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

Percentage Accurate: 67.5% → 88.6%

Time: 34.3s

Alternatives: 28

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.5% 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: 88.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+71} \lor \neg \left(z \leq 4.5 \cdot 10^{+165}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - z}{y - z}}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6e+71) (not (<= z 4.5e+165)))
   (+ t (/ (- x t) (/ z (- y a))))
   (+ x (/ 1.0 (/ (/ (- a z) (- y z)) (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6e+71) || !(z <= 4.5e+165)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + (1.0 / (((a - z) / (y - 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 <= (-6d+71)) .or. (.not. (z <= 4.5d+165))) then
        tmp = t + ((x - t) / (z / (y - a)))
    else
        tmp = x + (1.0d0 / (((a - z) / (y - 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 <= -6e+71) || !(z <= 4.5e+165)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + (1.0 / (((a - z) / (y - z)) / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6e+71) or not (z <= 4.5e+165):
		tmp = t + ((x - t) / (z / (y - a)))
	else:
		tmp = x + (1.0 / (((a - z) / (y - z)) / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6e+71) || !(z <= 4.5e+165))
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = Float64(x + Float64(1.0 / Float64(Float64(Float64(a - z) / Float64(y - z)) / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6e+71) || ~((z <= 4.5e+165)))
		tmp = t + ((x - t) / (z / (y - a)));
	else
		tmp = x + (1.0 / (((a - z) / (y - z)) / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6e+71], N[Not[LessEqual[z, 4.5e+165]], $MachinePrecision]], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / N[(N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.00000000000000025e71 or 4.4999999999999996e165 < z

   1. Initial program 25.7%

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

      1. associate-*l/ 57.2%

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

   3. Simplified 57.2%

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

   5. Taylor expanded in z around inf 62.8%

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

      1. associate--l+ 62.8%

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

      2. associate-*r/ 62.8%

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

      3. associate-*r/ 62.8%

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

      4. div-sub 62.8%

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

      5. distribute-lft-out-- 62.8%

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

      6. associate-*r/ 62.8%

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

      7. mul-1-neg 62.8%

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

      8. distribute-rgt-out-- 62.9%

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

      9. unsub-neg 62.9%

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

      10. associate-/l* 85.1%

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

   7. Simplified 85.1%

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

   if -6.00000000000000025e71 < z < 4.4999999999999996e165

   1. Initial program 83.7%

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

      1. associate-*l/ 93.8%

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

   3. Simplified 93.8%

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

      1. associate-*l/ 83.7%

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

      2. clear-num 83.7%

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

      3. associate-/r* 93.9%

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

   6. Applied egg-rr 93.9%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+71} \lor \neg \left(z \leq 4.5 \cdot 10^{+165}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - z}{y - z}}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 45.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+109}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -17:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-243}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-50}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+24}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+132}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{+163}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+164}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y a))))
   (if (<= a -1.8e+109)
     x
     (if (<= a -17.0)
       t_1
       (if (<= a 4.8e-243)
         (- t (* t (/ y z)))
         (if (<= a 2.3e-50)
           (/ (* x (- y a)) z)
           (if (<= a 1.3e+24)
             (/ (- t) (/ (- a z) z))
             (if (<= a 2.1e+91)
               t_1
               (if (<= a 1.12e+96)
                 t
                 (if (<= a 4.6e+132)
                   x
                   (if (<= a 1.28e+163)
                     (* (- y z) (/ t a))
                     (if (<= a 1.35e+164) (* x (/ (- y a) z)) x))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / a);
	double tmp;
	if (a <= -1.8e+109) {
		tmp = x;
	} else if (a <= -17.0) {
		tmp = t_1;
	} else if (a <= 4.8e-243) {
		tmp = t - (t * (y / z));
	} else if (a <= 2.3e-50) {
		tmp = (x * (y - a)) / z;
	} else if (a <= 1.3e+24) {
		tmp = -t / ((a - z) / z);
	} else if (a <= 2.1e+91) {
		tmp = t_1;
	} else if (a <= 1.12e+96) {
		tmp = t;
	} else if (a <= 4.6e+132) {
		tmp = x;
	} else if (a <= 1.28e+163) {
		tmp = (y - z) * (t / a);
	} else if (a <= 1.35e+164) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - x) * (y / a)
    if (a <= (-1.8d+109)) then
        tmp = x
    else if (a <= (-17.0d0)) then
        tmp = t_1
    else if (a <= 4.8d-243) then
        tmp = t - (t * (y / z))
    else if (a <= 2.3d-50) then
        tmp = (x * (y - a)) / z
    else if (a <= 1.3d+24) then
        tmp = -t / ((a - z) / z)
    else if (a <= 2.1d+91) then
        tmp = t_1
    else if (a <= 1.12d+96) then
        tmp = t
    else if (a <= 4.6d+132) then
        tmp = x
    else if (a <= 1.28d+163) then
        tmp = (y - z) * (t / a)
    else if (a <= 1.35d+164) then
        tmp = x * ((y - a) / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / a);
	double tmp;
	if (a <= -1.8e+109) {
		tmp = x;
	} else if (a <= -17.0) {
		tmp = t_1;
	} else if (a <= 4.8e-243) {
		tmp = t - (t * (y / z));
	} else if (a <= 2.3e-50) {
		tmp = (x * (y - a)) / z;
	} else if (a <= 1.3e+24) {
		tmp = -t / ((a - z) / z);
	} else if (a <= 2.1e+91) {
		tmp = t_1;
	} else if (a <= 1.12e+96) {
		tmp = t;
	} else if (a <= 4.6e+132) {
		tmp = x;
	} else if (a <= 1.28e+163) {
		tmp = (y - z) * (t / a);
	} else if (a <= 1.35e+164) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / a)
	tmp = 0
	if a <= -1.8e+109:
		tmp = x
	elif a <= -17.0:
		tmp = t_1
	elif a <= 4.8e-243:
		tmp = t - (t * (y / z))
	elif a <= 2.3e-50:
		tmp = (x * (y - a)) / z
	elif a <= 1.3e+24:
		tmp = -t / ((a - z) / z)
	elif a <= 2.1e+91:
		tmp = t_1
	elif a <= 1.12e+96:
		tmp = t
	elif a <= 4.6e+132:
		tmp = x
	elif a <= 1.28e+163:
		tmp = (y - z) * (t / a)
	elif a <= 1.35e+164:
		tmp = x * ((y - a) / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / a))
	tmp = 0.0
	if (a <= -1.8e+109)
		tmp = x;
	elseif (a <= -17.0)
		tmp = t_1;
	elseif (a <= 4.8e-243)
		tmp = Float64(t - Float64(t * Float64(y / z)));
	elseif (a <= 2.3e-50)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (a <= 1.3e+24)
		tmp = Float64(Float64(-t) / Float64(Float64(a - z) / z));
	elseif (a <= 2.1e+91)
		tmp = t_1;
	elseif (a <= 1.12e+96)
		tmp = t;
	elseif (a <= 4.6e+132)
		tmp = x;
	elseif (a <= 1.28e+163)
		tmp = Float64(Float64(y - z) * Float64(t / a));
	elseif (a <= 1.35e+164)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / a);
	tmp = 0.0;
	if (a <= -1.8e+109)
		tmp = x;
	elseif (a <= -17.0)
		tmp = t_1;
	elseif (a <= 4.8e-243)
		tmp = t - (t * (y / z));
	elseif (a <= 2.3e-50)
		tmp = (x * (y - a)) / z;
	elseif (a <= 1.3e+24)
		tmp = -t / ((a - z) / z);
	elseif (a <= 2.1e+91)
		tmp = t_1;
	elseif (a <= 1.12e+96)
		tmp = t;
	elseif (a <= 4.6e+132)
		tmp = x;
	elseif (a <= 1.28e+163)
		tmp = (y - z) * (t / a);
	elseif (a <= 1.35e+164)
		tmp = x * ((y - a) / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8e+109], x, If[LessEqual[a, -17.0], t$95$1, If[LessEqual[a, 4.8e-243], N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e-50], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 1.3e+24], N[((-t) / N[(N[(a - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.1e+91], t$95$1, If[LessEqual[a, 1.12e+96], t, If[LessEqual[a, 4.6e+132], x, If[LessEqual[a, 1.28e+163], N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e+164], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], x]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -1.8e109 or 1.1199999999999999e96 < a < 4.6000000000000003e132 or 1.35000000000000003e164 < a

   1. Initial program 62.5%

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

      1. associate-*l/ 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in a around inf 59.3%

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

   if -1.8e109 < a < -17 or 1.2999999999999999e24 < a < 2.10000000000000008e91

   1. Initial program 78.7%

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

      1. associate-*l/ 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in y around -inf 53.3%

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

      1. associate-*l/ 57.0%

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

   7. Simplified 57.0%

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

   8. Taylor expanded in a around inf 49.4%

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

   if -17 < a < 4.8000000000000002e-243

   1. Initial program 64.9%

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

      1. associate-*l/ 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in x around 0 57.1%

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

   6. Taylor expanded in a around 0 52.3%

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

      1. associate-*r/ 52.3%

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

      2. *-commutative 52.3%

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

      3. neg-mul-1 52.3%

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

      4. distribute-rgt-neg-in 52.3%

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

   8. Simplified 52.3%

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

   9. Taylor expanded in y around 0 61.4%

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

       1. mul-1-neg 61.4%

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

       2. unsub-neg 61.4%

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

       3. *-commutative 61.4%

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

       4. associate-*l/ 65.3%

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

       5. *-commutative 65.3%

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

   11. Simplified 65.3%

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

   if 4.8000000000000002e-243 < a < 2.3000000000000002e-50

   1. Initial program 71.1%

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

      1. associate-*l/ 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in z around inf 72.6%

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

      1. associate--l+ 72.6%

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

      2. associate-*r/ 72.6%

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

      3. associate-*r/ 72.6%

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

      4. div-sub 72.6%

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

      5. distribute-lft-out-- 72.6%

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

      6. associate-*r/ 72.6%

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

      7. mul-1-neg 72.6%

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

      8. distribute-rgt-out-- 72.6%

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

      9. unsub-neg 72.6%

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

      10. associate-/l* 78.7%

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

   7. Simplified 78.7%

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

   8. Taylor expanded in t around 0 51.3%

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

   if 2.3000000000000002e-50 < a < 1.2999999999999999e24

   1. Initial program 47.3%

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

      1. associate-*l/ 72.3%

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

   3. Simplified 72.3%

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

   5. Taylor expanded in x around 0 39.7%

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

   6. Taylor expanded in y around 0 39.0%

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

      1. mul-1-neg 39.0%

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

      2. associate-/l* 59.1%

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

   8. Simplified 59.1%

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

   if 2.10000000000000008e91 < a < 1.1199999999999999e96

   1. Initial program 56.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 z around inf 100.0%

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

   if 4.6000000000000003e132 < a < 1.28e163

   1. Initial program 65.8%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in x around 0 53.2%

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

      1. associate-/l* 83.6%

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

   7. Simplified 83.6%

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

   8. Taylor expanded in a around inf 53.2%

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

      1. associate-/l* 68.0%

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

      2. associate-/r/ 68.5%

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

   10. Simplified 68.5%

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

   if 1.28e163 < a < 1.35000000000000003e164

   1. Initial program 4.7%

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

      1. associate-*l/ 2.2%

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

   3. Simplified 2.2%

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

   5. Taylor expanded in z around inf 4.7%

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

      1. associate--l+ 4.7%

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

      2. associate-*r/ 4.7%

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

      3. associate-*r/ 4.7%

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

      4. div-sub 4.7%

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

      5. distribute-lft-out-- 4.7%

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

      6. associate-*r/ 4.7%

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

      7. mul-1-neg 4.7%

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

      8. distribute-rgt-out-- 4.7%

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

      9. unsub-neg 4.7%

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

      10. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in t around 0 4.7%

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

      1. associate-*r/ 100.0%

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

   10. Simplified 100.0%

       \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} \]
3. Recombined 8 regimes into one program.

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+109}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -17:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-243}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-50}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+24}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+91}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+132}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{+163}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+164}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 56.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a - z}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{-26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-125}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-201}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-263}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a} + 1\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+148}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y (- a z)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= z -2.8e-26)
     t_2
     (if (<= z -6.8e-89)
       t_1
       (if (<= z -3e-125)
         (/ (- t) (/ (- a z) z))
         (if (<= z -1.35e-201)
           (* y (/ (- t x) (- a z)))
           (if (<= z -1.22e-263)
             t_1
             (if (<= z 5.6e-26)
               (* x (+ (/ (- z y) a) 1.0))
               (if (<= z 7.5e+148) t_2 (- t (/ a (/ z x))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2.8e-26) {
		tmp = t_2;
	} else if (z <= -6.8e-89) {
		tmp = t_1;
	} else if (z <= -3e-125) {
		tmp = -t / ((a - z) / z);
	} else if (z <= -1.35e-201) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= -1.22e-263) {
		tmp = t_1;
	} else if (z <= 5.6e-26) {
		tmp = x * (((z - y) / a) + 1.0);
	} else if (z <= 7.5e+148) {
		tmp = t_2;
	} else {
		tmp = t - (a / (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - x) * (y / (a - z))
    t_2 = t * ((y - z) / (a - z))
    if (z <= (-2.8d-26)) then
        tmp = t_2
    else if (z <= (-6.8d-89)) then
        tmp = t_1
    else if (z <= (-3d-125)) then
        tmp = -t / ((a - z) / z)
    else if (z <= (-1.35d-201)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= (-1.22d-263)) then
        tmp = t_1
    else if (z <= 5.6d-26) then
        tmp = x * (((z - y) / a) + 1.0d0)
    else if (z <= 7.5d+148) then
        tmp = t_2
    else
        tmp = t - (a / (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2.8e-26) {
		tmp = t_2;
	} else if (z <= -6.8e-89) {
		tmp = t_1;
	} else if (z <= -3e-125) {
		tmp = -t / ((a - z) / z);
	} else if (z <= -1.35e-201) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= -1.22e-263) {
		tmp = t_1;
	} else if (z <= 5.6e-26) {
		tmp = x * (((z - y) / a) + 1.0);
	} else if (z <= 7.5e+148) {
		tmp = t_2;
	} else {
		tmp = t - (a / (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / (a - z))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -2.8e-26:
		tmp = t_2
	elif z <= -6.8e-89:
		tmp = t_1
	elif z <= -3e-125:
		tmp = -t / ((a - z) / z)
	elif z <= -1.35e-201:
		tmp = y * ((t - x) / (a - z))
	elif z <= -1.22e-263:
		tmp = t_1
	elif z <= 5.6e-26:
		tmp = x * (((z - y) / a) + 1.0)
	elif z <= 7.5e+148:
		tmp = t_2
	else:
		tmp = t - (a / (z / x))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -2.8e-26)
		tmp = t_2;
	elseif (z <= -6.8e-89)
		tmp = t_1;
	elseif (z <= -3e-125)
		tmp = Float64(Float64(-t) / Float64(Float64(a - z) / z));
	elseif (z <= -1.35e-201)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= -1.22e-263)
		tmp = t_1;
	elseif (z <= 5.6e-26)
		tmp = Float64(x * Float64(Float64(Float64(z - y) / a) + 1.0));
	elseif (z <= 7.5e+148)
		tmp = t_2;
	else
		tmp = Float64(t - Float64(a / Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / (a - z));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -2.8e-26)
		tmp = t_2;
	elseif (z <= -6.8e-89)
		tmp = t_1;
	elseif (z <= -3e-125)
		tmp = -t / ((a - z) / z);
	elseif (z <= -1.35e-201)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= -1.22e-263)
		tmp = t_1;
	elseif (z <= 5.6e-26)
		tmp = x * (((z - y) / a) + 1.0);
	elseif (z <= 7.5e+148)
		tmp = t_2;
	else
		tmp = t - (a / (z / x));
	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[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e-26], t$95$2, If[LessEqual[z, -6.8e-89], t$95$1, If[LessEqual[z, -3e-125], N[((-t) / N[(N[(a - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.35e-201], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.22e-263], t$95$1, If[LessEqual[z, 5.6e-26], N[(x * N[(N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+148], t$95$2, N[(t - N[(a / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.8000000000000001e-26 or 5.6000000000000002e-26 < z < 7.50000000000000008e148

