Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3

Percentage Accurate: 68.3% → 90.6%

Time: 20.2s

Alternatives: 15

Speedup: 0.3×

Specification

Math

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

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(Float64(y - z) * 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[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 68.3% accurate, 1.0× speedup

Math

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

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(Float64(y - z) * 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[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 90.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-296} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -2e-296) (not (<= t_1 0.0)))
     (+ x (* (- t x) (/ (- y z) (- a z))))
     (- t (/ (* x (- a y)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -2e-296) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t - ((x * (a - 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 = x + (((y - z) * (t - x)) / (a - z))
    if ((t_1 <= (-2d-296)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) * ((y - z) / (a - z)))
    else
        tmp = t - ((x * (a - 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 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -2e-296) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t - ((x * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if (t_1 <= -2e-296) or not (t_1 <= 0.0):
		tmp = x + ((t - x) * ((y - z) / (a - z)))
	else:
		tmp = t - ((x * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -2e-296) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(t - Float64(Float64(x * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -2e-296) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	else
		tmp = t - ((x * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-296], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(x * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -2e-296 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 73.5%

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

      1. associate-*l/ 90.8%

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

   3. Simplified 90.8%

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

   if -2e-296 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.8%

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

      1. associate-*l/ 9.1%

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

   3. Simplified 9.1%

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

   4. Taylor expanded in z around inf 99.7%

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

      1. associate--l+ 99.7%

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

      2. associate-*r/ 99.7%

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

      3. associate-*r/ 99.7%

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

      4. div-sub 99.7%

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

      5. distribute-lft-out-- 99.7%

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

      6. associate-*r/ 99.7%

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

      7. mul-1-neg 99.7%

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

      8. unsub-neg 99.7%

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

      9. distribute-rgt-out-- 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in t around 0 99.7%

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

      1. associate-*r/ 99.7%

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

      2. mul-1-neg 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

   9. Simplified 99.7%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -2 \cdot 10^{-296} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x \cdot \left(a - y\right)}{z}\\ \end{array} \]

Alternative 2: 59.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+127}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-116}:\\ \;\;\;\;t - \frac{y}{\frac{-z}{x}}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.9e+127)
   (+ x (/ t (/ a y)))
   (if (<= a -1e+21)
     (* y (/ (- t x) (- a z)))
     (if (<= a -1.25e-13)
       (+ x (/ (* y t) a))
       (if (<= a 8e-116)
         (- t (/ y (/ (- z) x)))
         (if (<= a 2.35e+62)
           (* t (/ (- y z) (- a z)))
           (+ x (* y (/ t a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.9e+127) {
		tmp = x + (t / (a / y));
	} else if (a <= -1e+21) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= -1.25e-13) {
		tmp = x + ((y * t) / a);
	} else if (a <= 8e-116) {
		tmp = t - (y / (-z / x));
	} else if (a <= 2.35e+62) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.9d+127)) then
        tmp = x + (t / (a / y))
    else if (a <= (-1d+21)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= (-1.25d-13)) then
        tmp = x + ((y * t) / a)
    else if (a <= 8d-116) then
        tmp = t - (y / (-z / x))
    else if (a <= 2.35d+62) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.9e+127) {
		tmp = x + (t / (a / y));
	} else if (a <= -1e+21) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= -1.25e-13) {
		tmp = x + ((y * t) / a);
	} else if (a <= 8e-116) {
		tmp = t - (y / (-z / x));
	} else if (a <= 2.35e+62) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.9e+127:
		tmp = x + (t / (a / y))
	elif a <= -1e+21:
		tmp = y * ((t - x) / (a - z))
	elif a <= -1.25e-13:
		tmp = x + ((y * t) / a)
	elif a <= 8e-116:
		tmp = t - (y / (-z / x))
	elif a <= 2.35e+62:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.9e+127)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (a <= -1e+21)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= -1.25e-13)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= 8e-116)
		tmp = Float64(t - Float64(y / Float64(Float64(-z) / x)));
	elseif (a <= 2.35e+62)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.9e+127)
		tmp = x + (t / (a / y));
	elseif (a <= -1e+21)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= -1.25e-13)
		tmp = x + ((y * t) / a);
	elseif (a <= 8e-116)
		tmp = t - (y / (-z / x));
	elseif (a <= 2.35e+62)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.9e+127], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1e+21], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.25e-13], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e-116], N[(t - N[(y / N[((-z) / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.35e+62], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -2.9000000000000002e127

   1. Initial program 52.8%

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

      1. associate-*l/ 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in z around 0 52.8%

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

   5. Taylor expanded in t around inf 53.5%

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

      1. associate-/l* 67.4%

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

   7. Simplified 67.4%

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

   if -2.9000000000000002e127 < a < -1e21

   1. Initial program 69.9%

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

      1. associate-*l/ 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in y around inf 65.3%

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

      1. div-sub 65.3%

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

   6. Simplified 65.3%

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

   if -1e21 < a < -1.24999999999999997e-13

   1. Initial program 72.1%

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

      1. associate-*l/ 72.2%

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

   3. Simplified 72.2%

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

   4. Taylor expanded in z around 0 72.5%

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

   5. Taylor expanded in t around inf 72.5%

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

   if -1.24999999999999997e-13 < a < 8e-116

   1. Initial program 70.6%

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

      1. associate-*l/ 75.8%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in z around inf 78.3%

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

      1. associate--l+ 78.3%

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

      2. associate-*r/ 78.3%

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

      3. associate-*r/ 78.3%

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

      4. div-sub 78.3%

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

      5. distribute-lft-out-- 78.3%

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

      6. associate-*r/ 78.3%

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

      7. mul-1-neg 78.3%

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

      8. unsub-neg 78.3%

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

      9. distribute-rgt-out-- 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in y around inf 76.4%

