Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 81.1% → 91.6%

Time: 20.0s

Alternatives: 23

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 81.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-282}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (- y z) (/ (- x t) (- a z))))))
   (if (<= t_1 -5e-282)
     (+ x (/ (- y z) (/ (- a z) (- t x))))
     (if (<= t_1 0.0) (+ t (/ (- x t) (/ z (- y a)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) * ((x - t) / (a - z)));
	double tmp;
	if (t_1 <= -5e-282) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else if (t_1 <= 0.0) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y - z) * ((x - t) / (a - z)))
    if (t_1 <= (-5d-282)) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else if (t_1 <= 0.0d0) then
        tmp = t + ((x - t) / (z / (y - a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) * ((x - t) / (a - z)));
	double tmp;
	if (t_1 <= -5e-282) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else if (t_1 <= 0.0) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y - z) * ((x - t) / (a - z)))
	tmp = 0
	if t_1 <= -5e-282:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	elif t_1 <= 0.0:
		tmp = t + ((x - t) / (z / (y - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y - z) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -5e-282)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y - z) * ((x - t) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -5e-282)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	elseif (t_1 <= 0.0)
		tmp = t + ((x - t) / (z / (y - a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y - z), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-282], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.0000000000000001e-282

   1. Initial program 91.0%

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

      1. clear-num 91.0%

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

      2. un-div-inv 92.0%

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

   3. Applied egg-rr 92.0%

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

   if -5.0000000000000001e-282 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.5%

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

   2. Taylor expanded in z around inf 90.9%

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

      1. associate--l+ 90.9%

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

      2. distribute-lft-out-- 90.9%

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

      3. div-sub 90.9%

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

      4. mul-1-neg 90.9%

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

      5. unsub-neg 90.9%

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

      6. distribute-rgt-out-- 91.0%

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

      7. associate-/l* 96.7%

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

   4. Simplified 96.7%

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

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

   1. Initial program 92.6%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq -5 \cdot 10^{-282}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq 0:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \end{array} \]

Alternative 2: 91.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-282} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (- y z) (/ (- x t) (- a z))))))
   (if (or (<= t_1 -5e-282) (not (<= t_1 0.0)))
     t_1
     (+ t (/ (- x t) (/ z (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-282) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y - z) * ((x - t) / (a - z)))
    if ((t_1 <= (-5d-282)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t + ((x - t) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-282) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y - z) * ((x - t) / (a - z)))
	tmp = 0
	if (t_1 <= -5e-282) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y - z) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -5e-282) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y - z) * ((x - t) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -5e-282) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y - z), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-282], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.0000000000000001e-282 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.8%

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

   if -5.0000000000000001e-282 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.5%

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

   2. Taylor expanded in z around inf 90.9%

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

      1. associate--l+ 90.9%

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

      2. distribute-lft-out-- 90.9%

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

      3. div-sub 90.9%

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

      4. mul-1-neg 90.9%

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

      5. unsub-neg 90.9%

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

      6. distribute-rgt-out-- 91.0%

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

      7. associate-/l* 96.7%

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

   4. Simplified 96.7%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq -5 \cdot 10^{-282} \lor \neg \left(x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq 0\right):\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 3: 71.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ t_2 := x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-46}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-26}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (* (- t x) (- a y)) z)))
        (t_2 (+ x (/ (- y z) (/ a (- t x))))))
   (if (<= a -3.4e+125)
     t_2
     (if (<= a -3.6e-46)
       (/ t (/ (- a z) (- y z)))
       (if (<= a -4.7e-83)
         (* y (/ (- t x) (- a z)))
         (if (<= a 2e-134)
           t_1
           (if (<= a 1.06e-26)
             (* t (/ (- y z) (- a z)))
             (if (<= a 2.9e+57) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((t - x) * (a - y)) / z);
	double t_2 = x + ((y - z) / (a / (t - x)));
	double tmp;
	if (a <= -3.4e+125) {
		tmp = t_2;
	} else if (a <= -3.6e-46) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= -4.7e-83) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 2e-134) {
		tmp = t_1;
	} else if (a <= 1.06e-26) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 2.9e+57) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (((t - x) * (a - y)) / z)
    t_2 = x + ((y - z) / (a / (t - x)))
    if (a <= (-3.4d+125)) then
        tmp = t_2
    else if (a <= (-3.6d-46)) then
        tmp = t / ((a - z) / (y - z))
    else if (a <= (-4.7d-83)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 2d-134) then
        tmp = t_1
    else if (a <= 1.06d-26) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= 2.9d+57) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((t - x) * (a - y)) / z);
	double t_2 = x + ((y - z) / (a / (t - x)));
	double tmp;
	if (a <= -3.4e+125) {
		tmp = t_2;
	} else if (a <= -3.6e-46) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= -4.7e-83) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 2e-134) {
		tmp = t_1;
	} else if (a <= 1.06e-26) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 2.9e+57) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (((t - x) * (a - y)) / z)
	t_2 = x + ((y - z) / (a / (t - x)))
	tmp = 0
	if a <= -3.4e+125:
		tmp = t_2
	elif a <= -3.6e-46:
		tmp = t / ((a - z) / (y - z))
	elif a <= -4.7e-83:
		tmp = y * ((t - x) / (a - z))
	elif a <= 2e-134:
		tmp = t_1
	elif a <= 1.06e-26:
		tmp = t * ((y - z) / (a - z))
	elif a <= 2.9e+57:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z))
	t_2 = Float64(x + Float64(Float64(y - z) / Float64(a / Float64(t - x))))
	tmp = 0.0
	if (a <= -3.4e+125)
		tmp = t_2;
	elseif (a <= -3.6e-46)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (a <= -4.7e-83)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 2e-134)
		tmp = t_1;
	elseif (a <= 1.06e-26)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= 2.9e+57)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (((t - x) * (a - y)) / z);
	t_2 = x + ((y - z) / (a / (t - x)));
	tmp = 0.0;
	if (a <= -3.4e+125)
		tmp = t_2;
	elseif (a <= -3.6e-46)
		tmp = t / ((a - z) / (y - z));
	elseif (a <= -4.7e-83)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 2e-134)
		tmp = t_1;
	elseif (a <= 1.06e-26)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= 2.9e+57)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.4e+125], t$95$2, If[LessEqual[a, -3.6e-46], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.7e-83], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2e-134], t$95$1, If[LessEqual[a, 1.06e-26], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e+57], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.3999999999999999e125 or 2.9000000000000002e57 < a

   1. Initial program 96.5%

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

      1. clear-num 95.7%

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

      2. un-div-inv 95.7%

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

   3. Applied egg-rr 95.7%

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

   4. Taylor expanded in a around inf 83.5%

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

   if -3.3999999999999999e125 < a < -3.6e-46

   1. Initial program 75.6%

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

   2. Taylor expanded in x around 0 57.9%

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

      1. associate-/l* 69.5%

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

   4. Simplified 69.5%

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

   if -3.6e-46 < a < -4.7000000000000003e-83

   1. Initial program 64.8%

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

   2. Taylor expanded in y around -inf 74.0%

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

      1. div-inv 74.0%

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

      2. associate-*l* 82.1%

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

      3. div-inv 82.9%

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

      4. sub-div 82.9%

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

      5. *-commutative 82.9%

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

      6. sub-div 82.9%

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

   4. Applied egg-rr 82.9%

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

   if -4.7000000000000003e-83 < a < 2.00000000000000008e-134 or 1.06000000000000001e-26 < a < 2.9000000000000002e57

   1. Initial program 67.7%

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

      1. clear-num 67.8%

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

      2. un-div-inv 68.9%

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

   3. Applied egg-rr 68.9%

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

   4. Taylor expanded in z around inf 86.6%

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

      1. associate--l+ 86.6%

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

      2. associate-*r/ 86.6%

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

      3. mul-1-neg 86.6%

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

      4. distribute-rgt-neg-out 86.6%

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

      5. associate-*r/ 86.6%

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

      6. div-sub 86.6%

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

      7. distribute-rgt-neg-out 86.6%

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

      8. mul-1-neg 86.6%

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

      9. distribute-lft-out-- 86.6%

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

      10. associate-*r/ 86.6%

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

      11. mul-1-neg 86.6%

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

      12. unsub-neg 86.6%

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

   6. Simplified 86.6%

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

   if 2.00000000000000008e-134 < a < 1.06000000000000001e-26

   1. Initial program 79.7%

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

      1. clear-num 79.9%

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

      2. un-div-inv 80.0%

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

   3. Applied egg-rr 80.0%

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

   4. Taylor expanded in x around 0 67.8%

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

      1. associate-*r/ 79.7%

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

   6. Simplified 79.7%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-46}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-134}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-26}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+57}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 4: 43.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-275}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.76 \cdot 10^{+58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+117}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z))) (t_2 (* t (- 1.0 (/ y z)))))
   (if (<= a -4.2e+119)
     x
     (if (<= a -4.5e-21)
       t_2
       (if (<= a -4.7e-278)
         t_1
         (if (<= a 1.45e-275)
           t_2
           (if (<= a 1.15e-201)
             t_1
             (if (<= a 1.76e+58)
               t_2
               (if (<= a 1.15e+117) (* y (/ (- t x) a)) x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -4.2e+119) {
		tmp = x;
	} else if (a <= -4.5e-21) {
		tmp = t_2;
	} else if (a <= -4.7e-278) {
		tmp = t_1;
	} else if (a <= 1.45e-275) {
		tmp = t_2;
	} else if (a <= 1.15e-201) {
		tmp = t_1;
	} else if (a <= 1.76e+58) {
		tmp = t_2;
	} else if (a <= 1.15e+117) {
		tmp = y * ((t - x) / a);
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    t_2 = t * (1.0d0 - (y / z))
    if (a <= (-4.2d+119)) then
        tmp = x
    else if (a <= (-4.5d-21)) then
        tmp = t_2
    else if (a <= (-4.7d-278)) then
        tmp = t_1
    else if (a <= 1.45d-275) then
        tmp = t_2
    else if (a <= 1.15d-201) then
        tmp = t_1
    else if (a <= 1.76d+58) then
        tmp = t_2
    else if (a <= 1.15d+117) then
        tmp = y * ((t - x) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -4.2e+119) {
		tmp = x;
	} else if (a <= -4.5e-21) {
		tmp = t_2;
	} else if (a <= -4.7e-278) {
		tmp = t_1;
	} else if (a <= 1.45e-275) {
		tmp = t_2;
	} else if (a <= 1.15e-201) {
		tmp = t_1;
	} else if (a <= 1.76e+58) {
		tmp = t_2;
	} else if (a <= 1.15e+117) {
		tmp = y * ((t - x) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	t_2 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -4.2e+119:
		tmp = x
	elif a <= -4.5e-21:
		tmp = t_2
	elif a <= -4.7e-278:
		tmp = t_1
	elif a <= 1.45e-275:
		tmp = t_2
	elif a <= 1.15e-201:
		tmp = t_1
	elif a <= 1.76e+58:
		tmp = t_2
	elif a <= 1.15e+117:
		tmp = y * ((t - x) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	t_2 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -4.2e+119)
		tmp = x;
	elseif (a <= -4.5e-21)
		tmp = t_2;
	elseif (a <= -4.7e-278)
		tmp = t_1;
	elseif (a <= 1.45e-275)
		tmp = t_2;
	elseif (a <= 1.15e-201)
		tmp = t_1;
	elseif (a <= 1.76e+58)
		tmp = t_2;
	elseif (a <= 1.15e+117)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	t_2 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -4.2e+119)
		tmp = x;
	elseif (a <= -4.5e-21)
		tmp = t_2;
	elseif (a <= -4.7e-278)
		tmp = t_1;
	elseif (a <= 1.45e-275)
		tmp = t_2;
	elseif (a <= 1.15e-201)
		tmp = t_1;
	elseif (a <= 1.76e+58)
		tmp = t_2;
	elseif (a <= 1.15e+117)
		tmp = y * ((t - x) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.2e+119], x, If[LessEqual[a, -4.5e-21], t$95$2, If[LessEqual[a, -4.7e-278], t$95$1, If[LessEqual[a, 1.45e-275], t$95$2, If[LessEqual[a, 1.15e-201], t$95$1, If[LessEqual[a, 1.76e+58], t$95$2, If[LessEqual[a, 1.15e+117], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.19999999999999966e119 or 1.14999999999999994e117 < a

