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

Percentage Accurate: 68.6% → 90.7%

Time: 22.6s

Alternatives: 30

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ t_2 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+289}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-283}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 10^{+188}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (- y z) (/ (- x t) (- a z)))))
        (t_2 (- x (/ (* (- y z) (- x t)) (- a z)))))
   (if (<= t_2 -5e+289)
     t_1
     (if (<= t_2 -1e-283)
       t_2
       (if (<= t_2 0.0)
         (+ t (/ (* (- t x) (- a y)) z))
         (if (<= t_2 1e+188) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) * ((x - t) / (a - z)));
	double t_2 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if (t_2 <= -5e+289) {
		tmp = t_1;
	} else if (t_2 <= -1e-283) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 1e+188) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - ((y - z) * ((x - t) / (a - z)))
    t_2 = x - (((y - z) * (x - t)) / (a - z))
    if (t_2 <= (-5d+289)) then
        tmp = t_1
    else if (t_2 <= (-1d-283)) then
        tmp = t_2
    else if (t_2 <= 0.0d0) then
        tmp = t + (((t - x) * (a - y)) / z)
    else if (t_2 <= 1d+188) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) * ((x - t) / (a - z)));
	double t_2 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if (t_2 <= -5e+289) {
		tmp = t_1;
	} else if (t_2 <= -1e-283) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 1e+188) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y - z) * ((x - t) / (a - z)))
	t_2 = x - (((y - z) * (x - t)) / (a - z))
	tmp = 0
	if t_2 <= -5e+289:
		tmp = t_1
	elif t_2 <= -1e-283:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t + (((t - x) * (a - y)) / z)
	elif t_2 <= 1e+188:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y - z) * Float64(Float64(x - t) / Float64(a - z))))
	t_2 = Float64(x - Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -5e+289)
		tmp = t_1;
	elseif (t_2 <= -1e-283)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (t_2 <= 1e+188)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y - z) * ((x - t) / (a - z)));
	t_2 = x - (((y - z) * (x - t)) / (a - z));
	tmp = 0.0;
	if (t_2 <= -5e+289)
		tmp = t_1;
	elseif (t_2 <= -1e-283)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (t_2 <= 1e+188)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y - z), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+289], t$95$1, If[LessEqual[t$95$2, -1e-283], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+188], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -5.00000000000000031e289 or 1e188 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 52.2%

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

      1. associate-/l* 88.7%

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

   3. Simplified 88.7%

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

   if -5.00000000000000031e289 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -9.99999999999999947e-284 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 1e188

   1. Initial program 96.8%

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

   if -9.99999999999999947e-284 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.5%

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

      1. associate-/l* 4.4%

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

   3. Simplified 4.4%

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

   5. Taylor expanded in z around inf 95.1%

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

      1. associate--l+ 95.1%

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

      2. associate-*r/ 95.1%

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

      3. associate-*r/ 95.1%

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

      4. mul-1-neg 95.1%

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

      5. div-sub 95.1%

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

      6. mul-1-neg 95.1%

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

      7. distribute-lft-out-- 95.1%

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

      8. associate-*r/ 95.1%

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

      9. mul-1-neg 95.1%

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

      10. unsub-neg 95.1%

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

      11. distribute-rgt-out-- 95.0%

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

   7. Simplified 95.0%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq -5 \cdot 10^{+289}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{elif}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq -1 \cdot 10^{-283}:\\ \;\;\;\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{elif}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq 10^{+188}:\\ \;\;\;\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-283} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a + y \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y z) (- x t)) (- a z)))))
   (if (or (<= t_1 -1e-283) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (+ t (/ (+ (* (- t x) a) (* y (- x t))) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-283) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = t + ((((t - x) * a) + (y * (x - t))) / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -1e-283) || !(t_1 <= 0.0))
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = Float64(t + Float64(Float64(Float64(Float64(t - x) * a) + Float64(y * Float64(x - t))) / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-283], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(t + N[(N[(N[(N[(t - x), $MachinePrecision] * a), $MachinePrecision] + N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -9.99999999999999947e-284 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 76.0%

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

      1. +-commutative 76.0%

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

      2. *-commutative 76.0%

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

      3. associate-/l* 92.3%

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

      4. fma-define 92.4%

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

   3. Simplified 92.4%

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

   if -9.99999999999999947e-284 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.5%

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

      1. associate-/l* 4.4%

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

   3. Simplified 4.4%

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

   5. Taylor expanded in z around -inf 95.1%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq -1 \cdot 10^{-283} \lor \neg \left(x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a + y \cdot \left(x - t\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-283} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{x - t}{\frac{a - z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a + y \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y z) (- x t)) (- a z)))))
   (if (or (<= t_1 -1e-283) (not (<= t_1 0.0)))
     (+ x (/ (- x t) (/ (- a z) (- z y))))
     (+ t (/ (+ (* (- t x) a) (* y (- x t))) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-283) || !(t_1 <= 0.0)) {
		tmp = x + ((x - t) / ((a - z) / (z - y)));
	} else {
		tmp = t + ((((t - x) * a) + (y * (x - t))) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((y - z) * (x - t)) / (a - z))
    if ((t_1 <= (-1d-283)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((x - t) / ((a - z) / (z - y)))
    else
        tmp = t + ((((t - x) * a) + (y * (x - t))) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-283) || !(t_1 <= 0.0)) {
		tmp = x + ((x - t) / ((a - z) / (z - y)));
	} else {
		tmp = t + ((((t - x) * a) + (y * (x - t))) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - z) * (x - t)) / (a - z))
	tmp = 0
	if (t_1 <= -1e-283) or not (t_1 <= 0.0):
		tmp = x + ((x - t) / ((a - z) / (z - y)))
	else:
		tmp = t + ((((t - x) * a) + (y * (x - t))) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -1e-283) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(x - t) / Float64(Float64(a - z) / Float64(z - y))));
	else
		tmp = Float64(t + Float64(Float64(Float64(Float64(t - x) * a) + Float64(y * Float64(x - t))) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - z) * (x - t)) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -1e-283) || ~((t_1 <= 0.0)))
		tmp = x + ((x - t) / ((a - z) / (z - y)));
	else
		tmp = t + ((((t - x) * a) + (y * (x - t))) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-283], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(x - t), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(N[(t - x), $MachinePrecision] * a), $MachinePrecision] + N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -9.99999999999999947e-284 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 76.0%

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

      1. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

      1. *-commutative 88.8%

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

      2. associate-*l/ 76.0%

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

      3. associate-*r/ 92.3%

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

      4. clear-num 92.3%

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

      5. un-div-inv 92.3%

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

   6. Applied egg-rr 92.3%

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

   if -9.99999999999999947e-284 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.5%

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

      1. associate-/l* 4.4%

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

   3. Simplified 4.4%

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

   5. Taylor expanded in z around -inf 95.1%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq -1 \cdot 10^{-283} \lor \neg \left(x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{x - t}{\frac{a - z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a + y \cdot \left(x - t\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 36.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+57}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-257}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-112}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 280:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+20}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+91}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+163}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 + \frac{a}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.4e+57)
   t
   (if (<= z -5.4e-257)
     x
     (if (<= z 5.5e-112)
       (* t (/ y (- a z)))
       (if (<= z 4.8e-52)
         x
         (if (<= z 280.0)
           t
           (if (<= z 3e+20)
             (* t (/ (- y z) a))
             (if (<= z 2.9e+91)
               (/ (* x y) z)
               (if (<= z 4.4e+163) x (* t (+ 1.0 (/ a z))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.4e+57) {
		tmp = t;
	} else if (z <= -5.4e-257) {
		tmp = x;
	} else if (z <= 5.5e-112) {
		tmp = t * (y / (a - z));
	} else if (z <= 4.8e-52) {
		tmp = x;
	} else if (z <= 280.0) {
		tmp = t;
	} else if (z <= 3e+20) {
		tmp = t * ((y - z) / a);
	} else if (z <= 2.9e+91) {
		tmp = (x * y) / z;
	} else if (z <= 4.4e+163) {
		tmp = x;
	} else {
		tmp = t * (1.0 + (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.4d+57)) then
        tmp = t
    else if (z <= (-5.4d-257)) then
        tmp = x
    else if (z <= 5.5d-112) then
        tmp = t * (y / (a - z))
    else if (z <= 4.8d-52) then
        tmp = x
    else if (z <= 280.0d0) then
        tmp = t
    else if (z <= 3d+20) then
        tmp = t * ((y - z) / a)
    else if (z <= 2.9d+91) then
        tmp = (x * y) / z
    else if (z <= 4.4d+163) then
        tmp = x
    else
        tmp = t * (1.0d0 + (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.4e+57) {
		tmp = t;
	} else if (z <= -5.4e-257) {
		tmp = x;
	} else if (z <= 5.5e-112) {
		tmp = t * (y / (a - z));
	} else if (z <= 4.8e-52) {
		tmp = x;
	} else if (z <= 280.0) {
		tmp = t;
	} else if (z <= 3e+20) {
		tmp = t * ((y - z) / a);
	} else if (z <= 2.9e+91) {
		tmp = (x * y) / z;
	} else if (z <= 4.4e+163) {
		tmp = x;
	} else {
		tmp = t * (1.0 + (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.4e+57:
		tmp = t
	elif z <= -5.4e-257:
		tmp = x
	elif z <= 5.5e-112:
		tmp = t * (y / (a - z))
	elif z <= 4.8e-52:
		tmp = x
	elif z <= 280.0:
		tmp = t
	elif z <= 3e+20:
		tmp = t * ((y - z) / a)
	elif z <= 2.9e+91:
		tmp = (x * y) / z
	elif z <= 4.4e+163:
		tmp = x
	else:
		tmp = t * (1.0 + (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.4e+57)
		tmp = t;
	elseif (z <= -5.4e-257)
		tmp = x;
	elseif (z <= 5.5e-112)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 4.8e-52)
		tmp = x;
	elseif (z <= 280.0)
		tmp = t;
	elseif (z <= 3e+20)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 2.9e+91)
		tmp = Float64(Float64(x * y) / z);
	elseif (z <= 4.4e+163)
		tmp = x;
	else
		tmp = Float64(t * Float64(1.0 + Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.4e+57)
		tmp = t;
	elseif (z <= -5.4e-257)
		tmp = x;
	elseif (z <= 5.5e-112)
		tmp = t * (y / (a - z));
	elseif (z <= 4.8e-52)
		tmp = x;
	elseif (z <= 280.0)
		tmp = t;
	elseif (z <= 3e+20)
		tmp = t * ((y - z) / a);
	elseif (z <= 2.9e+91)
		tmp = (x * y) / z;
	elseif (z <= 4.4e+163)
		tmp = x;
	else
		tmp = t * (1.0 + (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.4e+57], t, If[LessEqual[z, -5.4e-257], x, If[LessEqual[z, 5.5e-112], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e-52], x, If[LessEqual[z, 280.0], t, If[LessEqual[z, 3e+20], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+91], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 4.4e+163], x, N[(t * N[(1.0 + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -5.3999999999999997e57 or 4.8000000000000003e-52 < z < 280

   1. Initial program 48.8%

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

      1. associate-/l* 64.7%

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

   3. Simplified 64.7%

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

   5. Taylor expanded in z around inf 49.7%

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

   if -5.3999999999999997e57 < z < -5.3999999999999997e-257 or 5.5e-112 < z < 4.8000000000000003e-52 or 2.90000000000000014e91 < z < 4.39999999999999973e163

   1. Initial program 80.2%

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

      1. associate-/l* 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in a around inf 36.0%

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

   if -5.3999999999999997e-257 < z < 5.5e-112

   1. Initial program 89.3%

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

      1. associate-/l* 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in x around 0 51.0%

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

   6. Taylor expanded in y around inf 49.1%

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

      1. associate-/l* 56.8%

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

   8. Simplified 56.8%

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

   if 280 < z < 3e20

   1. Initial program 99.6%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around 0 76.0%

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

   6. Taylor expanded in a around inf 76.0%

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

      1. associate-/l* 76.0%

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

   8. Simplified 76.0%

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

   if 3e20 < z < 2.90000000000000014e91

   1. Initial program 88.7%

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

      1. associate-/l* 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in z around -inf 80.3%

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

   6. Taylor expanded in x around -inf 48.6%

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

      1. associate-/l* 48.7%

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

   8. Simplified 48.7%

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

   9. Taylor expanded in y around inf 41.8%

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

   if 4.39999999999999973e163 < z

   1. Initial program 34.4%

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

      1. associate-/l* 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in z around -inf 70.9%

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

   6. Taylor expanded in y around 0 67.4%

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

      1. associate-*r/ 78.3%

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

   8. Simplified 78.3%

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

   9. Taylor expanded in t around inf 70.4%

      \[\leadsto \color{blue}{t \cdot \left(1 + \frac{a}{z}\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+57}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-257}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-112}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 280:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+20}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+91}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+163}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 + \frac{a}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 36.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ t_2 := t \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{if}\;z \leq -1.56 \cdot 10^{+59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-258}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-111}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 165:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+175}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z))) (t_2 (* t (+ 1.0 (/ a z)))))
   (if (<= z -1.56e+59)
     t_2
     (if (<= z -2.35e-94)
       t_1
       (if (<= z -6.4e-258)
         x
         (if (<= z 1.6e-111)
           (* t (/ y (- a z)))
           (if (<= z 165.0)
             x
             (if (<= z 8e+18)
               (* t (/ (- y z) a))
               (if (<= z 7.8e+121) t_1 (if (<= z 1.2e+175) x t_2))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = t * (1.0 + (a / z));
	double tmp;
	if (z <= -1.56e+59) {
		tmp = t_2;
	} else if (z <= -2.35e-94) {
		tmp = t_1;
	} else if (z <= -6.4e-258) {
		tmp = x;
	} else if (z <= 1.6e-111) {
		tmp = t * (y / (a - z));
	} else if (z <= 165.0) {
		tmp = x;
	} else if (z <= 8e+18) {
		tmp = t * ((y - z) / a);
	} else if (z <= 7.8e+121) {
		tmp = t_1;
	} else if (z <= 1.2e+175) {
		tmp = x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    t_2 = t * (1.0d0 + (a / z))
    if (z <= (-1.56d+59)) then
        tmp = t_2
    else if (z <= (-2.35d-94)) then
        tmp = t_1
    else if (z <= (-6.4d-258)) then
        tmp = x
    else if (z <= 1.6d-111) then
        tmp = t * (y / (a - z))
    else if (z <= 165.0d0) then
        tmp = x
    else if (z <= 8d+18) then
        tmp = t * ((y - z) / a)
    else if (z <= 7.8d+121) then
        tmp = t_1
    else if (z <= 1.2d+175) then
        tmp = x
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = t * (1.0 + (a / z));
	double tmp;
	if (z <= -1.56e+59) {
		tmp = t_2;
	} else if (z <= -2.35e-94) {
		tmp = t_1;
	} else if (z <= -6.4e-258) {
		tmp = x;
	} else if (z <= 1.6e-111) {
		tmp = t * (y / (a - z));
	} else if (z <= 165.0) {
		tmp = x;
	} else if (z <= 8e+18) {
		tmp = t * ((y - z) / a);
	} else if (z <= 7.8e+121) {
		tmp = t_1;
	} else if (z <= 1.2e+175) {
		tmp = x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	t_2 = t * (1.0 + (a / z))
	tmp = 0
	if z <= -1.56e+59:
		tmp = t_2
	elif z <= -2.35e-94:
		tmp = t_1
	elif z <= -6.4e-258:
		tmp = x
	elif z <= 1.6e-111:
		tmp = t * (y / (a - z))
	elif z <= 165.0:
		tmp = x
	elif z <= 8e+18:
		tmp = t * ((y - z) / a)
	elif z <= 7.8e+121:
		tmp = t_1
	elif z <= 1.2e+175:
		tmp = x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	t_2 = Float64(t * Float64(1.0 + Float64(a / z)))
	tmp = 0.0
	if (z <= -1.56e+59)
		tmp = t_2;
	elseif (z <= -2.35e-94)
		tmp = t_1;
	elseif (z <= -6.4e-258)
		tmp = x;
	elseif (z <= 1.6e-111)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 165.0)
		tmp = x;
	elseif (z <= 8e+18)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 7.8e+121)
		tmp = t_1;
	elseif (z <= 1.2e+175)
		tmp = x;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	t_2 = t * (1.0 + (a / z));
	tmp = 0.0;
	if (z <= -1.56e+59)
		tmp = t_2;
	elseif (z <= -2.35e-94)
		tmp = t_1;
	elseif (z <= -6.4e-258)
		tmp = x;
	elseif (z <= 1.6e-111)
		tmp = t * (y / (a - z));
	elseif (z <= 165.0)
		tmp = x;
	elseif (z <= 8e+18)
		tmp = t * ((y - z) / a);
	elseif (z <= 7.8e+121)
		tmp = t_1;
	elseif (z <= 1.2e+175)
		tmp = x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.56e+59], t$95$2, If[LessEqual[z, -2.35e-94], t$95$1, If[LessEqual[z, -6.4e-258], x, If[LessEqual[z, 1.6e-111], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 165.0], x, If[LessEqual[z, 8e+18], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e+121], t$95$1, If[LessEqual[z, 1.2e+175], x, t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.56000000000000004e59 or 1.2e175 < z

