Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.4% → 94.2%

Time: 19.3s

Alternatives: 22

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: 94.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-235} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{-z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- x t) (- a z))))))
   (if (or (<= t_1 -1e-235) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (+ t (* (/ x (- z)) (- a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-235) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = t + ((x / -z) * (a - y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-235) || !(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(-z)) * Float64(a - y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-235], 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 / (-z)), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999996e-236 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 94.3%

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

      1. +-commutative 94.3%

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

      2. associate-*r/ 76.2%

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

      3. *-commutative 76.2%

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

      4. associate-*r/ 96.4%

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

      5. fma-def 96.4%

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

   3. Simplified 96.4%

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

   if -9.9999999999999996e-236 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.3%

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

      1. *-commutative 3.3%

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

      2. flip-- 2.5%

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

      3. associate-*r/ 2.6%

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

   3. Applied egg-rr 2.6%

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

   4. Taylor expanded in z around -inf 71.1%

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

      1. +-commutative 71.1%

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

      2. mul-1-neg 71.1%

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

      3. associate-/l* 99.8%

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

      4. mul-1-neg 99.8%

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

      5. sub-neg 99.8%

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

      6. unsub-neg 99.8%

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

      7. associate-/r/ 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in t around 0 99.8%

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

      1. metadata-eval 99.8%

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

      2. times-frac 99.8%

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

      3. *-lft-identity 99.8%

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

      4. neg-mul-1 99.8%

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

   9. Simplified 99.8%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -1 \cdot 10^{-235} \lor \neg \left(x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{-z} \cdot \left(a - y\right)\\ \end{array} \]

Alternative 2: 90.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-235} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{-z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- x t) (- a z))))))
   (if (or (<= t_1 -1e-235) (not (<= t_1 0.0)))
     t_1
     (+ t (* (/ x (- z)) (- a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-235) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((x / -z) * (a - y));
	}
	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) * ((x - t) / (a - z)))
    if ((t_1 <= (-1d-235)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t + ((x / -z) * (a - y))
    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) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-235) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((x / -z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - y) * ((x - t) / (a - z)))
	tmp = 0
	if (t_1 <= -1e-235) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t + ((x / -z) * (a - y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-235) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(x / Float64(-z)) * Float64(a - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - y) * ((x - t) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -1e-235) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t + ((x / -z) * (a - y));
	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[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-235], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t + N[(N[(x / (-z)), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999996e-236 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 94.3%

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

   if -9.9999999999999996e-236 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.3%

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

      1. *-commutative 3.3%

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

      2. flip-- 2.5%

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

      3. associate-*r/ 2.6%

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

   3. Applied egg-rr 2.6%

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

   4. Taylor expanded in z around -inf 71.1%

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

      1. +-commutative 71.1%

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

      2. mul-1-neg 71.1%

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

      3. associate-/l* 99.8%

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

      4. mul-1-neg 99.8%

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

      5. sub-neg 99.8%

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

      6. unsub-neg 99.8%

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

      7. associate-/r/ 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in t around 0 99.8%

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

      1. metadata-eval 99.8%

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

      2. times-frac 99.8%

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

      3. *-lft-identity 99.8%

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

      4. neg-mul-1 99.8%

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

   9. Simplified 99.8%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -1 \cdot 10^{-235} \lor \neg \left(x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{-z} \cdot \left(a - y\right)\\ \end{array} \]

Alternative 3: 45.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-135}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{-216}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-253}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+116}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 10^{+129}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -4.8e+122)
     t
     (if (<= z -7.8e-32)
       t_1
       (if (<= z -5e-135)
         (* t (/ y a))
         (if (<= z -1.42e-216)
           t_1
           (if (<= z -4.5e-253)
             (/ (* y t) a)
             (if (<= z 3.5e+85)
               t_1
               (if (<= z 2.5e+116)
                 (/ y (/ z x))
                 (if (<= z 1e+129) t_1 t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -4.8e+122) {
		tmp = t;
	} else if (z <= -7.8e-32) {
		tmp = t_1;
	} else if (z <= -5e-135) {
		tmp = t * (y / a);
	} else if (z <= -1.42e-216) {
		tmp = t_1;
	} else if (z <= -4.5e-253) {
		tmp = (y * t) / a;
	} else if (z <= 3.5e+85) {
		tmp = t_1;
	} else if (z <= 2.5e+116) {
		tmp = y / (z / x);
	} else if (z <= 1e+129) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-4.8d+122)) then
        tmp = t
    else if (z <= (-7.8d-32)) then
        tmp = t_1
    else if (z <= (-5d-135)) then
        tmp = t * (y / a)
    else if (z <= (-1.42d-216)) then
        tmp = t_1
    else if (z <= (-4.5d-253)) then
        tmp = (y * t) / a
    else if (z <= 3.5d+85) then
        tmp = t_1
    else if (z <= 2.5d+116) then
        tmp = y / (z / x)
    else if (z <= 1d+129) then
        tmp = t_1
    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 t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -4.8e+122) {
		tmp = t;
	} else if (z <= -7.8e-32) {
		tmp = t_1;
	} else if (z <= -5e-135) {
		tmp = t * (y / a);
	} else if (z <= -1.42e-216) {
		tmp = t_1;
	} else if (z <= -4.5e-253) {
		tmp = (y * t) / a;
	} else if (z <= 3.5e+85) {
		tmp = t_1;
	} else if (z <= 2.5e+116) {
		tmp = y / (z / x);
	} else if (z <= 1e+129) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -4.8e+122:
		tmp = t
	elif z <= -7.8e-32:
		tmp = t_1
	elif z <= -5e-135:
		tmp = t * (y / a)
	elif z <= -1.42e-216:
		tmp = t_1
	elif z <= -4.5e-253:
		tmp = (y * t) / a
	elif z <= 3.5e+85:
		tmp = t_1
	elif z <= 2.5e+116:
		tmp = y / (z / x)
	elif z <= 1e+129:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -4.8e+122)
		tmp = t;
	elseif (z <= -7.8e-32)
		tmp = t_1;
	elseif (z <= -5e-135)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= -1.42e-216)
		tmp = t_1;
	elseif (z <= -4.5e-253)
		tmp = Float64(Float64(y * t) / a);
	elseif (z <= 3.5e+85)
		tmp = t_1;
	elseif (z <= 2.5e+116)
		tmp = Float64(y / Float64(z / x));
	elseif (z <= 1e+129)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -4.8e+122)
		tmp = t;
	elseif (z <= -7.8e-32)
		tmp = t_1;
	elseif (z <= -5e-135)
		tmp = t * (y / a);
	elseif (z <= -1.42e-216)
		tmp = t_1;
	elseif (z <= -4.5e-253)
		tmp = (y * t) / a;
	elseif (z <= 3.5e+85)
		tmp = t_1;
	elseif (z <= 2.5e+116)
		tmp = y / (z / x);
	elseif (z <= 1e+129)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e+122], t, If[LessEqual[z, -7.8e-32], t$95$1, If[LessEqual[z, -5e-135], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.42e-216], t$95$1, If[LessEqual[z, -4.5e-253], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 3.5e+85], t$95$1, If[LessEqual[z, 2.5e+116], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+129], t$95$1, t]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.8000000000000004e122 or 1e129 < z

   1. Initial program 62.2%

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

   2. Taylor expanded in z around inf 62.4%

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

   if -4.8000000000000004e122 < z < -7.8000000000000003e-32 or -5.0000000000000002e-135 < z < -1.42000000000000004e-216 or -4.50000000000000029e-253 < z < 3.50000000000000005e85 or 2.50000000000000013e116 < z < 1e129

