Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.8% → 91.6%

Time: 16.1s

Alternatives: 18

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.8% 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: 91.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-282} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-282) (not (<= t_1 0.0)))
     (+ x (/ (- y z) (/ (- a z) (- t x))))
     (+ t (* (/ (- t x) z) (- a y))))))

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 <= -2e-282) || !(t_1 <= 0.0)) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t + (((t - x) / z) * (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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-282)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t + (((t - x) / z) * (a - y))
    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 <= -2e-282) || !(t_1 <= 0.0)) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -2e-282) or not (t_1 <= 0.0):
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t + (((t - x) / z) * (a - y))
	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 <= -2e-282) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	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 <= -2e-282) || ~((t_1 <= 0.0)))
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t + (((t - x) / z) * (a - y));
	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, -2e-282], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-282 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.2%

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

      1. clear-num 92.1%

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

      2. un-div-inv 92.7%

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

   4. Applied egg-rr 92.7%

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

   if -2e-282 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.5%

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

   3. Taylor expanded in z around inf 83.8%

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

      1. associate--l+ 83.8%

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

      2. distribute-lft-out-- 83.8%

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

      3. div-sub 83.8%

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

      4. mul-1-neg 83.8%

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

      5. unsub-neg 83.8%

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

      6. div-sub 83.8%

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

      7. associate-/l* 87.1%

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

      8. associate-/l* 99.8%

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

      9. distribute-rgt-out-- 99.7%

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

   5. Simplified 99.7%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-282} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-282} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-282) (not (<= t_1 0.0)))
     t_1
     (+ t (* (/ (- t x) z) (- a y))))))

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 <= -2e-282) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) / z) * (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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-282)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t + (((t - x) / z) * (a - y))
    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 <= -2e-282) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -2e-282) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t + (((t - x) / z) * (a - y))
	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 <= -2e-282) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	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 <= -2e-282) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t + (((t - x) / z) * (a - y));
	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, -2e-282], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-282 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.2%

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

   if -2e-282 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.5%

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

   3. Taylor expanded in z around inf 83.8%

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

      1. associate--l+ 83.8%

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

      2. distribute-lft-out-- 83.8%

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

      3. div-sub 83.8%

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

      4. mul-1-neg 83.8%

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

      5. unsub-neg 83.8%

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

      6. div-sub 83.8%

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

      7. associate-/l* 87.1%

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

      8. associate-/l* 99.8%

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

      9. distribute-rgt-out-- 99.7%

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

   5. Simplified 99.7%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-282} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - t \cdot \frac{y}{z}\\ t_2 := x - x \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.75 \cdot 10^{+23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-182}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{-245}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+235} \lor \neg \left(a \leq 2 \cdot 10^{+246}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* t (/ y z)))) (t_2 (- x (* x (/ y a)))))
   (if (<= a -1.75e+23)
     t_2
     (if (<= a -1.1e-182)
       t_1
       (if (<= a -2.35e-245)
         (* x (/ y z))
         (if (<= a 5.9e+54)
           t_1
           (if (or (<= a 2.9e+235) (not (<= a 2e+246)))
             t_2
             (* (- y z) (/ t a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (t * (y / z));
	double t_2 = x - (x * (y / a));
	double tmp;
	if (a <= -1.75e+23) {
		tmp = t_2;
	} else if (a <= -1.1e-182) {
		tmp = t_1;
	} else if (a <= -2.35e-245) {
		tmp = x * (y / z);
	} else if (a <= 5.9e+54) {
		tmp = t_1;
	} else if ((a <= 2.9e+235) || !(a <= 2e+246)) {
		tmp = t_2;
	} else {
		tmp = (y - z) * (t / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t - (t * (y / z))
    t_2 = x - (x * (y / a))
    if (a <= (-1.75d+23)) then
        tmp = t_2
    else if (a <= (-1.1d-182)) then
        tmp = t_1
    else if (a <= (-2.35d-245)) then
        tmp = x * (y / z)
    else if (a <= 5.9d+54) then
        tmp = t_1
    else if ((a <= 2.9d+235) .or. (.not. (a <= 2d+246))) then
        tmp = t_2
    else
        tmp = (y - z) * (t / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (t * (y / z));
	double t_2 = x - (x * (y / a));
	double tmp;
	if (a <= -1.75e+23) {
		tmp = t_2;
	} else if (a <= -1.1e-182) {
		tmp = t_1;
	} else if (a <= -2.35e-245) {
		tmp = x * (y / z);
	} else if (a <= 5.9e+54) {
		tmp = t_1;
	} else if ((a <= 2.9e+235) || !(a <= 2e+246)) {
		tmp = t_2;
	} else {
		tmp = (y - z) * (t / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (t * (y / z))
	t_2 = x - (x * (y / a))
	tmp = 0
	if a <= -1.75e+23:
		tmp = t_2
	elif a <= -1.1e-182:
		tmp = t_1
	elif a <= -2.35e-245:
		tmp = x * (y / z)
	elif a <= 5.9e+54:
		tmp = t_1
	elif (a <= 2.9e+235) or not (a <= 2e+246):
		tmp = t_2
	else:
		tmp = (y - z) * (t / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(t * Float64(y / z)))
	t_2 = Float64(x - Float64(x * Float64(y / a)))
	tmp = 0.0
	if (a <= -1.75e+23)
		tmp = t_2;
	elseif (a <= -1.1e-182)
		tmp = t_1;
	elseif (a <= -2.35e-245)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 5.9e+54)
		tmp = t_1;
	elseif ((a <= 2.9e+235) || !(a <= 2e+246))
		tmp = t_2;
	else
		tmp = Float64(Float64(y - z) * Float64(t / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (t * (y / z));
	t_2 = x - (x * (y / a));
	tmp = 0.0;
	if (a <= -1.75e+23)
		tmp = t_2;
	elseif (a <= -1.1e-182)
		tmp = t_1;
	elseif (a <= -2.35e-245)
		tmp = x * (y / z);
	elseif (a <= 5.9e+54)
		tmp = t_1;
	elseif ((a <= 2.9e+235) || ~((a <= 2e+246)))
		tmp = t_2;
	else
		tmp = (y - z) * (t / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.75e+23], t$95$2, If[LessEqual[a, -1.1e-182], t$95$1, If[LessEqual[a, -2.35e-245], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.9e+54], t$95$1, If[Or[LessEqual[a, 2.9e+235], N[Not[LessEqual[a, 2e+246]], $MachinePrecision]], t$95$2, N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.7500000000000001e23 or 5.8999999999999997e54 < a < 2.90000000000000021e235 or 2.00000000000000014e246 < a