   1. Initial program 35.6%

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

      1. associate-/l* 61.2%

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

   3. Simplified 61.2%

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

   5. Taylor expanded in z around -inf 64.6%

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

   6. Taylor expanded in y around 0 57.3%

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

      1. associate-*r/ 73.0%

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

   8. Simplified 73.0%

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

   9. Taylor expanded in t around inf 59.7%

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

   if -1.56000000000000004e59 < z < -2.35000000000000002e-94 or 8e18 < z < 7.79999999999999967e121

   1. Initial program 74.9%

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

      1. associate-/l* 84.1%

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

   3. Simplified 84.1%

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

   5. Taylor expanded in z around -inf 57.7%

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

   6. Taylor expanded in x around -inf 37.5%

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

      1. associate-/l* 39.2%

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

   8. Simplified 39.2%

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

   if -2.35000000000000002e-94 < z < -6.4000000000000004e-258 or 1.5999999999999999e-111 < z < 165 or 7.79999999999999967e121 < z < 1.2e175

   1. Initial program 86.1%

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

      1. associate-/l* 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in a around inf 43.4%

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

   if -6.4000000000000004e-258 < z < 1.5999999999999999e-111

   1. Initial program 89.3%

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

      1. associate-/l* 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in x around 0 51.0%

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

   6. Taylor expanded in y around inf 49.1%

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

      1. associate-/l* 56.8%

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

   8. Simplified 56.8%

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

   if 165 < z < 8e18

   1. Initial program 99.7%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 80.8%

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

   6. Taylor expanded in a around inf 62.7%

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

      1. associate-/l* 62.7%

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

   8. Simplified 62.7%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{+59}:\\ \;\;\;\;t \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-258}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-111}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 165:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+121}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+175}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 + \frac{a}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-283} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{x - t}{\frac{a - z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y z) (- x t)) (- a z)))))
   (if (or (<= t_1 -1e-283) (not (<= t_1 0.0)))
     (+ x (/ (- x t) (/ (- a z) (- z y))))
     (+ t (/ (* (- t x) (- a y)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-283) || !(t_1 <= 0.0)) {
		tmp = x + ((x - t) / ((a - z) / (z - y)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((y - z) * (x - t)) / (a - z))
    if ((t_1 <= (-1d-283)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((x - t) / ((a - z) / (z - y)))
    else
        tmp = t + (((t - x) * (a - y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-283) || !(t_1 <= 0.0)) {
		tmp = x + ((x - t) / ((a - z) / (z - y)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - z) * (x - t)) / (a - z))
	tmp = 0
	if (t_1 <= -1e-283) or not (t_1 <= 0.0):
		tmp = x + ((x - t) / ((a - z) / (z - y)))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -1e-283) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(x - t) / Float64(Float64(a - z) / Float64(z - y))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - z) * (x - t)) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -1e-283) || ~((t_1 <= 0.0)))
		tmp = x + ((x - t) / ((a - z) / (z - y)));
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-283], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(x - t), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -9.99999999999999947e-284 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 76.0%

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

      1. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

      1. *-commutative 88.8%

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

      2. associate-*l/ 76.0%

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

      3. associate-*r/ 92.3%

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

      4. clear-num 92.3%

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

      5. un-div-inv 92.3%

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

   6. Applied egg-rr 92.3%

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

   if -9.99999999999999947e-284 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.5%

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

      1. associate-/l* 4.4%

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

   3. Simplified 4.4%

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

   5. Taylor expanded in z around inf 95.1%

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

      1. associate--l+ 95.1%

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

      2. associate-*r/ 95.1%

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

      3. associate-*r/ 95.1%

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

      4. mul-1-neg 95.1%

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

      5. div-sub 95.1%

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

      6. mul-1-neg 95.1%

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

      7. distribute-lft-out-- 95.1%

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

      8. associate-*r/ 95.1%

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

      9. mul-1-neg 95.1%

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

      10. unsub-neg 95.1%

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

      11. distribute-rgt-out-- 95.0%

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

   7. Simplified 95.0%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq -1 \cdot 10^{-283} \lor \neg \left(x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{x - t}{\frac{a - z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -7900:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-203}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-257}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-96}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-64}:\\ \;\;\;\;x - \frac{y \cdot \left(x - t\right)}{a}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (/ (- t x) (/ a y)))))
   (if (<= a -7900.0)
     t_2
     (if (<= a -7.5e-74)
       t_1
       (if (<= a -8.5e-203)
         (* (- t x) (/ y (- a z)))
         (if (<= a -5.8e-257)
           t_1
           (if (<= a 2.45e-96)
             (+ t (* y (/ (- x t) z)))
             (if (<= a 5.5e-64)
               (- x (/ (* y (- x t)) a))
               (if (<= a 1.85e+18) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + ((t - x) / (a / y));
	double tmp;
	if (a <= -7900.0) {
		tmp = t_2;
	} else if (a <= -7.5e-74) {
		tmp = t_1;
	} else if (a <= -8.5e-203) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= -5.8e-257) {
		tmp = t_1;
	} else if (a <= 2.45e-96) {
		tmp = t + (y * ((x - t) / z));
	} else if (a <= 5.5e-64) {
		tmp = x - ((y * (x - t)) / a);
	} else if (a <= 1.85e+18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + ((t - x) / (a / y))
    if (a <= (-7900.0d0)) then
        tmp = t_2
    else if (a <= (-7.5d-74)) then
        tmp = t_1
    else if (a <= (-8.5d-203)) then
        tmp = (t - x) * (y / (a - z))
    else if (a <= (-5.8d-257)) then
        tmp = t_1
    else if (a <= 2.45d-96) then
        tmp = t + (y * ((x - t) / z))
    else if (a <= 5.5d-64) then
        tmp = x - ((y * (x - t)) / a)
    else if (a <= 1.85d+18) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + ((t - x) / (a / y));
	double tmp;
	if (a <= -7900.0) {
		tmp = t_2;
	} else if (a <= -7.5e-74) {
		tmp = t_1;
	} else if (a <= -8.5e-203) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= -5.8e-257) {
		tmp = t_1;
	} else if (a <= 2.45e-96) {
		tmp = t + (y * ((x - t) / z));
	} else if (a <= 5.5e-64) {
		tmp = x - ((y * (x - t)) / a);
	} else if (a <= 1.85e+18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + ((t - x) / (a / y))
	tmp = 0
	if a <= -7900.0:
		tmp = t_2
	elif a <= -7.5e-74:
		tmp = t_1
	elif a <= -8.5e-203:
		tmp = (t - x) * (y / (a - z))
	elif a <= -5.8e-257:
		tmp = t_1
	elif a <= 2.45e-96:
		tmp = t + (y * ((x - t) / z))
	elif a <= 5.5e-64:
		tmp = x - ((y * (x - t)) / a)
	elif a <= 1.85e+18:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(Float64(t - x) / Float64(a / y)))
	tmp = 0.0
	if (a <= -7900.0)
		tmp = t_2;
	elseif (a <= -7.5e-74)
		tmp = t_1;
	elseif (a <= -8.5e-203)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (a <= -5.8e-257)
		tmp = t_1;
	elseif (a <= 2.45e-96)
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	elseif (a <= 5.5e-64)
		tmp = Float64(x - Float64(Float64(y * Float64(x - t)) / a));
	elseif (a <= 1.85e+18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + ((t - x) / (a / y));
	tmp = 0.0;
	if (a <= -7900.0)
		tmp = t_2;
	elseif (a <= -7.5e-74)
		tmp = t_1;
	elseif (a <= -8.5e-203)
		tmp = (t - x) * (y / (a - z));
	elseif (a <= -5.8e-257)
		tmp = t_1;
	elseif (a <= 2.45e-96)
		tmp = t + (y * ((x - t) / z));
	elseif (a <= 5.5e-64)
		tmp = x - ((y * (x - t)) / a);
	elseif (a <= 1.85e+18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7900.0], t$95$2, If[LessEqual[a, -7.5e-74], t$95$1, If[LessEqual[a, -8.5e-203], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.8e-257], t$95$1, If[LessEqual[a, 2.45e-96], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e-64], N[(x - N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e+18], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -7900 or 1.85e18 < a

   1. Initial program 68.1%

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

      1. associate-/l* 87.1%

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

   3. Simplified 87.1%

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

      1. *-commutative 87.1%

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

      2. associate-*l/ 68.1%

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

      3. associate-*r/ 90.3%

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

      4. clear-num 90.3%

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

      5. un-div-inv 90.3%

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

   6. Applied egg-rr 90.3%

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

   7. Taylor expanded in z around 0 72.9%

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

   if -7900 < a < -7.5e-74 or -8.50000000000000031e-203 < a < -5.8000000000000003e-257 or 5.4999999999999999e-64 < a < 1.85e18

   1. Initial program 75.8%

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

      1. associate-/l* 80.0%

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

   3. Simplified 80.0%

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

   5. Taylor expanded in x around 0 70.0%

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

      1. associate-/l* 82.3%

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

   7. Simplified 82.3%

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

   if -7.5e-74 < a < -8.50000000000000031e-203

   1. Initial program 81.0%

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

      1. associate-/l* 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in y around -inf 81.6%

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

      1. *-commutative 81.6%

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

      2. associate-/l* 81.4%

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

   7. Applied egg-rr 81.4%

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

   if -5.8000000000000003e-257 < a < 2.45000000000000008e-96

   1. Initial program 62.3%

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

      1. associate-/l* 72.6%

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

   3. Simplified 72.6%

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

   5. Taylor expanded in z around -inf 84.2%

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

   6. Taylor expanded in a around 0 80.9%

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

      1. mul-1-neg 80.9%

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

      2. associate-*r/ 86.0%

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

      3. sub-neg 86.0%

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

   8. Simplified 86.0%

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

   if 2.45000000000000008e-96 < a < 5.4999999999999999e-64

   1. Initial program 99.8%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 99.8%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7900:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-74}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-203}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-257}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-96}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-64}:\\ \;\;\;\;x - \frac{y \cdot \left(x - t\right)}{a}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{t - x}{\frac{a}{y}}\\ t_3 := y \cdot \left(x - t\right)\\ \mathbf{if}\;a \leq -26000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-203}:\\ \;\;\;\;\frac{t\_3}{z - a}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-257}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-96}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-65}:\\ \;\;\;\;x - \frac{t\_3}{a}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z))))
        (t_2 (+ x (/ (- t x) (/ a y))))
        (t_3 (* y (- x t))))
   (if (<= a -26000.0)
     t_2
     (if (<= a -1.75e-75)
       t_1
       (if (<= a -1e-203)
         (/ t_3 (- z a))
         (if (<= a -5e-257)
           t_1
           (if (<= a 2.45e-96)
             (+ t (* y (/ (- x t) z)))
             (if (<= a 1.45e-65)
               (- x (/ t_3 a))
               (if (<= a 2.7e+18) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + ((t - x) / (a / y));
	double t_3 = y * (x - t);
	double tmp;
	if (a <= -26000.0) {
		tmp = t_2;
	} else if (a <= -1.75e-75) {
		tmp = t_1;
	} else if (a <= -1e-203) {
		tmp = t_3 / (z - a);
	} else if (a <= -5e-257) {
		tmp = t_1;
	} else if (a <= 2.45e-96) {
		tmp = t + (y * ((x - t) / z));
	} else if (a <= 1.45e-65) {
		tmp = x - (t_3 / a);
	} else if (a <= 2.7e+18) {
		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) :: t_3
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + ((t - x) / (a / y))
    t_3 = y * (x - t)
    if (a <= (-26000.0d0)) then
        tmp = t_2
    else if (a <= (-1.75d-75)) then
        tmp = t_1
    else if (a <= (-1d-203)) then
        tmp = t_3 / (z - a)
    else if (a <= (-5d-257)) then
        tmp = t_1
    else if (a <= 2.45d-96) then
        tmp = t + (y * ((x - t) / z))
    else if (a <= 1.45d-65) then
        tmp = x - (t_3 / a)
    else if (a <= 2.7d+18) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + ((t - x) / (a / y));
	double t_3 = y * (x - t);
	double tmp;
	if (a <= -26000.0) {
		tmp = t_2;
	} else if (a <= -1.75e-75) {
		tmp = t_1;
	} else if (a <= -1e-203) {
		tmp = t_3 / (z - a);
	} else if (a <= -5e-257) {
		tmp = t_1;
	} else if (a <= 2.45e-96) {
		tmp = t + (y * ((x - t) / z));
	} else if (a <= 1.45e-65) {
		tmp = x - (t_3 / a);
	} else if (a <= 2.7e+18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + ((t - x) / (a / y))
	t_3 = y * (x - t)
	tmp = 0
	if a <= -26000.0:
		tmp = t_2
	elif a <= -1.75e-75:
		tmp = t_1
	elif a <= -1e-203:
		tmp = t_3 / (z - a)
	elif a <= -5e-257:
		tmp = t_1
	elif a <= 2.45e-96:
		tmp = t + (y * ((x - t) / z))
	elif a <= 1.45e-65:
		tmp = x - (t_3 / a)
	elif a <= 2.7e+18:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(Float64(t - x) / Float64(a / y)))
	t_3 = Float64(y * Float64(x - t))
	tmp = 0.0
	if (a <= -26000.0)
		tmp = t_2;
	elseif (a <= -1.75e-75)
		tmp = t_1;
	elseif (a <= -1e-203)
		tmp = Float64(t_3 / Float64(z - a));
	elseif (a <= -5e-257)
		tmp = t_1;
	elseif (a <= 2.45e-96)
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	elseif (a <= 1.45e-65)
		tmp = Float64(x - Float64(t_3 / a));
	elseif (a <= 2.7e+18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + ((t - x) / (a / y));
	t_3 = y * (x - t);
	tmp = 0.0;
	if (a <= -26000.0)
		tmp = t_2;
	elseif (a <= -1.75e-75)
		tmp = t_1;
	elseif (a <= -1e-203)
		tmp = t_3 / (z - a);
	elseif (a <= -5e-257)
		tmp = t_1;
	elseif (a <= 2.45e-96)
		tmp = t + (y * ((x - t) / z));
	elseif (a <= 1.45e-65)
		tmp = x - (t_3 / a);
	elseif (a <= 2.7e+18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -26000.0], t$95$2, If[LessEqual[a, -1.75e-75], t$95$1, If[LessEqual[a, -1e-203], N[(t$95$3 / N[(z - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5e-257], t$95$1, If[LessEqual[a, 2.45e-96], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.45e-65], N[(x - N[(t$95$3 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e+18], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -26000 or 2.7e18 < a

