Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.4% → 94.0%

Time: 19.0s

Alternatives: 22

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: 79.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-306} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(t - \frac{y}{\frac{z}{t - x}}\right) + \frac{\left(t - x\right) \cdot a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-306) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+ (- t (/ y (/ z (- t x)))) (/ (* (- t x) a) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-306) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = (t - (y / (z / (t - x)))) + (((t - x) * a) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-1d-306)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = (t - (y / (z / (t - x)))) + (((t - x) * a) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-306) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = (t - (y / (z / (t - x)))) + (((t - x) * a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -1e-306) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = (t - (y / (z / (t - x)))) + (((t - x) * a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-306) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(Float64(t - Float64(y / Float64(z / Float64(t - x)))) + Float64(Float64(Float64(t - x) * a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -1e-306) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = (t - (y / (z / (t - x)))) + (((t - x) * a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-306], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t - x), $MachinePrecision] * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000003e-306 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.9%

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

   2. Taylor expanded in y around 0 80.1%

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

      1. div-sub 80.1%

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

      2. associate-*r/ 80.1%

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

      3. mul-1-neg 80.1%

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

      4. distribute-lft-neg-out 80.1%

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

      5. associate-*r/ 90.6%

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

      6. *-commutative 90.6%

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

      7. distribute-lft-out 91.9%

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

      8. sub-neg 91.9%

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

      9. associate-/r/ 94.3%

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

   4. Simplified 94.3%

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

   if -1.00000000000000003e-306 < (+.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. Taylor expanded in z around inf 81.6%

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

      1. sub-neg 81.6%

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

      2. +-commutative 81.6%

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

      3. mul-1-neg 81.6%

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

      4. unsub-neg 81.6%

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

      5. associate-/l* 92.6%

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

      6. mul-1-neg 92.6%

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

      7. remove-double-neg 92.6%

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

   4. Simplified 92.6%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-306} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(t - \frac{y}{\frac{z}{t - x}}\right) + \frac{\left(t - x\right) \cdot a}{z}\\ \end{array} \]

Alternative 2: 88.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-306} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-306) (not (<= t_1 0.0)))
     t_1
     (+ t (/ (* (- t x) (- a y)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-306) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-1d-306)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t + (((t - x) * (a - y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-306) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -1e-306) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-306) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -1e-306) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-306], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000003e-306 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.9%

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

   if -1.00000000000000003e-306 < (+.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. Taylor expanded in z around -inf 81.6%

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

      1. +-commutative 81.6%

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

      2. mul-1-neg 81.6%

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

      3. unsub-neg 81.6%

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

      4. distribute-rgt-out-- 81.6%

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

   4. Simplified 81.6%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-306} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]

Alternative 3: 93.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-306} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-306) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+ t (/ (* (- t x) (- a y)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-306) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-1d-306)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t + (((t - x) * (a - y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-306) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -1e-306) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-306) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -1e-306) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-306], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000003e-306 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.9%

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

   2. Taylor expanded in y around 0 80.1%

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

      1. div-sub 80.1%

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

      2. associate-*r/ 80.1%

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

      3. mul-1-neg 80.1%

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

      4. distribute-lft-neg-out 80.1%

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

      5. associate-*r/ 90.6%

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

      6. *-commutative 90.6%

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

      7. distribute-lft-out 91.9%

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

      8. sub-neg 91.9%

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

      9. associate-/r/ 94.3%

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

   4. Simplified 94.3%

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

   if -1.00000000000000003e-306 < (+.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. Taylor expanded in z around -inf 81.6%

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

      1. +-commutative 81.6%

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

      2. mul-1-neg 81.6%

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

      3. unsub-neg 81.6%

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

      4. distribute-rgt-out-- 81.6%

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

   4. Simplified 81.6%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-306} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]

Alternative 4: 47.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := t - \frac{y}{\frac{z}{t}}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{-297}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-88}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (- t (/ y (/ z t)))))
   (if (<= z -3.6e+61)
     t_2
     (if (<= z -4.8e-250)
       t_1
       (if (<= z -1.26e-297)
         (/ y (/ a t))
         (if (<= z 5.6e-191)
           t_1
           (if (<= z 2.05e-88)
             (* t (/ (- y z) a))
             (if (<= z 4.8e-66) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t - (y / (z / t));
	double tmp;
	if (z <= -3.6e+61) {
		tmp = t_2;
	} else if (z <= -4.8e-250) {
		tmp = t_1;
	} else if (z <= -1.26e-297) {
		tmp = y / (a / t);
	} else if (z <= 5.6e-191) {
		tmp = t_1;
	} else if (z <= 2.05e-88) {
		tmp = t * ((y - z) / a);
	} else if (z <= 4.8e-66) {
		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 = x * (1.0d0 - (y / a))
    t_2 = t - (y / (z / t))
    if (z <= (-3.6d+61)) then
        tmp = t_2
    else if (z <= (-4.8d-250)) then
        tmp = t_1
    else if (z <= (-1.26d-297)) then
        tmp = y / (a / t)
    else if (z <= 5.6d-191) then
        tmp = t_1
    else if (z <= 2.05d-88) then
        tmp = t * ((y - z) / a)
    else if (z <= 4.8d-66) 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 = x * (1.0 - (y / a));
	double t_2 = t - (y / (z / t));
	double tmp;
	if (z <= -3.6e+61) {
		tmp = t_2;
	} else if (z <= -4.8e-250) {
		tmp = t_1;
	} else if (z <= -1.26e-297) {
		tmp = y / (a / t);
	} else if (z <= 5.6e-191) {
		tmp = t_1;
	} else if (z <= 2.05e-88) {
		tmp = t * ((y - z) / a);
	} else if (z <= 4.8e-66) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = t - (y / (z / t))
	tmp = 0
	if z <= -3.6e+61:
		tmp = t_2
	elif z <= -4.8e-250:
		tmp = t_1
	elif z <= -1.26e-297:
		tmp = y / (a / t)
	elif z <= 5.6e-191:
		tmp = t_1
	elif z <= 2.05e-88:
		tmp = t * ((y - z) / a)
	elif z <= 4.8e-66:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(t - Float64(y / Float64(z / t)))
	tmp = 0.0
	if (z <= -3.6e+61)
		tmp = t_2;
	elseif (z <= -4.8e-250)
		tmp = t_1;
	elseif (z <= -1.26e-297)
		tmp = Float64(y / Float64(a / t));
	elseif (z <= 5.6e-191)
		tmp = t_1;
	elseif (z <= 2.05e-88)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 4.8e-66)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = t - (y / (z / t));
	tmp = 0.0;
	if (z <= -3.6e+61)
		tmp = t_2;
	elseif (z <= -4.8e-250)
		tmp = t_1;
	elseif (z <= -1.26e-297)
		tmp = y / (a / t);
	elseif (z <= 5.6e-191)
		tmp = t_1;
	elseif (z <= 2.05e-88)
		tmp = t * ((y - z) / a);
	elseif (z <= 4.8e-66)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e+61], t$95$2, If[LessEqual[z, -4.8e-250], t$95$1, If[LessEqual[z, -1.26e-297], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e-191], t$95$1, If[LessEqual[z, 2.05e-88], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e-66], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.6000000000000001e61 or 4.80000000000000052e-66 < z

   1. Initial program 71.8%

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

   2. Taylor expanded in x around 0 52.1%

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

      1. associate-*r/ 71.7%

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

   4. Simplified 71.7%

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

   5. Taylor expanded in a around 0 63.1%

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

      1. associate-*r/ 63.1%

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

      2. neg-mul-1 63.1%

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

   7. Simplified 63.1%

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

   8. Taylor expanded in y around 0 55.8%

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

      1. +-commutative 55.8%

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

      2. mul-1-neg 55.8%

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

      3. unsub-neg 55.8%

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

      4. associate-/l* 63.0%

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

   10. Simplified 63.0%

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

   if -3.6000000000000001e61 < z < -4.7999999999999998e-250 or -1.2599999999999999e-297 < z < 5.60000000000000023e-191 or 2.0500000000000001e-88 < z < 4.80000000000000052e-66

   1. Initial program 92.2%

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

   2. Taylor expanded in y around 0 91.3%

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

      1. div-sub 91.3%

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

      2. associate-*r/ 91.3%

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

      3. mul-1-neg 91.3%

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

      4. distribute-lft-neg-out 91.3%

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

      5. associate-*r/ 90.2%

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

      6. *-commutative 90.2%

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

      7. distribute-lft-out 92.2%

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

      8. sub-neg 92.2%

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

      9. associate-/r/ 95.0%

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

   4. Simplified 95.0%

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

   5. Taylor expanded in z around 0 75.3%

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

   6. Taylor expanded in x around inf 59.2%

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

      1. *-commutative 59.2%

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

      2. mul-1-neg 59.2%

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

      3. unsub-neg 59.2%

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

   8. Simplified 59.2%

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

   if -4.7999999999999998e-250 < z < -1.2599999999999999e-297

   1. Initial program 99.9%

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

   2. Taylor expanded in y around -inf 76.7%

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

   3. Taylor expanded in t around inf 64.1%

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

      1. associate-/l* 79.3%

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

   5. Simplified 79.3%

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

   6. Taylor expanded in a around inf 64.1%

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

      1. associate-/l* 79.3%

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

   8. Simplified 79.3%

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

   if 5.60000000000000023e-191 < z < 2.0500000000000001e-88

   1. Initial program 91.3%

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

   2. Taylor expanded in x around 0 53.9%

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

      1. associate-*r/ 58.1%

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

   4. Simplified 58.1%

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

   5. Taylor expanded in a around inf 53.5%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+61}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-250}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{-297}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-191}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-88}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \end{array} \]

