Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.4% → 89.9%

Time: 23.1s

Alternatives: 20

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-225} \lor \neg \left(t\_1 \leq 5 \cdot 10^{-154}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-225) (not (<= t_1 5e-154)))
     t_1
     (+ t (* (- t x) (/ (- a y) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-225) || !(t_1 <= 5e-154)) {
		tmp = t_1;
	} else {
		tmp = t + ((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) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-1d-225)) .or. (.not. (t_1 <= 5d-154))) then
        tmp = t_1
    else
        tmp = t + ((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 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-225) || !(t_1 <= 5e-154)) {
		tmp = t_1;
	} else {
		tmp = t + ((t - x) * ((a - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -1e-225) or not (t_1 <= 5e-154):
		tmp = t_1
	else:
		tmp = t + ((t - x) * ((a - y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-225) || !(t_1 <= 5e-154))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -1e-225) || ~((t_1 <= 5e-154)))
		tmp = t_1;
	else
		tmp = t + ((t - x) * ((a - y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-225], N[Not[LessEqual[t$95$1, 5e-154]], $MachinePrecision]], t$95$1, N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999996e-226 or 5.0000000000000002e-154 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 95.0%

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

   if -9.9999999999999996e-226 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5.0000000000000002e-154

   1. Initial program 6.1%

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

   3. Taylor expanded in z around inf 72.7%

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

      1. associate--l+ 72.7%

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

      2. distribute-lft-out-- 72.7%

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

      3. div-sub 72.8%

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

      4. mul-1-neg 72.8%

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

      5. unsub-neg 72.8%

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

      6. distribute-rgt-out-- 72.8%

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

      7. associate-/l* 92.3%

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

   5. Simplified 92.3%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-225} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 5 \cdot 10^{-154}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 42.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+134}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-82}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-148}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-284}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-252}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-47}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ z (- z a)))))
   (if (<= z -1.25e+134)
     t_1
     (if (<= z -1.8e+16)
       (* t (/ y (- a z)))
       (if (<= z -8e-82)
         (/ (* x y) z)
         (if (<= z -7.5e-148)
           x
           (if (<= z 3.3e-284)
             (/ y (/ a (- t x)))
             (if (<= z 6.8e-252)
               x
               (if (<= z 8.6e-47) (* y (/ (- t x) a)) t_1)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (z / (z - a));
	double tmp;
	if (z <= -1.25e+134) {
		tmp = t_1;
	} else if (z <= -1.8e+16) {
		tmp = t * (y / (a - z));
	} else if (z <= -8e-82) {
		tmp = (x * y) / z;
	} else if (z <= -7.5e-148) {
		tmp = x;
	} else if (z <= 3.3e-284) {
		tmp = y / (a / (t - x));
	} else if (z <= 6.8e-252) {
		tmp = x;
	} else if (z <= 8.6e-47) {
		tmp = y * ((t - x) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (z / (z - a))
    if (z <= (-1.25d+134)) then
        tmp = t_1
    else if (z <= (-1.8d+16)) then
        tmp = t * (y / (a - z))
    else if (z <= (-8d-82)) then
        tmp = (x * y) / z
    else if (z <= (-7.5d-148)) then
        tmp = x
    else if (z <= 3.3d-284) then
        tmp = y / (a / (t - x))
    else if (z <= 6.8d-252) then
        tmp = x
    else if (z <= 8.6d-47) then
        tmp = y * ((t - x) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (z / (z - a));
	double tmp;
	if (z <= -1.25e+134) {
		tmp = t_1;
	} else if (z <= -1.8e+16) {
		tmp = t * (y / (a - z));
	} else if (z <= -8e-82) {
		tmp = (x * y) / z;
	} else if (z <= -7.5e-148) {
		tmp = x;
	} else if (z <= 3.3e-284) {
		tmp = y / (a / (t - x));
	} else if (z <= 6.8e-252) {
		tmp = x;
	} else if (z <= 8.6e-47) {
		tmp = y * ((t - x) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (z / (z - a))
	tmp = 0
	if z <= -1.25e+134:
		tmp = t_1
	elif z <= -1.8e+16:
		tmp = t * (y / (a - z))
	elif z <= -8e-82:
		tmp = (x * y) / z
	elif z <= -7.5e-148:
		tmp = x
	elif z <= 3.3e-284:
		tmp = y / (a / (t - x))
	elif z <= 6.8e-252:
		tmp = x
	elif z <= 8.6e-47:
		tmp = y * ((t - x) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(z / Float64(z - a)))
	tmp = 0.0
	if (z <= -1.25e+134)
		tmp = t_1;
	elseif (z <= -1.8e+16)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= -8e-82)
		tmp = Float64(Float64(x * y) / z);
	elseif (z <= -7.5e-148)
		tmp = x;
	elseif (z <= 3.3e-284)
		tmp = Float64(y / Float64(a / Float64(t - x)));
	elseif (z <= 6.8e-252)
		tmp = x;
	elseif (z <= 8.6e-47)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (z / (z - a));
	tmp = 0.0;
	if (z <= -1.25e+134)
		tmp = t_1;
	elseif (z <= -1.8e+16)
		tmp = t * (y / (a - z));
	elseif (z <= -8e-82)
		tmp = (x * y) / z;
	elseif (z <= -7.5e-148)
		tmp = x;
	elseif (z <= 3.3e-284)
		tmp = y / (a / (t - x));
	elseif (z <= 6.8e-252)
		tmp = x;
	elseif (z <= 8.6e-47)
		tmp = y * ((t - x) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e+134], t$95$1, If[LessEqual[z, -1.8e+16], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8e-82], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -7.5e-148], x, If[LessEqual[z, 3.3e-284], N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e-252], x, If[LessEqual[z, 8.6e-47], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.24999999999999995e134 or 8.5999999999999995e-47 < z