   1. Initial program 68.1%

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

      1. associate-/l* 87.1%

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

   3. Simplified 87.1%

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

      1. *-commutative 87.1%

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

      2. associate-*l/ 68.1%

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

      3. associate-*r/ 90.3%

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

      4. clear-num 90.3%

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

      5. un-div-inv 90.3%

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

   6. Applied egg-rr 90.3%

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

   7. Taylor expanded in z around 0 72.9%

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

   if -26000 < a < -1.74999999999999993e-75 or -1e-203 < a < -4.99999999999999989e-257 or 1.4499999999999999e-65 < a < 2.7e18

   1. Initial program 75.8%

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

      1. associate-/l* 80.0%

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

   3. Simplified 80.0%

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

   5. Taylor expanded in x around 0 70.0%

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

      1. associate-/l* 82.3%

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

   7. Simplified 82.3%

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

   if -1.74999999999999993e-75 < a < -1e-203

   1. Initial program 81.0%

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

      1. associate-/l* 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in y around -inf 81.6%

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

   if -4.99999999999999989e-257 < a < 2.45000000000000008e-96

   1. Initial program 62.3%

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

      1. associate-/l* 72.6%

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

   3. Simplified 72.6%

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

   5. Taylor expanded in z around -inf 84.2%

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

   6. Taylor expanded in a around 0 80.9%

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

      1. mul-1-neg 80.9%

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

      2. associate-*r/ 86.0%

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

      3. sub-neg 86.0%

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

   8. Simplified 86.0%

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

   if 2.45000000000000008e-96 < a < 1.4499999999999999e-65

   1. Initial program 99.8%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 99.8%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -26000:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-75}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-203}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z - a}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-257}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-96}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-65}:\\ \;\;\;\;x - \frac{y \cdot \left(x - t\right)}{a}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y - z}{a}\\ t_2 := y \cdot \left(x - t\right)\\ \mathbf{if}\;a \leq -1.06 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-31}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-199}:\\ \;\;\;\;\frac{t\_2}{z - a}\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-96}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-67}:\\ \;\;\;\;x - \frac{t\_2}{a}\\ \mathbf{elif}\;a \leq 53000000000000:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ (- y z) a)))) (t_2 (* y (- x t))))
   (if (<= a -1.06e-8)
     t_1
     (if (<= a -4.8e-31)
       (- t (* x (/ a z)))
       (if (<= a -4.1e-199)
         (/ t_2 (- z a))
         (if (<= a 2.45e-96)
           (+ t (/ (* (- t x) (- a y)) z))
           (if (<= a 1.05e-67)
             (- x (/ t_2 a))
             (if (<= a 53000000000000.0) (* t (/ (- y z) (- a z))) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * ((y - z) / a));
	double t_2 = y * (x - t);
	double tmp;
	if (a <= -1.06e-8) {
		tmp = t_1;
	} else if (a <= -4.8e-31) {
		tmp = t - (x * (a / z));
	} else if (a <= -4.1e-199) {
		tmp = t_2 / (z - a);
	} else if (a <= 2.45e-96) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (a <= 1.05e-67) {
		tmp = x - (t_2 / a);
	} else if (a <= 53000000000000.0) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((t - x) * ((y - z) / a))
    t_2 = y * (x - t)
    if (a <= (-1.06d-8)) then
        tmp = t_1
    else if (a <= (-4.8d-31)) then
        tmp = t - (x * (a / z))
    else if (a <= (-4.1d-199)) then
        tmp = t_2 / (z - a)
    else if (a <= 2.45d-96) then
        tmp = t + (((t - x) * (a - y)) / z)
    else if (a <= 1.05d-67) then
        tmp = x - (t_2 / a)
    else if (a <= 53000000000000.0d0) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * ((y - z) / a));
	double t_2 = y * (x - t);
	double tmp;
	if (a <= -1.06e-8) {
		tmp = t_1;
	} else if (a <= -4.8e-31) {
		tmp = t - (x * (a / z));
	} else if (a <= -4.1e-199) {
		tmp = t_2 / (z - a);
	} else if (a <= 2.45e-96) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (a <= 1.05e-67) {
		tmp = x - (t_2 / a);
	} else if (a <= 53000000000000.0) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * ((y - z) / a))
	t_2 = y * (x - t)
	tmp = 0
	if a <= -1.06e-8:
		tmp = t_1
	elif a <= -4.8e-31:
		tmp = t - (x * (a / z))
	elif a <= -4.1e-199:
		tmp = t_2 / (z - a)
	elif a <= 2.45e-96:
		tmp = t + (((t - x) * (a - y)) / z)
	elif a <= 1.05e-67:
		tmp = x - (t_2 / a)
	elif a <= 53000000000000.0:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)))
	t_2 = Float64(y * Float64(x - t))
	tmp = 0.0
	if (a <= -1.06e-8)
		tmp = t_1;
	elseif (a <= -4.8e-31)
		tmp = Float64(t - Float64(x * Float64(a / z)));
	elseif (a <= -4.1e-199)
		tmp = Float64(t_2 / Float64(z - a));
	elseif (a <= 2.45e-96)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (a <= 1.05e-67)
		tmp = Float64(x - Float64(t_2 / a));
	elseif (a <= 53000000000000.0)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * ((y - z) / a));
	t_2 = y * (x - t);
	tmp = 0.0;
	if (a <= -1.06e-8)
		tmp = t_1;
	elseif (a <= -4.8e-31)
		tmp = t - (x * (a / z));
	elseif (a <= -4.1e-199)
		tmp = t_2 / (z - a);
	elseif (a <= 2.45e-96)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (a <= 1.05e-67)
		tmp = x - (t_2 / a);
	elseif (a <= 53000000000000.0)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.06e-8], t$95$1, If[LessEqual[a, -4.8e-31], N[(t - N[(x * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.1e-199], N[(t$95$2 / N[(z - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.45e-96], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e-67], N[(x - N[(t$95$2 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 53000000000000.0], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.06000000000000006e-8 or 5.3e13 < a

   1. Initial program 69.1%

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

      1. associate-/l* 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in a around inf 62.1%

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

      1. associate-/l* 76.5%

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

   7. Simplified 76.5%

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

   if -1.06000000000000006e-8 < a < -4.8e-31

   1. Initial program 77.8%

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

      1. associate-/l* 64.4%

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

   3. Simplified 64.4%

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

   5. Taylor expanded in z around -inf 82.8%

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

   6. Taylor expanded in y around 0 97.1%

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

      1. associate-*r/ 97.1%

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

   8. Simplified 97.1%

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

   9. Taylor expanded in t around 0 97.1%

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

       1. associate-*l/ 97.1%

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

       2. associate-*l* 97.1%

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

       3. *-commutative 97.1%

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

       4. mul-1-neg 97.1%

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

       5. distribute-frac-neg2 97.1%

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

   11. Simplified 97.1%

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

   if -4.8e-31 < a < -4.10000000000000022e-199

   1. Initial program 80.9%

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

      1. associate-/l* 78.6%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in y around -inf 78.3%

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

   if -4.10000000000000022e-199 < a < 2.45000000000000008e-96

   1. Initial program 64.6%

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

      1. associate-/l* 75.1%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in z around inf 84.5%

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

      1. associate--l+ 84.5%

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

      2. associate-*r/ 84.5%

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

      3. associate-*r/ 84.5%

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

      4. mul-1-neg 84.5%

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

      5. div-sub 84.5%

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

      6. mul-1-neg 84.5%

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

      7. distribute-lft-out-- 84.5%

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

      8. associate-*r/ 84.5%

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

      9. mul-1-neg 84.5%

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

      10. unsub-neg 84.5%

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

      11. distribute-rgt-out-- 84.4%

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

   7. Simplified 84.4%

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

   if 2.45000000000000008e-96 < a < 1.0500000000000001e-67

   1. Initial program 99.8%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 99.8%

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

   if 1.0500000000000001e-67 < a < 5.3e13

   1. Initial program 70.3%

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

      1. associate-/l* 78.1%

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

   3. Simplified 78.1%

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

   5. Taylor expanded in x around 0 67.7%

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

      1. associate-/l* 82.1%

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

   7. Simplified 82.1%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{-8}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-31}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-199}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z - a}\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-96}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-67}:\\ \;\;\;\;x - \frac{y \cdot \left(x - t\right)}{a}\\ \mathbf{elif}\;a \leq 53000000000000:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z}{z - a}\\ t_2 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;a \leq -2600:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-208}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-97}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-44} \lor \neg \left(a \leq 8.9 \cdot 10^{+15}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ z (- z a)))) (t_2 (+ x (/ (* y t) a))))
   (if (<= a -2600.0)
     t_2
     (if (<= a -2.8e-52)
       t_1
       (if (<= a -8.2e-208)
         (/ x (/ z (- y a)))
         (if (<= a 4.1e-97)
           (* t (- 1.0 (/ y z)))
           (if (or (<= a 4.8e-44) (not (<= a 8.9e+15))) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (z / (z - a));
	double t_2 = x + ((y * t) / a);
	double tmp;
	if (a <= -2600.0) {
		tmp = t_2;
	} else if (a <= -2.8e-52) {
		tmp = t_1;
	} else if (a <= -8.2e-208) {
		tmp = x / (z / (y - a));
	} else if (a <= 4.1e-97) {
		tmp = t * (1.0 - (y / z));
	} else if ((a <= 4.8e-44) || !(a <= 8.9e+15)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (z / (z - a))
    t_2 = x + ((y * t) / a)
    if (a <= (-2600.0d0)) then
        tmp = t_2
    else if (a <= (-2.8d-52)) then
        tmp = t_1
    else if (a <= (-8.2d-208)) then
        tmp = x / (z / (y - a))
    else if (a <= 4.1d-97) then
        tmp = t * (1.0d0 - (y / z))
    else if ((a <= 4.8d-44) .or. (.not. (a <= 8.9d+15))) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (z / (z - a));
	double t_2 = x + ((y * t) / a);
	double tmp;
	if (a <= -2600.0) {
		tmp = t_2;
	} else if (a <= -2.8e-52) {
		tmp = t_1;
	} else if (a <= -8.2e-208) {
		tmp = x / (z / (y - a));
	} else if (a <= 4.1e-97) {
		tmp = t * (1.0 - (y / z));
	} else if ((a <= 4.8e-44) || !(a <= 8.9e+15)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (z / (z - a))
	t_2 = x + ((y * t) / a)
	tmp = 0
	if a <= -2600.0:
		tmp = t_2
	elif a <= -2.8e-52:
		tmp = t_1
	elif a <= -8.2e-208:
		tmp = x / (z / (y - a))
	elif a <= 4.1e-97:
		tmp = t * (1.0 - (y / z))
	elif (a <= 4.8e-44) or not (a <= 8.9e+15):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(z / Float64(z - a)))
	t_2 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (a <= -2600.0)
		tmp = t_2;
	elseif (a <= -2.8e-52)
		tmp = t_1;
	elseif (a <= -8.2e-208)
		tmp = Float64(x / Float64(z / Float64(y - a)));
	elseif (a <= 4.1e-97)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif ((a <= 4.8e-44) || !(a <= 8.9e+15))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (z / (z - a));
	t_2 = x + ((y * t) / a);
	tmp = 0.0;
	if (a <= -2600.0)
		tmp = t_2;
	elseif (a <= -2.8e-52)
		tmp = t_1;
	elseif (a <= -8.2e-208)
		tmp = x / (z / (y - a));
	elseif (a <= 4.1e-97)
		tmp = t * (1.0 - (y / z));
	elseif ((a <= 4.8e-44) || ~((a <= 8.9e+15)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2600.0], t$95$2, If[LessEqual[a, -2.8e-52], t$95$1, If[LessEqual[a, -8.2e-208], N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.1e-97], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 4.8e-44], N[Not[LessEqual[a, 8.9e+15]], $MachinePrecision]], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2600 or 4.09999999999999993e-97 < a < 4.80000000000000017e-44 or 8.9e15 < a

   1. Initial program 69.8%

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

      1. associate-/l* 87.4%

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

   3. Simplified 87.4%

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

      1. *-commutative 87.4%

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

      2. associate-*l/ 69.8%

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

      3. associate-*r/ 89.6%

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

      4. clear-num 89.6%

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

      5. un-div-inv 89.6%

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

   6. Applied egg-rr 89.6%

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

   7. Taylor expanded in z around 0 73.5%

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

   8. Taylor expanded in t around inf 56.2%

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

   if -2600 < a < -2.79999999999999995e-52 or 4.80000000000000017e-44 < a < 8.9e15

   1. Initial program 79.7%

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

      1. associate-/l* 80.0%

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

   3. Simplified 80.0%

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

   5. Taylor expanded in x around 0 73.5%

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

   6. Taylor expanded in y around 0 61.0%

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

      1. associate-*r/ 61.0%

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

      2. associate-*r* 61.0%

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

      3. mul-1-neg 61.0%

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

   8. Simplified 61.0%

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

      1. associate-/l* 67.1%

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

      2. distribute-lft-neg-out 67.1%

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

   10. Applied egg-rr 67.1%

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

   if -2.79999999999999995e-52 < a < -8.1999999999999998e-208

   1. Initial program 76.2%

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

      1. associate-/l* 77.0%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in z around -inf 67.1%

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

   6. Taylor expanded in x around -inf 46.9%

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

      1. associate-/l* 47.0%

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

   8. Simplified 47.0%

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

      1. clear-num 47.0%

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

      2. un-div-inv 47.0%

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

   10. Applied egg-rr 47.0%

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

   if -8.1999999999999998e-208 < a < 4.09999999999999993e-97

   1. Initial program 65.9%

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

      1. associate-/l* 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in x around 0 56.8%