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

      1. associate-/l* 80.1%

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

   9. Simplified 80.1%

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

   10. Taylor expanded in t around 0 70.1%

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

       1. associate-*r/ 70.1%

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

       2. neg-mul-1 70.1%

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

   12. Simplified 70.1%

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

   if 8e-116 < a < 2.3500000000000001e62

   1. Initial program 71.3%

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

      1. associate-*l/ 81.0%

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

   3. Simplified 81.0%

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

   4. Taylor expanded in x around 0 54.6%

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

      1. associate-*r/ 63.5%

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

   6. Simplified 63.5%

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

   if 2.3500000000000001e62 < a

   1. Initial program 69.1%

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

      1. associate-*l/ 94.3%

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

   3. Simplified 94.3%

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

      1. associate-/r/ 93.3%

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

      2. div-inv 93.3%

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

      3. associate-/r* 94.3%

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

   5. Applied egg-rr 94.3%

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

   6. Taylor expanded in t around inf 77.6%

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

   7. Taylor expanded in z around 0 64.0%

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

      1. +-commutative 64.0%

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

      2. associate-/l* 70.8%

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

      3. associate-/r/ 73.0%

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

   9. Simplified 73.0%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+127}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-116}:\\ \;\;\;\;t - \frac{y}{\frac{-z}{x}}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 3: 38.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+133}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-276}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-282}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-131}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+104}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ a y))))
   (if (<= z -7.2e+133)
     t
     (if (<= z -1.2e-276)
       x
       (if (<= z 5.5e-282)
         t_1
         (if (<= z 1.1e-131)
           x
           (if (<= z 3e-87) t_1 (if (<= z 1.35e+104) (+ x t) t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a / y);
	double tmp;
	if (z <= -7.2e+133) {
		tmp = t;
	} else if (z <= -1.2e-276) {
		tmp = x;
	} else if (z <= 5.5e-282) {
		tmp = t_1;
	} else if (z <= 1.1e-131) {
		tmp = x;
	} else if (z <= 3e-87) {
		tmp = t_1;
	} else if (z <= 1.35e+104) {
		tmp = x + t;
	} 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 / (a / y)
    if (z <= (-7.2d+133)) then
        tmp = t
    else if (z <= (-1.2d-276)) then
        tmp = x
    else if (z <= 5.5d-282) then
        tmp = t_1
    else if (z <= 1.1d-131) then
        tmp = x
    else if (z <= 3d-87) then
        tmp = t_1
    else if (z <= 1.35d+104) then
        tmp = x + t
    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 / (a / y);
	double tmp;
	if (z <= -7.2e+133) {
		tmp = t;
	} else if (z <= -1.2e-276) {
		tmp = x;
	} else if (z <= 5.5e-282) {
		tmp = t_1;
	} else if (z <= 1.1e-131) {
		tmp = x;
	} else if (z <= 3e-87) {
		tmp = t_1;
	} else if (z <= 1.35e+104) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (a / y)
	tmp = 0
	if z <= -7.2e+133:
		tmp = t
	elif z <= -1.2e-276:
		tmp = x
	elif z <= 5.5e-282:
		tmp = t_1
	elif z <= 1.1e-131:
		tmp = x
	elif z <= 3e-87:
		tmp = t_1
	elif z <= 1.35e+104:
		tmp = x + t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(a / y))
	tmp = 0.0
	if (z <= -7.2e+133)
		tmp = t;
	elseif (z <= -1.2e-276)
		tmp = x;
	elseif (z <= 5.5e-282)
		tmp = t_1;
	elseif (z <= 1.1e-131)
		tmp = x;
	elseif (z <= 3e-87)
		tmp = t_1;
	elseif (z <= 1.35e+104)
		tmp = Float64(x + t);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (a / y);
	tmp = 0.0;
	if (z <= -7.2e+133)
		tmp = t;
	elseif (z <= -1.2e-276)
		tmp = x;
	elseif (z <= 5.5e-282)
		tmp = t_1;
	elseif (z <= 1.1e-131)
		tmp = x;
	elseif (z <= 3e-87)
		tmp = t_1;
	elseif (z <= 1.35e+104)
		tmp = x + t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e+133], t, If[LessEqual[z, -1.2e-276], x, If[LessEqual[z, 5.5e-282], t$95$1, If[LessEqual[z, 1.1e-131], x, If[LessEqual[z, 3e-87], t$95$1, If[LessEqual[z, 1.35e+104], N[(x + t), $MachinePrecision], t]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.19999999999999956e133 or 1.34999999999999992e104 < z

   1. Initial program 36.4%

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

      1. associate-*l/ 65.6%

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

   3. Simplified 65.6%

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

   4. Taylor expanded in z around inf 60.5%

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

   if -7.19999999999999956e133 < z < -1.19999999999999991e-276 or 5.5000000000000001e-282 < z < 1.1e-131

   1. Initial program 77.1%

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

      1. associate-*l/ 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in a around inf 37.6%

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

   if -1.19999999999999991e-276 < z < 5.5000000000000001e-282 or 1.1e-131 < z < 3.00000000000000016e-87

   1. Initial program 89.7%

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

      1. associate-*l/ 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in x around 0 41.4%