Alternative 5: 47.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := t - \frac{y}{\frac{z}{t}}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-298}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-189}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-88}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (- t (/ y (/ z t)))))
   (if (<= z -1.7e+63)
     t_2
     (if (<= z -3.5e-249)
       t_1
       (if (<= z -1.7e-298)
         (/ y (/ a t))
         (if (<= z 5.2e-189)
           (- x (/ y (/ a x)))
           (if (<= z 1.65e-88)
             (* t (/ (- y z) a))
             (if (<= z 8e-66) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t - (y / (z / t));
	double tmp;
	if (z <= -1.7e+63) {
		tmp = t_2;
	} else if (z <= -3.5e-249) {
		tmp = t_1;
	} else if (z <= -1.7e-298) {
		tmp = y / (a / t);
	} else if (z <= 5.2e-189) {
		tmp = x - (y / (a / x));
	} else if (z <= 1.65e-88) {
		tmp = t * ((y - z) / a);
	} else if (z <= 8e-66) {
		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 = x * (1.0d0 - (y / a))
    t_2 = t - (y / (z / t))
    if (z <= (-1.7d+63)) then
        tmp = t_2
    else if (z <= (-3.5d-249)) then
        tmp = t_1
    else if (z <= (-1.7d-298)) then
        tmp = y / (a / t)
    else if (z <= 5.2d-189) then
        tmp = x - (y / (a / x))
    else if (z <= 1.65d-88) then
        tmp = t * ((y - z) / a)
    else if (z <= 8d-66) 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 = x * (1.0 - (y / a));
	double t_2 = t - (y / (z / t));
	double tmp;
	if (z <= -1.7e+63) {
		tmp = t_2;
	} else if (z <= -3.5e-249) {
		tmp = t_1;
	} else if (z <= -1.7e-298) {
		tmp = y / (a / t);
	} else if (z <= 5.2e-189) {
		tmp = x - (y / (a / x));
	} else if (z <= 1.65e-88) {
		tmp = t * ((y - z) / a);
	} else if (z <= 8e-66) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = t - (y / (z / t))
	tmp = 0
	if z <= -1.7e+63:
		tmp = t_2
	elif z <= -3.5e-249:
		tmp = t_1
	elif z <= -1.7e-298:
		tmp = y / (a / t)
	elif z <= 5.2e-189:
		tmp = x - (y / (a / x))
	elif z <= 1.65e-88:
		tmp = t * ((y - z) / a)
	elif z <= 8e-66:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(t - Float64(y / Float64(z / t)))
	tmp = 0.0
	if (z <= -1.7e+63)
		tmp = t_2;
	elseif (z <= -3.5e-249)
		tmp = t_1;
	elseif (z <= -1.7e-298)
		tmp = Float64(y / Float64(a / t));
	elseif (z <= 5.2e-189)
		tmp = Float64(x - Float64(y / Float64(a / x)));
	elseif (z <= 1.65e-88)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 8e-66)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = t - (y / (z / t));
	tmp = 0.0;
	if (z <= -1.7e+63)
		tmp = t_2;
	elseif (z <= -3.5e-249)
		tmp = t_1;
	elseif (z <= -1.7e-298)
		tmp = y / (a / t);
	elseif (z <= 5.2e-189)
		tmp = x - (y / (a / x));
	elseif (z <= 1.65e-88)
		tmp = t * ((y - z) / a);
	elseif (z <= 8e-66)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+63], t$95$2, If[LessEqual[z, -3.5e-249], t$95$1, If[LessEqual[z, -1.7e-298], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-189], N[(x - N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e-88], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-66], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.6999999999999999e63 or 7.9999999999999998e-66 < z

   1. Initial program 71.8%

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

   2. Taylor expanded in x around 0 52.1%

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

      1. associate-*r/ 71.7%

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

   4. Simplified 71.7%

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

   5. Taylor expanded in a around 0 63.1%

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

      1. associate-*r/ 63.1%

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

      2. neg-mul-1 63.1%

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

   7. Simplified 63.1%

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

   8. Taylor expanded in y around 0 55.8%

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

      1. +-commutative 55.8%

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

      2. mul-1-neg 55.8%

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

      3. unsub-neg 55.8%

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

      4. associate-/l* 63.0%

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

   10. Simplified 63.0%

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

   if -1.6999999999999999e63 < z < -3.50000000000000013e-249 or 1.64999999999999997e-88 < z < 7.9999999999999998e-66

   1. Initial program 88.9%

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

   2. Taylor expanded in y around 0 87.6%

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

      1. div-sub 87.6%

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

      2. associate-*r/ 87.6%

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

      3. mul-1-neg 87.6%

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

      4. distribute-lft-neg-out 87.6%

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

      5. associate-*r/ 87.5%

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

      6. *-commutative 87.5%

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

      7. distribute-lft-out 88.9%

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

      8. sub-neg 88.9%

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

      9. associate-/r/ 92.8%

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

   4. Simplified 92.8%

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

   5. Taylor expanded in z around 0 64.6%

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

   6. Taylor expanded in x around inf 48.7%

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

      1. *-commutative 48.7%

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

      2. mul-1-neg 48.7%

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

      3. unsub-neg 48.7%

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

   8. Simplified 48.7%

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

   if -3.50000000000000013e-249 < z < -1.7e-298

   1. Initial program 99.9%

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

   2. Taylor expanded in y around -inf 76.7%

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

   3. Taylor expanded in t around inf 64.1%

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

      1. associate-/l* 79.3%

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

   5. Simplified 79.3%

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

   6. Taylor expanded in a around inf 64.1%

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

      1. associate-/l* 79.3%

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

   8. Simplified 79.3%

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

   if -1.7e-298 < z < 5.1999999999999998e-189

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 99.9%

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

      1. div-sub 99.9%

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

      2. associate-*r/ 99.9%

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

      3. mul-1-neg 99.9%

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

      4. distribute-lft-neg-out 99.9%

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

      5. associate-*r/ 96.7%

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

      6. *-commutative 96.7%

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

      7. distribute-lft-out 99.9%

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

      8. sub-neg 99.9%

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

      9. associate-/r/ 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around 0 100.0%

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

   6. Taylor expanded in t around 0 83.6%

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

      1. +-commutative 83.6%

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

      2. mul-1-neg 83.6%

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

      3. unsub-neg 83.6%

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

      4. associate-/l* 83.6%

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

   8. Simplified 83.6%

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

   if 5.1999999999999998e-189 < z < 1.64999999999999997e-88

   1. Initial program 91.3%

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

   2. Taylor expanded in x around 0 53.9%

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

      1. associate-*r/ 58.1%

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

   4. Simplified 58.1%

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

   5. Taylor expanded in a around inf 53.5%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+63}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-249}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-298}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-189}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-88}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \end{array} \]

