Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.2% → 95.0%

Time: 16.2s

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: 80.2% 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: 95.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-286} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- x t) (- a z))))))
   (if (or (<= t_1 -4e-286) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (- t (* x (/ (- a y) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -4e-286) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = t - (x * ((a - y) / z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -4e-286) || !(t_1 <= 0.0))
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = Float64(t - Float64(x * Float64(Float64(a - y) / z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e-286], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(t - N[(x * 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)))) < -4.0000000000000002e-286 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.5%

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

      1. +-commutative 92.5%

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

      2. associate-*r/ 76.7%

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

      3. *-commutative 76.7%

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

      4. associate-*r/ 95.3%

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

      5. fma-def 95.3%

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

   3. Simplified 95.3%

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

   if -4.0000000000000002e-286 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.6%

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

      1. clear-num 3.6%

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

      2. associate-/r/ 4.5%

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

   3. Applied egg-rr 4.5%

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

   4. Taylor expanded in z around -inf 86.1%

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

      1. +-commutative 86.1%

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

      2. mul-1-neg 86.1%

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

      3. distribute-rgt-out-- 86.1%

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

      4. unsub-neg 86.1%

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

      5. associate-*r/ 99.5%

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

   6. Simplified 99.5%

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

   7. Taylor expanded in t around 0 86.1%

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

      1. mul-1-neg 86.1%

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

      2. associate-*l/ 99.5%

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

      3. distribute-rgt-neg-out 99.5%

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

   9. Simplified 99.5%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -4 \cdot 10^{-286} \lor \neg \left(x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \end{array} \]

Alternative 2: 91.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-286} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- x t) (- a z))))))
   (if (or (<= t_1 -4e-286) (not (<= t_1 0.0)))
     t_1
     (- t (* x (/ (- a y) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -4e-286) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = 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 + ((z - y) * ((x - t) / (a - z)))
    if ((t_1 <= (-4d-286)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = 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 + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -4e-286) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t - (x * ((a - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - y) * ((x - t) / (a - z)))
	tmp = 0
	if (t_1 <= -4e-286) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t - (x * ((a - y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -4e-286) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t - Float64(x * Float64(Float64(a - y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - y) * ((x - t) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -4e-286) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = 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[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e-286], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t - N[(x * 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)))) < -4.0000000000000002e-286 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.5%

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

   if -4.0000000000000002e-286 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.6%

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

      1. clear-num 3.6%

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

      2. associate-/r/ 4.5%

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

   3. Applied egg-rr 4.5%

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

   4. Taylor expanded in z around -inf 86.1%

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

      1. +-commutative 86.1%

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

      2. mul-1-neg 86.1%

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

      3. distribute-rgt-out-- 86.1%

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

      4. unsub-neg 86.1%

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

      5. associate-*r/ 99.5%

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

   6. Simplified 99.5%

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

   7. Taylor expanded in t around 0 86.1%

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

      1. mul-1-neg 86.1%

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

      2. associate-*l/ 99.5%

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

      3. distribute-rgt-neg-out 99.5%

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

   9. Simplified 99.5%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -4 \cdot 10^{-286} \lor \neg \left(x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \end{array} \]

Alternative 3: 50.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+163}:\\ \;\;\;\;\frac{-t}{-1 + \frac{a}{z}}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+32}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-19}:\\ \;\;\;\;y \cdot \frac{t - x}{-z}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-196}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+136}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+190}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.3e+163)
   (/ (- t) (+ -1.0 (/ a z)))
   (if (<= z -2e+32)
     (- x (/ (* z t) a))
     (if (<= z -1.55e-19)
       (* y (/ (- t x) (- z)))
       (if (<= z -1.6e-196)
         (+ x (/ y (/ (- a) x)))
         (if (<= z 8.2e+136)
           (+ x (/ y (/ a t)))
           (if (<= z 3.5e+190) (/ (- y a) (/ z x)) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.3e+163) {
		tmp = -t / (-1.0 + (a / z));
	} else if (z <= -2e+32) {
		tmp = x - ((z * t) / a);
	} else if (z <= -1.55e-19) {
		tmp = y * ((t - x) / -z);
	} else if (z <= -1.6e-196) {
		tmp = x + (y / (-a / x));
	} else if (z <= 8.2e+136) {
		tmp = x + (y / (a / t));
	} else if (z <= 3.5e+190) {
		tmp = (y - a) / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.3d+163)) then
        tmp = -t / ((-1.0d0) + (a / z))
    else if (z <= (-2d+32)) then
        tmp = x - ((z * t) / a)
    else if (z <= (-1.55d-19)) then
        tmp = y * ((t - x) / -z)
    else if (z <= (-1.6d-196)) then
        tmp = x + (y / (-a / x))
    else if (z <= 8.2d+136) then
        tmp = x + (y / (a / t))
    else if (z <= 3.5d+190) then
        tmp = (y - a) / (z / x)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.3e+163) {
		tmp = -t / (-1.0 + (a / z));
	} else if (z <= -2e+32) {
		tmp = x - ((z * t) / a);
	} else if (z <= -1.55e-19) {
		tmp = y * ((t - x) / -z);
	} else if (z <= -1.6e-196) {
		tmp = x + (y / (-a / x));
	} else if (z <= 8.2e+136) {
		tmp = x + (y / (a / t));
	} else if (z <= 3.5e+190) {
		tmp = (y - a) / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.3e+163:
		tmp = -t / (-1.0 + (a / z))
	elif z <= -2e+32:
		tmp = x - ((z * t) / a)
	elif z <= -1.55e-19:
		tmp = y * ((t - x) / -z)
	elif z <= -1.6e-196:
		tmp = x + (y / (-a / x))
	elif z <= 8.2e+136:
		tmp = x + (y / (a / t))
	elif z <= 3.5e+190:
		tmp = (y - a) / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.3e+163)
		tmp = Float64(Float64(-t) / Float64(-1.0 + Float64(a / z)));
	elseif (z <= -2e+32)
		tmp = Float64(x - Float64(Float64(z * t) / a));
	elseif (z <= -1.55e-19)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(-z)));
	elseif (z <= -1.6e-196)
		tmp = Float64(x + Float64(y / Float64(Float64(-a) / x)));
	elseif (z <= 8.2e+136)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 3.5e+190)
		tmp = Float64(Float64(y - a) / Float64(z / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.3e+163)
		tmp = -t / (-1.0 + (a / z));
	elseif (z <= -2e+32)
		tmp = x - ((z * t) / a);
	elseif (z <= -1.55e-19)
		tmp = y * ((t - x) / -z);
	elseif (z <= -1.6e-196)
		tmp = x + (y / (-a / x));
	elseif (z <= 8.2e+136)
		tmp = x + (y / (a / t));
	elseif (z <= 3.5e+190)
		tmp = (y - a) / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.3e+163], N[((-t) / N[(-1.0 + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2e+32], N[(x - N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.55e-19], N[(y * N[(N[(t - x), $MachinePrecision] / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.6e-196], N[(x + N[(y / N[((-a) / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e+136], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+190], N[(N[(y - a), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -2.30000000000000002e163