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

      1. associate-*r/ 48.0%

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

   6. Simplified 48.0%

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

   7. Taylor expanded in z around 0 48.3%

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

      1. associate-/l* 54.8%

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

   9. Simplified 54.8%

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

   if 3.00000000000000016e-87 < z < 1.34999999999999992e104

   1. Initial program 81.9%

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

      1. associate-*l/ 87.8%

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

   3. Simplified 87.8%

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

      1. associate-/r/ 84.8%

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

      2. div-inv 84.8%

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

      3. associate-/r* 87.8%

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

   5. Applied egg-rr 87.8%

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

   6. Taylor expanded in t around inf 63.2%

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

   7. Taylor expanded in z around inf 41.6%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+133}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-276}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-282}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-131}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-87}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+104}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 38.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+133}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{-282}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-281}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-131}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-87}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+104}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.8e+133)
   t
   (if (<= z -1.26e-282)
     x
     (if (<= z 1.95e-281)
       (/ t (/ a y))
       (if (<= z 1.15e-131)
         x
         (if (<= z 1.7e-87) (/ (* y t) a) (if (<= z 1.3e+104) (+ x t) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.8e+133) {
		tmp = t;
	} else if (z <= -1.26e-282) {
		tmp = x;
	} else if (z <= 1.95e-281) {
		tmp = t / (a / y);
	} else if (z <= 1.15e-131) {
		tmp = x;
	} else if (z <= 1.7e-87) {
		tmp = (y * t) / a;
	} else if (z <= 1.3e+104) {
		tmp = x + t;
	} 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 <= (-3.8d+133)) then
        tmp = t
    else if (z <= (-1.26d-282)) then
        tmp = x
    else if (z <= 1.95d-281) then
        tmp = t / (a / y)
    else if (z <= 1.15d-131) then
        tmp = x
    else if (z <= 1.7d-87) then
        tmp = (y * t) / a
    else if (z <= 1.3d+104) then
        tmp = x + t
    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 <= -3.8e+133) {
		tmp = t;
	} else if (z <= -1.26e-282) {
		tmp = x;
	} else if (z <= 1.95e-281) {
		tmp = t / (a / y);
	} else if (z <= 1.15e-131) {
		tmp = x;
	} else if (z <= 1.7e-87) {
		tmp = (y * t) / a;
	} else if (z <= 1.3e+104) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.8e+133:
		tmp = t
	elif z <= -1.26e-282:
		tmp = x
	elif z <= 1.95e-281:
		tmp = t / (a / y)
	elif z <= 1.15e-131:
		tmp = x
	elif z <= 1.7e-87:
		tmp = (y * t) / a
	elif z <= 1.3e+104:
		tmp = x + t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.8e+133)
		tmp = t;
	elseif (z <= -1.26e-282)
		tmp = x;
	elseif (z <= 1.95e-281)
		tmp = Float64(t / Float64(a / y));
	elseif (z <= 1.15e-131)
		tmp = x;
	elseif (z <= 1.7e-87)
		tmp = Float64(Float64(y * t) / a);
	elseif (z <= 1.3e+104)
		tmp = Float64(x + t);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.8e+133)
		tmp = t;
	elseif (z <= -1.26e-282)
		tmp = x;
	elseif (z <= 1.95e-281)
		tmp = t / (a / y);
	elseif (z <= 1.15e-131)
		tmp = x;
	elseif (z <= 1.7e-87)
		tmp = (y * t) / a;
	elseif (z <= 1.3e+104)
		tmp = x + t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.8e+133], t, If[LessEqual[z, -1.26e-282], x, If[LessEqual[z, 1.95e-281], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e-131], x, If[LessEqual[z, 1.7e-87], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 1.3e+104], N[(x + t), $MachinePrecision], t]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.8000000000000002e133 or 1.3e104 < z

   1. Initial program 36.4%

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

      1. associate-*l/ 65.6%

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

   3. Simplified 65.6%

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

   4. Taylor expanded in z around inf 60.5%

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

   if -3.8000000000000002e133 < z < -1.26000000000000003e-282 or 1.9500000000000001e-281 < z < 1.15000000000000011e-131

   1. Initial program 77.1%

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

      1. associate-*l/ 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in a around inf 37.6%

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

   if -1.26000000000000003e-282 < z < 1.9500000000000001e-281

   1. Initial program 89.4%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 46.3%

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

      1. associate-*r/ 56.6%

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

   6. Simplified 56.6%

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

   7. Taylor expanded in z around 0 46.3%

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

      1. associate-/l* 56.5%

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

   9. Simplified 56.5%

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

   if 1.15000000000000011e-131 < z < 1.6999999999999999e-87

   1. Initial program 90.0%

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

      1. associate-*l/ 81.4%

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

   3. Simplified 81.4%

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

   4. Taylor expanded in x around 0 32.4%

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

      1. associate-*r/ 32.5%

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

   6. Simplified 32.5%

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

   7. Taylor expanded in z around 0 51.9%

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

   if 1.6999999999999999e-87 < z < 1.3e104

   1. Initial program 81.9%

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

      1. associate-*l/ 87.8%

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

   3. Simplified 87.8%

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

      1. associate-/r/ 84.8%

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

      2. div-inv 84.8%

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

      3. associate-/r* 87.8%

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

   5. Applied egg-rr 87.8%

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

   6. Taylor expanded in t around inf 63.2%

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

   7. Taylor expanded in z around inf 41.6%

      \[\leadsto x + \color{blue}{t} \]
3. Recombined 5 regimes into one program.

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+133}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{-282}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-281}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-131}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-87}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+104}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 47.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -7 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-167}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= a -7e-12)
     x
     (if (<= a 1.35e-211)
       t_1
       (if (<= a 1.4e-167) (* x (/ y z)) (if (<= a 1.35e+84) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -7e-12) {
		tmp = x;
	} else if (a <= 1.35e-211) {
		tmp = t_1;
	} else if (a <= 1.4e-167) {
		tmp = x * (y / z);
	} else if (a <= 1.35e+84) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (a <= (-7d-12)) then
        tmp = x
    else if (a <= 1.35d-211) then
        tmp = t_1
    else if (a <= 1.4d-167) then
        tmp = x * (y / z)
    else if (a <= 1.35d+84) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -7e-12) {
		tmp = x;
	} else if (a <= 1.35e-211) {
		tmp = t_1;
	} else if (a <= 1.4e-167) {
		tmp = x * (y / z);
	} else if (a <= 1.35e+84) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -7e-12:
		tmp = x
	elif a <= 1.35e-211:
		tmp = t_1
	elif a <= 1.4e-167:
		tmp = x * (y / z)
	elif a <= 1.35e+84:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -7e-12)
		tmp = x;
	elseif (a <= 1.35e-211)
		tmp = t_1;
	elseif (a <= 1.4e-167)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.35e+84)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -7e-12)
		tmp = x;
	elseif (a <= 1.35e-211)
		tmp = t_1;
	elseif (a <= 1.4e-167)
		tmp = x * (y / z);
	elseif (a <= 1.35e+84)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7e-12], x, If[LessEqual[a, 1.35e-211], t$95$1, If[LessEqual[a, 1.4e-167], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e+84], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.0000000000000001e-12 or 1.35e84 < a