Alternative 6: 47.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := t - \frac{y}{\frac{z}{t}}\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.66 \cdot 10^{-301}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-188}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-88}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (- t (/ y (/ z t)))))
   (if (<= z -7.8e+61)
     t_2
     (if (<= z -5.5e-250)
       t_1
       (if (<= z -1.66e-301)
         (/ y (/ a t))
         (if (<= z 1.95e-188)
           (- x (/ y (/ a x)))
           (if (<= z 2.05e-88)
             (/ t (/ a (- y z)))
             (if (<= z 9.2e-66) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t - (y / (z / t));
	double tmp;
	if (z <= -7.8e+61) {
		tmp = t_2;
	} else if (z <= -5.5e-250) {
		tmp = t_1;
	} else if (z <= -1.66e-301) {
		tmp = y / (a / t);
	} else if (z <= 1.95e-188) {
		tmp = x - (y / (a / x));
	} else if (z <= 2.05e-88) {
		tmp = t / (a / (y - z));
	} else if (z <= 9.2e-66) {
		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 = x * (1.0d0 - (y / a))
    t_2 = t - (y / (z / t))
    if (z <= (-7.8d+61)) then
        tmp = t_2
    else if (z <= (-5.5d-250)) then
        tmp = t_1
    else if (z <= (-1.66d-301)) then
        tmp = y / (a / t)
    else if (z <= 1.95d-188) then
        tmp = x - (y / (a / x))
    else if (z <= 2.05d-88) then
        tmp = t / (a / (y - z))
    else if (z <= 9.2d-66) 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 = x * (1.0 - (y / a));
	double t_2 = t - (y / (z / t));
	double tmp;
	if (z <= -7.8e+61) {
		tmp = t_2;
	} else if (z <= -5.5e-250) {
		tmp = t_1;
	} else if (z <= -1.66e-301) {
		tmp = y / (a / t);
	} else if (z <= 1.95e-188) {
		tmp = x - (y / (a / x));
	} else if (z <= 2.05e-88) {
		tmp = t / (a / (y - z));
	} else if (z <= 9.2e-66) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = t - (y / (z / t))
	tmp = 0
	if z <= -7.8e+61:
		tmp = t_2
	elif z <= -5.5e-250:
		tmp = t_1
	elif z <= -1.66e-301:
		tmp = y / (a / t)
	elif z <= 1.95e-188:
		tmp = x - (y / (a / x))
	elif z <= 2.05e-88:
		tmp = t / (a / (y - z))
	elif z <= 9.2e-66:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(t - Float64(y / Float64(z / t)))
	tmp = 0.0
	if (z <= -7.8e+61)
		tmp = t_2;
	elseif (z <= -5.5e-250)
		tmp = t_1;
	elseif (z <= -1.66e-301)
		tmp = Float64(y / Float64(a / t));
	elseif (z <= 1.95e-188)
		tmp = Float64(x - Float64(y / Float64(a / x)));
	elseif (z <= 2.05e-88)
		tmp = Float64(t / Float64(a / Float64(y - z)));
	elseif (z <= 9.2e-66)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = t - (y / (z / t));
	tmp = 0.0;
	if (z <= -7.8e+61)
		tmp = t_2;
	elseif (z <= -5.5e-250)
		tmp = t_1;
	elseif (z <= -1.66e-301)
		tmp = y / (a / t);
	elseif (z <= 1.95e-188)
		tmp = x - (y / (a / x));
	elseif (z <= 2.05e-88)
		tmp = t / (a / (y - z));
	elseif (z <= 9.2e-66)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e+61], t$95$2, If[LessEqual[z, -5.5e-250], t$95$1, If[LessEqual[z, -1.66e-301], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e-188], N[(x - N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e-88], N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e-66], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.79999999999999975e61 or 9.19999999999999967e-66 < z

   1. Initial program 71.8%

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

   2. Taylor expanded in x around 0 52.1%

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

      1. associate-*r/ 71.7%

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

   4. Simplified 71.7%

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

   5. Taylor expanded in a around 0 63.1%

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

      1. associate-*r/ 63.1%

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

      2. neg-mul-1 63.1%

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

   7. Simplified 63.1%

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

   8. Taylor expanded in y around 0 55.8%

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

      1. +-commutative 55.8%

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

      2. mul-1-neg 55.8%

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

      3. unsub-neg 55.8%

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

      4. associate-/l* 63.0%

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

   10. Simplified 63.0%

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

   if -7.79999999999999975e61 < z < -5.5e-250 or 2.0500000000000001e-88 < z < 9.19999999999999967e-66

   1. Initial program 88.9%

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

   2. Taylor expanded in y around 0 87.6%

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

      1. div-sub 87.6%

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

      2. associate-*r/ 87.6%

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

      3. mul-1-neg 87.6%

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

      4. distribute-lft-neg-out 87.6%

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

      5. associate-*r/ 87.5%

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

      6. *-commutative 87.5%

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

      7. distribute-lft-out 88.9%

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

      8. sub-neg 88.9%

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

      9. associate-/r/ 92.8%

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

   4. Simplified 92.8%

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

   5. Taylor expanded in z around 0 64.6%

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

   6. Taylor expanded in x around inf 48.7%

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

      1. *-commutative 48.7%

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

      2. mul-1-neg 48.7%

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

      3. unsub-neg 48.7%

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

   8. Simplified 48.7%

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

   if -5.5e-250 < z < -1.65999999999999991e-301

   1. Initial program 99.9%

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

   2. Taylor expanded in y around -inf 76.7%

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

   3. Taylor expanded in t around inf 64.1%

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

      1. associate-/l* 79.3%

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

   5. Simplified 79.3%

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

   6. Taylor expanded in a around inf 64.1%

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

      1. associate-/l* 79.3%

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

   8. Simplified 79.3%

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

   if -1.65999999999999991e-301 < z < 1.94999999999999988e-188

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 99.9%

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

      1. div-sub 99.9%

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

      2. associate-*r/ 99.9%

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

      3. mul-1-neg 99.9%

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

      4. distribute-lft-neg-out 99.9%

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

      5. associate-*r/ 96.7%

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

      6. *-commutative 96.7%

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

      7. distribute-lft-out 99.9%

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

      8. sub-neg 99.9%

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

      9. associate-/r/ 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around 0 100.0%

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

   6. Taylor expanded in t around 0 83.6%

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

      1. +-commutative 83.6%

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

      2. mul-1-neg 83.6%

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

      3. unsub-neg 83.6%

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

      4. associate-/l* 83.6%

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

   8. Simplified 83.6%

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

   if 1.94999999999999988e-188 < z < 2.0500000000000001e-88

   1. Initial program 91.3%

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

   2. Taylor expanded in x around 0 53.9%

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

      1. associate-*r/ 58.1%

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

   4. Simplified 58.1%

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

   5. Taylor expanded in a around inf 45.1%

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

      1. associate-/l* 53.5%

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

   7. Simplified 53.5%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+61}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-250}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -1.66 \cdot 10^{-301}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-188}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-88}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \end{array} \]

Alternative 7: 47.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := t - \frac{y}{\frac{z}{t}}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-299}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-189}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-88}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (- t (/ y (/ z t)))))
   (if (<= z -1.25e+64)
     t_2
     (if (<= z -2.8e-248)
       t_1
       (if (<= z -1.9e-299)
         (/ y (/ (- a z) t))
         (if (<= z 2.75e-189)
           (- x (/ y (/ a x)))
           (if (<= z 1.35e-88)
             (/ t (/ a (- y z)))
             (if (<= z 4.2e-66) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t - (y / (z / t));
	double tmp;
	if (z <= -1.25e+64) {
		tmp = t_2;
	} else if (z <= -2.8e-248) {
		tmp = t_1;
	} else if (z <= -1.9e-299) {
		tmp = y / ((a - z) / t);
	} else if (z <= 2.75e-189) {
		tmp = x - (y / (a / x));
	} else if (z <= 1.35e-88) {
		tmp = t / (a / (y - z));
	} else if (z <= 4.2e-66) {
		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 = x * (1.0d0 - (y / a))
    t_2 = t - (y / (z / t))
    if (z <= (-1.25d+64)) then
        tmp = t_2
    else if (z <= (-2.8d-248)) then
        tmp = t_1
    else if (z <= (-1.9d-299)) then
        tmp = y / ((a - z) / t)
    else if (z <= 2.75d-189) then
        tmp = x - (y / (a / x))
    else if (z <= 1.35d-88) then
        tmp = t / (a / (y - z))
    else if (z <= 4.2d-66) 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 = x * (1.0 - (y / a));
	double t_2 = t - (y / (z / t));
	double tmp;
	if (z <= -1.25e+64) {
		tmp = t_2;
	} else if (z <= -2.8e-248) {
		tmp = t_1;
	} else if (z <= -1.9e-299) {
		tmp = y / ((a - z) / t);
	} else if (z <= 2.75e-189) {
		tmp = x - (y / (a / x));
	} else if (z <= 1.35e-88) {
		tmp = t / (a / (y - z));
	} else if (z <= 4.2e-66) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = t - (y / (z / t))
	tmp = 0
	if z <= -1.25e+64:
		tmp = t_2
	elif z <= -2.8e-248:
		tmp = t_1
	elif z <= -1.9e-299:
		tmp = y / ((a - z) / t)
	elif z <= 2.75e-189:
		tmp = x - (y / (a / x))
	elif z <= 1.35e-88:
		tmp = t / (a / (y - z))
	elif z <= 4.2e-66:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(t - Float64(y / Float64(z / t)))
	tmp = 0.0
	if (z <= -1.25e+64)
		tmp = t_2;
	elseif (z <= -2.8e-248)
		tmp = t_1;
	elseif (z <= -1.9e-299)
		tmp = Float64(y / Float64(Float64(a - z) / t));
	elseif (z <= 2.75e-189)
		tmp = Float64(x - Float64(y / Float64(a / x)));
	elseif (z <= 1.35e-88)
		tmp = Float64(t / Float64(a / Float64(y - z)));
	elseif (z <= 4.2e-66)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = t - (y / (z / t));
	tmp = 0.0;
	if (z <= -1.25e+64)
		tmp = t_2;
	elseif (z <= -2.8e-248)
		tmp = t_1;
	elseif (z <= -1.9e-299)
		tmp = y / ((a - z) / t);
	elseif (z <= 2.75e-189)
		tmp = x - (y / (a / x));
	elseif (z <= 1.35e-88)
		tmp = t / (a / (y - z));
	elseif (z <= 4.2e-66)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e+64], t$95$2, If[LessEqual[z, -2.8e-248], t$95$1, If[LessEqual[z, -1.9e-299], N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.75e-189], N[(x - N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e-88], N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-66], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.25e64 or 4.2000000000000001e-66 < z

