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

Percentage Accurate: 67.4% → 90.0%

Time: 28.0s

Alternatives: 26

Speedup: 0.8×

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: 67.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{a - z}\\ \mathbf{if}\;t \leq -7 \cdot 10^{+15}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+63}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z} - x \cdot \left(\frac{y}{a - z} + \frac{-1 - {t_1}^{3}}{1 + \left({t_1}^{2} - t_1\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ z (- a z))))
   (if (<= t -7e+15)
     (+ x (* (/ (- y z) (- a z)) (- t x)))
     (if (<= t 2.9e+63)
       (-
        (/ (* t (- y z)) (- a z))
        (*
         x
         (+
          (/ y (- a z))
          (/ (- -1.0 (pow t_1 3.0)) (+ 1.0 (- (pow t_1 2.0) t_1))))))
       (+ x (/ (- y z) (/ (- a z) (- t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z / (a - z);
	double tmp;
	if (t <= -7e+15) {
		tmp = x + (((y - z) / (a - z)) * (t - x));
	} else if (t <= 2.9e+63) {
		tmp = ((t * (y - z)) / (a - z)) - (x * ((y / (a - z)) + ((-1.0 - pow(t_1, 3.0)) / (1.0 + (pow(t_1, 2.0) - t_1)))));
	} else {
		tmp = x + ((y - z) / ((a - z) / (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 = z / (a - z)
    if (t <= (-7d+15)) then
        tmp = x + (((y - z) / (a - z)) * (t - x))
    else if (t <= 2.9d+63) then
        tmp = ((t * (y - z)) / (a - z)) - (x * ((y / (a - z)) + (((-1.0d0) - (t_1 ** 3.0d0)) / (1.0d0 + ((t_1 ** 2.0d0) - t_1)))))
    else
        tmp = x + ((y - z) / ((a - z) / (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 = z / (a - z);
	double tmp;
	if (t <= -7e+15) {
		tmp = x + (((y - z) / (a - z)) * (t - x));
	} else if (t <= 2.9e+63) {
		tmp = ((t * (y - z)) / (a - z)) - (x * ((y / (a - z)) + ((-1.0 - Math.pow(t_1, 3.0)) / (1.0 + (Math.pow(t_1, 2.0) - t_1)))));
	} else {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z / (a - z)
	tmp = 0
	if t <= -7e+15:
		tmp = x + (((y - z) / (a - z)) * (t - x))
	elif t <= 2.9e+63:
		tmp = ((t * (y - z)) / (a - z)) - (x * ((y / (a - z)) + ((-1.0 - math.pow(t_1, 3.0)) / (1.0 + (math.pow(t_1, 2.0) - t_1)))))
	else:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z / Float64(a - z))
	tmp = 0.0
	if (t <= -7e+15)
		tmp = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * Float64(t - x)));
	elseif (t <= 2.9e+63)
		tmp = Float64(Float64(Float64(t * Float64(y - z)) / Float64(a - z)) - Float64(x * Float64(Float64(y / Float64(a - z)) + Float64(Float64(-1.0 - (t_1 ^ 3.0)) / Float64(1.0 + Float64((t_1 ^ 2.0) - t_1))))));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z / (a - z);
	tmp = 0.0;
	if (t <= -7e+15)
		tmp = x + (((y - z) / (a - z)) * (t - x));
	elseif (t <= 2.9e+63)
		tmp = ((t * (y - z)) / (a - z)) - (x * ((y / (a - z)) + ((-1.0 - (t_1 ^ 3.0)) / (1.0 + ((t_1 ^ 2.0) - t_1)))));
	else
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e+15], N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e+63], N[(N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] + N[(N[(-1.0 - N[Power[t$95$1, 3.0], $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(N[Power[t$95$1, 2.0], $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7e15

   1. Initial program 72.5%

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

      1. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

   if -7e15 < t < 2.8999999999999999e63

   1. Initial program 66.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 x around -inf 92.1%

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

      1. flip3-+ 92.1%

         \[\leadsto -1 \cdot \left(x \cdot \left(\frac{y}{a - z} - \color{blue}{\frac{{1}^{3} + {\left(\frac{z}{a - z}\right)}^{3}}{1 \cdot 1 + \left(\frac{z}{a - z} \cdot \frac{z}{a - z} - 1 \cdot \frac{z}{a - z}\right)}}\right)\right) + \frac{t \cdot \left(y - z\right)}{a - z} \]

      2. metadata-eval 92.1%

         \[\leadsto -1 \cdot \left(x \cdot \left(\frac{y}{a - z} - \frac{\color{blue}{1} + {\left(\frac{z}{a - z}\right)}^{3}}{1 \cdot 1 + \left(\frac{z}{a - z} \cdot \frac{z}{a - z} - 1 \cdot \frac{z}{a - z}\right)}\right)\right) + \frac{t \cdot \left(y - z\right)}{a - z} \]

      3. metadata-eval 92.1%

         \[\leadsto -1 \cdot \left(x \cdot \left(\frac{y}{a - z} - \frac{1 + {\left(\frac{z}{a - z}\right)}^{3}}{\color{blue}{1} + \left(\frac{z}{a - z} \cdot \frac{z}{a - z} - 1 \cdot \frac{z}{a - z}\right)}\right)\right) + \frac{t \cdot \left(y - z\right)}{a - z} \]

      4. pow2 92.1%

         \[\leadsto -1 \cdot \left(x \cdot \left(\frac{y}{a - z} - \frac{1 + {\left(\frac{z}{a - z}\right)}^{3}}{1 + \left(\color{blue}{{\left(\frac{z}{a - z}\right)}^{2}} - 1 \cdot \frac{z}{a - z}\right)}\right)\right) + \frac{t \cdot \left(y - z\right)}{a - z} \]

      5. *-un-lft-identity 92.1%

         \[\leadsto -1 \cdot \left(x \cdot \left(\frac{y}{a - z} - \frac{1 + {\left(\frac{z}{a - z}\right)}^{3}}{1 + \left({\left(\frac{z}{a - z}\right)}^{2} - \color{blue}{\frac{z}{a - z}}\right)}\right)\right) + \frac{t \cdot \left(y - z\right)}{a - z} \]

   6. Applied egg-rr 92.1%

      \[\leadsto -1 \cdot \left(x \cdot \left(\frac{y}{a - z} - \color{blue}{\frac{1 + {\left(\frac{z}{a - z}\right)}^{3}}{1 + \left({\left(\frac{z}{a - z}\right)}^{2} - \frac{z}{a - z}\right)}}\right)\right) + \frac{t \cdot \left(y - z\right)}{a - z} \]

   if 2.8999999999999999e63 < t

   1. Initial program 63.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+15}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+63}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z} - x \cdot \left(\frac{y}{a - z} + \frac{-1 - {\left(\frac{z}{a - z}\right)}^{3}}{1 + \left({\left(\frac{z}{a - z}\right)}^{2} - \frac{z}{a - z}\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]

Alternative 2: 89.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+70}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z} - x \cdot \left(\frac{y}{a - z} - \log \left(e^{1 + \frac{z}{a - z}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.8e+16)
   (+ x (* (/ (- y z) (- a z)) (- t x)))
   (if (<= t 6.6e+70)
     (-
      (/ (* t (- y z)) (- a z))
      (* x (- (/ y (- a z)) (log (exp (+ 1.0 (/ z (- a z))))))))
     (+ x (/ (- y z) (/ (- a z) (- t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+16) {
		tmp = x + (((y - z) / (a - z)) * (t - x));
	} else if (t <= 6.6e+70) {
		tmp = ((t * (y - z)) / (a - z)) - (x * ((y / (a - z)) - log(exp((1.0 + (z / (a - z)))))));
	} else {
		tmp = x + ((y - z) / ((a - z) / (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 (t <= (-2.8d+16)) then
        tmp = x + (((y - z) / (a - z)) * (t - x))
    else if (t <= 6.6d+70) then
        tmp = ((t * (y - z)) / (a - z)) - (x * ((y / (a - z)) - log(exp((1.0d0 + (z / (a - z)))))))
    else
        tmp = x + ((y - z) / ((a - z) / (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 (t <= -2.8e+16) {
		tmp = x + (((y - z) / (a - z)) * (t - x));
	} else if (t <= 6.6e+70) {
		tmp = ((t * (y - z)) / (a - z)) - (x * ((y / (a - z)) - Math.log(Math.exp((1.0 + (z / (a - z)))))));
	} else {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.8e+16:
		tmp = x + (((y - z) / (a - z)) * (t - x))
	elif t <= 6.6e+70:
		tmp = ((t * (y - z)) / (a - z)) - (x * ((y / (a - z)) - math.log(math.exp((1.0 + (z / (a - z)))))))
	else:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8e+16)
		tmp = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * Float64(t - x)));
	elseif (t <= 6.6e+70)
		tmp = Float64(Float64(Float64(t * Float64(y - z)) / Float64(a - z)) - Float64(x * Float64(Float64(y / Float64(a - z)) - log(exp(Float64(1.0 + Float64(z / Float64(a - z))))))));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.8e+16)
		tmp = x + (((y - z) / (a - z)) * (t - x));
	elseif (t <= 6.6e+70)
		tmp = ((t * (y - z)) / (a - z)) - (x * ((y / (a - z)) - log(exp((1.0 + (z / (a - z)))))));
	else
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8e+16], N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.6e+70], N[(N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] - N[Log[N[Exp[N[(1.0 + N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.8e16

   1. Initial program 72.5%

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

      1. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

   if -2.8e16 < t < 6.60000000000000033e70

   1. Initial program 66.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 x around -inf 92.1%

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

      1. add-log-exp 92.1%

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

   6. Applied egg-rr 92.1%

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

   if 6.60000000000000033e70 < t

   1. Initial program 63.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+70}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z} - x \cdot \left(\frac{y}{a - z} - \log \left(e^{1 + \frac{z}{a - z}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]

Alternative 3: 89.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+17}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+71}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z} + x \cdot \left(\left(1 + \frac{z}{a - z}\right) - \frac{y}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4e+17)
   (+ x (* (/ (- y z) (- a z)) (- t x)))
   (if (<= t 2.9e+71)
     (+
      (/ (* t (- y z)) (- a z))
      (* x (- (+ 1.0 (/ z (- a z))) (/ y (- a z)))))
     (+ x (/ (- y z) (/ (- a z) (- t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4e+17) {
		tmp = x + (((y - z) / (a - z)) * (t - x));
	} else if (t <= 2.9e+71) {
		tmp = ((t * (y - z)) / (a - z)) + (x * ((1.0 + (z / (a - z))) - (y / (a - z))));
	} else {
		tmp = x + ((y - z) / ((a - z) / (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 (t <= (-4d+17)) then
        tmp = x + (((y - z) / (a - z)) * (t - x))
    else if (t <= 2.9d+71) then
        tmp = ((t * (y - z)) / (a - z)) + (x * ((1.0d0 + (z / (a - z))) - (y / (a - z))))
    else
        tmp = x + ((y - z) / ((a - z) / (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 (t <= -4e+17) {
		tmp = x + (((y - z) / (a - z)) * (t - x));
	} else if (t <= 2.9e+71) {
		tmp = ((t * (y - z)) / (a - z)) + (x * ((1.0 + (z / (a - z))) - (y / (a - z))));
	} else {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4e+17:
		tmp = x + (((y - z) / (a - z)) * (t - x))
	elif t <= 2.9e+71:
		tmp = ((t * (y - z)) / (a - z)) + (x * ((1.0 + (z / (a - z))) - (y / (a - z))))
	else:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4e+17)
		tmp = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * Float64(t - x)));
	elseif (t <= 2.9e+71)
		tmp = Float64(Float64(Float64(t * Float64(y - z)) / Float64(a - z)) + Float64(x * Float64(Float64(1.0 + Float64(z / Float64(a - z))) - Float64(y / Float64(a - z)))));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4e+17)
		tmp = x + (((y - z) / (a - z)) * (t - x));
	elseif (t <= 2.9e+71)
		tmp = ((t * (y - z)) / (a - z)) + (x * ((1.0 + (z / (a - z))) - (y / (a - z))));
	else
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4e+17], N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e+71], N[(N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(1.0 + N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4e17