   1. Initial program 64.1%

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

      1. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in a around inf 49.2%

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

   if -7.0000000000000001e-12 < a < 1.35e-211 or 1.39999999999999993e-167 < a < 1.35e84

   1. Initial program 70.8%

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

      1. associate-*l/ 78.6%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in z around inf 63.4%

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

      1. associate--l+ 63.4%

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

      2. associate-*r/ 63.4%

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

      3. associate-*r/ 63.4%

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

      4. div-sub 64.2%

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

      5. distribute-lft-out-- 64.2%

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

      6. associate-*r/ 64.2%

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

      7. mul-1-neg 64.2%

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

      8. unsub-neg 64.2%

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

      9. distribute-rgt-out-- 64.3%

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

   6. Simplified 64.3%

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

   7. Taylor expanded in y around inf 60.5%

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

      1. associate-/l* 66.0%

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

   9. Simplified 66.0%

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

   10. Taylor expanded in t around inf 50.3%

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

   if 1.35e-211 < a < 1.39999999999999993e-167

   1. Initial program 61.4%

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

      1. associate-*l/ 70.9%

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

   3. Simplified 70.9%

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

   4. Taylor expanded in x around -inf 70.4%

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

      1. associate-*r* 70.4%

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

      2. neg-mul-1 70.4%

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

   6. Simplified 70.4%

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

   7. Taylor expanded in z around -inf 61.5%

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

      1. associate-/l* 70.8%

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

   9. Simplified 70.8%

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

       1. clear-num 70.8%

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

       2. associate-/r/ 70.9%

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

       3. clear-num 70.9%

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

   11. Applied egg-rr 70.9%

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

   12. Taylor expanded in y around inf 70.9%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-211}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-167}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+84}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 55.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-47}:\\ \;\;\;\;t - \frac{y}{\frac{-z}{x}}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+60}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+143}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.5e-15)
   (* x (- 1.0 (/ y a)))
   (if (<= a 2.9e-47)
     (- t (/ y (/ (- z) x)))
     (if (<= a 8.2e+60)
       (/ y (/ a (- t x)))
       (if (<= a 2.9e+143) (+ x t) (+ x (* y (/ t a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.5e-15) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= 2.9e-47) {
		tmp = t - (y / (-z / x));
	} else if (a <= 8.2e+60) {
		tmp = y / (a / (t - x));
	} else if (a <= 2.9e+143) {
		tmp = x + t;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.5d-15)) then
        tmp = x * (1.0d0 - (y / a))
    else if (a <= 2.9d-47) then
        tmp = t - (y / (-z / x))
    else if (a <= 8.2d+60) then
        tmp = y / (a / (t - x))
    else if (a <= 2.9d+143) then
        tmp = x + t
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.5e-15) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= 2.9e-47) {
		tmp = t - (y / (-z / x));
	} else if (a <= 8.2e+60) {
		tmp = y / (a / (t - x));
	} else if (a <= 2.9e+143) {
		tmp = x + t;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.5e-15:
		tmp = x * (1.0 - (y / a))
	elif a <= 2.9e-47:
		tmp = t - (y / (-z / x))
	elif a <= 8.2e+60:
		tmp = y / (a / (t - x))
	elif a <= 2.9e+143:
		tmp = x + t
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.5e-15)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (a <= 2.9e-47)
		tmp = Float64(t - Float64(y / Float64(Float64(-z) / x)));
	elseif (a <= 8.2e+60)
		tmp = Float64(y / Float64(a / Float64(t - x)));
	elseif (a <= 2.9e+143)
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.5e-15)
		tmp = x * (1.0 - (y / a));
	elseif (a <= 2.9e-47)
		tmp = t - (y / (-z / x));
	elseif (a <= 8.2e+60)
		tmp = y / (a / (t - x));
	elseif (a <= 2.9e+143)
		tmp = x + t;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.5e-15], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e-47], N[(t - N[(y / N[((-z) / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e+60], N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e+143], N[(x + t), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.5e-15

   1. Initial program 60.1%

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

      1. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in x around -inf 64.6%

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

      1. associate-*r* 64.6%

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

      2. neg-mul-1 64.6%

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

   6. Simplified 64.6%

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

   7. Taylor expanded in z around 0 59.1%

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

      1. mul-1-neg 59.1%

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

      2. *-commutative 59.1%

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

      3. distribute-rgt-neg-in 59.1%

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

      4. sub-neg 59.1%

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

      5. metadata-eval 59.1%

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

   9. Simplified 59.1%

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

   if -1.5e-15 < a < 2.9e-47

   1. Initial program 69.0%

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

      1. associate-*l/ 76.2%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in z around inf 74.1%

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

      1. associate--l+ 74.1%

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

      2. associate-*r/ 74.1%

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

      3. associate-*r/ 74.1%

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

      4. div-sub 74.1%

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

      5. distribute-lft-out-- 74.1%

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

      6. associate-*r/ 74.1%

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

      7. mul-1-neg 74.1%

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

      8. unsub-neg 74.1%

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

      9. distribute-rgt-out-- 74.1%

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

   6. Simplified 74.1%

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

   7. Taylor expanded in y around inf 71.7%

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

      1. associate-/l* 76.9%

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

   9. Simplified 76.9%

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

   10. Taylor expanded in t around 0 67.7%

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

       1. associate-*r/ 67.7%

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

       2. neg-mul-1 67.7%

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

   12. Simplified 67.7%

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

   if 2.9e-47 < a < 8.2e60

   1. Initial program 78.6%

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

      1. associate-*l/ 81.1%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in y around -inf 53.5%

