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

Percentage Accurate: 69.6% → 91.2%

Time: 20.5s

Alternatives: 20

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 69.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.2% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 74.2%

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

      1. associate-*l/ 90.0%

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

   3. Simplified 90.0%

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

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

   1. Initial program 4.5%

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

      1. +-commutative 4.5%

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

      2. associate-*l/ 4.5%

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

      3. fma-def 4.5%

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

   3. Simplified 4.5%

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

   4. Taylor expanded in z around -inf 99.9%

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

4. Final simplification 90.9%

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

Alternative 2: 69.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y - z}{a}\\ t_2 := t - \frac{t - x}{\frac{z}{y}}\\ t_3 := t - x \cdot \frac{a - y}{z}\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{+43}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-50}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-129}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.22 \cdot 10^{-211}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+77}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ (- y z) a))))
        (t_2 (- t (/ (- t x) (/ z y))))
        (t_3 (- t (* x (/ (- a y) z)))))
   (if (<= a -3.4e+125)
     t_1
     (if (<= a -5.5e+43)
       (/ t (/ (- a z) (- y z)))
       (if (<= a -1.3e+33)
         t_1
         (if (<= a -5.2e-50)
           t_3
           (if (<= a -3.2e-83)
             (* y (/ (- t x) (- a z)))
             (if (<= a -5.4e-129)
               t_2
               (if (<= a -1.22e-211)
                 t_3
                 (if (<= a 1.3e-127)
                   t_2
                   (if (<= a 3.9e+77)
                     (* t (/ (- y z) (- a z)))
                     (+ x (/ y (/ a (- t x)))))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * ((y - z) / a));
	double t_2 = t - ((t - x) / (z / y));
	double t_3 = t - (x * ((a - y) / z));
	double tmp;
	if (a <= -3.4e+125) {
		tmp = t_1;
	} else if (a <= -5.5e+43) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= -1.3e+33) {
		tmp = t_1;
	} else if (a <= -5.2e-50) {
		tmp = t_3;
	} else if (a <= -3.2e-83) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= -5.4e-129) {
		tmp = t_2;
	} else if (a <= -1.22e-211) {
		tmp = t_3;
	} else if (a <= 1.3e-127) {
		tmp = t_2;
	} else if (a <= 3.9e+77) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (t * ((y - z) / a))
    t_2 = t - ((t - x) / (z / y))
    t_3 = t - (x * ((a - y) / z))
    if (a <= (-3.4d+125)) then
        tmp = t_1
    else if (a <= (-5.5d+43)) then
        tmp = t / ((a - z) / (y - z))
    else if (a <= (-1.3d+33)) then
        tmp = t_1
    else if (a <= (-5.2d-50)) then
        tmp = t_3
    else if (a <= (-3.2d-83)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= (-5.4d-129)) then
        tmp = t_2
    else if (a <= (-1.22d-211)) then
        tmp = t_3
    else if (a <= 1.3d-127) then
        tmp = t_2
    else if (a <= 3.9d+77) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * ((y - z) / a));
	double t_2 = t - ((t - x) / (z / y));
	double t_3 = t - (x * ((a - y) / z));
	double tmp;
	if (a <= -3.4e+125) {
		tmp = t_1;
	} else if (a <= -5.5e+43) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= -1.3e+33) {
		tmp = t_1;
	} else if (a <= -5.2e-50) {
		tmp = t_3;
	} else if (a <= -3.2e-83) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= -5.4e-129) {
		tmp = t_2;
	} else if (a <= -1.22e-211) {
		tmp = t_3;
	} else if (a <= 1.3e-127) {
		tmp = t_2;
	} else if (a <= 3.9e+77) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * ((y - z) / a))
	t_2 = t - ((t - x) / (z / y))
	t_3 = t - (x * ((a - y) / z))
	tmp = 0
	if a <= -3.4e+125:
		tmp = t_1
	elif a <= -5.5e+43:
		tmp = t / ((a - z) / (y - z))
	elif a <= -1.3e+33:
		tmp = t_1
	elif a <= -5.2e-50:
		tmp = t_3
	elif a <= -3.2e-83:
		tmp = y * ((t - x) / (a - z))
	elif a <= -5.4e-129:
		tmp = t_2
	elif a <= -1.22e-211:
		tmp = t_3
	elif a <= 1.3e-127:
		tmp = t_2
	elif a <= 3.9e+77:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(Float64(y - z) / a)))
	t_2 = Float64(t - Float64(Float64(t - x) / Float64(z / y)))
	t_3 = Float64(t - Float64(x * Float64(Float64(a - y) / z)))
	tmp = 0.0
	if (a <= -3.4e+125)
		tmp = t_1;
	elseif (a <= -5.5e+43)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (a <= -1.3e+33)
		tmp = t_1;
	elseif (a <= -5.2e-50)
		tmp = t_3;
	elseif (a <= -3.2e-83)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= -5.4e-129)
		tmp = t_2;
	elseif (a <= -1.22e-211)
		tmp = t_3;
	elseif (a <= 1.3e-127)
		tmp = t_2;
	elseif (a <= 3.9e+77)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * ((y - z) / a));
	t_2 = t - ((t - x) / (z / y));
	t_3 = t - (x * ((a - y) / z));
	tmp = 0.0;
	if (a <= -3.4e+125)
		tmp = t_1;
	elseif (a <= -5.5e+43)
		tmp = t / ((a - z) / (y - z));
	elseif (a <= -1.3e+33)
		tmp = t_1;
	elseif (a <= -5.2e-50)
		tmp = t_3;
	elseif (a <= -3.2e-83)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= -5.4e-129)
		tmp = t_2;
	elseif (a <= -1.22e-211)
		tmp = t_3;
	elseif (a <= 1.3e-127)
		tmp = t_2;
	elseif (a <= 3.9e+77)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t - N[(x * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.4e+125], t$95$1, If[LessEqual[a, -5.5e+43], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.3e+33], t$95$1, If[LessEqual[a, -5.2e-50], t$95$3, If[LessEqual[a, -3.2e-83], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.4e-129], t$95$2, If[LessEqual[a, -1.22e-211], t$95$3, If[LessEqual[a, 1.3e-127], t$95$2, If[LessEqual[a, 3.9e+77], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -3.3999999999999999e125 or -5.49999999999999989e43 < a < -1.2999999999999999e33

   1. Initial program 70.1%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in a around inf 85.7%

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

   5. Taylor expanded in t around inf 82.2%

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

      1. associate-/r/ 82.2%

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

   7. Applied egg-rr 82.2%

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

   if -3.3999999999999999e125 < a < -5.49999999999999989e43

   1. Initial program 70.6%

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

      1. associate-*l/ 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in x around 0 69.9%

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

      1. associate-/l* 81.6%

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

   6. Simplified 81.6%

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

   if -1.2999999999999999e33 < a < -5.2000000000000003e-50 or -5.39999999999999998e-129 < a < -1.21999999999999996e-211

   1. Initial program 61.1%

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

      1. associate-*l/ 64.3%

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

   3. Simplified 64.3%

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

   4. Taylor expanded in z around inf 67.8%

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

      1. associate--l+ 67.8%

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

      2. associate-*r/ 67.8%

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

      3. associate-*r/ 67.8%

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

      4. div-sub 71.2%

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

      5. distribute-lft-out-- 71.2%

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

      6. associate-*r/ 71.2%

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

      7. distribute-rgt-out-- 71.2%

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

      8. mul-1-neg 71.2%

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

      9. unsub-neg 71.2%

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

      10. associate-/l* 77.3%

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

   6. Simplified 77.3%

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

   7. Taylor expanded in t around 0 71.1%

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

      1. associate-*r/ 77.4%

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

      2. neg-mul-1 77.4%

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

      3. distribute-rgt-neg-in 77.4%

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

      4. distribute-neg-frac 77.4%

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

   9. Simplified 77.4%

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

   if -5.2000000000000003e-50 < a < -3.2000000000000001e-83

   1. Initial program 78.2%

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

      1. associate-*l/ 78.0%

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

   3. Simplified 78.0%

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

   4. Taylor expanded in y around inf 89.8%

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

      1. div-sub 89.8%

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

   6. Simplified 89.8%

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

   if -3.2000000000000001e-83 < a < -5.39999999999999998e-129 or -1.21999999999999996e-211 < a < 1.29999999999999995e-127

