= 2.9d+68) then
        tmp = t_2
    else if (x <= 1d+200) then
        tmp = x - (y * (x / a))
    else
        tmp = (y - a) * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (x <= -6e+107) {
		tmp = x * (1.0 - (y / a));
	} else if (x <= -1.76e-50) {
		tmp = t_1;
	} else if (x <= 4.1e-43) {
		tmp = t_2;
	} else if (x <= 7.5e+55) {
		tmp = t_1;
	} else if (x <= 2.9e+68) {
		tmp = t_2;
	} else if (x <= 1e+200) {
		tmp = x - (y * (x / a));
	} else {
		tmp = (y - a) * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if x <= -6e+107:
		tmp = x * (1.0 - (y / a))
	elif x <= -1.76e-50:
		tmp = t_1
	elif x <= 4.1e-43:
		tmp = t_2
	elif x <= 7.5e+55:
		tmp = t_1
	elif x <= 2.9e+68:
		tmp = t_2
	elif x <= 1e+200:
		tmp = x - (y * (x / a))
	else:
		tmp = (y - a) * (x / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (x <= -6e+107)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (x <= -1.76e-50)
		tmp = t_1;
	elseif (x <= 4.1e-43)
		tmp = t_2;
	elseif (x <= 7.5e+55)
		tmp = t_1;
	elseif (x <= 2.9e+68)
		tmp = t_2;
	elseif (x <= 1e+200)
		tmp = Float64(x - Float64(y * Float64(x / a)));
	else
		tmp = Float64(Float64(y - a) * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (x <= -6e+107)
		tmp = x * (1.0 - (y / a));
	elseif (x <= -1.76e-50)
		tmp = t_1;
	elseif (x <= 4.1e-43)
		tmp = t_2;
	elseif (x <= 7.5e+55)
		tmp = t_1;
	elseif (x <= 2.9e+68)
		tmp = t_2;
	elseif (x <= 1e+200)
		tmp = x - (y * (x / a));
	else
		tmp = (y - a) * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6e+107], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.76e-50], t$95$1, If[LessEqual[x, 4.1e-43], t$95$2, If[LessEqual[x, 7.5e+55], t$95$1, If[LessEqual[x, 2.9e+68], t$95$2, If[LessEqual[x, 1e+200], N[(x - N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -6.00000000000000046e107

   1. Initial program 68.0%

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

   3. Taylor expanded in z around 0 55.2%

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

   4. Taylor expanded in x around inf 64.9%

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

      1. mul-1-neg 64.9%

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

   6. Simplified 64.9%

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

   if -6.00000000000000046e107 < x < -1.76e-50 or 4.0999999999999998e-43 < x < 7.50000000000000014e55

   1. Initial program 83.7%

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

   3. Taylor expanded in y around inf 59.3%

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

      1. div-sub 59.3%

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

   5. Simplified 59.3%

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

   if -1.76e-50 < x < 4.0999999999999998e-43 or 7.50000000000000014e55 < x < 2.90000000000000011e68

   1. Initial program 80.2%

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

   3. Taylor expanded in x around 0 65.9%

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

      1. associate-/l* 77.4%

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

   5. Simplified 77.4%

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

   if 2.90000000000000011e68 < x < 9.9999999999999997e199

   1. Initial program 76.8%

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

   3. Taylor expanded in z around 0 43.6%

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

      1. associate-/l* 61.2%

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

   5. Simplified 61.2%

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

   6. Taylor expanded in t around 0 60.8%

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

      1. neg-mul-1 60.8%

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

      2. distribute-neg-frac2 60.8%

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

   8. Simplified 60.8%

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

   if 9.9999999999999997e199 < x

   1. Initial program 45.6%

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

   3. Taylor expanded in z around inf 57.3%

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

      1. associate--l+ 57.3%

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

      2. associate-*r/ 57.3%

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

      3. associate-*r/ 57.3%

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

      4. mul-1-neg 57.3%

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

      5. div-sub 57.3%

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

      6. mul-1-neg 57.3%

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

      7. distribute-lft-out-- 57.3%

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

      8. associate-*r/ 57.3%

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

      9. mul-1-neg 57.3%

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

      10. unsub-neg 57.3%

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

      11. distribute-rgt-out-- 62.3%

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

   5. Simplified 62.3%

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

   6. Taylor expanded in t around 0 42.5%

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

      1. *-commutative 42.5%

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

      2. associate-*r/ 66.3%

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

      3. *-commutative 66.3%

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

   8. Simplified 66.3%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq -1.76 \cdot 10^{-50}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-43}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 10^{+200}:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{+175}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3350000000:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-19} \lor \neg \left(z \leq 3.9 \cdot 10^{+21}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -8.6e+175)
     (* x (/ (- y a) z))
     (if (<= z -1.25e+87)
       t_1
       (if (<= z -3350000000.0)
         (* y (/ (- t x) (- a z)))
         (if (or (<= z -1.65e-19) (not (<= z 3.9e+21)))
           t_1
           (+ x (/ (* y (- t x)) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -8.6e+175) {
		tmp = x * ((y - a) / z);
	} else if (z <= -1.25e+87) {
		tmp = t_1;
	} else if (z <= -3350000000.0) {
		tmp = y * ((t - x) / (a - z));
	} else if ((z <= -1.65e-19) || !(z <= 3.9e+21)) {
		tmp = t_1;
	} else {
		tmp = x + ((y * (t - x)) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-8.6d+175)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-1.25d+87)) then
        tmp = t_1
    else if (z <= (-3350000000.0d0)) then
        tmp = y * ((t - x) / (a - z))
    else if ((z <= (-1.65d-19)) .or. (.not. (z <= 3.9d+21))) then
        tmp = t_1
    else
        tmp = x + ((y * (t - x)) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -8.6e+175) {
		tmp = x * ((y - a) / z);
	} else if (z <= -1.25e+87) {
		tmp = t_1;
	} else if (z <= -3350000000.0) {
		tmp = y * ((t - x) / (a - z));
	} else if ((z <= -1.65e-19) || !(z <= 3.9e+21)) {
		tmp = t_1;
	} else {
		tmp = x + ((y * (t - x)) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -8.6e+175:
		tmp = x * ((y - a) / z)
	elif z <= -1.25e+87:
		tmp = t_1
	elif z <= -3350000000.0:
		tmp = y * ((t - x) / (a - z))
	elif (z <= -1.65e-19) or not (z <= 3.9e+21):
		tmp = t_1
	else:
		tmp = x + ((y * (t - x)) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -8.6e+175)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -1.25e+87)
		tmp = t_1;
	elseif (z <= -3350000000.0)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif ((z <= -1.65e-19) || !(z <= 3.9e+21))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -8.6e+175)
		tmp = x * ((y - a) / z);
	elseif (z <= -1.25e+87)
		tmp = t_1;
	elseif (z <= -3350000000.0)
		tmp = y * ((t - x) / (a - z));
	elseif ((z <= -1.65e-19) || ~((z <= 3.9e+21)))
		tmp = t_1;
	else
		tmp = x + ((y * (t - x)) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.6e+175], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.25e+87], t$95$1, If[LessEqual[z, -3350000000.0], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.65e-19], N[Not[LessEqual[z, 3.9e+21]], $MachinePrecision]], t$95$1, N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.59999999999999967e175