   1. Initial program 86.8%

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

   3. Taylor expanded in x around -inf 60.5%

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

      1. mul-1-neg 60.5%

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

      2. *-commutative 60.5%

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

      3. distribute-rgt-neg-in 60.5%

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

      4. +-commutative 60.5%

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

      5. associate--r+ 58.6%

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

      6. div-sub 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in z around 0 55.8%

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

   7. Taylor expanded in y around 0 49.2%

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

      1. mul-1-neg 49.2%

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

      2. unsub-neg 49.2%

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

      3. associate-/l* 55.8%

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

   9. Simplified 55.8%

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

   if -1.7500000000000001e23 < a < -1.1e-182 or -2.3500000000000001e-245 < a < 5.8999999999999997e54

   1. Initial program 75.8%

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

   3. Taylor expanded in x around 0 58.0%

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

   4. Taylor expanded in a around 0 46.2%

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

      1. associate-*r/ 46.2%

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

      2. mul-1-neg 46.2%

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

      3. *-commutative 46.2%

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

      4. distribute-rgt-neg-in 46.2%

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

   6. Simplified 46.2%

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

   7. Taylor expanded in y around inf 46.8%

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

   8. Taylor expanded in y around 0 55.9%

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

      1. mul-1-neg 55.9%

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

      2. associate-*r/ 59.7%

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

      3. unsub-neg 59.7%

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

   10. Simplified 59.7%

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

   if -1.1e-182 < a < -2.3500000000000001e-245

   1. Initial program 89.1%

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

   3. Taylor expanded in x around -inf 73.2%

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

      1. mul-1-neg 73.2%

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

      2. *-commutative 73.2%

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

      3. distribute-rgt-neg-in 73.2%

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

      4. +-commutative 73.2%

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

      5. associate--r+ 67.4%

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

      6. div-sub 67.4%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in a around 0 63.5%

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

      1. associate-/l* 73.2%

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

   8. Simplified 73.2%

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

   if 2.90000000000000021e235 < a < 2.00000000000000014e246

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0 51.8%

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

   4. Taylor expanded in a around inf 50.9%

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

      1. associate-/l* 80.2%

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

   6. Simplified 80.2%

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

   7. Taylor expanded in t around 0 50.9%

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

      1. *-commutative 50.9%

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

      2. associate-/l* 82.9%

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

   9. Simplified 82.9%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+23}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-182}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{-245}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{+54}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+235} \lor \neg \left(a \leq 2 \cdot 10^{+246}\right):\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 47.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - t \cdot \frac{y}{z}\\ \mathbf{if}\;a \leq -3.1 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-182}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-245}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+236}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+246}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* t (/ y z)))))
   (if (<= a -3.1e+60)
     x
     (if (<= a -1.1e-182)
       t_1
       (if (<= a -2.3e-245)
         (* x (/ y z))
         (if (<= a 3.7e+59)
           t_1
           (if (<= a 1.95e+236)
             x
             (if (<= a 3.6e+246) (* (- y z) (/ t a)) x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (t * (y / z));
	double tmp;
	if (a <= -3.1e+60) {
		tmp = x;
	} else if (a <= -1.1e-182) {
		tmp = t_1;
	} else if (a <= -2.3e-245) {
		tmp = x * (y / z);
	} else if (a <= 3.7e+59) {
		tmp = t_1;
	} else if (a <= 1.95e+236) {
		tmp = x;
	} else if (a <= 3.6e+246) {
		tmp = (y - z) * (t / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - (t * (y / z))
    if (a <= (-3.1d+60)) then
        tmp = x
    else if (a <= (-1.1d-182)) then
        tmp = t_1
    else if (a <= (-2.3d-245)) then
        tmp = x * (y / z)
    else if (a <= 3.7d+59) then
        tmp = t_1
    else if (a <= 1.95d+236) then
        tmp = x
    else if (a <= 3.6d+246) then
        tmp = (y - z) * (t / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (t * (y / z));
	double tmp;
	if (a <= -3.1e+60) {
		tmp = x;
	} else if (a <= -1.1e-182) {
		tmp = t_1;
	} else if (a <= -2.3e-245) {
		tmp = x * (y / z);
	} else if (a <= 3.7e+59) {
		tmp = t_1;
	} else if (a <= 1.95e+236) {
		tmp = x;
	} else if (a <= 3.6e+246) {
		tmp = (y - z) * (t / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (t * (y / z))
	tmp = 0
	if a <= -3.1e+60:
		tmp = x
	elif a <= -1.1e-182:
		tmp = t_1
	elif a <= -2.3e-245:
		tmp = x * (y / z)
	elif a <= 3.7e+59:
		tmp = t_1
	elif a <= 1.95e+236:
		tmp = x
	elif a <= 3.6e+246:
		tmp = (y - z) * (t / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(t * Float64(y / z)))
	tmp = 0.0
	if (a <= -3.1e+60)
		tmp = x;
	elseif (a <= -1.1e-182)
		tmp = t_1;
	elseif (a <= -2.3e-245)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 3.7e+59)
		tmp = t_1;
	elseif (a <= 1.95e+236)
		tmp = x;
	elseif (a <= 3.6e+246)
		tmp = Float64(Float64(y - z) * Float64(t / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (t * (y / z));
	tmp = 0.0;
	if (a <= -3.1e+60)
		tmp = x;
	elseif (a <= -1.1e-182)
		tmp = t_1;
	elseif (a <= -2.3e-245)
		tmp = x * (y / z);
	elseif (a <= 3.7e+59)
		tmp = t_1;
	elseif (a <= 1.95e+236)
		tmp = x;
	elseif (a <= 3.6e+246)
		tmp = (y - z) * (t / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.1e+60], x, If[LessEqual[a, -1.1e-182], t$95$1, If[LessEqual[a, -2.3e-245], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.7e+59], t$95$1, If[LessEqual[a, 1.95e+236], x, If[LessEqual[a, 3.6e+246], N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision], x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.1000000000000001e60 or 3.69999999999999997e59 < a < 1.95e236 or 3.6e246 < a