   1. Initial program 67.0%

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

      1. associate-*l/ 73.4%

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

   3. Simplified 73.4%

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

   4. Taylor expanded in z around inf 92.3%

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

      1. associate--l+ 92.3%

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

      2. associate-*r/ 92.3%

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

      3. associate-*r/ 92.3%

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

      4. div-sub 92.2%

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

      5. distribute-lft-out-- 92.2%

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

      6. associate-*r/ 92.2%

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

      7. distribute-rgt-out-- 92.2%

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

      8. mul-1-neg 92.2%

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

      9. unsub-neg 92.2%

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

      10. associate-/l* 90.7%

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

   6. Simplified 90.7%

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

   7. Taylor expanded in y around inf 88.3%

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

   if 1.29999999999999995e-127 < a < 3.8999999999999998e77

   1. Initial program 62.1%

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

      1. associate-*l/ 77.3%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in x around 0 57.4%

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

      1. associate-*r/ 72.3%

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

   6. Simplified 72.3%

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

   if 3.8999999999999998e77 < a

   1. Initial program 74.6%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around 0 65.2%

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

      1. associate-/l* 75.2%

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

   6. Simplified 75.2%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{+43}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{+33}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-50}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-129}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq -1.22 \cdot 10^{-211}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-127}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+77}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 3: 37.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{z}{y}}\\ t_2 := t + \frac{a}{\frac{z}{t}}\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -0.03:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-281}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.15 \cdot 10^{-280}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+116}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (/ z y))) (t_2 (+ t (/ a (/ z t)))))
   (if (<= a -3.4e+125)
     x
     (if (<= a -0.03)
       t_2
       (if (<= a -1.35e-281)
         t_1
         (if (<= a 4.15e-280)
           t_2
           (if (<= a 5.6e-201)
             t_1
             (if (<= a 4.6e+59)
               t_2
               (if (<= a 2.7e+116) (* y (/ (- t x) a)) x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (z / y);
	double t_2 = t + (a / (z / t));
	double tmp;
	if (a <= -3.4e+125) {
		tmp = x;
	} else if (a <= -0.03) {
		tmp = t_2;
	} else if (a <= -1.35e-281) {
		tmp = t_1;
	} else if (a <= 4.15e-280) {
		tmp = t_2;
	} else if (a <= 5.6e-201) {
		tmp = t_1;
	} else if (a <= 4.6e+59) {
		tmp = t_2;
	} else if (a <= 2.7e+116) {
		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 / (z / y)
    t_2 = t + (a / (z / t))
    if (a <= (-3.4d+125)) then
        tmp = x
    else if (a <= (-0.03d0)) then
        tmp = t_2
    else if (a <= (-1.35d-281)) then
        tmp = t_1
    else if (a <= 4.15d-280) then
        tmp = t_2
    else if (a <= 5.6d-201) then
        tmp = t_1
    else if (a <= 4.6d+59) then
        tmp = t_2
    else if (a <= 2.7d+116) 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 / (z / y);
	double t_2 = t + (a / (z / t));
	double tmp;
	if (a <= -3.4e+125) {
		tmp = x;
	} else if (a <= -0.03) {
		tmp = t_2;
	} else if (a <= -1.35e-281) {
		tmp = t_1;
	} else if (a <= 4.15e-280) {
		tmp = t_2;
	} else if (a <= 5.6e-201) {
		tmp = t_1;
	} else if (a <= 4.6e+59) {
		tmp = t_2;
	} else if (a <= 2.7e+116) {
		tmp = y * ((t - x) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (z / y)
	t_2 = t + (a / (z / t))
	tmp = 0
	if a <= -3.4e+125:
		tmp = x
	elif a <= -0.03:
		tmp = t_2
	elif a <= -1.35e-281:
		tmp = t_1
	elif a <= 4.15e-280:
		tmp = t_2
	elif a <= 5.6e-201:
		tmp = t_1
	elif a <= 4.6e+59:
		tmp = t_2
	elif a <= 2.7e+116:
		tmp = y * ((t - x) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(z / y))
	t_2 = Float64(t + Float64(a / Float64(z / t)))
	tmp = 0.0
	if (a <= -3.4e+125)
		tmp = x;
	elseif (a <= -0.03)
		tmp = t_2;
	elseif (a <= -1.35e-281)
		tmp = t_1;
	elseif (a <= 4.15e-280)
		tmp = t_2;
	elseif (a <= 5.6e-201)
		tmp = t_1;
	elseif (a <= 4.6e+59)
		tmp = t_2;
	elseif (a <= 2.7e+116)
		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 / (z / y);
	t_2 = t + (a / (z / t));
	tmp = 0.0;
	if (a <= -3.4e+125)
		tmp = x;
	elseif (a <= -0.03)
		tmp = t_2;
	elseif (a <= -1.35e-281)
		tmp = t_1;
	elseif (a <= 4.15e-280)
		tmp = t_2;
	elseif (a <= 5.6e-201)
		tmp = t_1;
	elseif (a <= 4.6e+59)
		tmp = t_2;
	elseif (a <= 2.7e+116)
		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[(z / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(a / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.4e+125], x, If[LessEqual[a, -0.03], t$95$2, If[LessEqual[a, -1.35e-281], t$95$1, If[LessEqual[a, 4.15e-280], t$95$2, If[LessEqual[a, 5.6e-201], t$95$1, If[LessEqual[a, 4.6e+59], t$95$2, If[LessEqual[a, 2.7e+116], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.3999999999999999e125 or 2.7e116 < a

   1. Initial program 70.8%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in a around inf 58.6%

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

   if -3.3999999999999999e125 < a < -0.029999999999999999 or -1.34999999999999995e-281 < a < 4.14999999999999985e-280 or 5.5999999999999998e-201 < a < 4.60000000000000016e59

   1. Initial program 61.4%

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

      1. associate-*l/ 75.6%

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

   3. Simplified 75.6%

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

   4. Taylor expanded in z around inf 66.2%

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

      1. associate--l+ 66.2%

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

      2. associate-*r/ 66.2%

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

      3. associate-*r/ 66.2%

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

      4. div-sub 67.3%

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

      5. distribute-lft-out-- 67.3%

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

      6. associate-*r/ 67.3%

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

      7. distribute-rgt-out-- 67.4%

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

      8. mul-1-neg 67.4%

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

      9. unsub-neg 67.4%

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

      10. associate-/l* 72.5%

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

   6. Simplified 72.5%

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

   7. Taylor expanded in y around 0 52.4%

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

      1. sub-neg 52.4%

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

      2. mul-1-neg 52.4%

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

      3. remove-double-neg 52.4%

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

      4. associate-/l* 56.5%

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

   9. Simplified 56.5%

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

   10. Taylor expanded in t around inf 47.6%

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

       1. associate-/l* 48.7%

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

   12. Simplified 48.7%

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

   if -0.029999999999999999 < a < -1.34999999999999995e-281 or 4.14999999999999985e-280 < a < 5.5999999999999998e-201

   1. Initial program 70.7%

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

      1. associate-*l/ 72.6%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in z around inf 79.1%