   1. Initial program 96.3%

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

   2. Taylor expanded in a around inf 57.9%

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

   if -4.19999999999999966e119 < a < -4.49999999999999968e-21 or -4.6999999999999997e-278 < a < 1.45e-275 or 1.14999999999999993e-201 < a < 1.7600000000000001e58

   1. Initial program 72.4%

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

   2. Taylor expanded in z around inf 67.3%

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

      1. associate--l+ 67.3%

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

      2. distribute-lft-out-- 67.3%

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

      3. div-sub 69.4%

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

      4. mul-1-neg 69.4%

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

      5. unsub-neg 69.4%

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

      6. distribute-rgt-out-- 69.4%

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

      7. associate-/l* 74.4%

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

   4. Simplified 74.4%

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

   5. Taylor expanded in y around inf 68.8%

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

   6. Taylor expanded in t around inf 60.9%

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

   if -4.49999999999999968e-21 < a < -4.6999999999999997e-278 or 1.45e-275 < a < 1.14999999999999993e-201

   1. Initial program 68.3%

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

   2. Taylor expanded in z around inf 79.4%

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

      1. associate--l+ 79.4%

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

      2. distribute-lft-out-- 79.4%

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

      3. div-sub 80.9%

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

      4. mul-1-neg 80.9%

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

      5. unsub-neg 80.9%

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

      6. distribute-rgt-out-- 80.9%

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

      7. associate-/l* 83.7%

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

   4. Simplified 83.7%

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

   5. Taylor expanded in t around 0 61.3%

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

      1. associate-*r/ 62.7%

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

   7. Simplified 62.7%

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

   if 1.7600000000000001e58 < a < 1.14999999999999994e117

   1. Initial program 97.6%

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

   2. Taylor expanded in y around inf 67.7%

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

   3. Taylor expanded in a around inf 49.0%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-275}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-201}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.76 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+117}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 43.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -7.7 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-275}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.36 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.1 \cdot 10^{+58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+116}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z))) (t_2 (* t (- 1.0 (/ y z)))))
   (if (<= a -7.7e+118)
     x
     (if (<= a -4.2e-19)
       t_2
       (if (<= a -4.2e-278)
         t_1
         (if (<= a 2.3e-275)
           t_2
           (if (<= a 1.36e-199)
             t_1
             (if (<= a 7.1e+58)
               t_2
               (if (<= a 2.6e+116) (* (- t x) (/ y a)) x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -7.7e+118) {
		tmp = x;
	} else if (a <= -4.2e-19) {
		tmp = t_2;
	} else if (a <= -4.2e-278) {
		tmp = t_1;
	} else if (a <= 2.3e-275) {
		tmp = t_2;
	} else if (a <= 1.36e-199) {
		tmp = t_1;
	} else if (a <= 7.1e+58) {
		tmp = t_2;
	} else if (a <= 2.6e+116) {
		tmp = (t - x) * (y / a);
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    t_2 = t * (1.0d0 - (y / z))
    if (a <= (-7.7d+118)) then
        tmp = x
    else if (a <= (-4.2d-19)) then
        tmp = t_2
    else if (a <= (-4.2d-278)) then
        tmp = t_1
    else if (a <= 2.3d-275) then
        tmp = t_2
    else if (a <= 1.36d-199) then
        tmp = t_1
    else if (a <= 7.1d+58) then
        tmp = t_2
    else if (a <= 2.6d+116) then
        tmp = (t - x) * (y / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -7.7e+118) {
		tmp = x;
	} else if (a <= -4.2e-19) {
		tmp = t_2;
	} else if (a <= -4.2e-278) {
		tmp = t_1;
	} else if (a <= 2.3e-275) {
		tmp = t_2;
	} else if (a <= 1.36e-199) {
		tmp = t_1;
	} else if (a <= 7.1e+58) {
		tmp = t_2;
	} else if (a <= 2.6e+116) {
		tmp = (t - x) * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	t_2 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -7.7e+118:
		tmp = x
	elif a <= -4.2e-19:
		tmp = t_2
	elif a <= -4.2e-278:
		tmp = t_1
	elif a <= 2.3e-275:
		tmp = t_2
	elif a <= 1.36e-199:
		tmp = t_1
	elif a <= 7.1e+58:
		tmp = t_2
	elif a <= 2.6e+116:
		tmp = (t - x) * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	t_2 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -7.7e+118)
		tmp = x;
	elseif (a <= -4.2e-19)
		tmp = t_2;
	elseif (a <= -4.2e-278)
		tmp = t_1;
	elseif (a <= 2.3e-275)
		tmp = t_2;
	elseif (a <= 1.36e-199)
		tmp = t_1;
	elseif (a <= 7.1e+58)
		tmp = t_2;
	elseif (a <= 2.6e+116)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	t_2 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -7.7e+118)
		tmp = x;
	elseif (a <= -4.2e-19)
		tmp = t_2;
	elseif (a <= -4.2e-278)
		tmp = t_1;
	elseif (a <= 2.3e-275)
		tmp = t_2;
	elseif (a <= 1.36e-199)
		tmp = t_1;
	elseif (a <= 7.1e+58)
		tmp = t_2;
	elseif (a <= 2.6e+116)
		tmp = (t - x) * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.7e+118], x, If[LessEqual[a, -4.2e-19], t$95$2, If[LessEqual[a, -4.2e-278], t$95$1, If[LessEqual[a, 2.3e-275], t$95$2, If[LessEqual[a, 1.36e-199], t$95$1, If[LessEqual[a, 7.1e+58], t$95$2, If[LessEqual[a, 2.6e+116], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.6999999999999997e118 or 2.59999999999999987e116 < a

   1. Initial program 96.3%

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

   2. Taylor expanded in a around inf 57.9%

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

   if -7.6999999999999997e118 < a < -4.1999999999999998e-19 or -4.20000000000000027e-278 < a < 2.2999999999999999e-275 or 1.3600000000000001e-199 < a < 7.10000000000000026e58

   1. Initial program 72.4%

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

   2. Taylor expanded in z around inf 67.3%

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

      1. associate--l+ 67.3%

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

      2. distribute-lft-out-- 67.3%

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

      3. div-sub 69.4%

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

      4. mul-1-neg 69.4%

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

      5. unsub-neg 69.4%

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

      6. distribute-rgt-out-- 69.4%

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

      7. associate-/l* 74.4%

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

   4. Simplified 74.4%

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

   5. Taylor expanded in y around inf 68.8%

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

   6. Taylor expanded in t around inf 60.9%

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

   if -4.1999999999999998e-19 < a < -4.20000000000000027e-278 or 2.2999999999999999e-275 < a < 1.3600000000000001e-199

   1. Initial program 68.3%

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

   2. Taylor expanded in z around inf 79.4%

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

      1. associate--l+ 79.4%

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

      2. distribute-lft-out-- 79.4%

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

      3. div-sub 80.9%

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

      4. mul-1-neg 80.9%

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

      5. unsub-neg 80.9%

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

      6. distribute-rgt-out-- 80.9%

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

      7. associate-/l* 83.7%

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

   4. Simplified 83.7%

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

   5. Taylor expanded in t around 0 61.3%

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

      1. associate-*r/ 62.7%

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

   7. Simplified 62.7%

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

   if 7.10000000000000026e58 < a < 2.59999999999999987e116

   1. Initial program 97.6%

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

   2. Taylor expanded in y around inf 67.7%

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

      1. div-sub 67.7%

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

      2. associate-*r/ 60.0%

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

      3. associate-/l* 62.8%

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

      4. associate-/r/ 69.6%

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

   4. Simplified 69.6%

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

   5. Taylor expanded in a around inf 49.2%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.7 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-19}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-275}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.36 \cdot 10^{-199}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 7.1 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+116}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 43.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -6.3 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-278}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-200}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= a -6.3e+118)
     x
     (if (<= a -5.6e-47)
       t_1
       (if (<= a -4.4e-278)
         (/ x (/ z y))
         (if (<= a 8e-277)
           t_1
           (if (<= a 4.4e-200) (* x (/ y z)) (if (<= a 1.8e+74) 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 <= -6.3e+118) {
		tmp = x;
	} else if (a <= -5.6e-47) {
		tmp = t_1;
	} else if (a <= -4.4e-278) {
		tmp = x / (z / y);
	} else if (a <= 8e-277) {
		tmp = t_1;
	} else if (a <= 4.4e-200) {
		tmp = x * (y / z);
	} else if (a <= 1.8e+74) {
		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 <= (-6.3d+118)) then
        tmp = x
    else if (a <= (-5.6d-47)) then
        tmp = t_1
    else if (a <= (-4.4d-278)) then
        tmp = x / (z / y)
    else if (a <= 8d-277) then
        tmp = t_1
    else if (a <= 4.4d-200) then
        tmp = x * (y / z)
    else if (a <= 1.8d+74) 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 <= -6.3e+118) {
		tmp = x;
	} else if (a <= -5.6e-47) {
		tmp = t_1;
	} else if (a <= -4.4e-278) {
		tmp = x / (z / y);
	} else if (a <= 8e-277) {
		tmp = t_1;
	} else if (a <= 4.4e-200) {
		tmp = x * (y / z);
	} else if (a <= 1.8e+74) {
		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 <= -6.3e+118:
		tmp = x
	elif a <= -5.6e-47:
		tmp = t_1
	elif a <= -4.4e-278:
		tmp = x / (z / y)
	elif a <= 8e-277:
		tmp = t_1
	elif a <= 4.4e-200:
		tmp = x * (y / z)
	elif a <= 1.8e+74:
		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 <= -6.3e+118)
		tmp = x;
	elseif (a <= -5.6e-47)
		tmp = t_1;
	elseif (a <= -4.4e-278)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 8e-277)
		tmp = t_1;
	elseif (a <= 4.4e-200)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.8e+74)
		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 <= -6.3e+118)
		tmp = x;
	elseif (a <= -5.6e-47)
		tmp = t_1;
	elseif (a <= -4.4e-278)
		tmp = x / (z / y);
	elseif (a <= 8e-277)
		tmp = t_1;
	elseif (a <= 4.4e-200)
		tmp = x * (y / z);
	elseif (a <= 1.8e+74)
		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, -6.3e+118], x, If[LessEqual[a, -5.6e-47], t$95$1, If[LessEqual[a, -4.4e-278], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e-277], t$95$1, If[LessEqual[a, 4.4e-200], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e+74], t$95$1, x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.30000000000000002e118 or 1.79999999999999994e74 < a