   1. Initial program 86.7%

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

   3. Taylor expanded in a around inf 50.1%

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

   if -3.1000000000000001e60 < a < -1.1e-182 or -2.3000000000000002e-245 < a < 3.69999999999999997e59

   1. Initial program 76.5%

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

   3. Taylor expanded in x around 0 57.7%

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

   4. Taylor expanded in a around 0 44.4%

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

      1. associate-*r/ 44.4%

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

      2. mul-1-neg 44.4%

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

      3. *-commutative 44.4%

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

      4. distribute-rgt-neg-in 44.4%

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

   6. Simplified 44.4%

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

   7. Taylor expanded in y around inf 45.7%

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

   8. Taylor expanded in y around 0 53.5%

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

      1. mul-1-neg 53.5%

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

      2. associate-*r/ 57.8%

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

      3. unsub-neg 57.8%

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

   10. Simplified 57.8%

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

   if -1.1e-182 < a < -2.3000000000000002e-245

   1. Initial program 89.1%

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

   3. Taylor expanded in x around -inf 73.2%

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

      1. mul-1-neg 73.2%

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

      2. *-commutative 73.2%

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

      3. distribute-rgt-neg-in 73.2%

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

      4. +-commutative 73.2%

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

      5. associate--r+ 67.4%

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

      6. div-sub 67.4%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in a around 0 63.5%

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

      1. associate-/l* 73.2%

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

   8. Simplified 73.2%

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

   if 1.95e236 < a < 3.6e246

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0 51.8%

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

   4. Taylor expanded in a around inf 50.9%

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

      1. associate-/l* 80.2%

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

   6. Simplified 80.2%

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

   7. Taylor expanded in t around 0 50.9%

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

      1. *-commutative 50.9%

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

      2. associate-/l* 82.9%

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

   9. Simplified 82.9%

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

Alternative 5: 75.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-113}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-229}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+158}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (/ (- t x) z) (- a y)))))
   (if (<= z -1.15e+139)
     t_1
     (if (<= z -4.3e-113)
       (+ x (* (- y z) (/ t (- a z))))
       (if (<= z 5.8e-229)
         (+ x (/ (- y z) (/ a (- t x))))
         (if (<= z 2e+158) (+ x (/ (- y z) (/ (- a z) t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((t - x) / z) * (a - y));
	double tmp;
	if (z <= -1.15e+139) {
		tmp = t_1;
	} else if (z <= -4.3e-113) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else if (z <= 5.8e-229) {
		tmp = x + ((y - z) / (a / (t - x)));
	} else if (z <= 2e+158) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (((t - x) / z) * (a - y))
    if (z <= (-1.15d+139)) then
        tmp = t_1
    else if (z <= (-4.3d-113)) then
        tmp = x + ((y - z) * (t / (a - z)))
    else if (z <= 5.8d-229) then
        tmp = x + ((y - z) / (a / (t - x)))
    else if (z <= 2d+158) then
        tmp = x + ((y - z) / ((a - z) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((t - x) / z) * (a - y));
	double tmp;
	if (z <= -1.15e+139) {
		tmp = t_1;
	} else if (z <= -4.3e-113) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else if (z <= 5.8e-229) {
		tmp = x + ((y - z) / (a / (t - x)));
	} else if (z <= 2e+158) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (((t - x) / z) * (a - y))
	tmp = 0
	if z <= -1.15e+139:
		tmp = t_1
	elif z <= -4.3e-113:
		tmp = x + ((y - z) * (t / (a - z)))
	elif z <= 5.8e-229:
		tmp = x + ((y - z) / (a / (t - x)))
	elif z <= 2e+158:
		tmp = x + ((y - z) / ((a - z) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)))
	tmp = 0.0
	if (z <= -1.15e+139)
		tmp = t_1;
	elseif (z <= -4.3e-113)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	elseif (z <= 5.8e-229)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(a / Float64(t - x))));
	elseif (z <= 2e+158)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (((t - x) / z) * (a - y));
	tmp = 0.0;
	if (z <= -1.15e+139)
		tmp = t_1;
	elseif (z <= -4.3e-113)
		tmp = x + ((y - z) * (t / (a - z)));
	elseif (z <= 5.8e-229)
		tmp = x + ((y - z) / (a / (t - x)));
	elseif (z <= 2e+158)
		tmp = x + ((y - z) / ((a - z) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e+139], t$95$1, If[LessEqual[z, -4.3e-113], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-229], N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+158], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.15e139 or 1.99999999999999991e158 < z

