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

Percentage Accurate: 68.5% → 89.5%

Time: 30.2s

Alternatives: 25

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.5% 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: 89.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+159} \lor \neg \left(z \leq 1.1 \cdot 10^{+120}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.6e+159) (not (<= z 1.1e+120)))
   (+ t (/ (- x t) (/ z (- y a))))
   (fma (/ (- y z) (- a z)) (- t x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e+159) || !(z <= 1.1e+120)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = fma(((y - z) / (a - z)), (t - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.6e+159) || !(z <= 1.1e+120))
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = fma(Float64(Float64(y - z) / Float64(a - z)), Float64(t - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.6e+159], N[Not[LessEqual[z, 1.1e+120]], $MachinePrecision]], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6e159 or 1.1000000000000001e120 < z

   1. Initial program 26.8%

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

      1. associate-*l/ 50.8%

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

   3. Simplified 50.8%

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

   5. Taylor expanded in z around inf 66.0%

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

      1. associate--l+ 66.0%

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

      2. associate-*r/ 66.0%

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

      3. associate-*r/ 66.0%

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

      4. div-sub 66.1%

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

      5. distribute-lft-out-- 66.1%

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

      6. associate-*r/ 66.1%

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

      7. mul-1-neg 66.1%

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

      8. distribute-rgt-out-- 66.1%

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

      9. unsub-neg 66.1%

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

      10. associate-/l* 90.7%

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

   7. Simplified 90.7%

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

   if -2.6e159 < z < 1.1000000000000001e120

   1. Initial program 84.9%

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

      1. +-commutative 84.9%

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

      2. associate-*l/ 94.1%

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

      3. fma-def 94.1%

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

   3. Simplified 94.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+159} \lor \neg \left(z \leq 1.1 \cdot 10^{+120}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 50.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{t \cdot y}{z}\\ t_2 := \frac{-t}{\frac{z}{y - z}}\\ t_3 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+83}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -96000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-24}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-75}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-44}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-7}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+102}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+146}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ (* t y) z)))
        (t_2 (/ (- t) (/ z (- y z))))
        (t_3 (* x (- 1.0 (/ y a)))))
   (if (<= z -2.9e+83)
     t_2
     (if (<= z -4.5e+60)
       (* x (/ (- y a) z))
       (if (<= z -96000000.0)
         t_1
         (if (<= z -1.35e-24)
           (* (- t x) (/ y a))
           (if (<= z -4.4e-27)
             t_1
             (if (<= z 1.8e-75)
               t_3
               (if (<= z 6e-44)
                 (/ (* t (- y z)) a)
                 (if (<= z 3.05e-7)
                   t_3
                   (if (<= z 7.8e+102)
                     (+ x (* t (/ y a)))
                     (if (<= z 7e+146) (* (/ y z) (- x t)) t_2))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((t * y) / z);
	double t_2 = -t / (z / (y - z));
	double t_3 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -2.9e+83) {
		tmp = t_2;
	} else if (z <= -4.5e+60) {
		tmp = x * ((y - a) / z);
	} else if (z <= -96000000.0) {
		tmp = t_1;
	} else if (z <= -1.35e-24) {
		tmp = (t - x) * (y / a);
	} else if (z <= -4.4e-27) {
		tmp = t_1;
	} else if (z <= 1.8e-75) {
		tmp = t_3;
	} else if (z <= 6e-44) {
		tmp = (t * (y - z)) / a;
	} else if (z <= 3.05e-7) {
		tmp = t_3;
	} else if (z <= 7.8e+102) {
		tmp = x + (t * (y / a));
	} else if (z <= 7e+146) {
		tmp = (y / z) * (x - t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t - ((t * y) / z)
    t_2 = -t / (z / (y - z))
    t_3 = x * (1.0d0 - (y / a))
    if (z <= (-2.9d+83)) then
        tmp = t_2
    else if (z <= (-4.5d+60)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-96000000.0d0)) then
        tmp = t_1
    else if (z <= (-1.35d-24)) then
        tmp = (t - x) * (y / a)
    else if (z <= (-4.4d-27)) then
        tmp = t_1
    else if (z <= 1.8d-75) then
        tmp = t_3
    else if (z <= 6d-44) then
        tmp = (t * (y - z)) / a
    else if (z <= 3.05d-7) then
        tmp = t_3
    else if (z <= 7.8d+102) then
        tmp = x + (t * (y / a))
    else if (z <= 7d+146) then
        tmp = (y / z) * (x - t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((t * y) / z);
	double t_2 = -t / (z / (y - z));
	double t_3 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -2.9e+83) {
		tmp = t_2;
	} else if (z <= -4.5e+60) {
		tmp = x * ((y - a) / z);
	} else if (z <= -96000000.0) {
		tmp = t_1;
	} else if (z <= -1.35e-24) {
		tmp = (t - x) * (y / a);
	} else if (z <= -4.4e-27) {
		tmp = t_1;
	} else if (z <= 1.8e-75) {
		tmp = t_3;
	} else if (z <= 6e-44) {
		tmp = (t * (y - z)) / a;
	} else if (z <= 3.05e-7) {
		tmp = t_3;
	} else if (z <= 7.8e+102) {
		tmp = x + (t * (y / a));
	} else if (z <= 7e+146) {
		tmp = (y / z) * (x - t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((t * y) / z)
	t_2 = -t / (z / (y - z))
	t_3 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -2.9e+83:
		tmp = t_2
	elif z <= -4.5e+60:
		tmp = x * ((y - a) / z)
	elif z <= -96000000.0:
		tmp = t_1
	elif z <= -1.35e-24:
		tmp = (t - x) * (y / a)
	elif z <= -4.4e-27:
		tmp = t_1
	elif z <= 1.8e-75:
		tmp = t_3
	elif z <= 6e-44:
		tmp = (t * (y - z)) / a
	elif z <= 3.05e-7:
		tmp = t_3
	elif z <= 7.8e+102:
		tmp = x + (t * (y / a))
	elif z <= 7e+146:
		tmp = (y / z) * (x - t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(t * y) / z))
	t_2 = Float64(Float64(-t) / Float64(z / Float64(y - z)))
	t_3 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -2.9e+83)
		tmp = t_2;
	elseif (z <= -4.5e+60)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -96000000.0)
		tmp = t_1;
	elseif (z <= -1.35e-24)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (z <= -4.4e-27)
		tmp = t_1;
	elseif (z <= 1.8e-75)
		tmp = t_3;
	elseif (z <= 6e-44)
		tmp = Float64(Float64(t * Float64(y - z)) / a);
	elseif (z <= 3.05e-7)
		tmp = t_3;
	elseif (z <= 7.8e+102)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 7e+146)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((t * y) / z);
	t_2 = -t / (z / (y - z));
	t_3 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -2.9e+83)
		tmp = t_2;
	elseif (z <= -4.5e+60)
		tmp = x * ((y - a) / z);
	elseif (z <= -96000000.0)
		tmp = t_1;
	elseif (z <= -1.35e-24)
		tmp = (t - x) * (y / a);
	elseif (z <= -4.4e-27)
		tmp = t_1;
	elseif (z <= 1.8e-75)
		tmp = t_3;
	elseif (z <= 6e-44)
		tmp = (t * (y - z)) / a;
	elseif (z <= 3.05e-7)
		tmp = t_3;
	elseif (z <= 7.8e+102)
		tmp = x + (t * (y / a));
	elseif (z <= 7e+146)
		tmp = (y / z) * (x - t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(t * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e+83], t$95$2, If[LessEqual[z, -4.5e+60], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -96000000.0], t$95$1, If[LessEqual[z, -1.35e-24], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.4e-27], t$95$1, If[LessEqual[z, 1.8e-75], t$95$3, If[LessEqual[z, 6e-44], N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 3.05e-7], t$95$3, If[LessEqual[z, 7.8e+102], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+146], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if z < -2.89999999999999999e83 or 7.0000000000000002e146 < z

   1. Initial program 33.0%

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

      1. associate-*l/ 56.5%

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

   3. Simplified 56.5%

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

   5. Taylor expanded in x around 0 34.9%

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

   6. Taylor expanded in a around 0 34.3%

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

      1. mul-1-neg 34.3%

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

      2. associate-/l* 57.8%

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

      3. distribute-neg-frac 57.8%

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

   8. Simplified 57.8%

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

   if -2.89999999999999999e83 < z < -4.50000000000000013e60

   1. Initial program 30.3%

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

      1. associate-*l/ 71.7%

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

   3. Simplified 71.7%

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

   5. Taylor expanded in z around inf 46.2%

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

      1. associate--l+ 46.2%

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

      2. associate-*r/ 46.2%

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

      3. associate-*r/ 46.2%

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

      4. div-sub 46.2%

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

      5. distribute-lft-out-- 46.2%

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

      6. associate-*r/ 46.2%

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

      7. mul-1-neg 46.2%

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

      8. distribute-rgt-out-- 46.2%

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

      9. unsub-neg 46.2%

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

      10. associate-/l* 72.4%

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

   7. Simplified 72.4%

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

   8. Taylor expanded in t around 0 47.1%

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

      1. associate-*r/ 73.5%

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

   10. Simplified 73.5%

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

   if -4.50000000000000013e60 < z < -9.6e7 or -1.35000000000000003e-24 < z < -4.39999999999999974e-27

   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/ 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. Add Preprocessing

   5. Taylor expanded in x around 0 85.8%

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

   6. Taylor expanded in z around inf 85.9%

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

      1. associate--l+ 85.9%

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

      2. associate-*r/ 85.9%

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

      3. associate-*r/ 85.9%

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

      4. div-sub 85.9%

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

      5. distribute-lft-out-- 85.9%

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

      6. associate-*r/ 85.9%

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

      7. mul-1-neg 85.9%

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

      8. unsub-neg 85.9%

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

      9. *-commutative 85.9%

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

      10. distribute-lft-out-- 85.9%

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

   8. Simplified 85.9%

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

   9. Taylor expanded in y around inf 84.2%

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

       1. *-commutative 84.2%

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

   11. Simplified 84.2%

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

   if -9.6e7 < z < -1.35000000000000003e-24

   1. Initial program 86.6%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around -inf 50.8%

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

      1. associate-*l/ 64.2%

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

   7. Simplified 64.2%

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

   8. Taylor expanded in a around inf 64.2%

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

   if -4.39999999999999974e-27 < z < 1.8e-75 or 6.0000000000000005e-44 < z < 3.04999999999999991e-7

   1. Initial program 93.5%

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

      1. associate-*l/ 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in z around 0 84.5%

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

   6. Taylor expanded in x around inf 72.2%

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

      1. mul-1-neg 72.2%

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

      2. unsub-neg 72.2%

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

   8. Simplified 72.2%

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

   if 1.8e-75 < z < 6.0000000000000005e-44

   1. Initial program 89.0%

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

      1. associate-*l/ 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in x around 0 77.8%

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

   6. Taylor expanded in a around inf 78.1%

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

   if 3.04999999999999991e-7 < z < 7.7999999999999997e102

   1. Initial program 61.3%

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

      1. associate-*l/ 80.7%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in z around 0 70.5%

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

   6. Taylor expanded in t around inf 65.7%

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

      1. associate-*r/ 70.4%

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

   8. Simplified 70.4%

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

   if 7.7999999999999997e102 < z < 7.0000000000000002e146

   1. Initial program 36.6%

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

      1. associate-*l/ 56.8%

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

   3. Simplified 56.8%

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

   5. Taylor expanded in y around -inf 38.3%

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

      1. associate-*l/ 68.5%

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

   7. Simplified 68.5%

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

   8. Taylor expanded in a around 0 68.6%

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

      1. associate-*r/ 68.6%

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

      2. neg-mul-1 68.6%

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

   10. Simplified 68.6%

       \[\leadsto \color{blue}{\frac{-y}{z}} \cdot \left(t - x\right) \]
3. Recombined 8 regimes into one program.

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+83}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -96000000:\\ \;\;\;\;t - \frac{t \cdot y}{z}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-24}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-27}:\\ \;\;\;\;t - \frac{t \cdot y}{z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-44}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+102}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+146}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-t}{\frac{z}{y - z}}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -9.8 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -0.0002:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-25}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-27}:\\ \;\;\;\;t - \frac{t \cdot y}{z}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-75}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-44}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a}\\ \mathbf{elif}\;z \leq 2.85:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+103}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+146}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t) (/ z (- y z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= z -9.8e+84)
     t_1
     (if (<= z -2.3e+60)
       (* x (/ (- y a) z))
       (if (<= z -0.0002)
         (/ (- t) (/ (- a z) z))
         (if (<= z -4.4e-25)
           (* (- t x) (/ y a))
           (if (<= z -2.8e-27)
             (- t (/ (* t y) z))
             (if (<= z 3.2e-75)
               t_2
               (if (<= z 6e-44)
                 (/ (* t (- y z)) a)
                 (if (<= z 2.85)
                   t_2
                   (if (<= z 4e+103)
                     (+ x (* t (/ y a)))
                     (if (<= z 3.3e+146) (* (/ y z) (- x t)) t_1))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / (z / (y - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -9.8e+84) {
		tmp = t_1;
	} else if (z <= -2.3e+60) {
		tmp = x * ((y - a) / z);
	} else if (z <= -0.0002) {
		tmp = -t / ((a - z) / z);
	} else if (z <= -4.4e-25) {
		tmp = (t - x) * (y / a);
	} else if (z <= -2.8e-27) {
		tmp = t - ((t * y) / z);
	} else if (z <= 3.2e-75) {
		tmp = t_2;
	} else if (z <= 6e-44) {
		tmp = (t * (y - z)) / a;
	} else if (z <= 2.85) {
		tmp = t_2;
	} else if (z <= 4e+103) {
		tmp = x + (t * (y / a));
	} else if (z <= 3.3e+146) {
		tmp = (y / z) * (x - t);
	} 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) :: t_2
    real(8) :: tmp
    t_1 = -t / (z / (y - z))
    t_2 = x * (1.0d0 - (y / a))
    if (z <= (-9.8d+84)) then
        tmp = t_1
    else if (z <= (-2.3d+60)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-0.0002d0)) then
        tmp = -t / ((a - z) / z)
    else if (z <= (-4.4d-25)) then
        tmp = (t - x) * (y / a)
    else if (z <= (-2.8d-27)) then
        tmp = t - ((t * y) / z)
    else if (z <= 3.2d-75) then
        tmp = t_2
    else if (z <= 6d-44) then
        tmp = (t * (y - z)) / a
    else if (z <= 2.85d0) then
        tmp = t_2
    else if (z <= 4d+103) then
        tmp = x + (t * (y / a))
    else if (z <= 3.3d+146) then
        tmp = (y / z) * (x - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / (z / (y - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -9.8e+84) {
		tmp = t_1;
	} else if (z <= -2.3e+60) {
		tmp = x * ((y - a) / z);
	} else if (z <= -0.0002) {
		tmp = -t / ((a - z) / z);
	} else if (z <= -4.4e-25) {
		tmp = (t - x) * (y / a);
	} else if (z <= -2.8e-27) {
		tmp = t - ((t * y) / z);
	} else if (z <= 3.2e-75) {
		tmp = t_2;
	} else if (z <= 6e-44) {
		tmp = (t * (y - z)) / a;
	} else if (z <= 2.85) {
		tmp = t_2;
	} else if (z <= 4e+103) {
		tmp = x + (t * (y / a));
	} else if (z <= 3.3e+146) {
		tmp = (y / z) * (x - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -t / (z / (y - z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -9.8e+84:
		tmp = t_1
	elif z <= -2.3e+60:
		tmp = x * ((y - a) / z)
	elif z <= -0.0002:
		tmp = -t / ((a - z) / z)
	elif z <= -4.4e-25:
		tmp = (t - x) * (y / a)
	elif z <= -2.8e-27:
		tmp = t - ((t * y) / z)
	elif z <= 3.2e-75:
		tmp = t_2
	elif z <= 6e-44:
		tmp = (t * (y - z)) / a
	elif z <= 2.85:
		tmp = t_2
	elif z <= 4e+103:
		tmp = x + (t * (y / a))
	elif z <= 3.3e+146:
		tmp = (y / z) * (x - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-t) / Float64(z / Float64(y - z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -9.8e+84)
		tmp = t_1;
	elseif (z <= -2.3e+60)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -0.0002)
		tmp = Float64(Float64(-t) / Float64(Float64(a - z) / z));
	elseif (z <= -4.4e-25)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (z <= -2.8e-27)
		tmp = Float64(t - Float64(Float64(t * y) / z));
	elseif (z <= 3.2e-75)
		tmp = t_2;
	elseif (z <= 6e-44)
		tmp = Float64(Float64(t * Float64(y - z)) / a);
	elseif (z <= 2.85)
		tmp = t_2;
	elseif (z <= 4e+103)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 3.3e+146)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -t / (z / (y - z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -9.8e+84)
		tmp = t_1;
	elseif (z <= -2.3e+60)
		tmp = x * ((y - a) / z);
	elseif (z <= -0.0002)
		tmp = -t / ((a - z) / z);
	elseif (z <= -4.4e-25)
		tmp = (t - x) * (y / a);
	elseif (z <= -2.8e-27)
		tmp = t - ((t * y) / z);
	elseif (z <= 3.2e-75)
		tmp = t_2;
	elseif (z <= 6e-44)
		tmp = (t * (y - z)) / a;
	elseif (z <= 2.85)
		tmp = t_2;
	elseif (z <= 4e+103)
		tmp = x + (t * (y / a));
	elseif (z <= 3.3e+146)
		tmp = (y / z) * (x - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.8e+84], t$95$1, If[LessEqual[z, -2.3e+60], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.0002], N[((-t) / N[(N[(a - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.4e-25], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.8e-27], N[(t - N[(N[(t * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-75], t$95$2, If[LessEqual[z, 6e-44], N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 2.85], t$95$2, If[LessEqual[z, 4e+103], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+146], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if z < -9.8e84 or 3.30000000000000016e146 < z