   1. Initial program 45.6%

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

   3. Taylor expanded in x around -inf 36.1%

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

      1. mul-1-neg 36.1%

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

      2. *-commutative 36.1%

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

      3. distribute-rgt-neg-in 36.1%

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

   5. Simplified 36.1%

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

   6. Taylor expanded in z around -inf 41.2%

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

      1. associate-/l* 55.1%

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

   8. Simplified 55.1%

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

   if -8.59999999999999967e175 < z < -1.24999999999999995e87 or -3.35e9 < z < -1.6499999999999999e-19 or 3.9e21 < z

   1. Initial program 62.0%

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

   3. Taylor expanded in x around 0 41.1%

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

      1. associate-/l* 62.3%

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

   5. Simplified 62.3%

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

   if -1.24999999999999995e87 < z < -3.35e9

   1. Initial program 87.1%

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

   3. Taylor expanded in y around inf 59.5%

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

      1. div-sub 59.5%

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

   5. Simplified 59.5%

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

   if -1.6499999999999999e-19 < z < 3.9e21

   1. Initial program 88.8%

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

   3. Taylor expanded in z around 0 79.4%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+175}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -3350000000:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-19} \lor \neg \left(z \leq 3.9 \cdot 10^{+21}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;a \leq -2 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-184}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{-211}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-133}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{z}{a} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= a -2e+25)
     x
     (if (<= a -8.5e-184)
       t
       (if (<= a 1.26e-211)
         t_1
         (if (<= a 7e-133)
           t
           (if (<= a 7.5e-12) t_1 (* x (+ (/ z a) 1.0)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -2e+25) {
		tmp = x;
	} else if (a <= -8.5e-184) {
		tmp = t;
	} else if (a <= 1.26e-211) {
		tmp = t_1;
	} else if (a <= 7e-133) {
		tmp = t;
	} else if (a <= 7.5e-12) {
		tmp = t_1;
	} else {
		tmp = x * ((z / a) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / z)
    if (a <= (-2d+25)) then
        tmp = x
    else if (a <= (-8.5d-184)) then
        tmp = t
    else if (a <= 1.26d-211) then
        tmp = t_1
    else if (a <= 7d-133) then
        tmp = t
    else if (a <= 7.5d-12) then
        tmp = t_1
    else
        tmp = x * ((z / a) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -2e+25) {
		tmp = x;
	} else if (a <= -8.5e-184) {
		tmp = t;
	} else if (a <= 1.26e-211) {
		tmp = t_1;
	} else if (a <= 7e-133) {
		tmp = t;
	} else if (a <= 7.5e-12) {
		tmp = t_1;
	} else {
		tmp = x * ((z / a) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	tmp = 0
	if a <= -2e+25:
		tmp = x
	elif a <= -8.5e-184:
		tmp = t
	elif a <= 1.26e-211:
		tmp = t_1
	elif a <= 7e-133:
		tmp = t
	elif a <= 7.5e-12:
		tmp = t_1
	else:
		tmp = x * ((z / a) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (a <= -2e+25)
		tmp = x;
	elseif (a <= -8.5e-184)
		tmp = t;
	elseif (a <= 1.26e-211)
		tmp = t_1;
	elseif (a <= 7e-133)
		tmp = t;
	elseif (a <= 7.5e-12)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(z / a) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (a <= -2e+25)
		tmp = x;
	elseif (a <= -8.5e-184)
		tmp = t;
	elseif (a <= 1.26e-211)
		tmp = t_1;
	elseif (a <= 7e-133)
		tmp = t;
	elseif (a <= 7.5e-12)
		tmp = t_1;
	else
		tmp = x * ((z / a) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2e+25], x, If[LessEqual[a, -8.5e-184], t, If[LessEqual[a, 1.26e-211], t$95$1, If[LessEqual[a, 7e-133], t, If[LessEqual[a, 7.5e-12], t$95$1, N[(x * N[(N[(z / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.00000000000000018e25

   1. Initial program 85.7%

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

   3. Taylor expanded in a around inf 44.4%

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

   if -2.00000000000000018e25 < a < -8.50000000000000036e-184 or 1.26000000000000009e-211 < a < 7.00000000000000006e-133

   1. Initial program 58.3%

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

   3. Taylor expanded in z around inf 46.7%

      \[\leadsto \color{blue}{t} \]

   if -8.50000000000000036e-184 < a < 1.26000000000000009e-211 or 7.00000000000000006e-133 < a < 7.5e-12