   1. Initial program 69.3%

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

   3. Taylor expanded in x around 0 43.9%

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

      1. associate-/l* 65.7%

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

   5. Simplified 65.7%

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

   6. Taylor expanded in y around 0 54.6%

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

      1. neg-mul-1 54.6%

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

      2. distribute-neg-frac2 54.6%

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

   8. Simplified 54.6%

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

   if -1.24999999999999995e134 < z < -1.8e16

   1. Initial program 85.9%

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

   3. Taylor expanded in x around 0 47.9%

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

      1. associate-/l* 48.3%

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

   5. Simplified 48.3%

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

   6. Taylor expanded in y around inf 36.5%

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

      1. associate-/l* 36.5%

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

   8. Simplified 36.5%

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

   if -1.8e16 < z < -8e-82

   1. Initial program 94.3%

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

   3. Taylor expanded in y around inf 55.0%

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

      1. div-sub 55.0%

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

   5. Simplified 55.0%

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

   6. Taylor expanded in t around 0 42.8%

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

      1. neg-mul-1 42.8%

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

      2. distribute-neg-frac 42.8%

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

   8. Simplified 42.8%

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

   9. Taylor expanded in a around 0 43.5%

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

   if -8e-82 < z < -7.5000000000000005e-148 or 3.30000000000000008e-284 < z < 6.7999999999999999e-252

   1. Initial program 90.3%

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

   3. Taylor expanded in a around inf 66.7%

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

   if -7.5000000000000005e-148 < z < 3.30000000000000008e-284

   1. Initial program 97.3%

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

   3. Taylor expanded in y around inf 67.7%

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

      1. div-sub 70.2%

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

   5. Simplified 70.2%

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

      1. clear-num 70.2%

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

      2. un-div-inv 70.3%

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

   7. Applied egg-rr 70.3%

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

   8. Taylor expanded in a around inf 67.8%

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

   if 6.7999999999999999e-252 < z < 8.5999999999999995e-47

   1. Initial program 91.2%

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

   3. Taylor expanded in y around inf 63.3%

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

      1. div-sub 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in a around inf 52.5%

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

      1. associate-*r/ 60.7%

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

   8. Simplified 60.7%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+134}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-82}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-148}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-284}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-252}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-47}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 46.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+107}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.1 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq -0.0024:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+214}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.5e+107)
   x
   (if (<= a -5.1e+39)
     (* x (/ y (- z a)))
     (if (<= a -0.0024)
       x
       (if (<= a 1.7e-7)
         (* t (/ (- z y) z))
         (if (<= a 8.5e+214) (/ y (/ a (- t x))) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.5e+107) {
		tmp = x;
	} else if (a <= -5.1e+39) {
		tmp = x * (y / (z - a));
	} else if (a <= -0.0024) {
		tmp = x;
	} else if (a <= 1.7e-7) {
		tmp = t * ((z - y) / z);
	} else if (a <= 8.5e+214) {
		tmp = y / (a / (t - 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+107)) then
        tmp = x
    else if (a <= (-5.1d+39)) then
        tmp = x * (y / (z - a))
    else if (a <= (-0.0024d0)) then
        tmp = x
    else if (a <= 1.7d-7) then
        tmp = t * ((z - y) / z)
    else if (a <= 8.5d+214) then
        tmp = y / (a / (t - 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+107) {
		tmp = x;
	} else if (a <= -5.1e+39) {
		tmp = x * (y / (z - a));
	} else if (a <= -0.0024) {
		tmp = x;
	} else if (a <= 1.7e-7) {
		tmp = t * ((z - y) / z);
	} else if (a <= 8.5e+214) {
		tmp = y / (a / (t - x));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.5e+107:
		tmp = x
	elif a <= -5.1e+39:
		tmp = x * (y / (z - a))
	elif a <= -0.0024:
		tmp = x
	elif a <= 1.7e-7:
		tmp = t * ((z - y) / z)
	elif a <= 8.5e+214:
		tmp = y / (a / (t - x))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.5e+107)
		tmp = x;
	elseif (a <= -5.1e+39)
		tmp = Float64(x * Float64(y / Float64(z - a)));
	elseif (a <= -0.0024)
		tmp = x;
	elseif (a <= 1.7e-7)
		tmp = Float64(t * Float64(Float64(z - y) / z));
	elseif (a <= 8.5e+214)
		tmp = Float64(y / Float64(a / Float64(t - 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+107)
		tmp = x;
	elseif (a <= -5.1e+39)
		tmp = x * (y / (z - a));
	elseif (a <= -0.0024)
		tmp = x;
	elseif (a <= 1.7e-7)
		tmp = t * ((z - y) / z);
	elseif (a <= 8.5e+214)
		tmp = y / (a / (t - x));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.5e+107], x, If[LessEqual[a, -5.1e+39], N[(x * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -0.0024], x, If[LessEqual[a, 1.7e-7], N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e+214], N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.50000000000000012e107 or -5.0999999999999998e39 < a < -0.00239999999999999979 or 8.50000000000000045e214 < a

   1. Initial program 95.6%

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

   3. Taylor expanded in a around inf 56.8%

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

   if -1.50000000000000012e107 < a < -5.0999999999999998e39

   1. Initial program 80.4%

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

   3. Taylor expanded in y around inf 50.9%

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

      1. div-sub 50.9%

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

   5. Simplified 50.9%

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

   6. Taylor expanded in t around 0 37.8%

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

      1. mul-1-neg 37.8%

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

      2. associate-/l* 39.6%

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

      3. distribute-rgt-neg-in 39.6%

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

      4. distribute-neg-frac2 39.6%

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

   8. Simplified 39.6%

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

   if -0.00239999999999999979 < a < 1.69999999999999987e-7

   1. Initial program 73.6%

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

   3. Taylor expanded in x around 0 53.1%

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

      1. associate-/l* 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in a around 0 59.9%