   1. Initial program 71.8%

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

   2. Taylor expanded in x around 0 52.1%

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

      1. associate-*r/ 71.7%

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

   4. Simplified 71.7%

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

   5. Taylor expanded in a around 0 63.1%

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

      1. associate-*r/ 63.1%

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

      2. neg-mul-1 63.1%

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

   7. Simplified 63.1%

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

   8. Taylor expanded in y around 0 55.8%

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

      1. +-commutative 55.8%

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

      2. mul-1-neg 55.8%

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

      3. unsub-neg 55.8%

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

      4. associate-/l* 63.0%

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

   10. Simplified 63.0%

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

   if -1.25e64 < z < -2.8000000000000001e-248 or 1.34999999999999997e-88 < z < 4.2000000000000001e-66

   1. Initial program 88.9%

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

   2. Taylor expanded in y around 0 87.6%

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

      1. div-sub 87.6%

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

      2. associate-*r/ 87.6%

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

      3. mul-1-neg 87.6%

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

      4. distribute-lft-neg-out 87.6%

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

      5. associate-*r/ 87.5%

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

      6. *-commutative 87.5%

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

      7. distribute-lft-out 88.9%

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

      8. sub-neg 88.9%

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

      9. associate-/r/ 92.8%

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

   4. Simplified 92.8%

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

   5. Taylor expanded in z around 0 64.6%

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

   6. Taylor expanded in x around inf 48.7%

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

      1. *-commutative 48.7%

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

      2. mul-1-neg 48.7%

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

      3. unsub-neg 48.7%

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

   8. Simplified 48.7%

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

   if -2.8000000000000001e-248 < z < -1.9000000000000001e-299

   1. Initial program 99.9%

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

   2. Taylor expanded in y around -inf 76.7%

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

   3. Taylor expanded in t around inf 64.1%

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

      1. associate-/l* 79.3%

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

   5. Simplified 79.3%

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

   if -1.9000000000000001e-299 < z < 2.7499999999999999e-189

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 99.9%

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

      1. div-sub 99.9%

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

      2. associate-*r/ 99.9%

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

      3. mul-1-neg 99.9%

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

      4. distribute-lft-neg-out 99.9%

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

      5. associate-*r/ 96.7%

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

      6. *-commutative 96.7%

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

      7. distribute-lft-out 99.9%

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

      8. sub-neg 99.9%

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

      9. associate-/r/ 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around 0 100.0%

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

   6. Taylor expanded in t around 0 83.6%

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

      1. +-commutative 83.6%

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

      2. mul-1-neg 83.6%

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

      3. unsub-neg 83.6%

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

      4. associate-/l* 83.6%

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

   8. Simplified 83.6%

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

   if 2.7499999999999999e-189 < z < 1.34999999999999997e-88

   1. Initial program 91.3%

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

   2. Taylor expanded in x around 0 53.9%

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

      1. associate-*r/ 58.1%

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

   4. Simplified 58.1%

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

   5. Taylor expanded in a around inf 45.1%

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

      1. associate-/l* 53.5%

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

   7. Simplified 53.5%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+64}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-248}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-299}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-189}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-88}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \end{array} \]

Alternative 8: 47.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-303}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-188}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-88}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -3.7e+61)
     (* t (/ (- z y) z))
     (if (<= z -4.8e-250)
       t_1
       (if (<= z -7.8e-303)
         (/ y (/ (- a z) t))
         (if (<= z 4.8e-188)
           (- x (/ y (/ a x)))
           (if (<= z 2.4e-88)
             (/ t (/ a (- y z)))
             (if (<= z 2.4e-66) t_1 (- t (/ y (/ z t)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -3.7e+61) {
		tmp = t * ((z - y) / z);
	} else if (z <= -4.8e-250) {
		tmp = t_1;
	} else if (z <= -7.8e-303) {
		tmp = y / ((a - z) / t);
	} else if (z <= 4.8e-188) {
		tmp = x - (y / (a / x));
	} else if (z <= 2.4e-88) {
		tmp = t / (a / (y - z));
	} else if (z <= 2.4e-66) {
		tmp = t_1;
	} else {
		tmp = t - (y / (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-3.7d+61)) then
        tmp = t * ((z - y) / z)
    else if (z <= (-4.8d-250)) then
        tmp = t_1
    else if (z <= (-7.8d-303)) then
        tmp = y / ((a - z) / t)
    else if (z <= 4.8d-188) then
        tmp = x - (y / (a / x))
    else if (z <= 2.4d-88) then
        tmp = t / (a / (y - z))
    else if (z <= 2.4d-66) then
        tmp = t_1
    else
        tmp = t - (y / (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -3.7e+61) {
		tmp = t * ((z - y) / z);
	} else if (z <= -4.8e-250) {
		tmp = t_1;
	} else if (z <= -7.8e-303) {
		tmp = y / ((a - z) / t);
	} else if (z <= 4.8e-188) {
		tmp = x - (y / (a / x));
	} else if (z <= 2.4e-88) {
		tmp = t / (a / (y - z));
	} else if (z <= 2.4e-66) {
		tmp = t_1;
	} else {
		tmp = t - (y / (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -3.7e+61:
		tmp = t * ((z - y) / z)
	elif z <= -4.8e-250:
		tmp = t_1
	elif z <= -7.8e-303:
		tmp = y / ((a - z) / t)
	elif z <= 4.8e-188:
		tmp = x - (y / (a / x))
	elif z <= 2.4e-88:
		tmp = t / (a / (y - z))
	elif z <= 2.4e-66:
		tmp = t_1
	else:
		tmp = t - (y / (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -3.7e+61)
		tmp = Float64(t * Float64(Float64(z - y) / z));
	elseif (z <= -4.8e-250)
		tmp = t_1;
	elseif (z <= -7.8e-303)
		tmp = Float64(y / Float64(Float64(a - z) / t));
	elseif (z <= 4.8e-188)
		tmp = Float64(x - Float64(y / Float64(a / x)));
	elseif (z <= 2.4e-88)
		tmp = Float64(t / Float64(a / Float64(y - z)));
	elseif (z <= 2.4e-66)
		tmp = t_1;
	else
		tmp = Float64(t - Float64(y / Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -3.7e+61)
		tmp = t * ((z - y) / z);
	elseif (z <= -4.8e-250)
		tmp = t_1;
	elseif (z <= -7.8e-303)
		tmp = y / ((a - z) / t);
	elseif (z <= 4.8e-188)
		tmp = x - (y / (a / x));
	elseif (z <= 2.4e-88)
		tmp = t / (a / (y - z));
	elseif (z <= 2.4e-66)
		tmp = t_1;
	else
		tmp = t - (y / (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.7e+61], N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.8e-250], t$95$1, If[LessEqual[z, -7.8e-303], N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e-188], N[(x - N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e-88], N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e-66], t$95$1, N[(t - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.70000000000000003e61

   1. Initial program 68.8%

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

   2. Taylor expanded in x around 0 45.4%

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

      1. associate-*r/ 64.5%

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

   4. Simplified 64.5%

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

   5. Taylor expanded in a around 0 59.5%

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

      1. associate-*r/ 59.5%

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

      2. neg-mul-1 59.5%

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

   7. Simplified 59.5%

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

   if -3.70000000000000003e61 < z < -4.7999999999999998e-250 or 2.4e-88 < z < 2.40000000000000026e-66

   1. Initial program 88.9%

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

   2. Taylor expanded in y around 0 87.6%

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

      1. div-sub 87.6%

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

      2. associate-*r/ 87.6%

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

      3. mul-1-neg 87.6%

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

      4. distribute-lft-neg-out 87.6%

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

      5. associate-*r/ 87.5%

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

      6. *-commutative 87.5%

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

      7. distribute-lft-out 88.9%

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

      8. sub-neg 88.9%

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

      9. associate-/r/ 92.8%

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

   4. Simplified 92.8%

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

   5. Taylor expanded in z around 0 64.6%

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

   6. Taylor expanded in x around inf 48.7%

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

      1. *-commutative 48.7%

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

      2. mul-1-neg 48.7%

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

      3. unsub-neg 48.7%

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

   8. Simplified 48.7%

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

   if -4.7999999999999998e-250 < z < -7.7999999999999998e-303

   1. Initial program 99.9%

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

   2. Taylor expanded in y around -inf 76.7%

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

   3. Taylor expanded in t around inf 64.1%

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

      1. associate-/l* 79.3%

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

   5. Simplified 79.3%

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

   if -7.7999999999999998e-303 < z < 4.8e-188

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 99.9%

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

      1. div-sub 99.9%

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

      2. associate-*r/ 99.9%

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

      3. mul-1-neg 99.9%

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

      4. distribute-lft-neg-out 99.9%

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

      5. associate-*r/ 96.7%

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

      6. *-commutative 96.7%

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

      7. distribute-lft-out 99.9%

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

      8. sub-neg 99.9%

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

      9. associate-/r/ 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around 0 100.0%