   1. Initial program 67.1%

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

   2. Taylor expanded in y around 0 30.0%

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

      1. mul-1-neg 30.0%

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

      2. unsub-neg 30.0%

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

      3. *-commutative 30.0%

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

      4. associate-/l* 68.6%

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

      5. div-sub 68.6%

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

      6. *-inverses 68.6%

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

   4. Simplified 68.6%

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

   5. Taylor expanded in x around 0 84.2%

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

      1. sub-neg 84.2%

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

      2. metadata-eval 84.2%

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

      3. associate-*r/ 84.2%

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

      4. mul-1-neg 84.2%

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

      5. +-commutative 84.2%

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

   7. Simplified 84.2%

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

   if -2.30000000000000002e163 < z < -2.00000000000000011e32

   1. Initial program 85.1%

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

   2. Taylor expanded in y around 0 44.5%

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

      1. mul-1-neg 44.5%

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

      2. unsub-neg 44.5%

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

      3. *-commutative 44.5%

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

      4. associate-/l* 55.4%

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

      5. div-sub 55.4%

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

      6. *-inverses 55.4%

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

   4. Simplified 55.4%

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

   5. Taylor expanded in a around -inf 43.3%

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

      1. +-commutative 43.3%

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

      2. mul-1-neg 43.3%

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

      3. unsub-neg 43.3%

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

      4. *-commutative 43.3%

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

      5. associate-/l* 50.9%

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

   7. Simplified 50.9%

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

   8. Taylor expanded in t around inf 47.6%

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

   if -2.00000000000000011e32 < z < -1.5499999999999999e-19

   1. Initial program 85.1%

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

   2. Taylor expanded in y around inf 70.3%

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

      1. div-sub 70.3%

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

      2. *-commutative 70.3%

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

      3. associate-*r/ 70.2%

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

      4. associate-/l* 69.8%

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

   4. Simplified 69.8%

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

   5. Taylor expanded in a around 0 62.6%

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

      1. associate-*r/ 62.6%

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

      2. associate-*r* 62.6%

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

      3. mul-1-neg 62.6%

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

   7. Simplified 62.6%

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

      1. frac-2neg 62.6%

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

      2. div-inv 62.5%

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

      3. distribute-lft-neg-out 62.5%

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

      4. remove-double-neg 62.5%

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

   9. Applied egg-rr 62.5%

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

       1. associate-*l* 63.1%

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

       2. associate-*r/ 63.3%

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

       3. *-rgt-identity 63.3%

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

   11. Simplified 63.3%

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

   if -1.5499999999999999e-19 < z < -1.6e-196

   1. Initial program 91.8%

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

   2. Taylor expanded in z around 0 74.4%

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

      1. +-commutative 74.4%

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

      2. associate-/l* 74.0%

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

   4. Simplified 74.0%

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

   5. Taylor expanded in t around 0 66.1%

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

      1. associate-*r/ 66.1%

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

      2. neg-mul-1 66.1%

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

   7. Simplified 66.1%

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

   if -1.6e-196 < z < 8.1999999999999995e136

   1. Initial program 90.9%

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

   2. Taylor expanded in z around 0 64.8%

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

      1. +-commutative 64.8%

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

      2. associate-/l* 71.1%

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

   4. Simplified 71.1%

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

   5. Taylor expanded in t around inf 64.1%

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

   if 8.1999999999999995e136 < z < 3.4999999999999999e190

   1. Initial program 33.6%

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

   2. Taylor expanded in x around -inf 52.0%

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

   3. Taylor expanded in z around inf 62.1%

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

      1. associate-/l* 71.6%

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

      2. mul-1-neg 71.6%

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

      3. unsub-neg 71.6%

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

   5. Simplified 71.6%

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

   if 3.4999999999999999e190 < z

   1. Initial program 59.3%

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

   2. Taylor expanded in z around inf 75.0%

      \[\leadsto \color{blue}{t} \]
3. Recombined 7 regimes into one program.

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+163}:\\ \;\;\;\;\frac{-t}{-1 + \frac{a}{z}}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+32}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-19}:\\ \;\;\;\;y \cdot \frac{t - x}{-z}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-196}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+136}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+190}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 50.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.45 \cdot 10^{+165}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+32}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-20}:\\ \;\;\;\;y \cdot \frac{t - x}{-z}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-201}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+156}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.45e+165)
   t
   (if (<= z -1.55e+32)
     (- x (/ (* z t) a))
     (if (<= z -9.2e-20)
       (* y (/ (- t x) (- z)))
       (if (<= z -7e-201)
         (+ x (/ y (/ (- a) x)))
         (if (<= z 7.2e+156) (+ x (/ y (/ a t))) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.45e+165) {
		tmp = t;
	} else if (z <= -1.55e+32) {
		tmp = x - ((z * t) / a);
	} else if (z <= -9.2e-20) {
		tmp = y * ((t - x) / -z);
	} else if (z <= -7e-201) {
		tmp = x + (y / (-a / x));
	} else if (z <= 7.2e+156) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.45d+165)) then
        tmp = t
    else if (z <= (-1.55d+32)) then
        tmp = x - ((z * t) / a)
    else if (z <= (-9.2d-20)) then
        tmp = y * ((t - x) / -z)
    else if (z <= (-7d-201)) then
        tmp = x + (y / (-a / x))
    else if (z <= 7.2d+156) then
        tmp = x + (y / (a / t))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.45e+165) {
		tmp = t;
	} else if (z <= -1.55e+32) {
		tmp = x - ((z * t) / a);
	} else if (z <= -9.2e-20) {
		tmp = y * ((t - x) / -z);
	} else if (z <= -7e-201) {
		tmp = x + (y / (-a / x));
	} else if (z <= 7.2e+156) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.45e+165:
		tmp = t
	elif z <= -1.55e+32:
		tmp = x - ((z * t) / a)
	elif z <= -9.2e-20:
		tmp = y * ((t - x) / -z)
	elif z <= -7e-201:
		tmp = x + (y / (-a / x))
	elif z <= 7.2e+156:
		tmp = x + (y / (a / t))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.45e+165)
		tmp = t;
	elseif (z <= -1.55e+32)
		tmp = Float64(x - Float64(Float64(z * t) / a));
	elseif (z <= -9.2e-20)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(-z)));
	elseif (z <= -7e-201)
		tmp = Float64(x + Float64(y / Float64(Float64(-a) / x)));
	elseif (z <= 7.2e+156)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.45e+165)
		tmp = t;
	elseif (z <= -1.55e+32)
		tmp = x - ((z * t) / a);
	elseif (z <= -9.2e-20)
		tmp = y * ((t - x) / -z);
	elseif (z <= -7e-201)
		tmp = x + (y / (-a / x));
	elseif (z <= 7.2e+156)
		tmp = x + (y / (a / t));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.45e+165], t, If[LessEqual[z, -1.55e+32], N[(x - N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.2e-20], N[(y * N[(N[(t - x), $MachinePrecision] / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7e-201], N[(x + N[(y / N[((-a) / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e+156], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.45000000000000003e165 or 7.19999999999999958e156 < z