   1. Initial program 92.5%

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

   2. Taylor expanded in z around 0 59.2%

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

      1. +-commutative 59.2%

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

      2. associate-/l* 66.2%

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

   4. Simplified 66.2%

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

   5. Taylor expanded in x around inf 51.3%

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

      1. *-commutative 51.3%

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

      2. mul-1-neg 51.3%

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

      3. unsub-neg 51.3%

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

   7. Simplified 51.3%

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

   if -7.8000000000000003e-32 < z < -5.0000000000000002e-135

   1. Initial program 83.5%

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

   2. Taylor expanded in t around inf 76.8%

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

      1. div-sub 76.8%

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

   4. Simplified 76.8%

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

   5. Taylor expanded in z around 0 43.7%

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

   if -1.42000000000000004e-216 < z < -4.50000000000000029e-253

   1. Initial program 91.6%

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

   2. Taylor expanded in x around 0 60.4%

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

   3. Taylor expanded in z around 0 69.5%

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

   if 3.50000000000000005e85 < z < 2.50000000000000013e116

   1. Initial program 73.1%

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

   2. Taylor expanded in a around 0 54.6%

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

      1. associate-*r/ 54.6%

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

      2. neg-mul-1 54.6%

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

   4. Simplified 54.6%

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

   5. Taylor expanded in x around inf 51.9%

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

      1. associate-/l* 61.2%

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

   7. Simplified 61.2%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-135}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{-216}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-253}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+116}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 10^{+129}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 48.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-134}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-144}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-174}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-76}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+126}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8e+122)
   t
   (if (<= z -7.8e-32)
     (* x (- 1.0 (/ y a)))
     (if (<= z -4.5e-134)
       (/ t (/ a (- y z)))
       (if (<= z -3.2e-144)
         (- x (/ y (/ a x)))
         (if (<= z -4.8e-174)
           (* y (/ (- t x) a))
           (if (<= z 9.5e-76)
             (+ x (/ (* y t) a))
             (if (<= z 4.2e+126) (* y (/ (- x t) z)) t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e+122) {
		tmp = t;
	} else if (z <= -7.8e-32) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= -4.5e-134) {
		tmp = t / (a / (y - z));
	} else if (z <= -3.2e-144) {
		tmp = x - (y / (a / x));
	} else if (z <= -4.8e-174) {
		tmp = y * ((t - x) / a);
	} else if (z <= 9.5e-76) {
		tmp = x + ((y * t) / a);
	} else if (z <= 4.2e+126) {
		tmp = y * ((x - t) / z);
	} 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 <= (-8d+122)) then
        tmp = t
    else if (z <= (-7.8d-32)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= (-4.5d-134)) then
        tmp = t / (a / (y - z))
    else if (z <= (-3.2d-144)) then
        tmp = x - (y / (a / x))
    else if (z <= (-4.8d-174)) then
        tmp = y * ((t - x) / a)
    else if (z <= 9.5d-76) then
        tmp = x + ((y * t) / a)
    else if (z <= 4.2d+126) then
        tmp = y * ((x - t) / z)
    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 <= -8e+122) {
		tmp = t;
	} else if (z <= -7.8e-32) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= -4.5e-134) {
		tmp = t / (a / (y - z));
	} else if (z <= -3.2e-144) {
		tmp = x - (y / (a / x));
	} else if (z <= -4.8e-174) {
		tmp = y * ((t - x) / a);
	} else if (z <= 9.5e-76) {
		tmp = x + ((y * t) / a);
	} else if (z <= 4.2e+126) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8e+122:
		tmp = t
	elif z <= -7.8e-32:
		tmp = x * (1.0 - (y / a))
	elif z <= -4.5e-134:
		tmp = t / (a / (y - z))
	elif z <= -3.2e-144:
		tmp = x - (y / (a / x))
	elif z <= -4.8e-174:
		tmp = y * ((t - x) / a)
	elif z <= 9.5e-76:
		tmp = x + ((y * t) / a)
	elif z <= 4.2e+126:
		tmp = y * ((x - t) / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8e+122)
		tmp = t;
	elseif (z <= -7.8e-32)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= -4.5e-134)
		tmp = Float64(t / Float64(a / Float64(y - z)));
	elseif (z <= -3.2e-144)
		tmp = Float64(x - Float64(y / Float64(a / x)));
	elseif (z <= -4.8e-174)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 9.5e-76)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 4.2e+126)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8e+122)
		tmp = t;
	elseif (z <= -7.8e-32)
		tmp = x * (1.0 - (y / a));
	elseif (z <= -4.5e-134)
		tmp = t / (a / (y - z));
	elseif (z <= -3.2e-144)
		tmp = x - (y / (a / x));
	elseif (z <= -4.8e-174)
		tmp = y * ((t - x) / a);
	elseif (z <= 9.5e-76)
		tmp = x + ((y * t) / a);
	elseif (z <= 4.2e+126)
		tmp = y * ((x - t) / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8e+122], t, If[LessEqual[z, -7.8e-32], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.5e-134], N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.2e-144], N[(x - N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.8e-174], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-76], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+126], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -8.00000000000000012e122 or 4.1999999999999998e126 < z

   1. Initial program 62.2%

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

   2. Taylor expanded in z around inf 62.4%

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

   if -8.00000000000000012e122 < z < -7.8000000000000003e-32

   1. Initial program 94.3%

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

   2. Taylor expanded in z around 0 42.4%

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

      1. +-commutative 42.4%

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

      2. associate-/l* 53.2%

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

   4. Simplified 53.2%

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

   5. Taylor expanded in x around inf 50.2%

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

      1. *-commutative 50.2%

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

      2. mul-1-neg 50.2%

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

      3. unsub-neg 50.2%

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

   7. Simplified 50.2%

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

   if -7.8000000000000003e-32 < z < -4.5000000000000005e-134

   1. Initial program 83.5%

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

   2. Taylor expanded in x around 0 65.7%

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

   3. Taylor expanded in a around inf 39.0%

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

      1. associate-/l* 49.7%

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

   5. Simplified 49.7%

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

   if -4.5000000000000005e-134 < z < -3.19999999999999973e-144

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-/l* 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot x}{a} + x} \]
   6. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

   if -3.19999999999999973e-144 < z < -4.8e-174

   1. Initial program 88.1%

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

   2. Taylor expanded in z around 0 65.0%

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

      1. +-commutative 65.0%

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

      2. associate-/l* 87.7%

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

   4. Simplified 87.7%

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

   5. Taylor expanded in y around inf 88.1%

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

      1. div-sub 88.1%

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

      2. *-commutative 88.1%

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

   7. Simplified 88.1%

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

   if -4.8e-174 < z < 9.49999999999999984e-76

   1. Initial program 95.1%

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

   2. Taylor expanded in z around 0 79.1%

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

      1. +-commutative 79.1%

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

      2. associate-/l* 82.3%

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

   4. Simplified 82.3%

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

   5. Taylor expanded in t around inf 64.6%

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

   if 9.49999999999999984e-76 < z < 4.1999999999999998e126

   1. Initial program 81.6%

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

   2. Taylor expanded in a around 0 39.9%

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

      1. associate-*r/ 39.9%

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

      2. neg-mul-1 39.9%

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

   4. Simplified 39.9%

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

   5. Taylor expanded in y around inf 45.4%

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

      1. div-sub 45.4%

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

   7. Simplified 45.4%

      \[\leadsto \color{blue}{y \cdot \frac{x - t}{z}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-134}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-144}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-174}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-76}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+126}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 66.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot \frac{x - t}{z}\\ t_2 := x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{+93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-124}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+23}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* y (/ (- x t) z)))) (t_2 (+ x (/ y (/ a (- t x))))))
   (if (<= a -2.5e+93)
     t_2
     (if (<= a -4.7e-27)
       t_1
       (if (<= a -3e-124)
         (+ x (/ (* y (- t x)) a))
         (if (<= a 7e-135)
           t_1
           (if (<= a 1.55e+23)
             (* t (/ (- y z) (- a z)))
             (if (<= a 1.25e+49) (* y (/ (- t x) (- a z))) 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 / (a / (t - x)));
	double tmp;
	if (a <= -2.5e+93) {
		tmp = t_2;
	} else if (a <= -4.7e-27) {
		tmp = t_1;
	} else if (a <= -3e-124) {
		tmp = x + ((y * (t - x)) / a);
	} else if (a <= 7e-135) {
		tmp = t_1;
	} else if (a <= 1.55e+23) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 1.25e+49) {
		tmp = y * ((t - x) / (a - z));
	} 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 / (a / (t - x)))
    if (a <= (-2.5d+93)) then
        tmp = t_2
    else if (a <= (-4.7d-27)) then
        tmp = t_1
    else if (a <= (-3d-124)) then
        tmp = x + ((y * (t - x)) / a)
    else if (a <= 7d-135) then
        tmp = t_1
    else if (a <= 1.55d+23) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= 1.25d+49) then
        tmp = y * ((t - x) / (a - z))
    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 / (a / (t - x)));
	double tmp;
	if (a <= -2.5e+93) {
		tmp = t_2;
	} else if (a <= -4.7e-27) {
		tmp = t_1;
	} else if (a <= -3e-124) {
		tmp = x + ((y * (t - x)) / a);
	} else if (a <= 7e-135) {
		tmp = t_1;
	} else if (a <= 1.55e+23) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 1.25e+49) {
		tmp = y * ((t - x) / (a - z));
	} 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 / (a / (t - x)))
	tmp = 0
	if a <= -2.5e+93:
		tmp = t_2
	elif a <= -4.7e-27:
		tmp = t_1
	elif a <= -3e-124:
		tmp = x + ((y * (t - x)) / a)
	elif a <= 7e-135:
		tmp = t_1
	elif a <= 1.55e+23:
		tmp = t * ((y - z) / (a - z))
	elif a <= 1.25e+49:
		tmp = y * ((t - x) / (a - z))
	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(a / Float64(t - x))))
	tmp = 0.0
	if (a <= -2.5e+93)
		tmp = t_2;
	elseif (a <= -4.7e-27)
		tmp = t_1;
	elseif (a <= -3e-124)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	elseif (a <= 7e-135)
		tmp = t_1;
	elseif (a <= 1.55e+23)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= 1.25e+49)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	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 / (a / (t - x)));
	tmp = 0.0;
	if (a <= -2.5e+93)
		tmp = t_2;
	elseif (a <= -4.7e-27)
		tmp = t_1;
	elseif (a <= -3e-124)
		tmp = x + ((y * (t - x)) / a);
	elseif (a <= 7e-135)
		tmp = t_1;
	elseif (a <= 1.55e+23)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= 1.25e+49)
		tmp = y * ((t - x) / (a - z));
	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[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.5e+93], t$95$2, If[LessEqual[a, -4.7e-27], t$95$1, If[LessEqual[a, -3e-124], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e-135], t$95$1, If[LessEqual[a, 1.55e+23], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e+49], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.5000000000000001e93 or 1.2500000000000001e49 < a

   1. Initial program 88.7%

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

   2. Taylor expanded in z around 0 60.2%

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

      1. +-commutative 60.2%

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

      2. associate-/l* 71.1%

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

   4. Simplified 71.1%

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

   if -2.5000000000000001e93 < a < -4.70000000000000032e-27 or -3e-124 < a < 6.9999999999999997e-135