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

      1. associate--l+ 79.1%

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

      2. associate-*r/ 79.1%

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

      3. associate-*r/ 79.1%

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

      4. div-sub 82.0%

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

      5. distribute-lft-out-- 82.0%

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

      6. associate-*r/ 82.0%

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

      7. distribute-rgt-out-- 82.0%

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

      8. mul-1-neg 82.0%

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

      9. unsub-neg 82.0%

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

      10. associate-/l* 84.7%

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

   6. Simplified 84.7%

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

   7. Taylor expanded in t around 0 59.3%

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

      1. associate-/l* 62.1%

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

   9. Simplified 62.1%

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

   10. Taylor expanded in y around inf 53.1%

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

   if 4.60000000000000016e59 < a < 2.7e116

   1. Initial program 86.1%

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

      1. associate-*l/ 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 67.7%

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

   5. 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 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -0.03:\\ \;\;\;\;t + \frac{a}{\frac{z}{t}}\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-281}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 4.15 \cdot 10^{-280}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t}}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+59}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t}}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+116}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 48.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - t \cdot \frac{y}{z}\\ t_2 := x + t \cdot \frac{y}{a}\\ t_3 := \frac{x}{\frac{z}{y}}\\ \mathbf{if}\;a \leq -6 \cdot 10^{+118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-278}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-201}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* t (/ y z))))
        (t_2 (+ x (* t (/ y a))))
        (t_3 (/ x (/ z y))))
   (if (<= a -6e+118)
     t_2
     (if (<= a -5e-46)
       t_1
       (if (<= a -4.7e-278)
         t_3
         (if (<= a 2.7e-278)
           t_1
           (if (<= a 1.15e-201) t_3 (if (<= a 4.6e+58) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (t * (y / z));
	double t_2 = x + (t * (y / a));
	double t_3 = x / (z / y);
	double tmp;
	if (a <= -6e+118) {
		tmp = t_2;
	} else if (a <= -5e-46) {
		tmp = t_1;
	} else if (a <= -4.7e-278) {
		tmp = t_3;
	} else if (a <= 2.7e-278) {
		tmp = t_1;
	} else if (a <= 1.15e-201) {
		tmp = t_3;
	} else if (a <= 4.6e+58) {
		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 - (t * (y / z))
    t_2 = x + (t * (y / a))
    t_3 = x / (z / y)
    if (a <= (-6d+118)) then
        tmp = t_2
    else if (a <= (-5d-46)) then
        tmp = t_1
    else if (a <= (-4.7d-278)) then
        tmp = t_3
    else if (a <= 2.7d-278) then
        tmp = t_1
    else if (a <= 1.15d-201) then
        tmp = t_3
    else if (a <= 4.6d+58) 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 * (y / z));
	double t_2 = x + (t * (y / a));
	double t_3 = x / (z / y);
	double tmp;
	if (a <= -6e+118) {
		tmp = t_2;
	} else if (a <= -5e-46) {
		tmp = t_1;
	} else if (a <= -4.7e-278) {
		tmp = t_3;
	} else if (a <= 2.7e-278) {
		tmp = t_1;
	} else if (a <= 1.15e-201) {
		tmp = t_3;
	} else if (a <= 4.6e+58) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (t * (y / z))
	t_2 = x + (t * (y / a))
	t_3 = x / (z / y)
	tmp = 0
	if a <= -6e+118:
		tmp = t_2
	elif a <= -5e-46:
		tmp = t_1
	elif a <= -4.7e-278:
		tmp = t_3
	elif a <= 2.7e-278:
		tmp = t_1
	elif a <= 1.15e-201:
		tmp = t_3
	elif a <= 4.6e+58:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(t * Float64(y / z)))
	t_2 = Float64(x + Float64(t * Float64(y / a)))
	t_3 = Float64(x / Float64(z / y))
	tmp = 0.0
	if (a <= -6e+118)
		tmp = t_2;
	elseif (a <= -5e-46)
		tmp = t_1;
	elseif (a <= -4.7e-278)
		tmp = t_3;
	elseif (a <= 2.7e-278)
		tmp = t_1;
	elseif (a <= 1.15e-201)
		tmp = t_3;
	elseif (a <= 4.6e+58)
		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 * (y / z));
	t_2 = x + (t * (y / a));
	t_3 = x / (z / y);
	tmp = 0.0;
	if (a <= -6e+118)
		tmp = t_2;
	elseif (a <= -5e-46)
		tmp = t_1;
	elseif (a <= -4.7e-278)
		tmp = t_3;
	elseif (a <= 2.7e-278)
		tmp = t_1;
	elseif (a <= 1.15e-201)
		tmp = t_3;
	elseif (a <= 4.6e+58)
		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[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6e+118], t$95$2, If[LessEqual[a, -5e-46], t$95$1, If[LessEqual[a, -4.7e-278], t$95$3, If[LessEqual[a, 2.7e-278], t$95$1, If[LessEqual[a, 1.15e-201], t$95$3, If[LessEqual[a, 4.6e+58], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6e118 or 4.60000000000000005e58 < a

   1. Initial program 72.4%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in z around 0 64.4%

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

      1. associate-/l* 76.1%

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

   6. Simplified 76.1%

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

   7. Taylor expanded in t around inf 60.5%

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

      1. associate-*r/ 69.5%

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

   9. Simplified 69.5%

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

   if -6e118 < a < -4.99999999999999992e-46 or -4.6999999999999997e-278 < a < 2.7000000000000001e-278 or 1.14999999999999993e-201 < a < 4.60000000000000005e58

   1. Initial program 60.2%

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

      1. associate-*l/ 73.4%

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

   3. Simplified 73.4%

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

   4. Taylor expanded in z around inf 66.7%

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

      1. associate--l+ 66.7%

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

      2. associate-*r/ 66.7%

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

      3. associate-*r/ 66.7%

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

      4. div-sub 68.7%

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

      5. distribute-lft-out-- 68.7%

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

      6. associate-*r/ 68.7%

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

      7. distribute-rgt-out-- 68.8%

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

      8. mul-1-neg 68.8%

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

      9. unsub-neg 68.8%

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

      10. associate-/l* 74.4%

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

   6. Simplified 74.4%

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

   7. Taylor expanded in y around inf 67.1%

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

   8. Taylor expanded in t around inf 56.7%

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

      1. associate-*r/ 59.5%

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

   10. Simplified 59.5%

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

   if -4.99999999999999992e-46 < a < -4.6999999999999997e-278 or 2.7000000000000001e-278 < a < 1.14999999999999993e-201

   1. Initial program 74.7%

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

      1. associate-*l/ 75.4%

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

   3. Simplified 75.4%

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

   4. Taylor expanded in z around inf 81.1%

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

      1. associate--l+ 81.1%

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

      2. associate-*r/ 81.1%

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

      3. associate-*r/ 81.1%

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

      4. div-sub 82.7%

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

      5. distribute-lft-out-- 82.7%

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

      6. associate-*r/ 82.7%

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

      7. distribute-rgt-out-- 82.7%

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

      8. mul-1-neg 82.7%

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

      9. unsub-neg 82.7%

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

      10. associate-/l* 84.3%

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

   6. Simplified 84.3%

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

   7. Taylor expanded in t around 0 62.0%

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

      1. associate-/l* 63.5%

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

   9. Simplified 63.5%

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

   10. Taylor expanded in y around inf 56.4%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+118}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-46}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-278}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-278}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+58}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 5: 49.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - t \cdot \frac{y}{z}\\ t_2 := x + t \cdot \frac{y}{a}\\ t_3 := \frac{x}{\frac{z}{y - a}}\\ \mathbf{if}\;a \leq -6 \cdot 10^{+118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-278}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{-201}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* t (/ y z))))
        (t_2 (+ x (* t (/ y a))))
        (t_3 (/ x (/ z (- y a)))))
   (if (<= a -6e+118)
     t_2
     (if (<= a -5.5e-20)
       t_1
       (if (<= a -4.6e-278)
         t_3
         (if (<= a 2.1e-275)
           t_1
           (if (<= a 1.32e-201) t_3 (if (<= a 5.6e+57) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (t * (y / z));
	double t_2 = x + (t * (y / a));
	double t_3 = x / (z / (y - a));
	double tmp;
	if (a <= -6e+118) {
		tmp = t_2;
	} else if (a <= -5.5e-20) {
		tmp = t_1;
	} else if (a <= -4.6e-278) {
		tmp = t_3;
	} else if (a <= 2.1e-275) {
		tmp = t_1;
	} else if (a <= 1.32e-201) {
		tmp = t_3;
	} else if (a <= 5.6e+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 - (t * (y / z))
    t_2 = x + (t * (y / a))
    t_3 = x / (z / (y - a))
    if (a <= (-6d+118)) then
        tmp = t_2
    else if (a <= (-5.5d-20)) then
        tmp = t_1
    else if (a <= (-4.6d-278)) then
        tmp = t_3
    else if (a <= 2.1d-275) then
        tmp = t_1
    else if (a <= 1.32d-201) then
        tmp = t_3
    else if (a <= 5.6d+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 * (y / z));
	double t_2 = x + (t * (y / a));
	double t_3 = x / (z / (y - a));
	double tmp;
	if (a <= -6e+118) {
		tmp = t_2;
	} else if (a <= -5.5e-20) {
		tmp = t_1;
	} else if (a <= -4.6e-278) {
		tmp = t_3;
	} else if (a <= 2.1e-275) {
		tmp = t_1;
	} else if (a <= 1.32e-201) {
		tmp = t_3;
	} else if (a <= 5.6e+57) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (t * (y / z))
	t_2 = x + (t * (y / a))
	t_3 = x / (z / (y - a))
	tmp = 0
	if a <= -6e+118:
		tmp = t_2
	elif a <= -5.5e-20:
		tmp = t_1
	elif a <= -4.6e-278:
		tmp = t_3
	elif a <= 2.1e-275:
		tmp = t_1
	elif a <= 1.32e-201:
		tmp = t_3
	elif a <= 5.6e+57:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(t * Float64(y / z)))
	t_2 = Float64(x + Float64(t * Float64(y / a)))
	t_3 = Float64(x / Float64(z / Float64(y - a)))
	tmp = 0.0
	if (a <= -6e+118)
		tmp = t_2;
	elseif (a <= -5.5e-20)
		tmp = t_1;
	elseif (a <= -4.6e-278)
		tmp = t_3;
	elseif (a <= 2.1e-275)
		tmp = t_1;
	elseif (a <= 1.32e-201)
		tmp = t_3;
	elseif (a <= 5.6e+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 * (y / z));
	t_2 = x + (t * (y / a));
	t_3 = x / (z / (y - a));
	tmp = 0.0;
	if (a <= -6e+118)
		tmp = t_2;
	elseif (a <= -5.5e-20)
		tmp = t_1;
	elseif (a <= -4.6e-278)
		tmp = t_3;
	elseif (a <= 2.1e-275)
		tmp = t_1;
	elseif (a <= 1.32e-201)
		tmp = t_3;
	elseif (a <= 5.6e+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[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6e+118], t$95$2, If[LessEqual[a, -5.5e-20], t$95$1, If[LessEqual[a, -4.6e-278], t$95$3, If[LessEqual[a, 2.1e-275], t$95$1, If[LessEqual[a, 1.32e-201], t$95$3, If[LessEqual[a, 5.6e+57], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6e118 or 5.59999999999999999e57 < a