   1. Initial program 56.4%

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

   3. Taylor expanded in z around inf 57.1%

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

      1. associate--l+ 57.1%

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

      2. distribute-lft-out-- 57.1%

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

      3. div-sub 57.1%

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

      4. mul-1-neg 57.1%

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

      5. unsub-neg 57.1%

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

      6. div-sub 57.1%

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

      7. associate-/l* 67.2%

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

      8. associate-/l* 83.2%

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

      9. distribute-rgt-out-- 83.2%

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

   5. Simplified 83.2%

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

   if -1.15e139 < z < -4.3e-113

   1. Initial program 94.2%

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

   3. Taylor expanded in t around inf 81.4%

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

   if -4.3e-113 < z < 5.7999999999999999e-229

   1. Initial program 96.0%

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

      1. clear-num 96.1%

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

      2. un-div-inv 97.9%

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

   4. Applied egg-rr 97.9%

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

   5. Taylor expanded in a around inf 91.2%

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

   if 5.7999999999999999e-229 < z < 1.99999999999999991e158

   1. Initial program 88.2%

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

      1. clear-num 88.3%

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

      2. un-div-inv 88.8%

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

   4. Applied egg-rr 88.8%

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

   5. Taylor expanded in t around inf 70.7%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+139}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-113}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-229}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+158}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - t \cdot \frac{y}{z}\\ t_2 := x - x \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -3.7 \cdot 10^{+22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-246}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* t (/ y z)))) (t_2 (- x (* x (/ y a)))))
   (if (<= a -3.7e+22)
     t_2
     (if (<= a -1.4e-175)
       t_1
       (if (<= a -5.8e-246)
         (* x (/ y (- z a)))
         (if (<= a 1.5e+55) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (t * (y / z));
	double t_2 = x - (x * (y / a));
	double tmp;
	if (a <= -3.7e+22) {
		tmp = t_2;
	} else if (a <= -1.4e-175) {
		tmp = t_1;
	} else if (a <= -5.8e-246) {
		tmp = x * (y / (z - a));
	} else if (a <= 1.5e+55) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t - (t * (y / z))
    t_2 = x - (x * (y / a))
    if (a <= (-3.7d+22)) then
        tmp = t_2
    else if (a <= (-1.4d-175)) then
        tmp = t_1
    else if (a <= (-5.8d-246)) then
        tmp = x * (y / (z - a))
    else if (a <= 1.5d+55) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (t * (y / z));
	double t_2 = x - (x * (y / a));
	double tmp;
	if (a <= -3.7e+22) {
		tmp = t_2;
	} else if (a <= -1.4e-175) {
		tmp = t_1;
	} else if (a <= -5.8e-246) {
		tmp = x * (y / (z - a));
	} else if (a <= 1.5e+55) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (t * (y / z))
	t_2 = x - (x * (y / a))
	tmp = 0
	if a <= -3.7e+22:
		tmp = t_2
	elif a <= -1.4e-175:
		tmp = t_1
	elif a <= -5.8e-246:
		tmp = x * (y / (z - a))
	elif a <= 1.5e+55:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(t * Float64(y / z)))
	t_2 = Float64(x - Float64(x * Float64(y / a)))
	tmp = 0.0
	if (a <= -3.7e+22)
		tmp = t_2;
	elseif (a <= -1.4e-175)
		tmp = t_1;
	elseif (a <= -5.8e-246)
		tmp = Float64(x * Float64(y / Float64(z - a)));
	elseif (a <= 1.5e+55)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (t * (y / z));
	t_2 = x - (x * (y / a));
	tmp = 0.0;
	if (a <= -3.7e+22)
		tmp = t_2;
	elseif (a <= -1.4e-175)
		tmp = t_1;
	elseif (a <= -5.8e-246)
		tmp = x * (y / (z - a));
	elseif (a <= 1.5e+55)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.7e+22], t$95$2, If[LessEqual[a, -1.4e-175], t$95$1, If[LessEqual[a, -5.8e-246], N[(x * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e+55], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.6999999999999998e22 or 1.50000000000000008e55 < a

   1. Initial program 87.4%

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

   3. Taylor expanded in x around -inf 57.7%

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

      1. mul-1-neg 57.7%

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

      2. *-commutative 57.7%

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

      3. distribute-rgt-neg-in 57.7%

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

      4. +-commutative 57.7%

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

      5. associate--r+ 55.9%

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

      6. div-sub 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in z around 0 53.1%

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

   7. Taylor expanded in y around 0 46.8%

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

      1. mul-1-neg 46.8%

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

      2. unsub-neg 46.8%

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

      3. associate-/l* 53.1%

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

   9. Simplified 53.1%

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

   if -3.6999999999999998e22 < a < -1.4e-175 or -5.7999999999999999e-246 < a < 1.50000000000000008e55

   1. Initial program 75.4%

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

   3. Taylor expanded in x around 0 58.9%

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

   4. Taylor expanded in a around 0 46.2%

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

      1. associate-*r/ 46.2%

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

      2. mul-1-neg 46.2%

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

      3. *-commutative 46.2%

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

      4. distribute-rgt-neg-in 46.2%

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

   6. Simplified 46.2%

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

   7. Taylor expanded in y around inf 46.7%

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

   8. Taylor expanded in y around 0 56.0%

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

      1. mul-1-neg 56.0%

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

      2. associate-*r/ 59.9%

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

      3. unsub-neg 59.9%

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

   10. Simplified 59.9%

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

   if -1.4e-175 < a < -5.7999999999999999e-246

   1. Initial program 91.0%

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

   3. Taylor expanded in x around -inf 78.0%

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

      1. mul-1-neg 78.0%

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

      2. *-commutative 78.0%

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

      3. distribute-rgt-neg-in 78.0%

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

      4. +-commutative 78.0%

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

      5. associate--r+ 73.3%

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

      6. div-sub 73.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in y around inf 78.0%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+22}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-175}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-246}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+55}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 41.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -8 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-32}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-145}:\\ \;\;\;\;y \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 980000:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= y -8e+143)
     t_1
     (if (<= y -1.35e-32)
       (+ x t)
       (if (<= y -4e-145) (* y (/ t y)) (if (<= y 980000.0) (+ x t) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (y <= -8e+143) {
		tmp = t_1;
	} else if (y <= -1.35e-32) {
		tmp = x + t;
	} else if (y <= -4e-145) {
		tmp = y * (t / y);
	} else if (y <= 980000.0) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (a - z))
    if (y <= (-8d+143)) then
        tmp = t_1
    else if (y <= (-1.35d-32)) then
        tmp = x + t
    else if (y <= (-4d-145)) then
        tmp = y * (t / y)
    else if (y <= 980000.0d0) then
        tmp = x + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (y <= -8e+143) {
		tmp = t_1;
	} else if (y <= -1.35e-32) {
		tmp = x + t;
	} else if (y <= -4e-145) {
		tmp = y * (t / y);
	} else if (y <= 980000.0) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if y <= -8e+143:
		tmp = t_1
	elif y <= -1.35e-32:
		tmp = x + t
	elif y <= -4e-145:
		tmp = y * (t / y)
	elif y <= 980000.0:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (y <= -8e+143)
		tmp = t_1;
	elseif (y <= -1.35e-32)
		tmp = Float64(x + t);
	elseif (y <= -4e-145)
		tmp = Float64(y * Float64(t / y));
	elseif (y <= 980000.0)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (y <= -8e+143)
		tmp = t_1;
	elseif (y <= -1.35e-32)
		tmp = x + t;
	elseif (y <= -4e-145)
		tmp = y * (t / y);
	elseif (y <= 980000.0)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8e+143], t$95$1, If[LessEqual[y, -1.35e-32], N[(x + t), $MachinePrecision], If[LessEqual[y, -4e-145], N[(y * N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 980000.0], N[(x + t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.0000000000000002e143 or 9.8e5 < y