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

   6. Taylor expanded in a around 0 51.4%

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

      1. mul-1-neg 51.4%

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

      2. associate-/l* 66.3%

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

      3. div-sub 66.3%

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

      4. *-inverses 66.3%

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

   8. Simplified 66.3%

      \[\leadsto \color{blue}{-t \cdot \left(\frac{y}{z} - 1\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2600:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-208}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-97}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-44} \lor \neg \left(a \leq 8.9 \cdot 10^{+15}\right):\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;a \leq -49000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-53}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-208}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-96}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-43} \lor \neg \left(a \leq 1.08 \cdot 10^{+18}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))))
   (if (<= a -49000.0)
     t_1
     (if (<= a -5e-53)
       (* t (/ z (- z a)))
       (if (<= a -8.2e-208)
         (/ x (/ z (- y a)))
         (if (<= a 2.45e-96)
           (* t (- 1.0 (/ y z)))
           (if (or (<= a 1.2e-43) (not (<= a 1.08e+18)))
             t_1
             (/ t (- 1.0 (/ a z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (a <= -49000.0) {
		tmp = t_1;
	} else if (a <= -5e-53) {
		tmp = t * (z / (z - a));
	} else if (a <= -8.2e-208) {
		tmp = x / (z / (y - a));
	} else if (a <= 2.45e-96) {
		tmp = t * (1.0 - (y / z));
	} else if ((a <= 1.2e-43) || !(a <= 1.08e+18)) {
		tmp = t_1;
	} else {
		tmp = t / (1.0 - (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    if (a <= (-49000.0d0)) then
        tmp = t_1
    else if (a <= (-5d-53)) then
        tmp = t * (z / (z - a))
    else if (a <= (-8.2d-208)) then
        tmp = x / (z / (y - a))
    else if (a <= 2.45d-96) then
        tmp = t * (1.0d0 - (y / z))
    else if ((a <= 1.2d-43) .or. (.not. (a <= 1.08d+18))) then
        tmp = t_1
    else
        tmp = t / (1.0d0 - (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (a <= -49000.0) {
		tmp = t_1;
	} else if (a <= -5e-53) {
		tmp = t * (z / (z - a));
	} else if (a <= -8.2e-208) {
		tmp = x / (z / (y - a));
	} else if (a <= 2.45e-96) {
		tmp = t * (1.0 - (y / z));
	} else if ((a <= 1.2e-43) || !(a <= 1.08e+18)) {
		tmp = t_1;
	} else {
		tmp = t / (1.0 - (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	tmp = 0
	if a <= -49000.0:
		tmp = t_1
	elif a <= -5e-53:
		tmp = t * (z / (z - a))
	elif a <= -8.2e-208:
		tmp = x / (z / (y - a))
	elif a <= 2.45e-96:
		tmp = t * (1.0 - (y / z))
	elif (a <= 1.2e-43) or not (a <= 1.08e+18):
		tmp = t_1
	else:
		tmp = t / (1.0 - (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (a <= -49000.0)
		tmp = t_1;
	elseif (a <= -5e-53)
		tmp = Float64(t * Float64(z / Float64(z - a)));
	elseif (a <= -8.2e-208)
		tmp = Float64(x / Float64(z / Float64(y - a)));
	elseif (a <= 2.45e-96)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif ((a <= 1.2e-43) || !(a <= 1.08e+18))
		tmp = t_1;
	else
		tmp = Float64(t / Float64(1.0 - Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	tmp = 0.0;
	if (a <= -49000.0)
		tmp = t_1;
	elseif (a <= -5e-53)
		tmp = t * (z / (z - a));
	elseif (a <= -8.2e-208)
		tmp = x / (z / (y - a));
	elseif (a <= 2.45e-96)
		tmp = t * (1.0 - (y / z));
	elseif ((a <= 1.2e-43) || ~((a <= 1.08e+18)))
		tmp = t_1;
	else
		tmp = t / (1.0 - (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -49000.0], t$95$1, If[LessEqual[a, -5e-53], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.2e-208], N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.45e-96], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 1.2e-43], N[Not[LessEqual[a, 1.08e+18]], $MachinePrecision]], t$95$1, N[(t / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -49000 or 2.45000000000000008e-96 < a < 1.2000000000000001e-43 or 1.08e18 < a

   1. Initial program 69.8%

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

      1. associate-/l* 87.4%

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

   3. Simplified 87.4%

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

      1. *-commutative 87.4%

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

      2. associate-*l/ 69.8%

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

      3. associate-*r/ 89.6%

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

      4. clear-num 89.6%

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

      5. un-div-inv 89.6%

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

   6. Applied egg-rr 89.6%

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

   7. Taylor expanded in z around 0 73.5%

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

   8. Taylor expanded in t around inf 56.2%

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

   if -49000 < a < -5e-53

   1. Initial program 85.7%

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

      1. associate-/l* 77.4%

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

   3. Simplified 77.4%

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

   5. Taylor expanded in x around 0 82.3%

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

   6. Taylor expanded in y around 0 65.4%

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

      1. associate-*r/ 65.4%

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

      2. associate-*r* 65.4%

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

      3. mul-1-neg 65.4%

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

   8. Simplified 65.4%

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

      1. associate-/l* 65.6%

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

      2. distribute-lft-neg-out 65.6%

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

   10. Applied egg-rr 65.6%

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

   if -5e-53 < a < -8.1999999999999998e-208

   1. Initial program 76.2%

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

      1. associate-/l* 77.0%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in z around -inf 67.1%

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

   6. Taylor expanded in x around -inf 46.9%

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

      1. associate-/l* 47.0%

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

   8. Simplified 47.0%

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

      1. clear-num 47.0%

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

      2. un-div-inv 47.0%

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

   10. Applied egg-rr 47.0%

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

   if -8.1999999999999998e-208 < a < 2.45000000000000008e-96

   1. Initial program 65.9%

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

      1. associate-/l* 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in x around 0 56.8%

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

   6. Taylor expanded in a around 0 51.4%

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

      1. mul-1-neg 51.4%

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

      2. associate-/l* 66.3%

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

      3. div-sub 66.3%

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

      4. *-inverses 66.3%

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

   8. Simplified 66.3%

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

   if 1.2000000000000001e-43 < a < 1.08e18

   1. Initial program 73.6%

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

      1. associate-/l* 82.7%

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

   3. Simplified 82.7%

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

   5. Taylor expanded in x around 0 64.7%

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

   6. Taylor expanded in y around 0 56.5%

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

      1. associate-*r/ 56.5%

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

      2. associate-*r* 56.5%

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

      3. mul-1-neg 56.5%

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

   8. Simplified 56.5%

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

      1. associate-/l* 68.7%

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

      2. distribute-lft-neg-out 68.7%

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

   10. Applied egg-rr 68.7%

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

   11. Taylor expanded in t around 0 56.5%

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

       1. associate-*l/ 60.5%

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

       2. associate-/r/ 68.8%

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

       3. div-sub 68.8%

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

       4. sub-neg 68.8%

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

       5. *-inverses 68.8%

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

       6. metadata-eval 68.8%

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

   13. Simplified 68.8%

       \[\leadsto -\color{blue}{\frac{t}{\frac{a}{z} + -1}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -49000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-53}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-208}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-96}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-43} \lor \neg \left(a \leq 1.08 \cdot 10^{+18}\right):\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 36.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+56}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-258}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+92} \lor \neg \left(z \leq 4.4 \cdot 10^{+163}\right):\\ \;\;\;\;t \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.1e+56)
   t
   (if (<= z -3.9e-258)
     x
     (if (<= z 4.3e-39)
       (* t (/ y (- a z)))
       (if (or (<= z 6e+92) (not (<= z 4.4e+163))) (* t (+ 1.0 (/ a z))) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.1e+56) {
		tmp = t;
	} else if (z <= -3.9e-258) {
		tmp = x;
	} else if (z <= 4.3e-39) {
		tmp = t * (y / (a - z));
	} else if ((z <= 6e+92) || !(z <= 4.4e+163)) {
		tmp = t * (1.0 + (a / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.1d+56)) then
        tmp = t
    else if (z <= (-3.9d-258)) then
        tmp = x
    else if (z <= 4.3d-39) then
        tmp = t * (y / (a - z))
    else if ((z <= 6d+92) .or. (.not. (z <= 4.4d+163))) then
        tmp = t * (1.0d0 + (a / z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.1e+56) {
		tmp = t;
	} else if (z <= -3.9e-258) {
		tmp = x;
	} else if (z <= 4.3e-39) {
		tmp = t * (y / (a - z));
	} else if ((z <= 6e+92) || !(z <= 4.4e+163)) {
		tmp = t * (1.0 + (a / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.1e+56:
		tmp = t
	elif z <= -3.9e-258:
		tmp = x
	elif z <= 4.3e-39:
		tmp = t * (y / (a - z))
	elif (z <= 6e+92) or not (z <= 4.4e+163):
		tmp = t * (1.0 + (a / z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.1e+56)
		tmp = t;
	elseif (z <= -3.9e-258)
		tmp = x;
	elseif (z <= 4.3e-39)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif ((z <= 6e+92) || !(z <= 4.4e+163))
		tmp = Float64(t * Float64(1.0 + Float64(a / z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.1e+56)
		tmp = t;
	elseif (z <= -3.9e-258)
		tmp = x;
	elseif (z <= 4.3e-39)
		tmp = t * (y / (a - z));
	elseif ((z <= 6e+92) || ~((z <= 4.4e+163)))
		tmp = t * (1.0 + (a / z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.1e+56], t, If[LessEqual[z, -3.9e-258], x, If[LessEqual[z, 4.3e-39], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 6e+92], N[Not[LessEqual[z, 4.4e+163]], $MachinePrecision]], N[(t * N[(1.0 + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.10000000000000017e56

   1. Initial program 36.4%

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

      1. associate-/l* 54.9%

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

   3. Simplified 54.9%

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

   5. Taylor expanded in z around inf 52.7%

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

   if -2.10000000000000017e56 < z < -3.90000000000000004e-258 or 6.00000000000000026e92 < z < 4.39999999999999973e163

   1. Initial program 81.5%

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

      1. associate-/l* 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in a around inf 34.8%

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

   if -3.90000000000000004e-258 < z < 4.2999999999999999e-39

   1. Initial program 85.4%

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

      1. associate-/l* 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in x around 0 46.7%

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

   6. Taylor expanded in y around inf 43.7%

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

      1. associate-/l* 51.4%

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

   8. Simplified 51.4%

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

   if 4.2999999999999999e-39 < z < 6.00000000000000026e92 or 4.39999999999999973e163 < z

   1. Initial program 66.5%

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

      1. associate-/l* 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in z around -inf 65.5%

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

   6. Taylor expanded in y around 0 52.6%

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

      1. associate-*r/ 57.7%

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

   8. Simplified 57.7%

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

   9. Taylor expanded in t around inf 52.5%

      \[\leadsto \color{blue}{t \cdot \left(1 + \frac{a}{z}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+56}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-258}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+92} \lor \neg \left(z \leq 4.4 \cdot 10^{+163}\right):\\ \;\;\;\;t \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 47.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ t_2 := t \cdot \left(1 + \frac{a}{z}\right)\\ t_3 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+20}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+163}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z)))
        (t_2 (* t (+ 1.0 (/ a z))))
        (t_3 (+ x (/ (* y t) a))))
   (if (<= z -1.4e+59)
     t_2
     (if (<= z -2.2e-92)
       t_1
       (if (<= z 3e+20)
         t_3
         (if (<= z 4.1e+105) t_1 (if (<= z 4.4e+163) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = t * (1.0 + (a / z));
	double t_3 = x + ((y * t) / a);
	double tmp;
	if (z <= -1.4e+59) {
		tmp = t_2;
	} else if (z <= -2.2e-92) {
		tmp = t_1;
	} else if (z <= 3e+20) {
		tmp = t_3;
	} else if (z <= 4.1e+105) {
		tmp = t_1;
	} else if (z <= 4.4e+163) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    t_2 = t * (1.0d0 + (a / z))
    t_3 = x + ((y * t) / a)
    if (z <= (-1.4d+59)) then
        tmp = t_2
    else if (z <= (-2.2d-92)) then
        tmp = t_1
    else if (z <= 3d+20) then
        tmp = t_3
    else if (z <= 4.1d+105) then
        tmp = t_1
    else if (z <= 4.4d+163) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = t * (1.0 + (a / z));
	double t_3 = x + ((y * t) / a);
	double tmp;
	if (z <= -1.4e+59) {
		tmp = t_2;
	} else if (z <= -2.2e-92) {
		tmp = t_1;
	} else if (z <= 3e+20) {
		tmp = t_3;
	} else if (z <= 4.1e+105) {
		tmp = t_1;
	} else if (z <= 4.4e+163) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	t_2 = t * (1.0 + (a / z))
	t_3 = x + ((y * t) / a)
	tmp = 0
	if z <= -1.4e+59:
		tmp = t_2
	elif z <= -2.2e-92:
		tmp = t_1
	elif z <= 3e+20:
		tmp = t_3
	elif z <= 4.1e+105:
		tmp = t_1
	elif z <= 4.4e+163:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	t_2 = Float64(t * Float64(1.0 + Float64(a / z)))
	t_3 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (z <= -1.4e+59)
		tmp = t_2;
	elseif (z <= -2.2e-92)
		tmp = t_1;
	elseif (z <= 3e+20)
		tmp = t_3;
	elseif (z <= 4.1e+105)
		tmp = t_1;
	elseif (z <= 4.4e+163)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	t_2 = t * (1.0 + (a / z));
	t_3 = x + ((y * t) / a);
	tmp = 0.0;
	if (z <= -1.4e+59)
		tmp = t_2;
	elseif (z <= -2.2e-92)
		tmp = t_1;
	elseif (z <= 3e+20)
		tmp = t_3;
	elseif (z <= 4.1e+105)
		tmp = t_1;
	elseif (z <= 4.4e+163)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+59], t$95$2, If[LessEqual[z, -2.2e-92], t$95$1, If[LessEqual[z, 3e+20], t$95$3, If[LessEqual[z, 4.1e+105], t$95$1, If[LessEqual[z, 4.4e+163], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3999999999999999e59 or 4.39999999999999973e163 < z

   1. Initial program 36.1%

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

      1. associate-/l* 62.2%

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

   3. Simplified 62.2%

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

   5. Taylor expanded in z around -inf 64.2%

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

   6. Taylor expanded in y around 0 57.2%

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

      1. associate-*r/ 72.5%

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

   8. Simplified 72.5%

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

   9. Taylor expanded in t around inf 59.5%

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

   if -1.3999999999999999e59 < z < -2.19999999999999987e-92 or 3e20 < z < 4.1000000000000002e105

   1. Initial program 78.5%

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

      1. associate-/l* 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in z around -inf 59.4%

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

   6. Taylor expanded in x around -inf 38.9%

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

      1. associate-/l* 40.9%

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

   8. Simplified 40.9%

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

   if -2.19999999999999987e-92 < z < 3e20 or 4.1000000000000002e105 < z < 4.39999999999999973e163