   1. Initial program 62.7%

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

   3. Taylor expanded in x around -inf 50.8%

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

      1. mul-1-neg 50.8%

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

      2. *-commutative 50.8%

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

      3. distribute-rgt-neg-in 50.8%

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

   5. Simplified 50.8%

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

   6. Taylor expanded in z around -inf 43.6%

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

   7. Taylor expanded in y around inf 41.4%

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

      1. associate-/l* 47.8%

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

   9. Simplified 47.8%

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

   if 7.5e-12 < a

   1. Initial program 93.3%

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

   3. Taylor expanded in x around -inf 59.7%

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

      1. mul-1-neg 59.7%

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

      2. *-commutative 59.7%

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

      3. distribute-rgt-neg-in 59.7%

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

   5. Simplified 59.7%

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

   6. Taylor expanded in y around 0 47.5%

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

   7. Taylor expanded in z around 0 45.3%

      \[\leadsto x \cdot \color{blue}{\left(1 + \frac{z}{a}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-184}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-133}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{z}{a} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 38.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.6 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-188}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-214}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-136}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{z}{a} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.6e+23)
   x
   (if (<= a -1.05e-188)
     t
     (if (<= a 1.65e-214)
       (* x (/ y z))
       (if (<= a 5.5e-136)
         t
         (if (<= a 7e+18) (* x (/ (- y a) z)) (* x (+ (/ z a) 1.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.6e+23) {
		tmp = x;
	} else if (a <= -1.05e-188) {
		tmp = t;
	} else if (a <= 1.65e-214) {
		tmp = x * (y / z);
	} else if (a <= 5.5e-136) {
		tmp = t;
	} else if (a <= 7e+18) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = x * ((z / a) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9.6d+23)) then
        tmp = x
    else if (a <= (-1.05d-188)) then
        tmp = t
    else if (a <= 1.65d-214) then
        tmp = x * (y / z)
    else if (a <= 5.5d-136) then
        tmp = t
    else if (a <= 7d+18) then
        tmp = x * ((y - a) / z)
    else
        tmp = x * ((z / a) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.6e+23) {
		tmp = x;
	} else if (a <= -1.05e-188) {
		tmp = t;
	} else if (a <= 1.65e-214) {
		tmp = x * (y / z);
	} else if (a <= 5.5e-136) {
		tmp = t;
	} else if (a <= 7e+18) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = x * ((z / a) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.6e+23:
		tmp = x
	elif a <= -1.05e-188:
		tmp = t
	elif a <= 1.65e-214:
		tmp = x * (y / z)
	elif a <= 5.5e-136:
		tmp = t
	elif a <= 7e+18:
		tmp = x * ((y - a) / z)
	else:
		tmp = x * ((z / a) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.6e+23)
		tmp = x;
	elseif (a <= -1.05e-188)
		tmp = t;
	elseif (a <= 1.65e-214)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 5.5e-136)
		tmp = t;
	elseif (a <= 7e+18)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	else
		tmp = Float64(x * Float64(Float64(z / a) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.6e+23)
		tmp = x;
	elseif (a <= -1.05e-188)
		tmp = t;
	elseif (a <= 1.65e-214)
		tmp = x * (y / z);
	elseif (a <= 5.5e-136)
		tmp = t;
	elseif (a <= 7e+18)
		tmp = x * ((y - a) / z);
	else
		tmp = x * ((z / a) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.6e+23], x, If[LessEqual[a, -1.05e-188], t, If[LessEqual[a, 1.65e-214], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e-136], t, If[LessEqual[a, 7e+18], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -9.6e23

   1. Initial program 85.7%

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

   3. Taylor expanded in a around inf 44.4%

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

   if -9.6e23 < a < -1.05e-188 or 1.6499999999999999e-214 < a < 5.4999999999999999e-136

   1. Initial program 59.4%

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

   3. Taylor expanded in z around inf 47.5%

      \[\leadsto \color{blue}{t} \]

   if -1.05e-188 < a < 1.6499999999999999e-214

   1. Initial program 65.3%

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

   3. Taylor expanded in x around -inf 59.0%

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

      1. mul-1-neg 59.0%

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

      2. *-commutative 59.0%

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

      3. distribute-rgt-neg-in 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in z around -inf 50.7%

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

   7. Taylor expanded in y around inf 50.7%

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

      1. associate-/l* 54.5%

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

   9. Simplified 54.5%

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

   if 5.4999999999999999e-136 < a < 7e18

   1. Initial program 59.9%

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

   3. Taylor expanded in x around -inf 39.4%

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

      1. mul-1-neg 39.4%

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

      2. *-commutative 39.4%

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

      3. distribute-rgt-neg-in 39.4%

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

   5. Simplified 39.4%

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

   6. Taylor expanded in z around -inf 29.2%

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

      1. associate-/l* 41.0%

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

   8. Simplified 41.0%

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

   if 7e18 < a

   1. Initial program 94.3%

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

   3. Taylor expanded in x around -inf 61.1%

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

      1. mul-1-neg 61.1%

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

      2. *-commutative 61.1%

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

      3. distribute-rgt-neg-in 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in y around 0 49.0%