   1. Initial program 74.2%

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

      1. *-commutative 74.2%

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

      2. flip-- 51.3%

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

      3. associate-*r/ 44.9%

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

   3. Applied egg-rr 44.9%

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

   4. Taylor expanded in z around -inf 78.3%

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

      1. +-commutative 78.3%

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

      2. mul-1-neg 78.3%

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

      3. associate-/l* 89.3%

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

      4. mul-1-neg 89.3%

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

      5. sub-neg 89.3%

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

      6. unsub-neg 89.3%

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

      7. associate-/r/ 86.4%

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

   6. Simplified 86.4%

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

   7. Taylor expanded in y around inf 78.2%

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

      1. associate-*r/ 85.3%

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

   9. Simplified 85.3%

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

   if -4.70000000000000032e-27 < a < -3e-124

   1. Initial program 83.8%

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

   2. Taylor expanded in z around 0 73.0%

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

   if 6.9999999999999997e-135 < a < 1.54999999999999985e23

   1. Initial program 86.2%

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

   2. Taylor expanded in t around inf 72.3%

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

      1. div-sub 72.3%

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

   4. Simplified 72.3%

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

   if 1.54999999999999985e23 < a < 1.2500000000000001e49

   1. Initial program 99.7%

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

      1. clear-num 99.4%

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

      2. associate-/r/ 99.4%

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

   3. Applied egg-rr 99.4%

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

   4. Taylor expanded in y around inf 65.8%

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

      1. div-sub 65.8%

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

      2. *-commutative 65.8%

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

   6. Simplified 65.8%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+93}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-27}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-124}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-135}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+23}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 6: 66.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-26}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-126}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-135}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{+22}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a (- t x))))))
   (if (<= a -2.5e+93)
     t_1
     (if (<= a -5e-26)
       (- t (/ y (/ z (- t x))))
       (if (<= a -8.2e-126)
         (+ x (/ (* y (- t x)) a))
         (if (<= a 1.4e-135)
           (+ t (* y (/ (- x t) z)))
           (if (<= a 7.4e+22)
             (* t (/ (- y z) (- a z)))
             (if (<= a 1.3e+49) (* y (/ (- t x) (- a z))) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double tmp;
	if (a <= -2.5e+93) {
		tmp = t_1;
	} else if (a <= -5e-26) {
		tmp = t - (y / (z / (t - x)));
	} else if (a <= -8.2e-126) {
		tmp = x + ((y * (t - x)) / a);
	} else if (a <= 1.4e-135) {
		tmp = t + (y * ((x - t) / z));
	} else if (a <= 7.4e+22) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 1.3e+49) {
		tmp = y * ((t - x) / (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 + (y / (a / (t - x)))
    if (a <= (-2.5d+93)) then
        tmp = t_1
    else if (a <= (-5d-26)) then
        tmp = t - (y / (z / (t - x)))
    else if (a <= (-8.2d-126)) then
        tmp = x + ((y * (t - x)) / a)
    else if (a <= 1.4d-135) then
        tmp = t + (y * ((x - t) / z))
    else if (a <= 7.4d+22) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= 1.3d+49) then
        tmp = y * ((t - x) / (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 + (y / (a / (t - x)));
	double tmp;
	if (a <= -2.5e+93) {
		tmp = t_1;
	} else if (a <= -5e-26) {
		tmp = t - (y / (z / (t - x)));
	} else if (a <= -8.2e-126) {
		tmp = x + ((y * (t - x)) / a);
	} else if (a <= 1.4e-135) {
		tmp = t + (y * ((x - t) / z));
	} else if (a <= 7.4e+22) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 1.3e+49) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / (t - x)))
	tmp = 0
	if a <= -2.5e+93:
		tmp = t_1
	elif a <= -5e-26:
		tmp = t - (y / (z / (t - x)))
	elif a <= -8.2e-126:
		tmp = x + ((y * (t - x)) / a)
	elif a <= 1.4e-135:
		tmp = t + (y * ((x - t) / z))
	elif a <= 7.4e+22:
		tmp = t * ((y - z) / (a - z))
	elif a <= 1.3e+49:
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / Float64(t - x))))
	tmp = 0.0
	if (a <= -2.5e+93)
		tmp = t_1;
	elseif (a <= -5e-26)
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	elseif (a <= -8.2e-126)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	elseif (a <= 1.4e-135)
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	elseif (a <= 7.4e+22)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= 1.3e+49)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / (t - x)));
	tmp = 0.0;
	if (a <= -2.5e+93)
		tmp = t_1;
	elseif (a <= -5e-26)
		tmp = t - (y / (z / (t - x)));
	elseif (a <= -8.2e-126)
		tmp = x + ((y * (t - x)) / a);
	elseif (a <= 1.4e-135)
		tmp = t + (y * ((x - t) / z));
	elseif (a <= 7.4e+22)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= 1.3e+49)
		tmp = y * ((t - x) / (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[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.5e+93], t$95$1, If[LessEqual[a, -5e-26], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.2e-126], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e-135], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.4e+22], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e+49], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -2.5000000000000001e93 or 1.29999999999999994e49 < a

   1. Initial program 88.7%

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

   2. Taylor expanded in z around 0 60.2%

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

      1. +-commutative 60.2%

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

      2. associate-/l* 71.1%

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

   4. Simplified 71.1%

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

   if -2.5000000000000001e93 < a < -5.00000000000000019e-26

   1. Initial program 77.6%

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

   2. Taylor expanded in z around inf 58.1%

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

      1. +-commutative 58.1%

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

      2. associate--l+ 58.1%

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

      3. associate-*r/ 58.1%

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

      4. associate-*r/ 58.1%

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

      5. div-sub 58.1%

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

      6. distribute-lft-out-- 58.1%

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

      7. mul-1-neg 58.1%

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

      8. distribute-neg-frac 58.1%

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

      9. unsub-neg 58.1%

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

      10. distribute-rgt-out-- 58.1%

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

   4. Simplified 58.1%

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

   5. Taylor expanded in y around inf 57.6%

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

      1. associate-/l* 72.5%

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

   7. Simplified 72.5%

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

   if -5.00000000000000019e-26 < a < -8.1999999999999995e-126

   1. Initial program 83.8%

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

   2. Taylor expanded in z around 0 73.0%

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

   if -8.1999999999999995e-126 < a < 1.40000000000000012e-135

   1. Initial program 73.1%

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

      1. *-commutative 73.1%

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

      2. flip-- 52.8%

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

      3. associate-*r/ 46.7%

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

   3. Applied egg-rr 46.7%

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

   4. Taylor expanded in z around -inf 84.9%

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

      1. +-commutative 84.9%

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

      2. mul-1-neg 84.9%

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

      3. associate-/l* 93.4%

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

      4. mul-1-neg 93.4%

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

      5. sub-neg 93.4%

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

      6. unsub-neg 93.4%

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

      7. associate-/r/ 89.6%

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

   6. Simplified 89.6%

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

   7. Taylor expanded in y around inf 84.9%

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

      1. associate-*r/ 89.6%

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

   9. Simplified 89.6%

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

   if 1.40000000000000012e-135 < a < 7.3999999999999996e22

   1. Initial program 86.2%

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

   2. Taylor expanded in t around inf 72.3%

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

      1. div-sub 72.3%

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

   4. Simplified 72.3%

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

   if 7.3999999999999996e22 < a < 1.29999999999999994e49

   1. Initial program 99.7%

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

      1. clear-num 99.4%

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

      2. associate-/r/ 99.4%

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

   3. Applied egg-rr 99.4%

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

   4. Taylor expanded in y around inf 65.8%

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

      1. div-sub 65.8%

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

      2. *-commutative 65.8%

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

   6. Simplified 65.8%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+93}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-26}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-126}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-135}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{+22}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 7: 69.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{\frac{z}{t - x}}\\ t_2 := x - \frac{t - x}{a} \cdot \left(z - y\right)\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{+93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-124}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ y (/ z (- t x))))) (t_2 (- x (* (/ (- t x) a) (- z y)))))
   (if (<= a -2.5e+93)
     t_2
     (if (<= a -6e-26)
       t_1
       (if (<= a -2.7e-124)
         (+ x (/ (* y (- t x)) a))
         (if (<= a 8e-22) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (y / (z / (t - x)));
	double t_2 = x - (((t - x) / a) * (z - y));
	double tmp;
	if (a <= -2.5e+93) {
		tmp = t_2;
	} else if (a <= -6e-26) {
		tmp = t_1;
	} else if (a <= -2.7e-124) {
		tmp = x + ((y * (t - x)) / a);
	} else if (a <= 8e-22) {
		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 / (t - x)))
    t_2 = x - (((t - x) / a) * (z - y))
    if (a <= (-2.5d+93)) then
        tmp = t_2
    else if (a <= (-6d-26)) then
        tmp = t_1
    else if (a <= (-2.7d-124)) then
        tmp = x + ((y * (t - x)) / a)
    else if (a <= 8d-22) 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 / (t - x)));
	double t_2 = x - (((t - x) / a) * (z - y));
	double tmp;
	if (a <= -2.5e+93) {
		tmp = t_2;
	} else if (a <= -6e-26) {
		tmp = t_1;
	} else if (a <= -2.7e-124) {
		tmp = x + ((y * (t - x)) / a);
	} else if (a <= 8e-22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (y / (z / (t - x)))
	t_2 = x - (((t - x) / a) * (z - y))
	tmp = 0
	if a <= -2.5e+93:
		tmp = t_2
	elif a <= -6e-26:
		tmp = t_1
	elif a <= -2.7e-124:
		tmp = x + ((y * (t - x)) / a)
	elif a <= 8e-22:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(y / Float64(z / Float64(t - x))))
	t_2 = Float64(x - Float64(Float64(Float64(t - x) / a) * Float64(z - y)))
	tmp = 0.0
	if (a <= -2.5e+93)
		tmp = t_2;
	elseif (a <= -6e-26)
		tmp = t_1;
	elseif (a <= -2.7e-124)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	elseif (a <= 8e-22)
		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 / (t - x)));
	t_2 = x - (((t - x) / a) * (z - y));
	tmp = 0.0;
	if (a <= -2.5e+93)
		tmp = t_2;
	elseif (a <= -6e-26)
		tmp = t_1;
	elseif (a <= -2.7e-124)
		tmp = x + ((y * (t - x)) / a);
	elseif (a <= 8e-22)
		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[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.5e+93], t$95$2, If[LessEqual[a, -6e-26], t$95$1, If[LessEqual[a, -2.7e-124], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e-22], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.5000000000000001e93 or 8.0000000000000004e-22 < a

   1. Initial program 89.9%

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

   2. Taylor expanded in a around inf 78.3%

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

   if -2.5000000000000001e93 < a < -6.00000000000000023e-26 or -2.70000000000000018e-124 < a < 8.0000000000000004e-22

   1. Initial program 75.5%

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

   2. Taylor expanded in z around inf 75.4%

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

      1. +-commutative 75.4%

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

      2. associate--l+ 75.4%

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

      3. associate-*r/ 75.4%

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

      4. associate-*r/ 75.4%

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

      5. div-sub 76.3%

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

      6. distribute-lft-out-- 76.3%

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

      7. mul-1-neg 76.3%

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

      8. distribute-neg-frac 76.3%

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

      9. unsub-neg 76.3%

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

      10. distribute-rgt-out-- 76.2%

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

   4. Simplified 76.2%

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

   5. Taylor expanded in y around inf 74.8%

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

      1. associate-/l* 81.3%

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

   7. Simplified 81.3%

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

   if -6.00000000000000023e-26 < a < -2.70000000000000018e-124

   1. Initial program 83.8%

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

   2. Taylor expanded in z around 0 73.0%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+93}:\\ \;\;\;\;x - \frac{t - x}{a} \cdot \left(z - y\right)\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-26}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-124}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-22}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t - x}{a} \cdot \left(z - y\right)\\ \end{array} \]