   1. Initial program 86.4%

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

   3. Taylor expanded in x around 0 37.6%

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

   4. Taylor expanded in y around inf 36.0%

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

      1. associate-/l* 39.6%

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

   6. Simplified 39.6%

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

   if -8.0000000000000002e143 < y < -1.3499999999999999e-32 or -3.99999999999999966e-145 < y < 9.8e5

   1. Initial program 81.4%

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

      1. clear-num 81.4%

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

      2. un-div-inv 82.3%

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

   4. Applied egg-rr 82.3%

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

   5. Taylor expanded in t around inf 75.7%

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

   6. Taylor expanded in z around inf 51.2%

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

   if -1.3499999999999999e-32 < y < -3.99999999999999966e-145

   1. Initial program 61.4%

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

   3. Taylor expanded in x around 0 46.9%

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

   4. Taylor expanded in a around 0 37.2%

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

      1. associate-*r/ 37.2%

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

      2. mul-1-neg 37.2%

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

      3. *-commutative 37.2%

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

      4. distribute-rgt-neg-in 37.2%

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

   6. Simplified 37.2%

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

   7. Taylor expanded in y around inf 55.9%

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

   8. Taylor expanded in z around inf 50.7%

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

Alternative 8: 38.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+163}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-33}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-146}:\\ \;\;\;\;y \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+167}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.05e+163)
   (* x (/ y z))
   (if (<= y -8.8e-33)
     (+ x t)
     (if (<= y -4.5e-146)
       (* y (/ t y))
       (if (<= y 1.15e+167) (+ x t) (* t (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.05e+163) {
		tmp = x * (y / z);
	} else if (y <= -8.8e-33) {
		tmp = x + t;
	} else if (y <= -4.5e-146) {
		tmp = y * (t / y);
	} else if (y <= 1.15e+167) {
		tmp = x + t;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.05d+163)) then
        tmp = x * (y / z)
    else if (y <= (-8.8d-33)) then
        tmp = x + t
    else if (y <= (-4.5d-146)) then
        tmp = y * (t / y)
    else if (y <= 1.15d+167) then
        tmp = x + t
    else
        tmp = t * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.05e+163) {
		tmp = x * (y / z);
	} else if (y <= -8.8e-33) {
		tmp = x + t;
	} else if (y <= -4.5e-146) {
		tmp = y * (t / y);
	} else if (y <= 1.15e+167) {
		tmp = x + t;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.05e+163:
		tmp = x * (y / z)
	elif y <= -8.8e-33:
		tmp = x + t
	elif y <= -4.5e-146:
		tmp = y * (t / y)
	elif y <= 1.15e+167:
		tmp = x + t
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.05e+163)
		tmp = Float64(x * Float64(y / z));
	elseif (y <= -8.8e-33)
		tmp = Float64(x + t);
	elseif (y <= -4.5e-146)
		tmp = Float64(y * Float64(t / y));
	elseif (y <= 1.15e+167)
		tmp = Float64(x + t);
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.05e+163)
		tmp = x * (y / z);
	elseif (y <= -8.8e-33)
		tmp = x + t;
	elseif (y <= -4.5e-146)
		tmp = y * (t / y);
	elseif (y <= 1.15e+167)
		tmp = x + t;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.05e+163], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.8e-33], N[(x + t), $MachinePrecision], If[LessEqual[y, -4.5e-146], N[(y * N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+167], N[(x + t), $MachinePrecision], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.05e163

   1. Initial program 85.8%

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

   3. Taylor expanded in x around -inf 53.3%

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

      1. mul-1-neg 53.3%

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

      2. *-commutative 53.3%

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

      3. distribute-rgt-neg-in 53.3%

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

      4. +-commutative 53.3%

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

      5. associate--r+ 41.9%

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

      6. div-sub 41.9%

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

   5. Simplified 41.9%

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

   6. Taylor expanded in a around 0 32.1%

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

      1. associate-/l* 39.9%

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

   8. Simplified 39.9%

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

   if -1.05e163 < y < -8.80000000000000022e-33 or -4.5000000000000001e-146 < y < 1.14999999999999994e167

   1. Initial program 80.5%

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

      1. clear-num 80.5%

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

      2. un-div-inv 81.2%

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

   4. Applied egg-rr 81.2%

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

   5. Taylor expanded in t around inf 71.4%

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

   6. Taylor expanded in z around inf 45.8%

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

   if -8.80000000000000022e-33 < y < -4.5000000000000001e-146

   1. Initial program 61.4%

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

   3. Taylor expanded in x around 0 46.9%

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

   4. Taylor expanded in a around 0 37.2%

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

      1. associate-*r/ 37.2%

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

      2. mul-1-neg 37.2%

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

      3. *-commutative 37.2%

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

      4. distribute-rgt-neg-in 37.2%

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

   6. Simplified 37.2%

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

   7. Taylor expanded in y around inf 55.9%

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

   8. Taylor expanded in z around inf 50.7%

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

   if 1.14999999999999994e167 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 39.4%

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

   4. Taylor expanded in z around 0 42.9%

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

      1. associate-/l* 49.8%

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

   6. Simplified 49.8%

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

Alternative 9: 60.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-183}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq 9000000000000:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= t -1.15e-13)
     t_1
     (if (<= t -1.05e-183)
       (* y (/ (- t x) (- a z)))
       (if (<= t 9000000000000.0) (+ x (* y (/ (- t x) a))) 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 <= -1.15e-13) {
		tmp = t_1;
	} else if (t <= -1.05e-183) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= 9000000000000.0) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (t <= (-1.15d-13)) then
        tmp = t_1
    else if (t <= (-1.05d-183)) then
        tmp = y * ((t - x) / (a - z))
    else if (t <= 9000000000000.0d0) then
        tmp = x + (y * ((t - x) / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1.15e-13) {
		tmp = t_1;
	} else if (t <= -1.05e-183) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= 9000000000000.0) {
		tmp = x + (y * ((t - x) / a));
	} 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 <= -1.15e-13:
		tmp = t_1
	elif t <= -1.05e-183:
		tmp = y * ((t - x) / (a - z))
	elif t <= 9000000000000.0:
		tmp = x + (y * ((t - x) / a))
	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 <= -1.15e-13)
		tmp = t_1;
	elseif (t <= -1.05e-183)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (t <= 9000000000000.0)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -1.15e-13)
		tmp = t_1;
	elseif (t <= -1.05e-183)
		tmp = y * ((t - x) / (a - z));
	elseif (t <= 9000000000000.0)
		tmp = x + (y * ((t - x) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e-13], t$95$1, If[LessEqual[t, -1.05e-183], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9000000000000.0], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1499999999999999e-13 or 9e12 < t