   1. Initial program 72.5%

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

      1. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

   if -4e17 < t < 2.90000000000000007e71

   1. Initial program 66.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 x around -inf 92.1%

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

   if 2.90000000000000007e71 < t

   1. Initial program 63.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+17}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+71}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z} + x \cdot \left(\left(1 + \frac{z}{a - z}\right) - \frac{y}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]

Alternative 4: 58.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x - \frac{t}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -5.4 \cdot 10^{+91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-276}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-278}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-196}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (- x (/ t (/ a z)))))
   (if (<= a -5.4e+91)
     t_2
     (if (<= a -7e-191)
       t_1
       (if (<= a -3.8e-276)
         (* y (/ (- t x) (- a z)))
         (if (<= a 8.8e-278)
           (/ (- t) (/ z (- y z)))
           (if (<= a 2.4e-196)
             (/ (- y) (/ z (- t x)))
             (if (<= a 1.4e+137) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - (t / (a / z));
	double tmp;
	if (a <= -5.4e+91) {
		tmp = t_2;
	} else if (a <= -7e-191) {
		tmp = t_1;
	} else if (a <= -3.8e-276) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 8.8e-278) {
		tmp = -t / (z / (y - z));
	} else if (a <= 2.4e-196) {
		tmp = -y / (z / (t - x));
	} else if (a <= 1.4e+137) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x - (t / (a / z))
    if (a <= (-5.4d+91)) then
        tmp = t_2
    else if (a <= (-7d-191)) then
        tmp = t_1
    else if (a <= (-3.8d-276)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 8.8d-278) then
        tmp = -t / (z / (y - z))
    else if (a <= 2.4d-196) then
        tmp = -y / (z / (t - x))
    else if (a <= 1.4d+137) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - (t / (a / z));
	double tmp;
	if (a <= -5.4e+91) {
		tmp = t_2;
	} else if (a <= -7e-191) {
		tmp = t_1;
	} else if (a <= -3.8e-276) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 8.8e-278) {
		tmp = -t / (z / (y - z));
	} else if (a <= 2.4e-196) {
		tmp = -y / (z / (t - x));
	} else if (a <= 1.4e+137) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x - (t / (a / z))
	tmp = 0
	if a <= -5.4e+91:
		tmp = t_2
	elif a <= -7e-191:
		tmp = t_1
	elif a <= -3.8e-276:
		tmp = y * ((t - x) / (a - z))
	elif a <= 8.8e-278:
		tmp = -t / (z / (y - z))
	elif a <= 2.4e-196:
		tmp = -y / (z / (t - x))
	elif a <= 1.4e+137:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x - Float64(t / Float64(a / z)))
	tmp = 0.0
	if (a <= -5.4e+91)
		tmp = t_2;
	elseif (a <= -7e-191)
		tmp = t_1;
	elseif (a <= -3.8e-276)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 8.8e-278)
		tmp = Float64(Float64(-t) / Float64(z / Float64(y - z)));
	elseif (a <= 2.4e-196)
		tmp = Float64(Float64(-y) / Float64(z / Float64(t - x)));
	elseif (a <= 1.4e+137)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x - (t / (a / z));
	tmp = 0.0;
	if (a <= -5.4e+91)
		tmp = t_2;
	elseif (a <= -7e-191)
		tmp = t_1;
	elseif (a <= -3.8e-276)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 8.8e-278)
		tmp = -t / (z / (y - z));
	elseif (a <= 2.4e-196)
		tmp = -y / (z / (t - x));
	elseif (a <= 1.4e+137)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.4e+91], t$95$2, If[LessEqual[a, -7e-191], t$95$1, If[LessEqual[a, -3.8e-276], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.8e-278], N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e-196], N[((-y) / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e+137], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -5.4e91 or 1.4e137 < a

   1. Initial program 69.1%

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

      1. associate-*l/ 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in a around inf 67.4%

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

      1. associate-/l* 82.2%

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

   6. Simplified 82.2%

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

   7. Taylor expanded in y around 0 70.6%

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

      1. associate-*r/ 70.6%

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

      2. mul-1-neg 70.6%

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

   9. Simplified 70.6%

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

   10. Taylor expanded in t around inf 65.6%

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

       1. mul-1-neg 65.6%

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

       2. associate-/l* 70.4%

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

       3. distribute-neg-frac 70.4%

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

   12. Simplified 70.4%

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

   if -5.4e91 < a < -7.00000000000000013e-191 or 2.40000000000000021e-196 < a < 1.4e137

   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/ 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in x around 0 53.5%

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

      1. associate-*r/ 64.9%

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

   6. Simplified 64.9%

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

   if -7.00000000000000013e-191 < a < -3.8e-276

   1. Initial program 92.3%

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

      1. associate-*l/ 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in y around inf 77.3%

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

      1. div-sub 85.0%

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

   6. Simplified 85.0%

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

   if -3.8e-276 < a < 8.8000000000000003e-278

   1. Initial program 46.3%

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

      1. associate-*l/ 67.7%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in x around -inf 68.3%

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

   5. Taylor expanded in x around 0 52.1%

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

      1. associate-/l* 78.3%

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

      2. associate-/r/ 67.7%

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

   7. Simplified 67.7%

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

   8. Taylor expanded in a around 0 52.1%

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

      1. mul-1-neg 52.1%

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

      2. associate-/l* 78.3%

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

   10. Simplified 78.3%

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

   if 8.8000000000000003e-278 < a < 2.40000000000000021e-196

   1. Initial program 86.2%

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

      1. associate-*l/ 86.0%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in y around -inf 76.2%

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

   5. Taylor expanded in a around 0 76.2%

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

      1. mul-1-neg 76.2%

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

      2. associate-/l* 76.3%

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

      3. distribute-neg-frac 76.3%

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

   7. Simplified 76.3%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{+91}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-191}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-276}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-278}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-196}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+137}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 5: 58.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x - \frac{t}{\frac{a}{z}}\\ t_3 := \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{if}\;a \leq -5 \cdot 10^{+90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-304}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-277}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-196}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z))))
        (t_2 (- x (/ t (/ a z))))
        (t_3 (* (- t x) (/ y (- a z)))))
   (if (<= a -5e+90)
     t_2
     (if (<= a -5.8e-191)
       t_1
       (if (<= a -9.5e-304)
         t_3
         (if (<= a 2.15e-277)
           (/ (- t) (/ z (- y z)))
           (if (<= a 2.8e-196) t_3 (if (<= a 6e+137) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - (t / (a / z));
	double t_3 = (t - x) * (y / (a - z));
	double tmp;
	if (a <= -5e+90) {
		tmp = t_2;
	} else if (a <= -5.8e-191) {
		tmp = t_1;
	} else if (a <= -9.5e-304) {
		tmp = t_3;
	} else if (a <= 2.15e-277) {
		tmp = -t / (z / (y - z));
	} else if (a <= 2.8e-196) {
		tmp = t_3;
	} else if (a <= 6e+137) {
		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 * ((y - z) / (a - z))
    t_2 = x - (t / (a / z))
    t_3 = (t - x) * (y / (a - z))
    if (a <= (-5d+90)) then
        tmp = t_2
    else if (a <= (-5.8d-191)) then
        tmp = t_1
    else if (a <= (-9.5d-304)) then
        tmp = t_3
    else if (a <= 2.15d-277) then
        tmp = -t / (z / (y - z))
    else if (a <= 2.8d-196) then
        tmp = t_3
    else if (a <= 6d+137) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - (t / (a / z));
	double t_3 = (t - x) * (y / (a - z));
	double tmp;
	if (a <= -5e+90) {
		tmp = t_2;
	} else if (a <= -5.8e-191) {
		tmp = t_1;
	} else if (a <= -9.5e-304) {
		tmp = t_3;
	} else if (a <= 2.15e-277) {
		tmp = -t / (z / (y - z));
	} else if (a <= 2.8e-196) {
		tmp = t_3;
	} else if (a <= 6e+137) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x - (t / (a / z))
	t_3 = (t - x) * (y / (a - z))
	tmp = 0
	if a <= -5e+90:
		tmp = t_2
	elif a <= -5.8e-191:
		tmp = t_1
	elif a <= -9.5e-304:
		tmp = t_3
	elif a <= 2.15e-277:
		tmp = -t / (z / (y - z))
	elif a <= 2.8e-196:
		tmp = t_3
	elif a <= 6e+137:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x - Float64(t / Float64(a / z)))
	t_3 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (a <= -5e+90)
		tmp = t_2;
	elseif (a <= -5.8e-191)
		tmp = t_1;
	elseif (a <= -9.5e-304)
		tmp = t_3;
	elseif (a <= 2.15e-277)
		tmp = Float64(Float64(-t) / Float64(z / Float64(y - z)));
	elseif (a <= 2.8e-196)
		tmp = t_3;
	elseif (a <= 6e+137)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x - (t / (a / z));
	t_3 = (t - x) * (y / (a - z));
	tmp = 0.0;
	if (a <= -5e+90)
		tmp = t_2;
	elseif (a <= -5.8e-191)
		tmp = t_1;
	elseif (a <= -9.5e-304)
		tmp = t_3;
	elseif (a <= 2.15e-277)
		tmp = -t / (z / (y - z));
	elseif (a <= 2.8e-196)
		tmp = t_3;
	elseif (a <= 6e+137)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5e+90], t$95$2, If[LessEqual[a, -5.8e-191], t$95$1, If[LessEqual[a, -9.5e-304], t$95$3, If[LessEqual[a, 2.15e-277], N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e-196], t$95$3, If[LessEqual[a, 6e+137], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.0000000000000004e90 or 6.0000000000000002e137 < a

   1. Initial program 69.1%

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

      1. associate-*l/ 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in a around inf 67.4%

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

      1. associate-/l* 82.2%

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

   6. Simplified 82.2%

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

   7. Taylor expanded in y around 0 70.6%

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

      1. associate-*r/ 70.6%

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

      2. mul-1-neg 70.6%

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

   9. Simplified 70.6%

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

   10. Taylor expanded in t around inf 65.6%

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

       1. mul-1-neg 65.6%

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

       2. associate-/l* 70.4%

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

       3. distribute-neg-frac 70.4%

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

   12. Simplified 70.4%

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

   if -5.0000000000000004e90 < a < -5.7999999999999999e-191 or 2.7999999999999998e-196 < a < 6.0000000000000002e137

   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/ 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in x around 0 53.5%

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

      1. associate-*r/ 64.9%

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

   6. Simplified 64.9%

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

   if -5.7999999999999999e-191 < a < -9.50000000000000023e-304 or 2.14999999999999995e-277 < a < 2.7999999999999998e-196

   1. Initial program 78.3%

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

      1. associate-*l/ 81.0%

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

   3. Simplified 81.0%

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

   4. Taylor expanded in y around -inf 79.9%

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

      1. associate-*l/ 80.0%

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

   6. Simplified 80.0%

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

   if -9.50000000000000023e-304 < a < 2.14999999999999995e-277

   1. Initial program 46.7%

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

      1. associate-*l/ 78.6%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in x around -inf 47.3%