   1. Initial program 72.4%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in z around 0 64.4%

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

      1. associate-/l* 76.1%

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

   6. Simplified 76.1%

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

   7. Taylor expanded in t around inf 60.5%

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

      1. associate-*r/ 69.5%

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

   9. Simplified 69.5%

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

   if -6e118 < a < -5.4999999999999996e-20 or -4.60000000000000006e-278 < a < 2.09999999999999988e-275 or 1.31999999999999996e-201 < a < 5.59999999999999999e57

   1. Initial program 61.5%

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

      1. associate-*l/ 74.4%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in z around inf 67.3%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. 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. associate-*r/ 67.3%

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

      3. associate-*r/ 67.3%

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

      4. div-sub 69.4%

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

      5. distribute-lft-out-- 69.4%

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

      6. associate-*r/ 69.4%

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

      7. distribute-rgt-out-- 69.4%

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

      8. mul-1-neg 69.4%

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

      9. unsub-neg 69.4%

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

      10. associate-/l* 74.4%

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

   6. Simplified 74.4%

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

   7. Taylor expanded in y around inf 68.8%

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

   8. Taylor expanded in t around inf 58.9%

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

      1. associate-*r/ 60.9%

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

   10. Simplified 60.9%

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

   if -5.4999999999999996e-20 < a < -4.60000000000000006e-278 or 2.09999999999999988e-275 < a < 1.31999999999999996e-201

   1. Initial program 71.9%

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

      1. associate-*l/ 73.9%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in z around inf 79.4%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. 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. associate-*r/ 79.4%

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

      3. associate-*r/ 79.4%

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

      4. div-sub 80.9%

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

      5. distribute-lft-out-- 80.9%

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

      6. associate-*r/ 80.9%

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

      7. distribute-rgt-out-- 80.9%

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

      8. mul-1-neg 80.9%

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

      9. unsub-neg 80.9%

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

      10. associate-/l* 83.7%

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

   6. Simplified 83.7%

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

   7. Taylor expanded in t around 0 61.3%

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

      1. associate-/l* 62.7%

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

   9. Simplified 62.7%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+118}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-20}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-278}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-275}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+57}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 6: 62.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.95 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-127}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (* t (/ y a)))))
   (if (<= a -3.4e+125)
     t_2
     (if (<= a -5.6e-46)
       t_1
       (if (<= a -2.95e-83)
         (* y (/ (- t x) (- a z)))
         (if (<= a 1.3e-127)
           (+ t (* x (/ y z)))
           (if (<= a 2.7e+69) 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 * (y / a));
	double tmp;
	if (a <= -3.4e+125) {
		tmp = t_2;
	} else if (a <= -5.6e-46) {
		tmp = t_1;
	} else if (a <= -2.95e-83) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.3e-127) {
		tmp = t + (x * (y / z));
	} else if (a <= 2.7e+69) {
		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 * (y / a))
    if (a <= (-3.4d+125)) then
        tmp = t_2
    else if (a <= (-5.6d-46)) then
        tmp = t_1
    else if (a <= (-2.95d-83)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 1.3d-127) then
        tmp = t + (x * (y / z))
    else if (a <= 2.7d+69) 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 * (y / a));
	double tmp;
	if (a <= -3.4e+125) {
		tmp = t_2;
	} else if (a <= -5.6e-46) {
		tmp = t_1;
	} else if (a <= -2.95e-83) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.3e-127) {
		tmp = t + (x * (y / z));
	} else if (a <= 2.7e+69) {
		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 * (y / a))
	tmp = 0
	if a <= -3.4e+125:
		tmp = t_2
	elif a <= -5.6e-46:
		tmp = t_1
	elif a <= -2.95e-83:
		tmp = y * ((t - x) / (a - z))
	elif a <= 1.3e-127:
		tmp = t + (x * (y / z))
	elif a <= 2.7e+69:
		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(y / a)))
	tmp = 0.0
	if (a <= -3.4e+125)
		tmp = t_2;
	elseif (a <= -5.6e-46)
		tmp = t_1;
	elseif (a <= -2.95e-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 <= 2.7e+69)
		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 * (y / a));
	tmp = 0.0;
	if (a <= -3.4e+125)
		tmp = t_2;
	elseif (a <= -5.6e-46)
		tmp = t_1;
	elseif (a <= -2.95e-83)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 1.3e-127)
		tmp = t + (x * (y / z));
	elseif (a <= 2.7e+69)
		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[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.4e+125], t$95$2, If[LessEqual[a, -5.6e-46], t$95$1, If[LessEqual[a, -2.95e-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, 2.7e+69], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.3999999999999999e125 or 2.6999999999999998e69 < a

   1. Initial program 71.9%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in z around 0 64.6%

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

      1. associate-/l* 75.9%

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

   6. Simplified 75.9%

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

   7. Taylor expanded in t around inf 60.5%

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

      1. associate-*r/ 68.9%

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

   9. Simplified 68.9%

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

   if -3.3999999999999999e125 < a < -5.5999999999999997e-46 or 1.29999999999999995e-127 < a < 2.6999999999999998e69

   1. Initial program 63.0%

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

      1. associate-*l/ 76.6%

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

   3. Simplified 76.6%

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

   4. Taylor expanded in x around 0 57.6%

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

      1. associate-*r/ 71.1%

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

   6. Simplified 71.1%

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

   if -5.5999999999999997e-46 < a < -2.9499999999999998e-83

   1. Initial program 64.3%

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

      1. associate-*l/ 64.3%

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

   3. Simplified 64.3%

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

   4. Taylor expanded in y around inf 82.9%

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

      1. div-sub 82.9%

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

   6. Simplified 82.9%

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

   if -2.9499999999999998e-83 < a < 1.29999999999999995e-127

   1. Initial program 69.6%

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

      1. associate-*l/ 74.8%

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

   3. Simplified 74.8%

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

   4. Taylor expanded in z around inf 88.8%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. 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. associate-*r/ 88.8%

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

      3. associate-*r/ 88.8%

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

      4. div-sub 88.8%

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

      5. distribute-lft-out-- 88.8%

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

      6. associate-*r/ 88.8%

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

      7. distribute-rgt-out-- 88.8%

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

      8. mul-1-neg 88.8%

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

      9. unsub-neg 88.8%

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

      10. associate-/l* 87.6%

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

   6. Simplified 87.6%

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

   7. Taylor expanded in y around inf 83.1%

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

   8. Taylor expanded in t around 0 75.7%

      \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot y}{z}} \]
   9. 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%

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

   10. Simplified 74.5%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-46}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -2.95 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-127}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 7: 65.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + t \cdot \frac{y - z}{a}\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-127}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (* t (/ (- y z) a)))))
   (if (<= a -3.4e+125)
     t_2
     (if (<= a -5e-46)
       t_1
       (if (<= a -4.8e-83)
         (* y (/ (- t x) (- a z)))
         (if (<= a 1.35e-127)
           (+ t (* x (/ y z)))
           (if (<= a 4.7e+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 + (t * ((y - z) / a));
	double tmp;
	if (a <= -3.4e+125) {
		tmp = t_2;
	} else if (a <= -5e-46) {
		tmp = t_1;
	} else if (a <= -4.8e-83) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.35e-127) {
		tmp = t + (x * (y / z));
	} else if (a <= 4.7e+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 + (t * ((y - z) / a))
    if (a <= (-3.4d+125)) then
        tmp = t_2
    else if (a <= (-5d-46)) then
        tmp = t_1
    else if (a <= (-4.8d-83)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 1.35d-127) then
        tmp = t + (x * (y / z))
    else if (a <= 4.7d+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 + (t * ((y - z) / a));
	double tmp;
	if (a <= -3.4e+125) {
		tmp = t_2;
	} else if (a <= -5e-46) {
		tmp = t_1;
	} else if (a <= -4.8e-83) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.35e-127) {
		tmp = t + (x * (y / z));
	} else if (a <= 4.7e+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 + (t * ((y - z) / a))
	tmp = 0
	if a <= -3.4e+125:
		tmp = t_2
	elif a <= -5e-46:
		tmp = t_1
	elif a <= -4.8e-83:
		tmp = y * ((t - x) / (a - z))
	elif a <= 1.35e-127:
		tmp = t + (x * (y / z))
	elif a <= 4.7e+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(t * Float64(Float64(y - z) / a)))
	tmp = 0.0
	if (a <= -3.4e+125)
		tmp = t_2;
	elseif (a <= -5e-46)
		tmp = t_1;
	elseif (a <= -4.8e-83)
		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 <= 4.7e+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 + (t * ((y - z) / a));
	tmp = 0.0;
	if (a <= -3.4e+125)
		tmp = t_2;
	elseif (a <= -5e-46)
		tmp = t_1;
	elseif (a <= -4.8e-83)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 1.35e-127)
		tmp = t + (x * (y / z));
	elseif (a <= 4.7e+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[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.4e+125], t$95$2, If[LessEqual[a, -5e-46], t$95$1, If[LessEqual[a, -4.8e-83], 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, 4.7e+64], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.3999999999999999e125 or 4.70000000000000029e64 < a