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

   7. Taylor expanded in z around 0 46.7%

      \[\leadsto x \cdot \color{blue}{\left(1 + \frac{z}{a}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.6 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-188}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-214}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-136}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{z}{a} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.32 \cdot 10^{-55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 10^{+200}:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= x -1.2e+69)
     t_2
     (if (<= x -6e-34)
       t_1
       (if (<= x -1.32e-55)
         t_2
         (if (<= x 2.9e+19)
           t_1
           (if (<= x 1e+200) (- x (* y (/ x a))) (* (- y a) (/ x z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -1.2e+69) {
		tmp = t_2;
	} else if (x <= -6e-34) {
		tmp = t_1;
	} else if (x <= -1.32e-55) {
		tmp = t_2;
	} else if (x <= 2.9e+19) {
		tmp = t_1;
	} else if (x <= 1e+200) {
		tmp = x - (y * (x / a));
	} else {
		tmp = (y - a) * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x * (1.0d0 - (y / a))
    if (x <= (-1.2d+69)) then
        tmp = t_2
    else if (x <= (-6d-34)) then
        tmp = t_1
    else if (x <= (-1.32d-55)) then
        tmp = t_2
    else if (x <= 2.9d+19) then
        tmp = t_1
    else if (x <= 1d+200) then
        tmp = x - (y * (x / a))
    else
        tmp = (y - a) * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -1.2e+69) {
		tmp = t_2;
	} else if (x <= -6e-34) {
		tmp = t_1;
	} else if (x <= -1.32e-55) {
		tmp = t_2;
	} else if (x <= 2.9e+19) {
		tmp = t_1;
	} else if (x <= 1e+200) {
		tmp = x - (y * (x / a));
	} else {
		tmp = (y - a) * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if x <= -1.2e+69:
		tmp = t_2
	elif x <= -6e-34:
		tmp = t_1
	elif x <= -1.32e-55:
		tmp = t_2
	elif x <= 2.9e+19:
		tmp = t_1
	elif x <= 1e+200:
		tmp = x - (y * (x / a))
	else:
		tmp = (y - a) * (x / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (x <= -1.2e+69)
		tmp = t_2;
	elseif (x <= -6e-34)
		tmp = t_1;
	elseif (x <= -1.32e-55)
		tmp = t_2;
	elseif (x <= 2.9e+19)
		tmp = t_1;
	elseif (x <= 1e+200)
		tmp = Float64(x - Float64(y * Float64(x / a)));
	else
		tmp = Float64(Float64(y - a) * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (x <= -1.2e+69)
		tmp = t_2;
	elseif (x <= -6e-34)
		tmp = t_1;
	elseif (x <= -1.32e-55)
		tmp = t_2;
	elseif (x <= 2.9e+19)
		tmp = t_1;
	elseif (x <= 1e+200)
		tmp = x - (y * (x / a));
	else
		tmp = (y - a) * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e+69], t$95$2, If[LessEqual[x, -6e-34], t$95$1, If[LessEqual[x, -1.32e-55], t$95$2, If[LessEqual[x, 2.9e+19], t$95$1, If[LessEqual[x, 1e+200], N[(x - N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.2000000000000001e69 or -6e-34 < x < -1.31999999999999993e-55

   1. Initial program 72.2%

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

   3. Taylor expanded in z around 0 56.4%

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

   4. Taylor expanded in x around inf 64.5%

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

      1. mul-1-neg 64.5%

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

   6. Simplified 64.5%

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

   if -1.2000000000000001e69 < x < -6e-34 or -1.31999999999999993e-55 < x < 2.9e19

   1. Initial program 80.8%

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

   3. Taylor expanded in x around 0 59.6%

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

      1. associate-/l* 71.1%

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

   5. Simplified 71.1%

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

   if 2.9e19 < x < 9.9999999999999997e199

   1. Initial program 78.9%

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

   3. Taylor expanded in z around 0 42.2%

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

      1. associate-/l* 54.3%

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

   5. Simplified 54.3%

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

   6. Taylor expanded in t around 0 53.6%

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

      1. neg-mul-1 53.6%

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

      2. distribute-neg-frac2 53.6%

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

   8. Simplified 53.6%

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

   if 9.9999999999999997e199 < x

   1. Initial program 45.6%

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

   3. Taylor expanded in z around inf 57.3%

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

      1. associate--l+ 57.3%

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

      2. associate-*r/ 57.3%

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

      3. associate-*r/ 57.3%

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

      4. mul-1-neg 57.3%

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

      5. div-sub 57.3%

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

      6. mul-1-neg 57.3%

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

      7. distribute-lft-out-- 57.3%

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

      8. associate-*r/ 57.3%

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

      9. mul-1-neg 57.3%

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

      10. unsub-neg 57.3%

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

      11. distribute-rgt-out-- 62.3%

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

   5. Simplified 62.3%

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

   6. Taylor expanded in t around 0 42.5%

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

      1. *-commutative 42.5%

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

      2. associate-*r/ 66.3%

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

      3. *-commutative 66.3%

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

   8. Simplified 66.3%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-34}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq -1.32 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 10^{+200}:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-190}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-214}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-133}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= a -1.3e+23)
     x
     (if (<= a -5e-190)
       t
       (if (<= a 1.65e-214)
         t_1
         (if (<= a 3.8e-133) t (if (<= a 3.9e-13) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -1.3e+23) {
		tmp = x;
	} else if (a <= -5e-190) {
		tmp = t;
	} else if (a <= 1.65e-214) {
		tmp = t_1;
	} else if (a <= 3.8e-133) {
		tmp = t;
	} else if (a <= 3.9e-13) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / z)
    if (a <= (-1.3d+23)) then
        tmp = x
    else if (a <= (-5d-190)) then
        tmp = t
    else if (a <= 1.65d-214) then
        tmp = t_1
    else if (a <= 3.8d-133) then
        tmp = t
    else if (a <= 3.9d-13) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -1.3e+23) {
		tmp = x;
	} else if (a <= -5e-190) {
		tmp = t;
	} else if (a <= 1.65e-214) {
		tmp = t_1;
	} else if (a <= 3.8e-133) {
		tmp = t;
	} else if (a <= 3.9e-13) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	tmp = 0
	if a <= -1.3e+23:
		tmp = x
	elif a <= -5e-190:
		tmp = t
	elif a <= 1.65e-214:
		tmp = t_1
	elif a <= 3.8e-133:
		tmp = t
	elif a <= 3.9e-13:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (a <= -1.3e+23)
		tmp = x;
	elseif (a <= -5e-190)
		tmp = t;
	elseif (a <= 1.65e-214)
		tmp = t_1;
	elseif (a <= 3.8e-133)
		tmp = t;
	elseif (a <= 3.9e-13)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (a <= -1.3e+23)
		tmp = x;
	elseif (a <= -5e-190)
		tmp = t;
	elseif (a <= 1.65e-214)
		tmp = t_1;
	elseif (a <= 3.8e-133)
		tmp = t;
	elseif (a <= 3.9e-13)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.3e+23], x, If[LessEqual[a, -5e-190], t, If[LessEqual[a, 1.65e-214], t$95$1, If[LessEqual[a, 3.8e-133], t, If[LessEqual[a, 3.9e-13], t$95$1, x]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.29999999999999996e23 or 3.90000000000000004e-13 < a