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

      1. associate-*r/ 59.9%

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

      2. neg-mul-1 59.9%

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

   8. Simplified 59.9%

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

   if 1.69999999999999987e-7 < a < 8.50000000000000045e214

   1. Initial program 80.3%

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

   3. Taylor expanded in y around inf 60.7%

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

      1. div-sub 60.7%

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

   5. Simplified 60.7%

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

      1. clear-num 60.7%

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

      2. un-div-inv 60.8%

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

   7. Applied egg-rr 60.8%

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

   8. Taylor expanded in a around inf 50.3%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+107}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.1 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq -0.0024:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+214}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 46.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{+107}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{+38}:\\ \;\;\;\;\frac{y}{\frac{z - a}{x}}\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{+214}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.95e+107)
   x
   (if (<= a -5.2e+38)
     (/ y (/ (- z a) x))
     (if (<= a -2.9e-5)
       x
       (if (<= a 4.5e-8)
         (* t (/ (- z y) z))
         (if (<= a 3.05e+214) (/ y (/ a (- t x))) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.95e+107) {
		tmp = x;
	} else if (a <= -5.2e+38) {
		tmp = y / ((z - a) / x);
	} else if (a <= -2.9e-5) {
		tmp = x;
	} else if (a <= 4.5e-8) {
		tmp = t * ((z - y) / z);
	} else if (a <= 3.05e+214) {
		tmp = y / (a / (t - 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 <= (-1.95d+107)) then
        tmp = x
    else if (a <= (-5.2d+38)) then
        tmp = y / ((z - a) / x)
    else if (a <= (-2.9d-5)) then
        tmp = x
    else if (a <= 4.5d-8) then
        tmp = t * ((z - y) / z)
    else if (a <= 3.05d+214) then
        tmp = y / (a / (t - 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 <= -1.95e+107) {
		tmp = x;
	} else if (a <= -5.2e+38) {
		tmp = y / ((z - a) / x);
	} else if (a <= -2.9e-5) {
		tmp = x;
	} else if (a <= 4.5e-8) {
		tmp = t * ((z - y) / z);
	} else if (a <= 3.05e+214) {
		tmp = y / (a / (t - x));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.95e+107:
		tmp = x
	elif a <= -5.2e+38:
		tmp = y / ((z - a) / x)
	elif a <= -2.9e-5:
		tmp = x
	elif a <= 4.5e-8:
		tmp = t * ((z - y) / z)
	elif a <= 3.05e+214:
		tmp = y / (a / (t - x))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.95e+107)
		tmp = x;
	elseif (a <= -5.2e+38)
		tmp = Float64(y / Float64(Float64(z - a) / x));
	elseif (a <= -2.9e-5)
		tmp = x;
	elseif (a <= 4.5e-8)
		tmp = Float64(t * Float64(Float64(z - y) / z));
	elseif (a <= 3.05e+214)
		tmp = Float64(y / Float64(a / Float64(t - x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.95e+107)
		tmp = x;
	elseif (a <= -5.2e+38)
		tmp = y / ((z - a) / x);
	elseif (a <= -2.9e-5)
		tmp = x;
	elseif (a <= 4.5e-8)
		tmp = t * ((z - y) / z);
	elseif (a <= 3.05e+214)
		tmp = y / (a / (t - x));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.95e+107], x, If[LessEqual[a, -5.2e+38], N[(y / N[(N[(z - a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.9e-5], x, If[LessEqual[a, 4.5e-8], N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.05e+214], N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.9499999999999999e107 or -5.1999999999999998e38 < a < -2.9e-5 or 3.05000000000000018e214 < a

   1. Initial program 95.6%

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

   3. Taylor expanded in a around inf 56.8%

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

   if -1.9499999999999999e107 < a < -5.1999999999999998e38

   1. Initial program 80.4%

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

   3. Taylor expanded in y around inf 50.9%

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

      1. div-sub 50.9%

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

   5. Simplified 50.9%

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

      1. clear-num 50.8%

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

      2. un-div-inv 51.2%

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

   7. Applied egg-rr 51.2%

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

   8. Taylor expanded in t around 0 39.7%

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

      1. associate-*r/ 39.7%

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

      2. neg-mul-1 39.7%

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

   10. Simplified 39.7%

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

   if -2.9e-5 < a < 4.49999999999999993e-8

   1. Initial program 73.6%

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

   3. Taylor expanded in x around 0 53.1%

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

      1. associate-/l* 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in a around 0 59.9%

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

      1. associate-*r/ 59.9%

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

      2. neg-mul-1 59.9%

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

   8. Simplified 59.9%

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

   if 4.49999999999999993e-8 < a < 3.05000000000000018e214

   1. Initial program 80.3%

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

   3. Taylor expanded in y around inf 60.7%

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

      1. div-sub 60.7%

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

   5. Simplified 60.7%

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

      1. clear-num 60.7%

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

      2. un-div-inv 60.8%

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

   7. Applied egg-rr 60.8%

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

   8. Taylor expanded in a around inf 50.3%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{+107}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{+38}:\\ \;\;\;\;\frac{y}{\frac{z - a}{x}}\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{+214}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+182}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+132}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+27} \lor \neg \left(x \leq 7.4 \cdot 10^{+96}\right):\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -7.5e+182)
   (* y (/ (- t x) (- a z)))
   (if (<= x -2.8e+132)
     (* t (/ (- z y) z))
     (if (or (<= x -5e+27) (not (<= x 7.4e+96)))
       (+ x (/ (* y (- t x)) a))
       (* t (/ (- y z) (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -7.5e+182) {
		tmp = y * ((t - x) / (a - z));
	} else if (x <= -2.8e+132) {
		tmp = t * ((z - y) / z);
	} else if ((x <= -5e+27) || !(x <= 7.4e+96)) {
		tmp = x + ((y * (t - x)) / a);
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-7.5d+182)) then
        tmp = y * ((t - x) / (a - z))
    else if (x <= (-2.8d+132)) then
        tmp = t * ((z - y) / z)
    else if ((x <= (-5d+27)) .or. (.not. (x <= 7.4d+96))) then
        tmp = x + ((y * (t - x)) / a)
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -7.5e+182) {
		tmp = y * ((t - x) / (a - z));
	} else if (x <= -2.8e+132) {
		tmp = t * ((z - y) / z);
	} else if ((x <= -5e+27) || !(x <= 7.4e+96)) {
		tmp = x + ((y * (t - x)) / a);
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -7.5e+182:
		tmp = y * ((t - x) / (a - z))
	elif x <= -2.8e+132:
		tmp = t * ((z - y) / z)
	elif (x <= -5e+27) or not (x <= 7.4e+96):
		tmp = x + ((y * (t - x)) / a)
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -7.5e+182)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (x <= -2.8e+132)
		tmp = Float64(t * Float64(Float64(z - y) / z));
	elseif ((x <= -5e+27) || !(x <= 7.4e+96))
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -7.5e+182)
		tmp = y * ((t - x) / (a - z));
	elseif (x <= -2.8e+132)
		tmp = t * ((z - y) / z);
	elseif ((x <= -5e+27) || ~((x <= 7.4e+96)))
		tmp = x + ((y * (t - x)) / a);
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -7.5e+182], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.8e+132], N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -5e+27], N[Not[LessEqual[x, 7.4e+96]], $MachinePrecision]], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.49999999999999989e182

   1. Initial program 72.2%

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

   3. Taylor expanded in y around inf 51.5%

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

      1. div-sub 54.4%

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

   5. Simplified 54.4%

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

   if -7.49999999999999989e182 < x < -2.7999999999999999e132

   1. Initial program 64.2%

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

   3. Taylor expanded in x around 0 45.3%

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

      1. associate-/l* 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in a around 0 72.3%