   1. Initial program 58.7%

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

   2. Taylor expanded in z around inf 74.1%

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

   if -3.45000000000000003e165 < z < -1.54999999999999997e32

   1. Initial program 85.1%

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

   2. Taylor expanded in y around 0 44.5%

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

      1. mul-1-neg 44.5%

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

      2. unsub-neg 44.5%

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

      3. *-commutative 44.5%

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

      4. associate-/l* 55.4%

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

      5. div-sub 55.4%

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

      6. *-inverses 55.4%

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

   4. Simplified 55.4%

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

   5. Taylor expanded in a around -inf 43.3%

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

      1. +-commutative 43.3%

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

      2. mul-1-neg 43.3%

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

      3. unsub-neg 43.3%

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

      4. *-commutative 43.3%

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

      5. associate-/l* 50.9%

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

   7. Simplified 50.9%

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

   8. Taylor expanded in t around inf 47.6%

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

   if -1.54999999999999997e32 < z < -9.1999999999999997e-20

   1. Initial program 85.1%

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

   2. Taylor expanded in y around inf 70.3%

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

      1. div-sub 70.3%

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

      2. *-commutative 70.3%

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

      3. associate-*r/ 70.2%

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

      4. associate-/l* 69.8%

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

   4. Simplified 69.8%

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

   5. Taylor expanded in a around 0 62.6%

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

      1. associate-*r/ 62.6%

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

      2. associate-*r* 62.6%

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

      3. mul-1-neg 62.6%

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

   7. Simplified 62.6%

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

      1. frac-2neg 62.6%

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

      2. div-inv 62.5%

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

      3. distribute-lft-neg-out 62.5%

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

      4. remove-double-neg 62.5%

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

   9. Applied egg-rr 62.5%

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

       1. associate-*l* 63.1%

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

       2. associate-*r/ 63.3%

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

       3. *-rgt-identity 63.3%

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

   11. Simplified 63.3%

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

   if -9.1999999999999997e-20 < z < -7.00000000000000016e-201

   1. Initial program 91.8%

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

   2. Taylor expanded in z around 0 74.4%

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

      1. +-commutative 74.4%

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

      2. associate-/l* 74.0%

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

   4. Simplified 74.0%

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

   5. Taylor expanded in t around 0 66.1%

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

      1. associate-*r/ 66.1%

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

      2. neg-mul-1 66.1%

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

   7. Simplified 66.1%

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

   if -7.00000000000000016e-201 < z < 7.19999999999999958e156

   1. Initial program 89.7%

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

   2. Taylor expanded in z around 0 62.4%

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

      1. +-commutative 62.4%

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

      2. associate-/l* 69.1%

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

   4. Simplified 69.1%

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

   5. Taylor expanded in t around inf 62.5%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.45 \cdot 10^{+165}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+32}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-20}:\\ \;\;\;\;y \cdot \frac{t - x}{-z}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-201}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+156}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 50.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+162}:\\ \;\;\;\;\frac{-t}{-1 + \frac{a}{z}}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+32}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-19}:\\ \;\;\;\;y \cdot \frac{t - x}{-z}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-198}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+158}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.7e+162)
   (/ (- t) (+ -1.0 (/ a z)))
   (if (<= z -1e+32)
     (- x (/ (* z t) a))
     (if (<= z -1.6e-19)
       (* y (/ (- t x) (- z)))
       (if (<= z -1.6e-198)
         (+ x (/ y (/ (- a) x)))
         (if (<= z 1.75e+158) (+ x (/ y (/ a t))) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.7e+162) {
		tmp = -t / (-1.0 + (a / z));
	} else if (z <= -1e+32) {
		tmp = x - ((z * t) / a);
	} else if (z <= -1.6e-19) {
		tmp = y * ((t - x) / -z);
	} else if (z <= -1.6e-198) {
		tmp = x + (y / (-a / x));
	} else if (z <= 1.75e+158) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.7d+162)) then
        tmp = -t / ((-1.0d0) + (a / z))
    else if (z <= (-1d+32)) then
        tmp = x - ((z * t) / a)
    else if (z <= (-1.6d-19)) then
        tmp = y * ((t - x) / -z)
    else if (z <= (-1.6d-198)) then
        tmp = x + (y / (-a / x))
    else if (z <= 1.75d+158) then
        tmp = x + (y / (a / t))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.7e+162) {
		tmp = -t / (-1.0 + (a / z));
	} else if (z <= -1e+32) {
		tmp = x - ((z * t) / a);
	} else if (z <= -1.6e-19) {
		tmp = y * ((t - x) / -z);
	} else if (z <= -1.6e-198) {
		tmp = x + (y / (-a / x));
	} else if (z <= 1.75e+158) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.7e+162:
		tmp = -t / (-1.0 + (a / z))
	elif z <= -1e+32:
		tmp = x - ((z * t) / a)
	elif z <= -1.6e-19:
		tmp = y * ((t - x) / -z)
	elif z <= -1.6e-198:
		tmp = x + (y / (-a / x))
	elif z <= 1.75e+158:
		tmp = x + (y / (a / t))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.7e+162)
		tmp = Float64(Float64(-t) / Float64(-1.0 + Float64(a / z)));
	elseif (z <= -1e+32)
		tmp = Float64(x - Float64(Float64(z * t) / a));
	elseif (z <= -1.6e-19)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(-z)));
	elseif (z <= -1.6e-198)
		tmp = Float64(x + Float64(y / Float64(Float64(-a) / x)));
	elseif (z <= 1.75e+158)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.7e+162)
		tmp = -t / (-1.0 + (a / z));
	elseif (z <= -1e+32)
		tmp = x - ((z * t) / a);
	elseif (z <= -1.6e-19)
		tmp = y * ((t - x) / -z);
	elseif (z <= -1.6e-198)
		tmp = x + (y / (-a / x));
	elseif (z <= 1.75e+158)
		tmp = x + (y / (a / t));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.7e+162], N[((-t) / N[(-1.0 + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1e+32], N[(x - N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.6e-19], N[(y * N[(N[(t - x), $MachinePrecision] / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.6e-198], N[(x + N[(y / N[((-a) / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e+158], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -4.70000000000000003e162

   1. Initial program 67.1%

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

   2. Taylor expanded in y around 0 30.0%

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

      1. mul-1-neg 30.0%

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

      2. unsub-neg 30.0%

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

      3. *-commutative 30.0%

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

      4. associate-/l* 68.6%

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

      5. div-sub 68.6%

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

      6. *-inverses 68.6%

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

   4. Simplified 68.6%

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

   5. Taylor expanded in x around 0 84.2%

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

      1. sub-neg 84.2%

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

      2. metadata-eval 84.2%

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

      3. associate-*r/ 84.2%

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

      4. mul-1-neg 84.2%

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

      5. +-commutative 84.2%

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

   7. Simplified 84.2%

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

   if -4.70000000000000003e162 < z < -1.00000000000000005e32

   1. Initial program 85.1%

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

   2. Taylor expanded in y around 0 44.5%

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

      1. mul-1-neg 44.5%

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

      2. unsub-neg 44.5%

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

      3. *-commutative 44.5%

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

      4. associate-/l* 55.4%

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

      5. div-sub 55.4%

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

      6. *-inverses 55.4%

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

   4. Simplified 55.4%

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

   5. Taylor expanded in a around -inf 43.3%

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

      1. +-commutative 43.3%

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

      2. mul-1-neg 43.3%

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

      3. unsub-neg 43.3%

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

      4. *-commutative 43.3%

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

      5. associate-/l* 50.9%

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

   7. Simplified 50.9%

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

   8. Taylor expanded in t around inf 47.6%

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

   if -1.00000000000000005e32 < z < -1.59999999999999991e-19

   1. Initial program 85.1%

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

   2. Taylor expanded in y around inf 70.3%

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

      1. div-sub 70.3%

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

      2. *-commutative 70.3%

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

      3. associate-*r/ 70.2%

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

      4. associate-/l* 69.8%

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

   4. Simplified 69.8%

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

   5. Taylor expanded in a around 0 62.6%

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

      1. associate-*r/ 62.6%

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

      2. associate-*r* 62.6%

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

      3. mul-1-neg 62.6%

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

   7. Simplified 62.6%

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

      1. frac-2neg 62.6%

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

      2. div-inv 62.5%

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

      3. distribute-lft-neg-out 62.5%

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

      4. remove-double-neg 62.5%

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

   9. Applied egg-rr 62.5%

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

       1. associate-*l* 63.1%

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

       2. associate-*r/ 63.3%

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

       3. *-rgt-identity 63.3%

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

   11. Simplified 63.3%

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

   if -1.59999999999999991e-19 < z < -1.59999999999999997e-198

   1. Initial program 91.8%

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

   2. Taylor expanded in z around 0 74.4%

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

      1. +-commutative 74.4%

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

      2. associate-/l* 74.0%

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

   4. Simplified 74.0%

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

   5. Taylor expanded in t around 0 66.1%

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

      1. associate-*r/ 66.1%

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

      2. neg-mul-1 66.1%

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

   7. Simplified 66.1%

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

   if -1.59999999999999997e-198 < z < 1.7500000000000001e158

   1. Initial program 89.7%

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

   2. Taylor expanded in z around 0 62.4%

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

      1. +-commutative 62.4%

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

      2. associate-/l* 69.1%

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

   4. Simplified 69.1%

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

   5. Taylor expanded in t around inf 62.5%

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

   if 1.7500000000000001e158 < z

   1. Initial program 48.2%

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

   2. Taylor expanded in z around inf 65.8%

      \[\leadsto \color{blue}{t} \]
3. Recombined 6 regimes into one program.

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+162}:\\ \;\;\;\;\frac{-t}{-1 + \frac{a}{z}}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+32}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-19}:\\ \;\;\;\;y \cdot \frac{t - x}{-z}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-198}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+158}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6: 63.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-54}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+98} \lor \neg \left(z \leq 3.5 \cdot 10^{+190}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -4.5e+111)
     t_1
     (if (<= z 5.8e-54)
       (+ x (/ y (/ a (- t x))))
       (if (or (<= z 2.6e+98) (not (<= z 3.5e+190)))
         t_1
         (/ (- y a) (/ z x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -4.5e+111) {
		tmp = t_1;
	} else if (z <= 5.8e-54) {
		tmp = x + (y / (a / (t - x)));
	} else if ((z <= 2.6e+98) || !(z <= 3.5e+190)) {
		tmp = t_1;
	} else {
		tmp = (y - a) / (z / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-4.5d+111)) then
        tmp = t_1
    else if (z <= 5.8d-54) then
        tmp = x + (y / (a / (t - x)))
    else if ((z <= 2.6d+98) .or. (.not. (z <= 3.5d+190))) then
        tmp = t_1
    else
        tmp = (y - a) / (z / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -4.5e+111) {
		tmp = t_1;
	} else if (z <= 5.8e-54) {
		tmp = x + (y / (a / (t - x)));
	} else if ((z <= 2.6e+98) || !(z <= 3.5e+190)) {
		tmp = t_1;
	} else {
		tmp = (y - a) / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -4.5e+111:
		tmp = t_1
	elif z <= 5.8e-54:
		tmp = x + (y / (a / (t - x)))
	elif (z <= 2.6e+98) or not (z <= 3.5e+190):
		tmp = t_1
	else:
		tmp = (y - a) / (z / x)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -4.5e+111)
		tmp = t_1;
	elseif (z <= 5.8e-54)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif ((z <= 2.6e+98) || !(z <= 3.5e+190))
		tmp = t_1;
	else
		tmp = Float64(Float64(y - a) / Float64(z / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -4.5e+111)
		tmp = t_1;
	elseif (z <= 5.8e-54)
		tmp = x + (y / (a / (t - x)));
	elseif ((z <= 2.6e+98) || ~((z <= 3.5e+190)))
		tmp = t_1;
	else
		tmp = (y - a) / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+111], t$95$1, If[LessEqual[z, 5.8e-54], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 2.6e+98], N[Not[LessEqual[z, 3.5e+190]], $MachinePrecision]], t$95$1, N[(N[(y - a), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.50000000000000001e111 or 5.80000000000000029e-54 < z < 2.6e98 or 3.4999999999999999e190 < z