   1. Initial program 56.8%

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

      1. associate-*l/ 77.5%

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

   3. Simplified 77.5%

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

   5. Taylor expanded in x around 0 42.5%

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

      1. associate-/l* 57.8%

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

      2. div-inv 57.8%

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

      3. clear-num 57.8%

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

   7. Applied egg-rr 57.8%

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

   if -2.8000000000000001e-26 < z < -6.8000000000000001e-89 or -1.35000000000000003e-201 < z < -1.22000000000000005e-263

   1. Initial program 84.0%

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

      1. associate-*l/ 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in y around -inf 62.5%

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

      1. associate-*l/ 65.6%

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

   7. Simplified 65.6%

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

   if -6.8000000000000001e-89 < z < -2.9999999999999999e-125

   1. Initial program 83.2%

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

      1. associate-*l/ 83.7%

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

   3. Simplified 83.7%

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

   5. Taylor expanded in x around 0 83.9%

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

   6. Taylor expanded in y around 0 83.9%

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

      1. mul-1-neg 83.9%

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

      2. associate-/l* 84.4%

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

   8. Simplified 84.4%

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

   if -2.9999999999999999e-125 < z < -1.35000000000000003e-201

   1. Initial program 75.9%

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

      1. associate-*l/ 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in y around inf 70.0%

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

      1. div-sub 77.1%

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

   7. Simplified 77.1%

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

   if -1.22000000000000005e-263 < z < 5.6000000000000002e-26

   1. Initial program 90.0%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in a around inf 90.2%

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

   6. Taylor expanded in x around inf 77.3%

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

      1. mul-1-neg 77.3%

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

      2. unsub-neg 77.3%

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

   8. Simplified 77.3%

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

   if 7.50000000000000008e148 < z

   1. Initial program 23.0%

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

      1. associate-*l/ 57.3%

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

   3. Simplified 57.3%

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

   5. Taylor expanded in z around inf 56.1%

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

      1. associate--l+ 56.1%

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

      2. associate-*r/ 56.1%

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

      3. associate-*r/ 56.1%

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

      4. div-sub 56.1%

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

      5. distribute-lft-out-- 56.1%

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

      6. associate-*r/ 56.1%

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

      7. mul-1-neg 56.1%

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

      8. distribute-rgt-out-- 56.2%

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

      9. unsub-neg 56.2%

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

      10. associate-/l* 82.0%

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

   7. Simplified 82.0%

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

   8. Taylor expanded in y around 0 52.3%

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

      1. sub-neg 52.3%

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

      2. associate-*r/ 52.3%

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

      3. associate-*r* 52.3%

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

      4. neg-mul-1 52.3%

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

      5. associate-*r/ 68.2%

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

      6. distribute-lft-neg-out 68.2%

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

      7. remove-double-neg 68.2%

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

   10. Simplified 68.2%

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

   11. Taylor expanded in t around 0 56.1%

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

       1. mul-1-neg 56.1%

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

       2. associate-/l* 68.6%

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

       3. distribute-neg-frac 68.6%

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

   13. Simplified 68.6%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-26}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-89}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-125}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-201}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-263}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a} + 1\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+148}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 55.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{z - y}{a} + 1\right)\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{-30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-241}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.22 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+78}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (+ (/ (- z y) a) 1.0))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= z -2.25e-30)
     t_2
     (if (<= z -4.3e-88)
       t_1
       (if (<= z -2.3e-241)
         t_2
         (if (<= z 2.22e-23)
           t_1
           (if (<= z 6.5e+78)
             t_2
             (if (<= z 2.75e+104) t_1 (- t (/ a (/ z x)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (((z - y) / a) + 1.0);
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2.25e-30) {
		tmp = t_2;
	} else if (z <= -4.3e-88) {
		tmp = t_1;
	} else if (z <= -2.3e-241) {
		tmp = t_2;
	} else if (z <= 2.22e-23) {
		tmp = t_1;
	} else if (z <= 6.5e+78) {
		tmp = t_2;
	} else if (z <= 2.75e+104) {
		tmp = t_1;
	} else {
		tmp = t - (a / (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (((z - y) / a) + 1.0d0)
    t_2 = t * ((y - z) / (a - z))
    if (z <= (-2.25d-30)) then
        tmp = t_2
    else if (z <= (-4.3d-88)) then
        tmp = t_1
    else if (z <= (-2.3d-241)) then
        tmp = t_2
    else if (z <= 2.22d-23) then
        tmp = t_1
    else if (z <= 6.5d+78) then
        tmp = t_2
    else if (z <= 2.75d+104) then
        tmp = t_1
    else
        tmp = t - (a / (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (((z - y) / a) + 1.0);
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2.25e-30) {
		tmp = t_2;
	} else if (z <= -4.3e-88) {
		tmp = t_1;
	} else if (z <= -2.3e-241) {
		tmp = t_2;
	} else if (z <= 2.22e-23) {
		tmp = t_1;
	} else if (z <= 6.5e+78) {
		tmp = t_2;
	} else if (z <= 2.75e+104) {
		tmp = t_1;
	} else {
		tmp = t - (a / (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (((z - y) / a) + 1.0)
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -2.25e-30:
		tmp = t_2
	elif z <= -4.3e-88:
		tmp = t_1
	elif z <= -2.3e-241:
		tmp = t_2
	elif z <= 2.22e-23:
		tmp = t_1
	elif z <= 6.5e+78:
		tmp = t_2
	elif z <= 2.75e+104:
		tmp = t_1
	else:
		tmp = t - (a / (z / x))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(Float64(z - y) / a) + 1.0))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -2.25e-30)
		tmp = t_2;
	elseif (z <= -4.3e-88)
		tmp = t_1;
	elseif (z <= -2.3e-241)
		tmp = t_2;
	elseif (z <= 2.22e-23)
		tmp = t_1;
	elseif (z <= 6.5e+78)
		tmp = t_2;
	elseif (z <= 2.75e+104)
		tmp = t_1;
	else
		tmp = Float64(t - Float64(a / Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (((z - y) / a) + 1.0);
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -2.25e-30)
		tmp = t_2;
	elseif (z <= -4.3e-88)
		tmp = t_1;
	elseif (z <= -2.3e-241)
		tmp = t_2;
	elseif (z <= 2.22e-23)
		tmp = t_1;
	elseif (z <= 6.5e+78)
		tmp = t_2;
	elseif (z <= 2.75e+104)
		tmp = t_1;
	else
		tmp = t - (a / (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.25e-30], t$95$2, If[LessEqual[z, -4.3e-88], t$95$1, If[LessEqual[z, -2.3e-241], t$95$2, If[LessEqual[z, 2.22e-23], t$95$1, If[LessEqual[z, 6.5e+78], t$95$2, If[LessEqual[z, 2.75e+104], t$95$1, N[(t - N[(a / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.24999999999999984e-30 or -4.2999999999999997e-88 < z < -2.2999999999999999e-241 or 2.22e-23 < z < 6.50000000000000036e78

   1. Initial program 61.2%

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

      1. associate-*l/ 78.9%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in x around 0 46.5%

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

      1. associate-/l* 60.1%

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

      2. div-inv 60.1%

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

      3. clear-num 60.1%

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

   7. Applied egg-rr 60.1%

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

   if -2.24999999999999984e-30 < z < -4.2999999999999997e-88 or -2.2999999999999999e-241 < z < 2.22e-23 or 6.50000000000000036e78 < z < 2.75000000000000008e104

   1. Initial program 88.4%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in a around inf 84.9%

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

   6. Taylor expanded in x around inf 73.1%

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

      1. mul-1-neg 73.1%

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

      2. unsub-neg 73.1%

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

   8. Simplified 73.1%

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

   if 2.75000000000000008e104 < z

   1. Initial program 29.8%

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

      1. associate-*l/ 62.6%

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

   3. Simplified 62.6%

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

   5. Taylor expanded in z around inf 56.5%

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

      1. associate--l+ 56.5%

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

      2. associate-*r/ 56.5%

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

      3. associate-*r/ 56.5%

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

      4. div-sub 56.5%

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

      5. distribute-lft-out-- 56.5%

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

      6. associate-*r/ 56.5%

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

      7. mul-1-neg 56.5%

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

      8. distribute-rgt-out-- 56.6%

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

      9. unsub-neg 56.6%

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

      10. associate-/l* 80.0%

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

   7. Simplified 80.0%

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

   8. Taylor expanded in y around 0 50.9%

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

      1. sub-neg 50.9%

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

      2. associate-*r/ 50.9%

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

      3. associate-*r* 50.9%

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

      4. neg-mul-1 50.9%

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

      5. associate-*r/ 63.6%

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

      6. distribute-lft-neg-out 63.6%

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

      7. remove-double-neg 63.6%

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

   10. Simplified 63.6%

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

   11. Taylor expanded in t around 0 51.7%

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

       1. mul-1-neg 51.7%

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

       2. associate-/l* 64.4%

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

       3. distribute-neg-frac 64.4%

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

   13. Simplified 64.4%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-30}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a} + 1\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-241}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.22 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a} + 1\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+78}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y - z}{a}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -8.8 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{+43}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-223}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-50}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+38}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ (- y z) a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= a -8.8e+98)
     t_1
     (if (<= a -1.15e+43)
       (* (- t x) (/ y (- a z)))
       (if (<= a -1.05e+21)
         t_1
         (if (<= a 3.4e-223)
           t_2
           (if (<= a 9.5e-50)
             (* y (/ (- t x) (- a z)))
             (if (<= a 2.55e+38) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * ((y - z) / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -8.8e+98) {
		tmp = t_1;
	} else if (a <= -1.15e+43) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= -1.05e+21) {
		tmp = t_1;
	} else if (a <= 3.4e-223) {
		tmp = t_2;
	} else if (a <= 9.5e-50) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 2.55e+38) {
		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 = x + (t * ((y - z) / a))
    t_2 = t * ((y - z) / (a - z))
    if (a <= (-8.8d+98)) then
        tmp = t_1
    else if (a <= (-1.15d+43)) then
        tmp = (t - x) * (y / (a - z))
    else if (a <= (-1.05d+21)) then
        tmp = t_1
    else if (a <= 3.4d-223) then
        tmp = t_2
    else if (a <= 9.5d-50) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 2.55d+38) 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 = x + (t * ((y - z) / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -8.8e+98) {
		tmp = t_1;
	} else if (a <= -1.15e+43) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= -1.05e+21) {
		tmp = t_1;
	} else if (a <= 3.4e-223) {
		tmp = t_2;
	} else if (a <= 9.5e-50) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 2.55e+38) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * ((y - z) / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if a <= -8.8e+98:
		tmp = t_1
	elif a <= -1.15e+43:
		tmp = (t - x) * (y / (a - z))
	elif a <= -1.05e+21:
		tmp = t_1
	elif a <= 3.4e-223:
		tmp = t_2
	elif a <= 9.5e-50:
		tmp = y * ((t - x) / (a - z))
	elif a <= 2.55e+38:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(Float64(y - z) / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (a <= -8.8e+98)
		tmp = t_1;
	elseif (a <= -1.15e+43)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (a <= -1.05e+21)
		tmp = t_1;
	elseif (a <= 3.4e-223)
		tmp = t_2;
	elseif (a <= 9.5e-50)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 2.55e+38)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * ((y - z) / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (a <= -8.8e+98)
		tmp = t_1;
	elseif (a <= -1.15e+43)
		tmp = (t - x) * (y / (a - z));
	elseif (a <= -1.05e+21)
		tmp = t_1;
	elseif (a <= 3.4e-223)
		tmp = t_2;
	elseif (a <= 9.5e-50)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 2.55e+38)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.8e+98], t$95$1, If[LessEqual[a, -1.15e+43], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.05e+21], t$95$1, If[LessEqual[a, 3.4e-223], t$95$2, If[LessEqual[a, 9.5e-50], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.55e+38], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.80000000000000034e98 or -1.1500000000000001e43 < a < -1.05e21 or 2.5500000000000001e38 < a

   1. Initial program 66.8%

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

      1. associate-*l/ 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in a around inf 77.7%

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

   6. Taylor expanded in t around inf 61.3%

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

      1. associate-*r/ 72.3%

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

   8. Simplified 72.3%

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

   if -8.80000000000000034e98 < a < -1.1500000000000001e43

   1. Initial program 64.7%

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

      1. associate-*l/ 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 y around -inf 56.0%

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

      1. associate-*l/ 67.2%

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

   7. Simplified 67.2%

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

   if -1.05e21 < a < 3.3999999999999998e-223 or 9.4999999999999993e-50 < a < 2.5500000000000001e38

   1. Initial program 64.0%

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

      1. associate-*l/ 76.3%

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

   3. Simplified 76.3%

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

   5. Taylor expanded in x around 0 53.9%

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

      1. associate-/l* 65.4%

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

      2. div-inv 65.4%

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

      3. clear-num 65.4%

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

   7. Applied egg-rr 65.4%

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

   if 3.3999999999999998e-223 < a < 9.4999999999999993e-50

   1. Initial program 73.1%

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

      1. associate-*l/ 76.4%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in y around inf 64.2%

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

      1. div-sub 64.2%

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

   7. Simplified 64.2%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+98}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{+43}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{+21}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-223}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-50}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{y \cdot \left(x - t\right)}{z}\\ t_2 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{+127}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -2.25:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.45 \cdot 10^{-37}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (* y (- x t)) z))) (t_2 (+ x (* (- t x) (/ y a)))))
   (if (<= a -1.2e+127)
     (+ x (* t (/ (- y z) a)))
     (if (<= a -2.25)
       t_2
       (if (<= a -2.45e-37)
         (- t (/ a (/ z x)))
         (if (<= a 5.6e-124)
           t_1
           (if (<= a 4.2e-85)
             t_2
             (if (<= a 2.5e+24) t_1 (+ x (/ y (/ a (- t x))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((y * (x - t)) / z);
	double t_2 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -1.2e+127) {
		tmp = x + (t * ((y - z) / a));
	} else if (a <= -2.25) {
		tmp = t_2;
	} else if (a <= -2.45e-37) {
		tmp = t - (a / (z / x));
	} else if (a <= 5.6e-124) {
		tmp = t_1;
	} else if (a <= 4.2e-85) {
		tmp = t_2;
	} else if (a <= 2.5e+24) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + ((y * (x - t)) / z)
    t_2 = x + ((t - x) * (y / a))
    if (a <= (-1.2d+127)) then
        tmp = x + (t * ((y - z) / a))
    else if (a <= (-2.25d0)) then
        tmp = t_2
    else if (a <= (-2.45d-37)) then
        tmp = t - (a / (z / x))
    else if (a <= 5.6d-124) then
        tmp = t_1
    else if (a <= 4.2d-85) then
        tmp = t_2
    else if (a <= 2.5d+24) then
        tmp = t_1
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((y * (x - t)) / z);
	double t_2 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -1.2e+127) {
		tmp = x + (t * ((y - z) / a));
	} else if (a <= -2.25) {
		tmp = t_2;
	} else if (a <= -2.45e-37) {
		tmp = t - (a / (z / x));
	} else if (a <= 5.6e-124) {
		tmp = t_1;
	} else if (a <= 4.2e-85) {
		tmp = t_2;
	} else if (a <= 2.5e+24) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((y * (x - t)) / z)
	t_2 = x + ((t - x) * (y / a))
	tmp = 0
	if a <= -1.2e+127:
		tmp = x + (t * ((y - z) / a))
	elif a <= -2.25:
		tmp = t_2
	elif a <= -2.45e-37:
		tmp = t - (a / (z / x))
	elif a <= 5.6e-124:
		tmp = t_1
	elif a <= 4.2e-85:
		tmp = t_2
	elif a <= 2.5e+24:
		tmp = t_1
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(y * Float64(x - t)) / z))
	t_2 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	tmp = 0.0
	if (a <= -1.2e+127)
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / a)));
	elseif (a <= -2.25)
		tmp = t_2;
	elseif (a <= -2.45e-37)
		tmp = Float64(t - Float64(a / Float64(z / x)));
	elseif (a <= 5.6e-124)
		tmp = t_1;
	elseif (a <= 4.2e-85)
		tmp = t_2;
	elseif (a <= 2.5e+24)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((y * (x - t)) / z);
	t_2 = x + ((t - x) * (y / a));
	tmp = 0.0;
	if (a <= -1.2e+127)
		tmp = x + (t * ((y - z) / a));
	elseif (a <= -2.25)
		tmp = t_2;
	elseif (a <= -2.45e-37)
		tmp = t - (a / (z / x));
	elseif (a <= 5.6e-124)
		tmp = t_1;
	elseif (a <= 4.2e-85)
		tmp = t_2;
	elseif (a <= 2.5e+24)
		tmp = t_1;
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.2e+127], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.25], t$95$2, If[LessEqual[a, -2.45e-37], N[(t - N[(a / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.6e-124], t$95$1, If[LessEqual[a, 4.2e-85], t$95$2, If[LessEqual[a, 2.5e+24], t$95$1, N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.2000000000000001e127