   1. Initial program 96.4%

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

   2. Taylor expanded in a around inf 53.5%

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

   if -6.30000000000000002e118 < a < -5.59999999999999986e-47 or -4.4000000000000002e-278 < a < 7.99999999999999975e-277 or 4.40000000000000027e-200 < a < 1.79999999999999994e74

   1. Initial program 72.6%

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

   2. Taylor expanded in z around inf 65.2%

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

      1. associate--l+ 65.2%

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

      2. distribute-lft-out-- 65.2%

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

      3. div-sub 67.1%

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

      4. mul-1-neg 67.1%

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

      5. unsub-neg 67.1%

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

      6. distribute-rgt-out-- 67.2%

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

      7. associate-/l* 72.6%

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

   4. Simplified 72.6%

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

   5. Taylor expanded in y around inf 65.6%

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

   6. Taylor expanded in t around inf 58.3%

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

   if -5.59999999999999986e-47 < a < -4.4000000000000002e-278

   1. Initial program 71.4%

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

   2. Taylor expanded in y around inf 66.2%

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

   3. Taylor expanded in a around 0 53.6%

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

      1. distribute-lft-out-- 53.6%

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

      2. div-sub 53.7%

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

      3. mul-1-neg 53.7%

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

   5. Simplified 53.7%

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

   6. Taylor expanded in t around 0 48.7%

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

      1. associate-/l* 50.8%

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

   8. Simplified 50.8%

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

   if 7.99999999999999975e-277 < a < 4.40000000000000027e-200

   1. Initial program 63.4%

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

   2. Taylor expanded in z around inf 93.6%

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

      1. associate--l+ 93.6%

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

      2. distribute-lft-out-- 93.6%

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

      3. div-sub 93.5%

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

      4. mul-1-neg 93.5%

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

      5. unsub-neg 93.5%

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

      6. distribute-rgt-out-- 93.5%

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

      7. associate-/l* 93.6%

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

   4. Simplified 93.6%

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

   5. Taylor expanded in y around inf 86.6%

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

   6. Taylor expanded in t around 0 73.7%

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

      1. associate-*r/ 73.7%

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

   8. Simplified 73.7%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.3 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-47}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-278}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-277}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-200}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 43.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-276}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+67}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z))) (t_2 (* t (- 1.0 (/ y z)))))
   (if (<= a -9.5e+118)
     x
     (if (<= a -4.8e-21)
       t_2
       (if (<= a -4.5e-278)
         t_1
         (if (<= a 9e-276)
           t_2
           (if (<= a 1.05e-199) t_1 (if (<= a 9.5e+67) t_2 x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -9.5e+118) {
		tmp = x;
	} else if (a <= -4.8e-21) {
		tmp = t_2;
	} else if (a <= -4.5e-278) {
		tmp = t_1;
	} else if (a <= 9e-276) {
		tmp = t_2;
	} else if (a <= 1.05e-199) {
		tmp = t_1;
	} else if (a <= 9.5e+67) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    t_2 = t * (1.0d0 - (y / z))
    if (a <= (-9.5d+118)) then
        tmp = x
    else if (a <= (-4.8d-21)) then
        tmp = t_2
    else if (a <= (-4.5d-278)) then
        tmp = t_1
    else if (a <= 9d-276) then
        tmp = t_2
    else if (a <= 1.05d-199) then
        tmp = t_1
    else if (a <= 9.5d+67) then
        tmp = t_2
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -9.5e+118) {
		tmp = x;
	} else if (a <= -4.8e-21) {
		tmp = t_2;
	} else if (a <= -4.5e-278) {
		tmp = t_1;
	} else if (a <= 9e-276) {
		tmp = t_2;
	} else if (a <= 1.05e-199) {
		tmp = t_1;
	} else if (a <= 9.5e+67) {
		tmp = t_2;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	t_2 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -9.5e+118:
		tmp = x
	elif a <= -4.8e-21:
		tmp = t_2
	elif a <= -4.5e-278:
		tmp = t_1
	elif a <= 9e-276:
		tmp = t_2
	elif a <= 1.05e-199:
		tmp = t_1
	elif a <= 9.5e+67:
		tmp = t_2
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	t_2 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -9.5e+118)
		tmp = x;
	elseif (a <= -4.8e-21)
		tmp = t_2;
	elseif (a <= -4.5e-278)
		tmp = t_1;
	elseif (a <= 9e-276)
		tmp = t_2;
	elseif (a <= 1.05e-199)
		tmp = t_1;
	elseif (a <= 9.5e+67)
		tmp = t_2;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	t_2 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -9.5e+118)
		tmp = x;
	elseif (a <= -4.8e-21)
		tmp = t_2;
	elseif (a <= -4.5e-278)
		tmp = t_1;
	elseif (a <= 9e-276)
		tmp = t_2;
	elseif (a <= 1.05e-199)
		tmp = t_1;
	elseif (a <= 9.5e+67)
		tmp = t_2;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.5e+118], x, If[LessEqual[a, -4.8e-21], t$95$2, If[LessEqual[a, -4.5e-278], t$95$1, If[LessEqual[a, 9e-276], t$95$2, If[LessEqual[a, 1.05e-199], t$95$1, If[LessEqual[a, 9.5e+67], t$95$2, x]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.49999999999999974e118 or 9.5000000000000002e67 < a

   1. Initial program 96.4%

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

   2. Taylor expanded in a around inf 53.5%

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

   if -9.49999999999999974e118 < a < -4.7999999999999999e-21 or -4.4999999999999998e-278 < a < 8.99999999999999925e-276 or 1.05000000000000001e-199 < a < 9.5000000000000002e67

   1. Initial program 73.5%

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

   2. Taylor expanded in z around inf 65.7%

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

      1. associate--l+ 65.7%

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

      2. distribute-lft-out-- 65.7%

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

      3. div-sub 67.7%

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

      4. mul-1-neg 67.7%

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

      5. unsub-neg 67.7%

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

      6. distribute-rgt-out-- 67.7%

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

      7. associate-/l* 72.5%

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

   4. Simplified 72.5%

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

   5. Taylor expanded in y around inf 67.2%

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

   6. Taylor expanded in t around inf 59.6%

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

   if -4.7999999999999999e-21 < a < -4.4999999999999998e-278 or 8.99999999999999925e-276 < a < 1.05000000000000001e-199

   1. Initial program 68.3%

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

   2. Taylor expanded in z around inf 79.4%

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

      1. associate--l+ 79.4%

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

      2. distribute-lft-out-- 79.4%

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

      3. div-sub 80.9%

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

      4. mul-1-neg 80.9%

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

      5. unsub-neg 80.9%

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

      6. distribute-rgt-out-- 80.9%

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

      7. associate-/l* 83.7%

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

   4. Simplified 83.7%

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

   5. Taylor expanded in t around 0 61.3%

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

      1. associate-*r/ 62.7%

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

   7. Simplified 62.7%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-276}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-199}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 49.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ t_3 := x \cdot \frac{y - a}{z}\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{+118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-278}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-201}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z))))
        (t_2 (+ x (/ t (/ a y))))
        (t_3 (* x (/ (- y a) z))))
   (if (<= a -6.2e+118)
     t_2
     (if (<= a -2e-13)
       t_1
       (if (<= a -4.7e-278)
         t_3
         (if (<= a 2.5e-278)
           t_1
           (if (<= a 5e-201) t_3 (if (<= a 2.9e+57) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x + (t / (a / y));
	double t_3 = x * ((y - a) / z);
	double tmp;
	if (a <= -6.2e+118) {
		tmp = t_2;
	} else if (a <= -2e-13) {
		tmp = t_1;
	} else if (a <= -4.7e-278) {
		tmp = t_3;
	} else if (a <= 2.5e-278) {
		tmp = t_1;
	} else if (a <= 5e-201) {
		tmp = t_3;
	} else if (a <= 2.9e+57) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    t_2 = x + (t / (a / y))
    t_3 = x * ((y - a) / z)
    if (a <= (-6.2d+118)) then
        tmp = t_2
    else if (a <= (-2d-13)) then
        tmp = t_1
    else if (a <= (-4.7d-278)) then
        tmp = t_3
    else if (a <= 2.5d-278) then
        tmp = t_1
    else if (a <= 5d-201) then
        tmp = t_3
    else if (a <= 2.9d+57) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x + (t / (a / y));
	double t_3 = x * ((y - a) / z);
	double tmp;
	if (a <= -6.2e+118) {
		tmp = t_2;
	} else if (a <= -2e-13) {
		tmp = t_1;
	} else if (a <= -4.7e-278) {
		tmp = t_3;
	} else if (a <= 2.5e-278) {
		tmp = t_1;
	} else if (a <= 5e-201) {
		tmp = t_3;
	} else if (a <= 2.9e+57) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = x + (t / (a / y))
	t_3 = x * ((y - a) / z)
	tmp = 0
	if a <= -6.2e+118:
		tmp = t_2
	elif a <= -2e-13:
		tmp = t_1
	elif a <= -4.7e-278:
		tmp = t_3
	elif a <= 2.5e-278:
		tmp = t_1
	elif a <= 5e-201:
		tmp = t_3
	elif a <= 2.9e+57:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(x + Float64(t / Float64(a / y)))
	t_3 = Float64(x * Float64(Float64(y - a) / z))
	tmp = 0.0
	if (a <= -6.2e+118)
		tmp = t_2;
	elseif (a <= -2e-13)
		tmp = t_1;
	elseif (a <= -4.7e-278)
		tmp = t_3;
	elseif (a <= 2.5e-278)
		tmp = t_1;
	elseif (a <= 5e-201)
		tmp = t_3;
	elseif (a <= 2.9e+57)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = x + (t / (a / y));
	t_3 = x * ((y - a) / z);
	tmp = 0.0;
	if (a <= -6.2e+118)
		tmp = t_2;
	elseif (a <= -2e-13)
		tmp = t_1;
	elseif (a <= -4.7e-278)
		tmp = t_3;
	elseif (a <= 2.5e-278)
		tmp = t_1;
	elseif (a <= 5e-201)
		tmp = t_3;
	elseif (a <= 2.9e+57)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.2e+118], t$95$2, If[LessEqual[a, -2e-13], t$95$1, If[LessEqual[a, -4.7e-278], t$95$3, If[LessEqual[a, 2.5e-278], t$95$1, If[LessEqual[a, 5e-201], t$95$3, If[LessEqual[a, 2.9e+57], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.19999999999999973e118 or 2.9000000000000002e57 < a