   1. Initial program 70.1%

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

   2. Taylor expanded in t around inf 75.4%

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

      1. div-sub 75.4%

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

   4. Simplified 75.4%

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

   if -4.50000000000000001e111 < z < 5.80000000000000029e-54

   1. Initial program 93.9%

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

   2. Taylor expanded in z around 0 71.7%

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

      1. +-commutative 71.7%

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

      2. associate-/l* 75.4%

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

   4. Simplified 75.4%

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

   if 2.6e98 < z < 3.4999999999999999e190

   1. Initial program 49.7%

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

   2. Taylor expanded in x around -inf 60.0%

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

   3. Taylor expanded in z around inf 49.0%

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

      1. associate-/l* 54.6%

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

      2. mul-1-neg 54.6%

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

      3. unsub-neg 54.6%

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

   5. Simplified 54.6%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+111}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-54}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+98} \lor \neg \left(z \leq 3.5 \cdot 10^{+190}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \end{array} \]

Alternative 7: 58.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;a \leq -2.6 \cdot 10^{+82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-166}:\\ \;\;\;\;y \cdot \frac{t - x}{-z}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (/ y (/ a t)))))
   (if (<= a -2.6e+82)
     t_2
     (if (<= a -1.25e-219)
       t_1
       (if (<= a 6e-166) (* y (/ (- t x) (- z))) (if (<= a 9e+69) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (y / (a / t));
	double tmp;
	if (a <= -2.6e+82) {
		tmp = t_2;
	} else if (a <= -1.25e-219) {
		tmp = t_1;
	} else if (a <= 6e-166) {
		tmp = y * ((t - x) / -z);
	} else if (a <= 9e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + (y / (a / t))
    if (a <= (-2.6d+82)) then
        tmp = t_2
    else if (a <= (-1.25d-219)) then
        tmp = t_1
    else if (a <= 6d-166) then
        tmp = y * ((t - x) / -z)
    else if (a <= 9d+69) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (y / (a / t));
	double tmp;
	if (a <= -2.6e+82) {
		tmp = t_2;
	} else if (a <= -1.25e-219) {
		tmp = t_1;
	} else if (a <= 6e-166) {
		tmp = y * ((t - x) / -z);
	} else if (a <= 9e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + (y / (a / t))
	tmp = 0
	if a <= -2.6e+82:
		tmp = t_2
	elif a <= -1.25e-219:
		tmp = t_1
	elif a <= 6e-166:
		tmp = y * ((t - x) / -z)
	elif a <= 9e+69:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(y / Float64(a / t)))
	tmp = 0.0
	if (a <= -2.6e+82)
		tmp = t_2;
	elseif (a <= -1.25e-219)
		tmp = t_1;
	elseif (a <= 6e-166)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(-z)));
	elseif (a <= 9e+69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + (y / (a / t));
	tmp = 0.0;
	if (a <= -2.6e+82)
		tmp = t_2;
	elseif (a <= -1.25e-219)
		tmp = t_1;
	elseif (a <= 6e-166)
		tmp = y * ((t - x) / -z);
	elseif (a <= 9e+69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.6e+82], t$95$2, If[LessEqual[a, -1.25e-219], t$95$1, If[LessEqual[a, 6e-166], N[(y * N[(N[(t - x), $MachinePrecision] / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+69], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.5999999999999998e82 or 8.9999999999999999e69 < a

   1. Initial program 97.6%

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

   2. Taylor expanded in z around 0 70.0%

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

      1. +-commutative 70.0%

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

      2. associate-/l* 81.6%

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

   4. Simplified 81.6%

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

   5. Taylor expanded in t around inf 77.9%

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

   if -2.5999999999999998e82 < a < -1.25e-219 or 6.0000000000000005e-166 < a < 8.9999999999999999e69

   1. Initial program 70.4%

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

   2. Taylor expanded in t around inf 61.9%

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

      1. div-sub 61.9%

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

   4. Simplified 61.9%

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

   if -1.25e-219 < a < 6.0000000000000005e-166

   1. Initial program 76.3%

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

   2. Taylor expanded in y around inf 72.5%

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

      1. div-sub 72.5%

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

      2. *-commutative 72.5%

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

      3. associate-*r/ 70.4%

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

      4. associate-/l* 72.4%

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

   4. Simplified 72.4%

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

   5. Taylor expanded in a around 0 65.5%

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

      1. associate-*r/ 65.5%

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

      2. associate-*r* 65.5%

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

      3. mul-1-neg 65.5%

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

   7. Simplified 65.5%

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

      1. frac-2neg 65.5%

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

      2. div-inv 65.4%

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

      3. distribute-lft-neg-out 65.4%

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

      4. remove-double-neg 65.4%

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

   9. Applied egg-rr 65.4%

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

       1. associate-*l* 67.4%

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

       2. associate-*r/ 67.5%

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

       3. *-rgt-identity 67.5%

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

   11. Simplified 67.5%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+82}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-219}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-166}:\\ \;\;\;\;y \cdot \frac{t - x}{-z}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 8: 59.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;a \leq -7.2 \cdot 10^{+81}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-151}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (/ y (/ a t)))))
   (if (<= a -7.2e+81)
     t_2
     (if (<= a -6.2e-193)
       t_1
       (if (<= a 8.2e-151)
         (* y (/ (- t x) (- a z)))
         (if (<= a 5.2e+69) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (y / (a / t));
	double tmp;
	if (a <= -7.2e+81) {
		tmp = t_2;
	} else if (a <= -6.2e-193) {
		tmp = t_1;
	} else if (a <= 8.2e-151) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 5.2e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + (y / (a / t))
    if (a <= (-7.2d+81)) then
        tmp = t_2
    else if (a <= (-6.2d-193)) then
        tmp = t_1
    else if (a <= 8.2d-151) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 5.2d+69) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (y / (a / t));
	double tmp;
	if (a <= -7.2e+81) {
		tmp = t_2;
	} else if (a <= -6.2e-193) {
		tmp = t_1;
	} else if (a <= 8.2e-151) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 5.2e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + (y / (a / t))
	tmp = 0
	if a <= -7.2e+81:
		tmp = t_2
	elif a <= -6.2e-193:
		tmp = t_1
	elif a <= 8.2e-151:
		tmp = y * ((t - x) / (a - z))
	elif a <= 5.2e+69:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(y / Float64(a / t)))
	tmp = 0.0
	if (a <= -7.2e+81)
		tmp = t_2;
	elseif (a <= -6.2e-193)
		tmp = t_1;
	elseif (a <= 8.2e-151)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 5.2e+69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + (y / (a / t));
	tmp = 0.0;
	if (a <= -7.2e+81)
		tmp = t_2;
	elseif (a <= -6.2e-193)
		tmp = t_1;
	elseif (a <= 8.2e-151)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 5.2e+69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.2e+81], t$95$2, If[LessEqual[a, -6.2e-193], t$95$1, If[LessEqual[a, 8.2e-151], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e+69], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.20000000000000011e81 or 5.2000000000000004e69 < a

   1. Initial program 97.6%

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

   2. Taylor expanded in z around 0 70.0%

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

      1. +-commutative 70.0%

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

      2. associate-/l* 81.6%

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

   4. Simplified 81.6%

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

   5. Taylor expanded in t around inf 77.9%

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

   if -7.20000000000000011e81 < a < -6.2000000000000004e-193 or 8.2000000000000002e-151 < a < 5.2000000000000004e69