Alternative 8: 50.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-\frac{z}{a - z}\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-76}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+125}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- (/ z (- a z))))))
   (if (<= z -1.8e+109)
     t_1
     (if (<= z -6.2e-47)
       (* x (- 1.0 (/ y a)))
       (if (<= z -5e-100)
         t_1
         (if (<= z 4.3e-76)
           (+ x (/ (* y t) a))
           (if (<= z 8.2e+125) (* y (/ (- x t) z)) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * -(z / (a - z));
	double tmp;
	if (z <= -1.8e+109) {
		tmp = t_1;
	} else if (z <= -6.2e-47) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= -5e-100) {
		tmp = t_1;
	} else if (z <= 4.3e-76) {
		tmp = x + ((y * t) / a);
	} else if (z <= 8.2e+125) {
		tmp = y * ((x - t) / 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 = t * -(z / (a - z))
    if (z <= (-1.8d+109)) then
        tmp = t_1
    else if (z <= (-6.2d-47)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= (-5d-100)) then
        tmp = t_1
    else if (z <= 4.3d-76) then
        tmp = x + ((y * t) / a)
    else if (z <= 8.2d+125) then
        tmp = y * ((x - t) / 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 = t * -(z / (a - z));
	double tmp;
	if (z <= -1.8e+109) {
		tmp = t_1;
	} else if (z <= -6.2e-47) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= -5e-100) {
		tmp = t_1;
	} else if (z <= 4.3e-76) {
		tmp = x + ((y * t) / a);
	} else if (z <= 8.2e+125) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * -(z / (a - z))
	tmp = 0
	if z <= -1.8e+109:
		tmp = t_1
	elif z <= -6.2e-47:
		tmp = x * (1.0 - (y / a))
	elif z <= -5e-100:
		tmp = t_1
	elif z <= 4.3e-76:
		tmp = x + ((y * t) / a)
	elif z <= 8.2e+125:
		tmp = y * ((x - t) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(-Float64(z / Float64(a - z))))
	tmp = 0.0
	if (z <= -1.8e+109)
		tmp = t_1;
	elseif (z <= -6.2e-47)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= -5e-100)
		tmp = t_1;
	elseif (z <= 4.3e-76)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 8.2e+125)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * -(z / (a - z));
	tmp = 0.0;
	if (z <= -1.8e+109)
		tmp = t_1;
	elseif (z <= -6.2e-47)
		tmp = x * (1.0 - (y / a));
	elseif (z <= -5e-100)
		tmp = t_1;
	elseif (z <= 4.3e-76)
		tmp = x + ((y * t) / a);
	elseif (z <= 8.2e+125)
		tmp = y * ((x - t) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * (-N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[z, -1.8e+109], t$95$1, If[LessEqual[z, -6.2e-47], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5e-100], t$95$1, If[LessEqual[z, 4.3e-76], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e+125], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.8e109 or -6.1999999999999996e-47 < z < -5.0000000000000001e-100 or 8.19999999999999983e125 < z

   1. Initial program 64.2%

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

   2. Taylor expanded in t around inf 71.0%

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

      1. div-sub 71.0%

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

   4. Simplified 71.0%

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

   5. Taylor expanded in y around 0 65.0%

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

      1. neg-mul-1 65.0%

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

      2. distribute-neg-frac 65.0%

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

   7. Simplified 65.0%

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

   if -1.8e109 < z < -6.1999999999999996e-47

   1. Initial program 94.5%

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

   2. Taylor expanded in z around 0 43.0%

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

      1. +-commutative 43.0%

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

      2. associate-/l* 55.7%

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

   4. Simplified 55.7%

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

   5. Taylor expanded in x around inf 50.2%

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

      1. *-commutative 50.2%

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

      2. mul-1-neg 50.2%

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

      3. unsub-neg 50.2%

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

   7. Simplified 50.2%

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

   if -5.0000000000000001e-100 < z < 4.2999999999999999e-76

   1. Initial program 94.0%

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

   2. Taylor expanded in z around 0 77.6%

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

      1. +-commutative 77.6%

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

      2. associate-/l* 81.2%

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

   4. Simplified 81.2%

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

   5. Taylor expanded in t around inf 63.6%

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

   if 4.2999999999999999e-76 < z < 8.19999999999999983e125

   1. Initial program 81.6%

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

   2. Taylor expanded in a around 0 39.9%

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

      1. associate-*r/ 39.9%

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

      2. neg-mul-1 39.9%

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

   4. Simplified 39.9%

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

   5. Taylor expanded in y around inf 45.4%

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

      1. div-sub 45.4%

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

   7. Simplified 45.4%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+109}:\\ \;\;\;\;t \cdot \left(-\frac{z}{a - z}\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-100}:\\ \;\;\;\;t \cdot \left(-\frac{z}{a - z}\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-76}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+125}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-\frac{z}{a - z}\right)\\ \end{array} \]

Alternative 9: 50.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-\frac{z}{a - z}\right)\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{+117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-76}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+125}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- (/ z (- a z))))))
   (if (<= z -4.3e+117)
     t_1
     (if (<= z -6.6e-47)
       (* x (- 1.0 (/ y a)))
       (if (<= z -5e-100)
         t_1
         (if (<= z 3.8e-76)
           (+ x (/ (* y t) a))
           (if (<= z 1.6e+125)
             (* y (/ (- x t) z))
             (/ (- t) (/ z (- y z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * -(z / (a - z));
	double tmp;
	if (z <= -4.3e+117) {
		tmp = t_1;
	} else if (z <= -6.6e-47) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= -5e-100) {
		tmp = t_1;
	} else if (z <= 3.8e-76) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.6e+125) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = -t / (z / (y - 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 = t * -(z / (a - z))
    if (z <= (-4.3d+117)) then
        tmp = t_1
    else if (z <= (-6.6d-47)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= (-5d-100)) then
        tmp = t_1
    else if (z <= 3.8d-76) then
        tmp = x + ((y * t) / a)
    else if (z <= 1.6d+125) then
        tmp = y * ((x - t) / z)
    else
        tmp = -t / (z / (y - 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 * -(z / (a - z));
	double tmp;
	if (z <= -4.3e+117) {
		tmp = t_1;
	} else if (z <= -6.6e-47) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= -5e-100) {
		tmp = t_1;
	} else if (z <= 3.8e-76) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.6e+125) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = -t / (z / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * -(z / (a - z))
	tmp = 0
	if z <= -4.3e+117:
		tmp = t_1
	elif z <= -6.6e-47:
		tmp = x * (1.0 - (y / a))
	elif z <= -5e-100:
		tmp = t_1
	elif z <= 3.8e-76:
		tmp = x + ((y * t) / a)
	elif z <= 1.6e+125:
		tmp = y * ((x - t) / z)
	else:
		tmp = -t / (z / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(-Float64(z / Float64(a - z))))
	tmp = 0.0
	if (z <= -4.3e+117)
		tmp = t_1;
	elseif (z <= -6.6e-47)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= -5e-100)
		tmp = t_1;
	elseif (z <= 3.8e-76)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 1.6e+125)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = Float64(Float64(-t) / Float64(z / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * -(z / (a - z));
	tmp = 0.0;
	if (z <= -4.3e+117)
		tmp = t_1;
	elseif (z <= -6.6e-47)
		tmp = x * (1.0 - (y / a));
	elseif (z <= -5e-100)
		tmp = t_1;
	elseif (z <= 3.8e-76)
		tmp = x + ((y * t) / a);
	elseif (z <= 1.6e+125)
		tmp = y * ((x - t) / z);
	else
		tmp = -t / (z / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * (-N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[z, -4.3e+117], t$95$1, If[LessEqual[z, -6.6e-47], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5e-100], t$95$1, If[LessEqual[z, 3.8e-76], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+125], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.29999999999999998e117 or -6.60000000000000007e-47 < z < -5.0000000000000001e-100

   1. Initial program 61.5%

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

   2. Taylor expanded in t around inf 73.0%

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

      1. div-sub 73.0%

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

   4. Simplified 73.0%

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

   5. Taylor expanded in y around 0 67.5%

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

      1. neg-mul-1 67.5%

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

      2. distribute-neg-frac 67.5%

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

   7. Simplified 67.5%

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

   if -4.29999999999999998e117 < z < -6.60000000000000007e-47

   1. Initial program 94.5%

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

   2. Taylor expanded in z around 0 43.0%

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

      1. +-commutative 43.0%

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

      2. associate-/l* 55.7%

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

   4. Simplified 55.7%

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

   5. Taylor expanded in x around inf 50.2%

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

      1. *-commutative 50.2%

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

      2. mul-1-neg 50.2%

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

      3. unsub-neg 50.2%

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

   7. Simplified 50.2%

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

   if -5.0000000000000001e-100 < z < 3.8000000000000002e-76

   1. Initial program 94.0%

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

   2. Taylor expanded in z around 0 77.6%

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

      1. +-commutative 77.6%

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

      2. associate-/l* 81.2%

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

   4. Simplified 81.2%

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

   5. Taylor expanded in t around inf 63.6%

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

   if 3.8000000000000002e-76 < z < 1.59999999999999992e125

   1. Initial program 81.6%

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

   2. Taylor expanded in a around 0 39.9%

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

      1. associate-*r/ 39.9%

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

      2. neg-mul-1 39.9%

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

   4. Simplified 39.9%

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

   5. Taylor expanded in y around inf 45.4%

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

      1. div-sub 45.4%

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

   7. Simplified 45.4%

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

   if 1.59999999999999992e125 < z

   1. Initial program 66.7%

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

   2. Taylor expanded in x around 0 29.8%

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

   3. Taylor expanded in a around 0 28.3%

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

      1. mul-1-neg 28.3%

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

      2. associate-/l* 63.4%

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

      3. distribute-neg-frac 63.4%

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

   5. Simplified 63.4%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+117}:\\ \;\;\;\;t \cdot \left(-\frac{z}{a - z}\right)\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-100}:\\ \;\;\;\;t \cdot \left(-\frac{z}{a - z}\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-76}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+125}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \end{array} \]