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

      1. associate-*r/ 72.3%

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

      2. neg-mul-1 72.3%

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

   8. Simplified 72.3%

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

   if -2.7999999999999999e132 < x < -4.99999999999999979e27 or 7.39999999999999982e96 < x

   1. Initial program 78.8%

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

   3. Taylor expanded in z around 0 62.3%

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

   if -4.99999999999999979e27 < x < 7.39999999999999982e96

   1. Initial program 86.7%

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

   3. Taylor expanded in x around 0 61.4%

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

      1. associate-/l* 78.7%

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

   5. Simplified 78.7%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+182}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+132}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+27} \lor \neg \left(x \leq 7.4 \cdot 10^{+96}\right):\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 35.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-9}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \frac{y}{-a}\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{+214}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.2e+20)
   x
   (if (<= a 2.4e-9)
     t
     (if (<= a 1.15e+93)
       (* x (/ y (- a)))
       (if (<= a 3.05e+214) (* t (/ y (- a z))) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.2e+20) {
		tmp = x;
	} else if (a <= 2.4e-9) {
		tmp = t;
	} else if (a <= 1.15e+93) {
		tmp = x * (y / -a);
	} else if (a <= 3.05e+214) {
		tmp = t * (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) :: tmp
    if (a <= (-9.2d+20)) then
        tmp = x
    else if (a <= 2.4d-9) then
        tmp = t
    else if (a <= 1.15d+93) then
        tmp = x * (y / -a)
    else if (a <= 3.05d+214) then
        tmp = t * (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 tmp;
	if (a <= -9.2e+20) {
		tmp = x;
	} else if (a <= 2.4e-9) {
		tmp = t;
	} else if (a <= 1.15e+93) {
		tmp = x * (y / -a);
	} else if (a <= 3.05e+214) {
		tmp = t * (y / (a - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.2e+20:
		tmp = x
	elif a <= 2.4e-9:
		tmp = t
	elif a <= 1.15e+93:
		tmp = x * (y / -a)
	elif a <= 3.05e+214:
		tmp = t * (y / (a - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.2e+20)
		tmp = x;
	elseif (a <= 2.4e-9)
		tmp = t;
	elseif (a <= 1.15e+93)
		tmp = Float64(x * Float64(y / Float64(-a)));
	elseif (a <= 3.05e+214)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.2e+20)
		tmp = x;
	elseif (a <= 2.4e-9)
		tmp = t;
	elseif (a <= 1.15e+93)
		tmp = x * (y / -a);
	elseif (a <= 3.05e+214)
		tmp = t * (y / (a - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.2e+20], x, If[LessEqual[a, 2.4e-9], t, If[LessEqual[a, 1.15e+93], N[(x * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.05e+214], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.2e20 or 3.05000000000000018e214 < a

   1. Initial program 92.4%

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

   3. Taylor expanded in a around inf 48.9%

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

   if -9.2e20 < a < 2.4e-9

   1. Initial program 74.3%

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

   3. Taylor expanded in z around inf 45.8%

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

   if 2.4e-9 < a < 1.1500000000000001e93

   1. Initial program 81.1%

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

   3. Taylor expanded in y around inf 64.8%

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

      1. div-sub 64.8%

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

   5. Simplified 64.8%

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

   6. Taylor expanded in a around inf 51.9%

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

      1. associate-*r/ 57.7%

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

   8. Simplified 57.7%

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

   9. Taylor expanded in t around 0 38.9%

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

       1. mul-1-neg 38.9%

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

       2. associate-/l* 44.7%

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

       3. distribute-rgt-neg-in 44.7%

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

   11. Simplified 44.7%

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

   if 1.1500000000000001e93 < a < 3.05000000000000018e214

   1. Initial program 79.4%

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

   3. Taylor expanded in x around 0 43.4%

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

      1. associate-/l* 55.3%

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

   5. Simplified 55.3%

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

   6. Taylor expanded in y around inf 43.7%

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

      1. associate-/l* 51.5%

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

   8. Simplified 51.5%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-9}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \frac{y}{-a}\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{+214}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{-101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= t -1.45e-101)
     t_1
     (if (<= t 1.8e-209) (* x (/ y (- z a))) (if (<= t 1.1e-96) x 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 <= -1.45e-101) {
		tmp = t_1;
	} else if (t <= 1.8e-209) {
		tmp = x * (y / (z - a));
	} else if (t <= 1.1e-96) {
		tmp = 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) / (a - z))
    if (t <= (-1.45d-101)) then
        tmp = t_1
    else if (t <= 1.8d-209) then
        tmp = x * (y / (z - a))
    else if (t <= 1.1d-96) then
        tmp = 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) / (a - z));
	double tmp;
	if (t <= -1.45e-101) {
		tmp = t_1;
	} else if (t <= 1.8e-209) {
		tmp = x * (y / (z - a));
	} else if (t <= 1.1e-96) {
		tmp = x;
	} 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 <= -1.45e-101:
		tmp = t_1
	elif t <= 1.8e-209:
		tmp = x * (y / (z - a))
	elif t <= 1.1e-96:
		tmp = x
	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 <= -1.45e-101)
		tmp = t_1;
	elseif (t <= 1.8e-209)
		tmp = Float64(x * Float64(y / Float64(z - a)));
	elseif (t <= 1.1e-96)
		tmp = x;
	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 <= -1.45e-101)
		tmp = t_1;
	elseif (t <= 1.8e-209)
		tmp = x * (y / (z - a));
	elseif (t <= 1.1e-96)
		tmp = 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[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.45e-101], t$95$1, If[LessEqual[t, 1.8e-209], N[(x * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e-96], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.45e-101 or 1.0999999999999999e-96 < t