   1. Initial program 86.7%

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

      1. associate-/l* 91.7%

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

   3. Simplified 91.7%

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

      1. *-commutative 91.7%

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

      2. associate-*l/ 86.7%

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

      3. associate-*r/ 93.8%

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

      4. clear-num 93.8%

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

      5. un-div-inv 93.9%

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

   6. Applied egg-rr 93.9%

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

   7. Taylor expanded in z around 0 76.1%

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

   8. Taylor expanded in t around inf 58.4%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+59}:\\ \;\;\;\;t \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-92}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+20}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+163}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 + \frac{a}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 47.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 + \frac{a}{z}\right)\\ t_2 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;z \leq -1.42 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+163}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (+ 1.0 (/ a z)))) (t_2 (+ x (/ (* y t) a))))
   (if (<= z -1.42e+59)
     t_1
     (if (<= z -2.2e-92)
       (/ x (/ z (- y a)))
       (if (<= z 5.8e+22)
         t_2
         (if (<= z 4.1e+105)
           (* x (/ (- y a) z))
           (if (<= z 4.4e+163) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 + (a / z));
	double t_2 = x + ((y * t) / a);
	double tmp;
	if (z <= -1.42e+59) {
		tmp = t_1;
	} else if (z <= -2.2e-92) {
		tmp = x / (z / (y - a));
	} else if (z <= 5.8e+22) {
		tmp = t_2;
	} else if (z <= 4.1e+105) {
		tmp = x * ((y - a) / z);
	} else if (z <= 4.4e+163) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (1.0d0 + (a / z))
    t_2 = x + ((y * t) / a)
    if (z <= (-1.42d+59)) then
        tmp = t_1
    else if (z <= (-2.2d-92)) then
        tmp = x / (z / (y - a))
    else if (z <= 5.8d+22) then
        tmp = t_2
    else if (z <= 4.1d+105) then
        tmp = x * ((y - a) / z)
    else if (z <= 4.4d+163) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 + (a / z));
	double t_2 = x + ((y * t) / a);
	double tmp;
	if (z <= -1.42e+59) {
		tmp = t_1;
	} else if (z <= -2.2e-92) {
		tmp = x / (z / (y - a));
	} else if (z <= 5.8e+22) {
		tmp = t_2;
	} else if (z <= 4.1e+105) {
		tmp = x * ((y - a) / z);
	} else if (z <= 4.4e+163) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 + (a / z))
	t_2 = x + ((y * t) / a)
	tmp = 0
	if z <= -1.42e+59:
		tmp = t_1
	elif z <= -2.2e-92:
		tmp = x / (z / (y - a))
	elif z <= 5.8e+22:
		tmp = t_2
	elif z <= 4.1e+105:
		tmp = x * ((y - a) / z)
	elif z <= 4.4e+163:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 + Float64(a / z)))
	t_2 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (z <= -1.42e+59)
		tmp = t_1;
	elseif (z <= -2.2e-92)
		tmp = Float64(x / Float64(z / Float64(y - a)));
	elseif (z <= 5.8e+22)
		tmp = t_2;
	elseif (z <= 4.1e+105)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= 4.4e+163)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 + (a / z));
	t_2 = x + ((y * t) / a);
	tmp = 0.0;
	if (z <= -1.42e+59)
		tmp = t_1;
	elseif (z <= -2.2e-92)
		tmp = x / (z / (y - a));
	elseif (z <= 5.8e+22)
		tmp = t_2;
	elseif (z <= 4.1e+105)
		tmp = x * ((y - a) / z);
	elseif (z <= 4.4e+163)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.42e+59], t$95$1, If[LessEqual[z, -2.2e-92], N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+22], t$95$2, If[LessEqual[z, 4.1e+105], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e+163], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.42000000000000005e59 or 4.39999999999999973e163 < z

   1. Initial program 36.1%

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

      1. associate-/l* 62.2%

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

   3. Simplified 62.2%

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

   5. Taylor expanded in z around -inf 64.2%

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

   6. Taylor expanded in y around 0 57.2%

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

      1. associate-*r/ 72.5%

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

   8. Simplified 72.5%

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

   9. Taylor expanded in t around inf 59.5%

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

   if -1.42000000000000005e59 < z < -2.19999999999999987e-92

   1. Initial program 74.0%

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

      1. associate-/l* 84.0%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in z around -inf 50.5%

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

   6. Taylor expanded in x around -inf 37.3%

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

      1. associate-/l* 37.2%

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

   8. Simplified 37.2%

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

      1. clear-num 37.2%

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

      2. un-div-inv 37.2%

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

   10. Applied egg-rr 37.2%

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

   if -2.19999999999999987e-92 < z < 5.8e22 or 4.1000000000000002e105 < z < 4.39999999999999973e163

   1. Initial program 86.7%

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

      1. associate-/l* 91.7%

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

   3. Simplified 91.7%

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

      1. *-commutative 91.7%

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

      2. associate-*l/ 86.7%

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

      3. associate-*r/ 93.8%

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

      4. clear-num 93.8%

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

      5. un-div-inv 93.9%

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

   6. Applied egg-rr 93.9%

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

   7. Taylor expanded in z around 0 76.1%

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

   8. Taylor expanded in t around inf 58.4%

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

   if 5.8e22 < z < 4.1000000000000002e105

   1. Initial program 85.6%

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

      1. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in z around -inf 73.3%

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

   6. Taylor expanded in x around -inf 41.6%

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

      1. associate-/l* 46.7%

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

   8. Simplified 46.7%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+59}:\\ \;\;\;\;t \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+163}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 + \frac{a}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 47.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 + \frac{a}{z}\right)\\ t_2 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-92}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+163}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (+ 1.0 (/ a z)))) (t_2 (+ x (/ (* y t) a))))
   (if (<= z -1.8e+59)
     t_1
     (if (<= z -2.2e-92)
       (/ (* x (- y a)) z)
       (if (<= z 1.6e+22)
         t_2
         (if (<= z 2.1e+104)
           (* x (/ (- y a) z))
           (if (<= z 4.4e+163) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 + (a / z));
	double t_2 = x + ((y * t) / a);
	double tmp;
	if (z <= -1.8e+59) {
		tmp = t_1;
	} else if (z <= -2.2e-92) {
		tmp = (x * (y - a)) / z;
	} else if (z <= 1.6e+22) {
		tmp = t_2;
	} else if (z <= 2.1e+104) {
		tmp = x * ((y - a) / z);
	} else if (z <= 4.4e+163) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (1.0d0 + (a / z))
    t_2 = x + ((y * t) / a)
    if (z <= (-1.8d+59)) then
        tmp = t_1
    else if (z <= (-2.2d-92)) then
        tmp = (x * (y - a)) / z
    else if (z <= 1.6d+22) then
        tmp = t_2
    else if (z <= 2.1d+104) then
        tmp = x * ((y - a) / z)
    else if (z <= 4.4d+163) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 + (a / z));
	double t_2 = x + ((y * t) / a);
	double tmp;
	if (z <= -1.8e+59) {
		tmp = t_1;
	} else if (z <= -2.2e-92) {
		tmp = (x * (y - a)) / z;
	} else if (z <= 1.6e+22) {
		tmp = t_2;
	} else if (z <= 2.1e+104) {
		tmp = x * ((y - a) / z);
	} else if (z <= 4.4e+163) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 + (a / z))
	t_2 = x + ((y * t) / a)
	tmp = 0
	if z <= -1.8e+59:
		tmp = t_1
	elif z <= -2.2e-92:
		tmp = (x * (y - a)) / z
	elif z <= 1.6e+22:
		tmp = t_2
	elif z <= 2.1e+104:
		tmp = x * ((y - a) / z)
	elif z <= 4.4e+163:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 + Float64(a / z)))
	t_2 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (z <= -1.8e+59)
		tmp = t_1;
	elseif (z <= -2.2e-92)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (z <= 1.6e+22)
		tmp = t_2;
	elseif (z <= 2.1e+104)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= 4.4e+163)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 + (a / z));
	t_2 = x + ((y * t) / a);
	tmp = 0.0;
	if (z <= -1.8e+59)
		tmp = t_1;
	elseif (z <= -2.2e-92)
		tmp = (x * (y - a)) / z;
	elseif (z <= 1.6e+22)
		tmp = t_2;
	elseif (z <= 2.1e+104)
		tmp = x * ((y - a) / z);
	elseif (z <= 4.4e+163)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+59], t$95$1, If[LessEqual[z, -2.2e-92], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.6e+22], t$95$2, If[LessEqual[z, 2.1e+104], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e+163], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.7999999999999999e59 or 4.39999999999999973e163 < z

   1. Initial program 36.1%

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

      1. associate-/l* 62.2%

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

   3. Simplified 62.2%

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

   5. Taylor expanded in z around -inf 64.2%

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

   6. Taylor expanded in y around 0 57.2%

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

      1. associate-*r/ 72.5%

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

   8. Simplified 72.5%

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

   9. Taylor expanded in t around inf 59.5%

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

   if -1.7999999999999999e59 < z < -2.19999999999999987e-92

   1. Initial program 74.0%

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

      1. associate-/l* 84.0%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in z around -inf 50.5%

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

   6. Taylor expanded in x around -inf 37.3%

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

   if -2.19999999999999987e-92 < z < 1.6e22 or 2.0999999999999998e104 < z < 4.39999999999999973e163

   1. Initial program 86.7%

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

      1. associate-/l* 91.7%

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

   3. Simplified 91.7%

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

      1. *-commutative 91.7%

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

      2. associate-*l/ 86.7%

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

      3. associate-*r/ 93.8%

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

      4. clear-num 93.8%

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

      5. un-div-inv 93.9%

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

   6. Applied egg-rr 93.9%

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

   7. Taylor expanded in z around 0 76.1%

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

   8. Taylor expanded in t around inf 58.4%

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

   if 1.6e22 < z < 2.0999999999999998e104

   1. Initial program 85.6%

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

      1. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in z around -inf 73.3%

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

   6. Taylor expanded in x around -inf 41.6%

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

      1. associate-/l* 46.7%

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

   8. Simplified 46.7%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+59}:\\ \;\;\;\;t \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-92}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+163}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 + \frac{a}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-92}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+163}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))) (t_2 (+ x (/ (* y t) a))))
   (if (<= z -1.25e+59)
     t_1
     (if (<= z -2.2e-92)
       (/ (* x (- y a)) z)
       (if (<= z 6.8e+22)
         t_2
         (if (<= z 5.2e+106)
           (* x (/ (- y a) z))
           (if (<= z 4.4e+163) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x + ((y * t) / a);
	double tmp;
	if (z <= -1.25e+59) {
		tmp = t_1;
	} else if (z <= -2.2e-92) {
		tmp = (x * (y - a)) / z;
	} else if (z <= 6.8e+22) {
		tmp = t_2;
	} else if (z <= 5.2e+106) {
		tmp = x * ((y - a) / z);
	} else if (z <= 4.4e+163) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    t_2 = x + ((y * t) / a)
    if (z <= (-1.25d+59)) then
        tmp = t_1
    else if (z <= (-2.2d-92)) then
        tmp = (x * (y - a)) / z
    else if (z <= 6.8d+22) then
        tmp = t_2
    else if (z <= 5.2d+106) then
        tmp = x * ((y - a) / z)
    else if (z <= 4.4d+163) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x + ((y * t) / a);
	double tmp;
	if (z <= -1.25e+59) {
		tmp = t_1;
	} else if (z <= -2.2e-92) {
		tmp = (x * (y - a)) / z;
	} else if (z <= 6.8e+22) {
		tmp = t_2;
	} else if (z <= 5.2e+106) {
		tmp = x * ((y - a) / z);
	} else if (z <= 4.4e+163) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = x + ((y * t) / a)
	tmp = 0
	if z <= -1.25e+59:
		tmp = t_1
	elif z <= -2.2e-92:
		tmp = (x * (y - a)) / z
	elif z <= 6.8e+22:
		tmp = t_2
	elif z <= 5.2e+106:
		tmp = x * ((y - a) / z)
	elif z <= 4.4e+163:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (z <= -1.25e+59)
		tmp = t_1;
	elseif (z <= -2.2e-92)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (z <= 6.8e+22)
		tmp = t_2;
	elseif (z <= 5.2e+106)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= 4.4e+163)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = x + ((y * t) / a);
	tmp = 0.0;
	if (z <= -1.25e+59)
		tmp = t_1;
	elseif (z <= -2.2e-92)
		tmp = (x * (y - a)) / z;
	elseif (z <= 6.8e+22)
		tmp = t_2;
	elseif (z <= 5.2e+106)
		tmp = x * ((y - a) / z);
	elseif (z <= 4.4e+163)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e+59], t$95$1, If[LessEqual[z, -2.2e-92], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 6.8e+22], t$95$2, If[LessEqual[z, 5.2e+106], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e+163], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.2499999999999999e59 or 4.39999999999999973e163 < z

   1. Initial program 36.1%

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

      1. associate-/l* 62.2%

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

   3. Simplified 62.2%

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

   5. Taylor expanded in x around 0 39.9%

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

   6. Taylor expanded in a around 0 37.6%

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

      1. mul-1-neg 37.6%

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

      2. associate-/l* 64.7%

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

      3. div-sub 64.7%

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

      4. *-inverses 64.7%

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

   8. Simplified 64.7%

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

   if -1.2499999999999999e59 < z < -2.19999999999999987e-92

   1. Initial program 74.0%

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

      1. associate-/l* 84.0%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in z around -inf 50.5%

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

   6. Taylor expanded in x around -inf 37.3%

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

   if -2.19999999999999987e-92 < z < 6.8e22 or 5.20000000000000039e106 < z < 4.39999999999999973e163