   1. Initial program 69.4%

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

   2. Taylor expanded in t around inf 61.0%

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

      1. div-sub 61.0%

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

   4. Simplified 61.0%

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

   if -6.2000000000000004e-193 < a < 8.2000000000000002e-151

   1. Initial program 77.1%

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

      1. clear-num 76.8%

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

      2. associate-/r/ 76.7%

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

   3. Applied egg-rr 76.7%

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

   4. Taylor expanded in y around inf 72.3%

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

      1. div-sub 72.3%

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

      2. *-commutative 72.3%

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

   6. Simplified 72.3%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+81}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-193}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-151}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 9: 71.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \left(t - x\right) \cdot \frac{y - a}{z}\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-139}:\\ \;\;\;\;x \cdot \left(1 - \frac{y - z}{a - z}\right)\\ \mathbf{elif}\;z \leq 420000000:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (- t x) (/ (- y a) z)))))
   (if (<= z -3.3e+112)
     t_1
     (if (<= z -2.6e-139)
       (* x (- 1.0 (/ (- y z) (- a z))))
       (if (<= z 420000000.0) (+ x (/ y (/ a (- t x)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((t - x) * ((y - a) / z));
	double tmp;
	if (z <= -3.3e+112) {
		tmp = t_1;
	} else if (z <= -2.6e-139) {
		tmp = x * (1.0 - ((y - z) / (a - z)));
	} else if (z <= 420000000.0) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((t - x) * ((y - a) / z))
    if (z <= (-3.3d+112)) then
        tmp = t_1
    else if (z <= (-2.6d-139)) then
        tmp = x * (1.0d0 - ((y - z) / (a - z)))
    else if (z <= 420000000.0d0) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((t - x) * ((y - a) / z));
	double tmp;
	if (z <= -3.3e+112) {
		tmp = t_1;
	} else if (z <= -2.6e-139) {
		tmp = x * (1.0 - ((y - z) / (a - z)));
	} else if (z <= 420000000.0) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((t - x) * ((y - a) / z))
	tmp = 0
	if z <= -3.3e+112:
		tmp = t_1
	elif z <= -2.6e-139:
		tmp = x * (1.0 - ((y - z) / (a - z)))
	elif z <= 420000000.0:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(t - x) * Float64(Float64(y - a) / z)))
	tmp = 0.0
	if (z <= -3.3e+112)
		tmp = t_1;
	elseif (z <= -2.6e-139)
		tmp = Float64(x * Float64(1.0 - Float64(Float64(y - z) / Float64(a - z))));
	elseif (z <= 420000000.0)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((t - x) * ((y - a) / z));
	tmp = 0.0;
	if (z <= -3.3e+112)
		tmp = t_1;
	elseif (z <= -2.6e-139)
		tmp = x * (1.0 - ((y - z) / (a - z)));
	elseif (z <= 420000000.0)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(t - x), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e+112], t$95$1, If[LessEqual[z, -2.6e-139], N[(x * N[(1.0 - N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 420000000.0], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2999999999999999e112 or 4.2e8 < z

   1. Initial program 64.3%

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

      1. clear-num 64.2%

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

      2. associate-/r/ 64.2%

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

   3. Applied egg-rr 64.2%

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

   4. Taylor expanded in z around -inf 62.3%

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

      1. +-commutative 62.3%

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

      2. mul-1-neg 62.3%

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

      3. distribute-rgt-out-- 63.5%

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

      4. unsub-neg 63.5%

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

      5. associate-*r/ 83.4%

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

   6. Simplified 83.4%

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

   if -3.2999999999999999e112 < z < -2.5999999999999998e-139

   1. Initial program 89.3%

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

   2. Taylor expanded in x around inf 66.9%

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

      1. mul-1-neg 66.9%

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

      2. unsub-neg 66.9%

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

   4. Simplified 66.9%

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

   if -2.5999999999999998e-139 < z < 4.2e8

   1. Initial program 95.4%

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

   2. Taylor expanded in z around 0 76.2%

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

      1. +-commutative 76.2%

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

      2. associate-/l* 80.4%

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

   4. Simplified 80.4%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+112}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-139}:\\ \;\;\;\;x \cdot \left(1 - \frac{y - z}{a - z}\right)\\ \mathbf{elif}\;z \leq 420000000:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y - a}{z}\\ \end{array} \]

Alternative 10: 49.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+162}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-151}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-181}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+157}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.2e+162)
   t
   (if (<= z -4.2e-151)
     (- x (/ (* z t) a))
     (if (<= z -2.5e-181)
       (/ y (/ a (- t x)))
       (if (<= z 2.2e+157) (+ x (/ y (/ a t))) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e+162) {
		tmp = t;
	} else if (z <= -4.2e-151) {
		tmp = x - ((z * t) / a);
	} else if (z <= -2.5e-181) {
		tmp = y / (a / (t - x));
	} else if (z <= 2.2e+157) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7.2d+162)) then
        tmp = t
    else if (z <= (-4.2d-151)) then
        tmp = x - ((z * t) / a)
    else if (z <= (-2.5d-181)) then
        tmp = y / (a / (t - x))
    else if (z <= 2.2d+157) then
        tmp = x + (y / (a / t))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e+162) {
		tmp = t;
	} else if (z <= -4.2e-151) {
		tmp = x - ((z * t) / a);
	} else if (z <= -2.5e-181) {
		tmp = y / (a / (t - x));
	} else if (z <= 2.2e+157) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.2e+162:
		tmp = t
	elif z <= -4.2e-151:
		tmp = x - ((z * t) / a)
	elif z <= -2.5e-181:
		tmp = y / (a / (t - x))
	elif z <= 2.2e+157:
		tmp = x + (y / (a / t))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.2e+162)
		tmp = t;
	elseif (z <= -4.2e-151)
		tmp = Float64(x - Float64(Float64(z * t) / a));
	elseif (z <= -2.5e-181)
		tmp = Float64(y / Float64(a / Float64(t - x)));
	elseif (z <= 2.2e+157)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.2e+162)
		tmp = t;
	elseif (z <= -4.2e-151)
		tmp = x - ((z * t) / a);
	elseif (z <= -2.5e-181)
		tmp = y / (a / (t - x));
	elseif (z <= 2.2e+157)
		tmp = x + (y / (a / t));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.2e+162], t, If[LessEqual[z, -4.2e-151], N[(x - N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.5e-181], N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+157], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.19999999999999987e162 or 2.2000000000000001e157 < z