   1. Initial program 96.5%

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

   2. Taylor expanded in z around 0 64.4%

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

   3. Taylor expanded in t around inf 60.5%

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

      1. associate-/l* 69.4%

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

   5. Simplified 69.4%

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

   if -6.19999999999999973e118 < a < -2.0000000000000001e-13 or -4.6999999999999997e-278 < a < 2.49999999999999992e-278 or 4.9999999999999999e-201 < a < 2.9000000000000002e57

   1. Initial program 72.4%

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

   2. Taylor expanded in z around inf 67.3%

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

      1. associate--l+ 67.3%

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

      2. distribute-lft-out-- 67.3%

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

      3. div-sub 69.4%

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

      4. mul-1-neg 69.4%

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

      5. unsub-neg 69.4%

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

      6. distribute-rgt-out-- 69.4%

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

      7. associate-/l* 74.4%

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

   4. Simplified 74.4%

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

   5. Taylor expanded in y around inf 68.8%

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

   6. Taylor expanded in t around inf 60.9%

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

   if -2.0000000000000001e-13 < a < -4.6999999999999997e-278 or 2.49999999999999992e-278 < a < 4.9999999999999999e-201

   1. Initial program 68.3%

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

   2. Taylor expanded in z around inf 79.4%

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

      1. associate--l+ 79.4%

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

      2. distribute-lft-out-- 79.4%

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

      3. div-sub 80.9%

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

      4. mul-1-neg 80.9%

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

      5. unsub-neg 80.9%

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

      6. distribute-rgt-out-- 80.9%

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

      7. associate-/l* 83.7%

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

   4. Simplified 83.7%

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

   5. Taylor expanded in t around 0 61.3%

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

      1. associate-*r/ 62.7%

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

   7. Simplified 62.7%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+118}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-13}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-278}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-201}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+57}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 9: 49.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -6 \cdot 10^{+118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-278}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-201}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))) (t_2 (+ x (/ t (/ a y)))))
   (if (<= a -6e+118)
     t_2
     (if (<= a -3.2e-20)
       t_1
       (if (<= a -3.8e-278)
         (/ x (/ z (- y a)))
         (if (<= a 2.3e-275)
           t_1
           (if (<= a 6.8e-201)
             (* x (/ (- y a) z))
             (if (<= a 2.8e+57) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x + (t / (a / y));
	double tmp;
	if (a <= -6e+118) {
		tmp = t_2;
	} else if (a <= -3.2e-20) {
		tmp = t_1;
	} else if (a <= -3.8e-278) {
		tmp = x / (z / (y - a));
	} else if (a <= 2.3e-275) {
		tmp = t_1;
	} else if (a <= 6.8e-201) {
		tmp = x * ((y - a) / z);
	} else if (a <= 2.8e+57) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    t_2 = x + (t / (a / y))
    if (a <= (-6d+118)) then
        tmp = t_2
    else if (a <= (-3.2d-20)) then
        tmp = t_1
    else if (a <= (-3.8d-278)) then
        tmp = x / (z / (y - a))
    else if (a <= 2.3d-275) then
        tmp = t_1
    else if (a <= 6.8d-201) then
        tmp = x * ((y - a) / z)
    else if (a <= 2.8d+57) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x + (t / (a / y));
	double tmp;
	if (a <= -6e+118) {
		tmp = t_2;
	} else if (a <= -3.2e-20) {
		tmp = t_1;
	} else if (a <= -3.8e-278) {
		tmp = x / (z / (y - a));
	} else if (a <= 2.3e-275) {
		tmp = t_1;
	} else if (a <= 6.8e-201) {
		tmp = x * ((y - a) / z);
	} else if (a <= 2.8e+57) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = x + (t / (a / y))
	tmp = 0
	if a <= -6e+118:
		tmp = t_2
	elif a <= -3.2e-20:
		tmp = t_1
	elif a <= -3.8e-278:
		tmp = x / (z / (y - a))
	elif a <= 2.3e-275:
		tmp = t_1
	elif a <= 6.8e-201:
		tmp = x * ((y - a) / z)
	elif a <= 2.8e+57:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(x + Float64(t / Float64(a / y)))
	tmp = 0.0
	if (a <= -6e+118)
		tmp = t_2;
	elseif (a <= -3.2e-20)
		tmp = t_1;
	elseif (a <= -3.8e-278)
		tmp = Float64(x / Float64(z / Float64(y - a)));
	elseif (a <= 2.3e-275)
		tmp = t_1;
	elseif (a <= 6.8e-201)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 2.8e+57)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = x + (t / (a / y));
	tmp = 0.0;
	if (a <= -6e+118)
		tmp = t_2;
	elseif (a <= -3.2e-20)
		tmp = t_1;
	elseif (a <= -3.8e-278)
		tmp = x / (z / (y - a));
	elseif (a <= 2.3e-275)
		tmp = t_1;
	elseif (a <= 6.8e-201)
		tmp = x * ((y - a) / z);
	elseif (a <= 2.8e+57)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6e+118], t$95$2, If[LessEqual[a, -3.2e-20], t$95$1, If[LessEqual[a, -3.8e-278], N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e-275], t$95$1, If[LessEqual[a, 6.8e-201], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e+57], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6e118 or 2.8e57 < a

   1. Initial program 96.5%

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

   2. Taylor expanded in z around 0 64.4%

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

   3. Taylor expanded in t around inf 60.5%

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

      1. associate-/l* 69.4%

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

   5. Simplified 69.4%

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

   if -6e118 < a < -3.1999999999999997e-20 or -3.7999999999999999e-278 < a < 2.2999999999999999e-275 or 6.7999999999999997e-201 < a < 2.8e57

   1. Initial program 72.4%

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

   2. Taylor expanded in z around inf 67.3%

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

      1. associate--l+ 67.3%

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

      2. distribute-lft-out-- 67.3%

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

      3. div-sub 69.4%

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

      4. mul-1-neg 69.4%

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

      5. unsub-neg 69.4%

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

      6. distribute-rgt-out-- 69.4%

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

      7. associate-/l* 74.4%

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

   4. Simplified 74.4%

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

   5. Taylor expanded in y around inf 68.8%

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

   6. Taylor expanded in t around inf 60.9%

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

   if -3.1999999999999997e-20 < a < -3.7999999999999999e-278

   1. Initial program 69.7%

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

   2. Taylor expanded in z around inf 75.1%

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

      1. associate--l+ 75.1%

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

      2. distribute-lft-out-- 75.1%

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

      3. div-sub 77.1%

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

      4. mul-1-neg 77.1%

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

      5. unsub-neg 77.1%

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

      6. distribute-rgt-out-- 77.1%

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

      7. associate-/l* 80.8%

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

   4. Simplified 80.8%

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

   5. Taylor expanded in t around 0 55.7%

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

      1. associate-/l* 57.5%

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

   7. Simplified 57.5%

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

   if 2.2999999999999999e-275 < a < 6.7999999999999997e-201

   1. Initial program 63.4%

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

   2. Taylor expanded in z around inf 93.6%

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

      1. associate--l+ 93.6%

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

      2. distribute-lft-out-- 93.6%

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

      3. div-sub 93.5%

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

      4. mul-1-neg 93.5%

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

      5. unsub-neg 93.5%

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

      6. distribute-rgt-out-- 93.5%

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

      7. associate-/l* 93.6%

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

   4. Simplified 93.6%

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

   5. Taylor expanded in t around 0 80.2%

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

      1. associate-*r/ 80.2%

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

   7. Simplified 80.2%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+118}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-20}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-278}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-275}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-201}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+57}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 10: 62.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{+118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-83}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-127}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (/ t (/ a y)))))
   (if (<= a -6.2e+118)
     t_2
     (if (<= a -8.6e-46)
       t_1
       (if (<= a -1.65e-83)
         (* (- t x) (/ y (- a z)))
         (if (<= a 1.35e-127)
           (+ t (* x (/ y z)))
           (if (<= a 1.5e+76) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (t / (a / y));
	double tmp;
	if (a <= -6.2e+118) {
		tmp = t_2;
	} else if (a <= -8.6e-46) {
		tmp = t_1;
	} else if (a <= -1.65e-83) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 1.35e-127) {
		tmp = t + (x * (y / z));
	} else if (a <= 1.5e+76) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + (t / (a / y))
    if (a <= (-6.2d+118)) then
        tmp = t_2
    else if (a <= (-8.6d-46)) then
        tmp = t_1
    else if (a <= (-1.65d-83)) then
        tmp = (t - x) * (y / (a - z))
    else if (a <= 1.35d-127) then
        tmp = t + (x * (y / z))
    else if (a <= 1.5d+76) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (t / (a / y));
	double tmp;
	if (a <= -6.2e+118) {
		tmp = t_2;
	} else if (a <= -8.6e-46) {
		tmp = t_1;
	} else if (a <= -1.65e-83) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 1.35e-127) {
		tmp = t + (x * (y / z));
	} else if (a <= 1.5e+76) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + (t / (a / y))
	tmp = 0
	if a <= -6.2e+118:
		tmp = t_2
	elif a <= -8.6e-46:
		tmp = t_1
	elif a <= -1.65e-83:
		tmp = (t - x) * (y / (a - z))
	elif a <= 1.35e-127:
		tmp = t + (x * (y / z))
	elif a <= 1.5e+76:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(t / Float64(a / y)))
	tmp = 0.0
	if (a <= -6.2e+118)
		tmp = t_2;
	elseif (a <= -8.6e-46)
		tmp = t_1;
	elseif (a <= -1.65e-83)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (a <= 1.35e-127)
		tmp = Float64(t + Float64(x * Float64(y / z)));
	elseif (a <= 1.5e+76)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + (t / (a / y));
	tmp = 0.0;
	if (a <= -6.2e+118)
		tmp = t_2;
	elseif (a <= -8.6e-46)
		tmp = t_1;
	elseif (a <= -1.65e-83)
		tmp = (t - x) * (y / (a - z));
	elseif (a <= 1.35e-127)
		tmp = t + (x * (y / z));
	elseif (a <= 1.5e+76)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.2e+118], t$95$2, If[LessEqual[a, -8.6e-46], t$95$1, If[LessEqual[a, -1.65e-83], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e-127], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e+76], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.19999999999999973e118 or 1.4999999999999999e76 < a