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

   5. Taylor expanded in x around 0 58.4%

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

      1. associate-/l* 100.0%

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

      2. associate-/r/ 89.3%

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

   7. Simplified 89.3%

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

   8. Taylor expanded in a around 0 58.4%

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

      1. mul-1-neg 58.4%

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

      2. associate-/l* 100.0%

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

   10. Simplified 100.0%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+90}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-191}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-304}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-277}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-196}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+137}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 6: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y}}\\ t_2 := x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{if}\;a \leq -125000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.3 \cdot 10^{+140}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (- x t) (/ z y)))) (t_2 (+ x (/ (- y z) (/ (- a z) t)))))
   (if (<= a -125000000.0)
     t_2
     (if (<= a 4.7e-51)
       t_1
       (if (<= a 4.6e+27)
         t_2
         (if (<= a 3.5e+59)
           t_1
           (if (<= a 7.3e+140) (+ x (/ (- t x) (/ a (- y z)))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / y));
	double t_2 = x + ((y - z) / ((a - z) / t));
	double tmp;
	if (a <= -125000000.0) {
		tmp = t_2;
	} else if (a <= 4.7e-51) {
		tmp = t_1;
	} else if (a <= 4.6e+27) {
		tmp = t_2;
	} else if (a <= 3.5e+59) {
		tmp = t_1;
	} else if (a <= 7.3e+140) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + ((x - t) / (z / y))
    t_2 = x + ((y - z) / ((a - z) / t))
    if (a <= (-125000000.0d0)) then
        tmp = t_2
    else if (a <= 4.7d-51) then
        tmp = t_1
    else if (a <= 4.6d+27) then
        tmp = t_2
    else if (a <= 3.5d+59) then
        tmp = t_1
    else if (a <= 7.3d+140) then
        tmp = x + ((t - x) / (a / (y - z)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / y));
	double t_2 = x + ((y - z) / ((a - z) / t));
	double tmp;
	if (a <= -125000000.0) {
		tmp = t_2;
	} else if (a <= 4.7e-51) {
		tmp = t_1;
	} else if (a <= 4.6e+27) {
		tmp = t_2;
	} else if (a <= 3.5e+59) {
		tmp = t_1;
	} else if (a <= 7.3e+140) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x - t) / (z / y))
	t_2 = x + ((y - z) / ((a - z) / t))
	tmp = 0
	if a <= -125000000.0:
		tmp = t_2
	elif a <= 4.7e-51:
		tmp = t_1
	elif a <= 4.6e+27:
		tmp = t_2
	elif a <= 3.5e+59:
		tmp = t_1
	elif a <= 7.3e+140:
		tmp = x + ((t - x) / (a / (y - z)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x - t) / Float64(z / y)))
	t_2 = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (a <= -125000000.0)
		tmp = t_2;
	elseif (a <= 4.7e-51)
		tmp = t_1;
	elseif (a <= 4.6e+27)
		tmp = t_2;
	elseif (a <= 3.5e+59)
		tmp = t_1;
	elseif (a <= 7.3e+140)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x - t) / (z / y));
	t_2 = x + ((y - z) / ((a - z) / t));
	tmp = 0.0;
	if (a <= -125000000.0)
		tmp = t_2;
	elseif (a <= 4.7e-51)
		tmp = t_1;
	elseif (a <= 4.6e+27)
		tmp = t_2;
	elseif (a <= 3.5e+59)
		tmp = t_1;
	elseif (a <= 7.3e+140)
		tmp = x + ((t - x) / (a / (y - z)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -125000000.0], t$95$2, If[LessEqual[a, 4.7e-51], t$95$1, If[LessEqual[a, 4.6e+27], t$95$2, If[LessEqual[a, 3.5e+59], t$95$1, If[LessEqual[a, 7.3e+140], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.25e8 or 4.6999999999999997e-51 < a < 4.6000000000000001e27 or 7.3000000000000004e140 < a

   1. Initial program 72.5%

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

      1. associate-/l* 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in t around inf 83.2%

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

   if -1.25e8 < a < 4.6999999999999997e-51 or 4.6000000000000001e27 < a < 3.5e59

   1. Initial program 62.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 80.0%

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

      1. associate--l+ 80.0%

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

      2. associate-*r/ 80.0%

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

      3. associate-*r/ 80.0%

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

      4. div-sub 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* 87.7%

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

   6. Simplified 87.7%

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

   7. Taylor expanded in y around inf 83.7%

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

   if 3.5e59 < a < 7.3000000000000004e140

   1. Initial program 85.3%

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

      1. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in a around inf 70.9%

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

      1. associate-/l* 78.2%

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

   6. Simplified 78.2%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -125000000:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-51}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+27}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+59}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 7.3 \cdot 10^{+140}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \]

Alternative 7: 49.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-t}{\frac{z}{y - z}}\\ \mathbf{if}\;a \leq -1.34 \cdot 10^{+26}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-266}:\\ \;\;\;\;\frac{-x}{\frac{a - z}{y}}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-276}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-196}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t) (/ z (- y z)))))
   (if (<= a -1.34e+26)
     (- x (/ x (/ a y)))
     (if (<= a -1.35e-190)
       t_1
       (if (<= a -7.5e-266)
         (/ (- x) (/ (- a z) y))
         (if (<= a 3.6e-276)
           t_1
           (if (<= a 2.4e-196)
             (/ x (/ z y))
             (if (<= a 3.4e+61) t_1 (- x (/ t (/ a z)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / (z / (y - z));
	double tmp;
	if (a <= -1.34e+26) {
		tmp = x - (x / (a / y));
	} else if (a <= -1.35e-190) {
		tmp = t_1;
	} else if (a <= -7.5e-266) {
		tmp = -x / ((a - z) / y);
	} else if (a <= 3.6e-276) {
		tmp = t_1;
	} else if (a <= 2.4e-196) {
		tmp = x / (z / y);
	} else if (a <= 3.4e+61) {
		tmp = t_1;
	} else {
		tmp = x - (t / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -t / (z / (y - z))
    if (a <= (-1.34d+26)) then
        tmp = x - (x / (a / y))
    else if (a <= (-1.35d-190)) then
        tmp = t_1
    else if (a <= (-7.5d-266)) then
        tmp = -x / ((a - z) / y)
    else if (a <= 3.6d-276) then
        tmp = t_1
    else if (a <= 2.4d-196) then
        tmp = x / (z / y)
    else if (a <= 3.4d+61) then
        tmp = t_1
    else
        tmp = x - (t / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / (z / (y - z));
	double tmp;
	if (a <= -1.34e+26) {
		tmp = x - (x / (a / y));
	} else if (a <= -1.35e-190) {
		tmp = t_1;
	} else if (a <= -7.5e-266) {
		tmp = -x / ((a - z) / y);
	} else if (a <= 3.6e-276) {
		tmp = t_1;
	} else if (a <= 2.4e-196) {
		tmp = x / (z / y);
	} else if (a <= 3.4e+61) {
		tmp = t_1;
	} else {
		tmp = x - (t / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -t / (z / (y - z))
	tmp = 0
	if a <= -1.34e+26:
		tmp = x - (x / (a / y))
	elif a <= -1.35e-190:
		tmp = t_1
	elif a <= -7.5e-266:
		tmp = -x / ((a - z) / y)
	elif a <= 3.6e-276:
		tmp = t_1
	elif a <= 2.4e-196:
		tmp = x / (z / y)
	elif a <= 3.4e+61:
		tmp = t_1
	else:
		tmp = x - (t / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-t) / Float64(z / Float64(y - z)))
	tmp = 0.0
	if (a <= -1.34e+26)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (a <= -1.35e-190)
		tmp = t_1;
	elseif (a <= -7.5e-266)
		tmp = Float64(Float64(-x) / Float64(Float64(a - z) / y));
	elseif (a <= 3.6e-276)
		tmp = t_1;
	elseif (a <= 2.4e-196)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 3.4e+61)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(t / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -t / (z / (y - z));
	tmp = 0.0;
	if (a <= -1.34e+26)
		tmp = x - (x / (a / y));
	elseif (a <= -1.35e-190)
		tmp = t_1;
	elseif (a <= -7.5e-266)
		tmp = -x / ((a - z) / y);
	elseif (a <= 3.6e-276)
		tmp = t_1;
	elseif (a <= 2.4e-196)
		tmp = x / (z / y);
	elseif (a <= 3.4e+61)
		tmp = t_1;
	else
		tmp = x - (t / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.34e+26], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.35e-190], t$95$1, If[LessEqual[a, -7.5e-266], N[((-x) / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.6e-276], t$95$1, If[LessEqual[a, 2.4e-196], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e+61], t$95$1, N[(x - N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.34000000000000007e26

   1. Initial program 68.9%

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

      1. associate-*l/ 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in z around 0 71.4%

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

   5. Taylor expanded in t around 0 53.6%

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

      1. mul-1-neg 53.6%

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

      2. unsub-neg 53.6%

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

      3. associate-/l* 61.6%

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

   7. Simplified 61.6%

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

   if -1.34000000000000007e26 < a < -1.35e-190 or -7.4999999999999995e-266 < a < 3.59999999999999994e-276 or 2.40000000000000021e-196 < a < 3.40000000000000026e61

   1. Initial program 60.3%

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

      1. associate-*l/ 73.1%

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

   3. Simplified 73.1%

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

   4. Taylor expanded in x around -inf 75.3%

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

   5. Taylor expanded in x around 0 54.7%

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

      1. associate-/l* 68.7%

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

      2. associate-/r/ 55.7%

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

   7. Simplified 55.7%

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

   8. Taylor expanded in a around 0 46.5%

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

      1. mul-1-neg 46.5%

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

      2. associate-/l* 61.2%

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

   10. Simplified 61.2%

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

   if -1.35e-190 < a < -7.4999999999999995e-266

   1. Initial program 90.9%

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

      1. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in y around -inf 90.9%

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

   5. Taylor expanded in t around 0 73.1%

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

      1. mul-1-neg 73.1%

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

      2. associate-/l* 73.1%

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

      3. distribute-neg-frac 73.1%

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

   7. Simplified 73.1%

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

   if 3.59999999999999994e-276 < a < 2.40000000000000021e-196

   1. Initial program 86.2%

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

      1. associate-*l/ 86.0%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in y around -inf 76.2%