   1. Initial program 58.7%

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

   2. Taylor expanded in z around inf 74.1%

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

   if -7.19999999999999987e162 < z < -4.19999999999999981e-151

   1. Initial program 87.0%

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

   2. Taylor expanded in y around 0 52.7%

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

      1. mul-1-neg 52.7%

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

      2. unsub-neg 52.7%

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

      3. *-commutative 52.7%

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

      4. associate-/l* 55.8%

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

      5. div-sub 55.8%

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

      6. *-inverses 55.8%

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

   4. Simplified 55.8%

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

   5. Taylor expanded in a around -inf 49.5%

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

      1. +-commutative 49.5%

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

      2. mul-1-neg 49.5%

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

      3. unsub-neg 49.5%

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

      4. *-commutative 49.5%

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

      5. associate-/l* 52.8%

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

   7. Simplified 52.8%

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

   8. Taylor expanded in t around inf 48.2%

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

   if -4.19999999999999981e-151 < z < -2.5000000000000001e-181

   1. Initial program 99.5%

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

   2. Taylor expanded in y around inf 90.0%

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

      1. div-sub 90.0%

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

      2. *-commutative 90.0%

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

      3. associate-*r/ 90.3%

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

      4. associate-/l* 90.1%

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

   4. Simplified 90.1%

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

   5. Taylor expanded in a around inf 80.9%

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

   if -2.5000000000000001e-181 < z < 2.2000000000000001e157

   1. Initial program 89.4%

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

   2. Taylor expanded in z around 0 62.6%

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

      1. +-commutative 62.6%

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

      2. associate-/l* 69.1%

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

   4. Simplified 69.1%

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

   5. Taylor expanded in t around inf 61.7%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+162}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-151}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-181}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+157}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11: 49.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+162}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-151}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-179}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+158}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.2e+162)
   t
   (if (<= z -1.7e-151)
     (- x (/ (* z t) a))
     (if (<= z -3.5e-179)
       (/ (* y (- t x)) a)
       (if (<= z 7.4e+158) (+ x (/ y (/ a t))) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.2e+162) {
		tmp = t;
	} else if (z <= -1.7e-151) {
		tmp = x - ((z * t) / a);
	} else if (z <= -3.5e-179) {
		tmp = (y * (t - x)) / a;
	} else if (z <= 7.4e+158) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.2d+162)) then
        tmp = t
    else if (z <= (-1.7d-151)) then
        tmp = x - ((z * t) / a)
    else if (z <= (-3.5d-179)) then
        tmp = (y * (t - x)) / a
    else if (z <= 7.4d+158) then
        tmp = x + (y / (a / t))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.2e+162) {
		tmp = t;
	} else if (z <= -1.7e-151) {
		tmp = x - ((z * t) / a);
	} else if (z <= -3.5e-179) {
		tmp = (y * (t - x)) / a;
	} else if (z <= 7.4e+158) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.2e+162:
		tmp = t
	elif z <= -1.7e-151:
		tmp = x - ((z * t) / a)
	elif z <= -3.5e-179:
		tmp = (y * (t - x)) / a
	elif z <= 7.4e+158:
		tmp = x + (y / (a / t))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.2e+162)
		tmp = t;
	elseif (z <= -1.7e-151)
		tmp = Float64(x - Float64(Float64(z * t) / a));
	elseif (z <= -3.5e-179)
		tmp = Float64(Float64(y * Float64(t - x)) / a);
	elseif (z <= 7.4e+158)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.2e+162)
		tmp = t;
	elseif (z <= -1.7e-151)
		tmp = x - ((z * t) / a);
	elseif (z <= -3.5e-179)
		tmp = (y * (t - x)) / a;
	elseif (z <= 7.4e+158)
		tmp = x + (y / (a / t));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.2e+162], t, If[LessEqual[z, -1.7e-151], N[(x - N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.5e-179], N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 7.4e+158], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.2000000000000001e162 or 7.40000000000000021e158 < z

   1. Initial program 58.7%

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

   2. Taylor expanded in z around inf 74.1%

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

   if -4.2000000000000001e162 < z < -1.7000000000000001e-151

   1. Initial program 87.0%

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

   2. Taylor expanded in y around 0 52.7%

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

      1. mul-1-neg 52.7%

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

      2. unsub-neg 52.7%

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

      3. *-commutative 52.7%

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

      4. associate-/l* 55.8%

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

      5. div-sub 55.8%

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

      6. *-inverses 55.8%

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

   4. Simplified 55.8%

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

   5. Taylor expanded in a around -inf 49.5%

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

      1. +-commutative 49.5%

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

      2. mul-1-neg 49.5%

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

      3. unsub-neg 49.5%

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

      4. *-commutative 49.5%

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

      5. associate-/l* 52.8%

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

   7. Simplified 52.8%

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

   8. Taylor expanded in t around inf 48.2%

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

   if -1.7000000000000001e-151 < z < -3.50000000000000024e-179

   1. Initial program 99.5%

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

   2. Taylor expanded in y around inf 90.0%

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

      1. div-sub 90.0%

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

      2. *-commutative 90.0%

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

      3. associate-*r/ 90.3%

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

      4. associate-/l* 90.1%

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

   4. Simplified 90.1%

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

   5. Taylor expanded in a around inf 80.9%

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

   6. Taylor expanded in y around 0 81.1%

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

   if -3.50000000000000024e-179 < z < 7.40000000000000021e158

   1. Initial program 89.4%

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

   2. Taylor expanded in z around 0 62.6%

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

      1. +-commutative 62.6%

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

      2. associate-/l* 69.1%

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

   4. Simplified 69.1%

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

   5. Taylor expanded in t around inf 61.7%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+162}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-151}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-179}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+158}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 48.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;a \leq -1.75 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-186}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-143}:\\ \;\;\;\;y \cdot \frac{t - x}{-z}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+68}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a t)))))
   (if (<= a -1.75e+15)
     t_1
     (if (<= a -3.8e-186)
       t
       (if (<= a 1.2e-143)
         (* y (/ (- t x) (- z)))
         (if (<= a 3.2e+68) t t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double tmp;
	if (a <= -1.75e+15) {
		tmp = t_1;
	} else if (a <= -3.8e-186) {
		tmp = t;
	} else if (a <= 1.2e-143) {
		tmp = y * ((t - x) / -z);
	} else if (a <= 3.2e+68) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / t))
    if (a <= (-1.75d+15)) then
        tmp = t_1
    else if (a <= (-3.8d-186)) then
        tmp = t
    else if (a <= 1.2d-143) then
        tmp = y * ((t - x) / -z)
    else if (a <= 3.2d+68) then
        tmp = t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double tmp;
	if (a <= -1.75e+15) {
		tmp = t_1;
	} else if (a <= -3.8e-186) {
		tmp = t;
	} else if (a <= 1.2e-143) {
		tmp = y * ((t - x) / -z);
	} else if (a <= 3.2e+68) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / t))
	tmp = 0
	if a <= -1.75e+15:
		tmp = t_1
	elif a <= -3.8e-186:
		tmp = t
	elif a <= 1.2e-143:
		tmp = y * ((t - x) / -z)
	elif a <= 3.2e+68:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / t)))
	tmp = 0.0
	if (a <= -1.75e+15)
		tmp = t_1;
	elseif (a <= -3.8e-186)
		tmp = t;
	elseif (a <= 1.2e-143)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(-z)));
	elseif (a <= 3.2e+68)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / t));
	tmp = 0.0;
	if (a <= -1.75e+15)
		tmp = t_1;
	elseif (a <= -3.8e-186)
		tmp = t;
	elseif (a <= 1.2e-143)
		tmp = y * ((t - x) / -z);
	elseif (a <= 3.2e+68)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.75e+15], t$95$1, If[LessEqual[a, -3.8e-186], t, If[LessEqual[a, 1.2e-143], N[(y * N[(N[(t - x), $MachinePrecision] / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e+68], t, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.75e15 or 3.19999999999999994e68 < a

   1. Initial program 97.1%

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

   2. Taylor expanded in z around 0 68.6%

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

      1. +-commutative 68.6%

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

      2. associate-/l* 78.9%

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

   4. Simplified 78.9%

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

   5. Taylor expanded in t around inf 74.1%

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

   if -1.75e15 < a < -3.79999999999999974e-186 or 1.1999999999999999e-143 < a < 3.19999999999999994e68

   1. Initial program 66.9%

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

   2. Taylor expanded in z around inf 39.9%

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

   if -3.79999999999999974e-186 < a < 1.1999999999999999e-143

   1. Initial program 74.5%

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

   2. Taylor expanded in y around inf 70.1%

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

      1. div-sub 70.1%

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

      2. *-commutative 70.1%

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

      3. associate-*r/ 68.6%

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

      4. associate-/l* 70.0%

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

   4. Simplified 70.0%

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

   5. Taylor expanded in a around 0 61.7%

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

      1. associate-*r/ 61.7%

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

      2. associate-*r* 61.7%

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

      3. mul-1-neg 61.7%

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

   7. Simplified 61.7%

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

      1. frac-2neg 61.7%

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

      2. div-inv 61.6%

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

      3. distribute-lft-neg-out 61.6%

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

      4. remove-double-neg 61.6%

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

   9. Applied egg-rr 61.6%

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

       1. associate-*l* 63.1%

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

       2. associate-*r/ 63.1%

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

       3. *-rgt-identity 63.1%

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

   11. Simplified 63.1%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+15}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-186}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-143}:\\ \;\;\;\;y \cdot \frac{t - x}{-z}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+68}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 13: 70.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-136}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a (- t x))))))
   (if (<= a -2.7e+25)
     t_1
     (if (<= a 9e-136)
       (+ t (* (/ y z) (- x t)))
       (if (<= a 1.15e+45) (* t (/ (- y z) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double tmp;
	if (a <= -2.7e+25) {
		tmp = t_1;
	} else if (a <= 9e-136) {
		tmp = t + ((y / z) * (x - t));
	} else if (a <= 1.15e+45) {
		tmp = t * ((y - z) / (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 / (a / (t - x)))
    if (a <= (-2.7d+25)) then
        tmp = t_1
    else if (a <= 9d-136) then
        tmp = t + ((y / z) * (x - t))
    else if (a <= 1.15d+45) then
        tmp = t * ((y - z) / (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 / (a / (t - x)));
	double tmp;
	if (a <= -2.7e+25) {
		tmp = t_1;
	} else if (a <= 9e-136) {
		tmp = t + ((y / z) * (x - t));
	} else if (a <= 1.15e+45) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / (t - x)))
	tmp = 0
	if a <= -2.7e+25:
		tmp = t_1
	elif a <= 9e-136:
		tmp = t + ((y / z) * (x - t))
	elif a <= 1.15e+45:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / Float64(t - x))))
	tmp = 0.0
	if (a <= -2.7e+25)
		tmp = t_1;
	elseif (a <= 9e-136)
		tmp = Float64(t + Float64(Float64(y / z) * Float64(x - t)));
	elseif (a <= 1.15e+45)
		tmp = Float64(t * Float64(Float64(y - z) / 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 / (a / (t - x)));
	tmp = 0.0;
	if (a <= -2.7e+25)
		tmp = t_1;
	elseif (a <= 9e-136)
		tmp = t + ((y / z) * (x - t));
	elseif (a <= 1.15e+45)
		tmp = t * ((y - z) / (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[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.7e+25], t$95$1, If[LessEqual[a, 9e-136], N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e+45], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.7e25 or 1.15000000000000006e45 < a