   1. Initial program 89.7%

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

   3. Taylor expanded in a around inf 44.8%

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

   if -1.29999999999999996e23 < a < -5.00000000000000034e-190 or 1.6499999999999999e-214 < a < 3.8000000000000003e-133

   1. Initial program 58.3%

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

   3. Taylor expanded in z around inf 46.7%

      \[\leadsto \color{blue}{t} \]

   if -5.00000000000000034e-190 < a < 1.6499999999999999e-214 or 3.8000000000000003e-133 < a < 3.90000000000000004e-13

   1. Initial program 62.7%

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

   3. Taylor expanded in x around -inf 50.8%

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

      1. mul-1-neg 50.8%

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

      2. *-commutative 50.8%

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

      3. distribute-rgt-neg-in 50.8%

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

   5. Simplified 50.8%

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

   6. Taylor expanded in z around -inf 43.6%

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

   7. Taylor expanded in y around inf 41.4%

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

      1. associate-/l* 47.8%

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

   9. Simplified 47.8%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-190}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-214}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-133}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -3 \cdot 10^{+16}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-222}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 10000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (* y (/ (- t x) a)))))
   (if (<= a -3e+16)
     t_2
     (if (<= a -3.9e-192)
       t_1
       (if (<= a -2.4e-222)
         (* (- y a) (/ x z))
         (if (<= a 10000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -3e+16) {
		tmp = t_2;
	} else if (a <= -3.9e-192) {
		tmp = t_1;
	} else if (a <= -2.4e-222) {
		tmp = (y - a) * (x / z);
	} else if (a <= 10000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + (y * ((t - x) / a))
    if (a <= (-3d+16)) then
        tmp = t_2
    else if (a <= (-3.9d-192)) then
        tmp = t_1
    else if (a <= (-2.4d-222)) then
        tmp = (y - a) * (x / z)
    else if (a <= 10000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -3e+16) {
		tmp = t_2;
	} else if (a <= -3.9e-192) {
		tmp = t_1;
	} else if (a <= -2.4e-222) {
		tmp = (y - a) * (x / z);
	} else if (a <= 10000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + (y * ((t - x) / a))
	tmp = 0
	if a <= -3e+16:
		tmp = t_2
	elif a <= -3.9e-192:
		tmp = t_1
	elif a <= -2.4e-222:
		tmp = (y - a) * (x / z)
	elif a <= 10000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(y * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -3e+16)
		tmp = t_2;
	elseif (a <= -3.9e-192)
		tmp = t_1;
	elseif (a <= -2.4e-222)
		tmp = Float64(Float64(y - a) * Float64(x / z));
	elseif (a <= 10000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + (y * ((t - x) / a));
	tmp = 0.0;
	if (a <= -3e+16)
		tmp = t_2;
	elseif (a <= -3.9e-192)
		tmp = t_1;
	elseif (a <= -2.4e-222)
		tmp = (y - a) * (x / z);
	elseif (a <= 10000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3e+16], t$95$2, If[LessEqual[a, -3.9e-192], t$95$1, If[LessEqual[a, -2.4e-222], N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 10000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3e16 or 1e7 < a