   1. Initial program 86.7%

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

      1. associate-/l* 91.7%

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

   3. Simplified 91.7%

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

      1. *-commutative 91.7%

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

      2. associate-*l/ 86.7%

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

      3. associate-*r/ 93.8%

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

      4. clear-num 93.8%

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

      5. un-div-inv 93.9%

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

   6. Applied egg-rr 93.9%

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

   7. Taylor expanded in z around 0 76.1%

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

   8. Taylor expanded in t around inf 58.4%

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

   if 6.8e22 < z < 5.20000000000000039e106

   1. Initial program 85.6%

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

      1. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in z around -inf 73.3%

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

   6. Taylor expanded in x around -inf 41.6%

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

      1. associate-/l* 46.7%

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

   8. Simplified 46.7%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+59}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-92}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+163}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 71.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{if}\;a \leq -1.6 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{-30}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-208}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-96}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ (- y z) a)))))
   (if (<= a -1.6e-8)
     t_1
     (if (<= a -2.35e-30)
       (- t (* x (/ a z)))
       (if (<= a -8.2e-208)
         (* (- t x) (/ y (- a z)))
         (if (<= a 2.45e-96) (+ t (* y (/ (- x t) z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * ((y - z) / a));
	double tmp;
	if (a <= -1.6e-8) {
		tmp = t_1;
	} else if (a <= -2.35e-30) {
		tmp = t - (x * (a / z));
	} else if (a <= -8.2e-208) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 2.45e-96) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((t - x) * ((y - z) / a))
    if (a <= (-1.6d-8)) then
        tmp = t_1
    else if (a <= (-2.35d-30)) then
        tmp = t - (x * (a / z))
    else if (a <= (-8.2d-208)) then
        tmp = (t - x) * (y / (a - z))
    else if (a <= 2.45d-96) then
        tmp = t + (y * ((x - t) / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * ((y - z) / a));
	double tmp;
	if (a <= -1.6e-8) {
		tmp = t_1;
	} else if (a <= -2.35e-30) {
		tmp = t - (x * (a / z));
	} else if (a <= -8.2e-208) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 2.45e-96) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * ((y - z) / a))
	tmp = 0
	if a <= -1.6e-8:
		tmp = t_1
	elif a <= -2.35e-30:
		tmp = t - (x * (a / z))
	elif a <= -8.2e-208:
		tmp = (t - x) * (y / (a - z))
	elif a <= 2.45e-96:
		tmp = t + (y * ((x - t) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)))
	tmp = 0.0
	if (a <= -1.6e-8)
		tmp = t_1;
	elseif (a <= -2.35e-30)
		tmp = Float64(t - Float64(x * Float64(a / z)));
	elseif (a <= -8.2e-208)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (a <= 2.45e-96)
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * ((y - z) / a));
	tmp = 0.0;
	if (a <= -1.6e-8)
		tmp = t_1;
	elseif (a <= -2.35e-30)
		tmp = t - (x * (a / z));
	elseif (a <= -8.2e-208)
		tmp = (t - x) * (y / (a - z));
	elseif (a <= 2.45e-96)
		tmp = t + (y * ((x - t) / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.6e-8], t$95$1, If[LessEqual[a, -2.35e-30], N[(t - N[(x * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.2e-208], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.45e-96], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.6000000000000001e-8 or 2.45000000000000008e-96 < a

   1. Initial program 70.7%

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

      1. associate-/l* 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in a around inf 61.9%

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

      1. associate-/l* 73.7%

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

   7. Simplified 73.7%

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

   if -1.6000000000000001e-8 < a < -2.34999999999999985e-30

   1. Initial program 77.8%

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

      1. associate-/l* 64.4%

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

   3. Simplified 64.4%

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

   5. Taylor expanded in z around -inf 82.8%

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

   6. Taylor expanded in y around 0 97.1%

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

      1. associate-*r/ 97.1%

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

   8. Simplified 97.1%

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

   9. Taylor expanded in t around 0 97.1%

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

       1. associate-*l/ 97.1%

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

       2. associate-*l* 97.1%

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

       3. *-commutative 97.1%

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

       4. mul-1-neg 97.1%

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

       5. distribute-frac-neg2 97.1%

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

   11. Simplified 97.1%

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

   if -2.34999999999999985e-30 < a < -8.1999999999999998e-208

   1. Initial program 76.9%

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

      1. associate-/l* 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in y around -inf 74.5%

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

      1. *-commutative 74.5%

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

      2. associate-/l* 77.0%

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

   7. Applied egg-rr 77.0%

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

   if -8.1999999999999998e-208 < a < 2.45000000000000008e-96

   1. Initial program 65.9%

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

      1. associate-/l* 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in z around -inf 85.2%

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

   6. Taylor expanded in a around 0 82.4%

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

      1. mul-1-neg 82.4%

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

      2. associate-*r/ 85.1%

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

      3. sub-neg 85.1%

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

   8. Simplified 85.1%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-8}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{-30}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-208}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-96}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 57.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -380000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-203}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= a -380000.0)
     (+ x (/ (* y t) a))
     (if (<= a -2e-142)
       t_1
       (if (<= a -9e-203)
         (/ (* y (- x t)) z)
         (if (<= a 3.9e+146) t_1 (- x (* x (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -380000.0) {
		tmp = x + ((y * t) / a);
	} else if (a <= -2e-142) {
		tmp = t_1;
	} else if (a <= -9e-203) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 3.9e+146) {
		tmp = t_1;
	} else {
		tmp = x - (x * (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) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (a <= (-380000.0d0)) then
        tmp = x + ((y * t) / a)
    else if (a <= (-2d-142)) then
        tmp = t_1
    else if (a <= (-9d-203)) then
        tmp = (y * (x - t)) / z
    else if (a <= 3.9d+146) then
        tmp = t_1
    else
        tmp = x - (x * (y / 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 * ((y - z) / (a - z));
	double tmp;
	if (a <= -380000.0) {
		tmp = x + ((y * t) / a);
	} else if (a <= -2e-142) {
		tmp = t_1;
	} else if (a <= -9e-203) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 3.9e+146) {
		tmp = t_1;
	} else {
		tmp = x - (x * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if a <= -380000.0:
		tmp = x + ((y * t) / a)
	elif a <= -2e-142:
		tmp = t_1
	elif a <= -9e-203:
		tmp = (y * (x - t)) / z
	elif a <= 3.9e+146:
		tmp = t_1
	else:
		tmp = x - (x * (y / a))
	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 (a <= -380000.0)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= -2e-142)
		tmp = t_1;
	elseif (a <= -9e-203)
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	elseif (a <= 3.9e+146)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(x * Float64(y / a)));
	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 (a <= -380000.0)
		tmp = x + ((y * t) / a);
	elseif (a <= -2e-142)
		tmp = t_1;
	elseif (a <= -9e-203)
		tmp = (y * (x - t)) / z;
	elseif (a <= 3.9e+146)
		tmp = t_1;
	else
		tmp = x - (x * (y / a));
	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[a, -380000.0], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2e-142], t$95$1, If[LessEqual[a, -9e-203], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 3.9e+146], t$95$1, N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.8e5

   1. Initial program 76.2%

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

      1. associate-/l* 86.9%

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

   3. Simplified 86.9%

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

      1. *-commutative 86.9%

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

      2. associate-*l/ 76.2%

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

      3. associate-*r/ 92.9%

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

      4. clear-num 92.9%

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

      5. un-div-inv 92.9%

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

   6. Applied egg-rr 92.9%

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

   7. Taylor expanded in z around 0 77.8%

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

   8. Taylor expanded in t around inf 63.2%

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

   if -3.8e5 < a < -2.0000000000000001e-142 or -9.0000000000000003e-203 < a < 3.9e146

   1. Initial program 68.6%

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

      1. associate-/l* 78.6%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in x around 0 53.9%

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

      1. associate-/l* 66.7%

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

   7. Simplified 66.7%

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

   if -2.0000000000000001e-142 < a < -9.0000000000000003e-203

   1. Initial program 99.3%

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

      1. associate-/l* 84.9%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in y around -inf 91.9%

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

   6. Taylor expanded in a around 0 75.6%

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

      1. associate-*r/ 75.6%

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

      2. associate-*r* 75.6%

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

      3. neg-mul-1 75.6%

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

      4. *-commutative 75.6%

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

   8. Simplified 75.6%

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

   if 3.9e146 < a

   1. Initial program 56.3%

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

      1. associate-/l* 88.6%

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

   3. Simplified 88.6%

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

      1. *-commutative 88.6%

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

      2. associate-*l/ 56.3%

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

      3. associate-*r/ 88.7%

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

      4. clear-num 88.7%

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

      5. un-div-inv 88.9%

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

   6. Applied egg-rr 88.9%

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

   7. Taylor expanded in z around 0 69.9%

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

   8. Taylor expanded in t around 0 52.8%

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

      1. mul-1-neg 52.8%

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

      2. associate-*r/ 59.5%

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

      3. distribute-rgt-neg-in 59.5%

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

      4. distribute-frac-neg 59.5%

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

   10. Simplified 59.5%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -380000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-142}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-203}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+146}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 57.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -380000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-204}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= a -380000.0)
     (+ x (/ (* y t) a))
     (if (<= a -3.4e-75)
       t_1
       (if (<= a -3.2e-204)
         (* y (/ (- t x) (- a z)))
         (if (<= a 1.2e+144) t_1 (- x (* x (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -380000.0) {
		tmp = x + ((y * t) / a);
	} else if (a <= -3.4e-75) {
		tmp = t_1;
	} else if (a <= -3.2e-204) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.2e+144) {
		tmp = t_1;
	} else {
		tmp = x - (x * (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) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (a <= (-380000.0d0)) then
        tmp = x + ((y * t) / a)
    else if (a <= (-3.4d-75)) then
        tmp = t_1
    else if (a <= (-3.2d-204)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 1.2d+144) then
        tmp = t_1
    else
        tmp = x - (x * (y / 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 * ((y - z) / (a - z));
	double tmp;
	if (a <= -380000.0) {
		tmp = x + ((y * t) / a);
	} else if (a <= -3.4e-75) {
		tmp = t_1;
	} else if (a <= -3.2e-204) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.2e+144) {
		tmp = t_1;
	} else {
		tmp = x - (x * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if a <= -380000.0:
		tmp = x + ((y * t) / a)
	elif a <= -3.4e-75:
		tmp = t_1
	elif a <= -3.2e-204:
		tmp = y * ((t - x) / (a - z))
	elif a <= 1.2e+144:
		tmp = t_1
	else:
		tmp = x - (x * (y / a))
	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 (a <= -380000.0)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= -3.4e-75)
		tmp = t_1;
	elseif (a <= -3.2e-204)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 1.2e+144)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(x * Float64(y / a)));
	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 (a <= -380000.0)
		tmp = x + ((y * t) / a);
	elseif (a <= -3.4e-75)
		tmp = t_1;
	elseif (a <= -3.2e-204)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 1.2e+144)
		tmp = t_1;
	else
		tmp = x - (x * (y / a));
	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[a, -380000.0], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.4e-75], t$95$1, If[LessEqual[a, -3.2e-204], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e+144], t$95$1, N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.8e5

   1. Initial program 76.2%

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

      1. associate-/l* 86.9%

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

   3. Simplified 86.9%

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

      1. *-commutative 86.9%

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

      2. associate-*l/ 76.2%

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

      3. associate-*r/ 92.9%

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

      4. clear-num 92.9%

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

      5. un-div-inv 92.9%

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

   6. Applied egg-rr 92.9%

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

   7. Taylor expanded in z around 0 77.8%

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

   8. Taylor expanded in t around inf 63.2%

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

   if -3.8e5 < a < -3.40000000000000015e-75 or -3.2e-204 < a < 1.2e144

   1. Initial program 68.9%

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

      1. associate-/l* 79.2%

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

   3. Simplified 79.2%

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

   5. Taylor expanded in x around 0 54.1%

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

      1. associate-/l* 66.9%

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

   7. Simplified 66.9%

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

   if -3.40000000000000015e-75 < a < -3.2e-204

   1. Initial program 81.0%

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

      1. associate-/l* 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in y around inf 70.3%

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

      1. div-sub 74.4%

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

   7. Simplified 74.4%

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

   if 1.2e144 < a

   1. Initial program 56.3%

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

      1. associate-/l* 88.6%

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

   3. Simplified 88.6%

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

      1. *-commutative 88.6%

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

      2. associate-*l/ 56.3%

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

      3. associate-*r/ 88.7%

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

      4. clear-num 88.7%

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

      5. un-div-inv 88.9%

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

   6. Applied egg-rr 88.9%

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

   7. Taylor expanded in z around 0 69.9%

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

   8. Taylor expanded in t around 0 52.8%

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

      1. mul-1-neg 52.8%

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

      2. associate-*r/ 59.5%

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

      3. distribute-rgt-neg-in 59.5%

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

      4. distribute-frac-neg 59.5%

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

   10. Simplified 59.5%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -380000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-75}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-204}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+144}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 57.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -380000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-204}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= a -380000.0)
     (+ x (/ (* y t) a))
     (if (<= a -1.08e-75)
       t_1
       (if (<= a -3.4e-204)
         (* (- t x) (/ y (- a z)))
         (if (<= a 1.22e+147) t_1 (- x (* x (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -380000.0) {
		tmp = x + ((y * t) / a);
	} else if (a <= -1.08e-75) {
		tmp = t_1;
	} else if (a <= -3.4e-204) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 1.22e+147) {
		tmp = t_1;
	} else {
		tmp = x - (x * (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) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (a <= (-380000.0d0)) then
        tmp = x + ((y * t) / a)
    else if (a <= (-1.08d-75)) then
        tmp = t_1
    else if (a <= (-3.4d-204)) then
        tmp = (t - x) * (y / (a - z))
    else if (a <= 1.22d+147) then
        tmp = t_1
    else
        tmp = x - (x * (y / 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 * ((y - z) / (a - z));
	double tmp;
	if (a <= -380000.0) {
		tmp = x + ((y * t) / a);
	} else if (a <= -1.08e-75) {
		tmp = t_1;
	} else if (a <= -3.4e-204) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 1.22e+147) {
		tmp = t_1;
	} else {
		tmp = x - (x * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if a <= -380000.0:
		tmp = x + ((y * t) / a)
	elif a <= -1.08e-75:
		tmp = t_1
	elif a <= -3.4e-204:
		tmp = (t - x) * (y / (a - z))
	elif a <= 1.22e+147:
		tmp = t_1
	else:
		tmp = x - (x * (y / a))
	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 (a <= -380000.0)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= -1.08e-75)
		tmp = t_1;
	elseif (a <= -3.4e-204)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (a <= 1.22e+147)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(x * Float64(y / a)));
	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 (a <= -380000.0)
		tmp = x + ((y * t) / a);
	elseif (a <= -1.08e-75)
		tmp = t_1;
	elseif (a <= -3.4e-204)
		tmp = (t - x) * (y / (a - z));
	elseif (a <= 1.22e+147)
		tmp = t_1;
	else
		tmp = x - (x * (y / a));
	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[a, -380000.0], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.08e-75], t$95$1, If[LessEqual[a, -3.4e-204], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.22e+147], t$95$1, N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.8e5

   1. Initial program 76.2%

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

      1. associate-/l* 86.9%

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

   3. Simplified 86.9%

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

      1. *-commutative 86.9%

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

      2. associate-*l/ 76.2%

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

      3. associate-*r/ 92.9%

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

      4. clear-num 92.9%

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

      5. un-div-inv 92.9%

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

   6. Applied egg-rr 92.9%

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

   7. Taylor expanded in z around 0 77.8%

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

   8. Taylor expanded in t around inf 63.2%

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

   if -3.8e5 < a < -1.08e-75 or -3.4000000000000002e-204 < a < 1.21999999999999996e147

   1. Initial program 68.9%

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

      1. associate-/l* 79.2%

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

   3. Simplified 79.2%

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

   5. Taylor expanded in x around 0 54.1%

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

      1. associate-/l* 66.9%

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

   7. Simplified 66.9%

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

   if -1.08e-75 < a < -3.4000000000000002e-204

   1. Initial program 81.0%

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

      1. associate-/l* 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in y around -inf 81.6%