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

   5. Taylor expanded in t around 0 61.4%

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

      1. mul-1-neg 61.4%

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

      2. associate-/l* 68.4%

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

      3. distribute-neg-frac 68.4%

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

   7. Simplified 68.4%

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

   8. Taylor expanded in a around 0 61.4%

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

      1. associate-/l* 68.4%

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

   10. Simplified 68.4%

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

   if 3.40000000000000026e61 < a

   1. Initial program 76.1%

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

      1. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in a around inf 71.4%

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

      1. associate-/l* 80.2%

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

   6. Simplified 80.2%

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

   7. Taylor expanded in y around 0 67.4%

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

      1. associate-*r/ 67.4%

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

      2. mul-1-neg 67.4%

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

   9. Simplified 67.4%

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

   10. Taylor expanded in t around inf 60.5%

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

       1. mul-1-neg 60.5%

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

       2. associate-/l* 67.0%

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

       3. distribute-neg-frac 67.0%

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

   12. Simplified 67.0%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.34 \cdot 10^{+26}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-190}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-266}:\\ \;\;\;\;\frac{-x}{\frac{a - z}{y}}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-276}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-196}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+61}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 8: 50.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-t}{\frac{z}{y - z}}\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{+26}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-264}:\\ \;\;\;\;\frac{-x}{\frac{a - z}{y}}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-196}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t) (/ z (- y z)))))
   (if (<= a -1.55e+26)
     (- x (/ x (/ a y)))
     (if (<= a -3.2e-192)
       t_1
       (if (<= a -6.8e-264)
         (/ (- x) (/ (- a z) y))
         (if (<= a 7e-277)
           t_1
           (if (<= a 2.5e-196)
             (/ (- y) (/ z (- t x)))
             (if (<= a 1.55e+62) t_1 (- x (/ t (/ a z)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / (z / (y - z));
	double tmp;
	if (a <= -1.55e+26) {
		tmp = x - (x / (a / y));
	} else if (a <= -3.2e-192) {
		tmp = t_1;
	} else if (a <= -6.8e-264) {
		tmp = -x / ((a - z) / y);
	} else if (a <= 7e-277) {
		tmp = t_1;
	} else if (a <= 2.5e-196) {
		tmp = -y / (z / (t - x));
	} else if (a <= 1.55e+62) {
		tmp = t_1;
	} else {
		tmp = x - (t / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -t / (z / (y - z))
    if (a <= (-1.55d+26)) then
        tmp = x - (x / (a / y))
    else if (a <= (-3.2d-192)) then
        tmp = t_1
    else if (a <= (-6.8d-264)) then
        tmp = -x / ((a - z) / y)
    else if (a <= 7d-277) then
        tmp = t_1
    else if (a <= 2.5d-196) then
        tmp = -y / (z / (t - x))
    else if (a <= 1.55d+62) then
        tmp = t_1
    else
        tmp = x - (t / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / (z / (y - z));
	double tmp;
	if (a <= -1.55e+26) {
		tmp = x - (x / (a / y));
	} else if (a <= -3.2e-192) {
		tmp = t_1;
	} else if (a <= -6.8e-264) {
		tmp = -x / ((a - z) / y);
	} else if (a <= 7e-277) {
		tmp = t_1;
	} else if (a <= 2.5e-196) {
		tmp = -y / (z / (t - x));
	} else if (a <= 1.55e+62) {
		tmp = t_1;
	} else {
		tmp = x - (t / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -t / (z / (y - z))
	tmp = 0
	if a <= -1.55e+26:
		tmp = x - (x / (a / y))
	elif a <= -3.2e-192:
		tmp = t_1
	elif a <= -6.8e-264:
		tmp = -x / ((a - z) / y)
	elif a <= 7e-277:
		tmp = t_1
	elif a <= 2.5e-196:
		tmp = -y / (z / (t - x))
	elif a <= 1.55e+62:
		tmp = t_1
	else:
		tmp = x - (t / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-t) / Float64(z / Float64(y - z)))
	tmp = 0.0
	if (a <= -1.55e+26)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (a <= -3.2e-192)
		tmp = t_1;
	elseif (a <= -6.8e-264)
		tmp = Float64(Float64(-x) / Float64(Float64(a - z) / y));
	elseif (a <= 7e-277)
		tmp = t_1;
	elseif (a <= 2.5e-196)
		tmp = Float64(Float64(-y) / Float64(z / Float64(t - x)));
	elseif (a <= 1.55e+62)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(t / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -t / (z / (y - z));
	tmp = 0.0;
	if (a <= -1.55e+26)
		tmp = x - (x / (a / y));
	elseif (a <= -3.2e-192)
		tmp = t_1;
	elseif (a <= -6.8e-264)
		tmp = -x / ((a - z) / y);
	elseif (a <= 7e-277)
		tmp = t_1;
	elseif (a <= 2.5e-196)
		tmp = -y / (z / (t - x));
	elseif (a <= 1.55e+62)
		tmp = t_1;
	else
		tmp = x - (t / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.55e+26], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.2e-192], t$95$1, If[LessEqual[a, -6.8e-264], N[((-x) / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e-277], t$95$1, If[LessEqual[a, 2.5e-196], N[((-y) / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e+62], t$95$1, N[(x - N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.55e26

   1. Initial program 68.9%

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

      1. associate-*l/ 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in z around 0 71.4%

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

   5. Taylor expanded in t around 0 53.6%

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

      1. mul-1-neg 53.6%

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

      2. unsub-neg 53.6%

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

      3. associate-/l* 61.6%

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

   7. Simplified 61.6%

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

   if -1.55e26 < a < -3.2000000000000002e-192 or -6.7999999999999997e-264 < a < 6.99999999999999966e-277 or 2.5000000000000002e-196 < a < 1.55000000000000007e62

   1. Initial program 60.3%

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

      1. associate-*l/ 73.1%

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

   3. Simplified 73.1%

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

   4. Taylor expanded in x around -inf 75.3%

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

   5. Taylor expanded in x around 0 54.7%

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

      1. associate-/l* 68.7%

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

      2. associate-/r/ 55.7%

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

   7. Simplified 55.7%

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

   8. Taylor expanded in a around 0 46.5%

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

      1. mul-1-neg 46.5%

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

      2. associate-/l* 61.2%

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

   10. Simplified 61.2%

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

   if -3.2000000000000002e-192 < a < -6.7999999999999997e-264

   1. Initial program 90.9%

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

      1. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in y around -inf 90.9%

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

   5. Taylor expanded in t around 0 73.1%

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

      1. mul-1-neg 73.1%

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

      2. associate-/l* 73.1%

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

      3. distribute-neg-frac 73.1%

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

   7. Simplified 73.1%

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

   if 6.99999999999999966e-277 < a < 2.5000000000000002e-196

   1. Initial program 86.2%

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

      1. associate-*l/ 86.0%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in y around -inf 76.2%

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

   5. Taylor expanded in a around 0 76.2%

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

      1. mul-1-neg 76.2%

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

      2. associate-/l* 76.3%

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

      3. distribute-neg-frac 76.3%

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

   7. Simplified 76.3%

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

   if 1.55000000000000007e62 < a

   1. Initial program 76.1%

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

      1. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in a around inf 71.4%

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

      1. associate-/l* 80.2%

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

   6. Simplified 80.2%

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

   7. Taylor expanded in y around 0 67.4%

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

      1. associate-*r/ 67.4%

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

      2. mul-1-neg 67.4%

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

   9. Simplified 67.4%

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

   10. Taylor expanded in t around inf 60.5%

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

       1. mul-1-neg 60.5%

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

       2. associate-/l* 67.0%

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

       3. distribute-neg-frac 67.0%

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

   12. Simplified 67.0%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+26}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-192}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-264}:\\ \;\;\;\;\frac{-x}{\frac{a - z}{y}}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-277}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-196}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+62}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 9: 75.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -25000000 \lor \neg \left(a \leq 9.5 \cdot 10^{-51}\right) \land \left(a \leq 4.1 \cdot 10^{+27} \lor \neg \left(a \leq 4.9 \cdot 10^{+60}\right)\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -25000000.0)
         (and (not (<= a 9.5e-51)) (or (<= a 4.1e+27) (not (<= a 4.9e+60)))))
   (+ x (/ (- y z) (/ (- a z) t)))
   (+ t (* (- y a) (/ (- x t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -25000000.0) || (!(a <= 9.5e-51) && ((a <= 4.1e+27) || !(a <= 4.9e+60)))) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t + ((y - a) * ((x - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-25000000.0d0)) .or. (.not. (a <= 9.5d-51)) .and. (a <= 4.1d+27) .or. (.not. (a <= 4.9d+60))) then
        tmp = x + ((y - z) / ((a - z) / t))
    else
        tmp = t + ((y - a) * ((x - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -25000000.0) || (!(a <= 9.5e-51) && ((a <= 4.1e+27) || !(a <= 4.9e+60)))) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t + ((y - a) * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -25000000.0) or (not (a <= 9.5e-51) and ((a <= 4.1e+27) or not (a <= 4.9e+60))):
		tmp = x + ((y - z) / ((a - z) / t))
	else:
		tmp = t + ((y - a) * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -25000000.0) || (!(a <= 9.5e-51) && ((a <= 4.1e+27) || !(a <= 4.9e+60))))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(t + Float64(Float64(y - a) * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -25000000.0) || (~((a <= 9.5e-51)) && ((a <= 4.1e+27) || ~((a <= 4.9e+60)))))
		tmp = x + ((y - z) / ((a - z) / t));
	else
		tmp = t + ((y - a) * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -25000000.0], And[N[Not[LessEqual[a, 9.5e-51]], $MachinePrecision], Or[LessEqual[a, 4.1e+27], N[Not[LessEqual[a, 4.9e+60]], $MachinePrecision]]]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(y - a), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.5e7 or 9.4999999999999998e-51 < a < 4.1000000000000002e27 or 4.9000000000000003e60 < a

   1. Initial program 73.7%

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

      1. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in t around inf 82.5%

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

   if -2.5e7 < a < 9.4999999999999998e-51 or 4.1000000000000002e27 < a < 4.9000000000000003e60

   1. Initial program 62.7%

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

      1. associate-*l/ 74.5%

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

   3. Simplified 74.5%

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

   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 82.3%

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

      5. distribute-lft-out-- 82.3%

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

      6. associate-*r/ 82.3%

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

      7. distribute-rgt-out-- 83.0%

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

      8. mul-1-neg 83.0%

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

      9. unsub-neg 83.0%

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

      10. associate-/l* 87.8%

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

   6. Simplified 87.8%

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

      1. associate-/r/ 84.5%

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

   8. Applied egg-rr 84.5%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -25000000 \lor \neg \left(a \leq 9.5 \cdot 10^{-51}\right) \land \left(a \leq 4.1 \cdot 10^{+27} \lor \neg \left(a \leq 4.9 \cdot 10^{+60}\right)\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \end{array} \]

Alternative 10: 76.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{if}\;a \leq -820000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-54}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+27} \lor \neg \left(a \leq 3.6 \cdot 10^{+60}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ (- a z) t)))))
   (if (<= a -820000000.0)
     t_1
     (if (<= a 2.55e-54)
       (+ t (/ (- x t) (/ z (- y a))))
       (if (or (<= a 1.1e+27) (not (<= a 3.6e+60)))
         t_1
         (+ 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) / ((a - z) / t));
	double tmp;
	if (a <= -820000000.0) {
		tmp = t_1;
	} else if (a <= 2.55e-54) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else if ((a <= 1.1e+27) || !(a <= 3.6e+60)) {
		tmp = t_1;
	} 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) / ((a - z) / t))
    if (a <= (-820000000.0d0)) then
        tmp = t_1
    else if (a <= 2.55d-54) then
        tmp = t + ((x - t) / (z / (y - a)))
    else if ((a <= 1.1d+27) .or. (.not. (a <= 3.6d+60))) then
        tmp = t_1
    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) / ((a - z) / t));
	double tmp;
	if (a <= -820000000.0) {
		tmp = t_1;
	} else if (a <= 2.55e-54) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else if ((a <= 1.1e+27) || !(a <= 3.6e+60)) {
		tmp = t_1;
	} else {
		tmp = t + ((y - a) * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / ((a - z) / t))
	tmp = 0
	if a <= -820000000.0:
		tmp = t_1
	elif a <= 2.55e-54:
		tmp = t + ((x - t) / (z / (y - a)))
	elif (a <= 1.1e+27) or not (a <= 3.6e+60):
		tmp = t_1
	else:
		tmp = t + ((y - a) * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (a <= -820000000.0)
		tmp = t_1;
	elseif (a <= 2.55e-54)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	elseif ((a <= 1.1e+27) || !(a <= 3.6e+60))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(y - a) * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) / ((a - z) / t));
	tmp = 0.0;
	if (a <= -820000000.0)
		tmp = t_1;
	elseif (a <= 2.55e-54)
		tmp = t + ((x - t) / (z / (y - a)));
	elseif ((a <= 1.1e+27) || ~((a <= 3.6e+60)))
		tmp = t_1;
	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[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -820000000.0], t$95$1, If[LessEqual[a, 2.55e-54], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 1.1e+27], N[Not[LessEqual[a, 3.6e+60]], $MachinePrecision]], t$95$1, N[(t + N[(N[(y - a), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.2e8 or 2.55000000000000005e-54 < a < 1.0999999999999999e27 or 3.59999999999999968e60 < a

   1. Initial program 73.7%

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

      1. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in t around inf 82.5%

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

   if -8.2e8 < a < 2.55000000000000005e-54

   1. Initial program 63.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 80.4%

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

      1. associate--l+ 80.4%

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

      2. associate-*r/ 80.4%

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

      3. associate-*r/ 80.4%

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

      4. div-sub 83.5%

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

      5. distribute-lft-out-- 83.5%

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

      6. associate-*r/ 83.5%

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

      7. distribute-rgt-out-- 83.5%

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

      8. mul-1-neg 83.5%

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

      9. unsub-neg 83.5%

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

      10. associate-/l* 87.1%

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

   6. Simplified 87.1%

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

   if 1.0999999999999999e27 < a < 3.59999999999999968e60

   1. Initial program 52.3%

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

      1. associate-*l/ 76.2%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in z around inf 62.8%