   1. Initial program 96.4%

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

   2. Taylor expanded in z around 0 63.9%

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

   3. Taylor expanded in t around inf 59.9%

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

      1. associate-/l* 69.2%

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

   5. Simplified 69.2%

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

   if -6.19999999999999973e118 < a < -8.6000000000000007e-46 or 1.35e-127 < a < 1.4999999999999999e76

   1. Initial program 75.3%

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

      1. clear-num 75.3%

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

      2. un-div-inv 75.4%

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

   3. Applied egg-rr 75.4%

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

   4. Taylor expanded in x around 0 58.3%

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

      1. associate-*r/ 70.7%

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

   6. Simplified 70.7%

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

   if -8.6000000000000007e-46 < a < -1.65e-83

   1. Initial program 64.8%

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

   2. Taylor expanded in y around inf 82.9%

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

      1. div-sub 82.9%

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

      2. associate-*r/ 74.0%

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

      3. associate-/l* 82.7%

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

      4. associate-/r/ 82.3%

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

   4. Simplified 82.3%

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

   if -1.65e-83 < a < 1.35e-127

   1. Initial program 68.7%

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

   2. Taylor expanded in z around inf 88.8%

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

      1. associate--l+ 88.8%

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

      2. distribute-lft-out-- 88.8%

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

      3. div-sub 88.8%

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

      4. mul-1-neg 88.8%

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

      5. unsub-neg 88.8%

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

      6. distribute-rgt-out-- 88.8%

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

      7. associate-/l* 87.6%

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

   4. Simplified 87.6%

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

   5. Taylor expanded in y around inf 83.1%

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

   6. Taylor expanded in t around 0 75.7%

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

      1. associate-*r/ 74.5%

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

      2. neg-mul-1 74.5%

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

      3. distribute-rgt-neg-in 74.5%

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

      4. distribute-neg-frac 74.5%

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

   8. Simplified 74.5%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+118}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{-46}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-83}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-127}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+76}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 11: 62.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -7.4 \cdot 10^{+118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -9.6 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9.6 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-127}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (/ t (/ a y)))))
   (if (<= a -7.4e+118)
     t_2
     (if (<= a -9.6e-46)
       t_1
       (if (<= a -9.6e-84)
         (* y (/ (- t x) (- a z)))
         (if (<= a 1.35e-127)
           (+ t (* x (/ y z)))
           (if (<= a 4.4e+72) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (t / (a / y));
	double tmp;
	if (a <= -7.4e+118) {
		tmp = t_2;
	} else if (a <= -9.6e-46) {
		tmp = t_1;
	} else if (a <= -9.6e-84) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.35e-127) {
		tmp = t + (x * (y / z));
	} else if (a <= 4.4e+72) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + (t / (a / y))
    if (a <= (-7.4d+118)) then
        tmp = t_2
    else if (a <= (-9.6d-46)) then
        tmp = t_1
    else if (a <= (-9.6d-84)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 1.35d-127) then
        tmp = t + (x * (y / z))
    else if (a <= 4.4d+72) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (t / (a / y));
	double tmp;
	if (a <= -7.4e+118) {
		tmp = t_2;
	} else if (a <= -9.6e-46) {
		tmp = t_1;
	} else if (a <= -9.6e-84) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.35e-127) {
		tmp = t + (x * (y / z));
	} else if (a <= 4.4e+72) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + (t / (a / y))
	tmp = 0
	if a <= -7.4e+118:
		tmp = t_2
	elif a <= -9.6e-46:
		tmp = t_1
	elif a <= -9.6e-84:
		tmp = y * ((t - x) / (a - z))
	elif a <= 1.35e-127:
		tmp = t + (x * (y / z))
	elif a <= 4.4e+72:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(t / Float64(a / y)))
	tmp = 0.0
	if (a <= -7.4e+118)
		tmp = t_2;
	elseif (a <= -9.6e-46)
		tmp = t_1;
	elseif (a <= -9.6e-84)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 1.35e-127)
		tmp = Float64(t + Float64(x * Float64(y / z)));
	elseif (a <= 4.4e+72)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + (t / (a / y));
	tmp = 0.0;
	if (a <= -7.4e+118)
		tmp = t_2;
	elseif (a <= -9.6e-46)
		tmp = t_1;
	elseif (a <= -9.6e-84)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 1.35e-127)
		tmp = t + (x * (y / z));
	elseif (a <= 4.4e+72)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.4e+118], t$95$2, If[LessEqual[a, -9.6e-46], t$95$1, If[LessEqual[a, -9.6e-84], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e-127], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.4e+72], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.39999999999999973e118 or 4.4e72 < a

   1. Initial program 96.4%

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

   2. Taylor expanded in z around 0 63.9%

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

   3. Taylor expanded in t around inf 59.9%

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

      1. associate-/l* 69.2%

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

   5. Simplified 69.2%

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

   if -7.39999999999999973e118 < a < -9.60000000000000053e-46 or 1.35e-127 < a < 4.4e72

   1. Initial program 75.3%

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

      1. clear-num 75.3%

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

      2. un-div-inv 75.4%

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

   3. Applied egg-rr 75.4%

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

   4. Taylor expanded in x around 0 58.3%

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

      1. associate-*r/ 70.7%

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

   6. Simplified 70.7%

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

   if -9.60000000000000053e-46 < a < -9.6000000000000007e-84

   1. Initial program 64.8%

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

   2. Taylor expanded in y around -inf 74.0%

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

      1. div-inv 74.0%

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

      2. associate-*l* 82.1%

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

      3. div-inv 82.9%

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

      4. sub-div 82.9%

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

      5. *-commutative 82.9%

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

      6. sub-div 82.9%

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

   4. Applied egg-rr 82.9%

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

   if -9.6000000000000007e-84 < a < 1.35e-127

   1. Initial program 68.7%

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

   2. Taylor expanded in z around inf 88.8%

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

      1. associate--l+ 88.8%

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

      2. distribute-lft-out-- 88.8%

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

      3. div-sub 88.8%

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

      4. mul-1-neg 88.8%

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

      5. unsub-neg 88.8%

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

      6. distribute-rgt-out-- 88.8%

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

      7. associate-/l* 87.6%

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

   4. Simplified 87.6%

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

   5. Taylor expanded in y around inf 83.1%

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

   6. Taylor expanded in t around 0 75.7%

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

      1. associate-*r/ 74.5%

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

      2. neg-mul-1 74.5%

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

      3. distribute-rgt-neg-in 74.5%

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

      4. distribute-neg-frac 74.5%

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

   8. Simplified 74.5%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.4 \cdot 10^{+118}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -9.6 \cdot 10^{-46}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -9.6 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-127}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 12: 64.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -1.6 \cdot 10^{+119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-127}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (/ y (/ a (- t x))))))
   (if (<= a -1.6e+119)
     t_2
     (if (<= a -3.5e-46)
       t_1
       (if (<= a -1.05e-83)
         (* y (/ (- t x) (- a z)))
         (if (<= a 1.3e-127)
           (+ t (* x (/ y z)))
           (if (<= a 4.9e+64) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (y / (a / (t - x)));
	double tmp;
	if (a <= -1.6e+119) {
		tmp = t_2;
	} else if (a <= -3.5e-46) {
		tmp = t_1;
	} else if (a <= -1.05e-83) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.3e-127) {
		tmp = t + (x * (y / z));
	} else if (a <= 4.9e+64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + (y / (a / (t - x)))
    if (a <= (-1.6d+119)) then
        tmp = t_2
    else if (a <= (-3.5d-46)) then
        tmp = t_1
    else if (a <= (-1.05d-83)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 1.3d-127) then
        tmp = t + (x * (y / z))
    else if (a <= 4.9d+64) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (y / (a / (t - x)));
	double tmp;
	if (a <= -1.6e+119) {
		tmp = t_2;
	} else if (a <= -3.5e-46) {
		tmp = t_1;
	} else if (a <= -1.05e-83) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.3e-127) {
		tmp = t + (x * (y / z));
	} else if (a <= 4.9e+64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + (y / (a / (t - x)))
	tmp = 0
	if a <= -1.6e+119:
		tmp = t_2
	elif a <= -3.5e-46:
		tmp = t_1
	elif a <= -1.05e-83:
		tmp = y * ((t - x) / (a - z))
	elif a <= 1.3e-127:
		tmp = t + (x * (y / z))
	elif a <= 4.9e+64:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(y / Float64(a / Float64(t - x))))
	tmp = 0.0
	if (a <= -1.6e+119)
		tmp = t_2;
	elseif (a <= -3.5e-46)
		tmp = t_1;
	elseif (a <= -1.05e-83)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 1.3e-127)
		tmp = Float64(t + Float64(x * Float64(y / z)));
	elseif (a <= 4.9e+64)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + (y / (a / (t - x)));
	tmp = 0.0;
	if (a <= -1.6e+119)
		tmp = t_2;
	elseif (a <= -3.5e-46)
		tmp = t_1;
	elseif (a <= -1.05e-83)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 1.3e-127)
		tmp = t + (x * (y / z));
	elseif (a <= 4.9e+64)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.6e+119], t$95$2, If[LessEqual[a, -3.5e-46], t$95$1, If[LessEqual[a, -1.05e-83], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e-127], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.9e+64], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.59999999999999995e119 or 4.9000000000000003e64 < a

   1. Initial program 96.4%

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

   2. Taylor expanded in z around 0 63.9%

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

      1. associate-/l* 76.2%

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

   4. Simplified 76.2%

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

   if -1.59999999999999995e119 < a < -3.5000000000000002e-46 or 1.29999999999999995e-127 < a < 4.9000000000000003e64