   1. Initial program 33.0%

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

      1. associate-*l/ 56.5%

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

   3. Simplified 56.5%

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

   5. Taylor expanded in x around 0 34.9%

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

   6. Taylor expanded in a around 0 34.3%

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

      1. mul-1-neg 34.3%

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

      2. associate-/l* 57.8%

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

      3. distribute-neg-frac 57.8%

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

   8. Simplified 57.8%

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

   if -9.8e84 < z < -2.30000000000000017e60

   1. Initial program 30.3%

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

      1. associate-*l/ 71.7%

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

   3. Simplified 71.7%

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

   5. Taylor expanded in z around inf 46.2%

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

      1. associate--l+ 46.2%

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

      2. associate-*r/ 46.2%

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

      3. associate-*r/ 46.2%

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

      4. div-sub 46.2%

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

      5. distribute-lft-out-- 46.2%

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

      6. associate-*r/ 46.2%

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

      7. mul-1-neg 46.2%

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

      8. distribute-rgt-out-- 46.2%

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

      9. unsub-neg 46.2%

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

      10. associate-/l* 72.4%

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

   7. Simplified 72.4%

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

   8. Taylor expanded in t around 0 47.1%

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

      1. associate-*r/ 73.5%

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

   10. Simplified 73.5%

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

   if -2.30000000000000017e60 < z < -2.0000000000000001e-4

   1. Initial program 91.0%

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

      1. associate-*l/ 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around 0 82.2%

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

   6. Taylor expanded in y around 0 68.8%

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

      1. mul-1-neg 68.8%

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

      2. associate-/l* 68.8%

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

      3. distribute-neg-frac 68.8%

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

   8. Simplified 68.8%

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

   if -2.0000000000000001e-4 < z < -4.4000000000000004e-25

   1. Initial program 76.5%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around -inf 62.6%

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

      1. associate-*l/ 86.1%

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

   7. Simplified 86.1%

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

   8. Taylor expanded in a around inf 86.1%

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

   if -4.4000000000000004e-25 < z < -2.8e-27

   1. Initial program 99.5%

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

      1. associate-*l/ 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 99.5%

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

   6. Taylor expanded in z around inf 99.5%

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

      1. associate--l+ 99.5%

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

      2. associate-*r/ 99.5%

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

      3. associate-*r/ 99.5%

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

      4. div-sub 99.5%

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

      5. distribute-lft-out-- 99.5%

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

      6. associate-*r/ 99.5%

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

      7. mul-1-neg 99.5%

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

      8. unsub-neg 99.5%

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

      9. *-commutative 99.5%

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

      10. distribute-lft-out-- 99.5%

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

   8. Simplified 99.5%

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

   9. Taylor expanded in y around inf 99.5%

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

       1. *-commutative 99.5%

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

   11. Simplified 99.5%

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

   if -2.8e-27 < z < 3.19999999999999977e-75 or 6.0000000000000005e-44 < z < 2.85000000000000009

   1. Initial program 93.5%

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

      1. associate-*l/ 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in z around 0 84.5%

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

   6. Taylor expanded in x around inf 72.2%

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

      1. mul-1-neg 72.2%

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

      2. unsub-neg 72.2%

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

   8. Simplified 72.2%

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

   if 3.19999999999999977e-75 < z < 6.0000000000000005e-44

   1. Initial program 89.0%

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

      1. associate-*l/ 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in x around 0 77.8%

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

   6. Taylor expanded in a around inf 78.1%

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

   if 2.85000000000000009 < z < 4e103

   1. Initial program 61.3%

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

      1. associate-*l/ 80.7%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in z around 0 70.5%

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

   6. Taylor expanded in t around inf 65.7%

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

      1. associate-*r/ 70.4%

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

   8. Simplified 70.4%

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

   if 4e103 < z < 3.30000000000000016e146

   1. Initial program 36.6%

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

      1. associate-*l/ 56.8%

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

   3. Simplified 56.8%

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

   5. Taylor expanded in y around -inf 38.3%

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

      1. associate-*l/ 68.5%

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

   7. Simplified 68.5%

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

   8. Taylor expanded in a around 0 68.6%

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

      1. associate-*r/ 68.6%

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

      2. neg-mul-1 68.6%

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

   10. Simplified 68.6%

       \[\leadsto \color{blue}{\frac{-y}{z}} \cdot \left(t - x\right) \]
3. Recombined 9 regimes into one program.

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+84}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -0.0002:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-25}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-27}:\\ \;\;\;\;t - \frac{t \cdot y}{z}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-44}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a}\\ \mathbf{elif}\;z \leq 2.85:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+103}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+146}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-t}{\frac{z}{y - z}}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -1.52 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -0.0042:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a - z}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-24}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-27}:\\ \;\;\;\;t - \frac{t \cdot y}{z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-76}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-42}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a}\\ \mathbf{elif}\;z \leq 41000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+102}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+147}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t) (/ z (- y z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= z -1.52e+85)
     t_1
     (if (<= z -2.45e+60)
       (* x (/ (- y a) z))
       (if (<= z -0.0042)
         (/ (* z (- t)) (- a z))
         (if (<= z -1.5e-24)
           (* (- t x) (/ y a))
           (if (<= z -4e-27)
             (- t (/ (* t y) z))
             (if (<= z 4e-76)
               t_2
               (if (<= z 1.05e-42)
                 (/ (* t (- y z)) a)
                 (if (<= z 41000.0)
                   t_2
                   (if (<= z 1.15e+102)
                     (+ x (* t (/ y a)))
                     (if (<= z 8e+147) (* (/ y z) (- x t)) t_1))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / (z / (y - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -1.52e+85) {
		tmp = t_1;
	} else if (z <= -2.45e+60) {
		tmp = x * ((y - a) / z);
	} else if (z <= -0.0042) {
		tmp = (z * -t) / (a - z);
	} else if (z <= -1.5e-24) {
		tmp = (t - x) * (y / a);
	} else if (z <= -4e-27) {
		tmp = t - ((t * y) / z);
	} else if (z <= 4e-76) {
		tmp = t_2;
	} else if (z <= 1.05e-42) {
		tmp = (t * (y - z)) / a;
	} else if (z <= 41000.0) {
		tmp = t_2;
	} else if (z <= 1.15e+102) {
		tmp = x + (t * (y / a));
	} else if (z <= 8e+147) {
		tmp = (y / z) * (x - t);
	} 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) :: t_2
    real(8) :: tmp
    t_1 = -t / (z / (y - z))
    t_2 = x * (1.0d0 - (y / a))
    if (z <= (-1.52d+85)) then
        tmp = t_1
    else if (z <= (-2.45d+60)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-0.0042d0)) then
        tmp = (z * -t) / (a - z)
    else if (z <= (-1.5d-24)) then
        tmp = (t - x) * (y / a)
    else if (z <= (-4d-27)) then
        tmp = t - ((t * y) / z)
    else if (z <= 4d-76) then
        tmp = t_2
    else if (z <= 1.05d-42) then
        tmp = (t * (y - z)) / a
    else if (z <= 41000.0d0) then
        tmp = t_2
    else if (z <= 1.15d+102) then
        tmp = x + (t * (y / a))
    else if (z <= 8d+147) then
        tmp = (y / z) * (x - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / (z / (y - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -1.52e+85) {
		tmp = t_1;
	} else if (z <= -2.45e+60) {
		tmp = x * ((y - a) / z);
	} else if (z <= -0.0042) {
		tmp = (z * -t) / (a - z);
	} else if (z <= -1.5e-24) {
		tmp = (t - x) * (y / a);
	} else if (z <= -4e-27) {
		tmp = t - ((t * y) / z);
	} else if (z <= 4e-76) {
		tmp = t_2;
	} else if (z <= 1.05e-42) {
		tmp = (t * (y - z)) / a;
	} else if (z <= 41000.0) {
		tmp = t_2;
	} else if (z <= 1.15e+102) {
		tmp = x + (t * (y / a));
	} else if (z <= 8e+147) {
		tmp = (y / z) * (x - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -t / (z / (y - z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -1.52e+85:
		tmp = t_1
	elif z <= -2.45e+60:
		tmp = x * ((y - a) / z)
	elif z <= -0.0042:
		tmp = (z * -t) / (a - z)
	elif z <= -1.5e-24:
		tmp = (t - x) * (y / a)
	elif z <= -4e-27:
		tmp = t - ((t * y) / z)
	elif z <= 4e-76:
		tmp = t_2
	elif z <= 1.05e-42:
		tmp = (t * (y - z)) / a
	elif z <= 41000.0:
		tmp = t_2
	elif z <= 1.15e+102:
		tmp = x + (t * (y / a))
	elif z <= 8e+147:
		tmp = (y / z) * (x - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-t) / Float64(z / Float64(y - z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -1.52e+85)
		tmp = t_1;
	elseif (z <= -2.45e+60)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -0.0042)
		tmp = Float64(Float64(z * Float64(-t)) / Float64(a - z));
	elseif (z <= -1.5e-24)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (z <= -4e-27)
		tmp = Float64(t - Float64(Float64(t * y) / z));
	elseif (z <= 4e-76)
		tmp = t_2;
	elseif (z <= 1.05e-42)
		tmp = Float64(Float64(t * Float64(y - z)) / a);
	elseif (z <= 41000.0)
		tmp = t_2;
	elseif (z <= 1.15e+102)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 8e+147)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -t / (z / (y - z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -1.52e+85)
		tmp = t_1;
	elseif (z <= -2.45e+60)
		tmp = x * ((y - a) / z);
	elseif (z <= -0.0042)
		tmp = (z * -t) / (a - z);
	elseif (z <= -1.5e-24)
		tmp = (t - x) * (y / a);
	elseif (z <= -4e-27)
		tmp = t - ((t * y) / z);
	elseif (z <= 4e-76)
		tmp = t_2;
	elseif (z <= 1.05e-42)
		tmp = (t * (y - z)) / a;
	elseif (z <= 41000.0)
		tmp = t_2;
	elseif (z <= 1.15e+102)
		tmp = x + (t * (y / a));
	elseif (z <= 8e+147)
		tmp = (y / z) * (x - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.52e+85], t$95$1, If[LessEqual[z, -2.45e+60], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.0042], N[(N[(z * (-t)), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.5e-24], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4e-27], N[(t - N[(N[(t * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e-76], t$95$2, If[LessEqual[z, 1.05e-42], N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 41000.0], t$95$2, If[LessEqual[z, 1.15e+102], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+147], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if z < -1.52e85 or 7.9999999999999998e147 < z

   1. Initial program 33.0%

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

      1. associate-*l/ 56.5%

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

   3. Simplified 56.5%

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

   5. Taylor expanded in x around 0 34.9%

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

   6. Taylor expanded in a around 0 34.3%

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

      1. mul-1-neg 34.3%

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

      2. associate-/l* 57.8%

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

      3. distribute-neg-frac 57.8%

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

   8. Simplified 57.8%

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

   if -1.52e85 < z < -2.4500000000000001e60

   1. Initial program 30.3%

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

      1. associate-*l/ 71.7%

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

   3. Simplified 71.7%

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

   5. Taylor expanded in z around inf 46.2%

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

      1. associate--l+ 46.2%

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

      2. associate-*r/ 46.2%

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

      3. associate-*r/ 46.2%

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

      4. div-sub 46.2%

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

      5. distribute-lft-out-- 46.2%

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

      6. associate-*r/ 46.2%

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

      7. mul-1-neg 46.2%

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

      8. distribute-rgt-out-- 46.2%

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

      9. unsub-neg 46.2%

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

      10. associate-/l* 72.4%

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

   7. Simplified 72.4%

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

   8. Taylor expanded in t around 0 47.1%

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

      1. associate-*r/ 73.5%

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

   10. Simplified 73.5%

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

   if -2.4500000000000001e60 < z < -0.00419999999999999974

   1. Initial program 91.0%

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

      1. associate-*l/ 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around 0 82.2%

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

   6. Taylor expanded in y around 0 68.8%

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

      1. associate-*r/ 68.8%

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

      2. mul-1-neg 68.8%

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

      3. distribute-rgt-neg-out 68.8%

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

   8. Simplified 68.8%

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

   if -0.00419999999999999974 < z < -1.49999999999999998e-24

   1. Initial program 76.5%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around -inf 62.6%

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

      1. associate-*l/ 86.1%

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

   7. Simplified 86.1%

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

   8. Taylor expanded in a around inf 86.1%

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

   if -1.49999999999999998e-24 < z < -4.0000000000000002e-27

   1. Initial program 99.5%

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

      1. associate-*l/ 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 99.5%

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

   6. Taylor expanded in z around inf 99.5%

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

      1. associate--l+ 99.5%

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

      2. associate-*r/ 99.5%

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

      3. associate-*r/ 99.5%

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

      4. div-sub 99.5%

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

      5. distribute-lft-out-- 99.5%

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

      6. associate-*r/ 99.5%

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

      7. mul-1-neg 99.5%

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

      8. unsub-neg 99.5%

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

      9. *-commutative 99.5%

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

      10. distribute-lft-out-- 99.5%

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

   8. Simplified 99.5%

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

   9. Taylor expanded in y around inf 99.5%

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

       1. *-commutative 99.5%

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

   11. Simplified 99.5%

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

   if -4.0000000000000002e-27 < z < 3.99999999999999971e-76 or 1.05000000000000003e-42 < z < 41000

   1. Initial program 93.5%

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

      1. associate-*l/ 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in z around 0 84.5%

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

   6. Taylor expanded in x around inf 72.2%

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

      1. mul-1-neg 72.2%

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

      2. unsub-neg 72.2%

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

   8. Simplified 72.2%

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

   if 3.99999999999999971e-76 < z < 1.05000000000000003e-42

   1. Initial program 89.0%

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

      1. associate-*l/ 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in x around 0 77.8%

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

   6. Taylor expanded in a around inf 78.1%

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

   if 41000 < z < 1.1499999999999999e102

   1. Initial program 61.3%

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

      1. associate-*l/ 80.7%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in z around 0 70.5%

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

   6. Taylor expanded in t around inf 65.7%

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

      1. associate-*r/ 70.4%

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

   8. Simplified 70.4%

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

   if 1.1499999999999999e102 < z < 7.9999999999999998e147

   1. Initial program 36.6%

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

      1. associate-*l/ 56.8%

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

   3. Simplified 56.8%

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

   5. Taylor expanded in y around -inf 38.3%

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

      1. associate-*l/ 68.5%

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

   7. Simplified 68.5%

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

   8. Taylor expanded in a around 0 68.6%

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

      1. associate-*r/ 68.6%

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

      2. neg-mul-1 68.6%

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

   10. Simplified 68.6%

       \[\leadsto \color{blue}{\frac{-y}{z}} \cdot \left(t - x\right) \]
3. Recombined 9 regimes into one program.