Alternative 10: 50.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+109}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-100}:\\ \;\;\;\;t \cdot \left(-\frac{z}{a - z}\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-75}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+125}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.65e+109)
   (/ (- t) (/ (- a z) z))
   (if (<= z -5.6e-47)
     (* x (- 1.0 (/ y a)))
     (if (<= z -1.65e-100)
       (* t (- (/ z (- a z))))
       (if (<= z 3.7e-75)
         (+ x (/ (* y t) a))
         (if (<= z 1.6e+125) (* y (/ (- x t) z)) (/ (- t) (/ z (- y z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.65e+109) {
		tmp = -t / ((a - z) / z);
	} else if (z <= -5.6e-47) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= -1.65e-100) {
		tmp = t * -(z / (a - z));
	} else if (z <= 3.7e-75) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.6e+125) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = -t / (z / (y - 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 <= (-1.65d+109)) then
        tmp = -t / ((a - z) / z)
    else if (z <= (-5.6d-47)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= (-1.65d-100)) then
        tmp = t * -(z / (a - z))
    else if (z <= 3.7d-75) then
        tmp = x + ((y * t) / a)
    else if (z <= 1.6d+125) then
        tmp = y * ((x - t) / z)
    else
        tmp = -t / (z / (y - 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 <= -1.65e+109) {
		tmp = -t / ((a - z) / z);
	} else if (z <= -5.6e-47) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= -1.65e-100) {
		tmp = t * -(z / (a - z));
	} else if (z <= 3.7e-75) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.6e+125) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = -t / (z / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.65e+109:
		tmp = -t / ((a - z) / z)
	elif z <= -5.6e-47:
		tmp = x * (1.0 - (y / a))
	elif z <= -1.65e-100:
		tmp = t * -(z / (a - z))
	elif z <= 3.7e-75:
		tmp = x + ((y * t) / a)
	elif z <= 1.6e+125:
		tmp = y * ((x - t) / z)
	else:
		tmp = -t / (z / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.65e+109)
		tmp = Float64(Float64(-t) / Float64(Float64(a - z) / z));
	elseif (z <= -5.6e-47)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= -1.65e-100)
		tmp = Float64(t * Float64(-Float64(z / Float64(a - z))));
	elseif (z <= 3.7e-75)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 1.6e+125)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = Float64(Float64(-t) / Float64(z / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.65e+109)
		tmp = -t / ((a - z) / z);
	elseif (z <= -5.6e-47)
		tmp = x * (1.0 - (y / a));
	elseif (z <= -1.65e-100)
		tmp = t * -(z / (a - z));
	elseif (z <= 3.7e-75)
		tmp = x + ((y * t) / a);
	elseif (z <= 1.6e+125)
		tmp = y * ((x - t) / z);
	else
		tmp = -t / (z / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.65e+109], N[((-t) / N[(N[(a - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.6e-47], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.65e-100], N[(t * (-N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 3.7e-75], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+125], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.6499999999999999e109

   1. Initial program 57.7%

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

   2. Taylor expanded in t around inf 72.3%

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

      1. div-sub 72.3%

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

   4. Simplified 72.3%

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

   5. Taylor expanded in y around 0 40.2%

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

      1. mul-1-neg 40.2%

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

      2. associate-/l* 71.4%

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

      3. distribute-neg-frac 71.4%

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

   7. Simplified 71.4%

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

   if -1.6499999999999999e109 < z < -5.59999999999999986e-47

   1. Initial program 94.5%

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

   2. Taylor expanded in z around 0 43.0%

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

      1. +-commutative 43.0%

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

      2. associate-/l* 55.7%

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

   4. Simplified 55.7%

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

   5. Taylor expanded in x around inf 50.2%

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

      1. *-commutative 50.2%

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

      2. mul-1-neg 50.2%

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

      3. unsub-neg 50.2%

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

   7. Simplified 50.2%

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

   if -5.59999999999999986e-47 < z < -1.64999999999999998e-100

   1. Initial program 76.8%

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

   2. Taylor expanded in t around inf 75.8%

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

      1. div-sub 75.8%

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

   4. Simplified 75.8%

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

   5. Taylor expanded in y around 0 52.4%

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

      1. neg-mul-1 52.4%

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

      2. distribute-neg-frac 52.4%

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

   7. Simplified 52.4%

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

   if -1.64999999999999998e-100 < z < 3.70000000000000024e-75

   1. Initial program 94.0%

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

   2. Taylor expanded in z around 0 77.6%

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

      1. +-commutative 77.6%

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

      2. associate-/l* 81.2%

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

   4. Simplified 81.2%

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

   5. Taylor expanded in t around inf 63.6%

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

   if 3.70000000000000024e-75 < z < 1.59999999999999992e125

   1. Initial program 81.6%

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

   2. Taylor expanded in a around 0 39.9%

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

      1. associate-*r/ 39.9%

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

      2. neg-mul-1 39.9%

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

   4. Simplified 39.9%

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

   5. Taylor expanded in y around inf 45.4%

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

      1. div-sub 45.4%

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

   7. Simplified 45.4%

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

   if 1.59999999999999992e125 < z

   1. Initial program 66.7%

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

   2. Taylor expanded in x around 0 29.8%

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

   3. Taylor expanded in a around 0 28.3%

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

      1. mul-1-neg 28.3%

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

      2. associate-/l* 63.4%

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

      3. distribute-neg-frac 63.4%

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

   5. Simplified 63.4%

      \[\leadsto \color{blue}{\frac{-t}{\frac{z}{y - z}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+109}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-100}:\\ \;\;\;\;t \cdot \left(-\frac{z}{a - z}\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-75}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+125}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \end{array} \]

Alternative 11: 41.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -0.0062:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-307}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-157}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) a))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -0.0062)
     t_2
     (if (<= a -3.2e-176)
       t_1
       (if (<= a -1.05e-307)
         t
         (if (<= a 5.6e-157) (/ y (/ z x)) (if (<= a 3.4e+67) 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 * (1.0 - (y / a));
	double tmp;
	if (a <= -0.0062) {
		tmp = t_2;
	} else if (a <= -3.2e-176) {
		tmp = t_1;
	} else if (a <= -1.05e-307) {
		tmp = t;
	} else if (a <= 5.6e-157) {
		tmp = y / (z / x);
	} else if (a <= 3.4e+67) {
		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 * (1.0d0 - (y / a))
    if (a <= (-0.0062d0)) then
        tmp = t_2
    else if (a <= (-3.2d-176)) then
        tmp = t_1
    else if (a <= (-1.05d-307)) then
        tmp = t
    else if (a <= 5.6d-157) then
        tmp = y / (z / x)
    else if (a <= 3.4d+67) 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 * (1.0 - (y / a));
	double tmp;
	if (a <= -0.0062) {
		tmp = t_2;
	} else if (a <= -3.2e-176) {
		tmp = t_1;
	} else if (a <= -1.05e-307) {
		tmp = t;
	} else if (a <= 5.6e-157) {
		tmp = y / (z / x);
	} else if (a <= 3.4e+67) {
		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 * (1.0 - (y / a))
	tmp = 0
	if a <= -0.0062:
		tmp = t_2
	elif a <= -3.2e-176:
		tmp = t_1
	elif a <= -1.05e-307:
		tmp = t
	elif a <= 5.6e-157:
		tmp = y / (z / x)
	elif a <= 3.4e+67:
		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(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -0.0062)
		tmp = t_2;
	elseif (a <= -3.2e-176)
		tmp = t_1;
	elseif (a <= -1.05e-307)
		tmp = t;
	elseif (a <= 5.6e-157)
		tmp = Float64(y / Float64(z / x));
	elseif (a <= 3.4e+67)
		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 * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -0.0062)
		tmp = t_2;
	elseif (a <= -3.2e-176)
		tmp = t_1;
	elseif (a <= -1.05e-307)
		tmp = t;
	elseif (a <= 5.6e-157)
		tmp = y / (z / x);
	elseif (a <= 3.4e+67)
		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[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.0062], t$95$2, If[LessEqual[a, -3.2e-176], t$95$1, If[LessEqual[a, -1.05e-307], t, If[LessEqual[a, 5.6e-157], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e+67], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -0.00619999999999999978 or 3.4000000000000002e67 < a

   1. Initial program 85.7%

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

   2. Taylor expanded in z around 0 54.0%

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

      1. +-commutative 54.0%

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

      2. associate-/l* 64.2%

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

   4. Simplified 64.2%

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

   5. Taylor expanded in x around inf 52.2%

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

      1. *-commutative 52.2%

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

      2. mul-1-neg 52.2%

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

      3. unsub-neg 52.2%

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

   7. Simplified 52.2%

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

   if -0.00619999999999999978 < a < -3.19999999999999985e-176 or 5.6000000000000002e-157 < a < 3.4000000000000002e67