   1. Initial program 87.1%

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

   3. Taylor expanded in x around 0 52.4%

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

      1. associate-/l* 69.5%

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

   5. Simplified 69.5%

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

   if -1.45e-101 < t < 1.80000000000000008e-209

   1. Initial program 65.2%

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

   3. Taylor expanded in y around inf 53.6%

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

      1. div-sub 53.6%

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

   5. Simplified 53.6%

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

   6. Taylor expanded in t around 0 46.4%

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

      1. mul-1-neg 46.4%

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

      2. associate-/l* 51.9%

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

      3. distribute-rgt-neg-in 51.9%

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

      4. distribute-neg-frac2 51.9%

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

   8. Simplified 51.9%

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

   if 1.80000000000000008e-209 < t < 1.0999999999999999e-96

   1. Initial program 74.8%

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

   3. Taylor expanded in a around inf 59.6%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-101}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{-96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-210}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= t -4.6e-96)
     t_1
     (if (<= t 8.5e-210)
       (* y (/ (- t x) (- a z)))
       (if (<= t 1.02e-96) x 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 <= -4.6e-96) {
		tmp = t_1;
	} else if (t <= 8.5e-210) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= 1.02e-96) {
		tmp = 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) / (a - z))
    if (t <= (-4.6d-96)) then
        tmp = t_1
    else if (t <= 8.5d-210) then
        tmp = y * ((t - x) / (a - z))
    else if (t <= 1.02d-96) then
        tmp = 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) / (a - z));
	double tmp;
	if (t <= -4.6e-96) {
		tmp = t_1;
	} else if (t <= 8.5e-210) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= 1.02e-96) {
		tmp = x;
	} 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 <= -4.6e-96:
		tmp = t_1
	elif t <= 8.5e-210:
		tmp = y * ((t - x) / (a - z))
	elif t <= 1.02e-96:
		tmp = x
	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 <= -4.6e-96)
		tmp = t_1;
	elseif (t <= 8.5e-210)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (t <= 1.02e-96)
		tmp = x;
	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 <= -4.6e-96)
		tmp = t_1;
	elseif (t <= 8.5e-210)
		tmp = y * ((t - x) / (a - z));
	elseif (t <= 1.02e-96)
		tmp = 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[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.6e-96], t$95$1, If[LessEqual[t, 8.5e-210], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.02e-96], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.6e-96 or 1.02000000000000007e-96 < t

   1. Initial program 87.0%

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

   3. Taylor expanded in x around 0 52.2%

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

      1. associate-/l* 69.3%

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

   5. Simplified 69.3%

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

   if -4.6e-96 < t < 8.4999999999999997e-210

   1. Initial program 65.8%

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

   3. Taylor expanded in y around inf 54.4%

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

      1. div-sub 54.4%

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

   5. Simplified 54.4%

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

   if 8.4999999999999997e-210 < t < 1.02000000000000007e-96

   1. Initial program 74.8%

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

   3. Taylor expanded in a around inf 59.6%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-96}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-210}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{if}\;a \leq -0.46:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-132}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+126}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ a t)))))
   (if (<= a -0.46)
     t_1
     (if (<= a 2.6e-132)
       (* t (/ (- y z) (- a z)))
       (if (<= a 3.9e+126) (* y (/ (- t x) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / (a / t));
	double tmp;
	if (a <= -0.46) {
		tmp = t_1;
	} else if (a <= 2.6e-132) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 3.9e+126) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) / (a / t))
    if (a <= (-0.46d0)) then
        tmp = t_1
    else if (a <= 2.6d-132) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= 3.9d+126) then
        tmp = y * ((t - x) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / (a / t));
	double tmp;
	if (a <= -0.46) {
		tmp = t_1;
	} else if (a <= 2.6e-132) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 3.9e+126) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / (a / t))
	tmp = 0
	if a <= -0.46:
		tmp = t_1
	elif a <= 2.6e-132:
		tmp = t * ((y - z) / (a - z))
	elif a <= 3.9e+126:
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(a / t)))
	tmp = 0.0
	if (a <= -0.46)
		tmp = t_1;
	elseif (a <= 2.6e-132)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= 3.9e+126)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) / (a / t));
	tmp = 0.0;
	if (a <= -0.46)
		tmp = t_1;
	elseif (a <= 2.6e-132)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= 3.9e+126)
		tmp = y * ((t - x) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.46], t$95$1, If[LessEqual[a, 2.6e-132], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.9e+126], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -0.46000000000000002 or 3.89999999999999993e126 < a

   1. Initial program 90.0%

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

      1. clear-num 89.9%

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

      2. un-div-inv 90.0%

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

   4. Applied egg-rr 90.0%

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

   5. Taylor expanded in a around inf 78.2%

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

   6. Taylor expanded in t around inf 71.7%

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

   if -0.46000000000000002 < a < 2.6000000000000001e-132

   1. Initial program 74.7%

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

   3. Taylor expanded in x around 0 56.4%

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

      1. associate-/l* 71.9%

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

   5. Simplified 71.9%

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

   if 2.6000000000000001e-132 < a < 3.89999999999999993e126

   1. Initial program 77.4%

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

   3. Taylor expanded in y around inf 61.6%

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

      1. div-sub 61.6%

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

   5. Simplified 61.6%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.46:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-132}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+126}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{if}\;a \leq -1.65:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-127}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+122}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ a t)))))
   (if (<= a -1.65)
     t_1
     (if (<= a 1.1e-127)
       (/ t (/ (- a z) (- y z)))
       (if (<= a 9.5e+122) (* y (/ (- t x) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / (a / t));
	double tmp;
	if (a <= -1.65) {
		tmp = t_1;
	} else if (a <= 1.1e-127) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 9.5e+122) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) / (a / t))
    if (a <= (-1.65d0)) then
        tmp = t_1
    else if (a <= 1.1d-127) then
        tmp = t / ((a - z) / (y - z))
    else if (a <= 9.5d+122) then
        tmp = y * ((t - x) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / (a / t));
	double tmp;
	if (a <= -1.65) {
		tmp = t_1;
	} else if (a <= 1.1e-127) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 9.5e+122) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / (a / t))
	tmp = 0
	if a <= -1.65:
		tmp = t_1
	elif a <= 1.1e-127:
		tmp = t / ((a - z) / (y - z))
	elif a <= 9.5e+122:
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(a / t)))
	tmp = 0.0
	if (a <= -1.65)
		tmp = t_1;
	elseif (a <= 1.1e-127)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (a <= 9.5e+122)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) / (a / t));
	tmp = 0.0;
	if (a <= -1.65)
		tmp = t_1;
	elseif (a <= 1.1e-127)
		tmp = t / ((a - z) / (y - z));
	elseif (a <= 9.5e+122)
		tmp = y * ((t - x) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.65], t$95$1, If[LessEqual[a, 1.1e-127], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+122], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.6499999999999999 or 9.49999999999999986e122 < a