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+85}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -0.0042:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a - z}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-24}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-27}:\\ \;\;\;\;t - \frac{t \cdot y}{z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-42}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a}\\ \mathbf{elif}\;z \leq 41000:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+102}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+147}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 48.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_3 := t - \frac{t \cdot y}{z}\\ \mathbf{if}\;z \leq -3 \cdot 10^{+88}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -65000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-19}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-27}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-76}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-43}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-7}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+111}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z)))
        (t_2 (* x (- 1.0 (/ y a))))
        (t_3 (- t (/ (* t y) z))))
   (if (<= z -3e+88)
     t_3
     (if (<= z -2.7e+60)
       t_1
       (if (<= z -65000000.0)
         t_3
         (if (<= z -5.4e-19)
           (* (- t x) (/ y a))
           (if (<= z -4.4e-27)
             t_3
             (if (<= z 7.4e-76)
               t_2
               (if (<= z 6e-43)
                 (* y (/ (- t x) a))
                 (if (<= z 1.55e-7)
                   t_2
                   (if (<= z 3.9e+111)
                     (+ x (* t (/ y a)))
                     (if (<= z 2.05e+151) t_1 t_3))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = x * (1.0 - (y / a));
	double t_3 = t - ((t * y) / z);
	double tmp;
	if (z <= -3e+88) {
		tmp = t_3;
	} else if (z <= -2.7e+60) {
		tmp = t_1;
	} else if (z <= -65000000.0) {
		tmp = t_3;
	} else if (z <= -5.4e-19) {
		tmp = (t - x) * (y / a);
	} else if (z <= -4.4e-27) {
		tmp = t_3;
	} else if (z <= 7.4e-76) {
		tmp = t_2;
	} else if (z <= 6e-43) {
		tmp = y * ((t - x) / a);
	} else if (z <= 1.55e-7) {
		tmp = t_2;
	} else if (z <= 3.9e+111) {
		tmp = x + (t * (y / a));
	} else if (z <= 2.05e+151) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    t_2 = x * (1.0d0 - (y / a))
    t_3 = t - ((t * y) / z)
    if (z <= (-3d+88)) then
        tmp = t_3
    else if (z <= (-2.7d+60)) then
        tmp = t_1
    else if (z <= (-65000000.0d0)) then
        tmp = t_3
    else if (z <= (-5.4d-19)) then
        tmp = (t - x) * (y / a)
    else if (z <= (-4.4d-27)) then
        tmp = t_3
    else if (z <= 7.4d-76) then
        tmp = t_2
    else if (z <= 6d-43) then
        tmp = y * ((t - x) / a)
    else if (z <= 1.55d-7) then
        tmp = t_2
    else if (z <= 3.9d+111) then
        tmp = x + (t * (y / a))
    else if (z <= 2.05d+151) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = x * (1.0 - (y / a));
	double t_3 = t - ((t * y) / z);
	double tmp;
	if (z <= -3e+88) {
		tmp = t_3;
	} else if (z <= -2.7e+60) {
		tmp = t_1;
	} else if (z <= -65000000.0) {
		tmp = t_3;
	} else if (z <= -5.4e-19) {
		tmp = (t - x) * (y / a);
	} else if (z <= -4.4e-27) {
		tmp = t_3;
	} else if (z <= 7.4e-76) {
		tmp = t_2;
	} else if (z <= 6e-43) {
		tmp = y * ((t - x) / a);
	} else if (z <= 1.55e-7) {
		tmp = t_2;
	} else if (z <= 3.9e+111) {
		tmp = x + (t * (y / a));
	} else if (z <= 2.05e+151) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	t_2 = x * (1.0 - (y / a))
	t_3 = t - ((t * y) / z)
	tmp = 0
	if z <= -3e+88:
		tmp = t_3
	elif z <= -2.7e+60:
		tmp = t_1
	elif z <= -65000000.0:
		tmp = t_3
	elif z <= -5.4e-19:
		tmp = (t - x) * (y / a)
	elif z <= -4.4e-27:
		tmp = t_3
	elif z <= 7.4e-76:
		tmp = t_2
	elif z <= 6e-43:
		tmp = y * ((t - x) / a)
	elif z <= 1.55e-7:
		tmp = t_2
	elif z <= 3.9e+111:
		tmp = x + (t * (y / a))
	elif z <= 2.05e+151:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_3 = Float64(t - Float64(Float64(t * y) / z))
	tmp = 0.0
	if (z <= -3e+88)
		tmp = t_3;
	elseif (z <= -2.7e+60)
		tmp = t_1;
	elseif (z <= -65000000.0)
		tmp = t_3;
	elseif (z <= -5.4e-19)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (z <= -4.4e-27)
		tmp = t_3;
	elseif (z <= 7.4e-76)
		tmp = t_2;
	elseif (z <= 6e-43)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 1.55e-7)
		tmp = t_2;
	elseif (z <= 3.9e+111)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 2.05e+151)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	t_2 = x * (1.0 - (y / a));
	t_3 = t - ((t * y) / z);
	tmp = 0.0;
	if (z <= -3e+88)
		tmp = t_3;
	elseif (z <= -2.7e+60)
		tmp = t_1;
	elseif (z <= -65000000.0)
		tmp = t_3;
	elseif (z <= -5.4e-19)
		tmp = (t - x) * (y / a);
	elseif (z <= -4.4e-27)
		tmp = t_3;
	elseif (z <= 7.4e-76)
		tmp = t_2;
	elseif (z <= 6e-43)
		tmp = y * ((t - x) / a);
	elseif (z <= 1.55e-7)
		tmp = t_2;
	elseif (z <= 3.9e+111)
		tmp = x + (t * (y / a));
	elseif (z <= 2.05e+151)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t - N[(N[(t * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e+88], t$95$3, If[LessEqual[z, -2.7e+60], t$95$1, If[LessEqual[z, -65000000.0], t$95$3, If[LessEqual[z, -5.4e-19], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.4e-27], t$95$3, If[LessEqual[z, 7.4e-76], t$95$2, If[LessEqual[z, 6e-43], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-7], t$95$2, If[LessEqual[z, 3.9e+111], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+151], t$95$1, t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.00000000000000005e88 or -2.6999999999999999e60 < z < -6.5e7 or -5.4000000000000002e-19 < z < -4.39999999999999974e-27 or 2.0499999999999999e151 < z

   1. Initial program 40.3%

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

      1. associate-*l/ 60.9%

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

   3. Simplified 60.9%

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

   5. Taylor expanded in x around 0 41.4%

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

   6. Taylor expanded in z around inf 52.7%

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

      1. associate--l+ 52.7%

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

      2. associate-*r/ 52.7%

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

      3. associate-*r/ 52.7%

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

      4. div-sub 52.7%

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

      5. distribute-lft-out-- 52.7%

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

      6. associate-*r/ 52.7%

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

      7. mul-1-neg 52.7%

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

      8. unsub-neg 52.7%

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

      9. *-commutative 52.7%

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

      10. distribute-lft-out-- 52.7%

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

   8. Simplified 52.7%

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

   9. Taylor expanded in y around inf 55.9%

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

       1. *-commutative 55.9%

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

   11. Simplified 55.9%

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

   if -3.00000000000000005e88 < z < -2.6999999999999999e60 or 3.89999999999999979e111 < z < 2.0499999999999999e151

   1. Initial program 29.4%

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

      1. associate-*l/ 60.9%

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

   3. Simplified 60.9%

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

   5. Taylor expanded in z around inf 49.9%

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

      1. associate--l+ 49.9%

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

      2. associate-*r/ 49.9%

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

      3. associate-*r/ 49.9%

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

      4. div-sub 50.0%

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

      5. distribute-lft-out-- 50.0%

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

      6. associate-*r/ 50.0%

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

      7. mul-1-neg 50.0%

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

      8. distribute-rgt-out-- 50.0%

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

      9. unsub-neg 50.0%

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

      10. associate-/l* 80.2%

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

   7. Simplified 80.2%

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

   8. Taylor expanded in t around 0 50.3%

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

      1. associate-*r/ 74.7%

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

   10. Simplified 74.7%

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

   if -6.5e7 < z < -5.4000000000000002e-19

   1. Initial program 86.6%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around -inf 50.8%

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

      1. associate-*l/ 64.2%

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

   7. Simplified 64.2%

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

   8. Taylor expanded in a around inf 64.2%

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

   if -4.39999999999999974e-27 < z < 7.40000000000000023e-76 or 6.00000000000000007e-43 < z < 1.55e-7

   1. Initial program 93.5%

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

      1. associate-*l/ 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in z around 0 84.5%

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

   6. Taylor expanded in x around inf 72.2%

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

      1. mul-1-neg 72.2%

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

      2. unsub-neg 72.2%

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

   8. Simplified 72.2%

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

   if 7.40000000000000023e-76 < z < 6.00000000000000007e-43

   1. Initial program 89.0%

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

      1. associate-*l/ 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in z around 0 67.6%

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

      1. associate-*l/ 67.3%

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

      2. clear-num 67.3%

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

   7. Applied egg-rr 67.3%

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

      1. associate-/r/ 67.4%

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

      2. *-commutative 67.4%

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

   9. Simplified 67.4%

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

   10. Taylor expanded in y around inf 67.9%

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

       1. div-sub 67.9%

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

   12. Simplified 67.9%

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

   if 1.55e-7 < z < 3.89999999999999979e111

   1. Initial program 63.1%

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

      1. associate-*l/ 81.7%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in z around 0 67.4%

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

   6. Taylor expanded in t around inf 62.8%

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

      1. associate-*r/ 67.3%

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

   8. Simplified 67.3%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+88}:\\ \;\;\;\;t - \frac{t \cdot y}{z}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -65000000:\\ \;\;\;\;t - \frac{t \cdot y}{z}\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-19}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-27}:\\ \;\;\;\;t - \frac{t \cdot y}{z}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-43}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+111}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+151}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 48.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_3 := t - \frac{t \cdot y}{z}\\ \mathbf{if}\;z \leq -6 \cdot 10^{+88}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -45000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-16}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-27}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-75}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-6}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+111}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z)))
        (t_2 (* x (- 1.0 (/ y a))))
        (t_3 (- t (/ (* t y) z))))
   (if (<= z -6e+88)
     t_3
     (if (<= z -2.8e+60)
       t_1
       (if (<= z -45000000.0)
         t_3
         (if (<= z -7.8e-16)
           (* (- t x) (/ y a))
           (if (<= z -3.8e-27)
             t_3
             (if (<= z 2.6e-75)
               t_2
               (if (<= z 1.8e-43)
                 (/ t (/ a (- y z)))
                 (if (<= z 7.5e-6)
                   t_2
                   (if (<= z 2.35e+111)
                     (+ x (* t (/ y a)))
                     (if (<= z 1.06e+149) t_1 t_3))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = x * (1.0 - (y / a));
	double t_3 = t - ((t * y) / z);
	double tmp;
	if (z <= -6e+88) {
		tmp = t_3;
	} else if (z <= -2.8e+60) {
		tmp = t_1;
	} else if (z <= -45000000.0) {
		tmp = t_3;
	} else if (z <= -7.8e-16) {
		tmp = (t - x) * (y / a);
	} else if (z <= -3.8e-27) {
		tmp = t_3;
	} else if (z <= 2.6e-75) {
		tmp = t_2;
	} else if (z <= 1.8e-43) {
		tmp = t / (a / (y - z));
	} else if (z <= 7.5e-6) {
		tmp = t_2;
	} else if (z <= 2.35e+111) {
		tmp = x + (t * (y / a));
	} else if (z <= 1.06e+149) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    t_2 = x * (1.0d0 - (y / a))
    t_3 = t - ((t * y) / z)
    if (z <= (-6d+88)) then
        tmp = t_3
    else if (z <= (-2.8d+60)) then
        tmp = t_1
    else if (z <= (-45000000.0d0)) then
        tmp = t_3
    else if (z <= (-7.8d-16)) then
        tmp = (t - x) * (y / a)
    else if (z <= (-3.8d-27)) then
        tmp = t_3
    else if (z <= 2.6d-75) then
        tmp = t_2
    else if (z <= 1.8d-43) then
        tmp = t / (a / (y - z))
    else if (z <= 7.5d-6) then
        tmp = t_2
    else if (z <= 2.35d+111) then
        tmp = x + (t * (y / a))
    else if (z <= 1.06d+149) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = x * (1.0 - (y / a));
	double t_3 = t - ((t * y) / z);
	double tmp;
	if (z <= -6e+88) {
		tmp = t_3;
	} else if (z <= -2.8e+60) {
		tmp = t_1;
	} else if (z <= -45000000.0) {
		tmp = t_3;
	} else if (z <= -7.8e-16) {
		tmp = (t - x) * (y / a);
	} else if (z <= -3.8e-27) {
		tmp = t_3;
	} else if (z <= 2.6e-75) {
		tmp = t_2;
	} else if (z <= 1.8e-43) {
		tmp = t / (a / (y - z));
	} else if (z <= 7.5e-6) {
		tmp = t_2;
	} else if (z <= 2.35e+111) {
		tmp = x + (t * (y / a));
	} else if (z <= 1.06e+149) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	t_2 = x * (1.0 - (y / a))
	t_3 = t - ((t * y) / z)
	tmp = 0
	if z <= -6e+88:
		tmp = t_3
	elif z <= -2.8e+60:
		tmp = t_1
	elif z <= -45000000.0:
		tmp = t_3
	elif z <= -7.8e-16:
		tmp = (t - x) * (y / a)
	elif z <= -3.8e-27:
		tmp = t_3
	elif z <= 2.6e-75:
		tmp = t_2
	elif z <= 1.8e-43:
		tmp = t / (a / (y - z))
	elif z <= 7.5e-6:
		tmp = t_2
	elif z <= 2.35e+111:
		tmp = x + (t * (y / a))
	elif z <= 1.06e+149:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_3 = Float64(t - Float64(Float64(t * y) / z))
	tmp = 0.0
	if (z <= -6e+88)
		tmp = t_3;
	elseif (z <= -2.8e+60)
		tmp = t_1;
	elseif (z <= -45000000.0)
		tmp = t_3;
	elseif (z <= -7.8e-16)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (z <= -3.8e-27)
		tmp = t_3;
	elseif (z <= 2.6e-75)
		tmp = t_2;
	elseif (z <= 1.8e-43)
		tmp = Float64(t / Float64(a / Float64(y - z)));
	elseif (z <= 7.5e-6)
		tmp = t_2;
	elseif (z <= 2.35e+111)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 1.06e+149)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	t_2 = x * (1.0 - (y / a));
	t_3 = t - ((t * y) / z);
	tmp = 0.0;
	if (z <= -6e+88)
		tmp = t_3;
	elseif (z <= -2.8e+60)
		tmp = t_1;
	elseif (z <= -45000000.0)
		tmp = t_3;
	elseif (z <= -7.8e-16)
		tmp = (t - x) * (y / a);
	elseif (z <= -3.8e-27)
		tmp = t_3;
	elseif (z <= 2.6e-75)
		tmp = t_2;
	elseif (z <= 1.8e-43)
		tmp = t / (a / (y - z));
	elseif (z <= 7.5e-6)
		tmp = t_2;
	elseif (z <= 2.35e+111)
		tmp = x + (t * (y / a));
	elseif (z <= 1.06e+149)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t - N[(N[(t * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+88], t$95$3, If[LessEqual[z, -2.8e+60], t$95$1, If[LessEqual[z, -45000000.0], t$95$3, If[LessEqual[z, -7.8e-16], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.8e-27], t$95$3, If[LessEqual[z, 2.6e-75], t$95$2, If[LessEqual[z, 1.8e-43], N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e-6], t$95$2, If[LessEqual[z, 2.35e+111], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.06e+149], t$95$1, t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -6.00000000000000011e88 or -2.8e60 < z < -4.5e7 or -7.79999999999999954e-16 < z < -3.8e-27 or 1.05999999999999993e149 < z

   1. Initial program 40.3%

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

      1. associate-*l/ 60.9%

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

   3. Simplified 60.9%

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

   5. Taylor expanded in x around 0 41.4%

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

   6. Taylor expanded in z around inf 52.7%

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

      1. associate--l+ 52.7%

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

      2. associate-*r/ 52.7%

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

      3. associate-*r/ 52.7%

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

      4. div-sub 52.7%

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

      5. distribute-lft-out-- 52.7%

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

      6. associate-*r/ 52.7%

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

      7. mul-1-neg 52.7%

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

      8. unsub-neg 52.7%

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

      9. *-commutative 52.7%

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

      10. distribute-lft-out-- 52.7%

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

   8. Simplified 52.7%

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

   9. Taylor expanded in y around inf 55.9%

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

       1. *-commutative 55.9%

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

   11. Simplified 55.9%

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

   if -6.00000000000000011e88 < z < -2.8e60 or 2.35000000000000004e111 < z < 1.05999999999999993e149

   1. Initial program 29.4%

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

      1. associate-*l/ 60.9%

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

   3. Simplified 60.9%

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

   5. Taylor expanded in z around inf 49.9%

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

      1. associate--l+ 49.9%

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

      2. associate-*r/ 49.9%

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

      3. associate-*r/ 49.9%

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

      4. div-sub 50.0%

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

      5. distribute-lft-out-- 50.0%

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

      6. associate-*r/ 50.0%

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

      7. mul-1-neg 50.0%

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

      8. distribute-rgt-out-- 50.0%

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

      9. unsub-neg 50.0%

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

      10. associate-/l* 80.2%

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

   7. Simplified 80.2%

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

   8. Taylor expanded in t around 0 50.3%

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

      1. associate-*r/ 74.7%

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

   10. Simplified 74.7%

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

   if -4.5e7 < z < -7.79999999999999954e-16

   1. Initial program 86.6%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around -inf 50.8%

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

      1. associate-*l/ 64.2%

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

   7. Simplified 64.2%

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

   8. Taylor expanded in a around inf 64.2%

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

   if -3.8e-27 < z < 2.6e-75 or 1.7999999999999999e-43 < z < 7.50000000000000019e-6

   1. Initial program 93.5%

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

      1. associate-*l/ 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in z around 0 84.5%

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

   6. Taylor expanded in x around inf 72.2%

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

      1. mul-1-neg 72.2%

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

      2. unsub-neg 72.2%

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

   8. Simplified 72.2%

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

   if 2.6e-75 < z < 1.7999999999999999e-43

   1. Initial program 89.0%

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

      1. associate-*l/ 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in x around 0 77.8%

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

   6. Taylor expanded in a around inf 78.1%

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

      1. associate-/l* 77.7%

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

   8. Simplified 77.7%

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

   if 7.50000000000000019e-6 < z < 2.35000000000000004e111

   1. Initial program 63.1%

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

      1. associate-*l/ 81.7%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in z around 0 67.4%