   1. Initial program 91.8%

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

   3. Taylor expanded in x around 0 54.5%

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

      1. associate-/l* 79.5%

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

   5. Simplified 79.5%

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

   if -1.1499999999999999e-13 < t < -1.0500000000000001e-183

   1. Initial program 68.3%

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

      1. clear-num 68.1%

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

      2. un-div-inv 68.3%

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

   4. Applied egg-rr 68.3%

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

   5. Taylor expanded in y around inf 59.9%

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

      1. div-sub 59.9%

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

   7. Simplified 59.9%

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

   if -1.0500000000000001e-183 < t < 9e12

   1. Initial program 71.1%

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

   3. Taylor expanded in z around 0 52.2%

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

      1. associate-/l* 55.7%

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

   5. Simplified 55.7%

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

Alternative 10: 59.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-195}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+25}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= t -1.2e-13)
     t_1
     (if (<= t -1.05e-195)
       (* y (/ (- t x) (- a z)))
       (if (<= t 4e+25) (- x (* x (/ y a))) 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 <= -1.2e-13) {
		tmp = t_1;
	} else if (t <= -1.05e-195) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= 4e+25) {
		tmp = x - (x * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (t <= (-1.2d-13)) then
        tmp = t_1
    else if (t <= (-1.05d-195)) then
        tmp = y * ((t - x) / (a - z))
    else if (t <= 4d+25) then
        tmp = x - (x * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1.2e-13) {
		tmp = t_1;
	} else if (t <= -1.05e-195) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= 4e+25) {
		tmp = x - (x * (y / a));
	} 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 <= -1.2e-13:
		tmp = t_1
	elif t <= -1.05e-195:
		tmp = y * ((t - x) / (a - z))
	elif t <= 4e+25:
		tmp = x - (x * (y / a))
	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 <= -1.2e-13)
		tmp = t_1;
	elseif (t <= -1.05e-195)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (t <= 4e+25)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	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 <= -1.2e-13)
		tmp = t_1;
	elseif (t <= -1.05e-195)
		tmp = y * ((t - x) / (a - z));
	elseif (t <= 4e+25)
		tmp = x - (x * (y / a));
	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, -1.2e-13], t$95$1, If[LessEqual[t, -1.05e-195], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+25], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1999999999999999e-13 or 4.00000000000000036e25 < t

   1. Initial program 91.8%

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

   3. Taylor expanded in x around 0 54.5%

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

      1. associate-/l* 79.5%

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

   5. Simplified 79.5%

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

   if -1.1999999999999999e-13 < t < -1.05e-195

   1. Initial program 70.5%

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

      1. clear-num 70.4%

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

      2. un-div-inv 70.5%

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

   4. Applied egg-rr 70.5%

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

   5. Taylor expanded in y around inf 62.8%

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

      1. div-sub 62.8%

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

   7. Simplified 62.8%

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

   if -1.05e-195 < t < 4.00000000000000036e25

   1. Initial program 70.0%

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

   3. Taylor expanded in x around -inf 65.1%

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

      1. mul-1-neg 65.1%

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

      2. *-commutative 65.1%

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

      3. distribute-rgt-neg-in 65.1%

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

      4. +-commutative 65.1%

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

      5. associate--r+ 61.2%

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

      6. div-sub 61.2%

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

   5. Simplified 61.2%

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

   6. Taylor expanded in z around 0 50.5%

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

   7. Taylor expanded in y around 0 46.8%

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

      1. mul-1-neg 46.8%

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

      2. unsub-neg 46.8%

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

      3. associate-/l* 50.5%

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

   9. Simplified 50.5%

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

Alternative 11: 58.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;t \leq 3500000000:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= t -8.2e-27)
     t_1
     (if (<= t -1.15e-183)
       (* x (/ y (- z a)))
       (if (<= t 3500000000.0) (- x (* x (/ y a))) 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 <= -8.2e-27) {
		tmp = t_1;
	} else if (t <= -1.15e-183) {
		tmp = x * (y / (z - a));
	} else if (t <= 3500000000.0) {
		tmp = x - (x * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (t <= (-8.2d-27)) then
        tmp = t_1
    else if (t <= (-1.15d-183)) then
        tmp = x * (y / (z - a))
    else if (t <= 3500000000.0d0) then
        tmp = x - (x * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -8.2e-27) {
		tmp = t_1;
	} else if (t <= -1.15e-183) {
		tmp = x * (y / (z - a));
	} else if (t <= 3500000000.0) {
		tmp = x - (x * (y / a));
	} 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 <= -8.2e-27:
		tmp = t_1
	elif t <= -1.15e-183:
		tmp = x * (y / (z - a))
	elif t <= 3500000000.0:
		tmp = x - (x * (y / a))
	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 <= -8.2e-27)
		tmp = t_1;
	elseif (t <= -1.15e-183)
		tmp = Float64(x * Float64(y / Float64(z - a)));
	elseif (t <= 3500000000.0)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	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 <= -8.2e-27)
		tmp = t_1;
	elseif (t <= -1.15e-183)
		tmp = x * (y / (z - a));
	elseif (t <= 3500000000.0)
		tmp = x - (x * (y / a));
	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, -8.2e-27], t$95$1, If[LessEqual[t, -1.15e-183], N[(x * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3500000000.0], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.1999999999999997e-27 or 3.5e9 < t