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

      1. associate--l+ 62.8%

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

      2. associate-*r/ 62.8%

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

      3. associate-*r/ 62.8%

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

      4. div-sub 62.8%

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

      5. distribute-lft-out-- 62.8%

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

      6. associate-*r/ 62.8%

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

      7. distribute-rgt-out-- 75.3%

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

      8. mul-1-neg 75.3%

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

      9. unsub-neg 75.3%

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

      10. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

      1. associate-/r/ 99.8%

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

   8. Applied egg-rr 99.8%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -820000000:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-54}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+27} \lor \neg \left(a \leq 3.6 \cdot 10^{+60}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \end{array} \]

Alternative 11: 74.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y}}\\ t_2 := x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{if}\;a \leq -36000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+27}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (- x t) (/ z y)))) (t_2 (+ x (/ (- t x) (/ a (- y z))))))
   (if (<= a -36000000000000.0)
     t_2
     (if (<= a 7.5e-52)
       t_1
       (if (<= a 3.5e+27)
         (/ t (/ (- a z) (- y z)))
         (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 + ((x - t) / (z / y));
	double t_2 = x + ((t - x) / (a / (y - z)));
	double tmp;
	if (a <= -36000000000000.0) {
		tmp = t_2;
	} else if (a <= 7.5e-52) {
		tmp = t_1;
	} else if (a <= 3.5e+27) {
		tmp = t / ((a - z) / (y - z));
	} 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) :: tmp
    t_1 = t + ((x - t) / (z / y))
    t_2 = x + ((t - x) / (a / (y - z)))
    if (a <= (-36000000000000.0d0)) then
        tmp = t_2
    else if (a <= 7.5d-52) then
        tmp = t_1
    else if (a <= 3.5d+27) then
        tmp = t / ((a - z) / (y - z))
    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 + ((x - t) / (z / y));
	double t_2 = x + ((t - x) / (a / (y - z)));
	double tmp;
	if (a <= -36000000000000.0) {
		tmp = t_2;
	} else if (a <= 7.5e-52) {
		tmp = t_1;
	} else if (a <= 3.5e+27) {
		tmp = t / ((a - z) / (y - z));
	} 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 + ((x - t) / (z / y))
	t_2 = x + ((t - x) / (a / (y - z)))
	tmp = 0
	if a <= -36000000000000.0:
		tmp = t_2
	elif a <= 7.5e-52:
		tmp = t_1
	elif a <= 3.5e+27:
		tmp = t / ((a - z) / (y - z))
	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(Float64(x - t) / Float64(z / y)))
	t_2 = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))))
	tmp = 0.0
	if (a <= -36000000000000.0)
		tmp = t_2;
	elseif (a <= 7.5e-52)
		tmp = t_1;
	elseif (a <= 3.5e+27)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	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 + ((x - t) / (z / y));
	t_2 = x + ((t - x) / (a / (y - z)));
	tmp = 0.0;
	if (a <= -36000000000000.0)
		tmp = t_2;
	elseif (a <= 7.5e-52)
		tmp = t_1;
	elseif (a <= 3.5e+27)
		tmp = t / ((a - z) / (y - z));
	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[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -36000000000000.0], t$95$2, If[LessEqual[a, 7.5e-52], t$95$1, If[LessEqual[a, 3.5e+27], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.6e+58], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.6e13 or 4.60000000000000005e58 < a

   1. Initial program 72.8%

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

      1. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in a around inf 66.4%

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

      1. associate-/l* 78.7%

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

   6. Simplified 78.7%

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

   if -3.6e13 < a < 7.50000000000000006e-52 or 3.5000000000000002e27 < a < 4.60000000000000005e58

   1. Initial program 62.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 80.0%

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

      1. associate--l+ 80.0%

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

      2. associate-*r/ 80.0%

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

      3. associate-*r/ 80.0%

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

      4. div-sub 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* 87.7%

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

   6. Simplified 87.7%

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

   7. Taylor expanded in y around inf 83.7%

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

   if 7.50000000000000006e-52 < a < 3.5000000000000002e27

   1. Initial program 88.5%

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

      1. associate-*l/ 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in x around 0 75.2%

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

      1. associate-/l* 75.4%

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

   6. Simplified 75.4%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -36000000000000:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-52}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+27}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+58}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \]

Alternative 12: 57.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x - \frac{t}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{+92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-196}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (- x (/ t (/ a z)))))
   (if (<= a -1.3e+92)
     t_2
     (if (<= a 7.5e-278)
       t_1
       (if (<= a 2.7e-196)
         (/ (- y) (/ z (- t x)))
         (if (<= a 1.35e+137) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - (t / (a / z));
	double tmp;
	if (a <= -1.3e+92) {
		tmp = t_2;
	} else if (a <= 7.5e-278) {
		tmp = t_1;
	} else if (a <= 2.7e-196) {
		tmp = -y / (z / (t - x));
	} else if (a <= 1.35e+137) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x - (t / (a / z))
    if (a <= (-1.3d+92)) then
        tmp = t_2
    else if (a <= 7.5d-278) then
        tmp = t_1
    else if (a <= 2.7d-196) then
        tmp = -y / (z / (t - x))
    else if (a <= 1.35d+137) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - (t / (a / z));
	double tmp;
	if (a <= -1.3e+92) {
		tmp = t_2;
	} else if (a <= 7.5e-278) {
		tmp = t_1;
	} else if (a <= 2.7e-196) {
		tmp = -y / (z / (t - x));
	} else if (a <= 1.35e+137) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x - (t / (a / z))
	tmp = 0
	if a <= -1.3e+92:
		tmp = t_2
	elif a <= 7.5e-278:
		tmp = t_1
	elif a <= 2.7e-196:
		tmp = -y / (z / (t - x))
	elif a <= 1.35e+137:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x - Float64(t / Float64(a / z)))
	tmp = 0.0
	if (a <= -1.3e+92)
		tmp = t_2;
	elseif (a <= 7.5e-278)
		tmp = t_1;
	elseif (a <= 2.7e-196)
		tmp = Float64(Float64(-y) / Float64(z / Float64(t - x)));
	elseif (a <= 1.35e+137)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x - (t / (a / z));
	tmp = 0.0;
	if (a <= -1.3e+92)
		tmp = t_2;
	elseif (a <= 7.5e-278)
		tmp = t_1;
	elseif (a <= 2.7e-196)
		tmp = -y / (z / (t - x));
	elseif (a <= 1.35e+137)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.3e+92], t$95$2, If[LessEqual[a, 7.5e-278], t$95$1, If[LessEqual[a, 2.7e-196], N[((-y) / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e+137], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.2999999999999999e92 or 1.35000000000000009e137 < a

   1. Initial program 69.1%

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

      1. associate-*l/ 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in a around inf 67.4%

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

      1. associate-/l* 82.2%

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

   6. Simplified 82.2%

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

   7. Taylor expanded in y around 0 70.6%

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

      1. associate-*r/ 70.6%

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

      2. mul-1-neg 70.6%

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

   9. Simplified 70.6%

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

   10. Taylor expanded in t around inf 65.6%

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

       1. mul-1-neg 65.6%

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

       2. associate-/l* 70.4%

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

       3. distribute-neg-frac 70.4%

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

   12. Simplified 70.4%

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

   if -1.2999999999999999e92 < a < 7.49999999999999946e-278 or 2.69999999999999982e-196 < a < 1.35000000000000009e137

   1. Initial program 65.5%

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

      1. associate-*l/ 77.2%

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

   3. Simplified 77.2%

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

   4. Taylor expanded in x around 0 52.8%

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

      1. associate-*r/ 64.9%

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

   6. Simplified 64.9%

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

   if 7.49999999999999946e-278 < a < 2.69999999999999982e-196

   1. Initial program 86.2%

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

      1. associate-*l/ 86.0%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in y around -inf 76.2%

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

   5. Taylor expanded in a around 0 76.2%

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

      1. mul-1-neg 76.2%

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

      2. associate-/l* 76.3%

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

      3. distribute-neg-frac 76.3%

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

   7. Simplified 76.3%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+92}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-278}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-196}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+137}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 13: 70.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{if}\;a \leq -2700000000000:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+25}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (- x t) (/ z y)))))
   (if (<= a -2700000000000.0)
     (+ x (* (- t x) (/ y a)))
     (if (<= a 7.8e-51)
       t_1
       (if (<= a 1.8e+25)
         (* t (/ (- y z) (- a z)))
         (if (<= a 3.3e+59) t_1 (+ x (/ y (/ a (- t x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / y));
	double tmp;
	if (a <= -2700000000000.0) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= 7.8e-51) {
		tmp = t_1;
	} else if (a <= 1.8e+25) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 3.3e+59) {
		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 + ((x - t) / (z / y))
    if (a <= (-2700000000000.0d0)) then
        tmp = x + ((t - x) * (y / a))
    else if (a <= 7.8d-51) then
        tmp = t_1
    else if (a <= 1.8d+25) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= 3.3d+59) 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 + ((x - t) / (z / y));
	double tmp;
	if (a <= -2700000000000.0) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= 7.8e-51) {
		tmp = t_1;
	} else if (a <= 1.8e+25) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 3.3e+59) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x - t) / (z / y))
	tmp = 0
	if a <= -2700000000000.0:
		tmp = x + ((t - x) * (y / a))
	elif a <= 7.8e-51:
		tmp = t_1
	elif a <= 1.8e+25:
		tmp = t * ((y - z) / (a - z))
	elif a <= 3.3e+59:
		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(x - t) / Float64(z / y)))
	tmp = 0.0
	if (a <= -2700000000000.0)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (a <= 7.8e-51)
		tmp = t_1;
	elseif (a <= 1.8e+25)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= 3.3e+59)
		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 + ((x - t) / (z / y));
	tmp = 0.0;
	if (a <= -2700000000000.0)
		tmp = x + ((t - x) * (y / a));
	elseif (a <= 7.8e-51)
		tmp = t_1;
	elseif (a <= 1.8e+25)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= 3.3e+59)
		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[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2700000000000.0], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.8e-51], t$95$1, If[LessEqual[a, 1.8e+25], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e+59], t$95$1, N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.7e12

   1. Initial program 70.2%

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

      1. associate-*l/ 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in z around 0 69.8%

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

   if -2.7e12 < a < 7.7999999999999995e-51 or 1.80000000000000008e25 < a < 3.2999999999999999e59

   1. Initial program 62.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 80.0%

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

      1. associate--l+ 80.0%

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

      2. associate-*r/ 80.0%

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

      3. associate-*r/ 80.0%

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

      4. div-sub 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* 87.7%

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

   6. Simplified 87.7%

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

   7. Taylor expanded in y around inf 83.7%

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

   if 7.7999999999999995e-51 < a < 1.80000000000000008e25

   1. Initial program 88.5%

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

      1. associate-*l/ 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in x around 0 75.2%