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

   6. Taylor expanded in t around 0 83.6%

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

      1. +-commutative 83.6%

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

      2. mul-1-neg 83.6%

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

      3. unsub-neg 83.6%

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

      4. associate-/l* 83.6%

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

   8. Simplified 83.6%

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

   if 4.8e-188 < z < 2.4e-88

   1. Initial program 91.3%

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

   2. Taylor expanded in x around 0 53.9%

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

      1. associate-*r/ 58.1%

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

   4. Simplified 58.1%

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

   5. Taylor expanded in a around inf 45.1%

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

      1. associate-/l* 53.5%

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

   7. Simplified 53.5%

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

   if 2.40000000000000026e-66 < z

   1. Initial program 74.2%

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

   2. Taylor expanded in x around 0 57.6%

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

      1. associate-*r/ 77.5%

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

   4. Simplified 77.5%

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

   5. Taylor expanded in a around 0 65.9%

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

      1. associate-*r/ 65.9%

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

      2. neg-mul-1 65.9%

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

   7. Simplified 65.9%

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

   8. Taylor expanded in y around 0 58.6%

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

      1. +-commutative 58.6%

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

      2. mul-1-neg 58.6%

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

      3. unsub-neg 58.6%

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

      4. associate-/l* 65.9%

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

   10. Simplified 65.9%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-250}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-303}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-188}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-88}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \end{array} \]

Alternative 9: 71.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.52 \cdot 10^{-142}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 310000:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ a (- t x))))))
   (if (<= a -5.2e-8)
     t_1
     (if (<= a -1.52e-142)
       (/ t (/ (- a z) (- y z)))
       (if (<= a 310000.0) (+ t (/ (* y (- x t)) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / (a / (t - x)));
	double tmp;
	if (a <= -5.2e-8) {
		tmp = t_1;
	} else if (a <= -1.52e-142) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 310000.0) {
		tmp = t + ((y * (x - t)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) / (a / (t - x)))
    if (a <= (-5.2d-8)) then
        tmp = t_1
    else if (a <= (-1.52d-142)) then
        tmp = t / ((a - z) / (y - z))
    else if (a <= 310000.0d0) then
        tmp = t + ((y * (x - t)) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / (a / (t - x)));
	double tmp;
	if (a <= -5.2e-8) {
		tmp = t_1;
	} else if (a <= -1.52e-142) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 310000.0) {
		tmp = t + ((y * (x - t)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / (a / (t - x)))
	tmp = 0
	if a <= -5.2e-8:
		tmp = t_1
	elif a <= -1.52e-142:
		tmp = t / ((a - z) / (y - z))
	elif a <= 310000.0:
		tmp = t + ((y * (x - t)) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(a / Float64(t - x))))
	tmp = 0.0
	if (a <= -5.2e-8)
		tmp = t_1;
	elseif (a <= -1.52e-142)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (a <= 310000.0)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) / (a / (t - x)));
	tmp = 0.0;
	if (a <= -5.2e-8)
		tmp = t_1;
	elseif (a <= -1.52e-142)
		tmp = t / ((a - z) / (y - z));
	elseif (a <= 310000.0)
		tmp = t + ((y * (x - t)) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.2e-8], t$95$1, If[LessEqual[a, -1.52e-142], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 310000.0], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.2000000000000002e-8 or 3.1e5 < a

   1. Initial program 92.1%

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

   2. Taylor expanded in a around inf 66.8%

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

      1. +-commutative 66.8%

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

      2. associate-/l* 79.9%

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

   4. Simplified 79.9%

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

   if -5.2000000000000002e-8 < a < -1.51999999999999992e-142

   1. Initial program 86.2%

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

   2. Taylor expanded in y around 0 79.1%

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

      1. div-sub 79.1%

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

      2. associate-*r/ 79.1%

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

      3. mul-1-neg 79.1%

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

      4. distribute-lft-neg-out 79.1%

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

      5. associate-*r/ 86.2%

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

      6. *-commutative 86.2%

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

      7. distribute-lft-out 86.2%

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

      8. sub-neg 86.2%

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

      9. associate-/r/ 96.4%

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

   4. Simplified 96.4%

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

   5. Taylor expanded in x around 0 75.8%

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

      1. associate-/l* 79.1%

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

   7. Simplified 79.1%

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

   if -1.51999999999999992e-142 < a < 3.1e5

   1. Initial program 71.1%

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

   2. Taylor expanded in z around -inf 78.5%

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

      1. +-commutative 78.5%

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

      2. mul-1-neg 78.5%

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

      3. unsub-neg 78.5%

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

      4. distribute-rgt-out-- 78.5%

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

   4. Simplified 78.5%

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

   5. Taylor expanded in y around inf 77.7%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq -1.52 \cdot 10^{-142}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 310000:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 10: 73.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -1.16 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-131}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 205000:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ a (- t x))))))
   (if (<= a -1.16e-9)
     t_1
     (if (<= a -1.3e-131)
       (/ t (/ (- a z) (- y z)))
       (if (<= a 205000.0) (+ t (/ (* (- t x) (- a y)) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / (a / (t - x)));
	double tmp;
	if (a <= -1.16e-9) {
		tmp = t_1;
	} else if (a <= -1.3e-131) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 205000.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) / (a / (t - x)))
    if (a <= (-1.16d-9)) then
        tmp = t_1
    else if (a <= (-1.3d-131)) then
        tmp = t / ((a - z) / (y - z))
    else if (a <= 205000.0d0) then
        tmp = t + (((t - x) * (a - y)) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / (a / (t - x)));
	double tmp;
	if (a <= -1.16e-9) {
		tmp = t_1;
	} else if (a <= -1.3e-131) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 205000.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / (a / (t - x)))
	tmp = 0
	if a <= -1.16e-9:
		tmp = t_1
	elif a <= -1.3e-131:
		tmp = t / ((a - z) / (y - z))
	elif a <= 205000.0:
		tmp = t + (((t - x) * (a - y)) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(a / Float64(t - x))))
	tmp = 0.0
	if (a <= -1.16e-9)
		tmp = t_1;
	elseif (a <= -1.3e-131)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (a <= 205000.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) / (a / (t - x)));
	tmp = 0.0;
	if (a <= -1.16e-9)
		tmp = t_1;
	elseif (a <= -1.3e-131)
		tmp = t / ((a - z) / (y - z));
	elseif (a <= 205000.0)
		tmp = t + (((t - x) * (a - y)) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.16e-9], t$95$1, If[LessEqual[a, -1.3e-131], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 205000.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.15999999999999992e-9 or 205000 < a