   1. Initial program 96.3%

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

   2. Taylor expanded in z around 0 69.1%

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

      1. +-commutative 69.1%

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

      2. associate-/l* 79.3%

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

   4. Simplified 79.3%

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

   if -2.7e25 < a < 8.99999999999999944e-136

   1. Initial program 72.6%

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

      1. clear-num 72.4%

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

      2. associate-/r/ 72.5%

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

   3. Applied egg-rr 72.5%

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

   4. Taylor expanded in z around -inf 76.1%

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

      1. +-commutative 76.1%

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

      2. mul-1-neg 76.1%

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

      3. distribute-rgt-out-- 76.1%

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

      4. unsub-neg 76.1%

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

      5. associate-*r/ 83.1%

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

   6. Simplified 83.1%

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

   7. Taylor expanded in y around inf 71.1%

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

      1. associate-*l/ 78.1%

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

   9. Simplified 78.1%

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

   if 8.99999999999999944e-136 < a < 1.15000000000000006e45

   1. Initial program 61.7%

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

   2. Taylor expanded in t around inf 65.4%

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

      1. div-sub 65.4%

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

   4. Simplified 65.4%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+25}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-136}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 14: 67.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+111}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-139}:\\ \;\;\;\;x \cdot \left(1 - \frac{y - z}{a - z}\right)\\ \mathbf{elif}\;z \leq 85000000000:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.3e+111)
   (+ t (* (/ y z) (- x t)))
   (if (<= z -9.8e-139)
     (* x (- 1.0 (/ (- y z) (- a z))))
     (if (<= z 85000000000.0)
       (+ x (/ y (/ a (- t x))))
       (- t (* x (/ (- a y) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.3e+111) {
		tmp = t + ((y / z) * (x - t));
	} else if (z <= -9.8e-139) {
		tmp = x * (1.0 - ((y - z) / (a - z)));
	} else if (z <= 85000000000.0) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = 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 (z <= (-4.3d+111)) then
        tmp = t + ((y / z) * (x - t))
    else if (z <= (-9.8d-139)) then
        tmp = x * (1.0d0 - ((y - z) / (a - z)))
    else if (z <= 85000000000.0d0) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = 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 (z <= -4.3e+111) {
		tmp = t + ((y / z) * (x - t));
	} else if (z <= -9.8e-139) {
		tmp = x * (1.0 - ((y - z) / (a - z)));
	} else if (z <= 85000000000.0) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t - (x * ((a - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.3e+111:
		tmp = t + ((y / z) * (x - t))
	elif z <= -9.8e-139:
		tmp = x * (1.0 - ((y - z) / (a - z)))
	elif z <= 85000000000.0:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t - (x * ((a - y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.3e+111)
		tmp = Float64(t + Float64(Float64(y / z) * Float64(x - t)));
	elseif (z <= -9.8e-139)
		tmp = Float64(x * Float64(1.0 - Float64(Float64(y - z) / Float64(a - z))));
	elseif (z <= 85000000000.0)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t - Float64(x * Float64(Float64(a - y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.3e+111)
		tmp = t + ((y / z) * (x - t));
	elseif (z <= -9.8e-139)
		tmp = x * (1.0 - ((y - z) / (a - z)));
	elseif (z <= 85000000000.0)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t - (x * ((a - y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.3e+111], N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.8e-139], N[(x * N[(1.0 - N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 85000000000.0], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(x * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.29999999999999993e111

   1. Initial program 68.9%

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

      1. clear-num 68.6%

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

      2. associate-/r/ 68.4%

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

   3. Applied egg-rr 68.4%

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

   4. Taylor expanded in z around -inf 55.0%

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

      1. +-commutative 55.0%

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

      2. mul-1-neg 55.0%

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

      3. distribute-rgt-out-- 57.6%

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

      4. unsub-neg 57.6%

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

      5. associate-*r/ 85.6%

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

   6. Simplified 85.6%

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

   7. Taylor expanded in y around inf 62.5%

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

      1. associate-*l/ 83.3%

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

   9. Simplified 83.3%

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

   if -4.29999999999999993e111 < z < -9.80000000000000063e-139

   1. Initial program 89.3%

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

   2. Taylor expanded in x around inf 66.9%

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

      1. mul-1-neg 66.9%

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

      2. unsub-neg 66.9%

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

   4. Simplified 66.9%

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

   if -9.80000000000000063e-139 < z < 8.5e10

   1. Initial program 95.4%

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

   2. Taylor expanded in z around 0 76.2%

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

      1. +-commutative 76.2%

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

      2. associate-/l* 80.4%

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

   4. Simplified 80.4%

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

   if 8.5e10 < z

   1. Initial program 60.9%

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

      1. clear-num 60.8%

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

      2. associate-/r/ 61.0%

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

   3. Applied egg-rr 61.0%

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

   4. Taylor expanded in z around -inf 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

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

      3. distribute-rgt-out-- 67.9%

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

      4. unsub-neg 67.9%

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

      5. associate-*r/ 81.8%

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

   6. Simplified 81.8%

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

   7. Taylor expanded in t around 0 68.4%

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

      1. mul-1-neg 68.4%

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

      2. associate-*l/ 71.8%

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

      3. distribute-rgt-neg-out 71.8%

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

   9. Simplified 71.8%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+111}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-139}:\\ \;\;\;\;x \cdot \left(1 - \frac{y - z}{a - z}\right)\\ \mathbf{elif}\;z \leq 85000000000:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \end{array} \]

Alternative 15: 68.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+113}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 8300000000:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.6e+113)
   (+ t (* (/ y z) (- x t)))
   (if (<= z 8300000000.0)
     (+ x (/ y (/ a (- t x))))
     (- t (* x (/ (- a y) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e+113) {
		tmp = t + ((y / z) * (x - t));
	} else if (z <= 8300000000.0) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = 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 (z <= (-2.6d+113)) then
        tmp = t + ((y / z) * (x - t))
    else if (z <= 8300000000.0d0) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = 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 (z <= -2.6e+113) {
		tmp = t + ((y / z) * (x - t));
	} else if (z <= 8300000000.0) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t - (x * ((a - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.6e+113:
		tmp = t + ((y / z) * (x - t))
	elif z <= 8300000000.0:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t - (x * ((a - y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.6e+113)
		tmp = Float64(t + Float64(Float64(y / z) * Float64(x - t)));
	elseif (z <= 8300000000.0)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t - Float64(x * Float64(Float64(a - y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.6e+113)
		tmp = t + ((y / z) * (x - t));
	elseif (z <= 8300000000.0)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t - (x * ((a - y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.6e+113], N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8300000000.0], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(x * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5999999999999999e113

   1. Initial program 68.9%

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

      1. clear-num 68.6%

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

      2. associate-/r/ 68.4%

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

   3. Applied egg-rr 68.4%

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

   4. Taylor expanded in z around -inf 55.0%

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

      1. +-commutative 55.0%

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

      2. mul-1-neg 55.0%

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

      3. distribute-rgt-out-- 57.6%

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

      4. unsub-neg 57.6%

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

      5. associate-*r/ 85.6%

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

   6. Simplified 85.6%

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

   7. Taylor expanded in y around inf 62.5%

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

      1. associate-*l/ 83.3%

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

   9. Simplified 83.3%

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

   if -2.5999999999999999e113 < z < 8.3e9

   1. Initial program 93.6%

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

   2. Taylor expanded in z around 0 69.9%

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

      1. +-commutative 69.9%

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

      2. associate-/l* 74.0%

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

   4. Simplified 74.0%

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

   if 8.3e9 < z

   1. Initial program 60.9%

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

      1. clear-num 60.8%

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

      2. associate-/r/ 61.0%

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

   3. Applied egg-rr 61.0%

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

   4. Taylor expanded in z around -inf 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

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

      3. distribute-rgt-out-- 67.9%

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

      4. unsub-neg 67.9%

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

      5. associate-*r/ 81.8%

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

   6. Simplified 81.8%

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

   7. Taylor expanded in t around 0 68.4%

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

      1. mul-1-neg 68.4%

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

      2. associate-*l/ 71.8%

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

      3. distribute-rgt-neg-out 71.8%

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

   9. Simplified 71.8%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+113}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 8300000000:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \end{array} \]