   1. Initial program 90.0%

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

      1. clear-num 89.9%

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

      2. un-div-inv 90.0%

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

   4. Applied egg-rr 90.0%

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

   5. Taylor expanded in a around inf 78.2%

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

   6. Taylor expanded in t around inf 71.7%

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

   if -1.6499999999999999 < a < 1.1000000000000001e-127

   1. Initial program 74.7%

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

   3. Taylor expanded in x around 0 56.4%

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

      1. associate-/l* 71.9%

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

   5. Simplified 71.9%

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

      1. clear-num 71.9%

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

      2. un-div-inv 71.9%

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

   7. Applied egg-rr 71.9%

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

   if 1.1000000000000001e-127 < a < 9.49999999999999986e122

   1. Initial program 77.4%

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

   3. Taylor expanded in y around inf 61.6%

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

      1. div-sub 61.6%

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

   5. Simplified 61.6%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-127}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+122}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{if}\;a \leq -0.062:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-126}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+154}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ a t)))))
   (if (<= a -0.062)
     t_1
     (if (<= a 2.75e-126)
       (/ t (/ (- a z) (- y z)))
       (if (<= a 8.5e+154) (/ y (/ (- a z) (- t x))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / (a / t));
	double tmp;
	if (a <= -0.062) {
		tmp = t_1;
	} else if (a <= 2.75e-126) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 8.5e+154) {
		tmp = y / ((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 = x + ((y - z) / (a / t))
    if (a <= (-0.062d0)) then
        tmp = t_1
    else if (a <= 2.75d-126) then
        tmp = t / ((a - z) / (y - z))
    else if (a <= 8.5d+154) then
        tmp = y / ((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 = x + ((y - z) / (a / t));
	double tmp;
	if (a <= -0.062) {
		tmp = t_1;
	} else if (a <= 2.75e-126) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 8.5e+154) {
		tmp = y / ((a - z) / (t - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / (a / t))
	tmp = 0
	if a <= -0.062:
		tmp = t_1
	elif a <= 2.75e-126:
		tmp = t / ((a - z) / (y - z))
	elif a <= 8.5e+154:
		tmp = y / ((a - z) / (t - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(a / t)))
	tmp = 0.0
	if (a <= -0.062)
		tmp = t_1;
	elseif (a <= 2.75e-126)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (a <= 8.5e+154)
		tmp = Float64(y / 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 = x + ((y - z) / (a / t));
	tmp = 0.0;
	if (a <= -0.062)
		tmp = t_1;
	elseif (a <= 2.75e-126)
		tmp = t / ((a - z) / (y - z));
	elseif (a <= 8.5e+154)
		tmp = y / ((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[(x + N[(N[(y - z), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.062], t$95$1, If[LessEqual[a, 2.75e-126], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e+154], N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -0.062 or 8.5000000000000002e154 < a

   1. Initial program 90.6%

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

      1. clear-num 90.6%

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

      2. un-div-inv 90.6%

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

   4. Applied egg-rr 90.6%

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

   5. Taylor expanded in a around inf 79.3%

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

   6. Taylor expanded in t around inf 72.5%

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

   if -0.062 < a < 2.74999999999999993e-126

   1. Initial program 74.7%

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

   3. Taylor expanded in x around 0 56.4%

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

      1. associate-/l* 71.9%

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

   5. Simplified 71.9%

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

      1. clear-num 71.9%

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

      2. un-div-inv 71.9%

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

   7. Applied egg-rr 71.9%

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

   if 2.74999999999999993e-126 < a < 8.5000000000000002e154

   1. Initial program 77.2%

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

   3. Taylor expanded in y around inf 60.9%

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

      1. div-sub 60.9%

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

   5. Simplified 60.9%

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

      1. clear-num 60.9%

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

      2. un-div-inv 60.9%

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

   7. Applied egg-rr 60.9%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.062:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-126}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+154}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-134}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+214}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.5e+21)
   x
   (if (<= a 6.5e-134) t (if (<= a 4.5e+214) (* y (/ (- t x) a)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.5e+21) {
		tmp = x;
	} else if (a <= 6.5e-134) {
		tmp = t;
	} else if (a <= 4.5e+214) {
		tmp = y * ((t - x) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.5d+21)) then
        tmp = x
    else if (a <= 6.5d-134) then
        tmp = t
    else if (a <= 4.5d+214) then
        tmp = y * ((t - x) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.5e+21) {
		tmp = x;
	} else if (a <= 6.5e-134) {
		tmp = t;
	} else if (a <= 4.5e+214) {
		tmp = y * ((t - x) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.5e+21:
		tmp = x
	elif a <= 6.5e-134:
		tmp = t
	elif a <= 4.5e+214:
		tmp = y * ((t - x) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.5e+21)
		tmp = x;
	elseif (a <= 6.5e-134)
		tmp = t;
	elseif (a <= 4.5e+214)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.5e+21)
		tmp = x;
	elseif (a <= 6.5e-134)
		tmp = t;
	elseif (a <= 4.5e+214)
		tmp = y * ((t - x) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.5e+21], x, If[LessEqual[a, 6.5e-134], t, If[LessEqual[a, 4.5e+214], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.5e21 or 4.49999999999999968e214 < a

   1. Initial program 92.4%

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

   3. Taylor expanded in a around inf 48.9%

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

   if -3.5e21 < a < 6.4999999999999998e-134

   1. Initial program 75.0%

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

   3. Taylor expanded in z around inf 50.0%

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

   if 6.4999999999999998e-134 < a < 4.49999999999999968e214

   1. Initial program 77.9%

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

   3. Taylor expanded in y around inf 58.9%

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

      1. div-sub 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in a around inf 42.6%

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

      1. associate-*r/ 45.0%

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

   8. Simplified 45.0%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-134}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+214}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-135}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{+214}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.45e+22)
   x
   (if (<= a 4.5e-135) t (if (<= a 3.05e+214) (/ y (/ a (- t x))) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.45e+22) {
		tmp = x;
	} else if (a <= 4.5e-135) {
		tmp = t;
	} else if (a <= 3.05e+214) {
		tmp = y / (a / (t - 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 <= (-2.45d+22)) then
        tmp = x
    else if (a <= 4.5d-135) then
        tmp = t
    else if (a <= 3.05d+214) then
        tmp = y / (a / (t - 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 <= -2.45e+22) {
		tmp = x;
	} else if (a <= 4.5e-135) {
		tmp = t;
	} else if (a <= 3.05e+214) {
		tmp = y / (a / (t - x));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.45e+22:
		tmp = x
	elif a <= 4.5e-135:
		tmp = t
	elif a <= 3.05e+214:
		tmp = y / (a / (t - x))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.45e+22)
		tmp = x;
	elseif (a <= 4.5e-135)
		tmp = t;
	elseif (a <= 3.05e+214)
		tmp = Float64(y / Float64(a / Float64(t - x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.45e+22)
		tmp = x;
	elseif (a <= 4.5e-135)
		tmp = t;
	elseif (a <= 3.05e+214)
		tmp = y / (a / (t - x));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.45e+22], x, If[LessEqual[a, 4.5e-135], t, If[LessEqual[a, 3.05e+214], N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.4499999999999999e22 or 3.05000000000000018e214 < a