   1. Initial program 90.4%

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

   3. Taylor expanded in z around 0 67.1%

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

      1. associate-/l* 74.0%

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

   5. Simplified 74.0%

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

   if -3e16 < a < -3.9000000000000003e-192 or -2.39999999999999993e-222 < a < 1e7

   1. Initial program 60.5%

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

   3. Taylor expanded in x around 0 46.0%

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

      1. associate-/l* 59.6%

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

   5. Simplified 59.6%

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

   if -3.9000000000000003e-192 < a < -2.39999999999999993e-222

   1. Initial program 56.7%

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

   3. Taylor expanded in z around inf 90.4%

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

      1. associate--l+ 90.4%

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

      2. associate-*r/ 90.4%

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

      3. associate-*r/ 90.4%

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

      4. mul-1-neg 90.4%

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

      5. div-sub 90.4%

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

      6. mul-1-neg 90.4%

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

      7. distribute-lft-out-- 90.4%

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

      8. associate-*r/ 90.4%

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

      9. mul-1-neg 90.4%

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

      10. unsub-neg 90.4%

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

      11. distribute-rgt-out-- 90.4%

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

   5. Simplified 90.4%

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

   6. Taylor expanded in t around 0 68.4%

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

      1. *-commutative 68.4%

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

      2. associate-*r/ 78.0%

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

      3. *-commutative 78.0%

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

   8. Simplified 78.0%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+16}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-192}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-222}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 10000000:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 69.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot \frac{x - t}{z}\\ t_2 := x + y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{-22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-89}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;a \leq 140000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* y (/ (- x t) z)))) (t_2 (+ x (* y (/ (- t x) a)))))
   (if (<= a -2.3e-22)
     t_2
     (if (<= a 3.4e-133)
       t_1
       (if (<= a 2.1e-89)
         (/ (* y (- t x)) (- a z))
         (if (<= a 140000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * ((x - t) / z));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -2.3e-22) {
		tmp = t_2;
	} else if (a <= 3.4e-133) {
		tmp = t_1;
	} else if (a <= 2.1e-89) {
		tmp = (y * (t - x)) / (a - z);
	} else if (a <= 140000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (y * ((x - t) / z))
    t_2 = x + (y * ((t - x) / a))
    if (a <= (-2.3d-22)) then
        tmp = t_2
    else if (a <= 3.4d-133) then
        tmp = t_1
    else if (a <= 2.1d-89) then
        tmp = (y * (t - x)) / (a - z)
    else if (a <= 140000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * ((x - t) / z));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -2.3e-22) {
		tmp = t_2;
	} else if (a <= 3.4e-133) {
		tmp = t_1;
	} else if (a <= 2.1e-89) {
		tmp = (y * (t - x)) / (a - z);
	} else if (a <= 140000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (y * ((x - t) / z))
	t_2 = x + (y * ((t - x) / a))
	tmp = 0
	if a <= -2.3e-22:
		tmp = t_2
	elif a <= 3.4e-133:
		tmp = t_1
	elif a <= 2.1e-89:
		tmp = (y * (t - x)) / (a - z)
	elif a <= 140000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(y * Float64(Float64(x - t) / z)))
	t_2 = Float64(x + Float64(y * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -2.3e-22)
		tmp = t_2;
	elseif (a <= 3.4e-133)
		tmp = t_1;
	elseif (a <= 2.1e-89)
		tmp = Float64(Float64(y * Float64(t - x)) / Float64(a - z));
	elseif (a <= 140000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (y * ((x - t) / z));
	t_2 = x + (y * ((t - x) / a));
	tmp = 0.0;
	if (a <= -2.3e-22)
		tmp = t_2;
	elseif (a <= 3.4e-133)
		tmp = t_1;
	elseif (a <= 2.1e-89)
		tmp = (y * (t - x)) / (a - z);
	elseif (a <= 140000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.3e-22], t$95$2, If[LessEqual[a, 3.4e-133], t$95$1, If[LessEqual[a, 2.1e-89], N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 140000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.2999999999999998e-22 or 1.4e8 < a

   1. Initial program 89.5%

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

   3. Taylor expanded in z around 0 66.7%

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

      1. associate-/l* 73.2%

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

   5. Simplified 73.2%

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

   if -2.2999999999999998e-22 < a < 3.40000000000000006e-133 or 2.1000000000000001e-89 < a < 1.4e8

   1. Initial program 59.7%

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

   3. Taylor expanded in z around inf 75.8%

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

      1. associate--l+ 75.8%

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

      2. associate-*r/ 75.8%

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

      3. associate-*r/ 75.8%

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

      4. mul-1-neg 75.8%

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

      5. div-sub 75.8%

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

      6. mul-1-neg 75.8%

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

      7. distribute-lft-out-- 75.8%

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

      8. associate-*r/ 75.8%

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

      9. mul-1-neg 75.8%

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

      10. unsub-neg 75.8%

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

      11. distribute-rgt-out-- 75.8%

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

   5. Simplified 75.8%

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

   6. Taylor expanded in y around inf 71.3%

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

      1. associate-/l* 76.4%

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

   8. Simplified 76.4%

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

   if 3.40000000000000006e-133 < a < 2.1000000000000001e-89

   1. Initial program 57.0%

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

   3. Taylor expanded in y around -inf 70.3%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-22}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-133}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-89}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;a \leq 140000000:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 64.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+130}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 165:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.75e+130)
   (+ t (/ (* x (- y a)) z))
   (if (<= z -1.5e+23)
     (* y (/ (- t x) (- a z)))
     (if (<= z 165.0) (+ x (/ (* y (- t x)) a)) (+ t (* y (/ (- x t) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.75e+130) {
		tmp = t + ((x * (y - a)) / z);
	} else if (z <= -1.5e+23) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 165.0) {
		tmp = x + ((y * (t - x)) / a);
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.75d+130)) then
        tmp = t + ((x * (y - a)) / z)
    else if (z <= (-1.5d+23)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 165.0d0) then
        tmp = x + ((y * (t - x)) / a)
    else
        tmp = t + (y * ((x - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.75e+130) {
		tmp = t + ((x * (y - a)) / z);
	} else if (z <= -1.5e+23) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 165.0) {
		tmp = x + ((y * (t - x)) / a);
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.75e+130:
		tmp = t + ((x * (y - a)) / z)
	elif z <= -1.5e+23:
		tmp = y * ((t - x) / (a - z))
	elif z <= 165.0:
		tmp = x + ((y * (t - x)) / a)
	else:
		tmp = t + (y * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.75e+130)
		tmp = Float64(t + Float64(Float64(x * Float64(y - a)) / z));
	elseif (z <= -1.5e+23)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 165.0)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	else
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.75e+130)
		tmp = t + ((x * (y - a)) / z);
	elseif (z <= -1.5e+23)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 165.0)
		tmp = x + ((y * (t - x)) / a);
	else
		tmp = t + (y * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.75e+130], N[(t + N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.5e+23], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 165.0], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.75e130

   1. Initial program 48.6%

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

   3. Taylor expanded in z around inf 73.1%

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

      1. associate--l+ 73.1%

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

      2. associate-*r/ 73.1%

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

      3. associate-*r/ 73.1%

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

      4. mul-1-neg 73.1%

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

      5. div-sub 73.1%

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

      6. mul-1-neg 73.1%

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

      7. distribute-lft-out-- 73.1%

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

      8. associate-*r/ 73.1%

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

      9. mul-1-neg 73.1%

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

      10. unsub-neg 73.1%

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

      11. distribute-rgt-out-- 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in t around 0 80.5%

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

      1. associate-*r/ 80.5%

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

      2. associate-*r* 80.5%

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

      3. mul-1-neg 80.5%

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

   8. Simplified 80.5%

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

   if -1.75e130 < z < -1.5e23

   1. Initial program 88.4%

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

   3. Taylor expanded in y around inf 56.8%

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

      1. div-sub 56.8%

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

   5. Simplified 56.8%

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

   if -1.5e23 < z < 165

   1. Initial program 88.9%

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

   3. Taylor expanded in z around 0 79.0%

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

   if 165 < z

   1. Initial program 60.2%

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

   3. Taylor expanded in z around inf 61.4%

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

      1. associate--l+ 61.4%

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

      2. associate-*r/ 61.4%

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

      3. associate-*r/ 61.4%

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

      4. mul-1-neg 61.4%

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

      5. div-sub 61.4%

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

      6. mul-1-neg 61.4%

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

      7. distribute-lft-out-- 61.4%

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

      8. associate-*r/ 61.4%

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

      9. mul-1-neg 61.4%

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

      10. unsub-neg 61.4%

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

      11. distribute-rgt-out-- 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in y around inf 60.1%