Alternative 16: 37.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-198}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-151}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+70}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.4e+15)
   x
   (if (<= a -9e-198)
     t
     (if (<= a 9.2e-151) (* y (/ x z)) (if (<= a 2.8e+70) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.4e+15) {
		tmp = x;
	} else if (a <= -9e-198) {
		tmp = t;
	} else if (a <= 9.2e-151) {
		tmp = y * (x / z);
	} else if (a <= 2.8e+70) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.4d+15)) then
        tmp = x
    else if (a <= (-9d-198)) then
        tmp = t
    else if (a <= 9.2d-151) then
        tmp = y * (x / z)
    else if (a <= 2.8d+70) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.4e+15) {
		tmp = x;
	} else if (a <= -9e-198) {
		tmp = t;
	} else if (a <= 9.2e-151) {
		tmp = y * (x / z);
	} else if (a <= 2.8e+70) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.4e+15:
		tmp = x
	elif a <= -9e-198:
		tmp = t
	elif a <= 9.2e-151:
		tmp = y * (x / z)
	elif a <= 2.8e+70:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.4e+15)
		tmp = x;
	elseif (a <= -9e-198)
		tmp = t;
	elseif (a <= 9.2e-151)
		tmp = Float64(y * Float64(x / z));
	elseif (a <= 2.8e+70)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.4e+15)
		tmp = x;
	elseif (a <= -9e-198)
		tmp = t;
	elseif (a <= 9.2e-151)
		tmp = y * (x / z);
	elseif (a <= 2.8e+70)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.4e+15], x, If[LessEqual[a, -9e-198], t, If[LessEqual[a, 9.2e-151], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e+70], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.4e15 or 2.7999999999999999e70 < a

   1. Initial program 97.1%

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

   2. Taylor expanded in a around inf 61.7%

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

   if -3.4e15 < a < -8.9999999999999996e-198 or 9.19999999999999984e-151 < a < 2.7999999999999999e70

   1. Initial program 65.9%

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

   2. Taylor expanded in z around inf 39.3%

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

   if -8.9999999999999996e-198 < a < 9.19999999999999984e-151

   1. Initial program 77.7%

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

   2. Taylor expanded in y around inf 72.5%

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

      1. div-sub 72.5%

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

      2. *-commutative 72.5%

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

      3. associate-*r/ 70.7%

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

      4. associate-/l* 72.3%

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

   4. Simplified 72.3%

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

   5. Taylor expanded in t around 0 56.8%

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

      1. mul-1-neg 56.8%

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

      2. associate-/l* 56.6%

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

      3. distribute-neg-frac 56.6%

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

   7. Simplified 56.6%

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

   8. Taylor expanded in a around 0 54.4%

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

      1. *-commutative 54.4%

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

      2. associate-/l* 54.3%

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

      3. associate-/r/ 54.3%

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

   10. Simplified 54.3%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-198}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-151}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+70}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 37.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{-198}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-151}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+68}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.8e+14)
   x
   (if (<= a -9.8e-198)
     t
     (if (<= a 7e-151) (/ (* x y) z) (if (<= a 9.5e+68) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.8e+14) {
		tmp = x;
	} else if (a <= -9.8e-198) {
		tmp = t;
	} else if (a <= 7e-151) {
		tmp = (x * y) / z;
	} else if (a <= 9.5e+68) {
		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 <= (-5.8d+14)) then
        tmp = x
    else if (a <= (-9.8d-198)) then
        tmp = t
    else if (a <= 7d-151) then
        tmp = (x * y) / z
    else if (a <= 9.5d+68) 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 <= -5.8e+14) {
		tmp = x;
	} else if (a <= -9.8e-198) {
		tmp = t;
	} else if (a <= 7e-151) {
		tmp = (x * y) / z;
	} else if (a <= 9.5e+68) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.8e+14:
		tmp = x
	elif a <= -9.8e-198:
		tmp = t
	elif a <= 7e-151:
		tmp = (x * y) / z
	elif a <= 9.5e+68:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.8e+14)
		tmp = x;
	elseif (a <= -9.8e-198)
		tmp = t;
	elseif (a <= 7e-151)
		tmp = Float64(Float64(x * y) / z);
	elseif (a <= 9.5e+68)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.8e+14)
		tmp = x;
	elseif (a <= -9.8e-198)
		tmp = t;
	elseif (a <= 7e-151)
		tmp = (x * y) / z;
	elseif (a <= 9.5e+68)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.8e+14], x, If[LessEqual[a, -9.8e-198], t, If[LessEqual[a, 7e-151], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 9.5e+68], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.8e14 or 9.50000000000000069e68 < a

   1. Initial program 97.1%

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

   2. Taylor expanded in a around inf 61.7%

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

   if -5.8e14 < a < -9.8000000000000004e-198 or 6.99999999999999991e-151 < a < 9.50000000000000069e68

   1. Initial program 65.9%

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

   2. Taylor expanded in z around inf 39.3%

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

   if -9.8000000000000004e-198 < a < 6.99999999999999991e-151

   1. Initial program 77.7%

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

   2. Taylor expanded in y around inf 72.5%

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

      1. div-sub 72.5%

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

      2. *-commutative 72.5%

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

      3. associate-*r/ 70.7%

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

      4. associate-/l* 72.3%

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

   4. Simplified 72.3%

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

   5. Taylor expanded in a around 0 64.6%

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

      1. associate-*r/ 64.6%

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

      2. associate-*r* 64.6%

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

      3. mul-1-neg 64.6%

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

   7. Simplified 64.6%

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

   8. Taylor expanded in t around 0 54.4%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{-198}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-151}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+68}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 51.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+174}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+157}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e+174) t (if (<= z 2.05e+157) (+ x (/ y (/ a t))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+174) {
		tmp = t;
	} else if (z <= 2.05e+157) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2d+174)) then
        tmp = t
    else if (z <= 2.05d+157) then
        tmp = x + (y / (a / t))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+174) {
		tmp = t;
	} else if (z <= 2.05e+157) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2e+174:
		tmp = t
	elif z <= 2.05e+157:
		tmp = x + (y / (a / t))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e+174)
		tmp = t;
	elseif (z <= 2.05e+157)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2e+174)
		tmp = t;
	elseif (z <= 2.05e+157)
		tmp = x + (y / (a / t));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e+174], t, If[LessEqual[z, 2.05e+157], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000014e174 or 2.05000000000000008e157 < z

   1. Initial program 57.9%

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

   2. Taylor expanded in z around inf 75.4%

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

   if -2.00000000000000014e174 < z < 2.05000000000000008e157

   1. Initial program 89.2%

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

   2. Taylor expanded in z around 0 60.1%

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

      1. +-commutative 60.1%

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

      2. associate-/l* 65.2%

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

   4. Simplified 65.2%

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

   5. Taylor expanded in t around inf 55.9%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+174}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+157}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19: 38.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.2e+15) x (if (<= a 1.15e+69) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e+15) {
		tmp = x;
	} else if (a <= 1.15e+69) {
		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 <= (-3.2d+15)) then
        tmp = x
    else if (a <= 1.15d+69) 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 <= -3.2e+15) {
		tmp = x;
	} else if (a <= 1.15e+69) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.2e+15:
		tmp = x
	elif a <= 1.15e+69:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.2e+15)
		tmp = x;
	elseif (a <= 1.15e+69)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.2e+15)
		tmp = x;
	elseif (a <= 1.15e+69)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.2e+15], x, If[LessEqual[a, 1.15e+69], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.2e15 or 1.15000000000000008e69 < a

   1. Initial program 97.1%

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

   2. Taylor expanded in a around inf 61.7%

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

   if -3.2e15 < a < 1.15000000000000008e69

   1. Initial program 70.1%

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

   2. Taylor expanded in z around inf 33.7%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 25.2% 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 82.8%

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

2. Taylor expanded in z around inf 23.5%

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

3. Final simplification 23.5%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023199 
(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)))))