   1. Initial program 59.6%

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

      1. associate-*l/ 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in a around inf 79.7%

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

   6. Taylor expanded in t around inf 57.4%

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

      1. associate-*r/ 80.0%

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

   8. Simplified 80.0%

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

   if -1.2000000000000001e127 < a < -2.25 or 5.59999999999999996e-124 < a < 4.2e-85

   1. Initial program 77.4%

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

      1. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in z around 0 71.8%

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

   if -2.25 < a < -2.45000000000000009e-37

   1. Initial program 56.4%

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

      1. associate-*l/ 85.0%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in z around inf 62.2%

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

      1. associate--l+ 62.2%

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

      2. associate-*r/ 62.2%

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

      3. associate-*r/ 62.2%

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

      4. div-sub 62.8%

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

      5. distribute-lft-out-- 62.8%

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

      6. associate-*r/ 62.8%

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

      7. mul-1-neg 62.8%

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

      8. distribute-rgt-out-- 62.8%

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

      9. unsub-neg 62.8%

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

      10. associate-/l* 70.1%

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

   7. Simplified 70.1%

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

   8. Taylor expanded in y around 0 71.3%

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

      1. sub-neg 71.3%

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

      2. associate-*r/ 71.3%

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

      3. associate-*r* 71.3%

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

      4. neg-mul-1 71.3%

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

      5. associate-*r/ 71.3%

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

      6. distribute-lft-neg-out 71.3%

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

      7. remove-double-neg 71.3%

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

   10. Simplified 71.3%

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

   11. Taylor expanded in t around 0 71.3%

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

       1. mul-1-neg 71.3%

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

       2. associate-/l* 71.3%

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

       3. distribute-neg-frac 71.3%

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

   13. Simplified 71.3%

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

   if -2.45000000000000009e-37 < a < 5.59999999999999996e-124 or 4.2e-85 < a < 2.50000000000000023e24

   1. Initial program 63.0%

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

      1. associate-*l/ 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 inf 79.6%

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

      1. associate--l+ 79.6%

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

      2. associate-*r/ 79.6%

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

      3. associate-*r/ 79.6%

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

      4. div-sub 80.6%

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

      5. distribute-lft-out-- 80.6%

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

      6. associate-*r/ 80.6%

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

      7. mul-1-neg 80.6%

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

      8. distribute-rgt-out-- 80.6%

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

      9. unsub-neg 80.6%

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

      10. associate-/l* 84.8%

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

   7. Simplified 84.8%

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

   8. Taylor expanded in y around inf 74.8%

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

   if 2.50000000000000023e24 < a

   1. Initial program 69.6%

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

      1. associate-*l/ 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in z around 0 59.3%

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

      1. associate-/l* 67.2%

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

   7. Simplified 67.2%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+127}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -2.25:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -2.45 \cdot 10^{-37}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-124}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-85}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+24}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 38.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+156}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -410:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-41}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-101}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-243}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.6e+156)
   x
   (if (<= a -410.0)
     (* (- y z) (/ t a))
     (if (<= a -5e-41)
       t
       (if (<= a -6.6e-101)
         (* t (/ y (- a z)))
         (if (<= a 1.85e-243)
           t
           (if (<= a 7.5e-55)
             (* x (/ (- y a) z))
             (if (<= a 2.35e+38) t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e+156) {
		tmp = x;
	} else if (a <= -410.0) {
		tmp = (y - z) * (t / a);
	} else if (a <= -5e-41) {
		tmp = t;
	} else if (a <= -6.6e-101) {
		tmp = t * (y / (a - z));
	} else if (a <= 1.85e-243) {
		tmp = t;
	} else if (a <= 7.5e-55) {
		tmp = x * ((y - a) / z);
	} else if (a <= 2.35e+38) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.6d+156)) then
        tmp = x
    else if (a <= (-410.0d0)) then
        tmp = (y - z) * (t / a)
    else if (a <= (-5d-41)) then
        tmp = t
    else if (a <= (-6.6d-101)) then
        tmp = t * (y / (a - z))
    else if (a <= 1.85d-243) then
        tmp = t
    else if (a <= 7.5d-55) then
        tmp = x * ((y - a) / z)
    else if (a <= 2.35d+38) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e+156) {
		tmp = x;
	} else if (a <= -410.0) {
		tmp = (y - z) * (t / a);
	} else if (a <= -5e-41) {
		tmp = t;
	} else if (a <= -6.6e-101) {
		tmp = t * (y / (a - z));
	} else if (a <= 1.85e-243) {
		tmp = t;
	} else if (a <= 7.5e-55) {
		tmp = x * ((y - a) / z);
	} else if (a <= 2.35e+38) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.6e+156:
		tmp = x
	elif a <= -410.0:
		tmp = (y - z) * (t / a)
	elif a <= -5e-41:
		tmp = t
	elif a <= -6.6e-101:
		tmp = t * (y / (a - z))
	elif a <= 1.85e-243:
		tmp = t
	elif a <= 7.5e-55:
		tmp = x * ((y - a) / z)
	elif a <= 2.35e+38:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.6e+156)
		tmp = x;
	elseif (a <= -410.0)
		tmp = Float64(Float64(y - z) * Float64(t / a));
	elseif (a <= -5e-41)
		tmp = t;
	elseif (a <= -6.6e-101)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (a <= 1.85e-243)
		tmp = t;
	elseif (a <= 7.5e-55)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 2.35e+38)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.6e+156)
		tmp = x;
	elseif (a <= -410.0)
		tmp = (y - z) * (t / a);
	elseif (a <= -5e-41)
		tmp = t;
	elseif (a <= -6.6e-101)
		tmp = t * (y / (a - z));
	elseif (a <= 1.85e-243)
		tmp = t;
	elseif (a <= 7.5e-55)
		tmp = x * ((y - a) / z);
	elseif (a <= 2.35e+38)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.6e+156], x, If[LessEqual[a, -410.0], N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5e-41], t, If[LessEqual[a, -6.6e-101], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e-243], t, If[LessEqual[a, 7.5e-55], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.35e+38], t, x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.60000000000000001e156 or 2.35e38 < a

   1. Initial program 65.3%

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

      1. associate-*l/ 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in a around inf 51.7%

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

   if -1.60000000000000001e156 < a < -410

   1. Initial program 70.5%

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

      1. associate-*l/ 88.6%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in x around 0 36.2%

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

      1. associate-/l* 49.0%

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

   7. Simplified 49.0%

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

   8. Taylor expanded in a around inf 31.9%

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

      1. associate-/l* 38.4%

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

      2. associate-/r/ 38.5%

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

   10. Simplified 38.5%

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

   if -410 < a < -4.9999999999999996e-41 or -6.59999999999999968e-101 < a < 1.85e-243 or 7.50000000000000023e-55 < a < 2.35e38

   1. Initial program 60.4%

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

      1. associate-*l/ 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in z around inf 48.3%

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

   if -4.9999999999999996e-41 < a < -6.59999999999999968e-101

   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/ 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in y around -inf 89.2%

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

      1. associate-*l/ 89.2%

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

   7. Simplified 89.2%

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

   8. Taylor expanded in t around inf 67.3%

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

      1. associate-*r/ 67.0%

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

   10. Simplified 67.0%

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

   if 1.85e-243 < a < 7.50000000000000023e-55

   1. Initial program 71.1%

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

      1. associate-*l/ 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in z around inf 72.6%

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

      1. associate--l+ 72.6%

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

      2. associate-*r/ 72.6%

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

      3. associate-*r/ 72.6%

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

      4. div-sub 72.6%

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

      5. distribute-lft-out-- 72.6%

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

      6. associate-*r/ 72.6%

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

      7. mul-1-neg 72.6%

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

      8. distribute-rgt-out-- 72.6%

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

      9. unsub-neg 72.6%

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

      10. associate-/l* 78.7%

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

   7. Simplified 78.7%

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

   8. Taylor expanded in t around 0 51.3%

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

      1. associate-*r/ 51.3%

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

   10. Simplified 51.3%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+156}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -410:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-41}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-101}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-243}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -15.5:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-43}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-101}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-244}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 10^{-54}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.1e+108)
   x
   (if (<= a -15.5)
     (* (- t x) (/ y a))
     (if (<= a -3.8e-43)
       t
       (if (<= a -5.4e-101)
         (* t (/ y (- a z)))
         (if (<= a 7.5e-244)
           t
           (if (<= a 1e-54) (* x (/ (- y a) z)) (if (<= a 2.1e+38) t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e+108) {
		tmp = x;
	} else if (a <= -15.5) {
		tmp = (t - x) * (y / a);
	} else if (a <= -3.8e-43) {
		tmp = t;
	} else if (a <= -5.4e-101) {
		tmp = t * (y / (a - z));
	} else if (a <= 7.5e-244) {
		tmp = t;
	} else if (a <= 1e-54) {
		tmp = x * ((y - a) / z);
	} else if (a <= 2.1e+38) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.1d+108)) then
        tmp = x
    else if (a <= (-15.5d0)) then
        tmp = (t - x) * (y / a)
    else if (a <= (-3.8d-43)) then
        tmp = t
    else if (a <= (-5.4d-101)) then
        tmp = t * (y / (a - z))
    else if (a <= 7.5d-244) then
        tmp = t
    else if (a <= 1d-54) then
        tmp = x * ((y - a) / z)
    else if (a <= 2.1d+38) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e+108) {
		tmp = x;
	} else if (a <= -15.5) {
		tmp = (t - x) * (y / a);
	} else if (a <= -3.8e-43) {
		tmp = t;
	} else if (a <= -5.4e-101) {
		tmp = t * (y / (a - z));
	} else if (a <= 7.5e-244) {
		tmp = t;
	} else if (a <= 1e-54) {
		tmp = x * ((y - a) / z);
	} else if (a <= 2.1e+38) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.1e+108:
		tmp = x
	elif a <= -15.5:
		tmp = (t - x) * (y / a)
	elif a <= -3.8e-43:
		tmp = t
	elif a <= -5.4e-101:
		tmp = t * (y / (a - z))
	elif a <= 7.5e-244:
		tmp = t
	elif a <= 1e-54:
		tmp = x * ((y - a) / z)
	elif a <= 2.1e+38:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.1e+108)
		tmp = x;
	elseif (a <= -15.5)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (a <= -3.8e-43)
		tmp = t;
	elseif (a <= -5.4e-101)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (a <= 7.5e-244)
		tmp = t;
	elseif (a <= 1e-54)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 2.1e+38)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.1e+108)
		tmp = x;
	elseif (a <= -15.5)
		tmp = (t - x) * (y / a);
	elseif (a <= -3.8e-43)
		tmp = t;
	elseif (a <= -5.4e-101)
		tmp = t * (y / (a - z));
	elseif (a <= 7.5e-244)
		tmp = t;
	elseif (a <= 1e-54)
		tmp = x * ((y - a) / z);
	elseif (a <= 2.1e+38)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.1e+108], x, If[LessEqual[a, -15.5], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.8e-43], t, If[LessEqual[a, -5.4e-101], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e-244], t, If[LessEqual[a, 1e-54], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.1e+38], t, x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.1000000000000001e108 or 2.1e38 < a

   1. Initial program 64.9%

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

      1. associate-*l/ 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in a around inf 49.3%

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

   if -1.1000000000000001e108 < a < -15.5

   1. Initial program 75.7%

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

      1. associate-*l/ 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in y around -inf 54.2%

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

      1. associate-*l/ 60.3%

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

   7. Simplified 60.3%

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

   8. Taylor expanded in a around inf 51.3%

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

   if -15.5 < a < -3.7999999999999997e-43 or -5.4000000000000003e-101 < a < 7.5000000000000003e-244 or 1e-54 < a < 2.1e38

   1. Initial program 59.9%

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

      1. associate-*l/ 75.1%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in z around inf 49.0%

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

   if -3.7999999999999997e-43 < a < -5.4000000000000003e-101

   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/ 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in y around -inf 89.2%

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

      1. associate-*l/ 89.2%

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

   7. Simplified 89.2%

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

   8. Taylor expanded in t around inf 67.3%

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

      1. associate-*r/ 67.0%

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

   10. Simplified 67.0%

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

   if 7.5000000000000003e-244 < a < 1e-54

   1. Initial program 71.1%

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

      1. associate-*l/ 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in z around inf 72.6%