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

   5. Taylor expanded in a around inf 51.1%

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

      1. associate-/l* 51.1%

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

   7. Simplified 51.1%

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

   if 8.2e60 < a < 2.8999999999999998e143

   1. Initial program 64.7%

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

      1. associate-*l/ 98.7%

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

   3. Simplified 98.7%

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

      1. associate-/r/ 98.4%

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

      2. div-inv 98.4%

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

      3. associate-/r* 98.4%

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

   5. Applied egg-rr 98.4%

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

   6. Taylor expanded in t around inf 82.9%

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

   7. Taylor expanded in z around inf 65.9%

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

   if 2.8999999999999998e143 < a

   1. Initial program 69.6%

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

      1. associate-*l/ 93.1%

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

   3. Simplified 93.1%

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

      1. associate-/r/ 91.9%

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

      2. div-inv 91.9%

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

      3. associate-/r* 93.1%

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

   5. Applied egg-rr 93.1%

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

   6. Taylor expanded in t around inf 77.1%

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

   7. Taylor expanded in z around 0 68.4%

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

      1. +-commutative 68.4%

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

      2. associate-/l* 77.2%

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

      3. associate-/r/ 80.0%

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

   9. Simplified 80.0%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-47}:\\ \;\;\;\;t - \frac{y}{\frac{-z}{x}}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+60}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+143}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 7: 58.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-114}:\\ \;\;\;\;t - \frac{y}{\frac{-z}{x}}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.5e-13)
   (* x (- 1.0 (/ y a)))
   (if (<= a 3.8e-114)
     (- t (/ y (/ (- z) x)))
     (if (<= a 3.2e+62) (* t (/ (- y z) (- a z))) (+ x (* y (/ t a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.5e-13) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= 3.8e-114) {
		tmp = t - (y / (-z / x));
	} else if (a <= 3.2e+62) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-8.5d-13)) then
        tmp = x * (1.0d0 - (y / a))
    else if (a <= 3.8d-114) then
        tmp = t - (y / (-z / x))
    else if (a <= 3.2d+62) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.5e-13) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= 3.8e-114) {
		tmp = t - (y / (-z / x));
	} else if (a <= 3.2e+62) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.5e-13:
		tmp = x * (1.0 - (y / a))
	elif a <= 3.8e-114:
		tmp = t - (y / (-z / x))
	elif a <= 3.2e+62:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.5e-13)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (a <= 3.8e-114)
		tmp = Float64(t - Float64(y / Float64(Float64(-z) / x)));
	elseif (a <= 3.2e+62)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.5e-13)
		tmp = x * (1.0 - (y / a));
	elseif (a <= 3.8e-114)
		tmp = t - (y / (-z / x));
	elseif (a <= 3.2e+62)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.5e-13], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e-114], N[(t - N[(y / N[((-z) / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e+62], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.5000000000000001e-13

   1. Initial program 60.1%

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

      1. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in x around -inf 64.6%

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

      1. associate-*r* 64.6%

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

      2. neg-mul-1 64.6%

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

   6. Simplified 64.6%

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

   7. Taylor expanded in z around 0 59.1%

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

      1. mul-1-neg 59.1%

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

      2. *-commutative 59.1%

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

      3. distribute-rgt-neg-in 59.1%

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

      4. sub-neg 59.1%

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

      5. metadata-eval 59.1%

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

   9. Simplified 59.1%

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

   if -8.5000000000000001e-13 < a < 3.7999999999999998e-114

   1. Initial program 70.6%

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

      1. associate-*l/ 75.8%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in z around inf 78.3%

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

      1. associate--l+ 78.3%

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

      2. associate-*r/ 78.3%

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

      3. associate-*r/ 78.3%

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

      4. div-sub 78.3%

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

      5. distribute-lft-out-- 78.3%

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

      6. associate-*r/ 78.3%

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

      7. mul-1-neg 78.3%

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

      8. unsub-neg 78.3%

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

      9. distribute-rgt-out-- 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in y around inf 76.4%

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

      1. associate-/l* 80.1%

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

   9. Simplified 80.1%

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

   10. Taylor expanded in t around 0 70.1%

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

       1. associate-*r/ 70.1%

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

       2. neg-mul-1 70.1%

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

   12. Simplified 70.1%

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

   if 3.7999999999999998e-114 < a < 3.19999999999999984e62

   1. Initial program 71.3%

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

      1. associate-*l/ 81.0%

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

   3. Simplified 81.0%

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

   4. Taylor expanded in x around 0 54.6%

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

      1. associate-*r/ 63.5%

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

   6. Simplified 63.5%

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

   if 3.19999999999999984e62 < a

   1. Initial program 69.1%

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

      1. associate-*l/ 94.3%

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

   3. Simplified 94.3%

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

      1. associate-/r/ 93.3%

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

      2. div-inv 93.3%

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

      3. associate-/r* 94.3%

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

   5. Applied egg-rr 94.3%

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

   6. Taylor expanded in t around inf 77.6%

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

   7. Taylor expanded in z around 0 64.0%

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

      1. +-commutative 64.0%

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

      2. associate-/l* 70.8%

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

      3. associate-/r/ 73.0%

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

   9. Simplified 73.0%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-114}:\\ \;\;\;\;t - \frac{y}{\frac{-z}{x}}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 8: 52.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+133}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+46}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+145}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.5e+133)
   (* t (- 1.0 (/ y z)))
   (if (<= z 6.5e+46)
     (+ x (/ t (/ a y)))
     (if (<= z 1.45e+145) (* x (/ (- y a) z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+133) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= 6.5e+46) {
		tmp = x + (t / (a / y));
	} else if (z <= 1.45e+145) {
		tmp = x * ((y - a) / 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 <= (-4.5d+133)) then
        tmp = t * (1.0d0 - (y / z))
    else if (z <= 6.5d+46) then
        tmp = x + (t / (a / y))
    else if (z <= 1.45d+145) then
        tmp = x * ((y - a) / 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 <= -4.5e+133) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= 6.5e+46) {
		tmp = x + (t / (a / y));
	} else if (z <= 1.45e+145) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.5e+133:
		tmp = t * (1.0 - (y / z))
	elif z <= 6.5e+46:
		tmp = x + (t / (a / y))
	elif z <= 1.45e+145:
		tmp = x * ((y - a) / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.5e+133)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (z <= 6.5e+46)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 1.45e+145)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.5e+133)
		tmp = t * (1.0 - (y / z));
	elseif (z <= 6.5e+46)
		tmp = x + (t / (a / y));
	elseif (z <= 1.45e+145)
		tmp = x * ((y - a) / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.5e+133], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+46], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+145], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.49999999999999985e133