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

      1. associate-*r/ 75.2%

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

   6. Simplified 75.2%

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

   if 3.2999999999999999e59 < a

   1. Initial program 76.6%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in z around 0 72.4%

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

      1. associate-/l* 74.7%

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

   6. Simplified 74.7%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2700000000000:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-51}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+25}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+59}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 14: 70.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{if}\;a \leq -62000000000:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+27}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (- x t) (/ z y)))))
   (if (<= a -62000000000.0)
     (+ x (* (- t x) (/ y a)))
     (if (<= a 3e-54)
       t_1
       (if (<= a 4.5e+27)
         (/ t (/ (- a z) (- y z)))
         (if (<= a 3.5e+58) t_1 (+ x (/ y (/ a (- t x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / y));
	double tmp;
	if (a <= -62000000000.0) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= 3e-54) {
		tmp = t_1;
	} else if (a <= 4.5e+27) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 3.5e+58) {
		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 + ((x - t) / (z / y))
    if (a <= (-62000000000.0d0)) then
        tmp = x + ((t - x) * (y / a))
    else if (a <= 3d-54) then
        tmp = t_1
    else if (a <= 4.5d+27) then
        tmp = t / ((a - z) / (y - z))
    else if (a <= 3.5d+58) 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 + ((x - t) / (z / y));
	double tmp;
	if (a <= -62000000000.0) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= 3e-54) {
		tmp = t_1;
	} else if (a <= 4.5e+27) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 3.5e+58) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x - t) / (z / y))
	tmp = 0
	if a <= -62000000000.0:
		tmp = x + ((t - x) * (y / a))
	elif a <= 3e-54:
		tmp = t_1
	elif a <= 4.5e+27:
		tmp = t / ((a - z) / (y - z))
	elif a <= 3.5e+58:
		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(x - t) / Float64(z / y)))
	tmp = 0.0
	if (a <= -62000000000.0)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (a <= 3e-54)
		tmp = t_1;
	elseif (a <= 4.5e+27)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (a <= 3.5e+58)
		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 + ((x - t) / (z / y));
	tmp = 0.0;
	if (a <= -62000000000.0)
		tmp = x + ((t - x) * (y / a));
	elseif (a <= 3e-54)
		tmp = t_1;
	elseif (a <= 4.5e+27)
		tmp = t / ((a - z) / (y - z));
	elseif (a <= 3.5e+58)
		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[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -62000000000.0], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3e-54], t$95$1, If[LessEqual[a, 4.5e+27], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e+58], t$95$1, N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.2e10

   1. Initial program 70.2%

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

      1. associate-*l/ 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in z around 0 69.8%

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

   if -6.2e10 < a < 3.00000000000000009e-54 or 4.4999999999999999e27 < a < 3.4999999999999997e58

   1. Initial program 62.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 80.0%

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

      1. associate--l+ 80.0%

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

      2. associate-*r/ 80.0%

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

      3. associate-*r/ 80.0%

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

      4. div-sub 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* 87.7%

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

   6. Simplified 87.7%

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

   7. Taylor expanded in y around inf 83.7%

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

   if 3.00000000000000009e-54 < a < 4.4999999999999999e27

   1. Initial program 88.5%

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

      1. associate-*l/ 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in x around 0 75.2%

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

      1. associate-/l* 75.4%

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

   6. Simplified 75.4%

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

   if 3.4999999999999997e58 < a

   1. Initial program 76.6%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in z around 0 72.4%

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

      1. associate-/l* 74.7%

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

   6. Simplified 74.7%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -62000000000:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-54}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+27}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+58}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 15: 88.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{+207}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+104}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.08e+207)
   (+ t (/ (- x t) (/ z (- y a))))
   (if (<= z 1.9e+104)
     (+ x (* (/ (- y z) (- a z)) (- t x)))
     (+ t (* (- y a) (/ (- x t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.08e+207) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else if (z <= 1.9e+104) {
		tmp = x + (((y - z) / (a - z)) * (t - x));
	} else {
		tmp = t + ((y - a) * ((x - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.08d+207)) then
        tmp = t + ((x - t) / (z / (y - a)))
    else if (z <= 1.9d+104) then
        tmp = x + (((y - z) / (a - z)) * (t - x))
    else
        tmp = t + ((y - a) * ((x - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.08e+207) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else if (z <= 1.9e+104) {
		tmp = x + (((y - z) / (a - z)) * (t - x));
	} else {
		tmp = t + ((y - a) * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.08e+207:
		tmp = t + ((x - t) / (z / (y - a)))
	elif z <= 1.9e+104:
		tmp = x + (((y - z) / (a - z)) * (t - x))
	else:
		tmp = t + ((y - a) * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.08e+207)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	elseif (z <= 1.9e+104)
		tmp = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * Float64(t - x)));
	else
		tmp = Float64(t + Float64(Float64(y - a) * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.08e+207)
		tmp = t + ((x - t) / (z / (y - a)));
	elseif (z <= 1.9e+104)
		tmp = x + (((y - z) / (a - z)) * (t - x));
	else
		tmp = t + ((y - a) * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.08e+207], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+104], N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(y - a), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.08000000000000001e207

   1. Initial program 20.0%

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

      1. associate-*l/ 44.2%

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

   3. Simplified 44.2%

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

   4. Taylor expanded in z around inf 76.0%

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

      1. associate--l+ 76.0%

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

      2. associate-*r/ 76.0%

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

      3. associate-*r/ 76.0%

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

      4. div-sub 76.0%

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

      5. distribute-lft-out-- 76.0%

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

      6. associate-*r/ 76.0%

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

      7. distribute-rgt-out-- 76.0%

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

      8. mul-1-neg 76.0%

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

      9. unsub-neg 76.0%

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

      10. associate-/l* 96.1%

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

   6. Simplified 96.1%

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

   if -1.08000000000000001e207 < z < 1.89999999999999984e104

   1. Initial program 82.7%

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

      1. associate-*l/ 91.2%

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

   3. Simplified 91.2%

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

   if 1.89999999999999984e104 < z

   1. Initial program 27.0%

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

      1. associate-*l/ 63.1%

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

   3. Simplified 63.1%

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

   4. Taylor expanded in z around inf 70.1%

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

      1. associate--l+ 70.1%

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

      2. associate-*r/ 70.1%

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

      3. associate-*r/ 70.1%

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

      4. div-sub 70.1%

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

      5. distribute-lft-out-- 70.1%

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

      6. associate-*r/ 70.1%

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

      7. distribute-rgt-out-- 70.4%

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

      8. mul-1-neg 70.4%

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

      9. unsub-neg 70.4%

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

      10. associate-/l* 87.3%

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

   6. Simplified 87.3%

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

      1. associate-/r/ 87.4%

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

   8. Applied egg-rr 87.4%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{+207}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+104}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \end{array} \]

Alternative 16: 49.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-t}{\frac{z}{y - z}}\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+26}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{-276}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-196}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t) (/ z (- y z)))))
   (if (<= a -1.8e+26)
     (- x (/ x (/ a y)))
     (if (<= a 1.52e-276)
       t_1
       (if (<= a 2.4e-196)
         (/ x (/ z y))
         (if (<= a 9.5e+58) t_1 (* x (- 1.0 (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / (z / (y - z));
	double tmp;
	if (a <= -1.8e+26) {
		tmp = x - (x / (a / y));
	} else if (a <= 1.52e-276) {
		tmp = t_1;
	} else if (a <= 2.4e-196) {
		tmp = x / (z / y);
	} else if (a <= 9.5e+58) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -t / (z / (y - z))
    if (a <= (-1.8d+26)) then
        tmp = x - (x / (a / y))
    else if (a <= 1.52d-276) then
        tmp = t_1
    else if (a <= 2.4d-196) then
        tmp = x / (z / y)
    else if (a <= 9.5d+58) then
        tmp = t_1
    else
        tmp = x * (1.0d0 - (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / (z / (y - z));
	double tmp;
	if (a <= -1.8e+26) {
		tmp = x - (x / (a / y));
	} else if (a <= 1.52e-276) {
		tmp = t_1;
	} else if (a <= 2.4e-196) {
		tmp = x / (z / y);
	} else if (a <= 9.5e+58) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -t / (z / (y - z))
	tmp = 0
	if a <= -1.8e+26:
		tmp = x - (x / (a / y))
	elif a <= 1.52e-276:
		tmp = t_1
	elif a <= 2.4e-196:
		tmp = x / (z / y)
	elif a <= 9.5e+58:
		tmp = t_1
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-t) / Float64(z / Float64(y - z)))
	tmp = 0.0
	if (a <= -1.8e+26)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (a <= 1.52e-276)
		tmp = t_1;
	elseif (a <= 2.4e-196)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 9.5e+58)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -t / (z / (y - z));
	tmp = 0.0;
	if (a <= -1.8e+26)
		tmp = x - (x / (a / y));
	elseif (a <= 1.52e-276)
		tmp = t_1;
	elseif (a <= 2.4e-196)
		tmp = x / (z / y);
	elseif (a <= 9.5e+58)
		tmp = t_1;
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8e+26], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.52e-276], t$95$1, If[LessEqual[a, 2.4e-196], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+58], t$95$1, N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.80000000000000012e26

   1. Initial program 68.9%

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

      1. associate-*l/ 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in z around 0 71.4%

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

   5. Taylor expanded in t around 0 53.6%

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

      1. mul-1-neg 53.6%

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

      2. unsub-neg 53.6%

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

      3. associate-/l* 61.6%

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

   7. Simplified 61.6%

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

   if -1.80000000000000012e26 < a < 1.51999999999999994e-276 or 2.40000000000000021e-196 < a < 9.5000000000000002e58

   1. Initial program 62.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 x around -inf 76.3%

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

   5. Taylor expanded in x around 0 54.4%

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

      1. associate-/l* 67.4%

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

      2. associate-/r/ 55.4%

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

   7. Simplified 55.4%

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

   8. Taylor expanded in a around 0 45.3%

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

      1. mul-1-neg 45.3%

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

      2. associate-/l* 58.3%

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

   10. Simplified 58.3%

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

   if 1.51999999999999994e-276 < a < 2.40000000000000021e-196

   1. Initial program 86.2%

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

      1. associate-*l/ 86.0%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in y around -inf 76.2%

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

   5. Taylor expanded in t around 0 61.4%

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

      1. mul-1-neg 61.4%

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

      2. associate-/l* 68.4%

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

      3. distribute-neg-frac 68.4%

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

   7. Simplified 68.4%

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

   8. Taylor expanded in a around 0 61.4%

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

      1. associate-/l* 68.4%

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

   10. Simplified 68.4%

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

   if 9.5000000000000002e58 < a

   1. Initial program 76.6%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in z around 0 70.5%

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

   5. Taylor expanded in x around inf 61.9%

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

      1. mul-1-neg 61.9%

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

      2. unsub-neg 61.9%

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

   7. Simplified 61.9%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+26}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{-276}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-196}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 17: 49.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-t}{\frac{z}{y - z}}\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{+26}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-196}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t) (/ z (- y z)))))
   (if (<= a -1.7e+26)
     (- x (/ x (/ a y)))
     (if (<= a 7.5e-277)
       t_1
       (if (<= a 2.6e-196)
         (/ x (/ z y))
         (if (<= a 6.6e+62) t_1 (- x (/ t (/ a z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / (z / (y - z));
	double tmp;
	if (a <= -1.7e+26) {
		tmp = x - (x / (a / y));
	} else if (a <= 7.5e-277) {
		tmp = t_1;
	} else if (a <= 2.6e-196) {
		tmp = x / (z / y);
	} else if (a <= 6.6e+62) {
		tmp = t_1;
	} else {
		tmp = x - (t / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -t / (z / (y - z))
    if (a <= (-1.7d+26)) then
        tmp = x - (x / (a / y))
    else if (a <= 7.5d-277) then
        tmp = t_1
    else if (a <= 2.6d-196) then
        tmp = x / (z / y)
    else if (a <= 6.6d+62) then
        tmp = t_1
    else
        tmp = x - (t / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / (z / (y - z));
	double tmp;
	if (a <= -1.7e+26) {
		tmp = x - (x / (a / y));
	} else if (a <= 7.5e-277) {
		tmp = t_1;
	} else if (a <= 2.6e-196) {
		tmp = x / (z / y);
	} else if (a <= 6.6e+62) {
		tmp = t_1;
	} else {
		tmp = x - (t / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -t / (z / (y - z))
	tmp = 0
	if a <= -1.7e+26:
		tmp = x - (x / (a / y))
	elif a <= 7.5e-277:
		tmp = t_1
	elif a <= 2.6e-196:
		tmp = x / (z / y)
	elif a <= 6.6e+62:
		tmp = t_1
	else:
		tmp = x - (t / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-t) / Float64(z / Float64(y - z)))
	tmp = 0.0
	if (a <= -1.7e+26)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (a <= 7.5e-277)
		tmp = t_1;
	elseif (a <= 2.6e-196)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 6.6e+62)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(t / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -t / (z / (y - z));
	tmp = 0.0;
	if (a <= -1.7e+26)
		tmp = x - (x / (a / y));
	elseif (a <= 7.5e-277)
		tmp = t_1;
	elseif (a <= 2.6e-196)
		tmp = x / (z / y);
	elseif (a <= 6.6e+62)
		tmp = t_1;
	else
		tmp = x - (t / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.7e+26], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e-277], t$95$1, If[LessEqual[a, 2.6e-196], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.6e+62], t$95$1, N[(x - N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.7000000000000001e26