   1. Initial program 86.1%

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

   2. Taylor expanded in z around 0 50.1%

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

      1. +-commutative 50.1%

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

      2. associate-/l* 48.8%

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

   4. Simplified 48.8%

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

   5. Taylor expanded in y around inf 41.4%

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

      1. div-sub 42.9%

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

      2. *-commutative 42.9%

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

   7. Simplified 42.9%

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

   if -3.19999999999999985e-176 < a < -1.0500000000000001e-307

   1. Initial program 73.9%

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

   2. Taylor expanded in z around inf 55.5%

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

   if -1.0500000000000001e-307 < a < 5.6000000000000002e-157

   1. Initial program 72.1%

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

   2. Taylor expanded in a around 0 65.8%

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

      1. associate-*r/ 65.8%

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

      2. neg-mul-1 65.8%

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

   4. Simplified 65.8%

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

   5. Taylor expanded in x around inf 43.1%

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

      1. associate-/l* 51.8%

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

   7. Simplified 51.8%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0062:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-176}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-307}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-157}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+67}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 12: 49.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x - t}{z}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{-74}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- x t) z))))
   (if (<= z -2.9e+122)
     t
     (if (<= z -6e-47)
       (* x (- 1.0 (/ y a)))
       (if (<= z -3.2e-105)
         t_1
         (if (<= z 1e-74) (+ x (/ (* y t) a)) (if (<= z 4.5e+127) t_1 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((x - t) / z);
	double tmp;
	if (z <= -2.9e+122) {
		tmp = t;
	} else if (z <= -6e-47) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= -3.2e-105) {
		tmp = t_1;
	} else if (z <= 1e-74) {
		tmp = x + ((y * t) / a);
	} else if (z <= 4.5e+127) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * ((x - t) / z)
    if (z <= (-2.9d+122)) then
        tmp = t
    else if (z <= (-6d-47)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= (-3.2d-105)) then
        tmp = t_1
    else if (z <= 1d-74) then
        tmp = x + ((y * t) / a)
    else if (z <= 4.5d+127) then
        tmp = t_1
    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 t_1 = y * ((x - t) / z);
	double tmp;
	if (z <= -2.9e+122) {
		tmp = t;
	} else if (z <= -6e-47) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= -3.2e-105) {
		tmp = t_1;
	} else if (z <= 1e-74) {
		tmp = x + ((y * t) / a);
	} else if (z <= 4.5e+127) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((x - t) / z)
	tmp = 0
	if z <= -2.9e+122:
		tmp = t
	elif z <= -6e-47:
		tmp = x * (1.0 - (y / a))
	elif z <= -3.2e-105:
		tmp = t_1
	elif z <= 1e-74:
		tmp = x + ((y * t) / a)
	elif z <= 4.5e+127:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(x - t) / z))
	tmp = 0.0
	if (z <= -2.9e+122)
		tmp = t;
	elseif (z <= -6e-47)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= -3.2e-105)
		tmp = t_1;
	elseif (z <= 1e-74)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 4.5e+127)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((x - t) / z);
	tmp = 0.0;
	if (z <= -2.9e+122)
		tmp = t;
	elseif (z <= -6e-47)
		tmp = x * (1.0 - (y / a));
	elseif (z <= -3.2e-105)
		tmp = t_1;
	elseif (z <= 1e-74)
		tmp = x + ((y * t) / a);
	elseif (z <= 4.5e+127)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e+122], t, If[LessEqual[z, -6e-47], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.2e-105], t$95$1, If[LessEqual[z, 1e-74], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+127], t$95$1, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.9000000000000001e122 or 4.50000000000000034e127 < z

   1. Initial program 62.2%

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

   2. Taylor expanded in z around inf 62.4%

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

   if -2.9000000000000001e122 < z < -6.00000000000000033e-47

   1. Initial program 94.7%

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

   2. Taylor expanded in z around 0 42.0%

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

      1. +-commutative 42.0%

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

      2. associate-/l* 54.4%

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

   4. Simplified 54.4%

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

   5. Taylor expanded in x around inf 48.9%

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

      1. *-commutative 48.9%

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

      2. mul-1-neg 48.9%

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

      3. unsub-neg 48.9%

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

   7. Simplified 48.9%

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

   if -6.00000000000000033e-47 < z < -3.19999999999999981e-105 or 9.99999999999999958e-75 < z < 4.50000000000000034e127

   1. Initial program 81.5%

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

   2. Taylor expanded in a around 0 43.4%

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

      1. associate-*r/ 43.4%

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

      2. neg-mul-1 43.4%

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

   4. Simplified 43.4%

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

   5. Taylor expanded in y around inf 45.2%

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

      1. div-sub 45.2%

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

   7. Simplified 45.2%

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

   if -3.19999999999999981e-105 < z < 9.99999999999999958e-75

   1. Initial program 93.9%

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

   2. Taylor expanded in z around 0 77.1%

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

      1. +-commutative 77.1%

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

      2. associate-/l* 80.8%

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

   4. Simplified 80.8%

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

   5. Taylor expanded in t around inf 62.8%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-105}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 10^{-74}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+127}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13: 64.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+55} \lor \neg \left(z \leq -3.5 \cdot 10^{+29}\right) \land \left(z \leq -3.3 \cdot 10^{-133} \lor \neg \left(z \leq 5.5 \cdot 10^{-64}\right)\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.5e+55)
         (and (not (<= z -3.5e+29))
              (or (<= z -3.3e-133) (not (<= z 5.5e-64)))))
   (* t (/ (- y z) (- a z)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.5e+55) || (!(z <= -3.5e+29) && ((z <= -3.3e-133) || !(z <= 5.5e-64)))) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y / (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 ((z <= (-5.5d+55)) .or. (.not. (z <= (-3.5d+29))) .and. (z <= (-3.3d-133)) .or. (.not. (z <= 5.5d-64))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + (y / (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 ((z <= -5.5e+55) || (!(z <= -3.5e+29) && ((z <= -3.3e-133) || !(z <= 5.5e-64)))) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.5e+55) or (not (z <= -3.5e+29) and ((z <= -3.3e-133) or not (z <= 5.5e-64))):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.5e+55) || (!(z <= -3.5e+29) && ((z <= -3.3e-133) || !(z <= 5.5e-64))))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.5e+55) || (~((z <= -3.5e+29)) && ((z <= -3.3e-133) || ~((z <= 5.5e-64)))))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.5e+55], And[N[Not[LessEqual[z, -3.5e+29]], $MachinePrecision], Or[LessEqual[z, -3.3e-133], N[Not[LessEqual[z, 5.5e-64]], $MachinePrecision]]]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5000000000000004e55 or -3.49999999999999979e29 < z < -3.30000000000000009e-133 or 5.4999999999999999e-64 < z

   1. Initial program 75.0%

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

   2. Taylor expanded in t around inf 62.9%

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

      1. div-sub 62.9%

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

   4. Simplified 62.9%

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

   if -5.5000000000000004e55 < z < -3.49999999999999979e29 or -3.30000000000000009e-133 < z < 5.4999999999999999e-64

   1. Initial program 94.1%

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

   2. Taylor expanded in z around 0 75.1%

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

      1. +-commutative 75.1%

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

      2. associate-/l* 81.4%

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

   4. Simplified 81.4%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+55} \lor \neg \left(z \leq -3.5 \cdot 10^{+29}\right) \land \left(z \leq -3.3 \cdot 10^{-133} \lor \neg \left(z \leq 5.5 \cdot 10^{-64}\right)\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 14: 57.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-117} \lor \neg \left(t \leq 1.95 \cdot 10^{+83}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= t -2.9e-24)
     t_1
     (if (<= t 6.7e-186)
       (* x (- 1.0 (/ y a)))
       (if (or (<= t 1.45e-117) (not (<= t 1.95e+83)))
         t_1
         (- x (/ y (/ a x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -2.9e-24) {
		tmp = t_1;
	} else if (t <= 6.7e-186) {
		tmp = x * (1.0 - (y / a));
	} else if ((t <= 1.45e-117) || !(t <= 1.95e+83)) {
		tmp = t_1;
	} else {
		tmp = x - (y / (a / 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 = t * ((y - z) / (a - z))
    if (t <= (-2.9d-24)) then
        tmp = t_1
    else if (t <= 6.7d-186) then
        tmp = x * (1.0d0 - (y / a))
    else if ((t <= 1.45d-117) .or. (.not. (t <= 1.95d+83))) then
        tmp = t_1
    else
        tmp = x - (y / (a / 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 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -2.9e-24) {
		tmp = t_1;
	} else if (t <= 6.7e-186) {
		tmp = x * (1.0 - (y / a));
	} else if ((t <= 1.45e-117) || !(t <= 1.95e+83)) {
		tmp = t_1;
	} else {
		tmp = x - (y / (a / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -2.9e-24:
		tmp = t_1
	elif t <= 6.7e-186:
		tmp = x * (1.0 - (y / a))
	elif (t <= 1.45e-117) or not (t <= 1.95e+83):
		tmp = t_1
	else:
		tmp = x - (y / (a / x))
	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 (t <= -2.9e-24)
		tmp = t_1;
	elseif (t <= 6.7e-186)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif ((t <= 1.45e-117) || !(t <= 1.95e+83))
		tmp = t_1;
	else
		tmp = Float64(x - Float64(y / Float64(a / x)));
	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 (t <= -2.9e-24)
		tmp = t_1;
	elseif (t <= 6.7e-186)
		tmp = x * (1.0 - (y / a));
	elseif ((t <= 1.45e-117) || ~((t <= 1.95e+83)))
		tmp = t_1;
	else
		tmp = x - (y / (a / x));
	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[t, -2.9e-24], t$95$1, If[LessEqual[t, 6.7e-186], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 1.45e-117], N[Not[LessEqual[t, 1.95e+83]], $MachinePrecision]], t$95$1, N[(x - N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.8999999999999999e-24 or 6.70000000000000034e-186 < t < 1.45e-117 or 1.9500000000000001e83 < t

   1. Initial program 88.1%

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

   2. Taylor expanded in t around inf 77.5%

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

      1. div-sub 77.5%

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

   4. Simplified 77.5%

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

   if -2.8999999999999999e-24 < t < 6.70000000000000034e-186

   1. Initial program 70.2%

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

   2. Taylor expanded in z around 0 49.5%

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

      1. +-commutative 49.5%

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

      2. associate-/l* 51.9%

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

   4. Simplified 51.9%

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

   5. Taylor expanded in x around inf 51.8%

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

      1. *-commutative 51.8%

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

      2. mul-1-neg 51.8%

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

      3. unsub-neg 51.8%

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

   7. Simplified 51.8%

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

   if 1.45e-117 < t < 1.9500000000000001e83

   1. Initial program 90.5%

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

   2. Taylor expanded in z around 0 66.3%

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

      1. +-commutative 66.3%

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

      2. associate-/l* 68.9%

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

   4. Simplified 68.9%

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

   5. Taylor expanded in t around 0 54.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot x}{a} + x} \]
   6. Step-by-step derivation

      1. +-commutative 54.4%

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

      2. mul-1-neg 54.4%

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

      3. unsub-neg 54.4%

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

      4. associate-/l* 57.1%

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

   7. Simplified 57.1%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-24}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-117} \lor \neg \left(t \leq 1.95 \cdot 10^{+83}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \end{array} \]