   1. Initial program 71.9%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in a around inf 83.8%

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

   5. Taylor expanded in t around inf 76.7%

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

      1. associate-/r/ 76.7%

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

   7. Applied egg-rr 76.7%

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

   if -3.3999999999999999e125 < a < -4.99999999999999992e-46 or 1.35e-127 < a < 4.70000000000000029e64

   1. Initial program 63.0%

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

      1. associate-*l/ 76.6%

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

   3. Simplified 76.6%

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

   4. Taylor expanded in x around 0 57.6%

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

      1. associate-*r/ 71.1%

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

   6. Simplified 71.1%

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

   if -4.99999999999999992e-46 < a < -4.8000000000000002e-83

   1. Initial program 64.3%

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

      1. associate-*l/ 64.3%

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

   3. Simplified 64.3%

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

   4. Taylor expanded in y around inf 82.9%

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

      1. div-sub 82.9%

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

   6. Simplified 82.9%

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

   if -4.8000000000000002e-83 < a < 1.35e-127

   1. Initial program 69.6%

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

      1. associate-*l/ 74.8%

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

   3. Simplified 74.8%

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

   4. Taylor expanded in z around inf 88.8%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. 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. associate-*r/ 88.8%

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

      3. associate-*r/ 88.8%

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

      4. div-sub 88.8%

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

      5. distribute-lft-out-- 88.8%

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

      6. associate-*r/ 88.8%

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

      7. distribute-rgt-out-- 88.8%

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

      8. mul-1-neg 88.8%

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

      9. unsub-neg 88.8%

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

      10. associate-/l* 87.6%

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

   6. Simplified 87.6%

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

   7. Taylor expanded in y around inf 83.1%

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

   8. Taylor expanded in t around 0 75.7%

      \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot y}{z}} \]
   9. 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%

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

   10. Simplified 74.5%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-46}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-127}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+64}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \end{array} \]

Alternative 8: 65.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.25 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{-127}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= a -3.4e+125)
     (+ x (* t (/ (- y z) a)))
     (if (<= a -1.55e-46)
       t_1
       (if (<= a -3.25e-83)
         (* y (/ (- t x) (- a z)))
         (if (<= a 1.28e-127)
           (+ t (* x (/ y z)))
           (if (<= a 4.5e+75) 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 <= -3.4e+125) {
		tmp = x + (t * ((y - z) / a));
	} else if (a <= -1.55e-46) {
		tmp = t_1;
	} else if (a <= -3.25e-83) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.28e-127) {
		tmp = t + (x * (y / z));
	} else if (a <= 4.5e+75) {
		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 <= (-3.4d+125)) then
        tmp = x + (t * ((y - z) / a))
    else if (a <= (-1.55d-46)) then
        tmp = t_1
    else if (a <= (-3.25d-83)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 1.28d-127) then
        tmp = t + (x * (y / z))
    else if (a <= 4.5d+75) 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 <= -3.4e+125) {
		tmp = x + (t * ((y - z) / a));
	} else if (a <= -1.55e-46) {
		tmp = t_1;
	} else if (a <= -3.25e-83) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.28e-127) {
		tmp = t + (x * (y / z));
	} else if (a <= 4.5e+75) {
		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 <= -3.4e+125:
		tmp = x + (t * ((y - z) / a))
	elif a <= -1.55e-46:
		tmp = t_1
	elif a <= -3.25e-83:
		tmp = y * ((t - x) / (a - z))
	elif a <= 1.28e-127:
		tmp = t + (x * (y / z))
	elif a <= 4.5e+75:
		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 <= -3.4e+125)
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / a)));
	elseif (a <= -1.55e-46)
		tmp = t_1;
	elseif (a <= -3.25e-83)
		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 <= 4.5e+75)
		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 <= -3.4e+125)
		tmp = x + (t * ((y - z) / a));
	elseif (a <= -1.55e-46)
		tmp = t_1;
	elseif (a <= -3.25e-83)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 1.28e-127)
		tmp = t + (x * (y / z));
	elseif (a <= 4.5e+75)
		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, -3.4e+125], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.55e-46], t$95$1, If[LessEqual[a, -3.25e-83], 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, 4.5e+75], 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 < -3.3999999999999999e125

   1. Initial program 67.5%

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

      1. associate-/l* 97.0%

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

   3. Simplified 97.0%

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

   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%

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

      1. associate-/r/ 82.6%

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

   7. Applied egg-rr 82.6%

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

   if -3.3999999999999999e125 < a < -1.55e-46 or 1.2799999999999999e-127 < a < 4.5000000000000004e75

   1. Initial program 63.0%

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

      1. associate-*l/ 76.6%

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

   3. Simplified 76.6%

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

   4. Taylor expanded in x around 0 57.6%

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

      1. associate-*r/ 71.1%

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

   6. Simplified 71.1%

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

   if -1.55e-46 < a < -3.25e-83

   1. Initial program 64.3%

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

      1. associate-*l/ 64.3%

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

   3. Simplified 64.3%

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

   4. Taylor expanded in y around inf 82.9%

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

      1. div-sub 82.9%

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

   6. Simplified 82.9%

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

   if -3.25e-83 < a < 1.2799999999999999e-127

   1. Initial program 69.6%

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

      1. associate-*l/ 74.8%

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

   3. Simplified 74.8%

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

   4. Taylor expanded in z around inf 88.8%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. 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. associate-*r/ 88.8%

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

      3. associate-*r/ 88.8%

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

      4. div-sub 88.8%

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

      5. distribute-lft-out-- 88.8%

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

      6. associate-*r/ 88.8%

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

      7. distribute-rgt-out-- 88.8%

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

      8. mul-1-neg 88.8%

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

      9. unsub-neg 88.8%

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

      10. associate-/l* 87.6%

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

   6. Simplified 87.6%

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

   7. Taylor expanded in y around inf 83.1%

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

   8. Taylor expanded in t around 0 75.7%

      \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot y}{z}} \]
   9. 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%

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

   10. Simplified 74.5%

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

   if 4.5000000000000004e75 < a

   1. Initial program 74.6%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around 0 65.2%

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

      1. associate-/l* 75.2%

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

   6. 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-46}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -3.25 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{-127}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 9: 37.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-46}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 4.15 \cdot 10^{+58}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+116}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.4e+125)
   x
   (if (<= a -1.1e-46)
     t
     (if (<= a 8e-201)
       (/ x (/ z y))
       (if (<= a 4.15e+58) t (if (<= a 2.3e+116) (* y (/ (- t x) a)) 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 <= -1.1e-46) {
		tmp = t;
	} else if (a <= 8e-201) {
		tmp = x / (z / y);
	} else if (a <= 4.15e+58) {
		tmp = t;
	} else if (a <= 2.3e+116) {
		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) :: tmp
    if (a <= (-3.4d+125)) then
        tmp = x
    else if (a <= (-1.1d-46)) then
        tmp = t
    else if (a <= 8d-201) then
        tmp = x / (z / y)
    else if (a <= 4.15d+58) then
        tmp = t
    else if (a <= 2.3d+116) 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 tmp;
	if (a <= -3.4e+125) {
		tmp = x;
	} else if (a <= -1.1e-46) {
		tmp = t;
	} else if (a <= 8e-201) {
		tmp = x / (z / y);
	} else if (a <= 4.15e+58) {
		tmp = t;
	} else if (a <= 2.3e+116) {
		tmp = y * ((t - x) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.4e+125:
		tmp = x
	elif a <= -1.1e-46:
		tmp = t
	elif a <= 8e-201:
		tmp = x / (z / y)
	elif a <= 4.15e+58:
		tmp = t
	elif a <= 2.3e+116:
		tmp = y * ((t - x) / a)
	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 <= -1.1e-46)
		tmp = t;
	elseif (a <= 8e-201)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 4.15e+58)
		tmp = t;
	elseif (a <= 2.3e+116)
		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)
	tmp = 0.0;
	if (a <= -3.4e+125)
		tmp = x;
	elseif (a <= -1.1e-46)
		tmp = t;
	elseif (a <= 8e-201)
		tmp = x / (z / y);
	elseif (a <= 4.15e+58)
		tmp = t;
	elseif (a <= 2.3e+116)
		tmp = y * ((t - x) / a);
	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, -1.1e-46], t, If[LessEqual[a, 8e-201], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.15e+58], t, If[LessEqual[a, 2.3e+116], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.3999999999999999e125 or 2.29999999999999995e116 < a