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

      1. associate-/l* 64.0%

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

   8. Simplified 64.0%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+130}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 165:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+177}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+91}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+76}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.05e+177)
   (* x (/ (- y a) z))
   (if (<= z -2.9e+91) t (if (<= z 3.5e+76) (+ x (* t (/ y a))) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+177) {
		tmp = x * ((y - a) / z);
	} else if (z <= -2.9e+91) {
		tmp = t;
	} else if (z <= 3.5e+76) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.05d+177)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-2.9d+91)) then
        tmp = t
    else if (z <= 3.5d+76) then
        tmp = x + (t * (y / a))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+177) {
		tmp = x * ((y - a) / z);
	} else if (z <= -2.9e+91) {
		tmp = t;
	} else if (z <= 3.5e+76) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.05e+177:
		tmp = x * ((y - a) / z)
	elif z <= -2.9e+91:
		tmp = t
	elif z <= 3.5e+76:
		tmp = x + (t * (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.05e+177)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -2.9e+91)
		tmp = t;
	elseif (z <= 3.5e+76)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.05e+177)
		tmp = x * ((y - a) / z);
	elseif (z <= -2.9e+91)
		tmp = t;
	elseif (z <= 3.5e+76)
		tmp = x + (t * (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.05e+177], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.9e+91], t, If[LessEqual[z, 3.5e+76], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05000000000000006e177

   1. Initial program 45.6%

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

   3. Taylor expanded in x around -inf 36.1%

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

      1. mul-1-neg 36.1%

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

      2. *-commutative 36.1%

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

      3. distribute-rgt-neg-in 36.1%

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

   5. Simplified 36.1%

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

   6. Taylor expanded in z around -inf 41.2%

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

      1. associate-/l* 55.1%

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

   8. Simplified 55.1%

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

   if -1.05000000000000006e177 < z < -2.90000000000000014e91 or 3.5e76 < z

   1. Initial program 55.6%

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

   3. Taylor expanded in z around inf 53.8%

      \[\leadsto \color{blue}{t} \]

   if -2.90000000000000014e91 < z < 3.5e76

   1. Initial program 87.8%

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

   3. Taylor expanded in z around 0 66.0%

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

      1. associate-/l* 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in t around inf 55.4%

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

      1. associate-/l* 57.5%

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

   8. Simplified 57.5%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+177}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+91}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+76}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 70.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+101}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+43}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.25e+101)
   (+ t (/ (* x (- y a)) z))
   (if (<= z 1.95e+43)
     (+ x (* (- t x) (/ (- y z) a)))
     (+ t (* y (/ (- x t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.25e+101) {
		tmp = t + ((x * (y - a)) / z);
	} else if (z <= 1.95e+43) {
		tmp = x + ((t - x) * ((y - z) / a));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.25d+101)) then
        tmp = t + ((x * (y - a)) / z)
    else if (z <= 1.95d+43) then
        tmp = x + ((t - x) * ((y - z) / a))
    else
        tmp = t + (y * ((x - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.25e+101) {
		tmp = t + ((x * (y - a)) / z);
	} else if (z <= 1.95e+43) {
		tmp = x + ((t - x) * ((y - z) / a));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.25e+101:
		tmp = t + ((x * (y - a)) / z)
	elif z <= 1.95e+43:
		tmp = x + ((t - x) * ((y - z) / a))
	else:
		tmp = t + (y * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.25e+101)
		tmp = Float64(t + Float64(Float64(x * Float64(y - a)) / z));
	elseif (z <= 1.95e+43)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)));
	else
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.25e+101)
		tmp = t + ((x * (y - a)) / z);
	elseif (z <= 1.95e+43)
		tmp = x + ((t - x) * ((y - z) / a));
	else
		tmp = t + (y * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.25e+101], N[(t + N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e+43], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.24999999999999997e101

   1. Initial program 49.8%

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

   3. Taylor expanded in z around inf 71.4%

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

      1. associate--l+ 71.4%

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

      2. associate-*r/ 71.4%

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

      3. associate-*r/ 71.4%

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

      4. mul-1-neg 71.4%

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

      5. div-sub 71.4%

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

      6. mul-1-neg 71.4%

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

      7. distribute-lft-out-- 71.4%

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

      8. associate-*r/ 71.4%

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

      9. mul-1-neg 71.4%

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

      10. unsub-neg 71.4%

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

      11. distribute-rgt-out-- 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in t around 0 78.6%