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

      1. associate--l+ 72.6%

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

      2. associate-*r/ 72.6%

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

      3. associate-*r/ 72.6%

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

      4. div-sub 72.6%

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

      5. distribute-lft-out-- 72.6%

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

      6. associate-*r/ 72.6%

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

      7. mul-1-neg 72.6%

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

      8. distribute-rgt-out-- 72.6%

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

      9. unsub-neg 72.6%

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

      10. associate-/l* 78.7%

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

   7. Simplified 78.7%

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

   8. Taylor expanded in t around 0 51.3%

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

      1. associate-*r/ 51.3%

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

   10. Simplified 51.3%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -15.5:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-43}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-101}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-244}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 10^{-54}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 46.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - t \cdot \frac{y}{z}\\ t_2 := \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -8 \cdot 10^{+107}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -10.8:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-242}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+91}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* t (/ y z)))) (t_2 (* (- t x) (/ y a))))
   (if (<= a -8e+107)
     x
     (if (<= a -10.8)
       t_2
       (if (<= a 2.7e-242)
         t_1
         (if (<= a 5.8e-55)
           (* x (/ (- y a) z))
           (if (<= a 4.4e+29)
             t_1
             (if (<= a 2.3e+91) t_2 (if (<= a 1.2e+96) t x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (t * (y / z));
	double t_2 = (t - x) * (y / a);
	double tmp;
	if (a <= -8e+107) {
		tmp = x;
	} else if (a <= -10.8) {
		tmp = t_2;
	} else if (a <= 2.7e-242) {
		tmp = t_1;
	} else if (a <= 5.8e-55) {
		tmp = x * ((y - a) / z);
	} else if (a <= 4.4e+29) {
		tmp = t_1;
	} else if (a <= 2.3e+91) {
		tmp = t_2;
	} else if (a <= 1.2e+96) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t - (t * (y / z))
    t_2 = (t - x) * (y / a)
    if (a <= (-8d+107)) then
        tmp = x
    else if (a <= (-10.8d0)) then
        tmp = t_2
    else if (a <= 2.7d-242) then
        tmp = t_1
    else if (a <= 5.8d-55) then
        tmp = x * ((y - a) / z)
    else if (a <= 4.4d+29) then
        tmp = t_1
    else if (a <= 2.3d+91) then
        tmp = t_2
    else if (a <= 1.2d+96) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (t * (y / z));
	double t_2 = (t - x) * (y / a);
	double tmp;
	if (a <= -8e+107) {
		tmp = x;
	} else if (a <= -10.8) {
		tmp = t_2;
	} else if (a <= 2.7e-242) {
		tmp = t_1;
	} else if (a <= 5.8e-55) {
		tmp = x * ((y - a) / z);
	} else if (a <= 4.4e+29) {
		tmp = t_1;
	} else if (a <= 2.3e+91) {
		tmp = t_2;
	} else if (a <= 1.2e+96) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (t * (y / z))
	t_2 = (t - x) * (y / a)
	tmp = 0
	if a <= -8e+107:
		tmp = x
	elif a <= -10.8:
		tmp = t_2
	elif a <= 2.7e-242:
		tmp = t_1
	elif a <= 5.8e-55:
		tmp = x * ((y - a) / z)
	elif a <= 4.4e+29:
		tmp = t_1
	elif a <= 2.3e+91:
		tmp = t_2
	elif a <= 1.2e+96:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(t * Float64(y / z)))
	t_2 = Float64(Float64(t - x) * Float64(y / a))
	tmp = 0.0
	if (a <= -8e+107)
		tmp = x;
	elseif (a <= -10.8)
		tmp = t_2;
	elseif (a <= 2.7e-242)
		tmp = t_1;
	elseif (a <= 5.8e-55)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 4.4e+29)
		tmp = t_1;
	elseif (a <= 2.3e+91)
		tmp = t_2;
	elseif (a <= 1.2e+96)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (t * (y / z));
	t_2 = (t - x) * (y / a);
	tmp = 0.0;
	if (a <= -8e+107)
		tmp = x;
	elseif (a <= -10.8)
		tmp = t_2;
	elseif (a <= 2.7e-242)
		tmp = t_1;
	elseif (a <= 5.8e-55)
		tmp = x * ((y - a) / z);
	elseif (a <= 4.4e+29)
		tmp = t_1;
	elseif (a <= 2.3e+91)
		tmp = t_2;
	elseif (a <= 1.2e+96)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8e+107], x, If[LessEqual[a, -10.8], t$95$2, If[LessEqual[a, 2.7e-242], t$95$1, If[LessEqual[a, 5.8e-55], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.4e+29], t$95$1, If[LessEqual[a, 2.3e+91], t$95$2, If[LessEqual[a, 1.2e+96], t, x]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -7.9999999999999998e107 or 1.19999999999999996e96 < a

   1. Initial program 62.0%

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

      1. associate-*l/ 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in a around inf 54.8%

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

   if -7.9999999999999998e107 < a < -10.800000000000001 or 4.4000000000000003e29 < a < 2.29999999999999991e91

   1. Initial program 78.7%

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

      1. associate-*l/ 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in y around -inf 53.3%

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

      1. associate-*l/ 57.0%

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

   7. Simplified 57.0%

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

   8. Taylor expanded in a around inf 49.4%

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

   if -10.800000000000001 < a < 2.7e-242 or 5.8e-55 < a < 4.4000000000000003e29

   1. Initial program 62.0%

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

      1. associate-*l/ 76.0%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in x around 0 54.3%

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

   6. Taylor expanded in a around 0 50.1%

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

      1. associate-*r/ 50.1%

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

      2. *-commutative 50.1%

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

      3. neg-mul-1 50.1%

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

      4. distribute-rgt-neg-in 50.1%

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

   8. Simplified 50.1%

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

   9. Taylor expanded in y around 0 59.8%

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

       1. mul-1-neg 59.8%

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

       2. unsub-neg 59.8%

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

       3. *-commutative 59.8%

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

       4. associate-*l/ 64.2%

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

       5. *-commutative 64.2%

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

   11. Simplified 64.2%

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

   if 2.7e-242 < a < 5.8e-55

   1. Initial program 71.1%

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

      1. associate-*l/ 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in z around inf 72.6%

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

      1. associate--l+ 72.6%

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

      2. associate-*r/ 72.6%

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

      3. associate-*r/ 72.6%

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

      4. div-sub 72.6%

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

      5. distribute-lft-out-- 72.6%

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

      6. associate-*r/ 72.6%

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

      7. mul-1-neg 72.6%

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

      8. distribute-rgt-out-- 72.6%

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

      9. unsub-neg 72.6%

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

      10. associate-/l* 78.7%

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

   7. Simplified 78.7%

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

   8. Taylor expanded in t around 0 51.3%

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

      1. associate-*r/ 51.3%

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

   10. Simplified 51.3%

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

   if 2.29999999999999991e91 < a < 1.19999999999999996e96

   1. Initial program 56.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 z around inf 100.0%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+107}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -10.8:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-242}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+29}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+91}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 46.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - t \cdot \frac{y}{z}\\ t_2 := \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -8 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -14.2:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-243}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-46}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+90}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* t (/ y z)))) (t_2 (* (- t x) (/ y a))))
   (if (<= a -8e+106)
     x
     (if (<= a -14.2)
       t_2
       (if (<= a 3.4e-243)
         t_1
         (if (<= a 1.65e-46)
           (/ (* x (- y a)) z)
           (if (<= a 2.1e+25)
             t_1
             (if (<= a 6.6e+90) t_2 (if (<= a 1.4e+96) t x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (t * (y / z));
	double t_2 = (t - x) * (y / a);
	double tmp;
	if (a <= -8e+106) {
		tmp = x;
	} else if (a <= -14.2) {
		tmp = t_2;
	} else if (a <= 3.4e-243) {
		tmp = t_1;
	} else if (a <= 1.65e-46) {
		tmp = (x * (y - a)) / z;
	} else if (a <= 2.1e+25) {
		tmp = t_1;
	} else if (a <= 6.6e+90) {
		tmp = t_2;
	} else if (a <= 1.4e+96) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t - (t * (y / z))
    t_2 = (t - x) * (y / a)
    if (a <= (-8d+106)) then
        tmp = x
    else if (a <= (-14.2d0)) then
        tmp = t_2
    else if (a <= 3.4d-243) then
        tmp = t_1
    else if (a <= 1.65d-46) then
        tmp = (x * (y - a)) / z
    else if (a <= 2.1d+25) then
        tmp = t_1
    else if (a <= 6.6d+90) then
        tmp = t_2
    else if (a <= 1.4d+96) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (t * (y / z));
	double t_2 = (t - x) * (y / a);
	double tmp;
	if (a <= -8e+106) {
		tmp = x;
	} else if (a <= -14.2) {
		tmp = t_2;
	} else if (a <= 3.4e-243) {
		tmp = t_1;
	} else if (a <= 1.65e-46) {
		tmp = (x * (y - a)) / z;
	} else if (a <= 2.1e+25) {
		tmp = t_1;
	} else if (a <= 6.6e+90) {
		tmp = t_2;
	} else if (a <= 1.4e+96) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (t * (y / z))
	t_2 = (t - x) * (y / a)
	tmp = 0
	if a <= -8e+106:
		tmp = x
	elif a <= -14.2:
		tmp = t_2
	elif a <= 3.4e-243:
		tmp = t_1
	elif a <= 1.65e-46:
		tmp = (x * (y - a)) / z
	elif a <= 2.1e+25:
		tmp = t_1
	elif a <= 6.6e+90:
		tmp = t_2
	elif a <= 1.4e+96:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(t * Float64(y / z)))
	t_2 = Float64(Float64(t - x) * Float64(y / a))
	tmp = 0.0
	if (a <= -8e+106)
		tmp = x;
	elseif (a <= -14.2)
		tmp = t_2;
	elseif (a <= 3.4e-243)
		tmp = t_1;
	elseif (a <= 1.65e-46)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (a <= 2.1e+25)
		tmp = t_1;
	elseif (a <= 6.6e+90)
		tmp = t_2;
	elseif (a <= 1.4e+96)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (t * (y / z));
	t_2 = (t - x) * (y / a);
	tmp = 0.0;
	if (a <= -8e+106)
		tmp = x;
	elseif (a <= -14.2)
		tmp = t_2;
	elseif (a <= 3.4e-243)
		tmp = t_1;
	elseif (a <= 1.65e-46)
		tmp = (x * (y - a)) / z;
	elseif (a <= 2.1e+25)
		tmp = t_1;
	elseif (a <= 6.6e+90)
		tmp = t_2;
	elseif (a <= 1.4e+96)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8e+106], x, If[LessEqual[a, -14.2], t$95$2, If[LessEqual[a, 3.4e-243], t$95$1, If[LessEqual[a, 1.65e-46], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 2.1e+25], t$95$1, If[LessEqual[a, 6.6e+90], t$95$2, If[LessEqual[a, 1.4e+96], t, x]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -8.00000000000000073e106 or 1.4e96 < a

   1. Initial program 62.0%

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

      1. associate-*l/ 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in a around inf 54.8%

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

   if -8.00000000000000073e106 < a < -14.199999999999999 or 2.0999999999999999e25 < a < 6.60000000000000016e90

   1. Initial program 78.7%

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

      1. associate-*l/ 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in y around -inf 53.3%

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

      1. associate-*l/ 57.0%

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

   7. Simplified 57.0%

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

   8. Taylor expanded in a around inf 49.4%

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

   if -14.199999999999999 < a < 3.39999999999999996e-243 or 1.65000000000000007e-46 < a < 2.0999999999999999e25

   1. Initial program 62.4%

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

      1. associate-*l/ 75.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in x around 0 54.8%

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

   6. Taylor expanded in a around 0 50.6%

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

      1. associate-*r/ 50.6%

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

      2. *-commutative 50.6%

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

      3. neg-mul-1 50.6%

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

      4. distribute-rgt-neg-in 50.6%

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

   8. Simplified 50.6%

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

   9. Taylor expanded in y around 0 60.5%

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

       1. mul-1-neg 60.5%

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

       2. unsub-neg 60.5%

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

       3. *-commutative 60.5%

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

       4. associate-*l/ 64.9%

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

       5. *-commutative 64.9%

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

   11. Simplified 64.9%

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

   if 3.39999999999999996e-243 < a < 1.65000000000000007e-46

   1. Initial program 69.9%

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

      1. associate-*l/ 74.7%

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

   3. Simplified 74.7%

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

   5. Taylor expanded in z around inf 70.6%

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

      1. associate--l+ 70.6%

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

      2. associate-*r/ 70.6%

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

      3. associate-*r/ 70.6%

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

      4. div-sub 70.6%

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

      5. distribute-lft-out-- 70.6%

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

      6. associate-*r/ 70.6%

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

      7. mul-1-neg 70.6%

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

      8. distribute-rgt-out-- 70.6%

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

      9. unsub-neg 70.6%

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

      10. associate-/l* 76.5%

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

   7. Simplified 76.5%

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

   8. Taylor expanded in t around 0 50.0%

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

   if 6.60000000000000016e90 < a < 1.4e96

   1. Initial program 56.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 z around inf 100.0%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -14.2:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-243}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-46}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+25}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+90}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -17:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-43}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-98}:\\ \;\;\;\;-\frac{t \cdot y}{z}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-242}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e+98)
   x
   (if (<= a -17.0)
     (/ (- x) (/ a y))
     (if (<= a -2.05e-43)
       t
       (if (<= a -2.2e-98)
         (- (/ (* t y) z))
         (if (<= a 2.4e-242)
           t
           (if (<= a 5.5e-47) (/ x (/ z y)) (if (<= a 1.9e+38) t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+98) {
		tmp = x;
	} else if (a <= -17.0) {
		tmp = -x / (a / y);
	} else if (a <= -2.05e-43) {
		tmp = t;
	} else if (a <= -2.2e-98) {
		tmp = -((t * y) / z);
	} else if (a <= 2.4e-242) {
		tmp = t;
	} else if (a <= 5.5e-47) {
		tmp = x / (z / y);
	} else if (a <= 1.9e+38) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9.5d+98)) then
        tmp = x
    else if (a <= (-17.0d0)) then
        tmp = -x / (a / y)
    else if (a <= (-2.05d-43)) then
        tmp = t
    else if (a <= (-2.2d-98)) then
        tmp = -((t * y) / z)
    else if (a <= 2.4d-242) then
        tmp = t
    else if (a <= 5.5d-47) then
        tmp = x / (z / y)
    else if (a <= 1.9d+38) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+98) {
		tmp = x;
	} else if (a <= -17.0) {
		tmp = -x / (a / y);
	} else if (a <= -2.05e-43) {
		tmp = t;
	} else if (a <= -2.2e-98) {
		tmp = -((t * y) / z);
	} else if (a <= 2.4e-242) {
		tmp = t;
	} else if (a <= 5.5e-47) {
		tmp = x / (z / y);
	} else if (a <= 1.9e+38) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.5e+98:
		tmp = x
	elif a <= -17.0:
		tmp = -x / (a / y)
	elif a <= -2.05e-43:
		tmp = t
	elif a <= -2.2e-98:
		tmp = -((t * y) / z)
	elif a <= 2.4e-242:
		tmp = t
	elif a <= 5.5e-47:
		tmp = x / (z / y)
	elif a <= 1.9e+38:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e+98)
		tmp = x;
	elseif (a <= -17.0)
		tmp = Float64(Float64(-x) / Float64(a / y));
	elseif (a <= -2.05e-43)
		tmp = t;
	elseif (a <= -2.2e-98)
		tmp = Float64(-Float64(Float64(t * y) / z));
	elseif (a <= 2.4e-242)
		tmp = t;
	elseif (a <= 5.5e-47)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 1.9e+38)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.5e+98)
		tmp = x;
	elseif (a <= -17.0)
		tmp = -x / (a / y);
	elseif (a <= -2.05e-43)
		tmp = t;
	elseif (a <= -2.2e-98)
		tmp = -((t * y) / z);
	elseif (a <= 2.4e-242)
		tmp = t;
	elseif (a <= 5.5e-47)
		tmp = x / (z / y);
	elseif (a <= 1.9e+38)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e+98], x, If[LessEqual[a, -17.0], N[((-x) / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.05e-43], t, If[LessEqual[a, -2.2e-98], (-N[(N[(t * y), $MachinePrecision] / z), $MachinePrecision]), If[LessEqual[a, 2.4e-242], t, If[LessEqual[a, 5.5e-47], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e+38], t, x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -9.5000000000000001e98 or 1.8999999999999999e38 < a

   1. Initial program 66.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 48.6%

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

   if -9.5000000000000001e98 < a < -17

   1. Initial program 72.2%

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

      1. associate-*l/ 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in y around -inf 54.4%

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

      1. associate-*l/ 61.4%

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

   7. Simplified 61.4%

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

   8. Taylor expanded in t around 0 32.0%

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

      1. mul-1-neg 32.0%

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

      2. associate-/l* 38.8%

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

   10. Simplified 38.8%

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

   11. Taylor expanded in a around inf 25.3%

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

       1. associate-/l* 32.1%

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

   13. Simplified 32.1%

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

   if -17 < a < -2.0499999999999999e-43 or -2.19999999999999996e-98 < a < 2.4000000000000001e-242 or 5.5000000000000002e-47 < a < 1.8999999999999999e38