Alternative 15: 58.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-15}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-6}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+171} \lor \neg \left(x \leq 4.1 \cdot 10^{+298}\right):\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.65e-15)
   (- x (/ y (/ a x)))
   (if (<= x 1.45e-6)
     (* t (/ (- y z) (- a z)))
     (if (or (<= x 2.7e+171) (not (<= x 4.1e+298)))
       (* y (/ (- t x) (- a z)))
       (* x (- 1.0 (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.65e-15) {
		tmp = x - (y / (a / x));
	} else if (x <= 1.45e-6) {
		tmp = t * ((y - z) / (a - z));
	} else if ((x <= 2.7e+171) || !(x <= 4.1e+298)) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = x * (1.0 - (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 (x <= (-1.65d-15)) then
        tmp = x - (y / (a / x))
    else if (x <= 1.45d-6) then
        tmp = t * ((y - z) / (a - z))
    else if ((x <= 2.7d+171) .or. (.not. (x <= 4.1d+298))) then
        tmp = y * ((t - x) / (a - z))
    else
        tmp = x * (1.0d0 - (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 (x <= -1.65e-15) {
		tmp = x - (y / (a / x));
	} else if (x <= 1.45e-6) {
		tmp = t * ((y - z) / (a - z));
	} else if ((x <= 2.7e+171) || !(x <= 4.1e+298)) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.65e-15:
		tmp = x - (y / (a / x))
	elif x <= 1.45e-6:
		tmp = t * ((y - z) / (a - z))
	elif (x <= 2.7e+171) or not (x <= 4.1e+298):
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.65e-15)
		tmp = Float64(x - Float64(y / Float64(a / x)));
	elseif (x <= 1.45e-6)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif ((x <= 2.7e+171) || !(x <= 4.1e+298))
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.65e-15)
		tmp = x - (y / (a / x));
	elseif (x <= 1.45e-6)
		tmp = t * ((y - z) / (a - z));
	elseif ((x <= 2.7e+171) || ~((x <= 4.1e+298)))
		tmp = y * ((t - x) / (a - z));
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.65e-15], N[(x - N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.45e-6], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 2.7e+171], N[Not[LessEqual[x, 4.1e+298]], $MachinePrecision]], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.65e-15

   1. Initial program 72.9%

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

   2. Taylor expanded in z around 0 52.3%

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

      1. +-commutative 52.3%

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

      2. associate-/l* 55.7%

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

   4. Simplified 55.7%

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

   5. Taylor expanded in t around 0 48.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot x}{a} + x} \]
   6. Step-by-step derivation

      1. +-commutative 48.6%

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

      2. mul-1-neg 48.6%

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

      3. unsub-neg 48.6%

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

      4. associate-/l* 52.0%

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

   7. Simplified 52.0%

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

   if -1.65e-15 < x < 1.4500000000000001e-6

   1. Initial program 87.7%

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

   2. Taylor expanded in t around inf 75.8%

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

      1. div-sub 75.8%

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

   4. Simplified 75.8%

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

   if 1.4500000000000001e-6 < x < 2.6999999999999998e171 or 4.10000000000000016e298 < x

   1. Initial program 89.5%

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

      1. clear-num 89.5%

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

      2. associate-/r/ 89.4%

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

   3. Applied egg-rr 89.4%

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

   4. Taylor expanded in y around inf 69.0%

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

      1. div-sub 69.0%

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

      2. *-commutative 69.0%

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

   6. Simplified 69.0%

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

   if 2.6999999999999998e171 < x < 4.10000000000000016e298

   1. Initial program 67.7%

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

   2. Taylor expanded in z around 0 53.7%

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

      1. +-commutative 53.7%

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

      2. associate-/l* 63.5%

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

   4. Simplified 63.5%

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

   5. Taylor expanded in x around inf 66.6%

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

      1. *-commutative 66.6%

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

      2. mul-1-neg 66.6%

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

      3. unsub-neg 66.6%

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

   7. Simplified 66.6%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-15}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-6}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+171} \lor \neg \left(x \leq 4.1 \cdot 10^{+298}\right):\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 16: 36.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-246}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-122}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= z -2.5e+122)
     t
     (if (<= z -4.7e-32)
       x
       (if (<= z 4.1e-246)
         t_1
         (if (<= z 1.15e-122) x (if (<= z 4.8e-33) t_1 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -2.5e+122) {
		tmp = t;
	} else if (z <= -4.7e-32) {
		tmp = x;
	} else if (z <= 4.1e-246) {
		tmp = t_1;
	} else if (z <= 1.15e-122) {
		tmp = x;
	} else if (z <= 4.8e-33) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (z <= (-2.5d+122)) then
        tmp = t
    else if (z <= (-4.7d-32)) then
        tmp = x
    else if (z <= 4.1d-246) then
        tmp = t_1
    else if (z <= 1.15d-122) then
        tmp = x
    else if (z <= 4.8d-33) then
        tmp = t_1
    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 t_1 = t * (y / a);
	double tmp;
	if (z <= -2.5e+122) {
		tmp = t;
	} else if (z <= -4.7e-32) {
		tmp = x;
	} else if (z <= 4.1e-246) {
		tmp = t_1;
	} else if (z <= 1.15e-122) {
		tmp = x;
	} else if (z <= 4.8e-33) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if z <= -2.5e+122:
		tmp = t
	elif z <= -4.7e-32:
		tmp = x
	elif z <= 4.1e-246:
		tmp = t_1
	elif z <= 1.15e-122:
		tmp = x
	elif z <= 4.8e-33:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (z <= -2.5e+122)
		tmp = t;
	elseif (z <= -4.7e-32)
		tmp = x;
	elseif (z <= 4.1e-246)
		tmp = t_1;
	elseif (z <= 1.15e-122)
		tmp = x;
	elseif (z <= 4.8e-33)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (z <= -2.5e+122)
		tmp = t;
	elseif (z <= -4.7e-32)
		tmp = x;
	elseif (z <= 4.1e-246)
		tmp = t_1;
	elseif (z <= 1.15e-122)
		tmp = x;
	elseif (z <= 4.8e-33)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e+122], t, If[LessEqual[z, -4.7e-32], x, If[LessEqual[z, 4.1e-246], t$95$1, If[LessEqual[z, 1.15e-122], x, If[LessEqual[z, 4.8e-33], t$95$1, t]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.49999999999999994e122 or 4.8e-33 < z

   1. Initial program 68.2%

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

   2. Taylor expanded in z around inf 47.6%

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

   if -2.49999999999999994e122 < z < -4.70000000000000019e-32 or 4.09999999999999986e-246 < z < 1.15000000000000003e-122

   1. Initial program 94.7%

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

   2. Taylor expanded in a around inf 39.4%

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

   if -4.70000000000000019e-32 < z < 4.09999999999999986e-246 or 1.15000000000000003e-122 < z < 4.8e-33

   1. Initial program 91.6%

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

   2. Taylor expanded in t around inf 50.2%

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

      1. div-sub 50.2%

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

   4. Simplified 50.2%

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

   5. Taylor expanded in z around 0 41.6%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-246}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-122}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-33}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 17: 44.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x - t}{z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{-123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{-308}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- x t) z))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -1.8e-123)
     t_2
     (if (<= a -7e-245)
       t_1
       (if (<= a 6.3e-308) t (if (<= a 3.2e+28) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((x - t) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -1.8e-123) {
		tmp = t_2;
	} else if (a <= -7e-245) {
		tmp = t_1;
	} else if (a <= 6.3e-308) {
		tmp = t;
	} else if (a <= 3.2e+28) {
		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 * ((x - t) / z)
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-1.8d-123)) then
        tmp = t_2
    else if (a <= (-7d-245)) then
        tmp = t_1
    else if (a <= 6.3d-308) then
        tmp = t
    else if (a <= 3.2d+28) 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 * ((x - t) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -1.8e-123) {
		tmp = t_2;
	} else if (a <= -7e-245) {
		tmp = t_1;
	} else if (a <= 6.3e-308) {
		tmp = t;
	} else if (a <= 3.2e+28) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((x - t) / z)
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -1.8e-123:
		tmp = t_2
	elif a <= -7e-245:
		tmp = t_1
	elif a <= 6.3e-308:
		tmp = t
	elif a <= 3.2e+28:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(x - t) / z))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -1.8e-123)
		tmp = t_2;
	elseif (a <= -7e-245)
		tmp = t_1;
	elseif (a <= 6.3e-308)
		tmp = t;
	elseif (a <= 3.2e+28)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((x - t) / z);
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -1.8e-123)
		tmp = t_2;
	elseif (a <= -7e-245)
		tmp = t_1;
	elseif (a <= 6.3e-308)
		tmp = t;
	elseif (a <= 3.2e+28)
		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[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8e-123], t$95$2, If[LessEqual[a, -7e-245], t$95$1, If[LessEqual[a, 6.3e-308], t, If[LessEqual[a, 3.2e+28], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.7999999999999998e-123 or 3.2e28 < a

   1. Initial program 86.5%

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

   2. Taylor expanded in z around 0 55.4%

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

      1. +-commutative 55.4%

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

      2. associate-/l* 62.9%

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

   4. Simplified 62.9%

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

   5. Taylor expanded in x around inf 49.2%

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

      1. *-commutative 49.2%

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

      2. mul-1-neg 49.2%

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

      3. unsub-neg 49.2%

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

   7. Simplified 49.2%

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

   if -1.7999999999999998e-123 < a < -7.00000000000000033e-245 or 6.2999999999999995e-308 < a < 3.2e28