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

   6. Taylor expanded in t around inf 62.8%

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

      1. associate-*r/ 67.3%

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

   8. Simplified 67.3%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+88}:\\ \;\;\;\;t - \frac{t \cdot y}{z}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -45000000:\\ \;\;\;\;t - \frac{t \cdot y}{z}\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-16}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-27}:\\ \;\;\;\;t - \frac{t \cdot y}{z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+111}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 47.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_3 := t - \frac{t \cdot y}{z}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+85}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -260000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -3.15 \cdot 10^{-24}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-27}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-75}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a}\\ \mathbf{elif}\;z \leq 0.0018:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+111}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z)))
        (t_2 (* x (- 1.0 (/ y a))))
        (t_3 (- t (/ (* t y) z))))
   (if (<= z -2e+85)
     t_3
     (if (<= z -2.65e+60)
       t_1
       (if (<= z -260000000.0)
         t_3
         (if (<= z -3.15e-24)
           (* (- t x) (/ y a))
           (if (<= z -3.4e-27)
             t_3
             (if (<= z 3.2e-75)
               t_2
               (if (<= z 1.8e-43)
                 (/ (* t (- y z)) a)
                 (if (<= z 0.0018)
                   t_2
                   (if (<= z 6.8e+111)
                     (+ x (* t (/ y a)))
                     (if (<= z 5.5e+149) t_1 t_3))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = x * (1.0 - (y / a));
	double t_3 = t - ((t * y) / z);
	double tmp;
	if (z <= -2e+85) {
		tmp = t_3;
	} else if (z <= -2.65e+60) {
		tmp = t_1;
	} else if (z <= -260000000.0) {
		tmp = t_3;
	} else if (z <= -3.15e-24) {
		tmp = (t - x) * (y / a);
	} else if (z <= -3.4e-27) {
		tmp = t_3;
	} else if (z <= 3.2e-75) {
		tmp = t_2;
	} else if (z <= 1.8e-43) {
		tmp = (t * (y - z)) / a;
	} else if (z <= 0.0018) {
		tmp = t_2;
	} else if (z <= 6.8e+111) {
		tmp = x + (t * (y / a));
	} else if (z <= 5.5e+149) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    t_2 = x * (1.0d0 - (y / a))
    t_3 = t - ((t * y) / z)
    if (z <= (-2d+85)) then
        tmp = t_3
    else if (z <= (-2.65d+60)) then
        tmp = t_1
    else if (z <= (-260000000.0d0)) then
        tmp = t_3
    else if (z <= (-3.15d-24)) then
        tmp = (t - x) * (y / a)
    else if (z <= (-3.4d-27)) then
        tmp = t_3
    else if (z <= 3.2d-75) then
        tmp = t_2
    else if (z <= 1.8d-43) then
        tmp = (t * (y - z)) / a
    else if (z <= 0.0018d0) then
        tmp = t_2
    else if (z <= 6.8d+111) then
        tmp = x + (t * (y / a))
    else if (z <= 5.5d+149) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = x * (1.0 - (y / a));
	double t_3 = t - ((t * y) / z);
	double tmp;
	if (z <= -2e+85) {
		tmp = t_3;
	} else if (z <= -2.65e+60) {
		tmp = t_1;
	} else if (z <= -260000000.0) {
		tmp = t_3;
	} else if (z <= -3.15e-24) {
		tmp = (t - x) * (y / a);
	} else if (z <= -3.4e-27) {
		tmp = t_3;
	} else if (z <= 3.2e-75) {
		tmp = t_2;
	} else if (z <= 1.8e-43) {
		tmp = (t * (y - z)) / a;
	} else if (z <= 0.0018) {
		tmp = t_2;
	} else if (z <= 6.8e+111) {
		tmp = x + (t * (y / a));
	} else if (z <= 5.5e+149) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	t_2 = x * (1.0 - (y / a))
	t_3 = t - ((t * y) / z)
	tmp = 0
	if z <= -2e+85:
		tmp = t_3
	elif z <= -2.65e+60:
		tmp = t_1
	elif z <= -260000000.0:
		tmp = t_3
	elif z <= -3.15e-24:
		tmp = (t - x) * (y / a)
	elif z <= -3.4e-27:
		tmp = t_3
	elif z <= 3.2e-75:
		tmp = t_2
	elif z <= 1.8e-43:
		tmp = (t * (y - z)) / a
	elif z <= 0.0018:
		tmp = t_2
	elif z <= 6.8e+111:
		tmp = x + (t * (y / a))
	elif z <= 5.5e+149:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_3 = Float64(t - Float64(Float64(t * y) / z))
	tmp = 0.0
	if (z <= -2e+85)
		tmp = t_3;
	elseif (z <= -2.65e+60)
		tmp = t_1;
	elseif (z <= -260000000.0)
		tmp = t_3;
	elseif (z <= -3.15e-24)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (z <= -3.4e-27)
		tmp = t_3;
	elseif (z <= 3.2e-75)
		tmp = t_2;
	elseif (z <= 1.8e-43)
		tmp = Float64(Float64(t * Float64(y - z)) / a);
	elseif (z <= 0.0018)
		tmp = t_2;
	elseif (z <= 6.8e+111)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 5.5e+149)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	t_2 = x * (1.0 - (y / a));
	t_3 = t - ((t * y) / z);
	tmp = 0.0;
	if (z <= -2e+85)
		tmp = t_3;
	elseif (z <= -2.65e+60)
		tmp = t_1;
	elseif (z <= -260000000.0)
		tmp = t_3;
	elseif (z <= -3.15e-24)
		tmp = (t - x) * (y / a);
	elseif (z <= -3.4e-27)
		tmp = t_3;
	elseif (z <= 3.2e-75)
		tmp = t_2;
	elseif (z <= 1.8e-43)
		tmp = (t * (y - z)) / a;
	elseif (z <= 0.0018)
		tmp = t_2;
	elseif (z <= 6.8e+111)
		tmp = x + (t * (y / a));
	elseif (z <= 5.5e+149)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t - N[(N[(t * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+85], t$95$3, If[LessEqual[z, -2.65e+60], t$95$1, If[LessEqual[z, -260000000.0], t$95$3, If[LessEqual[z, -3.15e-24], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.4e-27], t$95$3, If[LessEqual[z, 3.2e-75], t$95$2, If[LessEqual[z, 1.8e-43], N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 0.0018], t$95$2, If[LessEqual[z, 6.8e+111], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+149], t$95$1, t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2e85 or -2.6499999999999998e60 < z < -2.6e8 or -3.1499999999999999e-24 < z < -3.3999999999999997e-27 or 5.49999999999999999e149 < z

   1. Initial program 40.3%

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

      1. associate-*l/ 60.9%

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

   3. Simplified 60.9%

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

   5. Taylor expanded in x around 0 41.4%

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

   6. Taylor expanded in z around inf 52.7%

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

      1. associate--l+ 52.7%

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

      2. associate-*r/ 52.7%

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

      3. associate-*r/ 52.7%

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

      4. div-sub 52.7%

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

      5. distribute-lft-out-- 52.7%

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

      6. associate-*r/ 52.7%

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

      7. mul-1-neg 52.7%

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

      8. unsub-neg 52.7%

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

      9. *-commutative 52.7%

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

      10. distribute-lft-out-- 52.7%

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

   8. Simplified 52.7%

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

   9. Taylor expanded in y around inf 55.9%

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

       1. *-commutative 55.9%

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

   11. Simplified 55.9%

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

   if -2e85 < z < -2.6499999999999998e60 or 6.8000000000000003e111 < z < 5.49999999999999999e149

   1. Initial program 29.4%

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

      1. associate-*l/ 60.9%

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

   3. Simplified 60.9%

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

   5. Taylor expanded in z around inf 49.9%

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

      1. associate--l+ 49.9%

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

      2. associate-*r/ 49.9%

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

      3. associate-*r/ 49.9%

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

      4. div-sub 50.0%

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

      5. distribute-lft-out-- 50.0%

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

      6. associate-*r/ 50.0%

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

      7. mul-1-neg 50.0%

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

      8. distribute-rgt-out-- 50.0%

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

      9. unsub-neg 50.0%

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

      10. associate-/l* 80.2%

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

   7. Simplified 80.2%

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

   8. Taylor expanded in t around 0 50.3%

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

      1. associate-*r/ 74.7%

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

   10. Simplified 74.7%

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

   if -2.6e8 < z < -3.1499999999999999e-24

   1. Initial program 86.6%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around -inf 50.8%

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

      1. associate-*l/ 64.2%

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

   7. Simplified 64.2%

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

   8. Taylor expanded in a around inf 64.2%

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

   if -3.3999999999999997e-27 < z < 3.19999999999999977e-75 or 1.7999999999999999e-43 < z < 0.0018

   1. Initial program 93.5%

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

      1. associate-*l/ 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in z around 0 84.5%

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

   6. Taylor expanded in x around inf 72.2%

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

      1. mul-1-neg 72.2%

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

      2. unsub-neg 72.2%

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

   8. Simplified 72.2%

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

   if 3.19999999999999977e-75 < z < 1.7999999999999999e-43

   1. Initial program 89.0%

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

      1. associate-*l/ 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in x around 0 77.8%

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

   6. Taylor expanded in a around inf 78.1%

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

   if 0.0018 < z < 6.8000000000000003e111

   1. Initial program 63.1%

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

      1. associate-*l/ 81.7%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in z around 0 67.4%

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

   6. Taylor expanded in t around inf 62.8%

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

      1. associate-*r/ 67.3%

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

   8. Simplified 67.3%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+85}:\\ \;\;\;\;t - \frac{t \cdot y}{z}\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -260000000:\\ \;\;\;\;t - \frac{t \cdot y}{z}\\ \mathbf{elif}\;z \leq -3.15 \cdot 10^{-24}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-27}:\\ \;\;\;\;t - \frac{t \cdot y}{z}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a}\\ \mathbf{elif}\;z \leq 0.0018:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+111}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a}\\ t_2 := x \cdot \frac{y - a}{z}\\ t_3 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{+85}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+60}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -0.0105:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-75}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+111}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+146}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) a)))
        (t_2 (* x (/ (- y a) z)))
        (t_3 (* x (- 1.0 (/ y a)))))
   (if (<= z -5.6e+85)
     t
     (if (<= z -2.5e+60)
       t_2
       (if (<= z -0.0105)
         t
         (if (<= z -9.6e-34)
           t_1
           (if (<= z 1.9e-75)
             t_3
             (if (<= z 6e-44)
               t_1
               (if (<= z 3.1e+111) t_3 (if (<= z 7e+146) t_2 t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double t_2 = x * ((y - a) / z);
	double t_3 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -5.6e+85) {
		tmp = t;
	} else if (z <= -2.5e+60) {
		tmp = t_2;
	} else if (z <= -0.0105) {
		tmp = t;
	} else if (z <= -9.6e-34) {
		tmp = t_1;
	} else if (z <= 1.9e-75) {
		tmp = t_3;
	} else if (z <= 6e-44) {
		tmp = t_1;
	} else if (z <= 3.1e+111) {
		tmp = t_3;
	} else if (z <= 7e+146) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * ((t - x) / a)
    t_2 = x * ((y - a) / z)
    t_3 = x * (1.0d0 - (y / a))
    if (z <= (-5.6d+85)) then
        tmp = t
    else if (z <= (-2.5d+60)) then
        tmp = t_2
    else if (z <= (-0.0105d0)) then
        tmp = t
    else if (z <= (-9.6d-34)) then
        tmp = t_1
    else if (z <= 1.9d-75) then
        tmp = t_3
    else if (z <= 6d-44) then
        tmp = t_1
    else if (z <= 3.1d+111) then
        tmp = t_3
    else if (z <= 7d+146) then
        tmp = t_2
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double t_2 = x * ((y - a) / z);
	double t_3 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -5.6e+85) {
		tmp = t;
	} else if (z <= -2.5e+60) {
		tmp = t_2;
	} else if (z <= -0.0105) {
		tmp = t;
	} else if (z <= -9.6e-34) {
		tmp = t_1;
	} else if (z <= 1.9e-75) {
		tmp = t_3;
	} else if (z <= 6e-44) {
		tmp = t_1;
	} else if (z <= 3.1e+111) {
		tmp = t_3;
	} else if (z <= 7e+146) {
		tmp = t_2;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / a)
	t_2 = x * ((y - a) / z)
	t_3 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -5.6e+85:
		tmp = t
	elif z <= -2.5e+60:
		tmp = t_2
	elif z <= -0.0105:
		tmp = t
	elif z <= -9.6e-34:
		tmp = t_1
	elif z <= 1.9e-75:
		tmp = t_3
	elif z <= 6e-44:
		tmp = t_1
	elif z <= 3.1e+111:
		tmp = t_3
	elif z <= 7e+146:
		tmp = t_2
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / a))
	t_2 = Float64(x * Float64(Float64(y - a) / z))
	t_3 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -5.6e+85)
		tmp = t;
	elseif (z <= -2.5e+60)
		tmp = t_2;
	elseif (z <= -0.0105)
		tmp = t;
	elseif (z <= -9.6e-34)
		tmp = t_1;
	elseif (z <= 1.9e-75)
		tmp = t_3;
	elseif (z <= 6e-44)
		tmp = t_1;
	elseif (z <= 3.1e+111)
		tmp = t_3;
	elseif (z <= 7e+146)
		tmp = t_2;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / a);
	t_2 = x * ((y - a) / z);
	t_3 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -5.6e+85)
		tmp = t;
	elseif (z <= -2.5e+60)
		tmp = t_2;
	elseif (z <= -0.0105)
		tmp = t;
	elseif (z <= -9.6e-34)
		tmp = t_1;
	elseif (z <= 1.9e-75)
		tmp = t_3;
	elseif (z <= 6e-44)
		tmp = t_1;
	elseif (z <= 3.1e+111)
		tmp = t_3;
	elseif (z <= 7e+146)
		tmp = t_2;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.6e+85], t, If[LessEqual[z, -2.5e+60], t$95$2, If[LessEqual[z, -0.0105], t, If[LessEqual[z, -9.6e-34], t$95$1, If[LessEqual[z, 1.9e-75], t$95$3, If[LessEqual[z, 6e-44], t$95$1, If[LessEqual[z, 3.1e+111], t$95$3, If[LessEqual[z, 7e+146], t$95$2, t]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.5999999999999998e85 or -2.49999999999999987e60 < z < -0.0105000000000000007 or 7.0000000000000002e146 < z

   1. Initial program 40.3%

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

      1. associate-*l/ 60.9%

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

   3. Simplified 60.9%

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

   5. Taylor expanded in z around inf 49.5%

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

   if -5.5999999999999998e85 < z < -2.49999999999999987e60 or 3.1e111 < z < 7.0000000000000002e146

   1. Initial program 29.4%

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

      1. associate-*l/ 60.9%

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

   3. Simplified 60.9%

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

   5. Taylor expanded in z around inf 49.9%

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

      1. associate--l+ 49.9%

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

      2. associate-*r/ 49.9%

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

      3. associate-*r/ 49.9%

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

      4. div-sub 50.0%

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

      5. distribute-lft-out-- 50.0%

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

      6. associate-*r/ 50.0%

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

      7. mul-1-neg 50.0%

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

      8. distribute-rgt-out-- 50.0%

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

      9. unsub-neg 50.0%

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

      10. associate-/l* 80.2%

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

   7. Simplified 80.2%

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

   8. Taylor expanded in t around 0 50.3%

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

      1. associate-*r/ 74.7%

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

   10. Simplified 74.7%

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

   if -0.0105000000000000007 < z < -9.59999999999999965e-34 or 1.89999999999999997e-75 < z < 6.0000000000000005e-44

   1. Initial program 89.7%

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

      1. associate-*l/ 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in z around 0 69.2%

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

      1. associate-*l/ 64.1%

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

      2. clear-num 64.1%

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

   7. Applied egg-rr 64.1%

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

      1. associate-/r/ 64.2%

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

      2. *-commutative 64.2%

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

   9. Simplified 64.2%

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

   10. Taylor expanded in y around inf 66.4%

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

       1. div-sub 66.4%

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

   12. Simplified 66.4%

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

   if -9.59999999999999965e-34 < z < 1.89999999999999997e-75 or 6.0000000000000005e-44 < z < 3.1e111