   1. Initial program 36.5%

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

      1. associate-*l/ 59.9%

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

   3. Simplified 59.9%

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

   4. Taylor expanded in z around inf 68.0%

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

      1. associate--l+ 68.0%

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

      2. associate-*r/ 68.0%

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

      3. associate-*r/ 68.0%

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

      4. div-sub 68.0%

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

      5. distribute-lft-out-- 68.0%

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

      6. associate-*r/ 68.0%

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

      7. mul-1-neg 68.0%

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

      8. unsub-neg 68.0%

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

      9. distribute-rgt-out-- 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in y around inf 65.0%

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

      1. associate-/l* 79.3%

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

   9. Simplified 79.3%

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

   10. Taylor expanded in t around inf 67.1%

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

   if -4.49999999999999985e133 < z < 6.50000000000000008e46

   1. Initial program 80.9%

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

      1. associate-*l/ 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in z around 0 65.3%

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

   5. Taylor expanded in t around inf 54.6%

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

      1. associate-/l* 59.8%

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

   7. Simplified 59.8%

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

   if 6.50000000000000008e46 < z < 1.45e145

   1. Initial program 40.3%

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

      1. associate-*l/ 66.2%

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

   3. Simplified 66.2%

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

   4. Taylor expanded in x around -inf 51.1%

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

      1. associate-*r* 51.1%

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

      2. neg-mul-1 51.1%

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

   6. Simplified 51.1%

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

   7. Taylor expanded in z around -inf 35.7%

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

      1. associate-/l* 47.9%

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

   9. Simplified 47.9%

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

       1. clear-num 47.7%

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

       2. associate-/r/ 47.8%

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

       3. clear-num 47.8%

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

   11. Applied egg-rr 47.8%

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

   if 1.45e145 < z

   1. Initial program 42.9%

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

      1. associate-*l/ 78.9%

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

   3. Simplified 78.9%

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

   4. Taylor expanded in z around inf 80.3%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+133}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+46}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+145}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9: 52.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+133}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+155}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.8e+133)
   (* t (- 1.0 (/ y z)))
   (if (<= z 1.5e+42)
     (+ x (/ t (/ a y)))
     (if (<= z 2.3e+155) (/ x (/ z (- y a))) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.8e+133) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= 1.5e+42) {
		tmp = x + (t / (a / y));
	} else if (z <= 2.3e+155) {
		tmp = x / (z / (y - a));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.8d+133)) then
        tmp = t * (1.0d0 - (y / z))
    else if (z <= 1.5d+42) then
        tmp = x + (t / (a / y))
    else if (z <= 2.3d+155) then
        tmp = x / (z / (y - a))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.8e+133) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= 1.5e+42) {
		tmp = x + (t / (a / y));
	} else if (z <= 2.3e+155) {
		tmp = x / (z / (y - a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.8e+133:
		tmp = t * (1.0 - (y / z))
	elif z <= 1.5e+42:
		tmp = x + (t / (a / y))
	elif z <= 2.3e+155:
		tmp = x / (z / (y - a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.8e+133)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (z <= 1.5e+42)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 2.3e+155)
		tmp = Float64(x / Float64(z / Float64(y - a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.8e+133)
		tmp = t * (1.0 - (y / z));
	elseif (z <= 1.5e+42)
		tmp = x + (t / (a / y));
	elseif (z <= 2.3e+155)
		tmp = x / (z / (y - a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.8e+133], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+42], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e+155], N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.8000000000000002e133

   1. Initial program 36.5%

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

      1. associate-*l/ 59.9%

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

   3. Simplified 59.9%

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

   4. Taylor expanded in z around inf 68.0%

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

      1. associate--l+ 68.0%

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

      2. associate-*r/ 68.0%

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

      3. associate-*r/ 68.0%

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

      4. div-sub 68.0%

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

      5. distribute-lft-out-- 68.0%

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

      6. associate-*r/ 68.0%

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

      7. mul-1-neg 68.0%

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

      8. unsub-neg 68.0%

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

      9. distribute-rgt-out-- 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in y around inf 65.0%

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

      1. associate-/l* 79.3%

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

   9. Simplified 79.3%

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

   10. Taylor expanded in t around inf 67.1%

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

   if -3.8000000000000002e133 < z < 1.50000000000000014e42

   1. Initial program 80.9%

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

      1. associate-*l/ 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in z around 0 65.3%

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

   5. Taylor expanded in t around inf 54.6%

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

      1. associate-/l* 59.8%

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

   7. Simplified 59.8%

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

   if 1.50000000000000014e42 < z < 2.29999999999999998e155

   1. Initial program 40.3%

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

      1. associate-*l/ 66.2%

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

   3. Simplified 66.2%

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

   4. Taylor expanded in x around -inf 51.1%

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

      1. associate-*r* 51.1%

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

      2. neg-mul-1 51.1%

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

   6. Simplified 51.1%

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

   7. Taylor expanded in z around -inf 35.7%

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

      1. associate-/l* 47.9%

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

   9. Simplified 47.9%

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

   if 2.29999999999999998e155 < z

   1. Initial program 42.9%

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

      1. associate-*l/ 78.9%

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

   3. Simplified 78.9%

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

   4. Taylor expanded in z around inf 80.3%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+133}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+155}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10: 63.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+133} \lor \neg \left(z \leq 3.2 \cdot 10^{-57}\right):\\ \;\;\;\;t - \frac{y}{\frac{-z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.5e+133) (not (<= z 3.2e-57)))
   (- t (/ y (/ (- z) x)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.5e+133) || !(z <= 3.2e-57)) {
		tmp = t - (y / (-z / x));
	} 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 <= (-4.5d+133)) .or. (.not. (z <= 3.2d-57))) then
        tmp = t - (y / (-z / x))
    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 <= -4.5e+133) || !(z <= 3.2e-57)) {
		tmp = t - (y / (-z / x));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.5e+133) or not (z <= 3.2e-57):
		tmp = t - (y / (-z / x))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.5e+133) || !(z <= 3.2e-57))
		tmp = Float64(t - Float64(y / Float64(Float64(-z) / x)));
	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 <= -4.5e+133) || ~((z <= 3.2e-57)))
		tmp = t - (y / (-z / x));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.5e+133], N[Not[LessEqual[z, 3.2e-57]], $MachinePrecision]], N[(t - N[(y / N[((-z) / x), $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 < -4.49999999999999985e133 or 3.2000000000000001e-57 < z