   1. Initial program 75.3%

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

      1. clear-num 75.3%

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

      2. un-div-inv 75.4%

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

   3. Applied egg-rr 75.4%

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

   4. Taylor expanded in x around 0 58.3%

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

      1. associate-*r/ 70.7%

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

   6. Simplified 70.7%

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

   if -3.5000000000000002e-46 < a < -1.0499999999999999e-83

   1. Initial program 64.8%

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

   2. Taylor expanded in y around -inf 74.0%

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

      1. div-inv 74.0%

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

      2. associate-*l* 82.1%

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

      3. div-inv 82.9%

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

      4. sub-div 82.9%

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

      5. *-commutative 82.9%

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

      6. sub-div 82.9%

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

   4. Applied egg-rr 82.9%

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

   if -1.0499999999999999e-83 < a < 1.29999999999999995e-127

   1. Initial program 68.7%

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

   2. Taylor expanded in z around inf 88.8%

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

      1. associate--l+ 88.8%

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

      2. distribute-lft-out-- 88.8%

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

      3. div-sub 88.8%

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

      4. mul-1-neg 88.8%

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

      5. unsub-neg 88.8%

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

      6. distribute-rgt-out-- 88.8%

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

      7. associate-/l* 87.6%

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

   4. Simplified 87.6%

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

   5. Taylor expanded in y around inf 83.1%

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

   6. Taylor expanded in t around 0 75.7%

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

      1. associate-*r/ 74.5%

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

      2. neg-mul-1 74.5%

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

      3. distribute-rgt-neg-in 74.5%

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

      4. distribute-neg-frac 74.5%

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

   8. Simplified 74.5%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+119}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-46}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-127}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{+64}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 13: 65.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -6 \cdot 10^{+118}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.85 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{-127}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= a -6e+118)
     (+ x (/ (- y z) (/ a t)))
     (if (<= a -6.5e-46)
       t_1
       (if (<= a -3.85e-84)
         (* y (/ (- t x) (- a z)))
         (if (<= a 1.28e-127)
           (+ t (* x (/ y z)))
           (if (<= a 1.06e+68) t_1 (+ x (/ y (/ a (- t x)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -6e+118) {
		tmp = x + ((y - z) / (a / t));
	} else if (a <= -6.5e-46) {
		tmp = t_1;
	} else if (a <= -3.85e-84) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.28e-127) {
		tmp = t + (x * (y / z));
	} else if (a <= 1.06e+68) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (a <= (-6d+118)) then
        tmp = x + ((y - z) / (a / t))
    else if (a <= (-6.5d-46)) then
        tmp = t_1
    else if (a <= (-3.85d-84)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 1.28d-127) then
        tmp = t + (x * (y / z))
    else if (a <= 1.06d+68) then
        tmp = t_1
    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 t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -6e+118) {
		tmp = x + ((y - z) / (a / t));
	} else if (a <= -6.5e-46) {
		tmp = t_1;
	} else if (a <= -3.85e-84) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.28e-127) {
		tmp = t + (x * (y / z));
	} else if (a <= 1.06e+68) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if a <= -6e+118:
		tmp = x + ((y - z) / (a / t))
	elif a <= -6.5e-46:
		tmp = t_1
	elif a <= -3.85e-84:
		tmp = y * ((t - x) / (a - z))
	elif a <= 1.28e-127:
		tmp = t + (x * (y / z))
	elif a <= 1.06e+68:
		tmp = t_1
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (a <= -6e+118)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(a / t)));
	elseif (a <= -6.5e-46)
		tmp = t_1;
	elseif (a <= -3.85e-84)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 1.28e-127)
		tmp = Float64(t + Float64(x * Float64(y / z)));
	elseif (a <= 1.06e+68)
		tmp = t_1;
	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)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (a <= -6e+118)
		tmp = x + ((y - z) / (a / t));
	elseif (a <= -6.5e-46)
		tmp = t_1;
	elseif (a <= -3.85e-84)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 1.28e-127)
		tmp = t + (x * (y / z));
	elseif (a <= 1.06e+68)
		tmp = t_1;
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6e+118], N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.5e-46], t$95$1, If[LessEqual[a, -3.85e-84], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.28e-127], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.06e+68], t$95$1, N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -6e118

   1. Initial program 97.3%

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

      1. clear-num 97.2%

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

      2. un-div-inv 97.1%

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

   3. Applied egg-rr 97.1%

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

   4. Taylor expanded in a around inf 86.2%

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

   5. Taylor expanded in t around inf 83.0%

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

   if -6e118 < a < -6.49999999999999966e-46 or 1.2799999999999999e-127 < a < 1.06e68

   1. Initial program 75.3%

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

      1. clear-num 75.3%

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

      2. un-div-inv 75.4%

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

   3. Applied egg-rr 75.4%

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

   4. Taylor expanded in x around 0 58.3%

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

      1. associate-*r/ 70.7%

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

   6. Simplified 70.7%

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

   if -6.49999999999999966e-46 < a < -3.85e-84

   1. Initial program 64.8%

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

   2. Taylor expanded in y around -inf 74.0%

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

      1. div-inv 74.0%

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

      2. associate-*l* 82.1%

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

      3. div-inv 82.9%

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

      4. sub-div 82.9%

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

      5. *-commutative 82.9%

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

      6. sub-div 82.9%

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

   4. Applied egg-rr 82.9%

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

   if -3.85e-84 < a < 1.2799999999999999e-127

   1. Initial program 68.7%

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

   2. Taylor expanded in z around inf 88.8%

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

      1. associate--l+ 88.8%

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

      2. distribute-lft-out-- 88.8%

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

      3. div-sub 88.8%

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

      4. mul-1-neg 88.8%

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

      5. unsub-neg 88.8%

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

      6. distribute-rgt-out-- 88.8%

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

      7. associate-/l* 87.6%

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

   4. Simplified 87.6%

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

   5. Taylor expanded in y around inf 83.1%

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

   6. Taylor expanded in t around 0 75.7%

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

      1. associate-*r/ 74.5%

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

      2. neg-mul-1 74.5%

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

      3. distribute-rgt-neg-in 74.5%

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

      4. distribute-neg-frac 74.5%

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

   8. Simplified 74.5%

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

   if 1.06e68 < a

   1. Initial program 95.8%

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

   2. Taylor expanded in z around 0 65.2%

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

      1. associate-/l* 75.2%

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

   4. Simplified 75.2%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+118}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-46}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -3.85 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{-127}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 14: 72.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-46}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+57}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ a (- t x))))))
   (if (<= a -3.4e+125)
     t_1
     (if (<= a -1.3e-46)
       (/ t (/ (- a z) (- y z)))
       (if (<= a -4.8e-83)
         (* y (/ (- t x) (- a z)))
         (if (<= a 2.8e+57) (+ t (/ (- x t) (/ z y))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / (a / (t - x)));
	double tmp;
	if (a <= -3.4e+125) {
		tmp = t_1;
	} else if (a <= -1.3e-46) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= -4.8e-83) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 2.8e+57) {
		tmp = t + ((x - t) / (z / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) / (a / (t - x)))
    if (a <= (-3.4d+125)) then
        tmp = t_1
    else if (a <= (-1.3d-46)) then
        tmp = t / ((a - z) / (y - z))
    else if (a <= (-4.8d-83)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 2.8d+57) then
        tmp = t + ((x - t) / (z / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / (a / (t - x)));
	double tmp;
	if (a <= -3.4e+125) {
		tmp = t_1;
	} else if (a <= -1.3e-46) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= -4.8e-83) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 2.8e+57) {
		tmp = t + ((x - t) / (z / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / (a / (t - x)))
	tmp = 0
	if a <= -3.4e+125:
		tmp = t_1
	elif a <= -1.3e-46:
		tmp = t / ((a - z) / (y - z))
	elif a <= -4.8e-83:
		tmp = y * ((t - x) / (a - z))
	elif a <= 2.8e+57:
		tmp = t + ((x - t) / (z / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(a / Float64(t - x))))
	tmp = 0.0
	if (a <= -3.4e+125)
		tmp = t_1;
	elseif (a <= -1.3e-46)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (a <= -4.8e-83)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 2.8e+57)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) / (a / (t - x)));
	tmp = 0.0;
	if (a <= -3.4e+125)
		tmp = t_1;
	elseif (a <= -1.3e-46)
		tmp = t / ((a - z) / (y - z));
	elseif (a <= -4.8e-83)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 2.8e+57)
		tmp = t + ((x - t) / (z / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.4e+125], t$95$1, If[LessEqual[a, -1.3e-46], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.8e-83], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e+57], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.3999999999999999e125 or 2.8e57 < a

   1. Initial program 96.5%

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

      1. clear-num 95.7%

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

      2. un-div-inv 95.7%

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

   3. Applied egg-rr 95.7%

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

   4. Taylor expanded in a around inf 83.5%

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

   if -3.3999999999999999e125 < a < -1.3000000000000001e-46

   1. Initial program 75.6%

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

   2. Taylor expanded in x around 0 57.9%

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

      1. associate-/l* 69.5%

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

   4. Simplified 69.5%

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

   if -1.3000000000000001e-46 < a < -4.8000000000000002e-83

   1. Initial program 64.8%

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

   2. Taylor expanded in y around -inf 74.0%

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

      1. div-inv 74.0%

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

      2. associate-*l* 82.1%

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

      3. div-inv 82.9%

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

      4. sub-div 82.9%

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

      5. *-commutative 82.9%

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

      6. sub-div 82.9%

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

   4. Applied egg-rr 82.9%

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

   if -4.8000000000000002e-83 < a < 2.8e57

   1. Initial program 70.2%

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

   2. Taylor expanded in z around inf 81.2%

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

      1. associate--l+ 81.2%

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

      2. distribute-lft-out-- 81.2%

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

      3. div-sub 81.2%

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

      4. mul-1-neg 81.2%

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

      5. unsub-neg 81.2%

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

      6. distribute-rgt-out-- 81.2%

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

      7. associate-/l* 82.8%

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

   4. Simplified 82.8%

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

   5. Taylor expanded in y around inf 77.0%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-46}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+57}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 15: 62.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -8.6 \cdot 10^{+120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-127}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (/ t (/ a y)))))
   (if (<= a -8.6e+120)
     t_2
     (if (<= a -1.02e-44)
       t_1
       (if (<= a 1.25e-127)
         (+ t (* x (/ y z)))
         (if (<= a 2.55e+73) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (t / (a / y));
	double tmp;
	if (a <= -8.6e+120) {
		tmp = t_2;
	} else if (a <= -1.02e-44) {
		tmp = t_1;
	} else if (a <= 1.25e-127) {
		tmp = t + (x * (y / z));
	} else if (a <= 2.55e+73) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + (t / (a / y))
    if (a <= (-8.6d+120)) then
        tmp = t_2
    else if (a <= (-1.02d-44)) then
        tmp = t_1
    else if (a <= 1.25d-127) then
        tmp = t + (x * (y / z))
    else if (a <= 2.55d+73) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (t / (a / y));
	double tmp;
	if (a <= -8.6e+120) {
		tmp = t_2;
	} else if (a <= -1.02e-44) {
		tmp = t_1;
	} else if (a <= 1.25e-127) {
		tmp = t + (x * (y / z));
	} else if (a <= 2.55e+73) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + (t / (a / y))
	tmp = 0
	if a <= -8.6e+120:
		tmp = t_2
	elif a <= -1.02e-44:
		tmp = t_1
	elif a <= 1.25e-127:
		tmp = t + (x * (y / z))
	elif a <= 2.55e+73:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(t / Float64(a / y)))
	tmp = 0.0
	if (a <= -8.6e+120)
		tmp = t_2;
	elseif (a <= -1.02e-44)
		tmp = t_1;
	elseif (a <= 1.25e-127)
		tmp = Float64(t + Float64(x * Float64(y / z)));
	elseif (a <= 2.55e+73)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + (t / (a / y));
	tmp = 0.0;
	if (a <= -8.6e+120)
		tmp = t_2;
	elseif (a <= -1.02e-44)
		tmp = t_1;
	elseif (a <= 1.25e-127)
		tmp = t + (x * (y / z));
	elseif (a <= 2.55e+73)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.6e+120], t$95$2, If[LessEqual[a, -1.02e-44], t$95$1, If[LessEqual[a, 1.25e-127], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.55e+73], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.6000000000000003e120 or 2.55000000000000012e73 < a