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

      1. *-commutative 81.6%

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

      2. associate-/l* 81.4%

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

   7. Applied egg-rr 81.4%

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

   if 1.21999999999999996e147 < a

   1. Initial program 56.3%

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

      1. associate-/l* 88.6%

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

   3. Simplified 88.6%

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

      1. *-commutative 88.6%

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

      2. associate-*l/ 56.3%

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

      3. associate-*r/ 88.7%

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

      4. clear-num 88.7%

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

      5. un-div-inv 88.9%

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

   6. Applied egg-rr 88.9%

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

   7. Taylor expanded in z around 0 69.9%

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

   8. Taylor expanded in t around 0 52.8%

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

      1. mul-1-neg 52.8%

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

      2. associate-*r/ 59.5%

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

      3. distribute-rgt-neg-in 59.5%

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

      4. distribute-frac-neg 59.5%

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

   10. Simplified 59.5%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -380000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{-75}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-204}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{+147}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 63.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x - y \cdot \frac{x - t}{a}\\ \mathbf{if}\;a \leq -43000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-203}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (- x (* y (/ (- x t) a)))))
   (if (<= a -43000.0)
     t_2
     (if (<= a -3.6e-75)
       t_1
       (if (<= a -2.1e-203)
         (* (- t x) (/ y (- a z)))
         (if (<= a 9e+16) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - (y * ((x - t) / a));
	double tmp;
	if (a <= -43000.0) {
		tmp = t_2;
	} else if (a <= -3.6e-75) {
		tmp = t_1;
	} else if (a <= -2.1e-203) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 9e+16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x - (y * ((x - t) / a))
    if (a <= (-43000.0d0)) then
        tmp = t_2
    else if (a <= (-3.6d-75)) then
        tmp = t_1
    else if (a <= (-2.1d-203)) then
        tmp = (t - x) * (y / (a - z))
    else if (a <= 9d+16) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - (y * ((x - t) / a));
	double tmp;
	if (a <= -43000.0) {
		tmp = t_2;
	} else if (a <= -3.6e-75) {
		tmp = t_1;
	} else if (a <= -2.1e-203) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 9e+16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x - (y * ((x - t) / a))
	tmp = 0
	if a <= -43000.0:
		tmp = t_2
	elif a <= -3.6e-75:
		tmp = t_1
	elif a <= -2.1e-203:
		tmp = (t - x) * (y / (a - z))
	elif a <= 9e+16:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x - Float64(y * Float64(Float64(x - t) / a)))
	tmp = 0.0
	if (a <= -43000.0)
		tmp = t_2;
	elseif (a <= -3.6e-75)
		tmp = t_1;
	elseif (a <= -2.1e-203)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (a <= 9e+16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x - (y * ((x - t) / a));
	tmp = 0.0;
	if (a <= -43000.0)
		tmp = t_2;
	elseif (a <= -3.6e-75)
		tmp = t_1;
	elseif (a <= -2.1e-203)
		tmp = (t - x) * (y / (a - z));
	elseif (a <= 9e+16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -43000.0], t$95$2, If[LessEqual[a, -3.6e-75], t$95$1, If[LessEqual[a, -2.1e-203], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+16], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -43000 or 9e16 < a

   1. Initial program 68.1%

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

      1. associate-/l* 87.1%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in z around 0 61.1%

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

      1. associate-/l* 71.4%

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

   7. Simplified 71.4%

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

   if -43000 < a < -3.6e-75 or -2.10000000000000002e-203 < a < 9e16

   1. Initial program 70.5%

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

      1. associate-/l* 77.5%

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

   3. Simplified 77.5%

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

   5. Taylor expanded in x around 0 58.6%

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

      1. associate-/l* 69.9%

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

   7. Simplified 69.9%

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

   if -3.6e-75 < a < -2.10000000000000002e-203

   1. Initial program 81.0%

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

      1. associate-/l* 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in y around -inf 81.6%

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

      1. *-commutative 81.6%

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

      2. associate-/l* 81.4%

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

   7. Applied egg-rr 81.4%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -43000:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-75}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-203}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 63.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -44000:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-203}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= a -44000.0)
     (+ x (* (- t x) (/ y a)))
     (if (<= a -5e-74)
       t_1
       (if (<= a -7.5e-203)
         (* (- t x) (/ y (- a z)))
         (if (<= a 1.4e+18) t_1 (- x (* y (/ (- x t) a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -44000.0) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= -5e-74) {
		tmp = t_1;
	} else if (a <= -7.5e-203) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 1.4e+18) {
		tmp = t_1;
	} else {
		tmp = x - (y * ((x - 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) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (a <= (-44000.0d0)) then
        tmp = x + ((t - x) * (y / a))
    else if (a <= (-5d-74)) then
        tmp = t_1
    else if (a <= (-7.5d-203)) then
        tmp = (t - x) * (y / (a - z))
    else if (a <= 1.4d+18) then
        tmp = t_1
    else
        tmp = x - (y * ((x - 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 * ((y - z) / (a - z));
	double tmp;
	if (a <= -44000.0) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= -5e-74) {
		tmp = t_1;
	} else if (a <= -7.5e-203) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 1.4e+18) {
		tmp = t_1;
	} else {
		tmp = x - (y * ((x - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if a <= -44000.0:
		tmp = x + ((t - x) * (y / a))
	elif a <= -5e-74:
		tmp = t_1
	elif a <= -7.5e-203:
		tmp = (t - x) * (y / (a - z))
	elif a <= 1.4e+18:
		tmp = t_1
	else:
		tmp = x - (y * ((x - t) / a))
	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 (a <= -44000.0)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (a <= -5e-74)
		tmp = t_1;
	elseif (a <= -7.5e-203)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (a <= 1.4e+18)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(y * Float64(Float64(x - t) / a)));
	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 (a <= -44000.0)
		tmp = x + ((t - x) * (y / a));
	elseif (a <= -5e-74)
		tmp = t_1;
	elseif (a <= -7.5e-203)
		tmp = (t - x) * (y / (a - z));
	elseif (a <= 1.4e+18)
		tmp = t_1;
	else
		tmp = x - (y * ((x - t) / a));
	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[a, -44000.0], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5e-74], t$95$1, If[LessEqual[a, -7.5e-203], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e+18], t$95$1, N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -44000

   1. Initial program 76.2%

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

      1. associate-/l* 86.9%

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

   3. Simplified 86.9%

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

      1. *-commutative 86.9%

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

      2. associate-*l/ 76.2%

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

      3. associate-*r/ 92.9%

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

      4. clear-num 92.9%

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

      5. un-div-inv 92.9%

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

   6. Applied egg-rr 92.9%

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

   7. Taylor expanded in z around 0 77.8%

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

   8. Taylor expanded in t around 0 68.6%

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

      1. associate-*r/ 73.3%

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

      2. mul-1-neg 73.3%

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

      3. associate-*r/ 77.7%

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

      4. +-commutative 77.7%

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

      5. sub-neg 77.7%

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

      6. distribute-rgt-out-- 77.7%

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

   10. Simplified 77.7%

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

   if -44000 < a < -4.99999999999999998e-74 or -7.50000000000000027e-203 < a < 1.4e18

   1. Initial program 70.5%

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

      1. associate-/l* 77.5%

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

   3. Simplified 77.5%

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

   5. Taylor expanded in x around 0 58.6%

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

      1. associate-/l* 69.9%

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

   7. Simplified 69.9%

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

   if -4.99999999999999998e-74 < a < -7.50000000000000027e-203

   1. Initial program 81.0%

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

      1. associate-/l* 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in y around -inf 81.6%

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

      1. *-commutative 81.6%

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

      2. associate-/l* 81.4%

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

   7. Applied egg-rr 81.4%

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

   if 1.4e18 < a

   1. Initial program 59.4%

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

      1. associate-/l* 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in z around 0 52.9%

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

      1. associate-/l* 67.6%

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

   7. Simplified 67.6%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -44000:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-74}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-203}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 63.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -140000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -9.4 \cdot 10^{-203}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (/ (- t x) (/ a y)))))
   (if (<= a -140000.0)
     t_2
     (if (<= a -8.2e-74)
       t_1
       (if (<= a -9.4e-203)
         (* (- t x) (/ y (- a z)))
         (if (<= a 4.2e+19) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + ((t - x) / (a / y));
	double tmp;
	if (a <= -140000.0) {
		tmp = t_2;
	} else if (a <= -8.2e-74) {
		tmp = t_1;
	} else if (a <= -9.4e-203) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 4.2e+19) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + ((t - x) / (a / y))
    if (a <= (-140000.0d0)) then
        tmp = t_2
    else if (a <= (-8.2d-74)) then
        tmp = t_1
    else if (a <= (-9.4d-203)) then
        tmp = (t - x) * (y / (a - z))
    else if (a <= 4.2d+19) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + ((t - x) / (a / y));
	double tmp;
	if (a <= -140000.0) {
		tmp = t_2;
	} else if (a <= -8.2e-74) {
		tmp = t_1;
	} else if (a <= -9.4e-203) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 4.2e+19) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + ((t - x) / (a / y))
	tmp = 0
	if a <= -140000.0:
		tmp = t_2
	elif a <= -8.2e-74:
		tmp = t_1
	elif a <= -9.4e-203:
		tmp = (t - x) * (y / (a - z))
	elif a <= 4.2e+19:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(Float64(t - x) / Float64(a / y)))
	tmp = 0.0
	if (a <= -140000.0)
		tmp = t_2;
	elseif (a <= -8.2e-74)
		tmp = t_1;
	elseif (a <= -9.4e-203)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (a <= 4.2e+19)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + ((t - x) / (a / y));
	tmp = 0.0;
	if (a <= -140000.0)
		tmp = t_2;
	elseif (a <= -8.2e-74)
		tmp = t_1;
	elseif (a <= -9.4e-203)
		tmp = (t - x) * (y / (a - z));
	elseif (a <= 4.2e+19)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -140000.0], t$95$2, If[LessEqual[a, -8.2e-74], t$95$1, If[LessEqual[a, -9.4e-203], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e+19], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.4e5 or 4.2e19 < a

   1. Initial program 68.1%

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

      1. associate-/l* 87.1%

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

   3. Simplified 87.1%

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

      1. *-commutative 87.1%

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

      2. associate-*l/ 68.1%

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

      3. associate-*r/ 90.3%

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

      4. clear-num 90.3%

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

      5. un-div-inv 90.3%

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

   6. Applied egg-rr 90.3%

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

   7. Taylor expanded in z around 0 72.9%

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

   if -1.4e5 < a < -8.20000000000000063e-74 or -9.40000000000000012e-203 < a < 4.2e19

   1. Initial program 70.5%

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

      1. associate-/l* 77.5%

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

   3. Simplified 77.5%

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

   5. Taylor expanded in x around 0 58.6%

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

      1. associate-/l* 69.9%

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

   7. Simplified 69.9%

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

   if -8.20000000000000063e-74 < a < -9.40000000000000012e-203

   1. Initial program 81.0%

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

      1. associate-/l* 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in y around -inf 81.6%

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

      1. *-commutative 81.6%

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

      2. associate-/l* 81.4%

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

   7. Applied egg-rr 81.4%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -140000:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-74}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -9.4 \cdot 10^{-203}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 51.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;a \leq -55000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{-31}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-208}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 3000000000000:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))))
   (if (<= a -55000.0)
     t_1
     (if (<= a -2.25e-31)
       (* t (/ z (- z a)))
       (if (<= a -8.2e-208)
         (* x (/ y (- z a)))
         (if (<= a 3000000000000.0) (* t (- 1.0 (/ y z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (a <= -55000.0) {
		tmp = t_1;
	} else if (a <= -2.25e-31) {
		tmp = t * (z / (z - a));
	} else if (a <= -8.2e-208) {
		tmp = x * (y / (z - a));
	} else if (a <= 3000000000000.0) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    if (a <= (-55000.0d0)) then
        tmp = t_1
    else if (a <= (-2.25d-31)) then
        tmp = t * (z / (z - a))
    else if (a <= (-8.2d-208)) then
        tmp = x * (y / (z - a))
    else if (a <= 3000000000000.0d0) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (a <= -55000.0) {
		tmp = t_1;
	} else if (a <= -2.25e-31) {
		tmp = t * (z / (z - a));
	} else if (a <= -8.2e-208) {
		tmp = x * (y / (z - a));
	} else if (a <= 3000000000000.0) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	tmp = 0
	if a <= -55000.0:
		tmp = t_1
	elif a <= -2.25e-31:
		tmp = t * (z / (z - a))
	elif a <= -8.2e-208:
		tmp = x * (y / (z - a))
	elif a <= 3000000000000.0:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (a <= -55000.0)
		tmp = t_1;
	elseif (a <= -2.25e-31)
		tmp = Float64(t * Float64(z / Float64(z - a)));
	elseif (a <= -8.2e-208)
		tmp = Float64(x * Float64(y / Float64(z - a)));
	elseif (a <= 3000000000000.0)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	tmp = 0.0;
	if (a <= -55000.0)
		tmp = t_1;
	elseif (a <= -2.25e-31)
		tmp = t * (z / (z - a));
	elseif (a <= -8.2e-208)
		tmp = x * (y / (z - a));
	elseif (a <= 3000000000000.0)
		tmp = t * (1.0 - (y / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -55000.0], t$95$1, If[LessEqual[a, -2.25e-31], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.2e-208], N[(x * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3000000000000.0], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -55000 or 3e12 < a

   1. Initial program 68.3%

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

      1. associate-/l* 87.2%

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

   3. Simplified 87.2%

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

      1. *-commutative 87.2%

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

      2. associate-*l/ 68.3%

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

      3. associate-*r/ 90.4%

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

      4. clear-num 90.4%

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

      5. un-div-inv 90.4%

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

   6. Applied egg-rr 90.4%

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

   7. Taylor expanded in z around 0 72.4%

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

   8. Taylor expanded in t around inf 55.1%

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

   if -55000 < a < -2.2500000000000002e-31

   1. Initial program 84.3%

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

      1. associate-/l* 75.1%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in x around 0 80.5%

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

   6. Taylor expanded in y around 0 71.4%

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

      1. associate-*r/ 71.4%

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

      2. associate-*r* 71.4%

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

      3. mul-1-neg 71.4%

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

   8. Simplified 71.4%

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

      1. associate-/l* 71.6%

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

      2. distribute-lft-neg-out 71.6%

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

   10. Applied egg-rr 71.6%

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

   if -2.2500000000000002e-31 < a < -8.1999999999999998e-208

   1. Initial program 76.9%

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

      1. associate-/l* 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in y around -inf 74.5%

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

   6. Taylor expanded in t around 0 51.7%

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

      1. mul-1-neg 51.7%

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

      2. associate-/l* 51.6%

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

      3. distribute-rgt-neg-in 51.6%

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

      4. distribute-frac-neg2 51.6%

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

      5. sub-neg 51.6%

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

      6. distribute-neg-in 51.6%

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

      7. remove-double-neg 51.6%

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

   8. Simplified 51.6%

      \[\leadsto \color{blue}{x \cdot \frac{y}{\left(-a\right) + z}} \]

   if -8.1999999999999998e-208 < a < 3e12

   1. Initial program 69.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 77.7%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 77.7%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 56.3%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]

   6. Taylor expanded in a around 0 46.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot \left(y - z\right)}{z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 46.9%

         \[\leadsto \color{blue}{-\frac{t \cdot \left(y - z\right)}{z}} \]

      2. associate-/l* 60.6%

         \[\leadsto -\color{blue}{t \cdot \frac{y - z}{z}} \]