   1. Initial program 49.1%

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

      1. associate-*l/ 71.7%

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

   3. Simplified 71.7%

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

   4. Taylor expanded in z around inf 62.7%

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

      1. associate--l+ 62.7%

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

      2. associate-*r/ 62.7%

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

      3. associate-*r/ 62.7%

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

      4. div-sub 62.7%

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

      5. distribute-lft-out-- 62.7%

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

      6. associate-*r/ 62.7%

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

      7. mul-1-neg 62.7%

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

      8. unsub-neg 62.7%

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

      9. distribute-rgt-out-- 63.0%

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

   6. Simplified 63.0%

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

   7. Taylor expanded in y around inf 58.8%

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

      1. associate-/l* 70.1%

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

   9. Simplified 70.1%

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

   10. Taylor expanded in t around 0 67.3%

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

       1. associate-*r/ 67.3%

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

       2. neg-mul-1 67.3%

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

   12. Simplified 67.3%

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

   if -4.49999999999999985e133 < z < 3.2000000000000001e-57

   1. Initial program 79.7%

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

      1. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in z around 0 67.3%

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

      1. associate-/l* 77.0%

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

   6. Simplified 77.0%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+133} \lor \neg \left(z \leq 3.2 \cdot 10^{-57}\right):\\ \;\;\;\;t - \frac{y}{\frac{-z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 11: 68.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+63} \lor \neg \left(z \leq 1.2 \cdot 10^{-61}\right):\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.8e+63) (not (<= z 1.2e-61)))
   (- t (/ y (/ z (- t x))))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.8e+63) || !(z <= 1.2e-61)) {
		tmp = t - (y / (z / (t - x)));
	} 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 <= (-5.8d+63)) .or. (.not. (z <= 1.2d-61))) then
        tmp = t - (y / (z / (t - x)))
    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 <= -5.8e+63) || !(z <= 1.2e-61)) {
		tmp = t - (y / (z / (t - x)));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.8e+63) or not (z <= 1.2e-61):
		tmp = t - (y / (z / (t - x)))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.8e+63) || !(z <= 1.2e-61))
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	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 <= -5.8e+63) || ~((z <= 1.2e-61)))
		tmp = t - (y / (z / (t - x)));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.8e+63], N[Not[LessEqual[z, 1.2e-61]], $MachinePrecision]], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $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 < -5.7999999999999999e63 or 1.2e-61 < z

   1. Initial program 48.5%

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

      1. associate-*l/ 70.8%

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

   3. Simplified 70.8%

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

   4. Taylor expanded in z around inf 61.7%

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

      1. associate--l+ 61.7%

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

      2. associate-*r/ 61.7%

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

      3. associate-*r/ 61.7%

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

      4. div-sub 61.7%

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

      5. distribute-lft-out-- 61.7%

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

      6. associate-*r/ 61.7%

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

      7. mul-1-neg 61.7%

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

      8. unsub-neg 61.7%

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

      9. distribute-rgt-out-- 61.9%

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

   6. Simplified 61.9%

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

   7. Taylor expanded in y around inf 56.3%

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

      1. associate-/l* 67.0%

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

   9. Simplified 67.0%

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

   if -5.7999999999999999e63 < z < 1.2e-61

   1. Initial program 83.2%

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

      1. associate-*l/ 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in z around 0 70.2%

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

      1. associate-/l* 80.9%

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

   6. Simplified 80.9%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+63} \lor \neg \left(z \leq 1.2 \cdot 10^{-61}\right):\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 12: 37.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+134}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-25}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+50}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e+134)
   t
   (if (<= z 2.4e-124)
     x
     (if (<= z 6e-25) (* y (/ x z)) (if (<= z 4e+50) (+ x t) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+134) {
		tmp = t;
	} else if (z <= 2.4e-124) {
		tmp = x;
	} else if (z <= 6e-25) {
		tmp = y * (x / z);
	} else if (z <= 4e+50) {
		tmp = x + t;
	} 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 <= (-2d+134)) then
        tmp = t
    else if (z <= 2.4d-124) then
        tmp = x
    else if (z <= 6d-25) then
        tmp = y * (x / z)
    else if (z <= 4d+50) then
        tmp = x + t
    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 <= -2e+134) {
		tmp = t;
	} else if (z <= 2.4e-124) {
		tmp = x;
	} else if (z <= 6e-25) {
		tmp = y * (x / z);
	} else if (z <= 4e+50) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2e+134:
		tmp = t
	elif z <= 2.4e-124:
		tmp = x
	elif z <= 6e-25:
		tmp = y * (x / z)
	elif z <= 4e+50:
		tmp = x + t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e+134)
		tmp = t;
	elseif (z <= 2.4e-124)
		tmp = x;
	elseif (z <= 6e-25)
		tmp = Float64(y * Float64(x / z));
	elseif (z <= 4e+50)
		tmp = Float64(x + t);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2e+134)
		tmp = t;
	elseif (z <= 2.4e-124)
		tmp = x;
	elseif (z <= 6e-25)
		tmp = y * (x / z);
	elseif (z <= 4e+50)
		tmp = x + t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e+134], t, If[LessEqual[z, 2.4e-124], x, If[LessEqual[z, 6e-25], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+50], N[(x + t), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.99999999999999984e134 or 4.0000000000000003e50 < z