   1. Initial program 88.6%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in z around 0 82.3%

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

   6. Taylor expanded in x around inf 68.7%

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

      1. mul-1-neg 68.7%

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

      2. unsub-neg 68.7%

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

   8. Simplified 68.7%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+85}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -0.0105:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-34}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+111}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 47.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+88}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -280000000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-28}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-75}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+111}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= z -6.5e+88)
     t
     (if (<= z -2.3e+60)
       t_1
       (if (<= z -280000000.0)
         t
         (if (<= z -1.85e-28)
           (* (- t x) (/ y a))
           (if (<= z 3.2e-75)
             t_2
             (if (<= z 6e-44)
               (* y (/ (- t x) a))
               (if (<= z 2.35e+111) t_2 (if (<= z 1.45e+150) t_1 t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -6.5e+88) {
		tmp = t;
	} else if (z <= -2.3e+60) {
		tmp = t_1;
	} else if (z <= -280000000.0) {
		tmp = t;
	} else if (z <= -1.85e-28) {
		tmp = (t - x) * (y / a);
	} else if (z <= 3.2e-75) {
		tmp = t_2;
	} else if (z <= 6e-44) {
		tmp = y * ((t - x) / a);
	} else if (z <= 2.35e+111) {
		tmp = t_2;
	} else if (z <= 1.45e+150) {
		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) :: t_2
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    t_2 = x * (1.0d0 - (y / a))
    if (z <= (-6.5d+88)) then
        tmp = t
    else if (z <= (-2.3d+60)) then
        tmp = t_1
    else if (z <= (-280000000.0d0)) then
        tmp = t
    else if (z <= (-1.85d-28)) then
        tmp = (t - x) * (y / a)
    else if (z <= 3.2d-75) then
        tmp = t_2
    else if (z <= 6d-44) then
        tmp = y * ((t - x) / a)
    else if (z <= 2.35d+111) then
        tmp = t_2
    else if (z <= 1.45d+150) 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 * ((y - a) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -6.5e+88) {
		tmp = t;
	} else if (z <= -2.3e+60) {
		tmp = t_1;
	} else if (z <= -280000000.0) {
		tmp = t;
	} else if (z <= -1.85e-28) {
		tmp = (t - x) * (y / a);
	} else if (z <= 3.2e-75) {
		tmp = t_2;
	} else if (z <= 6e-44) {
		tmp = y * ((t - x) / a);
	} else if (z <= 2.35e+111) {
		tmp = t_2;
	} else if (z <= 1.45e+150) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -6.5e+88:
		tmp = t
	elif z <= -2.3e+60:
		tmp = t_1
	elif z <= -280000000.0:
		tmp = t
	elif z <= -1.85e-28:
		tmp = (t - x) * (y / a)
	elif z <= 3.2e-75:
		tmp = t_2
	elif z <= 6e-44:
		tmp = y * ((t - x) / a)
	elif z <= 2.35e+111:
		tmp = t_2
	elif z <= 1.45e+150:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -6.5e+88)
		tmp = t;
	elseif (z <= -2.3e+60)
		tmp = t_1;
	elseif (z <= -280000000.0)
		tmp = t;
	elseif (z <= -1.85e-28)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (z <= 3.2e-75)
		tmp = t_2;
	elseif (z <= 6e-44)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 2.35e+111)
		tmp = t_2;
	elseif (z <= 1.45e+150)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -6.5e+88)
		tmp = t;
	elseif (z <= -2.3e+60)
		tmp = t_1;
	elseif (z <= -280000000.0)
		tmp = t;
	elseif (z <= -1.85e-28)
		tmp = (t - x) * (y / a);
	elseif (z <= 3.2e-75)
		tmp = t_2;
	elseif (z <= 6e-44)
		tmp = y * ((t - x) / a);
	elseif (z <= 2.35e+111)
		tmp = t_2;
	elseif (z <= 1.45e+150)
		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[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+88], t, If[LessEqual[z, -2.3e+60], t$95$1, If[LessEqual[z, -280000000.0], t, If[LessEqual[z, -1.85e-28], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-75], t$95$2, If[LessEqual[z, 6e-44], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e+111], t$95$2, If[LessEqual[z, 1.45e+150], t$95$1, t]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.5000000000000002e88 or -2.30000000000000017e60 < z < -2.8e8 or 1.45000000000000005e150 < z

   1. Initial program 38.2%

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

      1. associate-*l/ 59.5%

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

   3. Simplified 59.5%

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

   5. Taylor expanded in z around inf 51.1%

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

   if -6.5000000000000002e88 < z < -2.30000000000000017e60 or 2.35000000000000004e111 < z < 1.45000000000000005e150

   1. Initial program 29.4%

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

      1. associate-*l/ 60.9%

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

   3. Simplified 60.9%

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

   5. Taylor expanded in z around inf 49.9%

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

      1. associate--l+ 49.9%

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

      2. associate-*r/ 49.9%

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

      3. associate-*r/ 49.9%

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

      4. div-sub 50.0%

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

      5. distribute-lft-out-- 50.0%

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

      6. associate-*r/ 50.0%

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

      7. mul-1-neg 50.0%

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

      8. distribute-rgt-out-- 50.0%

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

      9. unsub-neg 50.0%

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

      10. associate-/l* 80.2%

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

   7. Simplified 80.2%

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

   8. Taylor expanded in t around 0 50.3%

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

      1. associate-*r/ 74.7%

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

   10. Simplified 74.7%

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

   if -2.8e8 < z < -1.8500000000000001e-28

   1. Initial program 91.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around -inf 62.8%

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

      1. associate-*l/ 70.7%

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

   7. Simplified 70.7%

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

   8. Taylor expanded in a around inf 63.0%

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

   if -1.8500000000000001e-28 < z < 3.19999999999999977e-75 or 6.0000000000000005e-44 < z < 2.35000000000000004e111

   1. Initial program 88.7%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in z around 0 81.7%

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

   6. Taylor expanded in x around inf 68.2%

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

      1. mul-1-neg 68.2%

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

      2. unsub-neg 68.2%

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

   8. Simplified 68.2%

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

   if 3.19999999999999977e-75 < z < 6.0000000000000005e-44

   1. Initial program 89.0%

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

      1. associate-*l/ 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in z around 0 67.6%

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

      1. associate-*l/ 67.3%

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

      2. clear-num 67.3%

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

   7. Applied egg-rr 67.3%

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

      1. associate-/r/ 67.4%

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

      2. *-commutative 67.4%

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

   9. Simplified 67.4%

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

   10. Taylor expanded in y around inf 67.9%

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

       1. div-sub 67.9%

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

   12. Simplified 67.9%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+88}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -280000000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-28}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+111}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+150}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := x \cdot \frac{y - a}{z}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+88}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+60}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -160000000:\\ \;\;\;\;t + \frac{a}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-28}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-43}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+148}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (* x (/ (- y a) z))))
   (if (<= z -1.8e+88)
     t
     (if (<= z -2.3e+60)
       t_2
       (if (<= z -160000000.0)
         (+ t (/ a (/ z t)))
         (if (<= z -3.9e-28)
           (* (- t x) (/ y a))
           (if (<= z 1e-78)
             t_1
             (if (<= z 1.8e-43)
               (* y (/ (- t x) a))
               (if (<= z 3.8e+111) t_1 (if (<= z 2.45e+148) t_2 t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = x * ((y - a) / z);
	double tmp;
	if (z <= -1.8e+88) {
		tmp = t;
	} else if (z <= -2.3e+60) {
		tmp = t_2;
	} else if (z <= -160000000.0) {
		tmp = t + (a / (z / t));
	} else if (z <= -3.9e-28) {
		tmp = (t - x) * (y / a);
	} else if (z <= 1e-78) {
		tmp = t_1;
	} else if (z <= 1.8e-43) {
		tmp = y * ((t - x) / a);
	} else if (z <= 3.8e+111) {
		tmp = t_1;
	} else if (z <= 2.45e+148) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    t_2 = x * ((y - a) / z)
    if (z <= (-1.8d+88)) then
        tmp = t
    else if (z <= (-2.3d+60)) then
        tmp = t_2
    else if (z <= (-160000000.0d0)) then
        tmp = t + (a / (z / t))
    else if (z <= (-3.9d-28)) then
        tmp = (t - x) * (y / a)
    else if (z <= 1d-78) then
        tmp = t_1
    else if (z <= 1.8d-43) then
        tmp = y * ((t - x) / a)
    else if (z <= 3.8d+111) then
        tmp = t_1
    else if (z <= 2.45d+148) then
        tmp = t_2
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = x * ((y - a) / z);
	double tmp;
	if (z <= -1.8e+88) {
		tmp = t;
	} else if (z <= -2.3e+60) {
		tmp = t_2;
	} else if (z <= -160000000.0) {
		tmp = t + (a / (z / t));
	} else if (z <= -3.9e-28) {
		tmp = (t - x) * (y / a);
	} else if (z <= 1e-78) {
		tmp = t_1;
	} else if (z <= 1.8e-43) {
		tmp = y * ((t - x) / a);
	} else if (z <= 3.8e+111) {
		tmp = t_1;
	} else if (z <= 2.45e+148) {
		tmp = t_2;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = x * ((y - a) / z)
	tmp = 0
	if z <= -1.8e+88:
		tmp = t
	elif z <= -2.3e+60:
		tmp = t_2
	elif z <= -160000000.0:
		tmp = t + (a / (z / t))
	elif z <= -3.9e-28:
		tmp = (t - x) * (y / a)
	elif z <= 1e-78:
		tmp = t_1
	elif z <= 1.8e-43:
		tmp = y * ((t - x) / a)
	elif z <= 3.8e+111:
		tmp = t_1
	elif z <= 2.45e+148:
		tmp = t_2
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(x * Float64(Float64(y - a) / z))
	tmp = 0.0
	if (z <= -1.8e+88)
		tmp = t;
	elseif (z <= -2.3e+60)
		tmp = t_2;
	elseif (z <= -160000000.0)
		tmp = Float64(t + Float64(a / Float64(z / t)));
	elseif (z <= -3.9e-28)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (z <= 1e-78)
		tmp = t_1;
	elseif (z <= 1.8e-43)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 3.8e+111)
		tmp = t_1;
	elseif (z <= 2.45e+148)
		tmp = t_2;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = x * ((y - a) / z);
	tmp = 0.0;
	if (z <= -1.8e+88)
		tmp = t;
	elseif (z <= -2.3e+60)
		tmp = t_2;
	elseif (z <= -160000000.0)
		tmp = t + (a / (z / t));
	elseif (z <= -3.9e-28)
		tmp = (t - x) * (y / a);
	elseif (z <= 1e-78)
		tmp = t_1;
	elseif (z <= 1.8e-43)
		tmp = y * ((t - x) / a);
	elseif (z <= 3.8e+111)
		tmp = t_1;
	elseif (z <= 2.45e+148)
		tmp = t_2;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+88], t, If[LessEqual[z, -2.3e+60], t$95$2, If[LessEqual[z, -160000000.0], N[(t + N[(a / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.9e-28], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-78], t$95$1, If[LessEqual[z, 1.8e-43], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+111], t$95$1, If[LessEqual[z, 2.45e+148], t$95$2, t]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.8000000000000001e88 or 2.45e148 < z

   1. Initial program 33.0%

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

      1. associate-*l/ 56.5%

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

   3. Simplified 56.5%

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

   5. Taylor expanded in z around inf 49.4%

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

   if -1.8000000000000001e88 < z < -2.30000000000000017e60 or 3.79999999999999976e111 < z < 2.45e148

   1. Initial program 29.4%

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

      1. associate-*l/ 60.9%

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

   3. Simplified 60.9%

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

   5. Taylor expanded in z around inf 49.9%

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

      1. associate--l+ 49.9%

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

      2. associate-*r/ 49.9%

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

      3. associate-*r/ 49.9%

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

      4. div-sub 50.0%

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

      5. distribute-lft-out-- 50.0%

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

      6. associate-*r/ 50.0%

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

      7. mul-1-neg 50.0%

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

      8. distribute-rgt-out-- 50.0%

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

      9. unsub-neg 50.0%

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

      10. associate-/l* 80.2%

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

   7. Simplified 80.2%

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

   8. Taylor expanded in t around 0 50.3%

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

      1. associate-*r/ 74.7%

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

   10. Simplified 74.7%

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

   if -2.30000000000000017e60 < z < -1.6e8

   1. Initial program 87.7%

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

      1. associate-*l/ 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in x around 0 80.6%

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

   6. Taylor expanded in z around inf 80.8%

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

      1. associate--l+ 80.8%

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

      2. associate-*r/ 80.8%

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

      3. associate-*r/ 80.8%

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

      4. div-sub 80.8%

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

      5. distribute-lft-out-- 80.8%

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

      6. associate-*r/ 80.8%

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

      7. mul-1-neg 80.8%

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

      8. unsub-neg 80.8%

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

      9. *-commutative 80.8%

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

      10. distribute-lft-out-- 80.8%

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

   8. Simplified 80.8%

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

   9. Taylor expanded in y around 0 69.0%

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

       1. sub-neg 69.0%

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

       2. mul-1-neg 69.0%

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

       3. remove-double-neg 69.0%

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

       4. associate-/l* 69.0%

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

   11. Simplified 69.0%

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

   if -1.6e8 < z < -3.89999999999999999e-28

   1. Initial program 91.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around -inf 62.8%

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

      1. associate-*l/ 70.7%

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

   7. Simplified 70.7%

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

   8. Taylor expanded in a around inf 63.0%

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

   if -3.89999999999999999e-28 < z < 9.99999999999999999e-79 or 1.7999999999999999e-43 < z < 3.79999999999999976e111

   1. Initial program 88.7%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in z around 0 81.7%

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

   6. Taylor expanded in x around inf 68.2%

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

      1. mul-1-neg 68.2%

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

      2. unsub-neg 68.2%

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

   8. Simplified 68.2%

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

   if 9.99999999999999999e-79 < z < 1.7999999999999999e-43

   1. Initial program 89.0%

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

      1. associate-*l/ 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in z around 0 67.6%

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

      1. associate-*l/ 67.3%

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

      2. clear-num 67.3%

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

   7. Applied egg-rr 67.3%

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

      1. associate-/r/ 67.4%

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

      2. *-commutative 67.4%

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

   9. Simplified 67.4%

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

   10. Taylor expanded in y around inf 67.9%

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

       1. div-sub 67.9%

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

   12. Simplified 67.9%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+88}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -160000000:\\ \;\;\;\;t + \frac{a}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-28}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 10^{-78}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-43}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+111}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 47.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{+87}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -50000000:\\ \;\;\;\;t + \frac{a}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-31}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{+111}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z))))
   (if (<= z -2.15e+87)
     t
     (if (<= z -2.3e+60)
       t_1
       (if (<= z -50000000.0)
         (+ t (/ a (/ z t)))
         (if (<= z -2.05e-31)
           (* (- t x) (/ y a))
           (if (<= z 3.2e-75)
             (* x (- 1.0 (/ y a)))
             (if (<= z 5e-36)
               (* y (/ (- t x) a))
               (if (<= z 9.4e+111)
                 (+ x (* t (/ y a)))
                 (if (<= z 2e+150) t_1 t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double tmp;
	if (z <= -2.15e+87) {
		tmp = t;
	} else if (z <= -2.3e+60) {
		tmp = t_1;
	} else if (z <= -50000000.0) {
		tmp = t + (a / (z / t));
	} else if (z <= -2.05e-31) {
		tmp = (t - x) * (y / a);
	} else if (z <= 3.2e-75) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 5e-36) {
		tmp = y * ((t - x) / a);
	} else if (z <= 9.4e+111) {
		tmp = x + (t * (y / a));
	} else if (z <= 2e+150) {
		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 * ((y - a) / z)
    if (z <= (-2.15d+87)) then
        tmp = t
    else if (z <= (-2.3d+60)) then
        tmp = t_1
    else if (z <= (-50000000.0d0)) then
        tmp = t + (a / (z / t))
    else if (z <= (-2.05d-31)) then
        tmp = (t - x) * (y / a)
    else if (z <= 3.2d-75) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 5d-36) then
        tmp = y * ((t - x) / a)
    else if (z <= 9.4d+111) then
        tmp = x + (t * (y / a))
    else if (z <= 2d+150) 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 * ((y - a) / z);
	double tmp;
	if (z <= -2.15e+87) {
		tmp = t;
	} else if (z <= -2.3e+60) {
		tmp = t_1;
	} else if (z <= -50000000.0) {
		tmp = t + (a / (z / t));
	} else if (z <= -2.05e-31) {
		tmp = (t - x) * (y / a);
	} else if (z <= 3.2e-75) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 5e-36) {
		tmp = y * ((t - x) / a);
	} else if (z <= 9.4e+111) {
		tmp = x + (t * (y / a));
	} else if (z <= 2e+150) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	tmp = 0
	if z <= -2.15e+87:
		tmp = t
	elif z <= -2.3e+60:
		tmp = t_1
	elif z <= -50000000.0:
		tmp = t + (a / (z / t))
	elif z <= -2.05e-31:
		tmp = (t - x) * (y / a)
	elif z <= 3.2e-75:
		tmp = x * (1.0 - (y / a))
	elif z <= 5e-36:
		tmp = y * ((t - x) / a)
	elif z <= 9.4e+111:
		tmp = x + (t * (y / a))
	elif z <= 2e+150:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	tmp = 0.0
	if (z <= -2.15e+87)
		tmp = t;
	elseif (z <= -2.3e+60)
		tmp = t_1;
	elseif (z <= -50000000.0)
		tmp = Float64(t + Float64(a / Float64(z / t)));
	elseif (z <= -2.05e-31)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (z <= 3.2e-75)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 5e-36)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 9.4e+111)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 2e+150)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	tmp = 0.0;
	if (z <= -2.15e+87)
		tmp = t;
	elseif (z <= -2.3e+60)
		tmp = t_1;
	elseif (z <= -50000000.0)
		tmp = t + (a / (z / t));
	elseif (z <= -2.05e-31)
		tmp = (t - x) * (y / a);
	elseif (z <= 3.2e-75)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 5e-36)
		tmp = y * ((t - x) / a);
	elseif (z <= 9.4e+111)
		tmp = x + (t * (y / a));
	elseif (z <= 2e+150)
		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[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.15e+87], t, If[LessEqual[z, -2.3e+60], t$95$1, If[LessEqual[z, -50000000.0], N[(t + N[(a / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.05e-31], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-75], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-36], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.4e+111], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+150], t$95$1, t]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -2.15e87 or 1.99999999999999996e150 < z