   1. Initial program 60.3%

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

      1. associate-*l/ 74.8%

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

   3. Simplified 74.8%

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

   5. Taylor expanded in z around inf 49.5%

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

   if -2.0499999999999999e-43 < a < -2.19999999999999996e-98

   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/ 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in x around 0 67.4%

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

   6. Taylor expanded in a around 0 57.0%

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

      1. associate-*r/ 57.0%

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

      2. *-commutative 57.0%

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

      3. neg-mul-1 57.0%

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

      4. distribute-rgt-neg-in 57.0%

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

   8. Simplified 57.0%

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

   9. Taylor expanded in y around inf 56.8%

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

       1. associate-*r/ 56.8%

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

       2. mul-1-neg 56.8%

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

   11. Simplified 56.8%

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

   if 2.4000000000000001e-242 < a < 5.5000000000000002e-47

   1. Initial program 69.9%

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

      1. associate-*l/ 74.7%

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

   3. Simplified 74.7%

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

   5. Taylor expanded in y around -inf 56.3%

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

      1. associate-*l/ 59.1%

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

   7. Simplified 59.1%

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

   8. Taylor expanded in t around 0 41.2%

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

      1. mul-1-neg 41.2%

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

      2. associate-/l* 41.3%

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

   10. Simplified 41.3%

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

   11. Taylor expanded in a around 0 41.7%

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

       1. mul-1-neg 41.7%

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

       2. associate-/l* 41.8%

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

       3. distribute-neg-frac 41.8%

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

   13. Simplified 41.8%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -17:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-43}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-98}:\\ \;\;\;\;-\frac{t \cdot y}{z}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-242}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+98}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-162}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-269}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+109}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= z -1.5e+98)
     t
     (if (<= z -6.6e-63)
       t_1
       (if (<= z -3e-125)
         t
         (if (<= z -5.6e-162)
           x
           (if (<= z -1.4e-269) t_1 (if (<= z 5.5e+109) x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (z <= -1.5e+98) {
		tmp = t;
	} else if (z <= -6.6e-63) {
		tmp = t_1;
	} else if (z <= -3e-125) {
		tmp = t;
	} else if (z <= -5.6e-162) {
		tmp = x;
	} else if (z <= -1.4e-269) {
		tmp = t_1;
	} else if (z <= 5.5e+109) {
		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) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (a - z))
    if (z <= (-1.5d+98)) then
        tmp = t
    else if (z <= (-6.6d-63)) then
        tmp = t_1
    else if (z <= (-3d-125)) then
        tmp = t
    else if (z <= (-5.6d-162)) then
        tmp = x
    else if (z <= (-1.4d-269)) then
        tmp = t_1
    else if (z <= 5.5d+109) 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 t_1 = t * (y / (a - z));
	double tmp;
	if (z <= -1.5e+98) {
		tmp = t;
	} else if (z <= -6.6e-63) {
		tmp = t_1;
	} else if (z <= -3e-125) {
		tmp = t;
	} else if (z <= -5.6e-162) {
		tmp = x;
	} else if (z <= -1.4e-269) {
		tmp = t_1;
	} else if (z <= 5.5e+109) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if z <= -1.5e+98:
		tmp = t
	elif z <= -6.6e-63:
		tmp = t_1
	elif z <= -3e-125:
		tmp = t
	elif z <= -5.6e-162:
		tmp = x
	elif z <= -1.4e-269:
		tmp = t_1
	elif z <= 5.5e+109:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.5e+98)
		tmp = t;
	elseif (z <= -6.6e-63)
		tmp = t_1;
	elseif (z <= -3e-125)
		tmp = t;
	elseif (z <= -5.6e-162)
		tmp = x;
	elseif (z <= -1.4e-269)
		tmp = t_1;
	elseif (z <= 5.5e+109)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (z <= -1.5e+98)
		tmp = t;
	elseif (z <= -6.6e-63)
		tmp = t_1;
	elseif (z <= -3e-125)
		tmp = t;
	elseif (z <= -5.6e-162)
		tmp = x;
	elseif (z <= -1.4e-269)
		tmp = t_1;
	elseif (z <= 5.5e+109)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e+98], t, If[LessEqual[z, -6.6e-63], t$95$1, If[LessEqual[z, -3e-125], t, If[LessEqual[z, -5.6e-162], x, If[LessEqual[z, -1.4e-269], t$95$1, If[LessEqual[z, 5.5e+109], x, t]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5000000000000001e98 or -6.59999999999999987e-63 < z < -2.9999999999999999e-125 or 5.4999999999999998e109 < z

   1. Initial program 33.4%

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

      1. associate-*l/ 64.0%

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

   3. Simplified 64.0%

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

   5. Taylor expanded in z around inf 46.4%

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

   if -1.5000000000000001e98 < z < -6.59999999999999987e-63 or -5.60000000000000043e-162 < z < -1.39999999999999997e-269

   1. Initial program 82.0%

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

      1. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in y around -inf 56.5%

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

      1. associate-*l/ 63.0%

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

   7. Simplified 63.0%

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

   8. Taylor expanded in t around inf 35.8%

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

      1. associate-*r/ 42.4%

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

   10. Simplified 42.4%

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

   if -2.9999999999999999e-125 < z < -5.60000000000000043e-162 or -1.39999999999999997e-269 < z < 5.4999999999999998e109

   1. Initial program 88.5%

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

      1. associate-*l/ 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in a around inf 46.4%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+98}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-63}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-162}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-269}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+109}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 45.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.6:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-242}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-46}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+99}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.2e+106)
   x
   (if (<= a -4.6)
     (* (- t x) (/ y a))
     (if (<= a 2.75e-242)
       (- t (* t (/ y z)))
       (if (<= a 2e-46)
         (/ (* x (- y a)) z)
         (if (<= a 4.8e+99) (- t (/ a (/ z x))) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e+106) {
		tmp = x;
	} else if (a <= -4.6) {
		tmp = (t - x) * (y / a);
	} else if (a <= 2.75e-242) {
		tmp = t - (t * (y / z));
	} else if (a <= 2e-46) {
		tmp = (x * (y - a)) / z;
	} else if (a <= 4.8e+99) {
		tmp = t - (a / (z / x));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.2d+106)) then
        tmp = x
    else if (a <= (-4.6d0)) then
        tmp = (t - x) * (y / a)
    else if (a <= 2.75d-242) then
        tmp = t - (t * (y / z))
    else if (a <= 2d-46) then
        tmp = (x * (y - a)) / z
    else if (a <= 4.8d+99) then
        tmp = t - (a / (z / x))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e+106) {
		tmp = x;
	} else if (a <= -4.6) {
		tmp = (t - x) * (y / a);
	} else if (a <= 2.75e-242) {
		tmp = t - (t * (y / z));
	} else if (a <= 2e-46) {
		tmp = (x * (y - a)) / z;
	} else if (a <= 4.8e+99) {
		tmp = t - (a / (z / x));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.2e+106:
		tmp = x
	elif a <= -4.6:
		tmp = (t - x) * (y / a)
	elif a <= 2.75e-242:
		tmp = t - (t * (y / z))
	elif a <= 2e-46:
		tmp = (x * (y - a)) / z
	elif a <= 4.8e+99:
		tmp = t - (a / (z / x))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.2e+106)
		tmp = x;
	elseif (a <= -4.6)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (a <= 2.75e-242)
		tmp = Float64(t - Float64(t * Float64(y / z)));
	elseif (a <= 2e-46)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (a <= 4.8e+99)
		tmp = Float64(t - Float64(a / Float64(z / x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.2e+106)
		tmp = x;
	elseif (a <= -4.6)
		tmp = (t - x) * (y / a);
	elseif (a <= 2.75e-242)
		tmp = t - (t * (y / z));
	elseif (a <= 2e-46)
		tmp = (x * (y - a)) / z;
	elseif (a <= 4.8e+99)
		tmp = t - (a / (z / x));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.2e+106], x, If[LessEqual[a, -4.6], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.75e-242], N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2e-46], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 4.8e+99], N[(t - N[(a / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.2e106 or 4.8000000000000002e99 < a

   1. Initial program 62.7%

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

      1. associate-*l/ 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in a around inf 55.3%

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

   if -1.2e106 < a < -4.5999999999999996

   1. Initial program 75.7%

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

      1. associate-*l/ 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in y around -inf 54.2%

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

      1. associate-*l/ 60.3%

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

   7. Simplified 60.3%

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

   8. Taylor expanded in a around inf 51.3%

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

   if -4.5999999999999996 < a < 2.7499999999999999e-242

   1. Initial program 64.9%

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

      1. associate-*l/ 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in x around 0 57.1%

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

   6. Taylor expanded in a around 0 52.3%

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

      1. associate-*r/ 52.3%

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

      2. *-commutative 52.3%

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

      3. neg-mul-1 52.3%

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

      4. distribute-rgt-neg-in 52.3%

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

   8. Simplified 52.3%

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

   9. Taylor expanded in y around 0 61.4%

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

       1. mul-1-neg 61.4%

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

       2. unsub-neg 61.4%

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

       3. *-commutative 61.4%

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

       4. associate-*l/ 65.3%

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

       5. *-commutative 65.3%

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

   11. Simplified 65.3%

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

   if 2.7499999999999999e-242 < a < 2.00000000000000005e-46

   1. Initial program 69.9%

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

      1. associate-*l/ 74.7%

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

   3. Simplified 74.7%

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

   5. Taylor expanded in z around inf 70.6%

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

      1. associate--l+ 70.6%

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

      2. associate-*r/ 70.6%

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

      3. associate-*r/ 70.6%

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

      4. div-sub 70.6%

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

      5. distribute-lft-out-- 70.6%

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

      6. associate-*r/ 70.6%

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

      7. mul-1-neg 70.6%

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

      8. distribute-rgt-out-- 70.6%

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

      9. unsub-neg 70.6%

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

      10. associate-/l* 76.5%

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

   7. Simplified 76.5%

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

   8. Taylor expanded in t around 0 50.0%

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

   if 2.00000000000000005e-46 < a < 4.8000000000000002e99

   1. Initial program 66.2%

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

      1. associate-*l/ 77.0%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in z around inf 37.4%

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

      1. associate--l+ 37.4%

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

      2. associate-*r/ 37.4%

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

      3. associate-*r/ 37.4%

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

      4. div-sub 40.5%

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

      5. distribute-lft-out-- 40.5%

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

      6. associate-*r/ 40.5%

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

      7. mul-1-neg 40.5%

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

      8. distribute-rgt-out-- 40.5%

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

      9. unsub-neg 40.5%

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

      10. associate-/l* 57.2%

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

   7. Simplified 57.2%

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

   8. Taylor expanded in y around 0 37.4%

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

      1. sub-neg 37.4%

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

      2. associate-*r/ 37.4%

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

      3. associate-*r* 37.4%

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

      4. neg-mul-1 37.4%

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

      5. associate-*r/ 51.3%

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

      6. distribute-lft-neg-out 51.3%

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

      7. remove-double-neg 51.3%

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

   10. Simplified 51.3%

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

   11. Taylor expanded in t around 0 40.8%

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

       1. mul-1-neg 40.8%

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

       2. associate-/l* 51.8%

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

       3. distribute-neg-frac 51.8%

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

   13. Simplified 51.8%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.6:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-242}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-46}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+99}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 45.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -46:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-242}:\\ \;\;\;\;\frac{t}{\frac{-z}{y - z}}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-47}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+96}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.5e+108)
   x
   (if (<= a -46.0)
     (* (- t x) (/ y a))
     (if (<= a 1.15e-242)
       (/ t (/ (- z) (- y z)))
       (if (<= a 4.6e-47)
         (/ (* x (- y a)) z)
         (if (<= a 6.5e+96) (- t (/ a (/ z x))) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.5e+108) {
		tmp = x;
	} else if (a <= -46.0) {
		tmp = (t - x) * (y / a);
	} else if (a <= 1.15e-242) {
		tmp = t / (-z / (y - z));
	} else if (a <= 4.6e-47) {
		tmp = (x * (y - a)) / z;
	} else if (a <= 6.5e+96) {
		tmp = t - (a / (z / x));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.5d+108)) then
        tmp = x
    else if (a <= (-46.0d0)) then
        tmp = (t - x) * (y / a)
    else if (a <= 1.15d-242) then
        tmp = t / (-z / (y - z))
    else if (a <= 4.6d-47) then
        tmp = (x * (y - a)) / z
    else if (a <= 6.5d+96) then
        tmp = t - (a / (z / x))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.5e+108) {
		tmp = x;
	} else if (a <= -46.0) {
		tmp = (t - x) * (y / a);
	} else if (a <= 1.15e-242) {
		tmp = t / (-z / (y - z));
	} else if (a <= 4.6e-47) {
		tmp = (x * (y - a)) / z;
	} else if (a <= 6.5e+96) {
		tmp = t - (a / (z / x));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.5e+108:
		tmp = x
	elif a <= -46.0:
		tmp = (t - x) * (y / a)
	elif a <= 1.15e-242:
		tmp = t / (-z / (y - z))
	elif a <= 4.6e-47:
		tmp = (x * (y - a)) / z
	elif a <= 6.5e+96:
		tmp = t - (a / (z / x))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.5e+108)
		tmp = x;
	elseif (a <= -46.0)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (a <= 1.15e-242)
		tmp = Float64(t / Float64(Float64(-z) / Float64(y - z)));
	elseif (a <= 4.6e-47)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (a <= 6.5e+96)
		tmp = Float64(t - Float64(a / Float64(z / x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.5e+108)
		tmp = x;
	elseif (a <= -46.0)
		tmp = (t - x) * (y / a);
	elseif (a <= 1.15e-242)
		tmp = t / (-z / (y - z));
	elseif (a <= 4.6e-47)
		tmp = (x * (y - a)) / z;
	elseif (a <= 6.5e+96)
		tmp = t - (a / (z / x));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.5e+108], x, If[LessEqual[a, -46.0], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e-242], N[(t / N[((-z) / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.6e-47], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 6.5e+96], N[(t - N[(a / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.49999999999999992e108 or 6.5e96 < a

   1. Initial program 62.7%

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

      1. associate-*l/ 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in a around inf 55.3%

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

   if -1.49999999999999992e108 < a < -46

   1. Initial program 75.7%

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

      1. associate-*l/ 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in y around -inf 54.2%

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

      1. associate-*l/ 60.3%

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

   7. Simplified 60.3%

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

   8. Taylor expanded in a around inf 51.3%

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

   if -46 < a < 1.14999999999999992e-242

   1. Initial program 64.9%

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

      1. associate-*l/ 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in x around 0 57.1%

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

      1. associate-/l* 68.8%

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

   7. Simplified 68.8%

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

   8. Taylor expanded in a around 0 65.3%

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

      1. neg-mul-1 65.3%

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

      2. distribute-neg-frac 65.3%

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

   10. Simplified 65.3%

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

   if 1.14999999999999992e-242 < a < 4.59999999999999964e-47

   1. Initial program 69.9%

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

      1. associate-*l/ 74.7%

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

   3. Simplified 74.7%

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

   5. Taylor expanded in z around inf 70.6%

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

      1. associate--l+ 70.6%

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

      2. associate-*r/ 70.6%

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

      3. associate-*r/ 70.6%

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

      4. div-sub 70.6%

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

      5. distribute-lft-out-- 70.6%

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

      6. associate-*r/ 70.6%

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

      7. mul-1-neg 70.6%

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

      8. distribute-rgt-out-- 70.6%

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

      9. unsub-neg 70.6%

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

      10. associate-/l* 76.5%

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

   7. Simplified 76.5%

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

   8. Taylor expanded in t around 0 50.0%

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

   if 4.59999999999999964e-47 < a < 6.5e96

   1. Initial program 66.2%

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

      1. associate-*l/ 77.0%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in z around inf 37.4%