   1. Initial program 70.8%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in a around inf 58.6%

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

   if -3.3999999999999999e125 < a < -1.1e-46 or 7.99999999999999957e-201 < a < 4.1499999999999998e58

   1. Initial program 62.0%

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

      1. associate-*l/ 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in z around inf 43.0%

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

   if -1.1e-46 < a < 7.99999999999999957e-201

   1. Initial program 69.5%

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

      1. associate-*l/ 72.6%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in z around inf 84.0%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. 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. associate-*r/ 84.0%

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

      3. associate-*r/ 84.0%

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

      4. div-sub 85.3%

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

      5. distribute-lft-out-- 85.3%

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

      6. associate-*r/ 85.3%

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

      7. distribute-rgt-out-- 85.3%

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

      8. mul-1-neg 85.3%

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

      9. unsub-neg 85.3%

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

      10. associate-/l* 86.6%

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

   6. Simplified 86.6%

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

   7. Taylor expanded in t around 0 55.7%

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

      1. associate-/l* 57.0%

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

   9. Simplified 57.0%

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

   10. Taylor expanded in y around inf 51.0%

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

   if 4.1499999999999998e58 < a < 2.29999999999999995e116

   1. Initial program 86.1%

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

      1. associate-*l/ 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 67.7%

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

   5. 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 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-46}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 4.15 \cdot 10^{+58}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+116}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 62.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-127}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (* t (/ y a)))))
   (if (<= a -3.4e+125)
     t_2
     (if (<= a -1.25e-44)
       t_1
       (if (<= a 1.35e-127)
         (+ t (* x (/ y z)))
         (if (<= a 8.5e+68) 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 * (y / a));
	double tmp;
	if (a <= -3.4e+125) {
		tmp = t_2;
	} else if (a <= -1.25e-44) {
		tmp = t_1;
	} else if (a <= 1.35e-127) {
		tmp = t + (x * (y / z));
	} else if (a <= 8.5e+68) {
		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 * (y / a))
    if (a <= (-3.4d+125)) then
        tmp = t_2
    else if (a <= (-1.25d-44)) then
        tmp = t_1
    else if (a <= 1.35d-127) then
        tmp = t + (x * (y / z))
    else if (a <= 8.5d+68) 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 * (y / a));
	double tmp;
	if (a <= -3.4e+125) {
		tmp = t_2;
	} else if (a <= -1.25e-44) {
		tmp = t_1;
	} else if (a <= 1.35e-127) {
		tmp = t + (x * (y / z));
	} else if (a <= 8.5e+68) {
		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 * (y / a))
	tmp = 0
	if a <= -3.4e+125:
		tmp = t_2
	elif a <= -1.25e-44:
		tmp = t_1
	elif a <= 1.35e-127:
		tmp = t + (x * (y / z))
	elif a <= 8.5e+68:
		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(y / a)))
	tmp = 0.0
	if (a <= -3.4e+125)
		tmp = t_2;
	elseif (a <= -1.25e-44)
		tmp = t_1;
	elseif (a <= 1.35e-127)
		tmp = Float64(t + Float64(x * Float64(y / z)));
	elseif (a <= 8.5e+68)
		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 * (y / a));
	tmp = 0.0;
	if (a <= -3.4e+125)
		tmp = t_2;
	elseif (a <= -1.25e-44)
		tmp = t_1;
	elseif (a <= 1.35e-127)
		tmp = t + (x * (y / z));
	elseif (a <= 8.5e+68)
		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[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.4e+125], t$95$2, If[LessEqual[a, -1.25e-44], t$95$1, If[LessEqual[a, 1.35e-127], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e+68], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.3999999999999999e125 or 8.49999999999999966e68 < a

   1. Initial program 71.9%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in z around 0 64.6%

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

      1. associate-/l* 75.9%

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

   6. Simplified 75.9%

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

   7. Taylor expanded in t around inf 60.5%

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

      1. associate-*r/ 68.9%

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

   9. Simplified 68.9%

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

   if -3.3999999999999999e125 < a < -1.2500000000000001e-44 or 1.35e-127 < a < 8.49999999999999966e68

   1. Initial program 63.7%

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

      1. associate-*l/ 76.3%

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

   3. Simplified 76.3%

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

   4. Taylor expanded in x around 0 58.2%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   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 -1.2500000000000001e-44 < a < 1.35e-127

   1. Initial program 68.3%

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

      1. associate-*l/ 73.8%

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

   3. Simplified 73.8%

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

   4. Taylor expanded in z around inf 81.8%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. 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. associate-*r/ 81.8%

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

      3. associate-*r/ 81.8%

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

      4. div-sub 82.9%

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

      5. distribute-lft-out-- 82.9%

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

      6. associate-*r/ 82.9%

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

      7. distribute-rgt-out-- 82.9%

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

      8. mul-1-neg 82.9%

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

      9. unsub-neg 82.9%

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

      10. associate-/l* 83.9%

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

   6. Simplified 83.9%

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

   7. Taylor expanded in y around inf 78.6%

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

   8. Taylor expanded in t around 0 71.1%

      \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot y}{z}} \]
   9. 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%

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

   10. Simplified 71.1%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-44}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-127}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 11: 69.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+125}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+57}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.5e+125)
   (+ x (* t (/ (- y z) a)))
   (if (<= a -1.2e-45)
     (* t (/ (- y z) (- a z)))
     (if (<= a -4.5e-84)
       (* y (/ (- t x) (- a z)))
       (if (<= a 2.8e+57)
         (- t (/ (- t x) (/ z y)))
         (+ x (/ y (/ a (- t x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.5e+125) {
		tmp = x + (t * ((y - z) / a));
	} else if (a <= -1.2e-45) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= -4.5e-84) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 2.8e+57) {
		tmp = t - ((t - x) / (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 <= (-3.5d+125)) then
        tmp = x + (t * ((y - z) / a))
    else if (a <= (-1.2d-45)) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= (-4.5d-84)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 2.8d+57) then
        tmp = t - ((t - x) / (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 <= -3.5e+125) {
		tmp = x + (t * ((y - z) / a));
	} else if (a <= -1.2e-45) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= -4.5e-84) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 2.8e+57) {
		tmp = t - ((t - x) / (z / y));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.5e+125:
		tmp = x + (t * ((y - z) / a))
	elif a <= -1.2e-45:
		tmp = t * ((y - z) / (a - z))
	elif a <= -4.5e-84:
		tmp = y * ((t - x) / (a - z))
	elif a <= 2.8e+57:
		tmp = t - ((t - x) / (z / y))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.5e+125)
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / a)));
	elseif (a <= -1.2e-45)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= -4.5e-84)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 2.8e+57)
		tmp = Float64(t - Float64(Float64(t - x) / 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 <= -3.5e+125)
		tmp = x + (t * ((y - z) / a));
	elseif (a <= -1.2e-45)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= -4.5e-84)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 2.8e+57)
		tmp = t - ((t - x) / (z / y));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.5e+125], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.2e-45], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.5e-84], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e+57], N[(t - N[(N[(t - x), $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 < -3.50000000000000011e125

   1. Initial program 67.5%

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

      1. associate-/l* 97.0%

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

   3. Simplified 97.0%

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

   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%

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

      1. associate-/r/ 82.6%

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

   7. Applied egg-rr 82.6%

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

   if -3.50000000000000011e125 < a < -1.19999999999999995e-45

   1. Initial program 64.3%

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

      1. associate-*l/ 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in x around 0 57.9%

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

      1. associate-*r/ 69.5%

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

   6. Simplified 69.5%

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

   if -1.19999999999999995e-45 < a < -4.50000000000000016e-84

   1. Initial program 64.3%

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

      1. associate-*l/ 64.3%

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

   3. Simplified 64.3%

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

   4. Taylor expanded in y around inf 82.9%

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

      1. div-sub 82.9%

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

   6. Simplified 82.9%

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

   if -4.50000000000000016e-84 < a < 2.8e57

   1. Initial program 65.8%

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

      1. associate-*l/ 74.9%

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

   3. Simplified 74.9%

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

   4. Taylor expanded in z around inf 81.2%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. 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. associate-*r/ 81.2%