   1. Initial program 33.0%

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

      1. associate-*l/ 56.5%

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

   3. Simplified 56.5%

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

   5. Taylor expanded in z around inf 49.4%

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

   if -2.15e87 < z < -2.30000000000000017e60 or 9.40000000000000015e111 < z < 1.99999999999999996e150

   1. Initial program 29.4%

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

      1. associate-*l/ 60.9%

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

   3. Simplified 60.9%

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

   5. Taylor expanded in z around inf 49.9%

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

      1. associate--l+ 49.9%

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

      2. associate-*r/ 49.9%

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

      3. associate-*r/ 49.9%

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

      4. div-sub 50.0%

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

      5. distribute-lft-out-- 50.0%

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

      6. associate-*r/ 50.0%

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

      7. mul-1-neg 50.0%

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

      8. distribute-rgt-out-- 50.0%

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

      9. unsub-neg 50.0%

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

      10. associate-/l* 80.2%

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

   7. Simplified 80.2%

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

   8. Taylor expanded in t around 0 50.3%

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

      1. associate-*r/ 74.7%

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

   10. Simplified 74.7%

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

   if -2.30000000000000017e60 < z < -5e7

   1. Initial program 87.7%

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

      1. associate-*l/ 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in x around 0 80.6%

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

   6. Taylor expanded in z around inf 80.8%

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

      1. associate--l+ 80.8%

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

      2. associate-*r/ 80.8%

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

      3. associate-*r/ 80.8%

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

      4. div-sub 80.8%

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

      5. distribute-lft-out-- 80.8%

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

      6. associate-*r/ 80.8%

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

      7. mul-1-neg 80.8%

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

      8. unsub-neg 80.8%

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

      9. *-commutative 80.8%

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

      10. distribute-lft-out-- 80.8%

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

   8. Simplified 80.8%

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

   9. Taylor expanded in y around 0 69.0%

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

       1. sub-neg 69.0%

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

       2. mul-1-neg 69.0%

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

       3. remove-double-neg 69.0%

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

       4. associate-/l* 69.0%

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

   11. Simplified 69.0%

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

   if -5e7 < z < -2.0499999999999998e-31

   1. Initial program 91.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around -inf 62.8%

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

      1. associate-*l/ 70.7%

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

   7. Simplified 70.7%

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

   8. Taylor expanded in a around inf 63.0%

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

   if -2.0499999999999998e-31 < z < 3.19999999999999977e-75

   1. Initial program 92.9%

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

      1. associate-*l/ 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in z around 0 85.9%

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

   6. Taylor expanded in x around inf 72.3%

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

      1. mul-1-neg 72.3%

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

      2. unsub-neg 72.3%

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

   8. Simplified 72.3%

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

   if 3.19999999999999977e-75 < z < 5.00000000000000004e-36

   1. Initial program 90.1%

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

      1. associate-*l/ 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in z around 0 70.9%

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

      1. associate-*l/ 70.5%

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

      2. clear-num 70.5%

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

   7. Applied egg-rr 70.5%

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

      1. associate-/r/ 70.7%

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

      2. *-commutative 70.7%

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

   9. Simplified 70.7%

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

   10. Taylor expanded in y around inf 71.1%

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

       1. div-sub 71.1%

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

   12. Simplified 71.1%

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

   if 5.00000000000000004e-36 < z < 9.40000000000000015e111

   1. Initial program 72.4%

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

      1. associate-*l/ 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in z around 0 64.9%

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

   6. Taylor expanded in t around inf 54.9%

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

      1. associate-*r/ 58.2%

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

   8. Simplified 58.2%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+87}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -50000000:\\ \;\;\;\;t + \frac{a}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-31}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{+111}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+150}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;y \leq -5 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-287}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-158}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{+35}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))) (t_2 (+ x (* t (/ y a)))))
   (if (<= y -5e+99)
     t_1
     (if (<= y -8.2e-10)
       (- x (/ (* x y) a))
       (if (<= y -7.4e-118)
         t_1
         (if (<= y -4.1e-287)
           t_2
           (if (<= y 1.8e-158)
             (/ (- t) (/ (- a z) z))
             (if (<= y 1.46e+35) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = x + (t * (y / a));
	double tmp;
	if (y <= -5e+99) {
		tmp = t_1;
	} else if (y <= -8.2e-10) {
		tmp = x - ((x * y) / a);
	} else if (y <= -7.4e-118) {
		tmp = t_1;
	} else if (y <= -4.1e-287) {
		tmp = t_2;
	} else if (y <= 1.8e-158) {
		tmp = -t / ((a - z) / z);
	} else if (y <= 1.46e+35) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    t_2 = x + (t * (y / a))
    if (y <= (-5d+99)) then
        tmp = t_1
    else if (y <= (-8.2d-10)) then
        tmp = x - ((x * y) / a)
    else if (y <= (-7.4d-118)) then
        tmp = t_1
    else if (y <= (-4.1d-287)) then
        tmp = t_2
    else if (y <= 1.8d-158) then
        tmp = -t / ((a - z) / z)
    else if (y <= 1.46d+35) then
        tmp = t_2
    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 = y * ((t - x) / (a - z));
	double t_2 = x + (t * (y / a));
	double tmp;
	if (y <= -5e+99) {
		tmp = t_1;
	} else if (y <= -8.2e-10) {
		tmp = x - ((x * y) / a);
	} else if (y <= -7.4e-118) {
		tmp = t_1;
	} else if (y <= -4.1e-287) {
		tmp = t_2;
	} else if (y <= 1.8e-158) {
		tmp = -t / ((a - z) / z);
	} else if (y <= 1.46e+35) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	t_2 = x + (t * (y / a))
	tmp = 0
	if y <= -5e+99:
		tmp = t_1
	elif y <= -8.2e-10:
		tmp = x - ((x * y) / a)
	elif y <= -7.4e-118:
		tmp = t_1
	elif y <= -4.1e-287:
		tmp = t_2
	elif y <= 1.8e-158:
		tmp = -t / ((a - z) / z)
	elif y <= 1.46e+35:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	t_2 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (y <= -5e+99)
		tmp = t_1;
	elseif (y <= -8.2e-10)
		tmp = Float64(x - Float64(Float64(x * y) / a));
	elseif (y <= -7.4e-118)
		tmp = t_1;
	elseif (y <= -4.1e-287)
		tmp = t_2;
	elseif (y <= 1.8e-158)
		tmp = Float64(Float64(-t) / Float64(Float64(a - z) / z));
	elseif (y <= 1.46e+35)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	t_2 = x + (t * (y / a));
	tmp = 0.0;
	if (y <= -5e+99)
		tmp = t_1;
	elseif (y <= -8.2e-10)
		tmp = x - ((x * y) / a);
	elseif (y <= -7.4e-118)
		tmp = t_1;
	elseif (y <= -4.1e-287)
		tmp = t_2;
	elseif (y <= 1.8e-158)
		tmp = -t / ((a - z) / z);
	elseif (y <= 1.46e+35)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e+99], t$95$1, If[LessEqual[y, -8.2e-10], N[(x - N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.4e-118], t$95$1, If[LessEqual[y, -4.1e-287], t$95$2, If[LessEqual[y, 1.8e-158], N[((-t) / N[(N[(a - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.46e+35], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.00000000000000008e99 or -8.1999999999999996e-10 < y < -7.40000000000000029e-118 or 1.4599999999999999e35 < y

   1. Initial program 68.4%

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

      1. associate-*l/ 84.4%

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

   3. Simplified 84.4%

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

   5. Taylor expanded in y around inf 73.7%

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

      1. div-sub 74.5%

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

   7. Simplified 74.5%

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

   if -5.00000000000000008e99 < y < -8.1999999999999996e-10

   1. Initial program 67.5%

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

      1. associate-*l/ 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in z around 0 63.3%

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

   6. Taylor expanded in t around 0 59.6%

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

      1. mul-1-neg 59.6%

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

   8. Simplified 59.6%

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

   if -7.40000000000000029e-118 < y < -4.1000000000000002e-287 or 1.79999999999999995e-158 < y < 1.4599999999999999e35

   1. Initial program 71.8%

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

      1. associate-*l/ 79.2%

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

   3. Simplified 79.2%

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

   5. Taylor expanded in z around 0 54.9%

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

   6. Taylor expanded in t around inf 53.0%

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

      1. associate-*r/ 53.0%

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

   8. Simplified 53.0%

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

   if -4.1000000000000002e-287 < y < 1.79999999999999995e-158

   1. Initial program 63.1%

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

      1. associate-*l/ 74.0%

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

   3. Simplified 74.0%

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

   5. Taylor expanded in x around 0 51.5%

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

   6. Taylor expanded in y around 0 51.7%

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

      1. mul-1-neg 51.7%

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

      2. associate-/l* 66.1%

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

      3. distribute-neg-frac 66.1%

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

   8. Simplified 66.1%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+99}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{-118}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-287}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-158}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{+35}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 53.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a - z}\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;y \leq -2.75 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-6}:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-287}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-159}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y (- a z)))) (t_2 (+ x (* t (/ y a)))))
   (if (<= y -2.75e+93)
     t_1
     (if (<= y -2e-6)
       (- x (* y (/ x a)))
       (if (<= y -1.7e-117)
         t_1
         (if (<= y -3.9e-287)
           t_2
           (if (<= y 2e-159)
             (/ (- t) (/ (- a z) z))
             (if (<= y 3.7e+34) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double t_2 = x + (t * (y / a));
	double tmp;
	if (y <= -2.75e+93) {
		tmp = t_1;
	} else if (y <= -2e-6) {
		tmp = x - (y * (x / a));
	} else if (y <= -1.7e-117) {
		tmp = t_1;
	} else if (y <= -3.9e-287) {
		tmp = t_2;
	} else if (y <= 2e-159) {
		tmp = -t / ((a - z) / z);
	} else if (y <= 3.7e+34) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (t - x) * (y / (a - z))
    t_2 = x + (t * (y / a))
    if (y <= (-2.75d+93)) then
        tmp = t_1
    else if (y <= (-2d-6)) then
        tmp = x - (y * (x / a))
    else if (y <= (-1.7d-117)) then
        tmp = t_1
    else if (y <= (-3.9d-287)) then
        tmp = t_2
    else if (y <= 2d-159) then
        tmp = -t / ((a - z) / z)
    else if (y <= 3.7d+34) then
        tmp = t_2
    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 - x) * (y / (a - z));
	double t_2 = x + (t * (y / a));
	double tmp;
	if (y <= -2.75e+93) {
		tmp = t_1;
	} else if (y <= -2e-6) {
		tmp = x - (y * (x / a));
	} else if (y <= -1.7e-117) {
		tmp = t_1;
	} else if (y <= -3.9e-287) {
		tmp = t_2;
	} else if (y <= 2e-159) {
		tmp = -t / ((a - z) / z);
	} else if (y <= 3.7e+34) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / (a - z))
	t_2 = x + (t * (y / a))
	tmp = 0
	if y <= -2.75e+93:
		tmp = t_1
	elif y <= -2e-6:
		tmp = x - (y * (x / a))
	elif y <= -1.7e-117:
		tmp = t_1
	elif y <= -3.9e-287:
		tmp = t_2
	elif y <= 2e-159:
		tmp = -t / ((a - z) / z)
	elif y <= 3.7e+34:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	t_2 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (y <= -2.75e+93)
		tmp = t_1;
	elseif (y <= -2e-6)
		tmp = Float64(x - Float64(y * Float64(x / a)));
	elseif (y <= -1.7e-117)
		tmp = t_1;
	elseif (y <= -3.9e-287)
		tmp = t_2;
	elseif (y <= 2e-159)
		tmp = Float64(Float64(-t) / Float64(Float64(a - z) / z));
	elseif (y <= 3.7e+34)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / (a - z));
	t_2 = x + (t * (y / a));
	tmp = 0.0;
	if (y <= -2.75e+93)
		tmp = t_1;
	elseif (y <= -2e-6)
		tmp = x - (y * (x / a));
	elseif (y <= -1.7e-117)
		tmp = t_1;
	elseif (y <= -3.9e-287)
		tmp = t_2;
	elseif (y <= 2e-159)
		tmp = -t / ((a - z) / z);
	elseif (y <= 3.7e+34)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.75e+93], t$95$1, If[LessEqual[y, -2e-6], N[(x - N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.7e-117], t$95$1, If[LessEqual[y, -3.9e-287], t$95$2, If[LessEqual[y, 2e-159], N[((-t) / N[(N[(a - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e+34], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.75000000000000015e93 or -1.99999999999999991e-6 < y < -1.70000000000000017e-117 or 3.70000000000000009e34 < y

   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/ 84.7%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in y around -inf 62.1%

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

      1. associate-*l/ 77.2%

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

   7. Simplified 77.2%

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

   if -2.75000000000000015e93 < y < -1.99999999999999991e-6

   1. Initial program 64.6%

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

      1. associate-*l/ 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in z around 0 60.0%

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

   6. Taylor expanded in x around inf 55.8%

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

      1. mul-1-neg 55.8%

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

      2. unsub-neg 55.8%

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

   8. Simplified 55.8%

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

   9. Taylor expanded in y around 0 55.9%

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

       1. metadata-eval 55.9%

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

       2. associate-/l* 55.8%

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

       3. cancel-sign-sub-inv 55.8%

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

       4. *-lft-identity 55.8%

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

       5. associate-/r/ 55.9%

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

       6. *-commutative 55.9%

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

   11. Simplified 55.9%

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

   if -1.70000000000000017e-117 < y < -3.9e-287 or 1.99999999999999998e-159 < y < 3.70000000000000009e34

   1. Initial program 71.8%

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

      1. associate-*l/ 79.2%

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

   3. Simplified 79.2%

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

   5. Taylor expanded in z around 0 54.9%

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

   6. Taylor expanded in t around inf 53.0%

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

      1. associate-*r/ 53.0%

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

   8. Simplified 53.0%

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

   if -3.9e-287 < y < 1.99999999999999998e-159

   1. Initial program 63.1%

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

      1. associate-*l/ 74.0%

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

   3. Simplified 74.0%

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

   5. Taylor expanded in x around 0 51.5%

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

   6. Taylor expanded in y around 0 51.7%

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

      1. mul-1-neg 51.7%

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

      2. associate-/l* 66.1%

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

      3. distribute-neg-frac 66.1%

         \[\leadsto \color{blue}{\frac{-t}{\frac{a - z}{z}}} \]

   8. Simplified 66.1%

      \[\leadsto \color{blue}{\frac{-t}{\frac{a - z}{z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{+93}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-6}:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-117}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-287}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-159}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+34}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{t \cdot y}{z}\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{-51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-268}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-210}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+138} \lor \neg \left(a \leq 4.6 \cdot 10^{+264}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ (* t y) z))) (t_2 (+ x (* t (/ y a)))))
   (if (<= a -1.45e-51)
     t_2
     (if (<= a -6.2e-268)
       t_1
       (if (<= a 8.8e-210)
         (/ (- y) (/ z (- t x)))
         (if (<= a 1.05e-89)
           t_1
           (if (or (<= a 2.55e+138) (not (<= a 4.6e+264)))
             (* x (- 1.0 (/ y a)))
             t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((t * y) / z);
	double t_2 = x + (t * (y / a));
	double tmp;
	if (a <= -1.45e-51) {
		tmp = t_2;
	} else if (a <= -6.2e-268) {
		tmp = t_1;
	} else if (a <= 8.8e-210) {
		tmp = -y / (z / (t - x));
	} else if (a <= 1.05e-89) {
		tmp = t_1;
	} else if ((a <= 2.55e+138) || !(a <= 4.6e+264)) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t - ((t * y) / z)
    t_2 = x + (t * (y / a))
    if (a <= (-1.45d-51)) then
        tmp = t_2
    else if (a <= (-6.2d-268)) then
        tmp = t_1
    else if (a <= 8.8d-210) then
        tmp = -y / (z / (t - x))
    else if (a <= 1.05d-89) then
        tmp = t_1
    else if ((a <= 2.55d+138) .or. (.not. (a <= 4.6d+264))) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((t * y) / z);
	double t_2 = x + (t * (y / a));
	double tmp;
	if (a <= -1.45e-51) {
		tmp = t_2;
	} else if (a <= -6.2e-268) {
		tmp = t_1;
	} else if (a <= 8.8e-210) {
		tmp = -y / (z / (t - x));
	} else if (a <= 1.05e-89) {
		tmp = t_1;
	} else if ((a <= 2.55e+138) || !(a <= 4.6e+264)) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((t * y) / z)
	t_2 = x + (t * (y / a))
	tmp = 0
	if a <= -1.45e-51:
		tmp = t_2
	elif a <= -6.2e-268:
		tmp = t_1
	elif a <= 8.8e-210:
		tmp = -y / (z / (t - x))
	elif a <= 1.05e-89:
		tmp = t_1
	elif (a <= 2.55e+138) or not (a <= 4.6e+264):
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(t * y) / z))
	t_2 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (a <= -1.45e-51)
		tmp = t_2;
	elseif (a <= -6.2e-268)
		tmp = t_1;
	elseif (a <= 8.8e-210)
		tmp = Float64(Float64(-y) / Float64(z / Float64(t - x)));
	elseif (a <= 1.05e-89)
		tmp = t_1;
	elseif ((a <= 2.55e+138) || !(a <= 4.6e+264))
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((t * y) / z);
	t_2 = x + (t * (y / a));
	tmp = 0.0;
	if (a <= -1.45e-51)
		tmp = t_2;
	elseif (a <= -6.2e-268)
		tmp = t_1;
	elseif (a <= 8.8e-210)
		tmp = -y / (z / (t - x));
	elseif (a <= 1.05e-89)
		tmp = t_1;
	elseif ((a <= 2.55e+138) || ~((a <= 4.6e+264)))
		tmp = x * (1.0 - (y / a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(t * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.45e-51], t$95$2, If[LessEqual[a, -6.2e-268], t$95$1, If[LessEqual[a, 8.8e-210], N[((-y) / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e-89], t$95$1, If[Or[LessEqual[a, 2.55e+138], N[Not[LessEqual[a, 4.6e+264]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.44999999999999986e-51 or 2.5499999999999999e138 < a < 4.6000000000000003e264