   1. Initial program 91.2%

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

   3. Taylor expanded in x around 0 54.4%

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

      1. associate-/l* 79.1%

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

   5. Simplified 79.1%

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

   if -8.1999999999999997e-27 < t < -1.15000000000000008e-183

   1. Initial program 69.2%

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

   3. Taylor expanded in x around -inf 67.1%

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

      1. mul-1-neg 67.1%

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

      2. *-commutative 67.1%

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

      3. distribute-rgt-neg-in 67.1%

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

      4. +-commutative 67.1%

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

      5. associate--r+ 54.1%

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

      6. div-sub 54.1%

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

   5. Simplified 54.1%

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

   6. Taylor expanded in y around inf 50.3%

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

   if -1.15000000000000008e-183 < t < 3.5e9

   1. Initial program 71.1%

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

   3. Taylor expanded in x around -inf 65.5%

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

      1. mul-1-neg 65.5%

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

      2. *-commutative 65.5%

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

      3. distribute-rgt-neg-in 65.5%

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

      4. +-commutative 65.5%

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

      5. associate--r+ 61.7%

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

      6. div-sub 61.7%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in z around 0 51.4%

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

   7. Taylor expanded in y around 0 47.9%

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

      1. mul-1-neg 47.9%

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

      2. unsub-neg 47.9%

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

      3. associate-/l* 51.4%

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

   9. Simplified 51.4%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-27}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;t \leq 3500000000:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 40.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+138}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-56}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-173}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+142}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.15e+138)
   t
   (if (<= z -1.15e-56)
     (+ x t)
     (if (<= z 4.9e-173) x (if (<= z 1.4e+142) (+ x t) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+138) {
		tmp = t;
	} else if (z <= -1.15e-56) {
		tmp = x + t;
	} else if (z <= 4.9e-173) {
		tmp = x;
	} else if (z <= 1.4e+142) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.15d+138)) then
        tmp = t
    else if (z <= (-1.15d-56)) then
        tmp = x + t
    else if (z <= 4.9d-173) then
        tmp = x
    else if (z <= 1.4d+142) then
        tmp = x + t
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+138) {
		tmp = t;
	} else if (z <= -1.15e-56) {
		tmp = x + t;
	} else if (z <= 4.9e-173) {
		tmp = x;
	} else if (z <= 1.4e+142) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.15e+138:
		tmp = t
	elif z <= -1.15e-56:
		tmp = x + t
	elif z <= 4.9e-173:
		tmp = x
	elif z <= 1.4e+142:
		tmp = x + t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.15e+138)
		tmp = t;
	elseif (z <= -1.15e-56)
		tmp = Float64(x + t);
	elseif (z <= 4.9e-173)
		tmp = x;
	elseif (z <= 1.4e+142)
		tmp = Float64(x + t);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.15e+138)
		tmp = t;
	elseif (z <= -1.15e-56)
		tmp = x + t;
	elseif (z <= 4.9e-173)
		tmp = x;
	elseif (z <= 1.4e+142)
		tmp = x + t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.15e+138], t, If[LessEqual[z, -1.15e-56], N[(x + t), $MachinePrecision], If[LessEqual[z, 4.9e-173], x, If[LessEqual[z, 1.4e+142], N[(x + t), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15000000000000004e138 or 1.4e142 < z

   1. Initial program 58.0%

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

   3. Taylor expanded in z around inf 48.5%

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

   if -1.15000000000000004e138 < z < -1.15000000000000001e-56 or 4.89999999999999991e-173 < z < 1.4e142

   1. Initial program 89.9%

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

      1. clear-num 89.9%

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

      2. un-div-inv 90.3%

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

   4. Applied egg-rr 90.3%

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

   5. Taylor expanded in t around inf 72.8%

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

   6. Taylor expanded in z around inf 43.7%

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

   if -1.15000000000000001e-56 < z < 4.89999999999999991e-173

   1. Initial program 96.0%

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

   3. Taylor expanded in a around inf 37.3%

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

Alternative 13: 71.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+164} \lor \neg \left(y \leq 2.1 \cdot 10^{+64}\right):\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -6.2e+164) (not (<= y 2.1e+64)))
   (* y (/ (- t x) (- a z)))
   (+ x (/ (- y z) (/ (- a z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -6.2e+164) || !(y <= 2.1e+64)) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = x + ((y - z) / ((a - 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) :: tmp
    if ((y <= (-6.2d+164)) .or. (.not. (y <= 2.1d+64))) then
        tmp = y * ((t - x) / (a - z))
    else
        tmp = x + ((y - z) / ((a - z) / 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 ((y <= -6.2e+164) || !(y <= 2.1e+64)) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = x + ((y - z) / ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -6.2e+164) or not (y <= 2.1e+64):
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = x + ((y - z) / ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -6.2e+164) || !(y <= 2.1e+64))
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -6.2e+164) || ~((y <= 2.1e+64)))
		tmp = y * ((t - x) / (a - z));
	else
		tmp = x + ((y - z) / ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -6.2e+164], N[Not[LessEqual[y, 2.1e+64]], $MachinePrecision]], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.2000000000000003e164 or 2.1e64 < y

   1. Initial program 87.6%

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

      1. clear-num 87.7%

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

      2. un-div-inv 87.7%

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

   4. Applied egg-rr 87.7%

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

   5. Taylor expanded in y around inf 80.5%

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

      1. div-sub 82.9%

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

   7. Simplified 82.9%

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

   if -6.2000000000000003e164 < y < 2.1e64

   1. Initial program 78.9%

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

      1. clear-num 78.9%

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

      2. un-div-inv 79.6%

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

   4. Applied egg-rr 79.6%

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

   5. Taylor expanded in t around inf 73.2%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+164} \lor \neg \left(y \leq 2.1 \cdot 10^{+64}\right):\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 71.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+168} \lor \neg \left(y \leq 3.6 \cdot 10^{+64}\right):\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.4e+168) (not (<= y 3.6e+64)))
   (* y (/ (- t x) (- a z)))
   (+ x (* (- y z) (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.4e+168) || !(y <= 3.6e+64)) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = x + ((y - z) * (t / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.4d+168)) .or. (.not. (y <= 3.6d+64))) then
        tmp = y * ((t - x) / (a - z))
    else
        tmp = x + ((y - z) * (t / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.4e+168) || !(y <= 3.6e+64)) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = x + ((y - z) * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.4e+168) or not (y <= 3.6e+64):
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = x + ((y - z) * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.4e+168) || !(y <= 3.6e+64))
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.4e+168) || ~((y <= 3.6e+64)))
		tmp = y * ((t - x) / (a - z));
	else
		tmp = x + ((y - z) * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.4e+168], N[Not[LessEqual[y, 3.6e+64]], $MachinePrecision]], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.39999999999999995e168 or 3.60000000000000014e64 < y