   1. Initial program 38.8%

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

      1. associate-*l/ 67.0%

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

   3. Simplified 67.0%

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

   4. Taylor expanded in z around inf 56.6%

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

   if -1.99999999999999984e134 < z < 2.39999999999999992e-124

   1. Initial program 78.8%

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

      1. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in a around inf 35.8%

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

   if 2.39999999999999992e-124 < z < 5.9999999999999995e-25

   1. Initial program 85.1%

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

      1. associate-*l/ 80.7%

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

   3. Simplified 80.7%

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

   4. Taylor expanded in x around -inf 66.3%

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

      1. associate-*r* 66.3%

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

      2. neg-mul-1 66.3%

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

   6. Simplified 66.3%

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

   7. Taylor expanded in z around -inf 45.0%

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

      1. associate-/l* 40.4%

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

   9. Simplified 40.4%

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

   10. Taylor expanded in y around inf 45.1%

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

       1. associate-*l/ 40.1%

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

       2. *-commutative 40.1%

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

   12. Simplified 40.1%

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

   if 5.9999999999999995e-25 < z < 4.0000000000000003e50

   1. Initial program 99.9%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/r/ 99.7%

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

      2. div-inv 99.7%

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

      3. associate-/r* 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in t around inf 84.5%

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

   7. Taylor expanded in z around inf 44.8%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+134}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-25}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+50}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13: 37.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+133}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 10^{+51}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.8e+133)
   t
   (if (<= z 2.4e-124)
     x
     (if (<= z 1.05e-25) (* x (/ y z)) (if (<= z 1e+51) (+ x t) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e+133) {
		tmp = t;
	} else if (z <= 2.4e-124) {
		tmp = x;
	} else if (z <= 1.05e-25) {
		tmp = x * (y / z);
	} else if (z <= 1e+51) {
		tmp = x + t;
	} 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 <= (-8.8d+133)) then
        tmp = t
    else if (z <= 2.4d-124) then
        tmp = x
    else if (z <= 1.05d-25) then
        tmp = x * (y / z)
    else if (z <= 1d+51) then
        tmp = x + t
    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 <= -8.8e+133) {
		tmp = t;
	} else if (z <= 2.4e-124) {
		tmp = x;
	} else if (z <= 1.05e-25) {
		tmp = x * (y / z);
	} else if (z <= 1e+51) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.8e+133:
		tmp = t
	elif z <= 2.4e-124:
		tmp = x
	elif z <= 1.05e-25:
		tmp = x * (y / z)
	elif z <= 1e+51:
		tmp = x + t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.8e+133)
		tmp = t;
	elseif (z <= 2.4e-124)
		tmp = x;
	elseif (z <= 1.05e-25)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= 1e+51)
		tmp = Float64(x + t);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.8e+133)
		tmp = t;
	elseif (z <= 2.4e-124)
		tmp = x;
	elseif (z <= 1.05e-25)
		tmp = x * (y / z);
	elseif (z <= 1e+51)
		tmp = x + t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.8e+133], t, If[LessEqual[z, 2.4e-124], x, If[LessEqual[z, 1.05e-25], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+51], N[(x + t), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.8e133 or 1e51 < z

   1. Initial program 38.8%

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

      1. associate-*l/ 67.0%

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

   3. Simplified 67.0%

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

   4. Taylor expanded in z around inf 56.6%

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

   if -8.8e133 < z < 2.39999999999999992e-124

   1. Initial program 78.8%

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

      1. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in a around inf 35.8%

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

   if 2.39999999999999992e-124 < z < 1.05000000000000001e-25

   1. Initial program 85.1%

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

      1. associate-*l/ 80.7%

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

   3. Simplified 80.7%

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

   4. Taylor expanded in x around -inf 66.3%

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

      1. associate-*r* 66.3%

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

      2. neg-mul-1 66.3%

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

   6. Simplified 66.3%

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

   7. Taylor expanded in z around -inf 45.0%

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

      1. associate-/l* 40.4%

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

   9. Simplified 40.4%

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

       1. clear-num 40.4%

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

       2. associate-/r/ 40.5%

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

       3. clear-num 40.5%

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

   11. Applied egg-rr 40.5%

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

   12. Taylor expanded in y around inf 40.5%

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

   if 1.05000000000000001e-25 < z < 1e51

   1. Initial program 99.9%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/r/ 99.7%

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

      2. div-inv 99.7%

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

      3. associate-/r* 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in t around inf 84.5%

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

   7. Taylor expanded in z around inf 44.8%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+133}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 10^{+51}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 38.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+133}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.6e+133) t (if (<= z 2.9e+48) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.6e+133) {
		tmp = t;
	} else if (z <= 2.9e+48) {
		tmp = 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 <= (-8.6d+133)) then
        tmp = t
    else if (z <= 2.9d+48) then
        tmp = 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 <= -8.6e+133) {
		tmp = t;
	} else if (z <= 2.9e+48) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.6e+133:
		tmp = t
	elif z <= 2.9e+48:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.6e+133)
		tmp = t;
	elseif (z <= 2.9e+48)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.6e+133)
		tmp = t;
	elseif (z <= 2.9e+48)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.6e+133], t, If[LessEqual[z, 2.9e+48], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -8.59999999999999989e133 or 2.8999999999999999e48 < z

   1. Initial program 38.8%

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

      1. associate-*l/ 67.0%

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

   3. Simplified 67.0%

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

   4. Taylor expanded in z around inf 56.6%

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

   if -8.59999999999999989e133 < z < 2.8999999999999999e48

   1. Initial program 81.0%

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

      1. associate-*l/ 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in a around inf 34.0%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+133}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15: 24.9% 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 67.6%

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

   1. associate-*l/ 83.8%

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

3. Simplified 83.8%

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

4. Taylor expanded in z around inf 25.4%

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

5. Final simplification 25.4%

   \[\leadsto t \]

Developer target: 83.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} 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 - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023279 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

  (+ x (/ (* (- y z) (- t x)) (- a z))))