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

      1. associate--l+ 37.4%

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

      2. associate-*r/ 37.4%

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

      3. associate-*r/ 37.4%

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

      4. div-sub 40.5%

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

      5. distribute-lft-out-- 40.5%

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

      6. associate-*r/ 40.5%

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

      7. mul-1-neg 40.5%

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

      8. distribute-rgt-out-- 40.5%

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

      9. unsub-neg 40.5%

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

      10. associate-/l* 57.2%

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

   7. Simplified 57.2%

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

   8. Taylor expanded in y around 0 37.4%

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

      1. sub-neg 37.4%

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

      2. associate-*r/ 37.4%

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

      3. associate-*r* 37.4%

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

      4. neg-mul-1 37.4%

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

      5. associate-*r/ 51.3%

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

      6. distribute-lft-neg-out 51.3%

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

      7. remove-double-neg 51.3%

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

   10. Simplified 51.3%

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

   11. Taylor expanded in t around 0 40.8%

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

       1. mul-1-neg 40.8%

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

       2. associate-/l* 51.8%

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

       3. distribute-neg-frac 51.8%

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

   13. Simplified 51.8%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -46:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-242}:\\ \;\;\;\;\frac{t}{\frac{-z}{y - z}}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-47}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+96}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 70.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.29 \lor \neg \left(a \leq 5.6 \cdot 10^{-124}\right) \land \left(a \leq 1.35 \cdot 10^{-85} \lor \neg \left(a \leq 1.18 \cdot 10^{+38}\right)\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -0.29)
         (and (not (<= a 5.6e-124))
              (or (<= a 1.35e-85) (not (<= a 1.18e+38)))))
   (+ x (* (- t x) (/ (- y z) a)))
   (+ t (/ (* y (- x t)) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.29) || (!(a <= 5.6e-124) && ((a <= 1.35e-85) || !(a <= 1.18e+38)))) {
		tmp = x + ((t - x) * ((y - z) / a));
	} else {
		tmp = t + ((y * (x - t)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-0.29d0)) .or. (.not. (a <= 5.6d-124)) .and. (a <= 1.35d-85) .or. (.not. (a <= 1.18d+38))) then
        tmp = x + ((t - x) * ((y - z) / a))
    else
        tmp = t + ((y * (x - t)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.29) || (!(a <= 5.6e-124) && ((a <= 1.35e-85) || !(a <= 1.18e+38)))) {
		tmp = x + ((t - x) * ((y - z) / a));
	} else {
		tmp = t + ((y * (x - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -0.29) or (not (a <= 5.6e-124) and ((a <= 1.35e-85) or not (a <= 1.18e+38))):
		tmp = x + ((t - x) * ((y - z) / a))
	else:
		tmp = t + ((y * (x - t)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -0.29) || (!(a <= 5.6e-124) && ((a <= 1.35e-85) || !(a <= 1.18e+38))))
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)));
	else
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -0.29) || (~((a <= 5.6e-124)) && ((a <= 1.35e-85) || ~((a <= 1.18e+38)))))
		tmp = x + ((t - x) * ((y - z) / a));
	else
		tmp = t + ((y * (x - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -0.29], And[N[Not[LessEqual[a, 5.6e-124]], $MachinePrecision], Or[LessEqual[a, 1.35e-85], N[Not[LessEqual[a, 1.18e+38]], $MachinePrecision]]]], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -0.28999999999999998 or 5.59999999999999996e-124 < a < 1.3500000000000001e-85 or 1.18e38 < a

   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/ 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in a around inf 77.9%

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

   if -0.28999999999999998 < a < 5.59999999999999996e-124 or 1.3500000000000001e-85 < a < 1.18e38

   1. Initial program 62.9%

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

      1. associate-*l/ 74.3%

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

   3. Simplified 74.3%

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

   5. Taylor expanded in z around inf 77.1%

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

      1. associate--l+ 77.1%

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

      2. associate-*r/ 77.1%

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

      3. associate-*r/ 77.1%

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

      4. div-sub 78.0%

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

      5. distribute-lft-out-- 78.0%

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

      6. associate-*r/ 78.0%

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

      7. mul-1-neg 78.0%

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

      8. distribute-rgt-out-- 78.0%

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

      9. unsub-neg 78.0%

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

      10. associate-/l* 82.5%

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

   7. Simplified 82.5%

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

   8. Taylor expanded in y around inf 73.1%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.29 \lor \neg \left(a \leq 5.6 \cdot 10^{-124}\right) \land \left(a \leq 1.35 \cdot 10^{-85} \lor \neg \left(a \leq 1.18 \cdot 10^{+38}\right)\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 70.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{y \cdot \left(x - t\right)}{z}\\ t_2 := x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{if}\;a \leq -18:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (* y (- x t)) z))) (t_2 (+ x (* (- t x) (/ (- y z) a)))))
   (if (<= a -18.0)
     t_2
     (if (<= a 2.15e-125)
       t_1
       (if (<= a 1.55e-85)
         t_2
         (if (<= a 1.18e+38) t_1 (+ x (/ (- t x) (/ a (- y z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((y * (x - t)) / z);
	double t_2 = x + ((t - x) * ((y - z) / a));
	double tmp;
	if (a <= -18.0) {
		tmp = t_2;
	} else if (a <= 2.15e-125) {
		tmp = t_1;
	} else if (a <= 1.55e-85) {
		tmp = t_2;
	} else if (a <= 1.18e+38) {
		tmp = t_1;
	} else {
		tmp = x + ((t - x) / (a / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + ((y * (x - t)) / z)
    t_2 = x + ((t - x) * ((y - z) / a))
    if (a <= (-18.0d0)) then
        tmp = t_2
    else if (a <= 2.15d-125) then
        tmp = t_1
    else if (a <= 1.55d-85) then
        tmp = t_2
    else if (a <= 1.18d+38) then
        tmp = t_1
    else
        tmp = x + ((t - x) / (a / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((y * (x - t)) / z);
	double t_2 = x + ((t - x) * ((y - z) / a));
	double tmp;
	if (a <= -18.0) {
		tmp = t_2;
	} else if (a <= 2.15e-125) {
		tmp = t_1;
	} else if (a <= 1.55e-85) {
		tmp = t_2;
	} else if (a <= 1.18e+38) {
		tmp = t_1;
	} else {
		tmp = x + ((t - x) / (a / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((y * (x - t)) / z)
	t_2 = x + ((t - x) * ((y - z) / a))
	tmp = 0
	if a <= -18.0:
		tmp = t_2
	elif a <= 2.15e-125:
		tmp = t_1
	elif a <= 1.55e-85:
		tmp = t_2
	elif a <= 1.18e+38:
		tmp = t_1
	else:
		tmp = x + ((t - x) / (a / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(y * Float64(x - t)) / z))
	t_2 = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)))
	tmp = 0.0
	if (a <= -18.0)
		tmp = t_2;
	elseif (a <= 2.15e-125)
		tmp = t_1;
	elseif (a <= 1.55e-85)
		tmp = t_2;
	elseif (a <= 1.18e+38)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((y * (x - t)) / z);
	t_2 = x + ((t - x) * ((y - z) / a));
	tmp = 0.0;
	if (a <= -18.0)
		tmp = t_2;
	elseif (a <= 2.15e-125)
		tmp = t_1;
	elseif (a <= 1.55e-85)
		tmp = t_2;
	elseif (a <= 1.18e+38)
		tmp = t_1;
	else
		tmp = x + ((t - x) / (a / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -18.0], t$95$2, If[LessEqual[a, 2.15e-125], t$95$1, If[LessEqual[a, 1.55e-85], t$95$2, If[LessEqual[a, 1.18e+38], t$95$1, N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -18 or 2.1500000000000001e-125 < a < 1.5500000000000001e-85

   1. Initial program 69.0%

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

      1. associate-*l/ 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in a around inf 80.0%

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

   if -18 < a < 2.1500000000000001e-125 or 1.5500000000000001e-85 < a < 1.18e38

   1. Initial program 62.9%

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

      1. associate-*l/ 74.3%

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

   3. Simplified 74.3%

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

   5. Taylor expanded in z around inf 77.1%

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

      1. associate--l+ 77.1%

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

      2. associate-*r/ 77.1%

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

      3. associate-*r/ 77.1%

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

      4. div-sub 78.0%

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

      5. distribute-lft-out-- 78.0%

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

      6. associate-*r/ 78.0%

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

      7. mul-1-neg 78.0%

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

      8. distribute-rgt-out-- 78.0%

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

      9. unsub-neg 78.0%

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

      10. associate-/l* 82.5%

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

   7. Simplified 82.5%

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

   8. Taylor expanded in y around inf 73.1%

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

   if 1.18e38 < a

   1. Initial program 68.6%

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

      1. associate-*l/ 86.1%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in a around inf 61.9%

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

      1. associate-/l* 74.9%

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

   7. Simplified 74.9%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -18:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-125}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-85}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{+38}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 75.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y - a}}\\ t_2 := x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{if}\;a \leq -3.3:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.14 \cdot 10^{-85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (- x t) (/ z (- y a)))))
        (t_2 (+ x (* (- t x) (/ (- y z) a)))))
   (if (<= a -3.3)
     t_2
     (if (<= a 5.6e-124)
       t_1
       (if (<= a 1.14e-85)
         t_2
         (if (<= a 9.6e+26) t_1 (+ x (/ (- t x) (/ a (- y z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / (y - a)));
	double t_2 = x + ((t - x) * ((y - z) / a));
	double tmp;
	if (a <= -3.3) {
		tmp = t_2;
	} else if (a <= 5.6e-124) {
		tmp = t_1;
	} else if (a <= 1.14e-85) {
		tmp = t_2;
	} else if (a <= 9.6e+26) {
		tmp = t_1;
	} else {
		tmp = x + ((t - x) / (a / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + ((x - t) / (z / (y - a)))
    t_2 = x + ((t - x) * ((y - z) / a))
    if (a <= (-3.3d0)) then
        tmp = t_2
    else if (a <= 5.6d-124) then
        tmp = t_1
    else if (a <= 1.14d-85) then
        tmp = t_2
    else if (a <= 9.6d+26) then
        tmp = t_1
    else
        tmp = x + ((t - x) / (a / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / (y - a)));
	double t_2 = x + ((t - x) * ((y - z) / a));
	double tmp;
	if (a <= -3.3) {
		tmp = t_2;
	} else if (a <= 5.6e-124) {
		tmp = t_1;
	} else if (a <= 1.14e-85) {
		tmp = t_2;
	} else if (a <= 9.6e+26) {
		tmp = t_1;
	} else {
		tmp = x + ((t - x) / (a / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x - t) / (z / (y - a)))
	t_2 = x + ((t - x) * ((y - z) / a))
	tmp = 0
	if a <= -3.3:
		tmp = t_2
	elif a <= 5.6e-124:
		tmp = t_1
	elif a <= 1.14e-85:
		tmp = t_2
	elif a <= 9.6e+26:
		tmp = t_1
	else:
		tmp = x + ((t - x) / (a / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))))
	t_2 = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)))
	tmp = 0.0
	if (a <= -3.3)
		tmp = t_2;
	elseif (a <= 5.6e-124)
		tmp = t_1;
	elseif (a <= 1.14e-85)
		tmp = t_2;
	elseif (a <= 9.6e+26)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x - t) / (z / (y - a)));
	t_2 = x + ((t - x) * ((y - z) / a));
	tmp = 0.0;
	if (a <= -3.3)
		tmp = t_2;
	elseif (a <= 5.6e-124)
		tmp = t_1;
	elseif (a <= 1.14e-85)
		tmp = t_2;
	elseif (a <= 9.6e+26)
		tmp = t_1;
	else
		tmp = x + ((t - x) / (a / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.3], t$95$2, If[LessEqual[a, 5.6e-124], t$95$1, If[LessEqual[a, 1.14e-85], t$95$2, If[LessEqual[a, 9.6e+26], t$95$1, N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.2999999999999998 or 5.59999999999999996e-124 < a < 1.1400000000000001e-85

   1. Initial program 69.0%

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

      1. associate-*l/ 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in a around inf 80.0%

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

   if -3.2999999999999998 < a < 5.59999999999999996e-124 or 1.1400000000000001e-85 < a < 9.60000000000000018e26

   1. Initial program 62.3%

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

      1. associate-*l/ 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in z around inf 77.5%

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

      1. associate--l+ 77.5%

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

      2. associate-*r/ 77.5%

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

      3. associate-*r/ 77.5%

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

      4. div-sub 78.5%

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

      5. distribute-lft-out-- 78.5%

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

      6. associate-*r/ 78.5%

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

      7. mul-1-neg 78.5%

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

      8. distribute-rgt-out-- 78.5%

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

      9. unsub-neg 78.5%

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

      10. associate-/l* 83.1%

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

   7. Simplified 83.1%

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

   if 9.60000000000000018e26 < a

   1. Initial program 69.6%

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

      1. associate-*l/ 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in a around inf 61.5%

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

      1. associate-/l* 74.1%

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

   7. Simplified 74.1%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-124}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 1.14 \cdot 10^{-85}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{+26}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 56.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -2.65 \cdot 10^{-123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-239}:\\ \;\;\;\;\frac{-x}{\frac{a - z}{y}}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-179}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= t -2.65e-123)
     t_1
     (if (<= t 1.45e-239)
       (/ (- x) (/ (- a z) y))
       (if (<= t 4.5e-188) x (if (<= t 1.9e-179) (/ x (/ z y)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -2.65e-123) {
		tmp = t_1;
	} else if (t <= 1.45e-239) {
		tmp = -x / ((a - z) / y);
	} else if (t <= 4.5e-188) {
		tmp = x;
	} else if (t <= 1.9e-179) {
		tmp = x / (z / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (t <= (-2.65d-123)) then
        tmp = t_1
    else if (t <= 1.45d-239) then
        tmp = -x / ((a - z) / y)
    else if (t <= 4.5d-188) then
        tmp = x
    else if (t <= 1.9d-179) then
        tmp = x / (z / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -2.65e-123) {
		tmp = t_1;
	} else if (t <= 1.45e-239) {
		tmp = -x / ((a - z) / y);
	} else if (t <= 4.5e-188) {
		tmp = x;
	} else if (t <= 1.9e-179) {
		tmp = x / (z / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -2.65e-123:
		tmp = t_1
	elif t <= 1.45e-239:
		tmp = -x / ((a - z) / y)
	elif t <= 4.5e-188:
		tmp = x
	elif t <= 1.9e-179:
		tmp = x / (z / y)
	else:
		tmp = t_1
	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 (t <= -2.65e-123)
		tmp = t_1;
	elseif (t <= 1.45e-239)
		tmp = Float64(Float64(-x) / Float64(Float64(a - z) / y));
	elseif (t <= 4.5e-188)
		tmp = x;
	elseif (t <= 1.9e-179)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = t_1;
	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 (t <= -2.65e-123)
		tmp = t_1;
	elseif (t <= 1.45e-239)
		tmp = -x / ((a - z) / y);
	elseif (t <= 4.5e-188)
		tmp = x;
	elseif (t <= 1.9e-179)
		tmp = x / (z / y);
	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[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.65e-123], t$95$1, If[LessEqual[t, 1.45e-239], N[((-x) / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-188], x, If[LessEqual[t, 1.9e-179], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.64999999999999985e-123 or 1.89999999999999987e-179 < t