   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/ 89.1%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 89.1%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 71.0%

      \[\leadsto x + \color{blue}{\frac{y}{a}} \cdot \left(t - x\right) \]

   6. Taylor expanded in t around inf 57.2%

      \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]
   7. Step-by-step derivation

      1. associate-*r/ 61.1%

         \[\leadsto x + \color{blue}{t \cdot \frac{y}{a}} \]

   8. Simplified 61.1%

      \[\leadsto x + \color{blue}{t \cdot \frac{y}{a}} \]

   if -1.44999999999999986e-51 < a < -6.1999999999999996e-268 or 8.79999999999999958e-210 < a < 1.05e-89

   1. Initial program 62.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 71.0%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 71.0%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 53.4%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]

   6. Taylor expanded in z around inf 58.4%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{t \cdot y}{z}\right) - -1 \cdot \frac{a \cdot t}{z}} \]
   7. Step-by-step derivation

      1. associate--l+ 58.4%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{t \cdot y}{z} - -1 \cdot \frac{a \cdot t}{z}\right)} \]

      2. associate-*r/ 58.4%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(t \cdot y\right)}{z}} - -1 \cdot \frac{a \cdot t}{z}\right) \]

      3. associate-*r/ 58.4%

         \[\leadsto t + \left(\frac{-1 \cdot \left(t \cdot y\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot t\right)}{z}}\right) \]

      4. div-sub 58.4%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(t \cdot y\right) - -1 \cdot \left(a \cdot t\right)}{z}} \]

      5. distribute-lft-out-- 58.4%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(t \cdot y - a \cdot t\right)}}{z} \]

      6. associate-*r/ 58.4%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{t \cdot y - a \cdot t}{z}} \]

      7. mul-1-neg 58.4%

         \[\leadsto t + \color{blue}{\left(-\frac{t \cdot y - a \cdot t}{z}\right)} \]

      8. unsub-neg 58.4%

         \[\leadsto \color{blue}{t - \frac{t \cdot y - a \cdot t}{z}} \]

      9. *-commutative 58.4%

         \[\leadsto t - \frac{t \cdot y - \color{blue}{t \cdot a}}{z} \]

      10. distribute-lft-out-- 58.4%

          \[\leadsto t - \frac{\color{blue}{t \cdot \left(y - a\right)}}{z} \]

   8. Simplified 58.4%

      \[\leadsto \color{blue}{t - \frac{t \cdot \left(y - a\right)}{z}} \]

   9. Taylor expanded in y around inf 58.1%

      \[\leadsto t - \frac{\color{blue}{t \cdot y}}{z} \]
   10. Step-by-step derivation

       1. *-commutative 58.1%

          \[\leadsto t - \frac{\color{blue}{y \cdot t}}{z} \]

   11. Simplified 58.1%

       \[\leadsto t - \frac{\color{blue}{y \cdot t}}{z} \]

   if -6.1999999999999996e-268 < a < 8.79999999999999958e-210

   1. Initial program 62.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 74.6%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 74.6%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 83.5%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 83.5%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 83.5%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 83.5%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      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. mul-1-neg 83.5%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 83.5%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 83.5%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 95.5%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   7. Simplified 95.5%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   8. Taylor expanded in y around -inf 58.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right)}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 58.4%

         \[\leadsto \color{blue}{-\frac{y \cdot \left(t - x\right)}{z}} \]

      2. associate-/l* 70.5%

         \[\leadsto -\color{blue}{\frac{y}{\frac{z}{t - x}}} \]

   10. Simplified 70.5%

       \[\leadsto \color{blue}{-\frac{y}{\frac{z}{t - x}}} \]

   if 1.05e-89 < a < 2.5499999999999999e138 or 4.6000000000000003e264 < a

   1. Initial program 71.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 85.5%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 85.5%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 66.8%

      \[\leadsto x + \color{blue}{\frac{y}{a}} \cdot \left(t - x\right) \]

   6. Taylor expanded in x around inf 58.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{a}\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 58.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{y}{a}\right)}\right) \]

      2. unsub-neg 58.6%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y}{a}\right)} \]

   8. Simplified 58.6%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-51}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-268}:\\ \;\;\;\;t - \frac{t \cdot y}{z}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-210}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-89}:\\ \;\;\;\;t - \frac{t \cdot y}{z}\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+138} \lor \neg \left(a \leq 4.6 \cdot 10^{+264}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 65.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -0.00026:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+103}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+145}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -1.02e+82)
     t_1
     (if (<= z -4.2e+60)
       (* x (/ (- y a) z))
       (if (<= z -0.00026)
         t_1
         (if (<= z 7.5e+103)
           (+ x (* (- t x) (/ y a)))
           (if (<= z 1.35e+145)
             (* (/ y z) (- x t))
             (+ t (/ a (/ z (- t x)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.02e+82) {
		tmp = t_1;
	} else if (z <= -4.2e+60) {
		tmp = x * ((y - a) / z);
	} else if (z <= -0.00026) {
		tmp = t_1;
	} else if (z <= 7.5e+103) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 1.35e+145) {
		tmp = (y / z) * (x - t);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-1.02d+82)) then
        tmp = t_1
    else if (z <= (-4.2d+60)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-0.00026d0)) then
        tmp = t_1
    else if (z <= 7.5d+103) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 1.35d+145) then
        tmp = (y / z) * (x - t)
    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 t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.02e+82) {
		tmp = t_1;
	} else if (z <= -4.2e+60) {
		tmp = x * ((y - a) / z);
	} else if (z <= -0.00026) {
		tmp = t_1;
	} else if (z <= 7.5e+103) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 1.35e+145) {
		tmp = (y / z) * (x - t);
	} else {
		tmp = t + (a / (z / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -1.02e+82:
		tmp = t_1
	elif z <= -4.2e+60:
		tmp = x * ((y - a) / z)
	elif z <= -0.00026:
		tmp = t_1
	elif z <= 7.5e+103:
		tmp = x + ((t - x) * (y / a))
	elif z <= 1.35e+145:
		tmp = (y / z) * (x - t)
	else:
		tmp = t + (a / (z / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.02e+82)
		tmp = t_1;
	elseif (z <= -4.2e+60)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -0.00026)
		tmp = t_1;
	elseif (z <= 7.5e+103)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 1.35e+145)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	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)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -1.02e+82)
		tmp = t_1;
	elseif (z <= -4.2e+60)
		tmp = x * ((y - a) / z);
	elseif (z <= -0.00026)
		tmp = t_1;
	elseif (z <= 7.5e+103)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 1.35e+145)
		tmp = (y / z) * (x - t);
	else
		tmp = t + (a / (z / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.02e+82], t$95$1, If[LessEqual[z, -4.2e+60], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.00026], t$95$1, If[LessEqual[z, 7.5e+103], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+145], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.0200000000000001e82 or -4.2000000000000002e60 < z < -2.59999999999999977e-4

   1. Initial program 45.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 70.1%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 70.1%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 43.4%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. div-inv 43.3%

         \[\leadsto \color{blue}{\left(t \cdot \left(y - z\right)\right) \cdot \frac{1}{a - z}} \]

      2. *-commutative 43.3%

         \[\leadsto \color{blue}{\left(\left(y - z\right) \cdot t\right)} \cdot \frac{1}{a - z} \]

      3. associate-*l* 60.8%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \left(t \cdot \frac{1}{a - z}\right)} \]

      4. div-inv 60.8%

         \[\leadsto \left(y - z\right) \cdot \color{blue}{\frac{t}{a - z}} \]

      5. clear-num 59.6%

         \[\leadsto \left(y - z\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{t}}} \]

      6. div-inv 59.6%

         \[\leadsto \color{blue}{\frac{y - z}{\frac{a - z}{t}}} \]

      7. associate-/r/ 66.7%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   7. Applied egg-rr 66.7%

      \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   if -1.0200000000000001e82 < z < -4.2000000000000002e60

   1. Initial program 34.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 67.0%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 67.0%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 53.9%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 53.9%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 53.9%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 53.9%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 53.9%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 53.9%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. associate-*r/ 53.9%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      7. mul-1-neg 53.9%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 53.9%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 53.9%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 84.4%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   7. Simplified 84.4%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   8. Taylor expanded in t around 0 53.9%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z}} \]
   9. Step-by-step derivation

      1. associate-*r/ 84.6%

         \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} \]

   10. Simplified 84.6%

       \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} \]

   if -2.59999999999999977e-4 < z < 7.49999999999999922e103

   1. Initial program 88.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 96.1%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 96.1%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 81.1%

      \[\leadsto x + \color{blue}{\frac{y}{a}} \cdot \left(t - x\right) \]

   if 7.49999999999999922e103 < z < 1.35000000000000011e145

   1. Initial program 40.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 63.5%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 63.5%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around -inf 41.7%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-*l/ 75.8%

         \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   7. Simplified 75.8%

      \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   8. Taylor expanded in a around 0 75.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{y}{z}\right)} \cdot \left(t - x\right) \]
   9. Step-by-step derivation

      1. associate-*r/ 75.9%

         \[\leadsto \color{blue}{\frac{-1 \cdot y}{z}} \cdot \left(t - x\right) \]

      2. neg-mul-1 75.9%

         \[\leadsto \frac{\color{blue}{-y}}{z} \cdot \left(t - x\right) \]

   10. Simplified 75.9%

       \[\leadsto \color{blue}{\frac{-y}{z}} \cdot \left(t - x\right) \]

   if 1.35000000000000011e145 < z

   1. Initial program 32.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 49.2%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 49.2%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 66.0%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 66.0%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 66.0%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 66.0%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 66.1%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 66.1%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. associate-*r/ 66.1%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      7. mul-1-neg 66.1%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 66.2%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 66.2%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 88.8%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   7. Simplified 88.8%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   8. Taylor expanded in y around 0 54.5%

      \[\leadsto \color{blue}{t - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   9. Step-by-step derivation

      1. sub-neg 54.5%

         \[\leadsto \color{blue}{t + \left(--1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. mul-1-neg 54.5%

         \[\leadsto t + \left(-\color{blue}{\left(-\frac{a \cdot \left(t - x\right)}{z}\right)}\right) \]

      3. remove-double-neg 54.5%

         \[\leadsto t + \color{blue}{\frac{a \cdot \left(t - x\right)}{z}} \]

      4. associate-/l* 66.9%

         \[\leadsto t + \color{blue}{\frac{a}{\frac{z}{t - x}}} \]

   10. Simplified 66.9%

       \[\leadsto \color{blue}{t + \frac{a}{\frac{z}{t - x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+82}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -0.00026:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+103}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+145}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 36.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{-72}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-294}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= a -4.2e-72)
     x
     (if (<= a -5.2e-186)
       t_1
       (if (<= a 3.2e-294) t (if (<= a 2.5e+19) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -4.2e-72) {
		tmp = x;
	} else if (a <= -5.2e-186) {
		tmp = t_1;
	} else if (a <= 3.2e-294) {
		tmp = t;
	} else if (a <= 2.5e+19) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / z)
    if (a <= (-4.2d-72)) then
        tmp = x
    else if (a <= (-5.2d-186)) then
        tmp = t_1
    else if (a <= 3.2d-294) then
        tmp = t
    else if (a <= 2.5d+19) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -4.2e-72) {
		tmp = x;
	} else if (a <= -5.2e-186) {
		tmp = t_1;
	} else if (a <= 3.2e-294) {
		tmp = t;
	} else if (a <= 2.5e+19) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	tmp = 0
	if a <= -4.2e-72:
		tmp = x
	elif a <= -5.2e-186:
		tmp = t_1
	elif a <= 3.2e-294:
		tmp = t
	elif a <= 2.5e+19:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (a <= -4.2e-72)
		tmp = x;
	elseif (a <= -5.2e-186)
		tmp = t_1;
	elseif (a <= 3.2e-294)
		tmp = t;
	elseif (a <= 2.5e+19)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (a <= -4.2e-72)
		tmp = x;
	elseif (a <= -5.2e-186)
		tmp = t_1;
	elseif (a <= 3.2e-294)
		tmp = t;
	elseif (a <= 2.5e+19)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.2e-72], x, If[LessEqual[a, -5.2e-186], t$95$1, If[LessEqual[a, 3.2e-294], t, If[LessEqual[a, 2.5e+19], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.2e-72 or 2.5e19 < a

   1. Initial program 72.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.1%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 89.1%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 39.4%

      \[\leadsto \color{blue}{x} \]

   if -4.2e-72 < a < -5.19999999999999986e-186 or 3.20000000000000019e-294 < a < 2.5e19

   1. Initial program 63.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 70.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 70.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around -inf 57.2%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-*l/ 64.5%

         \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   7. Simplified 64.5%

      \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   8. Taylor expanded in a around 0 52.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{y}{z}\right)} \cdot \left(t - x\right) \]
   9. Step-by-step derivation

      1. associate-*r/ 52.5%

         \[\leadsto \color{blue}{\frac{-1 \cdot y}{z}} \cdot \left(t - x\right) \]

      2. neg-mul-1 52.5%

         \[\leadsto \frac{\color{blue}{-y}}{z} \cdot \left(t - x\right) \]

   10. Simplified 52.5%

       \[\leadsto \color{blue}{\frac{-y}{z}} \cdot \left(t - x\right) \]

   11. Taylor expanded in t around 0 39.5%

       \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   12. Step-by-step derivation

       1. associate-*r/ 46.9%

          \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]

   13. Simplified 46.9%

       \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]

   if -5.19999999999999986e-186 < a < 3.20000000000000019e-294

   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/ 80.7%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 80.7%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 49.4%

      \[\leadsto \color{blue}{t} \]
3. Recombined 3 regimes into one program.