   1. Initial program 87.6%

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

      1. clear-num 87.7%

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

      2. un-div-inv 87.7%

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

   4. Applied egg-rr 87.7%

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

   5. Taylor expanded in y around inf 80.5%

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

      1. div-sub 82.9%

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

   7. Simplified 82.9%

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

   if -1.39999999999999995e168 < y < 3.60000000000000014e64

   1. Initial program 78.9%

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

   3. Taylor expanded in t around inf 72.5%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+168} \lor \neg \left(y \leq 3.6 \cdot 10^{+64}\right):\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 39.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+177} \lor \neg \left(y \leq 1.15 \cdot 10^{+167}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3.6e+177) (not (<= y 1.15e+167))) (* t (/ y a)) (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.6e+177) || !(y <= 1.15e+167)) {
		tmp = t * (y / a);
	} else {
		tmp = x + 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 ((y <= (-3.6d+177)) .or. (.not. (y <= 1.15d+167))) then
        tmp = t * (y / a)
    else
        tmp = x + 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 ((y <= -3.6e+177) || !(y <= 1.15e+167)) {
		tmp = t * (y / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3.6e+177) or not (y <= 1.15e+167):
		tmp = t * (y / a)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3.6e+177) || !(y <= 1.15e+167))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -3.6e+177) || ~((y <= 1.15e+167)))
		tmp = t * (y / a);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3.6e+177], N[Not[LessEqual[y, 1.15e+167]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.60000000000000003e177 or 1.14999999999999994e167 < y

   1. Initial program 91.3%

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

   3. Taylor expanded in x around 0 42.0%

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

   4. Taylor expanded in z around 0 38.5%

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

      1. associate-/l* 44.5%

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

   6. Simplified 44.5%

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

   if -3.60000000000000003e177 < y < 1.14999999999999994e167

   1. Initial program 79.0%

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

      1. clear-num 79.0%

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

      2. un-div-inv 79.6%

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

   4. Applied egg-rr 79.6%

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

   5. Taylor expanded in t around inf 69.5%

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

   6. Taylor expanded in z around inf 43.5%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+177} \lor \neg \left(y \leq 1.15 \cdot 10^{+167}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 39.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+169}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+167}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.12e+169)
   (* x (/ y z))
   (if (<= y 1.15e+167) (+ x t) (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.12e+169) {
		tmp = x * (y / z);
	} else if (y <= 1.15e+167) {
		tmp = x + t;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.12d+169)) then
        tmp = x * (y / z)
    else if (y <= 1.15d+167) then
        tmp = x + t
    else
        tmp = t * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.12e+169) {
		tmp = x * (y / z);
	} else if (y <= 1.15e+167) {
		tmp = x + t;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.12e+169:
		tmp = x * (y / z)
	elif y <= 1.15e+167:
		tmp = x + t
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.12e+169)
		tmp = Float64(x * Float64(y / z));
	elseif (y <= 1.15e+167)
		tmp = Float64(x + t);
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.12e+169)
		tmp = x * (y / z);
	elseif (y <= 1.15e+167)
		tmp = x + t;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.12e+169], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+167], N[(x + t), $MachinePrecision], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.11999999999999996e169

   1. Initial program 85.8%

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

   3. Taylor expanded in x around -inf 53.3%

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

      1. mul-1-neg 53.3%

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

      2. *-commutative 53.3%

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

      3. distribute-rgt-neg-in 53.3%

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

      4. +-commutative 53.3%

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

      5. associate--r+ 41.9%

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

      6. div-sub 41.9%

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

   5. Simplified 41.9%

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

   6. Taylor expanded in a around 0 32.1%

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

      1. associate-/l* 39.9%

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

   8. Simplified 39.9%

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

   if -1.11999999999999996e169 < y < 1.14999999999999994e167

   1. Initial program 78.5%

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

      1. clear-num 78.6%

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

      2. un-div-inv 79.1%

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

   4. Applied egg-rr 79.1%

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

   5. Taylor expanded in t around inf 69.8%

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

   6. Taylor expanded in z around inf 43.9%

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

   if 1.14999999999999994e167 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 39.4%

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

   4. Taylor expanded in z around 0 42.9%

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

      1. associate-/l* 49.8%

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

   6. Simplified 49.8%

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

Alternative 17: 35.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+127}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-167}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.2e+127) t (if (<= z 1.3e-167) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e+127) {
		tmp = t;
	} else if (z <= 1.3e-167) {
		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 <= (-2.2d+127)) then
        tmp = t
    else if (z <= 1.3d-167) 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 <= -2.2e+127) {
		tmp = t;
	} else if (z <= 1.3e-167) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.2e+127:
		tmp = t
	elif z <= 1.3e-167:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.2e+127)
		tmp = t;
	elseif (z <= 1.3e-167)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.2e+127)
		tmp = t;
	elseif (z <= 1.3e-167)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.2e+127], t, If[LessEqual[z, 1.3e-167], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2000000000000002e127 or 1.2999999999999999e-167 < z

   1. Initial program 70.1%

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

   3. Taylor expanded in z around inf 41.4%

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

   if -2.2000000000000002e127 < z < 1.2999999999999999e-167

   1. Initial program 95.4%

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

   3. Taylor expanded in a around inf 37.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 25.4% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 t)

C

double code(double x, double y, double z, double t, double a) {
	return t;
}

Fortran

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

Java

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

Python

def code(x, y, z, t, a):
	return t

Julia

function code(x, y, z, t, a)
	return t
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 81.8%

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

3. Taylor expanded in z around inf 26.8%

   \[\leadsto \color{blue}{t} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024097 
(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)))))