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

      3. associate-*r/ 81.2%

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

      4. div-sub 81.2%

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

      5. distribute-lft-out-- 81.2%

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

      6. associate-*r/ 81.2%

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

      7. distribute-rgt-out-- 81.2%

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

      8. mul-1-neg 81.2%

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

      9. unsub-neg 81.2%

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

      10. associate-/l* 82.8%

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

   6. Simplified 82.8%

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

   7. Taylor expanded in y around inf 77.0%

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

   if 2.8e57 < a

   1. Initial program 76.3%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in z around 0 65.8%

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

      1. associate-/l* 75.2%

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

   6. 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+125}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+57}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 12: 69.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-47}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+57}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.4e+125)
   (+ x (* t (/ (- y z) a)))
   (if (<= a -7.6e-47)
     (/ t (/ (- a z) (- y z)))
     (if (<= a -4.8e-83)
       (* y (/ (- t x) (- a z)))
       (if (<= a 2.8e+57)
         (- t (/ (- t x) (/ 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 + (t * ((y - z) / a));
	} else if (a <= -7.6e-47) {
		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 - ((t - x) / (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 + (t * ((y - z) / a))
    else if (a <= (-7.6d-47)) then
        tmp = t / ((a - z) / (y - z))
    else if (a <= (-4.8d-83)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 2.8d+57) then
        tmp = t - ((t - x) / (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 + (t * ((y - z) / a));
	} else if (a <= -7.6e-47) {
		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 - ((t - x) / (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 + (t * ((y - z) / a))
	elif a <= -7.6e-47:
		tmp = t / ((a - z) / (y - z))
	elif a <= -4.8e-83:
		tmp = y * ((t - x) / (a - z))
	elif a <= 2.8e+57:
		tmp = t - ((t - x) / (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(t * Float64(Float64(y - z) / a)));
	elseif (a <= -7.6e-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 <= 2.8e+57)
		tmp = Float64(t - Float64(Float64(t - x) / 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 + (t * ((y - z) / a));
	elseif (a <= -7.6e-47)
		tmp = t / ((a - z) / (y - z));
	elseif (a <= -4.8e-83)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 2.8e+57)
		tmp = t - ((t - x) / (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[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.6e-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, 2.8e+57], N[(t - N[(N[(t - x), $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 67.5%

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

      1. associate-/l* 97.0%

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

   3. Simplified 97.0%

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

   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%

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

      1. associate-/r/ 82.6%

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

   7. Applied egg-rr 82.6%

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

   if -3.3999999999999999e125 < a < -7.60000000000000029e-47

   1. Initial program 64.3%

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

      1. associate-*l/ 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in x around 0 57.9%

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

      1. associate-/l* 69.5%

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

   6. Simplified 69.5%

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

   if -7.60000000000000029e-47 < a < -4.8000000000000002e-83

   1. Initial program 64.3%

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

      1. associate-*l/ 64.3%

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

   3. Simplified 64.3%

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

   4. Taylor expanded in y around inf 82.9%

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

      1. div-sub 82.9%

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

   6. Simplified 82.9%

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

   if -4.8000000000000002e-83 < a < 2.8e57

   1. Initial program 65.8%

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

      1. associate-*l/ 74.9%

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

   3. Simplified 74.9%

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

   4. Taylor expanded in z around inf 81.2%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. 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. associate-*r/ 81.2%

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

      3. associate-*r/ 81.2%

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

      4. div-sub 81.2%

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

      5. distribute-lft-out-- 81.2%

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

      6. associate-*r/ 81.2%

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

      7. distribute-rgt-out-- 81.2%

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

      8. mul-1-neg 81.2%

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

      9. unsub-neg 81.2%

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

      10. associate-/l* 82.8%

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

   6. Simplified 82.8%

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

   7. Taylor expanded in y around inf 77.0%

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

   if 2.8e57 < a

   1. Initial program 76.3%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in z around 0 65.8%

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

      1. associate-/l* 75.2%

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

   6. 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-47}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+57}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 13: 71.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+78} \lor \neg \left(z \leq 3.6 \cdot 10^{+46}\right):\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.9e+78) (not (<= z 3.6e+46)))
   (- t (* x (/ (- a y) z)))
   (+ x (/ (- y z) (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.9e+78) || !(z <= 3.6e+46)) {
		tmp = t - (x * ((a - y) / z));
	} else {
		tmp = x + ((y - z) / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.9d+78)) .or. (.not. (z <= 3.6d+46))) then
        tmp = t - (x * ((a - y) / z))
    else
        tmp = x + ((y - z) / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.9e+78) || !(z <= 3.6e+46)) {
		tmp = t - (x * ((a - y) / z));
	} else {
		tmp = x + ((y - z) / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.9e+78) or not (z <= 3.6e+46):
		tmp = t - (x * ((a - y) / z))
	else:
		tmp = x + ((y - z) / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.9e+78) || !(z <= 3.6e+46))
		tmp = Float64(t - Float64(x * Float64(Float64(a - y) / z)));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.9e+78) || ~((z <= 3.6e+46)))
		tmp = t - (x * ((a - y) / z));
	else
		tmp = x + ((y - z) / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.9e+78], N[Not[LessEqual[z, 3.6e+46]], $MachinePrecision]], N[(t - N[(x * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9e78 or 3.5999999999999999e46 < z

   1. Initial program 40.7%

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

      1. associate-*l/ 68.1%

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

   3. Simplified 68.1%

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

   4. Taylor expanded in z around inf 68.3%

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

      1. associate--l+ 68.3%

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

      2. associate-*r/ 68.3%

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

      3. associate-*r/ 68.3%

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

      4. div-sub 68.3%

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

      5. distribute-lft-out-- 68.3%

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

      6. associate-*r/ 68.3%

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

      7. distribute-rgt-out-- 68.4%

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

      8. mul-1-neg 68.4%

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

      9. unsub-neg 68.4%

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

      10. associate-/l* 81.0%

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

   6. Simplified 81.0%

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

   7. Taylor expanded in t around 0 72.0%

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

      1. associate-*r/ 76.7%

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

      2. neg-mul-1 76.7%

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

      3. distribute-rgt-neg-in 76.7%

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

      4. distribute-neg-frac 76.7%

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

   9. Simplified 76.7%

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

   if -1.9e78 < z < 3.5999999999999999e46

   1. Initial program 85.0%

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

      1. associate-/l* 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in a around inf 72.9%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+78} \lor \neg \left(z \leq 3.6 \cdot 10^{+46}\right):\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 14: 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 72.4%

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

      1. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   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 65.7%

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

      1. associate-*l/ 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in z around inf 72.2%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. 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. associate-*r/ 72.2%

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

      3. associate-*r/ 72.2%

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

      4. div-sub 74.1%

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

      5. distribute-lft-out-- 74.1%

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

      6. associate-*r/ 74.1%

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

      7. distribute-rgt-out-- 74.1%

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

      8. mul-1-neg 74.1%

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

      9. unsub-neg 74.1%

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

      10. associate-/l* 78.2%

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

   6. 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 15: 36.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-47}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-199}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+58}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.4e+125)
   x
   (if (<= a -6.5e-47)
     t
     (if (<= a 8.2e-199) (* y (/ x z)) (if (<= a 7.2e+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 <= -6.5e-47) {
		tmp = t;
	} else if (a <= 8.2e-199) {
		tmp = y * (x / z);
	} else if (a <= 7.2e+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 <= (-6.5d-47)) then
        tmp = t
    else if (a <= 8.2d-199) then
        tmp = y * (x / z)
    else if (a <= 7.2d+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 <= -6.5e-47) {
		tmp = t;
	} else if (a <= 8.2e-199) {
		tmp = y * (x / z);
	} else if (a <= 7.2e+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 <= -6.5e-47:
		tmp = t
	elif a <= 8.2e-199:
		tmp = y * (x / z)
	elif a <= 7.2e+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 <= -6.5e-47)
		tmp = t;
	elseif (a <= 8.2e-199)
		tmp = Float64(y * Float64(x / z));
	elseif (a <= 7.2e+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 <= -6.5e-47)
		tmp = t;
	elseif (a <= 8.2e-199)
		tmp = y * (x / z);
	elseif (a <= 7.2e+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, -6.5e-47], t, If[LessEqual[a, 8.2e-199], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.2e+58], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.3999999999999999e125 or 7.19999999999999993e58 < a

   1. Initial program 73.1%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in a around inf 52.9%

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

   if -3.3999999999999999e125 < a < -6.5000000000000004e-47 or 8.20000000000000043e-199 < a < 7.19999999999999993e58

   1. Initial program 62.0%

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

      1. associate-*l/ 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in z around inf 43.0%

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

   if -6.5000000000000004e-47 < a < 8.20000000000000043e-199

   1. Initial program 69.5%

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

      1. associate-*l/ 72.6%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in z around inf 84.0%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. 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. associate-*r/ 84.0%