   1. Initial program 62.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 x around 0 47.9%

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

      1. associate-/l* 62.5%

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

      2. div-inv 62.5%

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

      3. clear-num 62.6%

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

   7. Applied egg-rr 62.6%

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

   if -2.64999999999999985e-123 < t < 1.4500000000000001e-239

   1. Initial program 75.6%

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

      1. associate-*l/ 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in y around -inf 51.8%

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

      1. associate-*l/ 53.2%

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

   7. Simplified 53.2%

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

   8. Taylor expanded in t around 0 47.1%

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

      1. mul-1-neg 47.1%

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

      2. associate-/l* 49.2%

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

   10. Simplified 49.2%

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

   if 1.4500000000000001e-239 < t < 4.49999999999999993e-188

   1. Initial program 67.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 a around inf 50.3%

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

   if 4.49999999999999993e-188 < t < 1.89999999999999987e-179

   1. Initial program 100.0%

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

      1. associate-*l/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around -inf 52.1%

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

      1. associate-*l/ 51.3%

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

   7. Simplified 51.3%

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

   8. Taylor expanded in t around 0 52.1%

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

      1. mul-1-neg 52.1%

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

      2. associate-/l* 52.1%

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

   10. Simplified 52.1%

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

   11. Taylor expanded in a around 0 53.9%

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

       1. mul-1-neg 53.9%

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

       2. associate-/l* 53.9%

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

       3. distribute-neg-frac 53.9%

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

   13. Simplified 53.9%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.65 \cdot 10^{-123}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-239}:\\ \;\;\;\;\frac{-x}{\frac{a - z}{y}}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-179}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 62.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{-26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-217}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= z -1.1e-26)
     t_2
     (if (<= z -8.5e-89)
       t_1
       (if (<= z -6e-217) t_2 (if (<= z 1.5e+128) t_1 (- t (/ a (/ z x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.1e-26) {
		tmp = t_2;
	} else if (z <= -8.5e-89) {
		tmp = t_1;
	} else if (z <= -6e-217) {
		tmp = t_2;
	} else if (z <= 1.5e+128) {
		tmp = t_1;
	} else {
		tmp = t - (a / (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((t - x) * (y / a))
    t_2 = t * ((y - z) / (a - z))
    if (z <= (-1.1d-26)) then
        tmp = t_2
    else if (z <= (-8.5d-89)) then
        tmp = t_1
    else if (z <= (-6d-217)) then
        tmp = t_2
    else if (z <= 1.5d+128) then
        tmp = t_1
    else
        tmp = t - (a / (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.1e-26) {
		tmp = t_2;
	} else if (z <= -8.5e-89) {
		tmp = t_1;
	} else if (z <= -6e-217) {
		tmp = t_2;
	} else if (z <= 1.5e+128) {
		tmp = t_1;
	} else {
		tmp = t - (a / (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (y / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -1.1e-26:
		tmp = t_2
	elif z <= -8.5e-89:
		tmp = t_1
	elif z <= -6e-217:
		tmp = t_2
	elif z <= 1.5e+128:
		tmp = t_1
	else:
		tmp = t - (a / (z / x))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.1e-26)
		tmp = t_2;
	elseif (z <= -8.5e-89)
		tmp = t_1;
	elseif (z <= -6e-217)
		tmp = t_2;
	elseif (z <= 1.5e+128)
		tmp = t_1;
	else
		tmp = Float64(t - Float64(a / Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * (y / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -1.1e-26)
		tmp = t_2;
	elseif (z <= -8.5e-89)
		tmp = t_1;
	elseif (z <= -6e-217)
		tmp = t_2;
	elseif (z <= 1.5e+128)
		tmp = t_1;
	else
		tmp = t - (a / (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e-26], t$95$2, If[LessEqual[z, -8.5e-89], t$95$1, If[LessEqual[z, -6e-217], t$95$2, If[LessEqual[z, 1.5e+128], t$95$1, N[(t - N[(a / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1e-26 or -8.49999999999999937e-89 < z < -6.00000000000000009e-217

   1. Initial program 55.5%

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

      1. associate-*l/ 76.2%

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

   3. Simplified 76.2%

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

   5. Taylor expanded in x around 0 43.9%

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

      1. associate-/l* 60.5%

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

      2. div-inv 60.6%

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

      3. clear-num 60.6%

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

   7. Applied egg-rr 60.6%

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

   if -1.1e-26 < z < -8.49999999999999937e-89 or -6.00000000000000009e-217 < z < 1.4999999999999999e128

   1. Initial program 86.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 75.9%

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

   if 1.4999999999999999e128 < z

   1. Initial program 29.2%

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

      1. associate-*l/ 62.2%

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

   3. Simplified 62.2%

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

   5. Taylor expanded in z around inf 58.3%

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

      1. associate--l+ 58.3%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 58.3%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 58.3%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 58.3%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 58.3%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. associate-*r/ 58.3%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      7. mul-1-neg 58.3%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 58.5%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 58.5%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 81.2%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   7. Simplified 81.2%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   8. Taylor expanded in y around 0 52.2%

      \[\leadsto \color{blue}{t - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   9. Step-by-step derivation

      1. sub-neg 52.2%

         \[\leadsto \color{blue}{t + \left(--1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 52.2%

         \[\leadsto t + \left(-\color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      3. associate-*r* 52.2%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(-1 \cdot a\right) \cdot \left(t - x\right)}}{z}\right) \]

      4. neg-mul-1 52.2%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(-a\right)} \cdot \left(t - x\right)}{z}\right) \]

      5. associate-*r/ 66.3%

         \[\leadsto t + \left(-\color{blue}{\left(-a\right) \cdot \frac{t - x}{z}}\right) \]

      6. distribute-lft-neg-out 66.3%

         \[\leadsto t + \left(-\color{blue}{\left(-a \cdot \frac{t - x}{z}\right)}\right) \]

      7. remove-double-neg 66.3%

         \[\leadsto t + \color{blue}{a \cdot \frac{t - x}{z}} \]

   10. Simplified 66.3%

       \[\leadsto \color{blue}{t + a \cdot \frac{t - x}{z}} \]

   11. Taylor expanded in t around 0 55.9%

       \[\leadsto t + \color{blue}{-1 \cdot \frac{a \cdot x}{z}} \]
   12. Step-by-step derivation

       1. mul-1-neg 55.9%

          \[\leadsto t + \color{blue}{\left(-\frac{a \cdot x}{z}\right)} \]

       2. associate-/l* 66.9%

          \[\leadsto t + \left(-\color{blue}{\frac{a}{\frac{z}{x}}}\right) \]

       3. distribute-neg-frac 66.9%

          \[\leadsto t + \color{blue}{\frac{-a}{\frac{z}{x}}} \]

   13. Simplified 66.9%

       \[\leadsto t + \color{blue}{\frac{-a}{\frac{z}{x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-26}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-89}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-217}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+128}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 38.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+192}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{+98}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-269}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.3e+192)
   t
   (if (<= z -3.8e+125)
     (* x (/ (- y a) z))
     (if (<= z -1.32e+98)
       t
       (if (<= z -1.12e-269) (* t (/ y (- a z))) (if (<= z 6.8e+106) x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+192) {
		tmp = t;
	} else if (z <= -3.8e+125) {
		tmp = x * ((y - a) / z);
	} else if (z <= -1.32e+98) {
		tmp = t;
	} else if (z <= -1.12e-269) {
		tmp = t * (y / (a - z));
	} else if (z <= 6.8e+106) {
		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 <= (-1.3d+192)) then
        tmp = t
    else if (z <= (-3.8d+125)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-1.32d+98)) then
        tmp = t
    else if (z <= (-1.12d-269)) then
        tmp = t * (y / (a - z))
    else if (z <= 6.8d+106) 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 <= -1.3e+192) {
		tmp = t;
	} else if (z <= -3.8e+125) {
		tmp = x * ((y - a) / z);
	} else if (z <= -1.32e+98) {
		tmp = t;
	} else if (z <= -1.12e-269) {
		tmp = t * (y / (a - z));
	} else if (z <= 6.8e+106) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.3e+192:
		tmp = t
	elif z <= -3.8e+125:
		tmp = x * ((y - a) / z)
	elif z <= -1.32e+98:
		tmp = t
	elif z <= -1.12e-269:
		tmp = t * (y / (a - z))
	elif z <= 6.8e+106:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.3e+192)
		tmp = t;
	elseif (z <= -3.8e+125)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -1.32e+98)
		tmp = t;
	elseif (z <= -1.12e-269)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 6.8e+106)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.3e+192)
		tmp = t;
	elseif (z <= -3.8e+125)
		tmp = x * ((y - a) / z);
	elseif (z <= -1.32e+98)
		tmp = t;
	elseif (z <= -1.12e-269)
		tmp = t * (y / (a - z));
	elseif (z <= 6.8e+106)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.3e+192], t, If[LessEqual[z, -3.8e+125], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.32e+98], t, If[LessEqual[z, -1.12e-269], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+106], x, t]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.30000000000000002e192 or -3.80000000000000002e125 < z < -1.3200000000000001e98 or 6.79999999999999989e106 < z

   1. Initial program 26.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 62.4%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 62.4%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 53.2%

      \[\leadsto \color{blue}{t} \]

   if -1.30000000000000002e192 < z < -3.80000000000000002e125

   1. Initial program 32.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 56.9%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 56.9%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 60.6%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 60.6%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 60.6%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 60.6%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 60.6%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 60.6%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. associate-*r/ 60.6%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      7. mul-1-neg 60.6%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 60.6%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 60.6%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 76.4%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   7. Simplified 76.4%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   8. Taylor expanded in t around 0 44.3%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - a\right)}{z}} \]
   9. Step-by-step derivation

      1. associate-*r/ 51.8%

         \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} \]

   10. Simplified 51.8%

       \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} \]

   if -1.3200000000000001e98 < z < -1.12e-269

   1. Initial program 81.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.8%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 89.8%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around -inf 51.9%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-*l/ 57.0%

         \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   7. Simplified 57.0%

      \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   8. Taylor expanded in t around inf 30.1%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a - z}} \]
   9. Step-by-step derivation

      1. associate-*r/ 36.4%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a - z}} \]

   10. Simplified 36.4%

       \[\leadsto \color{blue}{t \cdot \frac{y}{a - z}} \]

   if -1.12e-269 < z < 6.79999999999999989e106

   1. Initial program 89.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 96.5%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 96.5%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 46.1%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+192}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{+98}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-269}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 37.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -11.8:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -2.75 \cdot 10^{-43}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-98}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e+98)
   x
   (if (<= a -11.8)
     (/ (- x) (/ a y))
     (if (<= a -2.75e-43)
       t
       (if (<= a -1.9e-98) (* (/ y z) (- t)) (if (<= a 1.45e+38) t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+98) {
		tmp = x;
	} else if (a <= -11.8) {
		tmp = -x / (a / y);
	} else if (a <= -2.75e-43) {
		tmp = t;
	} else if (a <= -1.9e-98) {
		tmp = (y / z) * -t;
	} else if (a <= 1.45e+38) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9.5d+98)) then
        tmp = x
    else if (a <= (-11.8d0)) then
        tmp = -x / (a / y)
    else if (a <= (-2.75d-43)) then
        tmp = t
    else if (a <= (-1.9d-98)) then
        tmp = (y / z) * -t
    else if (a <= 1.45d+38) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+98) {
		tmp = x;
	} else if (a <= -11.8) {
		tmp = -x / (a / y);
	} else if (a <= -2.75e-43) {
		tmp = t;
	} else if (a <= -1.9e-98) {
		tmp = (y / z) * -t;
	} else if (a <= 1.45e+38) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.5e+98:
		tmp = x
	elif a <= -11.8:
		tmp = -x / (a / y)
	elif a <= -2.75e-43:
		tmp = t
	elif a <= -1.9e-98:
		tmp = (y / z) * -t
	elif a <= 1.45e+38:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e+98)
		tmp = x;
	elseif (a <= -11.8)
		tmp = Float64(Float64(-x) / Float64(a / y));
	elseif (a <= -2.75e-43)
		tmp = t;
	elseif (a <= -1.9e-98)
		tmp = Float64(Float64(y / z) * Float64(-t));
	elseif (a <= 1.45e+38)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.5e+98)
		tmp = x;
	elseif (a <= -11.8)
		tmp = -x / (a / y);
	elseif (a <= -2.75e-43)
		tmp = t;
	elseif (a <= -1.9e-98)
		tmp = (y / z) * -t;
	elseif (a <= 1.45e+38)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e+98], x, If[LessEqual[a, -11.8], N[((-x) / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.75e-43], t, If[LessEqual[a, -1.9e-98], N[(N[(y / z), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[a, 1.45e+38], t, x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.5000000000000001e98 or 1.45000000000000003e38 < a

   1. Initial program 66.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 48.6%

      \[\leadsto \color{blue}{x} \]

   if -9.5000000000000001e98 < a < -11.800000000000001

   1. Initial program 72.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.4%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 88.4%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around -inf 54.4%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-*l/ 61.4%

         \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   7. Simplified 61.4%

      \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   8. Taylor expanded in t around 0 32.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{a - z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 32.0%

         \[\leadsto \color{blue}{-\frac{x \cdot y}{a - z}} \]

      2. associate-/l* 38.8%

         \[\leadsto -\color{blue}{\frac{x}{\frac{a - z}{y}}} \]

   10. Simplified 38.8%

       \[\leadsto \color{blue}{-\frac{x}{\frac{a - z}{y}}} \]

   11. Taylor expanded in a around inf 25.3%

       \[\leadsto -\color{blue}{\frac{x \cdot y}{a}} \]
   12. Step-by-step derivation

       1. associate-/l* 32.1%

          \[\leadsto -\color{blue}{\frac{x}{\frac{a}{y}}} \]

   13. Simplified 32.1%

       \[\leadsto -\color{blue}{\frac{x}{\frac{a}{y}}} \]

   if -11.800000000000001 < a < -2.75000000000000006e-43 or -1.9000000000000002e-98 < a < 1.45000000000000003e38

   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/ 74.7%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 74.7%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 42.0%

      \[\leadsto \color{blue}{t} \]

   if -2.75000000000000006e-43 < a < -1.9000000000000002e-98

   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/ 89.2%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 89.2%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around -inf 89.2%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-*l/ 89.2%

         \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   7. Simplified 89.2%

      \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   8. Taylor expanded in t around inf 67.3%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a - z}} \]
   9. Step-by-step derivation

      1. associate-*r/ 67.0%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a - z}} \]

   10. Simplified 67.0%

       \[\leadsto \color{blue}{t \cdot \frac{y}{a - z}} \]

   11. Taylor expanded in a around 0 56.6%

       \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \frac{y}{z}\right)} \]
   12. Step-by-step derivation

       1. associate-*r/ 56.6%

          \[\leadsto t \cdot \color{blue}{\frac{-1 \cdot y}{z}} \]

       2. neg-mul-1 56.6%

          \[\leadsto t \cdot \frac{\color{blue}{-y}}{z} \]