   1. Initial program 68.9%

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

      1. associate-*l/ 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in z around 0 71.4%

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

   5. Taylor expanded in t around 0 53.6%

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

      1. mul-1-neg 53.6%

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

      2. unsub-neg 53.6%

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

      3. associate-/l* 61.6%

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

   7. Simplified 61.6%

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

   if -1.7000000000000001e26 < a < 7.49999999999999971e-277 or 2.5999999999999998e-196 < a < 6.6e62

   1. Initial program 62.7%

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

      1. associate-*l/ 74.5%

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

   3. Simplified 74.5%

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

   4. Taylor expanded in x around -inf 76.5%

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

   5. Taylor expanded in x around 0 54.0%

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

      1. associate-/l* 67.0%

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

      2. associate-/r/ 55.0%

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

   7. Simplified 55.0%

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

   8. Taylor expanded in a around 0 45.0%

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

      1. mul-1-neg 45.0%

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

      2. associate-/l* 58.6%

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

   10. Simplified 58.6%

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

   if 7.49999999999999971e-277 < a < 2.5999999999999998e-196

   1. Initial program 86.2%

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

      1. associate-*l/ 86.0%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in y around -inf 76.2%

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

   5. Taylor expanded in t around 0 61.4%

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

      1. mul-1-neg 61.4%

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

      2. associate-/l* 68.4%

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

      3. distribute-neg-frac 68.4%

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

   7. Simplified 68.4%

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

   8. Taylor expanded in a around 0 61.4%

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

      1. associate-/l* 68.4%

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

   10. Simplified 68.4%

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

   if 6.6e62 < a

   1. Initial program 76.1%

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

      1. associate-*l/ 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in a around inf 71.4%

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

      1. associate-/l* 80.2%

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

   6. Simplified 80.2%

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

   7. Taylor expanded in y around 0 67.4%

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

      1. associate-*r/ 67.4%

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

      2. mul-1-neg 67.4%

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

   9. Simplified 67.4%

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

   10. Taylor expanded in t around inf 60.5%

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

       1. mul-1-neg 60.5%

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

       2. associate-/l* 67.0%

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

       3. distribute-neg-frac 67.0%

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

   12. Simplified 67.0%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+26}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-277}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-196}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+62}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 18: 38.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{z}{y}}\\ \mathbf{if}\;a \leq -31000000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-191}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-309}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-278}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+62}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (/ z y))))
   (if (<= a -31000000000000.0)
     x
     (if (<= a -1.15e-191)
       t
       (if (<= a 3e-309)
         t_1
         (if (<= a 5.4e-278)
           t
           (if (<= a 4.5e-196) t_1 (if (<= a 8.8e+62) t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (z / y);
	double tmp;
	if (a <= -31000000000000.0) {
		tmp = x;
	} else if (a <= -1.15e-191) {
		tmp = t;
	} else if (a <= 3e-309) {
		tmp = t_1;
	} else if (a <= 5.4e-278) {
		tmp = t;
	} else if (a <= 4.5e-196) {
		tmp = t_1;
	} else if (a <= 8.8e+62) {
		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) :: t_1
    real(8) :: tmp
    t_1 = x / (z / y)
    if (a <= (-31000000000000.0d0)) then
        tmp = x
    else if (a <= (-1.15d-191)) then
        tmp = t
    else if (a <= 3d-309) then
        tmp = t_1
    else if (a <= 5.4d-278) then
        tmp = t
    else if (a <= 4.5d-196) then
        tmp = t_1
    else if (a <= 8.8d+62) 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 t_1 = x / (z / y);
	double tmp;
	if (a <= -31000000000000.0) {
		tmp = x;
	} else if (a <= -1.15e-191) {
		tmp = t;
	} else if (a <= 3e-309) {
		tmp = t_1;
	} else if (a <= 5.4e-278) {
		tmp = t;
	} else if (a <= 4.5e-196) {
		tmp = t_1;
	} else if (a <= 8.8e+62) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (z / y)
	tmp = 0
	if a <= -31000000000000.0:
		tmp = x
	elif a <= -1.15e-191:
		tmp = t
	elif a <= 3e-309:
		tmp = t_1
	elif a <= 5.4e-278:
		tmp = t
	elif a <= 4.5e-196:
		tmp = t_1
	elif a <= 8.8e+62:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(z / y))
	tmp = 0.0
	if (a <= -31000000000000.0)
		tmp = x;
	elseif (a <= -1.15e-191)
		tmp = t;
	elseif (a <= 3e-309)
		tmp = t_1;
	elseif (a <= 5.4e-278)
		tmp = t;
	elseif (a <= 4.5e-196)
		tmp = t_1;
	elseif (a <= 8.8e+62)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (z / y);
	tmp = 0.0;
	if (a <= -31000000000000.0)
		tmp = x;
	elseif (a <= -1.15e-191)
		tmp = t;
	elseif (a <= 3e-309)
		tmp = t_1;
	elseif (a <= 5.4e-278)
		tmp = t;
	elseif (a <= 4.5e-196)
		tmp = t_1;
	elseif (a <= 8.8e+62)
		tmp = t;
	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]}, If[LessEqual[a, -31000000000000.0], x, If[LessEqual[a, -1.15e-191], t, If[LessEqual[a, 3e-309], t$95$1, If[LessEqual[a, 5.4e-278], t, If[LessEqual[a, 4.5e-196], t$95$1, If[LessEqual[a, 8.8e+62], t, x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.1e13 or 8.80000000000000058e62 < a

   1. Initial program 72.6%

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

      1. associate-*l/ 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in a around inf 54.1%

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

   if -3.1e13 < a < -1.15000000000000005e-191 or 3.000000000000001e-309 < a < 5.4000000000000003e-278 or 4.5e-196 < a < 8.80000000000000058e62

   1. Initial program 59.5%

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

      1. associate-*l/ 73.3%

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

   3. Simplified 73.3%

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

   4. Taylor expanded in z around inf 47.4%

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

   if -1.15000000000000005e-191 < a < 3.000000000000001e-309 or 5.4000000000000003e-278 < a < 4.5e-196

   1. Initial program 78.3%

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

      1. associate-*l/ 81.0%

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

   3. Simplified 81.0%

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

   4. Taylor expanded in y around -inf 79.9%

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

   5. Taylor expanded in t around 0 60.7%

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

      1. mul-1-neg 60.7%

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

      2. associate-/l* 65.8%

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

      3. distribute-neg-frac 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in a around 0 55.0%

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

      1. associate-/l* 57.7%

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

   10. Simplified 57.7%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -31000000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-191}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-309}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-278}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-196}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+62}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 37.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -530000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-192}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-307}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-279}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-196}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+60}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -530000000.0)
   x
   (if (<= a -1.15e-192)
     t
     (if (<= a 3.7e-307)
       (/ (* x y) z)
       (if (<= a 2.8e-279)
         t
         (if (<= a 4.1e-196) (/ x (/ z y)) (if (<= a 8.2e+60) t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -530000000.0) {
		tmp = x;
	} else if (a <= -1.15e-192) {
		tmp = t;
	} else if (a <= 3.7e-307) {
		tmp = (x * y) / z;
	} else if (a <= 2.8e-279) {
		tmp = t;
	} else if (a <= 4.1e-196) {
		tmp = x / (z / y);
	} else if (a <= 8.2e+60) {
		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 <= (-530000000.0d0)) then
        tmp = x
    else if (a <= (-1.15d-192)) then
        tmp = t
    else if (a <= 3.7d-307) then
        tmp = (x * y) / z
    else if (a <= 2.8d-279) then
        tmp = t
    else if (a <= 4.1d-196) then
        tmp = x / (z / y)
    else if (a <= 8.2d+60) 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 <= -530000000.0) {
		tmp = x;
	} else if (a <= -1.15e-192) {
		tmp = t;
	} else if (a <= 3.7e-307) {
		tmp = (x * y) / z;
	} else if (a <= 2.8e-279) {
		tmp = t;
	} else if (a <= 4.1e-196) {
		tmp = x / (z / y);
	} else if (a <= 8.2e+60) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -530000000.0:
		tmp = x
	elif a <= -1.15e-192:
		tmp = t
	elif a <= 3.7e-307:
		tmp = (x * y) / z
	elif a <= 2.8e-279:
		tmp = t
	elif a <= 4.1e-196:
		tmp = x / (z / y)
	elif a <= 8.2e+60:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -530000000.0)
		tmp = x;
	elseif (a <= -1.15e-192)
		tmp = t;
	elseif (a <= 3.7e-307)
		tmp = Float64(Float64(x * y) / z);
	elseif (a <= 2.8e-279)
		tmp = t;
	elseif (a <= 4.1e-196)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 8.2e+60)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -530000000.0)
		tmp = x;
	elseif (a <= -1.15e-192)
		tmp = t;
	elseif (a <= 3.7e-307)
		tmp = (x * y) / z;
	elseif (a <= 2.8e-279)
		tmp = t;
	elseif (a <= 4.1e-196)
		tmp = x / (z / y);
	elseif (a <= 8.2e+60)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -530000000.0], x, If[LessEqual[a, -1.15e-192], t, If[LessEqual[a, 3.7e-307], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 2.8e-279], t, If[LessEqual[a, 4.1e-196], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e+60], t, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.3e8 or 8.2e60 < a

   1. Initial program 72.6%

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

      1. associate-*l/ 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in a around inf 54.1%

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

   if -5.3e8 < a < -1.15000000000000009e-192 or 3.7e-307 < a < 2.8000000000000001e-279 or 4.10000000000000021e-196 < a < 8.2e60

   1. Initial program 59.5%

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

      1. associate-*l/ 73.3%

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

   3. Simplified 73.3%

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

   4. Taylor expanded in z around inf 47.4%

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

   if -1.15000000000000009e-192 < a < 3.7e-307

   1. Initial program 73.3%

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

      1. associate-*l/ 77.9%

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

   3. Simplified 77.9%

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

   4. Taylor expanded in y around -inf 82.3%

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

   5. Taylor expanded in t around 0 60.3%

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

      1. mul-1-neg 60.3%

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

      2. associate-/l* 64.2%

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

      3. distribute-neg-frac 64.2%

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

   7. Simplified 64.2%

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

   8. Taylor expanded in a around 0 51.0%

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

   if 2.8000000000000001e-279 < a < 4.10000000000000021e-196

   1. Initial program 86.2%

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

      1. associate-*l/ 86.0%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in y around -inf 76.2%