   1. Initial program 92.4%

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

   3. Taylor expanded in a around inf 48.9%

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

   if -2.4499999999999999e22 < a < 4.49999999999999987e-135

   1. Initial program 75.0%

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

   3. Taylor expanded in z around inf 50.0%

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

   if 4.49999999999999987e-135 < a < 3.05000000000000018e214

   1. Initial program 77.9%

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

   3. Taylor expanded in y around inf 58.9%

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

      1. div-sub 58.9%

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

   5. Simplified 58.9%

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

      1. clear-num 58.9%

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

      2. un-div-inv 58.9%

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

   7. Applied egg-rr 58.9%

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

   8. Taylor expanded in a around inf 45.0%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-135}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{+214}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 46.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.0024:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+214}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -0.0024)
   x
   (if (<= a 1.15e-8)
     (* t (/ (- z y) z))
     (if (<= a 7.2e+214) (/ y (/ a (- t x))) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.0024) {
		tmp = x;
	} else if (a <= 1.15e-8) {
		tmp = t * ((z - y) / z);
	} else if (a <= 7.2e+214) {
		tmp = y / (a / (t - 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 <= (-0.0024d0)) then
        tmp = x
    else if (a <= 1.15d-8) then
        tmp = t * ((z - y) / z)
    else if (a <= 7.2d+214) then
        tmp = y / (a / (t - 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 <= -0.0024) {
		tmp = x;
	} else if (a <= 1.15e-8) {
		tmp = t * ((z - y) / z);
	} else if (a <= 7.2e+214) {
		tmp = y / (a / (t - x));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -0.0024:
		tmp = x
	elif a <= 1.15e-8:
		tmp = t * ((z - y) / z)
	elif a <= 7.2e+214:
		tmp = y / (a / (t - x))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -0.0024)
		tmp = x;
	elseif (a <= 1.15e-8)
		tmp = Float64(t * Float64(Float64(z - y) / z));
	elseif (a <= 7.2e+214)
		tmp = Float64(y / Float64(a / Float64(t - x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -0.0024)
		tmp = x;
	elseif (a <= 1.15e-8)
		tmp = t * ((z - y) / z);
	elseif (a <= 7.2e+214)
		tmp = y / (a / (t - x));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -0.0024], x, If[LessEqual[a, 1.15e-8], N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.2e+214], N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -0.00239999999999999979 or 7.2000000000000002e214 < a

   1. Initial program 92.6%

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

   3. Taylor expanded in a around inf 48.4%

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

   if -0.00239999999999999979 < a < 1.15e-8

   1. Initial program 73.6%

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

   3. Taylor expanded in x around 0 53.1%

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

      1. associate-/l* 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in a around 0 59.9%

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

      1. associate-*r/ 59.9%

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

      2. neg-mul-1 59.9%

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

   8. Simplified 59.9%

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

   if 1.15e-8 < a < 7.2000000000000002e214

   1. Initial program 80.3%

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

   3. Taylor expanded in y around inf 60.7%

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

      1. div-sub 60.7%

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

   5. Simplified 60.7%

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

      1. clear-num 60.7%

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

      2. un-div-inv 60.8%

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

   7. Applied egg-rr 60.8%

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

   8. Taylor expanded in a around inf 50.3%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0024:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+214}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 37.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-7}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+100}:\\ \;\;\;\;x \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.6e+20)
   x
   (if (<= a 1.4e-7) t (if (<= a 1.25e+100) (* x (/ y (- a))) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.6e+20) {
		tmp = x;
	} else if (a <= 1.4e-7) {
		tmp = t;
	} else if (a <= 1.25e+100) {
		tmp = x * (y / -a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.6d+20)) then
        tmp = x
    else if (a <= 1.4d-7) then
        tmp = t
    else if (a <= 1.25d+100) then
        tmp = x * (y / -a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.6e+20) {
		tmp = x;
	} else if (a <= 1.4e-7) {
		tmp = t;
	} else if (a <= 1.25e+100) {
		tmp = x * (y / -a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.6e+20:
		tmp = x
	elif a <= 1.4e-7:
		tmp = t
	elif a <= 1.25e+100:
		tmp = x * (y / -a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.6e+20)
		tmp = x;
	elseif (a <= 1.4e-7)
		tmp = t;
	elseif (a <= 1.25e+100)
		tmp = Float64(x * Float64(y / Float64(-a)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.6e+20)
		tmp = x;
	elseif (a <= 1.4e-7)
		tmp = t;
	elseif (a <= 1.25e+100)
		tmp = x * (y / -a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.6e+20], x, If[LessEqual[a, 1.4e-7], t, If[LessEqual[a, 1.25e+100], N[(x * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.6e20 or 1.25e100 < a

   1. Initial program 89.3%

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

   3. Taylor expanded in a around inf 44.4%

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

   if -4.6e20 < a < 1.4000000000000001e-7

   1. Initial program 74.3%

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

   3. Taylor expanded in z around inf 45.8%

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

   if 1.4000000000000001e-7 < a < 1.25e100

   1. Initial program 81.7%

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

   3. Taylor expanded in y around inf 65.9%

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

      1. div-sub 65.9%

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

   5. Simplified 65.9%

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

   6. Taylor expanded in a around inf 50.7%

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

      1. associate-*r/ 56.3%

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

   8. Simplified 56.3%

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

   9. Taylor expanded in t around 0 37.8%

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

       1. mul-1-neg 37.8%

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

       2. associate-/l* 43.4%

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

       3. distribute-rgt-neg-in 43.4%

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

   11. Simplified 43.4%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-7}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+100}:\\ \;\;\;\;x \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 67.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.145 \lor \neg \left(a \leq 4.8 \cdot 10^{-17}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -0.145) (not (<= a 4.8e-17)))
   (+ x (/ (- y z) (/ a (- t x))))
   (/ t (/ (- a z) (- y z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.145) || !(a <= 4.8e-17)) {
		tmp = x + ((y - z) / (a / (t - x)));
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-0.145d0)) .or. (.not. (a <= 4.8d-17))) then
        tmp = x + ((y - z) / (a / (t - x)))
    else
        tmp = t / ((a - z) / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.145) || !(a <= 4.8e-17)) {
		tmp = x + ((y - z) / (a / (t - x)));
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -0.145) or not (a <= 4.8e-17):
		tmp = x + ((y - z) / (a / (t - x)))
	else:
		tmp = t / ((a - z) / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -0.145) || !(a <= 4.8e-17))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -0.145) || ~((a <= 4.8e-17)))
		tmp = x + ((y - z) / (a / (t - x)));
	else
		tmp = t / ((a - z) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -0.145], N[Not[LessEqual[a, 4.8e-17]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -0.14499999999999999 or 4.79999999999999973e-17 < a