   13. Simplified 56.6%

       \[\leadsto t \cdot \color{blue}{\frac{-y}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -11.8:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -2.75 \cdot 10^{-43}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-98}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 37.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.5:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-43}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-98}:\\ \;\;\;\;-\frac{t \cdot y}{z}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9e+98)
   x
   (if (<= a -4.5)
     (/ (- x) (/ a y))
     (if (<= a -2.05e-43)
       t
       (if (<= a -2.6e-98) (- (/ (* t y) z)) (if (<= a 1.65e+38) t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9e+98) {
		tmp = x;
	} else if (a <= -4.5) {
		tmp = -x / (a / y);
	} else if (a <= -2.05e-43) {
		tmp = t;
	} else if (a <= -2.6e-98) {
		tmp = -((t * y) / z);
	} else if (a <= 1.65e+38) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9d+98)) then
        tmp = x
    else if (a <= (-4.5d0)) then
        tmp = -x / (a / y)
    else if (a <= (-2.05d-43)) then
        tmp = t
    else if (a <= (-2.6d-98)) then
        tmp = -((t * y) / z)
    else if (a <= 1.65d+38) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9e+98) {
		tmp = x;
	} else if (a <= -4.5) {
		tmp = -x / (a / y);
	} else if (a <= -2.05e-43) {
		tmp = t;
	} else if (a <= -2.6e-98) {
		tmp = -((t * y) / z);
	} else if (a <= 1.65e+38) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9e+98:
		tmp = x
	elif a <= -4.5:
		tmp = -x / (a / y)
	elif a <= -2.05e-43:
		tmp = t
	elif a <= -2.6e-98:
		tmp = -((t * y) / z)
	elif a <= 1.65e+38:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9e+98)
		tmp = x;
	elseif (a <= -4.5)
		tmp = Float64(Float64(-x) / Float64(a / y));
	elseif (a <= -2.05e-43)
		tmp = t;
	elseif (a <= -2.6e-98)
		tmp = Float64(-Float64(Float64(t * y) / z));
	elseif (a <= 1.65e+38)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9e+98)
		tmp = x;
	elseif (a <= -4.5)
		tmp = -x / (a / y);
	elseif (a <= -2.05e-43)
		tmp = t;
	elseif (a <= -2.6e-98)
		tmp = -((t * y) / z);
	elseif (a <= 1.65e+38)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9e+98], x, If[LessEqual[a, -4.5], N[((-x) / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.05e-43], t, If[LessEqual[a, -2.6e-98], (-N[(N[(t * y), $MachinePrecision] / z), $MachinePrecision]), If[LessEqual[a, 1.65e+38], t, x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.0000000000000004e98 or 1.65e38 < a

   1. Initial program 66.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 48.6%

      \[\leadsto \color{blue}{x} \]

   if -9.0000000000000004e98 < a < -4.5

   1. Initial program 72.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.4%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 88.4%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around -inf 54.4%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-*l/ 61.4%

         \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   7. Simplified 61.4%

      \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   8. Taylor expanded in t around 0 32.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{a - z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 32.0%

         \[\leadsto \color{blue}{-\frac{x \cdot y}{a - z}} \]

      2. associate-/l* 38.8%

         \[\leadsto -\color{blue}{\frac{x}{\frac{a - z}{y}}} \]

   10. Simplified 38.8%

       \[\leadsto \color{blue}{-\frac{x}{\frac{a - z}{y}}} \]

   11. Taylor expanded in a around inf 25.3%

       \[\leadsto -\color{blue}{\frac{x \cdot y}{a}} \]
   12. Step-by-step derivation

       1. associate-/l* 32.1%

          \[\leadsto -\color{blue}{\frac{x}{\frac{a}{y}}} \]

   13. Simplified 32.1%

       \[\leadsto -\color{blue}{\frac{x}{\frac{a}{y}}} \]

   if -4.5 < a < -2.0499999999999999e-43 or -2.60000000000000013e-98 < a < 1.65e38

   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/ 74.7%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 74.7%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 42.0%

      \[\leadsto \color{blue}{t} \]

   if -2.0499999999999999e-43 < a < -2.60000000000000013e-98

   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/ 89.2%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 89.2%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 67.4%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]

   6. Taylor expanded in a around 0 57.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot \left(y - z\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 57.0%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot \left(y - z\right)\right)}{z}} \]

      2. *-commutative 57.0%

         \[\leadsto \frac{-1 \cdot \color{blue}{\left(\left(y - z\right) \cdot t\right)}}{z} \]

      3. neg-mul-1 57.0%

         \[\leadsto \frac{\color{blue}{-\left(y - z\right) \cdot t}}{z} \]

      4. distribute-rgt-neg-in 57.0%

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot \left(-t\right)}}{z} \]

   8. Simplified 57.0%

      \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(-t\right)}{z}} \]

   9. Taylor expanded in y around inf 56.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot y}{z}} \]
   10. Step-by-step derivation

       1. associate-*r/ 56.8%

          \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot y\right)}{z}} \]

       2. mul-1-neg 56.8%

          \[\leadsto \frac{\color{blue}{-t \cdot y}}{z} \]

   11. Simplified 56.8%

       \[\leadsto \color{blue}{\frac{-t \cdot y}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.5:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-43}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-98}:\\ \;\;\;\;-\frac{t \cdot y}{z}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 88.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+71} \lor \neg \left(z \leq 3.2 \cdot 10^{+165}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.2e+71) (not (<= z 3.2e+165)))
   (+ t (/ (- x t) (/ z (- y a))))
   (- x (* (- t x) (/ (- z y) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.2e+71) || !(z <= 3.2e+165)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x - ((t - x) * ((z - y) / (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 <= (-6.2d+71)) .or. (.not. (z <= 3.2d+165))) then
        tmp = t + ((x - t) / (z / (y - a)))
    else
        tmp = x - ((t - x) * ((z - y) / (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 <= -6.2e+71) || !(z <= 3.2e+165)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x - ((t - x) * ((z - y) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.2e+71) or not (z <= 3.2e+165):
		tmp = t + ((x - t) / (z / (y - a)))
	else:
		tmp = x - ((t - x) * ((z - y) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.2e+71) || !(z <= 3.2e+165))
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = Float64(x - Float64(Float64(t - x) * Float64(Float64(z - y) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.2e+71) || ~((z <= 3.2e+165)))
		tmp = t + ((x - t) / (z / (y - a)));
	else
		tmp = x - ((t - x) * ((z - y) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.2e+71], N[Not[LessEqual[z, 3.2e+165]], $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[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.20000000000000036e71 or 3.2e165 < z

   1. Initial program 25.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 57.2%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 57.2%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 62.8%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 62.8%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 62.8%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 62.8%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 62.8%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 62.8%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. associate-*r/ 62.8%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      7. mul-1-neg 62.8%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 62.9%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 62.9%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 85.1%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   7. Simplified 85.1%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   if -6.20000000000000036e71 < z < 3.2e165

   1. Initial program 83.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.8%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 93.8%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+71} \lor \neg \left(z \leq 3.2 \cdot 10^{+165}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 39.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{+59}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -5800000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.8e+108)
   x
   (if (<= a -1.25e+59)
     (* t (/ y a))
     (if (<= a -5800000000000.0) x (if (<= a 1.95e+38) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.8e+108) {
		tmp = x;
	} else if (a <= -1.25e+59) {
		tmp = t * (y / a);
	} else if (a <= -5800000000000.0) {
		tmp = x;
	} else if (a <= 1.95e+38) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.8d+108)) then
        tmp = x
    else if (a <= (-1.25d+59)) then
        tmp = t * (y / a)
    else if (a <= (-5800000000000.0d0)) then
        tmp = x
    else if (a <= 1.95d+38) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.8e+108) {
		tmp = x;
	} else if (a <= -1.25e+59) {
		tmp = t * (y / a);
	} else if (a <= -5800000000000.0) {
		tmp = x;
	} else if (a <= 1.95e+38) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.8e+108:
		tmp = x
	elif a <= -1.25e+59:
		tmp = t * (y / a)
	elif a <= -5800000000000.0:
		tmp = x
	elif a <= 1.95e+38:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.8e+108)
		tmp = x;
	elseif (a <= -1.25e+59)
		tmp = Float64(t * Float64(y / a));
	elseif (a <= -5800000000000.0)
		tmp = x;
	elseif (a <= 1.95e+38)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.8e+108)
		tmp = x;
	elseif (a <= -1.25e+59)
		tmp = t * (y / a);
	elseif (a <= -5800000000000.0)
		tmp = x;
	elseif (a <= 1.95e+38)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.8e+108], x, If[LessEqual[a, -1.25e+59], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5800000000000.0], x, If[LessEqual[a, 1.95e+38], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.80000000000000037e108 or -1.2499999999999999e59 < a < -5.8e12 or 1.95000000000000012e38 < a

   1. Initial program 64.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.0%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 88.0%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 47.6%

      \[\leadsto \color{blue}{x} \]

   if -4.80000000000000037e108 < a < -1.2499999999999999e59

   1. Initial program 82.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.2%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 94.2%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around -inf 59.9%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-*l/ 60.3%

         \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   7. Simplified 60.3%

      \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   8. Taylor expanded in t around inf 37.8%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a - z}} \]
   9. Step-by-step derivation

      1. associate-*r/ 38.1%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a - z}} \]

   10. Simplified 38.1%

       \[\leadsto \color{blue}{t \cdot \frac{y}{a - z}} \]

   11. Taylor expanded in a around inf 38.1%

       \[\leadsto t \cdot \color{blue}{\frac{y}{a}} \]

   if -5.8e12 < a < 1.95000000000000012e38

   1. Initial program 65.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 76.2%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 76.2%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 38.4%

      \[\leadsto \color{blue}{t} \]
3. Recombined 3 regimes into one program.

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{+59}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -5800000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 38.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.2:\\ \;\;\;\;x \cdot \frac{-y}{a}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.8e+98)
   x
   (if (<= a -3.2) (* x (/ (- y) a)) (if (<= a 1.65e+38) t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.8e+98) {
		tmp = x;
	} else if (a <= -3.2) {
		tmp = x * (-y / a);
	} else if (a <= 1.65e+38) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-8.8d+98)) then
        tmp = x
    else if (a <= (-3.2d0)) then
        tmp = x * (-y / a)
    else if (a <= 1.65d+38) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.8e+98) {
		tmp = x;
	} else if (a <= -3.2) {
		tmp = x * (-y / a);
	} else if (a <= 1.65e+38) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.8e+98:
		tmp = x
	elif a <= -3.2:
		tmp = x * (-y / a)
	elif a <= 1.65e+38:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.8e+98)
		tmp = x;
	elseif (a <= -3.2)
		tmp = Float64(x * Float64(Float64(-y) / a));
	elseif (a <= 1.65e+38)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.8e+98)
		tmp = x;
	elseif (a <= -3.2)
		tmp = x * (-y / a);
	elseif (a <= 1.65e+38)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.8e+98], x, If[LessEqual[a, -3.2], N[(x * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e+38], t, x]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.80000000000000034e98 or 1.65e38 < a

   1. Initial program 66.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 48.6%

      \[\leadsto \color{blue}{x} \]

   if -8.80000000000000034e98 < a < -3.2000000000000002

   1. Initial program 72.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.4%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 88.4%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around -inf 54.4%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-*l/ 61.4%

         \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   7. Simplified 61.4%

      \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   8. Taylor expanded in t around 0 32.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{a - z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 32.0%

         \[\leadsto \color{blue}{-\frac{x \cdot y}{a - z}} \]

      2. associate-/l* 38.8%

         \[\leadsto -\color{blue}{\frac{x}{\frac{a - z}{y}}} \]

   10. Simplified 38.8%

       \[\leadsto \color{blue}{-\frac{x}{\frac{a - z}{y}}} \]

   11. Taylor expanded in a around inf 25.3%

       \[\leadsto -\color{blue}{\frac{x \cdot y}{a}} \]
   12. Step-by-step derivation

       1. *-lft-identity 25.3%

          \[\leadsto -\frac{x \cdot y}{\color{blue}{1 \cdot a}} \]

       2. times-frac 32.1%

          \[\leadsto -\color{blue}{\frac{x}{1} \cdot \frac{y}{a}} \]

       3. /-rgt-identity 32.1%

          \[\leadsto -\color{blue}{x} \cdot \frac{y}{a} \]

   13. Simplified 32.1%

       \[\leadsto -\color{blue}{x \cdot \frac{y}{a}} \]

   if -3.2000000000000002 < a < 1.65e38

   1. Initial program 65.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 75.8%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 75.8%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 39.0%

      \[\leadsto \color{blue}{t} \]
3. Recombined 3 regimes into one program.

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.2:\\ \;\;\;\;x \cdot \frac{-y}{a}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 38.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.1:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.8e+98)
   x
   (if (<= a -4.1) (/ (- x) (/ a y)) (if (<= a 1.35e+38) t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.8e+98) {
		tmp = x;
	} else if (a <= -4.1) {
		tmp = -x / (a / y);
	} else if (a <= 1.35e+38) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-8.8d+98)) then
        tmp = x
    else if (a <= (-4.1d0)) then
        tmp = -x / (a / y)
    else if (a <= 1.35d+38) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.8e+98) {
		tmp = x;
	} else if (a <= -4.1) {
		tmp = -x / (a / y);
	} else if (a <= 1.35e+38) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.8e+98:
		tmp = x
	elif a <= -4.1:
		tmp = -x / (a / y)
	elif a <= 1.35e+38:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.8e+98)
		tmp = x;
	elseif (a <= -4.1)
		tmp = Float64(Float64(-x) / Float64(a / y));
	elseif (a <= 1.35e+38)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.8e+98)
		tmp = x;
	elseif (a <= -4.1)
		tmp = -x / (a / y);
	elseif (a <= 1.35e+38)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.8e+98], x, If[LessEqual[a, -4.1], N[((-x) / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e+38], t, x]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.80000000000000034e98 or 1.34999999999999998e38 < a

   1. Initial program 66.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 48.6%

      \[\leadsto \color{blue}{x} \]

   if -8.80000000000000034e98 < a < -4.0999999999999996

   1. Initial program 72.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.4%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 88.4%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around -inf 54.4%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-*l/ 61.4%

         \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   7. Simplified 61.4%

      \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]

   8. Taylor expanded in t around 0 32.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{a - z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 32.0%

         \[\leadsto \color{blue}{-\frac{x \cdot y}{a - z}} \]

      2. associate-/l* 38.8%

         \[\leadsto -\color{blue}{\frac{x}{\frac{a - z}{y}}} \]

   10. Simplified 38.8%

       \[\leadsto \color{blue}{-\frac{x}{\frac{a - z}{y}}} \]

   11. Taylor expanded in a around inf 25.3%

       \[\leadsto -\color{blue}{\frac{x \cdot y}{a}} \]
   12. Step-by-step derivation

       1. associate-/l* 32.1%

          \[\leadsto -\color{blue}{\frac{x}{\frac{a}{y}}} \]

   13. Simplified 32.1%

       \[\leadsto -\color{blue}{\frac{x}{\frac{a}{y}}} \]

   if -4.0999999999999996 < a < 1.34999999999999998e38

   1. Initial program 65.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 75.8%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 75.8%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 39.0%

      \[\leadsto \color{blue}{t} \]
3. Recombined 3 regimes into one program.

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.1:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 39.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5600000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5600000000.0) x (if (<= a 1.18e+38) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5600000000.0) {
		tmp = x;
	} else if (a <= 1.18e+38) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5600000000.0d0)) then
        tmp = x
    else if (a <= 1.18d+38) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5600000000.0) {
		tmp = x;
	} else if (a <= 1.18e+38) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5600000000.0:
		tmp = x
	elif a <= 1.18e+38:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5600000000.0)
		tmp = x;
	elseif (a <= 1.18e+38)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5600000000.0)
		tmp = x;
	elseif (a <= 1.18e+38)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5600000000.0], x, If[LessEqual[a, 1.18e+38], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -5.6e9 or 1.18e38 < a

   1. Initial program 66.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.8%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 88.8%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 42.7%

      \[\leadsto \color{blue}{x} \]

   if -5.6e9 < a < 1.18e38

   1. Initial program 65.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 76.2%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 76.2%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 38.4%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5600000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 26.1% 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 66.2%

   \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
2. Step-by-step derivation

   1. associate-*l/ 82.8%

      \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

3. Simplified 82.8%

   \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 24.6%

   \[\leadsto \color{blue}{t} \]

6. Final simplification 24.6%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 83.9% 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 2024027 
(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))))