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

   5. Taylor expanded in t around 0 61.4%

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

      1. mul-1-neg 61.4%

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

      2. associate-/l* 68.4%

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

      3. distribute-neg-frac 68.4%

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

   7. Simplified 68.4%

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

   8. Taylor expanded in a around 0 61.4%

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

      1. associate-/l* 68.4%

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

   10. Simplified 68.4%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -530000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-192}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-307}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-279}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-196}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+60}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 47.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;z \leq -2.85 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-307}:\\ \;\;\;\;\frac{t \cdot y}{a - z}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ x (/ a y)))))
   (if (<= z -2.85e+81)
     t
     (if (<= z -1.9e-249)
       t_1
       (if (<= z -2e-307) (/ (* t y) (- a z)) (if (<= z 2.35e+122) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x / (a / y));
	double tmp;
	if (z <= -2.85e+81) {
		tmp = t;
	} else if (z <= -1.9e-249) {
		tmp = t_1;
	} else if (z <= -2e-307) {
		tmp = (t * y) / (a - z);
	} else if (z <= 2.35e+122) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (x / (a / y))
    if (z <= (-2.85d+81)) then
        tmp = t
    else if (z <= (-1.9d-249)) then
        tmp = t_1
    else if (z <= (-2d-307)) then
        tmp = (t * y) / (a - z)
    else if (z <= 2.35d+122) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x / (a / y));
	double tmp;
	if (z <= -2.85e+81) {
		tmp = t;
	} else if (z <= -1.9e-249) {
		tmp = t_1;
	} else if (z <= -2e-307) {
		tmp = (t * y) / (a - z);
	} else if (z <= 2.35e+122) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x / (a / y))
	tmp = 0
	if z <= -2.85e+81:
		tmp = t
	elif z <= -1.9e-249:
		tmp = t_1
	elif z <= -2e-307:
		tmp = (t * y) / (a - z)
	elif z <= 2.35e+122:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x / Float64(a / y)))
	tmp = 0.0
	if (z <= -2.85e+81)
		tmp = t;
	elseif (z <= -1.9e-249)
		tmp = t_1;
	elseif (z <= -2e-307)
		tmp = Float64(Float64(t * y) / Float64(a - z));
	elseif (z <= 2.35e+122)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x / (a / y));
	tmp = 0.0;
	if (z <= -2.85e+81)
		tmp = t;
	elseif (z <= -1.9e-249)
		tmp = t_1;
	elseif (z <= -2e-307)
		tmp = (t * y) / (a - z);
	elseif (z <= 2.35e+122)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.85e+81], t, If[LessEqual[z, -1.9e-249], t$95$1, If[LessEqual[z, -2e-307], N[(N[(t * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e+122], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.85000000000000017e81 or 2.35000000000000012e122 < z

   1. Initial program 30.5%

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

      1. associate-*l/ 64.0%

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

   3. Simplified 64.0%

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

   4. Taylor expanded in z around inf 61.0%

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

   if -2.85000000000000017e81 < z < -1.9e-249 or -1.99999999999999982e-307 < z < 2.35000000000000012e122

   1. Initial program 87.3%

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

      1. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in z around 0 62.4%

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

   5. Taylor expanded in t around 0 47.2%

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

      1. mul-1-neg 47.2%

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

      2. unsub-neg 47.2%

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

      3. associate-/l* 50.9%

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

   7. Simplified 50.9%

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

   if -1.9e-249 < z < -1.99999999999999982e-307

   1. Initial program 100.0%

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

      1. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in x around -inf 91.7%

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

   5. Taylor expanded in x around 0 76.3%

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

      1. associate-/l* 68.4%

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

      2. associate-/r/ 68.5%

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

   7. Simplified 68.5%

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

   8. Taylor expanded in y around inf 76.3%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-249}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-307}:\\ \;\;\;\;\frac{t \cdot y}{a - z}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+122}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 21: 64.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.36 \cdot 10^{-85}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+108}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.36e-85)
   (* t (/ (- y z) (- a z)))
   (if (<= z 1.55e+108) (+ x (* (- t x) (/ y a))) (+ t (/ a (/ z (- t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.36e-85) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 1.55e+108) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t + (a / (z / (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 <= (-2.36d-85)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 1.55d+108) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t + (a / (z / (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 <= -2.36e-85) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 1.55e+108) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t + (a / (z / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.36e-85:
		tmp = t * ((y - z) / (a - z))
	elif z <= 1.55e+108:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t + (a / (z / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.36e-85)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 1.55e+108)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = Float64(t + Float64(a / Float64(z / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.36e-85)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 1.55e+108)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t + (a / (z / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.36e-85], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e+108], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.35999999999999999e-85

   1. Initial program 50.9%

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

      1. associate-*l/ 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in x around 0 45.2%

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

      1. associate-*r/ 61.2%

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

   6. Simplified 61.2%

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

   if -2.35999999999999999e-85 < z < 1.5500000000000001e108

   1. Initial program 91.1%

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

      1. associate-*l/ 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in z around 0 70.2%

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

   if 1.5500000000000001e108 < z

   1. Initial program 27.0%

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

      1. associate-*l/ 63.1%

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

   3. Simplified 63.1%

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

   4. Taylor expanded in z around inf 70.1%

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

      1. associate--l+ 70.1%

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

      2. associate-*r/ 70.1%

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

      3. associate-*r/ 70.1%

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

      4. div-sub 70.1%

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

      5. distribute-lft-out-- 70.1%

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

      6. associate-*r/ 70.1%

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

      7. distribute-rgt-out-- 70.4%

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

      8. mul-1-neg 70.4%

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

      9. unsub-neg 70.4%

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

      10. associate-/l* 87.3%

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

   6. Simplified 87.3%

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

   7. Taylor expanded in y around 0 69.8%

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

      1. sub-neg 69.8%

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

      2. mul-1-neg 69.8%

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

      3. remove-double-neg 69.8%

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

      4. associate-/l* 77.7%

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

   9. Simplified 77.7%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.36 \cdot 10^{-85}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+108}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \end{array} \]

Alternative 22: 63.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-85}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+74}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e-85)
   (* t (/ (- y z) (- a z)))
   (if (<= z 8.5e+74) (+ x (/ y (/ a (- t x)))) (+ t (/ a (/ z (- t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e-85) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 8.5e+74) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t + (a / (z / (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 <= (-2.4d-85)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 8.5d+74) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t + (a / (z / (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 <= -2.4e-85) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 8.5e+74) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t + (a / (z / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e-85:
		tmp = t * ((y - z) / (a - z))
	elif z <= 8.5e+74:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t + (a / (z / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e-85)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 8.5e+74)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t + Float64(a / Float64(z / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.4e-85)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 8.5e+74)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t + (a / (z / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e-85], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+74], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4000000000000001e-85

   1. Initial program 50.9%

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

      1. associate-*l/ 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in x around 0 45.2%

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

      1. associate-*r/ 61.2%

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

   6. Simplified 61.2%

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

   if -2.4000000000000001e-85 < z < 8.50000000000000028e74

   1. Initial program 94.4%

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

      1. associate-*l/ 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in z around 0 72.0%

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

      1. associate-/l* 72.7%

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

   6. Simplified 72.7%

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

   if 8.50000000000000028e74 < z

   1. Initial program 30.2%

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

      1. associate-*l/ 65.8%

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

   3. Simplified 65.8%

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

   4. Taylor expanded in z around inf 67.9%

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

      1. associate--l+ 67.9%

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

      2. associate-*r/ 67.9%

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

      3. associate-*r/ 67.9%

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

      4. div-sub 67.9%

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

      5. distribute-lft-out-- 67.9%

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

      6. associate-*r/ 67.9%

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

      7. distribute-rgt-out-- 68.1%

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

      8. mul-1-neg 68.1%

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

      9. unsub-neg 68.1%

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

      10. associate-/l* 82.1%

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

   6. Simplified 82.1%

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

   7. Taylor expanded in y around 0 65.8%

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

      1. sub-neg 65.8%

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

      2. mul-1-neg 65.8%

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

      3. remove-double-neg 65.8%

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

      4. associate-/l* 70.6%

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

   9. Simplified 70.6%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-85}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+74}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \end{array} \]

Alternative 23: 48.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+83}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e+83) t (if (<= z 1.85e+112) (* x (- 1.0 (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+83) {
		tmp = t;
	} else if (z <= 1.85e+112) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2d+83)) then
        tmp = t
    else if (z <= 1.85d+112) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+83) {
		tmp = t;
	} else if (z <= 1.85e+112) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2e+83:
		tmp = t
	elif z <= 1.85e+112:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e+83)
		tmp = t;
	elseif (z <= 1.85e+112)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2e+83)
		tmp = t;
	elseif (z <= 1.85e+112)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e+83], t, If[LessEqual[z, 1.85e+112], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000006e83 or 1.85000000000000002e112 < z

   1. Initial program 30.5%

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

      1. associate-*l/ 64.0%

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

   3. Simplified 64.0%

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

   4. Taylor expanded in z around inf 61.0%

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

   if -2.00000000000000006e83 < z < 1.85000000000000002e112

   1. Initial program 88.2%

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

      1. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in z around 0 63.9%

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

   5. Taylor expanded in x around inf 50.3%

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

      1. mul-1-neg 50.3%

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

      2. unsub-neg 50.3%

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

   7. Simplified 50.3%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+83}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 24: 48.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+83}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+114}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.3e+83) t (if (<= z 5e+114) (- x (/ x (/ a y))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e+83) {
		tmp = t;
	} else if (z <= 5e+114) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.3d+83)) then
        tmp = t
    else if (z <= 5d+114) then
        tmp = x - (x / (a / y))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e+83) {
		tmp = t;
	} else if (z <= 5e+114) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.3e+83:
		tmp = t
	elif z <= 5e+114:
		tmp = x - (x / (a / y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.3e+83)
		tmp = t;
	elseif (z <= 5e+114)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.3e+83)
		tmp = t;
	elseif (z <= 5e+114)
		tmp = x - (x / (a / y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.3e+83], t, If[LessEqual[z, 5e+114], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -3.29999999999999985e83 or 5.0000000000000001e114 < z

   1. Initial program 30.5%

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

      1. associate-*l/ 64.0%

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

   3. Simplified 64.0%

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

   4. Taylor expanded in z around inf 61.0%

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

   if -3.29999999999999985e83 < z < 5.0000000000000001e114

   1. Initial program 88.2%

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

      1. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in z around 0 63.9%

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

   5. Taylor expanded in t around 0 46.4%

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

      1. mul-1-neg 46.4%

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

      2. unsub-neg 46.4%

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

      3. associate-/l* 50.3%

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

   7. Simplified 50.3%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+83}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+114}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 25: 38.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5500000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+61}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5500000000000.0) x (if (<= a 4.8e+61) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5500000000000.0) {
		tmp = x;
	} else if (a <= 4.8e+61) {
		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 <= (-5500000000000.0d0)) then
        tmp = x
    else if (a <= 4.8d+61) 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 <= -5500000000000.0) {
		tmp = x;
	} else if (a <= 4.8e+61) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5500000000000.0:
		tmp = x
	elif a <= 4.8e+61:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5500000000000.0)
		tmp = x;
	elseif (a <= 4.8e+61)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5500000000000.0)
		tmp = x;
	elseif (a <= 4.8e+61)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5500000000000.0], x, If[LessEqual[a, 4.8e+61], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -5.5e12 or 4.7999999999999998e61 < a

   1. Initial program 72.6%

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

      1. associate-*l/ 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in a around inf 54.1%

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

   if -5.5e12 < a < 4.7999999999999998e61

   1. Initial program 64.1%

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

      1. associate-*l/ 75.2%

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

   3. Simplified 75.2%

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

   4. Taylor expanded in z around inf 40.0%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5500000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+61}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 26: 25.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 t)

C

double code(double x, double y, double z, double t, double a) {
	return t;
}

Fortran

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

Java

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

Python

def code(x, y, z, t, a):
	return t

Julia

function code(x, y, z, t, a)
	return t
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 67.7%

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

   1. associate-*l/ 82.2%

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

3. Simplified 82.2%

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

4. Taylor expanded in z around inf 27.9%

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

5. Final simplification 27.9%

   \[\leadsto t \]

Developer target: 83.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023308 
(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))))