   1. Initial program 87.2%

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

      1. clear-num 87.3%

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

      2. un-div-inv 87.3%

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

   4. Applied egg-rr 87.3%

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

   5. Taylor expanded in a around inf 74.2%

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

   if -0.14499999999999999 < a < 4.79999999999999973e-17

   1. Initial program 74.3%

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

   3. Taylor expanded in x around 0 54.3%

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

      1. associate-/l* 68.4%

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

   5. Simplified 68.4%

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

      1. clear-num 68.4%

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

      2. un-div-inv 68.4%

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

   7. Applied egg-rr 68.4%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.145 \lor \neg \left(a \leq 4.8 \cdot 10^{-17}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 75.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.000145 \lor \neg \left(a \leq 5.4 \cdot 10^{-21}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -0.000145) (not (<= a 5.4e-21)))
   (+ x (/ (- y z) (/ a (- t x))))
   (+ t (* (- t x) (/ (- a y) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.000145) || !(a <= 5.4e-21)) {
		tmp = x + ((y - z) / (a / (t - x)));
	} else {
		tmp = t + ((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) :: tmp
    if ((a <= (-0.000145d0)) .or. (.not. (a <= 5.4d-21))) then
        tmp = x + ((y - z) / (a / (t - x)))
    else
        tmp = t + ((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 tmp;
	if ((a <= -0.000145) || !(a <= 5.4e-21)) {
		tmp = x + ((y - z) / (a / (t - x)));
	} else {
		tmp = t + ((t - x) * ((a - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -0.000145) or not (a <= 5.4e-21):
		tmp = x + ((y - z) / (a / (t - x)))
	else:
		tmp = t + ((t - x) * ((a - y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -0.000145) || !(a <= 5.4e-21))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -0.000145) || ~((a <= 5.4e-21)))
		tmp = x + ((y - z) / (a / (t - x)));
	else
		tmp = t + ((t - x) * ((a - y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -0.000145], N[Not[LessEqual[a, 5.4e-21]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.45e-4 or 5.4000000000000002e-21 < a

   1. Initial program 87.3%

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

      1. clear-num 87.4%

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

      2. un-div-inv 87.4%

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

   4. Applied egg-rr 87.4%

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

   5. Taylor expanded in a around inf 74.3%

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

   if -1.45e-4 < a < 5.4000000000000002e-21

   1. Initial program 74.0%

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

   3. Taylor expanded in z around inf 80.3%

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

      1. associate--l+ 80.3%

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

      2. distribute-lft-out-- 80.3%

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

      3. div-sub 81.2%

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

      4. mul-1-neg 81.2%

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

      5. unsub-neg 81.2%

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

      6. distribute-rgt-out-- 81.2%

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

      7. associate-/l* 85.5%

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

   5. Simplified 85.5%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.000145 \lor \neg \left(a \leq 5.4 \cdot 10^{-21}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 36.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+75}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{+214}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.5e+23)
   x
   (if (<= a 6e+75) t (if (<= a 3.05e+214) (* t (/ y a)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.5e+23) {
		tmp = x;
	} else if (a <= 6e+75) {
		tmp = t;
	} else if (a <= 3.05e+214) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.5d+23)) then
        tmp = x
    else if (a <= 6d+75) then
        tmp = t
    else if (a <= 3.05d+214) then
        tmp = t * (y / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.5e+23) {
		tmp = x;
	} else if (a <= 6e+75) {
		tmp = t;
	} else if (a <= 3.05e+214) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.5e+23:
		tmp = x
	elif a <= 6e+75:
		tmp = t
	elif a <= 3.05e+214:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.5e+23)
		tmp = x;
	elseif (a <= 6e+75)
		tmp = t;
	elseif (a <= 3.05e+214)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.5e+23)
		tmp = x;
	elseif (a <= 6e+75)
		tmp = t;
	elseif (a <= 3.05e+214)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.5e+23], x, If[LessEqual[a, 6e+75], t, If[LessEqual[a, 3.05e+214], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.50000000000000004e23 or 3.05000000000000018e214 < a

   1. Initial program 92.4%

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

   3. Taylor expanded in a around inf 48.9%

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

   if -5.50000000000000004e23 < a < 6e75

   1. Initial program 74.7%

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

   3. Taylor expanded in z around inf 41.3%

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

   if 6e75 < a < 3.05000000000000018e214

   1. Initial program 83.4%

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

   3. Taylor expanded in x around 0 48.1%

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

      1. associate-/l* 54.5%

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

   5. Simplified 54.5%

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

   6. Taylor expanded in z around 0 38.8%

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

      1. associate-/l* 42.0%

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

   8. Simplified 42.0%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+75}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{+214}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 38.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+102}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.6e+19) x (if (<= a 1.7e+102) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.6e+19) {
		tmp = x;
	} else if (a <= 1.7e+102) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.6d+19)) then
        tmp = x
    else if (a <= 1.7d+102) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.6e+19) {
		tmp = x;
	} else if (a <= 1.7e+102) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.6e+19:
		tmp = x
	elif a <= 1.7e+102:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.6e+19)
		tmp = x;
	elseif (a <= 1.7e+102)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.6e+19)
		tmp = x;
	elseif (a <= 1.7e+102)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.6e+19], x, If[LessEqual[a, 1.7e+102], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.6e19 or 1.7e102 < a

   1. Initial program 89.2%

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

   3. Taylor expanded in a around inf 44.8%

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

   if -3.6e19 < a < 1.7e102

   1. Initial program 76.0%

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

   3. Taylor expanded in z around inf 39.3%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+102}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 25.4% 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 81.5%

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

3. Taylor expanded in z around inf 26.7%

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

4. Final simplification 26.7%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024044 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))