   1. Initial program 96.4%

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

   2. Taylor expanded in z around 0 63.9%

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

   3. Taylor expanded in t around inf 59.9%

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

      1. associate-/l* 69.2%

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

   5. Simplified 69.2%

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

   if -8.6000000000000003e120 < a < -1.0199999999999999e-44 or 1.2499999999999999e-127 < a < 2.55000000000000012e73

   1. Initial program 74.9%

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

      1. clear-num 75.0%

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

      2. un-div-inv 75.1%

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

   3. Applied egg-rr 75.1%

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

   4. Taylor expanded in x around 0 58.9%

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

      1. associate-*r/ 70.3%

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

   6. Simplified 70.3%

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

   if -1.0199999999999999e-44 < a < 1.2499999999999999e-127

   1. Initial program 68.5%

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

   2. Taylor expanded in z around inf 81.8%

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

      1. associate--l+ 81.8%

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

      2. distribute-lft-out-- 81.8%

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

      3. div-sub 82.9%

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

      4. mul-1-neg 82.9%

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

      5. unsub-neg 82.9%

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

      6. distribute-rgt-out-- 82.9%

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

      7. associate-/l* 83.9%

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

   4. Simplified 83.9%

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

   5. Taylor expanded in y around inf 78.6%

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

   6. Taylor expanded in t around 0 71.1%

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

      1. associate-*r/ 71.1%

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

      2. neg-mul-1 71.1%

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

      3. distribute-rgt-neg-in 71.1%

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

      4. distribute-neg-frac 71.1%

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

   8. Simplified 71.1%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{+120}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-44}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-127}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 16: 69.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+119}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-47}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+57}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.2e+119)
   (+ x (/ (- y z) (/ a t)))
   (if (<= a -8e-47)
     (* t (/ (- y z) (- a z)))
     (if (<= a -3.4e-83)
       (* y (/ (- t x) (- a z)))
       (if (<= a 5.6e+57)
         (+ t (/ (- x t) (/ z y)))
         (+ x (/ y (/ a (- t x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.2e+119) {
		tmp = x + ((y - z) / (a / t));
	} else if (a <= -8e-47) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= -3.4e-83) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 5.6e+57) {
		tmp = t + ((x - t) / (z / y));
	} 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 (a <= (-4.2d+119)) then
        tmp = x + ((y - z) / (a / t))
    else if (a <= (-8d-47)) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= (-3.4d-83)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 5.6d+57) then
        tmp = t + ((x - t) / (z / y))
    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 (a <= -4.2e+119) {
		tmp = x + ((y - z) / (a / t));
	} else if (a <= -8e-47) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= -3.4e-83) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 5.6e+57) {
		tmp = t + ((x - t) / (z / y));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.2e+119:
		tmp = x + ((y - z) / (a / t))
	elif a <= -8e-47:
		tmp = t * ((y - z) / (a - z))
	elif a <= -3.4e-83:
		tmp = y * ((t - x) / (a - z))
	elif a <= 5.6e+57:
		tmp = t + ((x - t) / (z / y))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.2e+119)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(a / t)));
	elseif (a <= -8e-47)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= -3.4e-83)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 5.6e+57)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	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 (a <= -4.2e+119)
		tmp = x + ((y - z) / (a / t));
	elseif (a <= -8e-47)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= -3.4e-83)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 5.6e+57)
		tmp = t + ((x - t) / (z / y));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.2e+119], N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8e-47], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.4e-83], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.6e+57], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.19999999999999966e119

   1. Initial program 97.3%

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

      1. clear-num 97.2%

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

      2. un-div-inv 97.1%

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

   3. Applied egg-rr 97.1%

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

   4. Taylor expanded in a around inf 86.2%

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

   5. Taylor expanded in t around inf 83.0%

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

   if -4.19999999999999966e119 < a < -7.9999999999999998e-47

   1. Initial program 74.8%

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

      1. clear-num 74.8%

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

      2. un-div-inv 74.9%

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

   3. Applied egg-rr 74.9%

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

   4. Taylor expanded in x around 0 59.6%

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

      1. associate-*r/ 68.5%

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

   6. Simplified 68.5%

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

   if -7.9999999999999998e-47 < a < -3.3999999999999998e-83

   1. Initial program 64.8%

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

   2. Taylor expanded in y around -inf 74.0%

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

      1. div-inv 74.0%

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

      2. associate-*l* 82.1%

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

      3. div-inv 82.9%

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

      4. sub-div 82.9%

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

      5. *-commutative 82.9%

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

      6. sub-div 82.9%

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

   4. Applied egg-rr 82.9%

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

   if -3.3999999999999998e-83 < a < 5.59999999999999999e57

   1. Initial program 70.2%

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

   2. Taylor expanded in z around inf 81.2%

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

      1. associate--l+ 81.2%

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

      2. distribute-lft-out-- 81.2%

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

      3. div-sub 81.2%

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

      4. mul-1-neg 81.2%

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

      5. unsub-neg 81.2%

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

      6. distribute-rgt-out-- 81.2%

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

      7. associate-/l* 82.8%

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

   4. Simplified 82.8%

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

   5. Taylor expanded in y around inf 77.0%

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

   if 5.59999999999999999e57 < a

   1. Initial program 96.1%

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

   2. Taylor expanded in z around 0 65.8%

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

      1. associate-/l* 75.2%

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

   4. Simplified 75.2%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+119}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-47}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+57}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 17: 69.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-47}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.14 \cdot 10^{+58}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.4e+125)
   (+ x (/ (- y z) (/ a t)))
   (if (<= a -6e-47)
     (/ t (/ (- a z) (- y z)))
     (if (<= a -4.8e-83)
       (* y (/ (- t x) (- a z)))
       (if (<= a 1.14e+58)
         (+ t (/ (- x t) (/ z y)))
         (+ x (/ y (/ a (- t x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.4e+125) {
		tmp = x + ((y - z) / (a / t));
	} else if (a <= -6e-47) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= -4.8e-83) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.14e+58) {
		tmp = t + ((x - t) / (z / y));
	} 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 (a <= (-3.4d+125)) then
        tmp = x + ((y - z) / (a / t))
    else if (a <= (-6d-47)) then
        tmp = t / ((a - z) / (y - z))
    else if (a <= (-4.8d-83)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 1.14d+58) then
        tmp = t + ((x - t) / (z / y))
    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 (a <= -3.4e+125) {
		tmp = x + ((y - z) / (a / t));
	} else if (a <= -6e-47) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= -4.8e-83) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.14e+58) {
		tmp = t + ((x - t) / (z / y));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.4e+125:
		tmp = x + ((y - z) / (a / t))
	elif a <= -6e-47:
		tmp = t / ((a - z) / (y - z))
	elif a <= -4.8e-83:
		tmp = y * ((t - x) / (a - z))
	elif a <= 1.14e+58:
		tmp = t + ((x - t) / (z / y))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.4e+125)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(a / t)));
	elseif (a <= -6e-47)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (a <= -4.8e-83)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 1.14e+58)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	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 (a <= -3.4e+125)
		tmp = x + ((y - z) / (a / t));
	elseif (a <= -6e-47)
		tmp = t / ((a - z) / (y - z));
	elseif (a <= -4.8e-83)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 1.14e+58)
		tmp = t + ((x - t) / (z / y));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.4e+125], N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6e-47], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.8e-83], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.14e+58], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.3999999999999999e125

   1. Initial program 97.2%

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

      1. clear-num 97.2%

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

      2. un-div-inv 97.0%

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

   3. Applied egg-rr 97.0%

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

   4. Taylor expanded in a around inf 85.9%

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

   5. Taylor expanded in t around inf 82.5%

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

   if -3.3999999999999999e125 < a < -6.00000000000000033e-47

   1. Initial program 75.6%

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

   2. Taylor expanded in x around 0 57.9%

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

      1. associate-/l* 69.5%

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

   4. Simplified 69.5%

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

   if -6.00000000000000033e-47 < a < -4.8000000000000002e-83

   1. Initial program 64.8%

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

   2. Taylor expanded in y around -inf 74.0%

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

      1. div-inv 74.0%

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

      2. associate-*l* 82.1%

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

      3. div-inv 82.9%

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

      4. sub-div 82.9%

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

      5. *-commutative 82.9%

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

      6. sub-div 82.9%

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

   4. Applied egg-rr 82.9%

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

   if -4.8000000000000002e-83 < a < 1.14e58

   1. Initial program 70.2%

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

   2. Taylor expanded in z around inf 81.2%

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

      1. associate--l+ 81.2%

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

      2. distribute-lft-out-- 81.2%

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

      3. div-sub 81.2%

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

      4. mul-1-neg 81.2%

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

      5. unsub-neg 81.2%

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

      6. distribute-rgt-out-- 81.2%

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

      7. associate-/l* 82.8%

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

   4. Simplified 82.8%

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

   5. Taylor expanded in y around inf 77.0%

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

   if 1.14e58 < a

   1. Initial program 96.1%

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

   2. Taylor expanded in z around 0 65.8%

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

      1. associate-/l* 75.2%

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

   4. Simplified 75.2%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-47}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.14 \cdot 10^{+58}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 18: 73.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+118} \lor \neg \left(a \leq 1.24 \cdot 10^{+58}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6e+118) (not (<= a 1.24e+58)))
   (+ x (/ (- y z) (/ a (- t x))))
   (+ t (/ (- x t) (/ z (- y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6e+118) || !(a <= 1.24e+58)) {
		tmp = x + ((y - z) / (a / (t - x)));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-6d+118)) .or. (.not. (a <= 1.24d+58))) then
        tmp = x + ((y - z) / (a / (t - x)))
    else
        tmp = t + ((x - t) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6e+118) || !(a <= 1.24e+58)) {
		tmp = x + ((y - z) / (a / (t - x)));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -6e+118) or not (a <= 1.24e+58):
		tmp = x + ((y - z) / (a / (t - x)))
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -6e+118) || !(a <= 1.24e+58))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -6e+118) || ~((a <= 1.24e+58)))
		tmp = x + ((y - z) / (a / (t - x)));
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -6e+118], N[Not[LessEqual[a, 1.24e+58]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6e118 or 1.24000000000000005e58 < a