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

      3. associate-*r/ 84.0%

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

      4. div-sub 85.3%

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

      5. distribute-lft-out-- 85.3%

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

      6. associate-*r/ 85.3%

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

      7. distribute-rgt-out-- 85.3%

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

      8. mul-1-neg 85.3%

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

      9. unsub-neg 85.3%

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

      10. associate-/l* 86.6%

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

   6. Simplified 86.6%

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

   7. Taylor expanded in t around 0 55.7%

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

      1. associate-/l* 57.0%

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

   9. Simplified 57.0%

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

   10. Taylor expanded in y around inf 49.6%

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

       1. associate-*l/ 48.9%

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

       2. *-commutative 48.9%

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

   12. Simplified 48.9%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-47}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-199}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+58}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 37.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{-47}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+57}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.4e+125)
   x
   (if (<= a -8.6e-47)
     t
     (if (<= a 2e-201) (/ x (/ z y)) (if (<= a 7e+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 <= -8.6e-47) {
		tmp = t;
	} else if (a <= 2e-201) {
		tmp = x / (z / y);
	} else if (a <= 7e+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 <= (-8.6d-47)) then
        tmp = t
    else if (a <= 2d-201) then
        tmp = x / (z / y)
    else if (a <= 7d+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 <= -8.6e-47) {
		tmp = t;
	} else if (a <= 2e-201) {
		tmp = x / (z / y);
	} else if (a <= 7e+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 <= -8.6e-47:
		tmp = t
	elif a <= 2e-201:
		tmp = x / (z / y)
	elif a <= 7e+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 <= -8.6e-47)
		tmp = t;
	elseif (a <= 2e-201)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 7e+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 <= -8.6e-47)
		tmp = t;
	elseif (a <= 2e-201)
		tmp = x / (z / y);
	elseif (a <= 7e+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, -8.6e-47], t, If[LessEqual[a, 2e-201], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e+57], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.3999999999999999e125 or 6.9999999999999995e57 < a

   1. Initial program 73.1%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in a around inf 52.9%

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

   if -3.3999999999999999e125 < a < -8.5999999999999995e-47 or 1.99999999999999989e-201 < a < 6.9999999999999995e57

   1. Initial program 62.0%

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

      1. associate-*l/ 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in z around inf 43.0%

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

   if -8.5999999999999995e-47 < a < 1.99999999999999989e-201

   1. Initial program 69.5%

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

      1. associate-*l/ 72.6%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in z around inf 84.0%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. 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. associate-*r/ 84.0%

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

      3. associate-*r/ 84.0%

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

      4. div-sub 85.3%

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

      5. distribute-lft-out-- 85.3%

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

      6. associate-*r/ 85.3%

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

      7. distribute-rgt-out-- 85.3%

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

      8. mul-1-neg 85.3%

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

      9. unsub-neg 85.3%

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

      10. associate-/l* 86.6%

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

   6. Simplified 86.6%

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

   7. Taylor expanded in t around 0 55.7%

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

      1. associate-/l* 57.0%

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

   9. Simplified 57.0%

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

   10. Taylor expanded in y around inf 51.0%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{-47}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+57}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 53.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+81} \lor \neg \left(z \leq 1.25 \cdot 10^{+93}\right):\\ \;\;\;\;t + \frac{a}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.45e+81) (not (<= z 1.25e+93)))
   (+ t (/ a (/ z t)))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.45e+81) || !(z <= 1.25e+93)) {
		tmp = t + (a / (z / t));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.45d+81)) .or. (.not. (z <= 1.25d+93))) then
        tmp = t + (a / (z / t))
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.45e+81) || !(z <= 1.25e+93)) {
		tmp = t + (a / (z / t));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.45e+81) or not (z <= 1.25e+93):
		tmp = t + (a / (z / t))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.45e+81) || !(z <= 1.25e+93))
		tmp = Float64(t + Float64(a / Float64(z / t)));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.45e+81) || ~((z <= 1.25e+93)))
		tmp = t + (a / (z / t));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.45e+81], N[Not[LessEqual[z, 1.25e+93]], $MachinePrecision]], N[(t + N[(a / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45e81 or 1.25e93 < z

   1. Initial program 37.6%

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

      1. associate-*l/ 67.5%

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

   3. Simplified 67.5%

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

   4. Taylor expanded in z around inf 68.6%

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

      1. associate--l+ 68.6%

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

      2. associate-*r/ 68.6%

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

      3. associate-*r/ 68.6%

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

      4. div-sub 68.6%

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

      5. distribute-lft-out-- 68.6%

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

      6. associate-*r/ 68.6%

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

      7. distribute-rgt-out-- 68.7%

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

      8. mul-1-neg 68.7%

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

      9. unsub-neg 68.7%

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

      10. associate-/l* 83.5%

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

   6. Simplified 83.5%

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

   7. Taylor expanded in y around 0 60.2%

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

      1. sub-neg 60.2%

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

      2. mul-1-neg 60.2%

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

      3. remove-double-neg 60.2%

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

      4. associate-/l* 65.6%

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

   9. Simplified 65.6%

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

   10. Taylor expanded in t around inf 54.9%

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

       1. associate-/l* 60.3%

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

   12. Simplified 60.3%

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

   if -1.45e81 < z < 1.25e93

   1. Initial program 82.9%

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

      1. associate-*l/ 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in z around 0 59.8%

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

      1. associate-/l* 63.6%

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

   6. Simplified 63.6%

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

   7. Taylor expanded in t around inf 47.1%

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

      1. associate-*r/ 52.6%

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

   9. Simplified 52.6%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+81} \lor \neg \left(z \leq 1.25 \cdot 10^{+93}\right):\\ \;\;\;\;t + \frac{a}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 18: 58.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+118} \lor \neg \left(a \leq 4.2 \cdot 10^{+57}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6e+118) (not (<= a 4.2e+57)))
   (+ x (* t (/ y a)))
   (+ t (* x (/ y z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6e+118) || !(a <= 4.2e+57)) {
		tmp = x + (t * (y / a));
	} 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 <= 4.2d+57))) then
        tmp = x + (t * (y / a))
    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 <= 4.2e+57)) {
		tmp = x + (t * (y / a));
	} 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 <= 4.2e+57):
		tmp = x + (t * (y / a))
	else:
		tmp = t + (x * (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -6e+118) || !(a <= 4.2e+57))
		tmp = Float64(x + Float64(t * Float64(y / a)));
	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 <= 4.2e+57)))
		tmp = x + (t * (y / a));
	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, 4.2e+57]], $MachinePrecision]], N[(x + N[(t * N[(y / a), $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 4.19999999999999982e57 < a

   1. Initial program 72.4%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in z around 0 64.4%

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

      1. associate-/l* 76.1%

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

   6. Simplified 76.1%

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

   7. Taylor expanded in t around inf 60.5%

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

      1. associate-*r/ 69.5%

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

   9. Simplified 69.5%

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

   if -6e118 < a < 4.19999999999999982e57

   1. Initial program 65.7%

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

      1. associate-*l/ 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in z around inf 72.2%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   5. 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. associate-*r/ 72.2%

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

      3. associate-*r/ 72.2%

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

      4. div-sub 74.1%

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

      5. distribute-lft-out-- 74.1%

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

      6. associate-*r/ 74.1%

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

      7. distribute-rgt-out-- 74.1%

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

      8. mul-1-neg 74.1%

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

      9. unsub-neg 74.1%

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

      10. associate-/l* 78.2%

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

   6. Simplified 78.2%

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

   7. Taylor expanded in y around inf 70.7%

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

   8. Taylor expanded in t around 0 60.4%

      \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot y}{z}} \]
   9. 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%

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

   10. Simplified 62.8%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+118} \lor \neg \left(a \leq 4.2 \cdot 10^{+57}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 19: 38.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.1 \cdot 10^{+59}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.4e+125) x (if (<= a 6.1e+59) 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 <= 6.1e+59) {
		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 <= 6.1d+59) 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 <= 6.1e+59) {
		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 <= 6.1e+59:
		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 <= 6.1e+59)
		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 <= 6.1e+59)
		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, 6.1e+59], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.3999999999999999e125 or 6.09999999999999973e59 < a

   1. Initial program 73.1%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in a around inf 52.9%

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

   if -3.3999999999999999e125 < a < 6.09999999999999973e59

   1. Initial program 65.4%

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

      1. associate-*l/ 74.3%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in z around inf 35.2%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.1 \cdot 10^{+59}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 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 68.2%

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

   1. associate-*l/ 82.7%

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

3. Simplified 82.7%

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

4. Taylor expanded in z around inf 27.0%

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

5. Final simplification 27.0%

   \[\leadsto t \]

Developer target: 84.2% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023320 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

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

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