   1. Initial program 92.1%

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

   2. Taylor expanded in a around inf 66.8%

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

      1. +-commutative 66.8%

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

      2. associate-/l* 79.9%

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

   4. Simplified 79.9%

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

   if -1.15999999999999992e-9 < a < -1.29999999999999998e-131

   1. Initial program 86.2%

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

   2. Taylor expanded in y around 0 79.1%

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

      1. div-sub 79.1%

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

      2. associate-*r/ 79.1%

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

      3. mul-1-neg 79.1%

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

      4. distribute-lft-neg-out 79.1%

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

      5. associate-*r/ 86.2%

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

      6. *-commutative 86.2%

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

      7. distribute-lft-out 86.2%

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

      8. sub-neg 86.2%

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

      9. associate-/r/ 96.4%

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

   4. Simplified 96.4%

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

   5. Taylor expanded in x around 0 75.8%

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

      1. associate-/l* 79.1%

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

   7. Simplified 79.1%

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

   if -1.29999999999999998e-131 < a < 205000

   1. Initial program 71.1%

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

   2. Taylor expanded in z around -inf 78.5%

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

      1. +-commutative 78.5%

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

      2. mul-1-neg 78.5%

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

      3. unsub-neg 78.5%

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

      4. distribute-rgt-out-- 78.5%

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

   4. Simplified 78.5%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.16 \cdot 10^{-9}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-131}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 205000:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 11: 36.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+91}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-191}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) a))))
   (if (<= z -1.5e+91)
     t
     (if (<= z -3.4e-300)
       t_1
       (if (<= z 4.3e-191) x (if (<= z 9.8e+123) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / a);
	double tmp;
	if (z <= -1.5e+91) {
		tmp = t;
	} else if (z <= -3.4e-300) {
		tmp = t_1;
	} else if (z <= 4.3e-191) {
		tmp = x;
	} else if (z <= 9.8e+123) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / a)
    if (z <= (-1.5d+91)) then
        tmp = t
    else if (z <= (-3.4d-300)) then
        tmp = t_1
    else if (z <= 4.3d-191) then
        tmp = x
    else if (z <= 9.8d+123) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / a);
	double tmp;
	if (z <= -1.5e+91) {
		tmp = t;
	} else if (z <= -3.4e-300) {
		tmp = t_1;
	} else if (z <= 4.3e-191) {
		tmp = x;
	} else if (z <= 9.8e+123) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / a)
	tmp = 0
	if z <= -1.5e+91:
		tmp = t
	elif z <= -3.4e-300:
		tmp = t_1
	elif z <= 4.3e-191:
		tmp = x
	elif z <= 9.8e+123:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / a))
	tmp = 0.0
	if (z <= -1.5e+91)
		tmp = t;
	elseif (z <= -3.4e-300)
		tmp = t_1;
	elseif (z <= 4.3e-191)
		tmp = x;
	elseif (z <= 9.8e+123)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / a);
	tmp = 0.0;
	if (z <= -1.5e+91)
		tmp = t;
	elseif (z <= -3.4e-300)
		tmp = t_1;
	elseif (z <= 4.3e-191)
		tmp = x;
	elseif (z <= 9.8e+123)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e+91], t, If[LessEqual[z, -3.4e-300], t$95$1, If[LessEqual[z, 4.3e-191], x, If[LessEqual[z, 9.8e+123], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.50000000000000003e91 or 9.79999999999999952e123 < z

   1. Initial program 60.1%

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

   2. Taylor expanded in z around inf 53.6%

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

   if -1.50000000000000003e91 < z < -3.40000000000000018e-300 or 4.29999999999999983e-191 < z < 9.79999999999999952e123

   1. Initial program 91.4%

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

   2. Taylor expanded in x around 0 46.4%

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

      1. associate-*r/ 52.1%

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

   4. Simplified 52.1%

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

   5. Taylor expanded in a around inf 35.8%

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

   if -3.40000000000000018e-300 < z < 4.29999999999999983e-191

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 63.1%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+91}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-300}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-191}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+123}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 56.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-268}:\\ \;\;\;\;\frac{-y}{\frac{a - z}{x}}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-94}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= t -1.1e-36)
     t_1
     (if (<= t -8.2e-268)
       (/ (- y) (/ (- a z) x))
       (if (<= t 2.2e-94) (- x (/ y (/ a x))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1.1e-36) {
		tmp = t_1;
	} else if (t <= -8.2e-268) {
		tmp = -y / ((a - z) / x);
	} else if (t <= 2.2e-94) {
		tmp = x - (y / (a / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (t <= (-1.1d-36)) then
        tmp = t_1
    else if (t <= (-8.2d-268)) then
        tmp = -y / ((a - z) / x)
    else if (t <= 2.2d-94) then
        tmp = x - (y / (a / x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1.1e-36) {
		tmp = t_1;
	} else if (t <= -8.2e-268) {
		tmp = -y / ((a - z) / x);
	} else if (t <= 2.2e-94) {
		tmp = x - (y / (a / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -1.1e-36:
		tmp = t_1
	elif t <= -8.2e-268:
		tmp = -y / ((a - z) / x)
	elif t <= 2.2e-94:
		tmp = x - (y / (a / x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -1.1e-36)
		tmp = t_1;
	elseif (t <= -8.2e-268)
		tmp = Float64(Float64(-y) / Float64(Float64(a - z) / x));
	elseif (t <= 2.2e-94)
		tmp = Float64(x - Float64(y / Float64(a / x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -1.1e-36)
		tmp = t_1;
	elseif (t <= -8.2e-268)
		tmp = -y / ((a - z) / x);
	elseif (t <= 2.2e-94)
		tmp = x - (y / (a / x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.1e-36], t$95$1, If[LessEqual[t, -8.2e-268], N[((-y) / N[(N[(a - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e-94], N[(x - N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1e-36 or 2.20000000000000001e-94 < t

   1. Initial program 87.5%

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

   2. Taylor expanded in x around 0 58.9%

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

      1. associate-*r/ 76.8%

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

   4. Simplified 76.8%

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

   if -1.1e-36 < t < -8.1999999999999998e-268

   1. Initial program 68.0%

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

   2. Taylor expanded in y around -inf 55.0%

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

   3. Taylor expanded in t around 0 52.2%

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

      1. mul-1-neg 52.2%

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

      2. associate-/l* 60.4%

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

      3. distribute-neg-frac 60.4%

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

   5. Simplified 60.4%

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

   if -8.1999999999999998e-268 < t < 2.20000000000000001e-94

   1. Initial program 78.2%

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

   2. Taylor expanded in y around 0 77.5%

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

      1. div-sub 77.5%

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

      2. associate-*r/ 77.5%

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

      3. mul-1-neg 77.5%

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

      4. distribute-lft-neg-out 77.5%

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

      5. associate-*r/ 78.1%

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

      6. *-commutative 78.1%

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

      7. distribute-lft-out 78.2%

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

      8. sub-neg 78.2%

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

      9. associate-/r/ 79.8%

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

   4. Simplified 79.8%

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

   5. Taylor expanded in z around 0 64.6%

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

   6. Taylor expanded in t around 0 56.3%

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

      1. +-commutative 56.3%

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

      2. mul-1-neg 56.3%

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

      3. unsub-neg 56.3%

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

      4. associate-/l* 58.2%

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

   8. Simplified 58.2%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-36}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-268}:\\ \;\;\;\;\frac{-y}{\frac{a - z}{x}}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-94}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 13: 57.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-299}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-94}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= t -2.6e-36)
     t_1
     (if (<= t -1.7e-299)
       (* y (/ (- t x) (- a z)))
       (if (<= t 2.4e-94) (- x (/ y (/ a x))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -2.6e-36) {
		tmp = t_1;
	} else if (t <= -1.7e-299) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= 2.4e-94) {
		tmp = x - (y / (a / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (t <= (-2.6d-36)) then
        tmp = t_1
    else if (t <= (-1.7d-299)) then
        tmp = y * ((t - x) / (a - z))
    else if (t <= 2.4d-94) then
        tmp = x - (y / (a / x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -2.6e-36) {
		tmp = t_1;
	} else if (t <= -1.7e-299) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= 2.4e-94) {
		tmp = x - (y / (a / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -2.6e-36:
		tmp = t_1
	elif t <= -1.7e-299:
		tmp = y * ((t - x) / (a - z))
	elif t <= 2.4e-94:
		tmp = x - (y / (a / x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -2.6e-36)
		tmp = t_1;
	elseif (t <= -1.7e-299)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (t <= 2.4e-94)
		tmp = Float64(x - Float64(y / Float64(a / x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -2.6e-36)
		tmp = t_1;
	elseif (t <= -1.7e-299)
		tmp = y * ((t - x) / (a - z));
	elseif (t <= 2.4e-94)
		tmp = x - (y / (a / x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.6e-36], t$95$1, If[LessEqual[t, -1.7e-299], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e-94], N[(x - N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.6e-36 or 2.4e-94 < t