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

      1. associate-*r/ 78.6%

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

      2. associate-*r* 78.6%

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

      3. mul-1-neg 78.6%

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

   8. Simplified 78.6%

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

   if -1.24999999999999997e101 < z < 1.95e43

   1. Initial program 88.3%

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

   3. Taylor expanded in a around inf 71.8%

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

      1. associate-/l* 77.1%

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

   5. Simplified 77.1%

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

   if 1.95e43 < z

   1. Initial program 56.4%

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

   3. Taylor expanded in z around inf 63.2%

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

      1. associate--l+ 63.2%

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

      2. associate-*r/ 63.2%

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

      3. associate-*r/ 63.2%

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

      4. mul-1-neg 63.2%

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

      5. div-sub 63.2%

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

      6. mul-1-neg 63.2%

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

      7. distribute-lft-out-- 63.2%

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

      8. associate-*r/ 63.2%

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

      9. mul-1-neg 63.2%

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

      10. unsub-neg 63.2%

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

      11. distribute-rgt-out-- 63.3%

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

   5. Simplified 63.3%

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

   6. Taylor expanded in y around inf 63.7%

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

      1. associate-/l* 68.3%

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

   8. Simplified 68.3%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+101}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+43}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-22}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq 12500:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.4e-22)
   (+ x (* (- t x) (/ (- y z) a)))
   (if (<= a 12500.0)
     (+ t (/ (* (- t x) (- a y)) z))
     (+ x (/ (- y z) (/ a (- t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.4e-22) {
		tmp = x + ((t - x) * ((y - z) / a));
	} else if (a <= 12500.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x + ((y - z) / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.4d-22)) then
        tmp = x + ((t - x) * ((y - z) / a))
    else if (a <= 12500.0d0) then
        tmp = t + (((t - x) * (a - y)) / z)
    else
        tmp = x + ((y - z) / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.4e-22) {
		tmp = x + ((t - x) * ((y - z) / a));
	} else if (a <= 12500.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x + ((y - z) / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.4e-22:
		tmp = x + ((t - x) * ((y - z) / a))
	elif a <= 12500.0:
		tmp = t + (((t - x) * (a - y)) / z)
	else:
		tmp = x + ((y - z) / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.4e-22)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)));
	elseif (a <= 12500.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.4e-22)
		tmp = x + ((t - x) * ((y - z) / a));
	elseif (a <= 12500.0)
		tmp = t + (((t - x) * (a - y)) / z);
	else
		tmp = x + ((y - z) / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.4e-22], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 12500.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.39999999999999997e-22

   1. Initial program 84.8%

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

   3. Taylor expanded in a around inf 68.7%

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

      1. associate-/l* 78.0%

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

   5. Simplified 78.0%

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

   if -1.39999999999999997e-22 < a < 12500

   1. Initial program 59.5%

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

   3. Taylor expanded in z around inf 73.5%

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

      1. associate--l+ 73.5%

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

      2. associate-*r/ 73.5%

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

      3. associate-*r/ 73.5%

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

      4. mul-1-neg 73.5%

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

      5. div-sub 73.5%

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

      6. mul-1-neg 73.5%

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

      7. distribute-lft-out-- 73.5%

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

      8. associate-*r/ 73.5%

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

      9. mul-1-neg 73.5%

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

      10. unsub-neg 73.5%

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

      11. distribute-rgt-out-- 73.5%

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

   5. Simplified 73.5%

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

   if 12500 < a

   1. Initial program 94.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 94.4%

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

      2. un-div-inv 94.5%

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

   4. Applied egg-rr 94.5%

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

   5. Taylor expanded in a around inf 82.2%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-22}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq 12500:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 69.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{-22} \lor \neg \left(a \leq 5.6 \cdot 10^{+15}\right):\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.7e-22) (not (<= a 5.6e+15)))
   (+ x (* y (/ (- t x) a)))
   (+ t (* y (/ (- x t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.7e-22) || !(a <= 5.6e+15)) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.7d-22)) .or. (.not. (a <= 5.6d+15))) then
        tmp = x + (y * ((t - x) / a))
    else
        tmp = t + (y * ((x - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.7e-22) || !(a <= 5.6e+15)) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.7e-22) or not (a <= 5.6e+15):
		tmp = x + (y * ((t - x) / a))
	else:
		tmp = t + (y * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.7e-22) || !(a <= 5.6e+15))
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	else
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.7e-22) || ~((a <= 5.6e+15)))
		tmp = x + (y * ((t - x) / a));
	else
		tmp = t + (y * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.7e-22], N[Not[LessEqual[a, 5.6e+15]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.6999999999999999e-22 or 5.6e15 < a

   1. Initial program 89.5%

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

   3. Taylor expanded in z around 0 66.7%

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

      1. associate-/l* 73.2%

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

   5. Simplified 73.2%

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

   if -1.6999999999999999e-22 < a < 5.6e15

   1. Initial program 59.5%

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

   3. Taylor expanded in z around inf 73.5%

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

      1. associate--l+ 73.5%

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

      2. associate-*r/ 73.5%

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

      3. associate-*r/ 73.5%

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

      4. mul-1-neg 73.5%

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

      5. div-sub 73.5%

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

      6. mul-1-neg 73.5%

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

      7. distribute-lft-out-- 73.5%

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

      8. associate-*r/ 73.5%

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

      9. mul-1-neg 73.5%

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

      10. unsub-neg 73.5%

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

      11. distribute-rgt-out-- 73.5%

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

   5. Simplified 73.5%

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

   6. Taylor expanded in y around inf 68.5%

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

      1. associate-/l* 72.4%

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

   8. Simplified 72.4%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{-22} \lor \neg \left(a \leq 5.6 \cdot 10^{+15}\right):\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 39.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.3 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 22000000000000:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.3e+20) x (if (<= a 22000000000000.0) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.3e+20) {
		tmp = x;
	} else if (a <= 22000000000000.0) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.3d+20)) then
        tmp = x
    else if (a <= 22000000000000.0d0) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.3e+20) {
		tmp = x;
	} else if (a <= 22000000000000.0) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.3e+20:
		tmp = x
	elif a <= 22000000000000.0:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.3e+20)
		tmp = x;
	elseif (a <= 22000000000000.0)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.3e+20)
		tmp = x;
	elseif (a <= 22000000000000.0)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.3e+20], x, If[LessEqual[a, 22000000000000.0], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -5.3e20 or 2.2e13 < a

   1. Initial program 90.2%

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

   3. Taylor expanded in a around inf 45.1%

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

   if -5.3e20 < a < 2.2e13

   1. Initial program 60.8%

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

   3. Taylor expanded in z around inf 38.5%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.3 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 22000000000000:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 24.7% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 75.5%

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

3. Taylor expanded in z around inf 23.7%

   \[\leadsto \color{blue}{t} \]

4. Final simplification 23.7%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024055 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))