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-72}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-294}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 59.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+224}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{+78}:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+54}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.2e+224)
   (* x (/ (- y a) z))
   (if (<= x -3.4e+78)
     (- x (* y (/ x a)))
     (if (<= x 2.7e+54) (* t (/ (- y z) (- a z))) (* x (- 1.0 (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.2e+224) {
		tmp = x * ((y - a) / z);
	} else if (x <= -3.4e+78) {
		tmp = x - (y * (x / a));
	} else if (x <= 2.7e+54) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-2.2d+224)) then
        tmp = x * ((y - a) / z)
    else if (x <= (-3.4d+78)) then
        tmp = x - (y * (x / a))
    else if (x <= 2.7d+54) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x * (1.0d0 - (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.2e+224) {
		tmp = x * ((y - a) / z);
	} else if (x <= -3.4e+78) {
		tmp = x - (y * (x / a));
	} else if (x <= 2.7e+54) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.2e+224:
		tmp = x * ((y - a) / z)
	elif x <= -3.4e+78:
		tmp = x - (y * (x / a))
	elif x <= 2.7e+54:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.2e+224)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (x <= -3.4e+78)
		tmp = Float64(x - Float64(y * Float64(x / a)));
	elseif (x <= 2.7e+54)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.2e+224)
		tmp = x * ((y - a) / z);
	elseif (x <= -3.4e+78)
		tmp = x - (y * (x / a));
	elseif (x <= 2.7e+54)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.2e+224], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.4e+78], N[(x - N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e+54], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.2e224

   1. Initial program 52.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. Add Preprocessing

   5. Taylor expanded in z around inf 42.4%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 42.4%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 42.4%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 42.4%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 50.0%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 50.0%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. associate-*r/ 50.0%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      7. mul-1-neg 50.0%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 50.2%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 50.2%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 76.7%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   7. Simplified 76.7%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   8. Taylor expanded in t around 0 43.6%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z}} \]
   9. Step-by-step derivation

      1. associate-*r/ 70.2%

         \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} \]

   10. Simplified 70.2%

       \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} \]

   if -2.2e224 < x < -3.40000000000000007e78

   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/ 88.3%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 88.3%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 76.4%

      \[\leadsto x + \color{blue}{\frac{y}{a}} \cdot \left(t - x\right) \]

   6. Taylor expanded in x around inf 70.5%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{a}\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 70.5%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{y}{a}\right)}\right) \]

      2. unsub-neg 70.5%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y}{a}\right)} \]

   8. Simplified 70.5%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]

   9. Taylor expanded in y around 0 70.3%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot y}{a}} \]
   10. Step-by-step derivation

       1. metadata-eval 70.3%

          \[\leadsto x + \color{blue}{\left(-1\right)} \cdot \frac{x \cdot y}{a} \]

       2. associate-/l* 70.5%

          \[\leadsto x + \left(-1\right) \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]

       3. cancel-sign-sub-inv 70.5%

          \[\leadsto \color{blue}{x - 1 \cdot \frac{x}{\frac{a}{y}}} \]

       4. *-lft-identity 70.5%

          \[\leadsto x - \color{blue}{\frac{x}{\frac{a}{y}}} \]

       5. associate-/r/ 70.5%

          \[\leadsto x - \color{blue}{\frac{x}{a} \cdot y} \]

       6. *-commutative 70.5%

          \[\leadsto x - \color{blue}{y \cdot \frac{x}{a}} \]

   11. Simplified 70.5%

       \[\leadsto \color{blue}{x - y \cdot \frac{x}{a}} \]

   if -3.40000000000000007e78 < x < 2.70000000000000011e54

   1. Initial program 76.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 87.1%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 87.1%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 53.6%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. div-inv 53.6%

         \[\leadsto \color{blue}{\left(t \cdot \left(y - z\right)\right) \cdot \frac{1}{a - z}} \]

      2. *-commutative 53.6%

         \[\leadsto \color{blue}{\left(\left(y - z\right) \cdot t\right)} \cdot \frac{1}{a - z} \]

      3. associate-*l* 57.6%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \left(t \cdot \frac{1}{a - z}\right)} \]

      4. div-inv 57.7%

         \[\leadsto \left(y - z\right) \cdot \color{blue}{\frac{t}{a - z}} \]

      5. clear-num 57.3%

         \[\leadsto \left(y - z\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{t}}} \]

      6. div-inv 57.3%

         \[\leadsto \color{blue}{\frac{y - z}{\frac{a - z}{t}}} \]

      7. associate-/r/ 65.2%

         \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   7. Applied egg-rr 65.2%

      \[\leadsto \color{blue}{\frac{y - z}{a - z} \cdot t} \]

   if 2.70000000000000011e54 < x

   1. Initial program 52.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 72.4%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 72.4%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 58.1%

      \[\leadsto x + \color{blue}{\frac{y}{a}} \cdot \left(t - x\right) \]

   6. Taylor expanded in x around inf 56.5%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{a}\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 56.5%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{y}{a}\right)}\right) \]

      2. unsub-neg 56.5%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y}{a}\right)} \]

   8. Simplified 56.5%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+224}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{+78}:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+54}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 89.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+162} \lor \neg \left(z \leq 4.9 \cdot 10^{+121}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.75e+162) (not (<= z 4.9e+121)))
   (+ t (/ (- x t) (/ z (- y a))))
   (+ x (* (- t x) (/ (- y z) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.75e+162) || !(z <= 4.9e+121)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((t - x) * ((y - z) / (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) :: tmp
    if ((z <= (-1.75d+162)) .or. (.not. (z <= 4.9d+121))) then
        tmp = t + ((x - t) / (z / (y - a)))
    else
        tmp = x + ((t - x) * ((y - z) / (a - 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 <= -1.75e+162) || !(z <= 4.9e+121)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.75e+162) or not (z <= 4.9e+121):
		tmp = t + ((x - t) / (z / (y - a)))
	else:
		tmp = x + ((t - x) * ((y - z) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.75e+162) || !(z <= 4.9e+121))
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.75e+162) || ~((z <= 4.9e+121)))
		tmp = t + ((x - t) / (z / (y - a)));
	else
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.75e+162], N[Not[LessEqual[z, 4.9e+121]], $MachinePrecision]], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.75000000000000009e162 or 4.8999999999999998e121 < z

   1. Initial program 26.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 50.8%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 50.8%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 66.0%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 66.0%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 66.0%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 66.0%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 66.1%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 66.1%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. associate-*r/ 66.1%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      7. mul-1-neg 66.1%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 66.1%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 66.1%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 90.7%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   7. Simplified 90.7%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   if -1.75000000000000009e162 < z < 4.8999999999999998e121

   1. Initial program 84.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.1%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 94.1%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+162} \lor \neg \left(z \leq 4.9 \cdot 10^{+121}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 48.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+161}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+111}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+147}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.35e+161)
   t
   (if (<= z 6.2e+111)
     (* x (- 1.0 (/ y a)))
     (if (<= z 8.4e+147) (* x (/ (- y a) z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e+161) {
		tmp = t;
	} else if (z <= 6.2e+111) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 8.4e+147) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.35d+161)) then
        tmp = t
    else if (z <= 6.2d+111) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 8.4d+147) then
        tmp = x * ((y - a) / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e+161) {
		tmp = t;
	} else if (z <= 6.2e+111) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 8.4e+147) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.35e+161:
		tmp = t
	elif z <= 6.2e+111:
		tmp = x * (1.0 - (y / a))
	elif z <= 8.4e+147:
		tmp = x * ((y - a) / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.35e+161)
		tmp = t;
	elseif (z <= 6.2e+111)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 8.4e+147)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.35e+161)
		tmp = t;
	elseif (z <= 6.2e+111)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 8.4e+147)
		tmp = x * ((y - a) / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.35e+161], t, If[LessEqual[z, 6.2e+111], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.4e+147], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3499999999999999e161 or 8.40000000000000024e147 < z

   1. Initial program 27.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 52.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 52.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 52.4%

      \[\leadsto \color{blue}{t} \]

   if -1.3499999999999999e161 < z < 6.2000000000000001e111

   1. Initial program 85.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. Add Preprocessing

   5. Taylor expanded in z around 0 73.0%

      \[\leadsto x + \color{blue}{\frac{y}{a}} \cdot \left(t - x\right) \]

   6. Taylor expanded in x around inf 58.8%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{a}\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 58.8%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{y}{a}\right)}\right) \]

      2. unsub-neg 58.8%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y}{a}\right)} \]

   8. Simplified 58.8%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]

   if 6.2000000000000001e111 < z < 8.40000000000000024e147

   1. Initial program 28.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 51.4%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 51.4%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 53.2%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 53.2%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 53.2%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 53.2%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 53.3%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 53.3%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. associate-*r/ 53.3%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      7. mul-1-neg 53.3%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 53.3%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 53.3%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 87.0%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   7. Simplified 87.0%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   8. Taylor expanded in t around 0 53.1%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z}} \]
   9. Step-by-step derivation

      1. associate-*r/ 75.8%

         \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} \]

   10. Simplified 75.8%

       \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+161}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+111}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+147}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 75.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -320000000 \lor \neg \left(z \leq 4.2 \cdot 10^{+112}\right):\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -320000000.0) (not (<= z 4.2e+112)))
   (- t (/ y (/ z (- t x))))
   (+ x (/ y (/ (- a z) (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -320000000.0) || !(z <= 4.2e+112)) {
		tmp = t - (y / (z / (t - x)));
	} else {
		tmp = x + (y / ((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 <= (-320000000.0d0)) .or. (.not. (z <= 4.2d+112))) then
        tmp = t - (y / (z / (t - x)))
    else
        tmp = x + (y / ((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 <= -320000000.0) || !(z <= 4.2e+112)) {
		tmp = t - (y / (z / (t - x)));
	} else {
		tmp = x + (y / ((a - z) / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -320000000.0) or not (z <= 4.2e+112):
		tmp = t - (y / (z / (t - x)))
	else:
		tmp = x + (y / ((a - z) / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -320000000.0) || !(z <= 4.2e+112))
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	else
		tmp = Float64(x + Float64(y / 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 ((z <= -320000000.0) || ~((z <= 4.2e+112)))
		tmp = t - (y / (z / (t - x)));
	else
		tmp = x + (y / ((a - z) / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -320000000.0], N[Not[LessEqual[z, 4.2e+112]], $MachinePrecision]], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2e8 or 4.1999999999999998e112 < z

   1. Initial program 36.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 59.7%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 59.7%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 64.2%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 64.2%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 64.2%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 64.2%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 64.2%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 64.2%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. associate-*r/ 64.2%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      7. mul-1-neg 64.2%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 64.2%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 64.2%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 85.5%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   7. Simplified 85.5%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   8. Taylor expanded in y around inf 60.4%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 75.7%

         \[\leadsto t - \color{blue}{\frac{y}{\frac{z}{t - x}}} \]

   10. Simplified 75.7%

       \[\leadsto t - \color{blue}{\frac{y}{\frac{z}{t - x}}} \]

   if -3.2e8 < z < 4.1999999999999998e112

   1. Initial program 89.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 88.9%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \]

      2. associate-/r/ 88.9%

         \[\leadsto x + \color{blue}{\frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)} \]

   4. Applied egg-rr 88.9%

      \[\leadsto x + \color{blue}{\frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)} \]

   5. Taylor expanded in y around inf 82.4%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-/l* 85.7%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - z}{t - x}}} \]

   7. Simplified 85.7%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a - z}{t - x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -320000000 \lor \neg \left(z \leq 4.2 \cdot 10^{+112}\right):\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 79.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -210000000 \lor \neg \left(z \leq 1.6 \cdot 10^{+117}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -210000000.0) (not (<= z 1.6e+117)))
   (+ t (/ (- x t) (/ z (- y a))))
   (+ x (/ y (/ (- a z) (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -210000000.0) || !(z <= 1.6e+117)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + (y / ((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 <= (-210000000.0d0)) .or. (.not. (z <= 1.6d+117))) then
        tmp = t + ((x - t) / (z / (y - a)))
    else
        tmp = x + (y / ((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 <= -210000000.0) || !(z <= 1.6e+117)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + (y / ((a - z) / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -210000000.0) or not (z <= 1.6e+117):
		tmp = t + ((x - t) / (z / (y - a)))
	else:
		tmp = x + (y / ((a - z) / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -210000000.0) || !(z <= 1.6e+117))
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = Float64(x + Float64(y / 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 ((z <= -210000000.0) || ~((z <= 1.6e+117)))
		tmp = t + ((x - t) / (z / (y - a)));
	else
		tmp = x + (y / ((a - z) / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -210000000.0], N[Not[LessEqual[z, 1.6e+117]], $MachinePrecision]], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1e8 or 1.60000000000000002e117 < z

   1. Initial program 36.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 58.5%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 58.5%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 65.9%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 65.9%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 65.9%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 65.9%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 65.9%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 65.9%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. associate-*r/ 65.9%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      7. mul-1-neg 65.9%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 66.0%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 66.0%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 86.1%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   7. Simplified 86.1%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   if -2.1e8 < z < 1.60000000000000002e117

   1. Initial program 88.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 88.0%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}} \]

      2. associate-/r/ 88.0%

         \[\leadsto x + \color{blue}{\frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)} \]

   4. Applied egg-rr 88.0%

      \[\leadsto x + \color{blue}{\frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)} \]

   5. Taylor expanded in y around inf 81.0%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-/l* 85.3%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - z}{t - x}}} \]

   7. Simplified 85.3%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a - z}{t - x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -210000000 \lor \neg \left(z \leq 1.6 \cdot 10^{+117}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 48.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+158}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+147}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e+158)
   t
   (if (<= z 2.85e+112)
     (* x (- 1.0 (/ y a)))
     (if (<= z 4.6e+147) (* x (/ y z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+158) {
		tmp = t;
	} else if (z <= 2.85e+112) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 4.6e+147) {
		tmp = x * (y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.5d+158)) then
        tmp = t
    else if (z <= 2.85d+112) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 4.6d+147) then
        tmp = x * (y / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+158) {
		tmp = t;
	} else if (z <= 2.85e+112) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 4.6e+147) {
		tmp = x * (y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.5e+158:
		tmp = t
	elif z <= 2.85e+112:
		tmp = x * (1.0 - (y / a))
	elif z <= 4.6e+147:
		tmp = x * (y / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e+158)
		tmp = t;
	elseif (z <= 2.85e+112)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 4.6e+147)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.5e+158)
		tmp = t;
	elseif (z <= 2.85e+112)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 4.6e+147)
		tmp = x * (y / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e+158], t, If[LessEqual[z, 2.85e+112], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+147], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.49999999999999978e158 or 4.5999999999999998e147 < z

   1. Initial program 27.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 52.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 52.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 52.4%

      \[\leadsto \color{blue}{t} \]

   if -8.49999999999999978e158 < z < 2.85000000000000016e112

   1. Initial program 85.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. Add Preprocessing

   5. Taylor expanded in z around 0 73.0%

      \[\leadsto x + \color{blue}{\frac{y}{a}} \cdot \left(t - x\right) \]

   6. Taylor expanded in x around inf 58.8%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{a}\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 58.8%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{y}{a}\right)}\right) \]

      2. unsub-neg 58.8%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y}{a}\right)} \]

   8. Simplified 58.8%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]

   if 2.85000000000000016e112 < z < 4.5999999999999998e147

   1. Initial program 28.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 51.4%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 51.4%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around -inf 42.4%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-*l/ 76.5%

         \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   7. Simplified 76.5%

      \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   8. Taylor expanded in a around 0 76.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{y}{z}\right)} \cdot \left(t - x\right) \]
   9. Step-by-step derivation

      1. associate-*r/ 76.5%

         \[\leadsto \color{blue}{\frac{-1 \cdot y}{z}} \cdot \left(t - x\right) \]

      2. neg-mul-1 76.5%

         \[\leadsto \frac{\color{blue}{-y}}{z} \cdot \left(t - x\right) \]

   10. Simplified 76.5%

       \[\leadsto \color{blue}{\frac{-y}{z}} \cdot \left(t - x\right) \]

   11. Taylor expanded in t around 0 42.0%

       \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   12. Step-by-step derivation

       1. associate-*r/ 64.7%

          \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]

   13. Simplified 64.7%

       \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+158}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+147}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 68.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -90000000 \lor \neg \left(z \leq 2.35 \cdot 10^{+111}\right):\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -90000000.0) (not (<= z 2.35e+111)))
   (- t (/ y (/ z (- t x))))
   (+ x (* (- t x) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -90000000.0) || !(z <= 2.35e+111)) {
		tmp = t - (y / (z / (t - x)));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-90000000.0d0)) .or. (.not. (z <= 2.35d+111))) then
        tmp = t - (y / (z / (t - x)))
    else
        tmp = x + ((t - x) * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -90000000.0) || !(z <= 2.35e+111)) {
		tmp = t - (y / (z / (t - x)));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -90000000.0) or not (z <= 2.35e+111):
		tmp = t - (y / (z / (t - x)))
	else:
		tmp = x + ((t - x) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -90000000.0) || !(z <= 2.35e+111))
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -90000000.0) || ~((z <= 2.35e+111)))
		tmp = t - (y / (z / (t - x)));
	else
		tmp = x + ((t - x) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -90000000.0], N[Not[LessEqual[z, 2.35e+111]], $MachinePrecision]], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9e7 or 2.35000000000000004e111 < z

   1. Initial program 36.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 59.7%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 59.7%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 64.2%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 64.2%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 64.2%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 64.2%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 64.2%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 64.2%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. associate-*r/ 64.2%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      7. mul-1-neg 64.2%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 64.2%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 64.2%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 85.5%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   7. Simplified 85.5%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   8. Taylor expanded in y around inf 60.4%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 75.7%

         \[\leadsto t - \color{blue}{\frac{y}{\frac{z}{t - x}}} \]

   10. Simplified 75.7%

       \[\leadsto t - \color{blue}{\frac{y}{\frac{z}{t - x}}} \]

   if -9e7 < z < 2.35000000000000004e111

   1. Initial program 89.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 96.2%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 96.2%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 79.8%

      \[\leadsto x + \color{blue}{\frac{y}{a}} \cdot \left(t - x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -90000000 \lor \neg \left(z \leq 2.35 \cdot 10^{+111}\right):\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 38.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-28}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.8e-28) t (if (<= z 2.6e+111) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e-28) {
		tmp = t;
	} else if (z <= 2.6e+111) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.8d-28)) then
        tmp = t
    else if (z <= 2.6d+111) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e-28) {
		tmp = t;
	} else if (z <= 2.6e+111) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.8e-28:
		tmp = t
	elif z <= 2.6e+111:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.8e-28)
		tmp = t;
	elseif (z <= 2.6e+111)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.8e-28)
		tmp = t;
	elseif (z <= 2.6e+111)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.8e-28], t, If[LessEqual[z, 2.6e+111], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -8.79999999999999984e-28 or 2.5999999999999999e111 < z

   1. Initial program 42.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 63.7%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 63.7%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 40.9%

      \[\leadsto \color{blue}{t} \]

   if -8.79999999999999984e-28 < z < 2.5999999999999999e111

   1. Initial program 88.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 95.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 95.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 39.6%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-28}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 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 68.8%

   \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
2. Step-by-step derivation

   1. associate-*l/ 82.1%

      \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

3. Simplified 82.1%

   \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 21.4%

   \[\leadsto \color{blue}{t} \]

6. Final simplification 21.4%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 84.0% accurate, 0.6× 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 2024036 
(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))))