   1. Initial program 87.5%

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

   2. Taylor expanded in x around 0 58.9%

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

      1. associate-*r/ 76.8%

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

   4. Simplified 76.8%

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

   if -2.6e-36 < t < -1.6999999999999999e-299

   1. Initial program 71.4%

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

   2. Taylor expanded in y around inf 62.2%

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

      1. div-sub 62.2%

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

      2. *-commutative 62.2%

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

   4. Simplified 62.2%

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

   if -1.6999999999999999e-299 < t < 2.4e-94

   1. Initial program 76.5%

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

   2. Taylor expanded in y around 0 75.8%

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

      1. div-sub 75.8%

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

      2. associate-*r/ 75.8%

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

      3. mul-1-neg 75.8%

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

      4. distribute-lft-neg-out 75.8%

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

      5. associate-*r/ 76.4%

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

      6. *-commutative 76.4%

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

      7. distribute-lft-out 76.5%

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

      8. sub-neg 76.5%

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

      9. associate-/r/ 78.2%

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

   4. Simplified 78.2%

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

   5. Taylor expanded in z around 0 65.5%

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

   6. Taylor expanded in t around 0 56.6%

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

      1. +-commutative 56.6%

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

      2. mul-1-neg 56.6%

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

      3. unsub-neg 56.6%

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

      4. associate-/l* 58.7%

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

   8. Simplified 58.7%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-36}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-299}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-94}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 14: 68.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -1.75 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-130}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 225000:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (- x t) (/ a y)))))
   (if (<= a -1.75e-6)
     t_1
     (if (<= a -1.1e-130)
       (* t (/ (- y z) (- a z)))
       (if (<= a 225000.0) (+ t (/ (* y (- x t)) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((x - t) / (a / y));
	double tmp;
	if (a <= -1.75e-6) {
		tmp = t_1;
	} else if (a <= -1.1e-130) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 225000.0) {
		tmp = t + ((y * (x - t)) / 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 - ((x - t) / (a / y))
    if (a <= (-1.75d-6)) then
        tmp = t_1
    else if (a <= (-1.1d-130)) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= 225000.0d0) then
        tmp = t + ((y * (x - t)) / 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 - ((x - t) / (a / y));
	double tmp;
	if (a <= -1.75e-6) {
		tmp = t_1;
	} else if (a <= -1.1e-130) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 225000.0) {
		tmp = t + ((y * (x - t)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((x - t) / (a / y))
	tmp = 0
	if a <= -1.75e-6:
		tmp = t_1
	elif a <= -1.1e-130:
		tmp = t * ((y - z) / (a - z))
	elif a <= 225000.0:
		tmp = t + ((y * (x - t)) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(x - t) / Float64(a / y)))
	tmp = 0.0
	if (a <= -1.75e-6)
		tmp = t_1;
	elseif (a <= -1.1e-130)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= 225000.0)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((x - t) / (a / y));
	tmp = 0.0;
	if (a <= -1.75e-6)
		tmp = t_1;
	elseif (a <= -1.1e-130)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= 225000.0)
		tmp = t + ((y * (x - t)) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(x - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.75e-6], t$95$1, If[LessEqual[a, -1.1e-130], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 225000.0], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.74999999999999997e-6 or 225000 < a

   1. Initial program 92.6%

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

   2. Taylor expanded in y around 0 83.2%

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

      1. div-sub 83.2%

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

      2. associate-*r/ 83.2%

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

      3. mul-1-neg 83.2%

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

      4. distribute-lft-neg-out 83.2%

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

      5. associate-*r/ 92.6%

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

      6. *-commutative 92.6%

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

      7. distribute-lft-out 92.6%

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

      8. sub-neg 92.6%

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

      9. associate-/r/ 94.1%

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

   4. Simplified 94.1%

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

   5. Taylor expanded in z around 0 74.3%

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

   if -1.74999999999999997e-6 < a < -1.0999999999999999e-130

   1. Initial program 84.1%

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

   2. Taylor expanded in x around 0 73.2%

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

      1. associate-*r/ 76.3%

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

   4. Simplified 76.3%

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

   if -1.0999999999999999e-130 < a < 225000

   1. Initial program 71.1%

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

   2. Taylor expanded in z around -inf 78.5%

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

      1. +-commutative 78.5%

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

      2. mul-1-neg 78.5%

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

      3. unsub-neg 78.5%

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

      4. distribute-rgt-out-- 78.5%

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

   4. Simplified 78.5%

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

   5. Taylor expanded in y around inf 77.7%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{-6}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-130}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 225000:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \end{array} \]

Alternative 15: 68.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -9.2 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-121}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 6000000:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (- x t) (/ a y)))))
   (if (<= a -9.2e-7)
     t_1
     (if (<= a -2.9e-121)
       (/ t (/ (- a z) (- y z)))
       (if (<= a 6000000.0) (+ t (/ (* y (- x t)) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((x - t) / (a / y));
	double tmp;
	if (a <= -9.2e-7) {
		tmp = t_1;
	} else if (a <= -2.9e-121) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 6000000.0) {
		tmp = t + ((y * (x - t)) / 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 - ((x - t) / (a / y))
    if (a <= (-9.2d-7)) then
        tmp = t_1
    else if (a <= (-2.9d-121)) then
        tmp = t / ((a - z) / (y - z))
    else if (a <= 6000000.0d0) then
        tmp = t + ((y * (x - t)) / 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 - ((x - t) / (a / y));
	double tmp;
	if (a <= -9.2e-7) {
		tmp = t_1;
	} else if (a <= -2.9e-121) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 6000000.0) {
		tmp = t + ((y * (x - t)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((x - t) / (a / y))
	tmp = 0
	if a <= -9.2e-7:
		tmp = t_1
	elif a <= -2.9e-121:
		tmp = t / ((a - z) / (y - z))
	elif a <= 6000000.0:
		tmp = t + ((y * (x - t)) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(x - t) / Float64(a / y)))
	tmp = 0.0
	if (a <= -9.2e-7)
		tmp = t_1;
	elseif (a <= -2.9e-121)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (a <= 6000000.0)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((x - t) / (a / y));
	tmp = 0.0;
	if (a <= -9.2e-7)
		tmp = t_1;
	elseif (a <= -2.9e-121)
		tmp = t / ((a - z) / (y - z));
	elseif (a <= 6000000.0)
		tmp = t + ((y * (x - t)) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(x - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.2e-7], t$95$1, If[LessEqual[a, -2.9e-121], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6000000.0], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.1999999999999998e-7 or 6e6 < a

   1. Initial program 92.6%

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

   2. Taylor expanded in y around 0 83.2%

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

      1. div-sub 83.2%

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

      2. associate-*r/ 83.2%

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

      3. mul-1-neg 83.2%

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

      4. distribute-lft-neg-out 83.2%

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

      5. associate-*r/ 92.6%

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

      6. *-commutative 92.6%

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

      7. distribute-lft-out 92.6%

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

      8. sub-neg 92.6%

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

      9. associate-/r/ 94.1%

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

   4. Simplified 94.1%

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

   5. Taylor expanded in z around 0 74.3%

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

   if -9.1999999999999998e-7 < a < -2.9e-121

   1. Initial program 84.1%

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

   2. Taylor expanded in y around 0 76.4%

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

      1. div-sub 76.4%

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

      2. associate-*r/ 76.4%

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

      3. mul-1-neg 76.4%

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

      4. distribute-lft-neg-out 76.4%

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

      5. associate-*r/ 84.1%

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

      6. *-commutative 84.1%

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

      7. distribute-lft-out 84.1%

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

      8. sub-neg 84.1%

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

      9. associate-/r/ 93.9%

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

   4. Simplified 93.9%

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

   5. Taylor expanded in x around 0 73.2%

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

      1. associate-/l* 76.4%

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

   7. Simplified 76.4%

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

   if -2.9e-121 < a < 6e6

   1. Initial program 71.1%

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

   2. Taylor expanded in z around -inf 78.5%

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

      1. +-commutative 78.5%

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

      2. mul-1-neg 78.5%

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

      3. unsub-neg 78.5%

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

      4. distribute-rgt-out-- 78.5%

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

   4. Simplified 78.5%

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

   5. Taylor expanded in y around inf 77.7%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{-7}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-121}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 6000000:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \end{array} \]

Alternative 16: 36.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -14500000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 110000000:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= a -14500000000.0)
     x
     (if (<= a -1.2e-173)
       t_1
       (if (<= a 110000000.0) t (if (<= a 1.85e+71) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (a <= -14500000000.0) {
		tmp = x;
	} else if (a <= -1.2e-173) {
		tmp = t_1;
	} else if (a <= 110000000.0) {
		tmp = t;
	} else if (a <= 1.85e+71) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (a <= (-14500000000.0d0)) then
        tmp = x
    else if (a <= (-1.2d-173)) then
        tmp = t_1
    else if (a <= 110000000.0d0) then
        tmp = t
    else if (a <= 1.85d+71) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (a <= -14500000000.0) {
		tmp = x;
	} else if (a <= -1.2e-173) {
		tmp = t_1;
	} else if (a <= 110000000.0) {
		tmp = t;
	} else if (a <= 1.85e+71) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if a <= -14500000000.0:
		tmp = x
	elif a <= -1.2e-173:
		tmp = t_1
	elif a <= 110000000.0:
		tmp = t
	elif a <= 1.85e+71:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (a <= -14500000000.0)
		tmp = x;
	elseif (a <= -1.2e-173)
		tmp = t_1;
	elseif (a <= 110000000.0)
		tmp = t;
	elseif (a <= 1.85e+71)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (a <= -14500000000.0)
		tmp = x;
	elseif (a <= -1.2e-173)
		tmp = t_1;
	elseif (a <= 110000000.0)
		tmp = t;
	elseif (a <= 1.85e+71)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -14500000000.0], x, If[LessEqual[a, -1.2e-173], t$95$1, If[LessEqual[a, 110000000.0], t, If[LessEqual[a, 1.85e+71], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.45e10 or 1.85e71 < a