   1. Initial program 79.0%

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

   2. Taylor expanded in a around 0 63.1%

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

      1. associate-*r/ 63.1%

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

      2. neg-mul-1 63.1%

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

   4. Simplified 63.1%

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

   5. Taylor expanded in y around inf 50.6%

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

      1. div-sub 52.7%

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

   7. Simplified 52.7%

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

   if -7.00000000000000033e-245 < a < 6.2999999999999995e-308

   1. Initial program 63.1%

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

   2. Taylor expanded in z around inf 77.5%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-123}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-245}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{-308}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+28}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 18: 44.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -5 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-245}:\\ \;\;\;\;\left(x - t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.35 \cdot 10^{-307}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= a -5e-123)
     t_1
     (if (<= a -9e-245)
       (* (- x t) (/ y z))
       (if (<= a 3.35e-307) t (if (<= a 5.6e+23) (* y (/ (- x t) z)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -5e-123) {
		tmp = t_1;
	} else if (a <= -9e-245) {
		tmp = (x - t) * (y / z);
	} else if (a <= 3.35e-307) {
		tmp = t;
	} else if (a <= 5.6e+23) {
		tmp = y * ((x - t) / 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 * (1.0d0 - (y / a))
    if (a <= (-5d-123)) then
        tmp = t_1
    else if (a <= (-9d-245)) then
        tmp = (x - t) * (y / z)
    else if (a <= 3.35d-307) then
        tmp = t
    else if (a <= 5.6d+23) then
        tmp = y * ((x - t) / 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 * (1.0 - (y / a));
	double tmp;
	if (a <= -5e-123) {
		tmp = t_1;
	} else if (a <= -9e-245) {
		tmp = (x - t) * (y / z);
	} else if (a <= 3.35e-307) {
		tmp = t;
	} else if (a <= 5.6e+23) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -5e-123:
		tmp = t_1
	elif a <= -9e-245:
		tmp = (x - t) * (y / z)
	elif a <= 3.35e-307:
		tmp = t
	elif a <= 5.6e+23:
		tmp = y * ((x - t) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -5e-123)
		tmp = t_1;
	elseif (a <= -9e-245)
		tmp = Float64(Float64(x - t) * Float64(y / z));
	elseif (a <= 3.35e-307)
		tmp = t;
	elseif (a <= 5.6e+23)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -5e-123)
		tmp = t_1;
	elseif (a <= -9e-245)
		tmp = (x - t) * (y / z);
	elseif (a <= 3.35e-307)
		tmp = t;
	elseif (a <= 5.6e+23)
		tmp = y * ((x - t) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5e-123], t$95$1, If[LessEqual[a, -9e-245], N[(N[(x - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.35e-307], t, If[LessEqual[a, 5.6e+23], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.0000000000000003e-123 or 5.6e23 < a

   1. Initial program 86.5%

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

   2. Taylor expanded in z around 0 55.4%

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

      1. +-commutative 55.4%

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

      2. associate-/l* 62.9%

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

   4. Simplified 62.9%

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

   5. Taylor expanded in x around inf 49.2%

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

      1. *-commutative 49.2%

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

      2. mul-1-neg 49.2%

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

      3. unsub-neg 49.2%

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

   7. Simplified 49.2%

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

   if -5.0000000000000003e-123 < a < -8.99999999999999937e-245

   1. Initial program 80.3%

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

   2. Taylor expanded in a around 0 73.7%

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

      1. associate-*r/ 73.7%

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

      2. neg-mul-1 73.7%

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

   4. Simplified 73.7%

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

   5. Taylor expanded in y around -inf 58.0%

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

      1. associate-/l* 61.2%

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

   7. Simplified 61.2%

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

      1. associate-/r/ 61.3%

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

   9. Applied egg-rr 61.3%

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

   if -8.99999999999999937e-245 < a < 3.3499999999999999e-307

   1. Initial program 63.1%

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

   2. Taylor expanded in z around inf 77.5%

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

   if 3.3499999999999999e-307 < a < 5.6e23

   1. Initial program 78.5%

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

   2. Taylor expanded in a around 0 58.3%

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

      1. associate-*r/ 58.3%

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

      2. neg-mul-1 58.3%

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

   4. Simplified 58.3%

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

   5. Taylor expanded in y around inf 47.3%

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

      1. div-sub 48.9%

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

   7. Simplified 48.9%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{-123}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-245}:\\ \;\;\;\;\left(x - t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.35 \cdot 10^{-307}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 19: 73.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.05 \cdot 10^{+93} \lor \neg \left(a \leq 2.2 \cdot 10^{-20}\right):\\ \;\;\;\;x - \frac{t - x}{a} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.05e+93) (not (<= a 2.2e-20)))
   (- x (* (/ (- t x) a) (- z y)))
   (+ t (* (- y a) (/ (- x t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.05e+93) || !(a <= 2.2e-20)) {
		tmp = x - (((t - x) / a) * (z - y));
	} else {
		tmp = t + ((y - a) * ((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 <= (-3.05d+93)) .or. (.not. (a <= 2.2d-20))) then
        tmp = x - (((t - x) / a) * (z - y))
    else
        tmp = t + ((y - a) * ((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 <= -3.05e+93) || !(a <= 2.2e-20)) {
		tmp = x - (((t - x) / a) * (z - y));
	} else {
		tmp = t + ((y - a) * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.05e+93) or not (a <= 2.2e-20):
		tmp = x - (((t - x) / a) * (z - y))
	else:
		tmp = t + ((y - a) * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.05e+93) || !(a <= 2.2e-20))
		tmp = Float64(x - Float64(Float64(Float64(t - x) / a) * Float64(z - y)));
	else
		tmp = Float64(t + Float64(Float64(y - a) * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.05e+93) || ~((a <= 2.2e-20)))
		tmp = x - (((t - x) / a) * (z - y));
	else
		tmp = t + ((y - a) * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.05e+93], N[Not[LessEqual[a, 2.2e-20]], $MachinePrecision]], N[(x - N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(y - a), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.05e93 or 2.19999999999999991e-20 < a

   1. Initial program 89.9%

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

   2. Taylor expanded in a around inf 78.3%

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

   if -3.05e93 < a < 2.19999999999999991e-20

   1. Initial program 76.6%

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

      1. *-commutative 76.6%

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

      2. flip-- 54.2%

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

      3. associate-*r/ 49.0%

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

   3. Applied egg-rr 49.0%

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

   4. Taylor expanded in z around -inf 73.1%

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

      1. +-commutative 73.1%

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

      2. mul-1-neg 73.1%

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

      3. associate-/l* 81.0%

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

      4. mul-1-neg 81.0%

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

      5. sub-neg 81.0%

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

      6. unsub-neg 81.0%

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

      7. associate-/r/ 79.1%

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

   6. Simplified 79.1%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.05 \cdot 10^{+93} \lor \neg \left(a \leq 2.2 \cdot 10^{-20}\right):\\ \;\;\;\;x - \frac{t - x}{a} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \end{array} \]

Alternative 20: 33.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-233}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+125}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e+122)
   t
   (if (<= z -1.05e-31)
     x
     (if (<= z 5.8e-233) (* t (/ y a)) (if (<= z 9.5e+125) (/ y (/ z x)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+122) {
		tmp = t;
	} else if (z <= -1.05e-31) {
		tmp = x;
	} else if (z <= 5.8e-233) {
		tmp = t * (y / a);
	} else if (z <= 9.5e+125) {
		tmp = y / (z / x);
	} 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 <= (-2.4d+122)) then
        tmp = t
    else if (z <= (-1.05d-31)) then
        tmp = x
    else if (z <= 5.8d-233) then
        tmp = t * (y / a)
    else if (z <= 9.5d+125) then
        tmp = y / (z / x)
    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 <= -2.4e+122) {
		tmp = t;
	} else if (z <= -1.05e-31) {
		tmp = x;
	} else if (z <= 5.8e-233) {
		tmp = t * (y / a);
	} else if (z <= 9.5e+125) {
		tmp = y / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e+122:
		tmp = t
	elif z <= -1.05e-31:
		tmp = x
	elif z <= 5.8e-233:
		tmp = t * (y / a)
	elif z <= 9.5e+125:
		tmp = y / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e+122)
		tmp = t;
	elseif (z <= -1.05e-31)
		tmp = x;
	elseif (z <= 5.8e-233)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 9.5e+125)
		tmp = Float64(y / Float64(z / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.4e+122)
		tmp = t;
	elseif (z <= -1.05e-31)
		tmp = x;
	elseif (z <= 5.8e-233)
		tmp = t * (y / a);
	elseif (z <= 9.5e+125)
		tmp = y / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e+122], t, If[LessEqual[z, -1.05e-31], x, If[LessEqual[z, 5.8e-233], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+125], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.4000000000000002e122 or 9.50000000000000041e125 < z

   1. Initial program 62.2%

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

   2. Taylor expanded in z around inf 62.4%

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

   if -2.4000000000000002e122 < z < -1.04999999999999996e-31

   1. Initial program 94.3%

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

   2. Taylor expanded in a around inf 36.1%

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

   if -1.04999999999999996e-31 < z < 5.79999999999999964e-233

   1. Initial program 93.8%

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

   2. Taylor expanded in t around inf 50.0%

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

      1. div-sub 50.0%

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

   4. Simplified 50.0%

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

   5. Taylor expanded in z around 0 42.7%

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

   if 5.79999999999999964e-233 < z < 9.50000000000000041e125

   1. Initial program 85.4%

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

   2. Taylor expanded in a around 0 38.8%

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

      1. associate-*r/ 38.8%

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

      2. neg-mul-1 38.8%

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

   4. Simplified 38.8%

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

   5. Taylor expanded in x around inf 30.5%

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

      1. associate-/l* 33.1%

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

   7. Simplified 33.1%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-233}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+125}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 21: 38.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.75 \cdot 10^{+93}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+49}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.75e+93) x (if (<= a 2e+49) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.75e+93) {
		tmp = x;
	} else if (a <= 2e+49) {
		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 <= (-2.75d+93)) then
        tmp = x
    else if (a <= 2d+49) 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 <= -2.75e+93) {
		tmp = x;
	} else if (a <= 2e+49) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.75e+93:
		tmp = x
	elif a <= 2e+49:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.75e+93)
		tmp = x;
	elseif (a <= 2e+49)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.75e+93)
		tmp = x;
	elseif (a <= 2e+49)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.75e+93], x, If[LessEqual[a, 2e+49], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.75000000000000015e93 or 1.99999999999999989e49 < a

   1. Initial program 88.7%

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

   2. Taylor expanded in a around inf 44.7%

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

   if -2.75000000000000015e93 < a < 1.99999999999999989e49

   1. Initial program 78.4%

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

   2. Taylor expanded in z around inf 35.1%

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

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.75 \cdot 10^{+93}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+49}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22: 25.2% 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 82.6%

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

2. Taylor expanded in z around inf 25.3%

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

3. Final simplification 25.3%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023192 
(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)))))