      3. div-sub 60.6%

         \[\leadsto -t \cdot \color{blue}{\left(\frac{y}{z} - \frac{z}{z}\right)} \]

      4. *-inverses 60.6%

         \[\leadsto -t \cdot \left(\frac{y}{z} - \color{blue}{1}\right) \]

   8. Simplified 60.6%

      \[\leadsto \color{blue}{-t \cdot \left(\frac{y}{z} - 1\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -55000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{-31}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-208}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 3000000000000:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 83.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+176}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+225}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.2e+176)
   (+ t (* a (/ (- t x) z)))
   (if (<= z 5.8e+225)
     (- x (* (- y z) (/ (- x t) (- a z))))
     (- t (* x (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e+176) {
		tmp = t + (a * ((t - x) / z));
	} else if (z <= 5.8e+225) {
		tmp = x - ((y - z) * ((x - t) / (a - z)));
	} else {
		tmp = t - (x * (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.2d+176)) then
        tmp = t + (a * ((t - x) / z))
    else if (z <= 5.8d+225) then
        tmp = x - ((y - z) * ((x - t) / (a - z)))
    else
        tmp = t - (x * (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e+176) {
		tmp = t + (a * ((t - x) / z));
	} else if (z <= 5.8e+225) {
		tmp = x - ((y - z) * ((x - t) / (a - z)));
	} else {
		tmp = t - (x * (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.2e+176:
		tmp = t + (a * ((t - x) / z))
	elif z <= 5.8e+225:
		tmp = x - ((y - z) * ((x - t) / (a - z)))
	else:
		tmp = t - (x * (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.2e+176)
		tmp = Float64(t + Float64(a * Float64(Float64(t - x) / z)));
	elseif (z <= 5.8e+225)
		tmp = Float64(x - Float64(Float64(y - z) * Float64(Float64(x - t) / Float64(a - z))));
	else
		tmp = Float64(t - Float64(x * Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.2e+176)
		tmp = t + (a * ((t - x) / z));
	elseif (z <= 5.8e+225)
		tmp = x - ((y - z) * ((x - t) / (a - z)));
	else
		tmp = t - (x * (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.2e+176], N[(t + N[(a * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+225], N[(x - N[(N[(y - z), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(x * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.20000000000000007e176

   1. Initial program 28.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 42.9%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 42.9%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around -inf 54.1%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

   6. Taylor expanded in y around 0 49.2%

      \[\leadsto \color{blue}{t + \frac{a \cdot \left(t - x\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 78.8%

         \[\leadsto t + \color{blue}{a \cdot \frac{t - x}{z}} \]

   8. Simplified 78.8%

      \[\leadsto \color{blue}{t + a \cdot \frac{t - x}{z}} \]

   if -2.20000000000000007e176 < z < 5.8000000000000003e225

   1. Initial program 78.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 88.3%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 88.3%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   if 5.8000000000000003e225 < z

   1. Initial program 13.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 59.8%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 59.8%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around -inf 68.3%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

   6. Taylor expanded in y around 0 76.1%

      \[\leadsto \color{blue}{t + \frac{a \cdot \left(t - x\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 92.0%

         \[\leadsto t + \color{blue}{a \cdot \frac{t - x}{z}} \]

   8. Simplified 92.0%

      \[\leadsto \color{blue}{t + a \cdot \frac{t - x}{z}} \]

   9. Taylor expanded in t around 0 76.1%

      \[\leadsto t + \color{blue}{-1 \cdot \frac{a \cdot x}{z}} \]
   10. Step-by-step derivation

       1. associate-*l/ 99.9%

          \[\leadsto t + -1 \cdot \color{blue}{\left(\frac{a}{z} \cdot x\right)} \]

       2. associate-*l* 99.9%

          \[\leadsto t + \color{blue}{\left(-1 \cdot \frac{a}{z}\right) \cdot x} \]

       3. *-commutative 99.9%

          \[\leadsto t + \color{blue}{x \cdot \left(-1 \cdot \frac{a}{z}\right)} \]

       4. mul-1-neg 99.9%

          \[\leadsto t + x \cdot \color{blue}{\left(-\frac{a}{z}\right)} \]

       5. distribute-frac-neg2 99.9%

          \[\leadsto t + x \cdot \color{blue}{\frac{a}{-z}} \]

   11. Simplified 99.9%

       \[\leadsto t + \color{blue}{x \cdot \frac{a}{-z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+176}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+225}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 52.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - x \cdot \frac{a}{z}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-91}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* x (/ a z)))))
   (if (<= z -3.4e+24)
     t_1
     (if (<= z -1.12e-91)
       (* x (/ y (- z a)))
       (if (<= z 3e+22) (+ x (/ (* y t) a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (x * (a / z));
	double tmp;
	if (z <= -3.4e+24) {
		tmp = t_1;
	} else if (z <= -1.12e-91) {
		tmp = x * (y / (z - a));
	} else if (z <= 3e+22) {
		tmp = x + ((y * t) / 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 - (x * (a / z))
    if (z <= (-3.4d+24)) then
        tmp = t_1
    else if (z <= (-1.12d-91)) then
        tmp = x * (y / (z - a))
    else if (z <= 3d+22) then
        tmp = x + ((y * t) / 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 - (x * (a / z));
	double tmp;
	if (z <= -3.4e+24) {
		tmp = t_1;
	} else if (z <= -1.12e-91) {
		tmp = x * (y / (z - a));
	} else if (z <= 3e+22) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (x * (a / z))
	tmp = 0
	if z <= -3.4e+24:
		tmp = t_1
	elif z <= -1.12e-91:
		tmp = x * (y / (z - a))
	elif z <= 3e+22:
		tmp = x + ((y * t) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(x * Float64(a / z)))
	tmp = 0.0
	if (z <= -3.4e+24)
		tmp = t_1;
	elseif (z <= -1.12e-91)
		tmp = Float64(x * Float64(y / Float64(z - a)));
	elseif (z <= 3e+22)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (x * (a / z));
	tmp = 0.0;
	if (z <= -3.4e+24)
		tmp = t_1;
	elseif (z <= -1.12e-91)
		tmp = x * (y / (z - a));
	elseif (z <= 3e+22)
		tmp = x + ((y * t) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(x * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+24], t$95$1, If[LessEqual[z, -1.12e-91], N[(x * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+22], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4000000000000001e24 or 3e22 < z

   1. Initial program 47.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 68.9%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 68.9%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around -inf 61.1%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

   6. Taylor expanded in y around 0 50.0%

      \[\leadsto \color{blue}{t + \frac{a \cdot \left(t - x\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 60.1%

         \[\leadsto t + \color{blue}{a \cdot \frac{t - x}{z}} \]

   8. Simplified 60.1%

      \[\leadsto \color{blue}{t + a \cdot \frac{t - x}{z}} \]

   9. Taylor expanded in t around 0 54.1%

      \[\leadsto t + \color{blue}{-1 \cdot \frac{a \cdot x}{z}} \]
   10. Step-by-step derivation

       1. associate-*l/ 60.8%

          \[\leadsto t + -1 \cdot \color{blue}{\left(\frac{a}{z} \cdot x\right)} \]

       2. associate-*l* 60.8%

          \[\leadsto t + \color{blue}{\left(-1 \cdot \frac{a}{z}\right) \cdot x} \]

       3. *-commutative 60.8%

          \[\leadsto t + \color{blue}{x \cdot \left(-1 \cdot \frac{a}{z}\right)} \]

       4. mul-1-neg 60.8%

          \[\leadsto t + x \cdot \color{blue}{\left(-\frac{a}{z}\right)} \]

       5. distribute-frac-neg2 60.8%

          \[\leadsto t + x \cdot \color{blue}{\frac{a}{-z}} \]

   11. Simplified 60.8%

       \[\leadsto t + \color{blue}{x \cdot \frac{a}{-z}} \]

   if -3.4000000000000001e24 < z < -1.12e-91

   1. Initial program 74.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 83.3%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 83.3%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around -inf 56.5%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]

   6. Taylor expanded in t around 0 44.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{a - z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 44.3%

         \[\leadsto \color{blue}{-\frac{x \cdot y}{a - z}} \]

      2. associate-/l* 48.5%

         \[\leadsto -\color{blue}{x \cdot \frac{y}{a - z}} \]

      3. distribute-rgt-neg-in 48.5%

         \[\leadsto \color{blue}{x \cdot \left(-\frac{y}{a - z}\right)} \]

      4. distribute-frac-neg2 48.5%

         \[\leadsto x \cdot \color{blue}{\frac{y}{-\left(a - z\right)}} \]

      5. sub-neg 48.5%

         \[\leadsto x \cdot \frac{y}{-\color{blue}{\left(a + \left(-z\right)\right)}} \]

      6. distribute-neg-in 48.5%

         \[\leadsto x \cdot \frac{y}{\color{blue}{\left(-a\right) + \left(-\left(-z\right)\right)}} \]

      7. remove-double-neg 48.5%

         \[\leadsto x \cdot \frac{y}{\left(-a\right) + \color{blue}{z}} \]

   8. Simplified 48.5%

      \[\leadsto \color{blue}{x \cdot \frac{y}{\left(-a\right) + z}} \]

   if -1.12e-91 < z < 3e22

   1. Initial program 91.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 94.5%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 94.5%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 94.5%

         \[\leadsto x + \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} \]

      2. associate-*l/ 91.3%

         \[\leadsto x + \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} \]

      3. associate-*r/ 96.7%

         \[\leadsto x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} \]

      4. clear-num 96.7%

         \[\leadsto x + \left(t - x\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{y - z}}} \]

      5. un-div-inv 96.8%

         \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   6. Applied egg-rr 96.8%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   7. Taylor expanded in z around 0 78.1%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{a}{y}}} \]

   8. Taylor expanded in t around inf 59.2%

      \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+24}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-91}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 36.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+54}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-257}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-38}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.2e+54)
   t
   (if (<= z -2.7e-257) x (if (<= z 2.05e-38) (* t (/ y a)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.2e+54) {
		tmp = t;
	} else if (z <= -2.7e-257) {
		tmp = x;
	} else if (z <= 2.05e-38) {
		tmp = t * (y / a);
	} 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 <= (-9.2d+54)) then
        tmp = t
    else if (z <= (-2.7d-257)) then
        tmp = x
    else if (z <= 2.05d-38) then
        tmp = t * (y / a)
    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 <= -9.2e+54) {
		tmp = t;
	} else if (z <= -2.7e-257) {
		tmp = x;
	} else if (z <= 2.05e-38) {
		tmp = t * (y / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.2e+54:
		tmp = t
	elif z <= -2.7e-257:
		tmp = x
	elif z <= 2.05e-38:
		tmp = t * (y / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.2e+54)
		tmp = t;
	elseif (z <= -2.7e-257)
		tmp = x;
	elseif (z <= 2.05e-38)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.2e+54)
		tmp = t;
	elseif (z <= -2.7e-257)
		tmp = x;
	elseif (z <= 2.05e-38)
		tmp = t * (y / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.2e+54], t, If[LessEqual[z, -2.7e-257], x, If[LessEqual[z, 2.05e-38], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.19999999999999977e54 or 2.0499999999999999e-38 < z

   1. Initial program 52.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 72.2%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 72.2%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 47.0%

      \[\leadsto \color{blue}{t} \]

   if -9.19999999999999977e54 < z < -2.6999999999999999e-257

   1. Initial program 88.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 90.6%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 90.6%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 33.0%

      \[\leadsto \color{blue}{x} \]

   if -2.6999999999999999e-257 < z < 2.0499999999999999e-38

   1. Initial program 85.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 92.5%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 92.5%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 46.7%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]

   6. Taylor expanded in z around 0 39.0%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 46.8%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   8. Simplified 46.8%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+54}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-257}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-38}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 36.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+54}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-257}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-38}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.8e+54)
   t
   (if (<= z -1.15e-257) x (if (<= z 6.6e-38) (/ t (/ a y)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e+54) {
		tmp = t;
	} else if (z <= -1.15e-257) {
		tmp = x;
	} else if (z <= 6.6e-38) {
		tmp = t / (a / y);
	} 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 <= (-6.8d+54)) then
        tmp = t
    else if (z <= (-1.15d-257)) then
        tmp = x
    else if (z <= 6.6d-38) then
        tmp = t / (a / y)
    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 <= -6.8e+54) {
		tmp = t;
	} else if (z <= -1.15e-257) {
		tmp = x;
	} else if (z <= 6.6e-38) {
		tmp = t / (a / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.8e+54:
		tmp = t
	elif z <= -1.15e-257:
		tmp = x
	elif z <= 6.6e-38:
		tmp = t / (a / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.8e+54)
		tmp = t;
	elseif (z <= -1.15e-257)
		tmp = x;
	elseif (z <= 6.6e-38)
		tmp = Float64(t / Float64(a / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.8e+54)
		tmp = t;
	elseif (z <= -1.15e-257)
		tmp = x;
	elseif (z <= 6.6e-38)
		tmp = t / (a / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.8e+54], t, If[LessEqual[z, -1.15e-257], x, If[LessEqual[z, 6.6e-38], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.8000000000000001e54 or 6.6000000000000005e-38 < z

   1. Initial program 52.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 72.2%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 72.2%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 47.0%

      \[\leadsto \color{blue}{t} \]

   if -6.8000000000000001e54 < z < -1.15e-257

   1. Initial program 88.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 90.6%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 90.6%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 33.0%

      \[\leadsto \color{blue}{x} \]

   if -1.15e-257 < z < 6.6000000000000005e-38

   1. Initial program 85.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 92.5%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 92.5%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 46.7%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]

   6. Taylor expanded in z around 0 39.0%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 46.8%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   8. Simplified 46.8%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]
   9. Step-by-step derivation

      1. clear-num 46.8%

         \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{a}{y}}} \]

      2. div-inv 46.9%

         \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

   10. Applied egg-rr 46.9%

       \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+54}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-257}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-38}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 37.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+55}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.4e+55) t (if (<= z 4.9e-39) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.4e+55) {
		tmp = t;
	} else if (z <= 4.9e-39) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.4d+55)) then
        tmp = t
    else if (z <= 4.9d-39) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.4e+55) {
		tmp = t;
	} else if (z <= 4.9e-39) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.4e+55:
		tmp = t
	elif z <= 4.9e-39:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.4e+55)
		tmp = t;
	elseif (z <= 4.9e-39)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.4e+55)
		tmp = t;
	elseif (z <= 4.9e-39)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.4e+55], t, If[LessEqual[z, 4.9e-39], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e55 or 4.89999999999999974e-39 < z

   1. Initial program 52.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 72.2%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 72.2%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 47.0%

      \[\leadsto \color{blue}{t} \]

   if -1.4e55 < z < 4.89999999999999974e-39

   1. Initial program 87.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 91.6%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 91.6%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 29.4%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+55}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 24.5% 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 70.4%

   \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
2. Step-by-step derivation

   1. associate-/l* 82.2%

      \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

3. Simplified 82.2%

   \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 25.5%

   \[\leadsto \color{blue}{t} \]

6. Final simplification 25.5%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 83.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024082 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :alt
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

  (+ x (/ (* (- y z) (- t x)) (- a z))))