   1. Initial program 92.2%

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

   2. Taylor expanded in a around inf 44.9%

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

   if -1.45e10 < a < -1.20000000000000008e-173 or 1.1e8 < a < 1.85e71

   1. Initial program 84.9%

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

   2. Taylor expanded in x around 0 63.4%

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

      1. associate-*r/ 69.9%

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

   4. Simplified 69.9%

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

   5. Taylor expanded in z around 0 43.5%

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

   if -1.20000000000000008e-173 < a < 1.1e8

   1. Initial program 72.3%

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

   2. Taylor expanded in z around inf 39.6%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -14500000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-173}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 110000000:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 36.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -980000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 180000000:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ a y))))
   (if (<= a -980000000.0)
     x
     (if (<= a -2.05e-175)
       t_1
       (if (<= a 180000000.0) t (if (<= a 3.8e+70) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a / y);
	double tmp;
	if (a <= -980000000.0) {
		tmp = x;
	} else if (a <= -2.05e-175) {
		tmp = t_1;
	} else if (a <= 180000000.0) {
		tmp = t;
	} else if (a <= 3.8e+70) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (a / y)
    if (a <= (-980000000.0d0)) then
        tmp = x
    else if (a <= (-2.05d-175)) then
        tmp = t_1
    else if (a <= 180000000.0d0) then
        tmp = t
    else if (a <= 3.8d+70) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a / y);
	double tmp;
	if (a <= -980000000.0) {
		tmp = x;
	} else if (a <= -2.05e-175) {
		tmp = t_1;
	} else if (a <= 180000000.0) {
		tmp = t;
	} else if (a <= 3.8e+70) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (a / y)
	tmp = 0
	if a <= -980000000.0:
		tmp = x
	elif a <= -2.05e-175:
		tmp = t_1
	elif a <= 180000000.0:
		tmp = t
	elif a <= 3.8e+70:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(a / y))
	tmp = 0.0
	if (a <= -980000000.0)
		tmp = x;
	elseif (a <= -2.05e-175)
		tmp = t_1;
	elseif (a <= 180000000.0)
		tmp = t;
	elseif (a <= 3.8e+70)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (a / y);
	tmp = 0.0;
	if (a <= -980000000.0)
		tmp = x;
	elseif (a <= -2.05e-175)
		tmp = t_1;
	elseif (a <= 180000000.0)
		tmp = t;
	elseif (a <= 3.8e+70)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -980000000.0], x, If[LessEqual[a, -2.05e-175], t$95$1, If[LessEqual[a, 180000000.0], t, If[LessEqual[a, 3.8e+70], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.8e8 or 3.7999999999999998e70 < a

   1. Initial program 92.2%

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

   2. Taylor expanded in a around inf 44.9%

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

   if -9.8e8 < a < -2.04999999999999999e-175 or 1.8e8 < a < 3.7999999999999998e70

   1. Initial program 84.9%

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

   2. Taylor expanded in x around 0 63.4%

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

      1. associate-*r/ 69.9%

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

   4. Simplified 69.9%

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

   5. Taylor expanded in z around 0 43.5%

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

      1. clear-num 43.5%

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

      2. un-div-inv 43.6%

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

   7. Applied egg-rr 43.6%

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

   if -2.04999999999999999e-175 < a < 1.8e8

   1. Initial program 72.3%

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

   2. Taylor expanded in z around inf 39.6%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -980000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-175}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 180000000:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+70}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 64.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+62} \lor \neg \left(z \leq 2.8 \cdot 10^{-117}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.5e+62) (not (<= z 2.8e-117)))
   (* t (/ (- y z) (- a z)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.5e+62) || !(z <= 2.8e-117)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.5d+62)) .or. (.not. (z <= 2.8d-117))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.5e+62) || !(z <= 2.8e-117)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.5e+62) or not (z <= 2.8e-117):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.5e+62) || !(z <= 2.8e-117))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.5e+62) || ~((z <= 2.8e-117)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.5e+62], N[Not[LessEqual[z, 2.8e-117]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.50000000000000014e62 or 2.8e-117 < z

   1. Initial program 72.8%

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

   2. Taylor expanded in x around 0 52.4%

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

      1. associate-*r/ 70.5%

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

   4. Simplified 70.5%

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

   if -2.50000000000000014e62 < z < 2.8e-117

   1. Initial program 94.2%

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

   2. Taylor expanded in z around 0 71.6%

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

      1. +-commutative 71.6%

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

      2. associate-/l* 76.2%

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

   4. Simplified 76.2%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+62} \lor \neg \left(z \leq 2.8 \cdot 10^{-117}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 19: 66.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+62} \lor \neg \left(z \leq 1.7 \cdot 10^{-66}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.2e+62) (not (<= z 1.7e-66)))
   (* t (/ (- y z) (- a z)))
   (- x (/ (- x t) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.2e+62) || !(z <= 1.7e-66)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x - ((x - t) / (a / y));
	}
	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 <= (-3.2d+62)) .or. (.not. (z <= 1.7d-66))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x - ((x - t) / (a / y))
    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 <= -3.2e+62) || !(z <= 1.7e-66)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x - ((x - t) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.2e+62) or not (z <= 1.7e-66):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x - ((x - t) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.2e+62) || !(z <= 1.7e-66))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x - Float64(Float64(x - t) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.2e+62) || ~((z <= 1.7e-66)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x - ((x - t) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.2e+62], N[Not[LessEqual[z, 1.7e-66]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.19999999999999984e62 or 1.69999999999999999e-66 < z

   1. Initial program 71.8%

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

   2. Taylor expanded in x around 0 52.1%

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

      1. associate-*r/ 71.7%

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

   4. Simplified 71.7%

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

   if -3.19999999999999984e62 < z < 1.69999999999999999e-66

   1. Initial program 92.7%

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

   2. Taylor expanded in y around 0 92.0%

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

      1. div-sub 92.0%

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

      2. associate-*r/ 92.0%

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

      3. mul-1-neg 92.0%

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

      4. distribute-lft-neg-out 92.0%

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

      5. associate-*r/ 90.5%

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

      6. *-commutative 90.5%

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

      7. distribute-lft-out 92.7%

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

      8. sub-neg 92.7%

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

      9. associate-/r/ 95.5%

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

   4. Simplified 95.5%

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

   5. Taylor expanded in z around 0 75.5%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+62} \lor \neg \left(z \leq 1.7 \cdot 10^{-66}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \end{array} \]

Alternative 20: 40.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+48}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.7e+48)
   t
   (if (<= t 1.7e+85) (* x (- 1.0 (/ y a))) (* t (/ (- y z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.7e+48) {
		tmp = t;
	} else if (t <= 1.7e+85) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t * ((y - z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.7d+48)) then
        tmp = t
    else if (t <= 1.7d+85) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t * ((y - z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.7e+48) {
		tmp = t;
	} else if (t <= 1.7e+85) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t * ((y - z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.7e+48:
		tmp = t
	elif t <= 1.7e+85:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t * ((y - z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.7e+48)
		tmp = t;
	elseif (t <= 1.7e+85)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = Float64(t * Float64(Float64(y - z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.7e+48)
		tmp = t;
	elseif (t <= 1.7e+85)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t * ((y - z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.7e+48], t, If[LessEqual[t, 1.7e+85], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.6999999999999999e48

   1. Initial program 93.3%

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

   2. Taylor expanded in z around inf 41.3%

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

   if -3.6999999999999999e48 < t < 1.7000000000000002e85

   1. Initial program 75.4%

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

   2. Taylor expanded in y around 0 74.3%

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

      1. div-sub 74.3%

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

      2. associate-*r/ 74.3%

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

      3. mul-1-neg 74.3%

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

      4. distribute-lft-neg-out 74.3%

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

      5. associate-*r/ 73.9%

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

      6. *-commutative 73.9%

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

      7. distribute-lft-out 75.4%

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

      8. sub-neg 75.4%

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

      9. associate-/r/ 77.3%

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

   4. Simplified 77.3%

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

   5. Taylor expanded in z around 0 51.5%

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

   6. Taylor expanded in x around inf 46.1%

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

      1. *-commutative 46.1%

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

      2. mul-1-neg 46.1%

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

      3. unsub-neg 46.1%

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

   8. Simplified 46.1%

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

   if 1.7000000000000002e85 < t

   1. Initial program 90.4%

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

   2. Taylor expanded in x around 0 72.1%

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

      1. associate-*r/ 91.9%

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

   4. Simplified 91.9%

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

   5. Taylor expanded in a around inf 57.9%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+48}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \end{array} \]

Alternative 21: 36.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-121}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.2e+122) t (if (<= z 4e-121) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e+122) {
		tmp = t;
	} else if (z <= 4e-121) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.2d+122)) then
        tmp = t
    else if (z <= 4d-121) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e+122) {
		tmp = t;
	} else if (z <= 4e-121) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.2e+122:
		tmp = t
	elif z <= 4e-121:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.2e+122)
		tmp = t;
	elseif (z <= 4e-121)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.2e+122)
		tmp = t;
	elseif (z <= 4e-121)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.2e+122], t, If[LessEqual[z, 4e-121], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2000000000000001e122 or 3.9999999999999999e-121 < z

   1. Initial program 71.8%

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

   2. Taylor expanded in z around inf 42.2%

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

   if -1.2000000000000001e122 < z < 3.9999999999999999e-121

   1. Initial program 92.8%

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

   2. Taylor expanded in a around inf 35.9%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-121}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 22: 24.9% 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 82.9%

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

2. Taylor expanded in z around inf 24.2%

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

3. Final simplification 24.2%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023268 
(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)))))