   1. Initial program 96.5%

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

      1. clear-num 95.8%

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

      2. un-div-inv 95.8%

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

   3. Applied egg-rr 95.8%

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

   4. Taylor expanded in a around inf 83.6%

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

   if -6e118 < a < 1.24000000000000005e58

   1. Initial program 70.7%

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

   2. Taylor expanded in z around inf 72.2%

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

      1. associate--l+ 72.2%

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

      2. distribute-lft-out-- 72.2%

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

      3. div-sub 74.1%

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

      4. mul-1-neg 74.1%

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

      5. unsub-neg 74.1%

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

      6. distribute-rgt-out-- 74.1%

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

      7. associate-/l* 78.2%

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

   4. Simplified 78.2%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+118} \lor \neg \left(a \leq 1.24 \cdot 10^{+58}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 19: 37.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.3 \cdot 10^{-46}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-201}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.36 \cdot 10^{+58}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.4e+125)
   x
   (if (<= a -5.3e-46)
     t
     (if (<= a 2.3e-201) (* x (/ y z)) (if (<= a 1.36e+58) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.4e+125) {
		tmp = x;
	} else if (a <= -5.3e-46) {
		tmp = t;
	} else if (a <= 2.3e-201) {
		tmp = x * (y / z);
	} else if (a <= 1.36e+58) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.4d+125)) then
        tmp = x
    else if (a <= (-5.3d-46)) then
        tmp = t
    else if (a <= 2.3d-201) then
        tmp = x * (y / z)
    else if (a <= 1.36d+58) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.4e+125) {
		tmp = x;
	} else if (a <= -5.3e-46) {
		tmp = t;
	} else if (a <= 2.3e-201) {
		tmp = x * (y / z);
	} else if (a <= 1.36e+58) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.4e+125:
		tmp = x
	elif a <= -5.3e-46:
		tmp = t
	elif a <= 2.3e-201:
		tmp = x * (y / z)
	elif a <= 1.36e+58:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.4e+125)
		tmp = x;
	elseif (a <= -5.3e-46)
		tmp = t;
	elseif (a <= 2.3e-201)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.36e+58)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.4e+125)
		tmp = x;
	elseif (a <= -5.3e-46)
		tmp = t;
	elseif (a <= 2.3e-201)
		tmp = x * (y / z);
	elseif (a <= 1.36e+58)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.4e+125], x, If[LessEqual[a, -5.3e-46], t, If[LessEqual[a, 2.3e-201], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.36e+58], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.3999999999999999e125 or 1.35999999999999997e58 < a

   1. Initial program 96.5%

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

   2. Taylor expanded in a around inf 52.9%

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

   if -3.3999999999999999e125 < a < -5.30000000000000018e-46 or 2.29999999999999986e-201 < a < 1.35999999999999997e58

   1. Initial program 73.7%

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

   2. Taylor expanded in z around inf 43.0%

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

   if -5.30000000000000018e-46 < a < 2.29999999999999986e-201

   1. Initial program 67.4%

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

   2. Taylor expanded in z around inf 84.0%

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

      1. associate--l+ 84.0%

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

      2. distribute-lft-out-- 84.0%

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

      3. div-sub 85.3%

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

      4. mul-1-neg 85.3%

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

      5. unsub-neg 85.3%

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

      6. distribute-rgt-out-- 85.3%

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

      7. associate-/l* 86.6%

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

   4. Simplified 86.6%

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

   5. Taylor expanded in y around inf 80.0%

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

   6. Taylor expanded in t around 0 49.6%

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

      1. associate-*r/ 50.9%

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

   8. Simplified 50.9%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.3 \cdot 10^{-46}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-201}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.36 \cdot 10^{+58}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 37.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-46}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+57}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.4e+125)
   x
   (if (<= a -2.3e-46)
     t
     (if (<= a 1.22e-201) (/ x (/ z y)) (if (<= a 3.5e+57) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.4e+125) {
		tmp = x;
	} else if (a <= -2.3e-46) {
		tmp = t;
	} else if (a <= 1.22e-201) {
		tmp = x / (z / y);
	} else if (a <= 3.5e+57) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.4d+125)) then
        tmp = x
    else if (a <= (-2.3d-46)) then
        tmp = t
    else if (a <= 1.22d-201) then
        tmp = x / (z / y)
    else if (a <= 3.5d+57) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.4e+125) {
		tmp = x;
	} else if (a <= -2.3e-46) {
		tmp = t;
	} else if (a <= 1.22e-201) {
		tmp = x / (z / y);
	} else if (a <= 3.5e+57) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.4e+125:
		tmp = x
	elif a <= -2.3e-46:
		tmp = t
	elif a <= 1.22e-201:
		tmp = x / (z / y)
	elif a <= 3.5e+57:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.4e+125)
		tmp = x;
	elseif (a <= -2.3e-46)
		tmp = t;
	elseif (a <= 1.22e-201)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 3.5e+57)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.4e+125)
		tmp = x;
	elseif (a <= -2.3e-46)
		tmp = t;
	elseif (a <= 1.22e-201)
		tmp = x / (z / y);
	elseif (a <= 3.5e+57)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.4e+125], x, If[LessEqual[a, -2.3e-46], t, If[LessEqual[a, 1.22e-201], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e+57], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.3999999999999999e125 or 3.4999999999999997e57 < a

   1. Initial program 96.5%

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

   2. Taylor expanded in a around inf 52.9%

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

   if -3.3999999999999999e125 < a < -2.2999999999999999e-46 or 1.22000000000000009e-201 < a < 3.4999999999999997e57

   1. Initial program 73.7%

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

   2. Taylor expanded in z around inf 43.0%

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

   if -2.2999999999999999e-46 < a < 1.22000000000000009e-201

   1. Initial program 67.4%

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

   2. Taylor expanded in y around inf 63.8%

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

   3. Taylor expanded in a around 0 55.6%

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

      1. distribute-lft-out-- 55.6%

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

      2. div-sub 55.6%

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

      3. mul-1-neg 55.6%

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

   5. Simplified 55.6%

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

   6. Taylor expanded in t around 0 49.6%

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

      1. associate-/l* 51.0%

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

   8. Simplified 51.0%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-46}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+57}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21: 58.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+118} \lor \neg \left(a \leq 4.5 \cdot 10^{+57}\right):\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6e+118) (not (<= a 4.5e+57)))
   (+ x (/ t (/ a y)))
   (+ t (* x (/ y z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6e+118) || !(a <= 4.5e+57)) {
		tmp = x + (t / (a / y));
	} else {
		tmp = t + (x * (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-6d+118)) .or. (.not. (a <= 4.5d+57))) then
        tmp = x + (t / (a / y))
    else
        tmp = t + (x * (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6e+118) || !(a <= 4.5e+57)) {
		tmp = x + (t / (a / y));
	} else {
		tmp = t + (x * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -6e+118) or not (a <= 4.5e+57):
		tmp = x + (t / (a / y))
	else:
		tmp = t + (x * (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -6e+118) || !(a <= 4.5e+57))
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(t + Float64(x * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -6e+118) || ~((a <= 4.5e+57)))
		tmp = x + (t / (a / y));
	else
		tmp = t + (x * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -6e+118], N[Not[LessEqual[a, 4.5e+57]], $MachinePrecision]], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6e118 or 4.49999999999999996e57 < a

   1. Initial program 96.5%

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

   2. Taylor expanded in z around 0 64.4%

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

   3. Taylor expanded in t around inf 60.5%

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

      1. associate-/l* 69.4%

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

   5. Simplified 69.4%

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

   if -6e118 < a < 4.49999999999999996e57

   1. Initial program 70.7%

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

   2. Taylor expanded in z around inf 72.2%

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

      1. associate--l+ 72.2%

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

      2. distribute-lft-out-- 72.2%

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

      3. div-sub 74.1%

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

      4. mul-1-neg 74.1%

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

      5. unsub-neg 74.1%

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

      6. distribute-rgt-out-- 74.1%

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

      7. associate-/l* 78.2%

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

   4. Simplified 78.2%

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

   5. Taylor expanded in y around inf 70.7%

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

   6. Taylor expanded in t around 0 60.4%

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

      1. associate-*r/ 62.8%

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

      2. neg-mul-1 62.8%

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

      3. distribute-rgt-neg-in 62.8%

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

      4. distribute-neg-frac 62.8%

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

   8. Simplified 62.8%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+118} \lor \neg \left(a \leq 4.5 \cdot 10^{+57}\right):\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 22: 38.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+58}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.4e+125) x (if (<= a 1.2e+58) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.4e+125) {
		tmp = x;
	} else if (a <= 1.2e+58) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.4d+125)) then
        tmp = x
    else if (a <= 1.2d+58) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.4e+125) {
		tmp = x;
	} else if (a <= 1.2e+58) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.4e+125:
		tmp = x
	elif a <= 1.2e+58:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.4e+125)
		tmp = x;
	elseif (a <= 1.2e+58)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.4e+125)
		tmp = x;
	elseif (a <= 1.2e+58)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.4e+125], x, If[LessEqual[a, 1.2e+58], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.3999999999999999e125 or 1.2e58 < a

   1. Initial program 96.5%

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

   2. Taylor expanded in a around inf 52.9%

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

   if -3.3999999999999999e125 < a < 1.2e58

   1. Initial program 70.9%

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

   2. Taylor expanded in z around inf 35.2%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+58}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 23: 24.7% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 t)

C

double code(double x, double y, double z, double t, double a) {
	return t;
}

Fortran

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

Java

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

Python

def code(x, y, z, t, a):
	return t

Julia

function code(x, y, z, t, a)
	return t
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 80.4%

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

2. Taylor expanded in z around inf 27.0%

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

3. Final simplification 27.0%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023320 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))