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

Percentage Accurate: 67.5% → 90.5%

Time: 18.3s

Alternatives: 19

Speedup: 0.9×

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: 67.5% 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: 90.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-266} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -1e-266) (not (<= t_1 0.0)))
     (fma (/ (- y z) (- a z)) (- t x) x)
     (+ t (/ (- x t) (/ z (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-266) || !(t_1 <= 0.0)) {
		tmp = fma(((y - z) / (a - z)), (t - x), x);
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -1e-266) || !(t_1 <= 0.0))
		tmp = fma(Float64(Float64(y - z) / Float64(a - z)), Float64(t - x), x);
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-266], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -9.9999999999999998e-267 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 72.4%

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

      1. +-commutative 72.4%

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

      2. associate-*l/ 90.0%

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

      3. fma-def 90.0%

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

   3. Simplified 90.0%

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

   if -9.9999999999999998e-267 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.3%

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

      1. associate-*l/ 4.3%

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

   3. Simplified 4.3%

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

   4. Taylor expanded in z around -inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. distribute-rgt-out-- 99.8%

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

      3. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{-266} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 2: 90.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-266} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -1e-266) (not (<= t_1 0.0)))
     (+ x (* (- t x) (/ (- y z) (- a z))))
     (+ t (/ (- x t) (/ z (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-266) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + ((x - t) / (z / (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 = x + (((y - z) * (t - x)) / (a - z))
    if ((t_1 <= (-1d-266)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) * ((y - z) / (a - z)))
    else
        tmp = t + ((x - t) / (z / (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 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-266) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if (t_1 <= -1e-266) or not (t_1 <= 0.0):
		tmp = x + ((t - x) * ((y - z) / (a - z)))
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -1e-266) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -1e-266) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	else
		tmp = t + ((x - t) / (z / (y - a)));
	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[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-266], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -9.9999999999999998e-267 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 72.4%

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

      1. associate-*l/ 90.0%

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

   3. Simplified 90.0%

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

   if -9.9999999999999998e-267 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.3%

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

      1. associate-*l/ 4.3%

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

   3. Simplified 4.3%

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

   4. Taylor expanded in z around -inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. distribute-rgt-out-- 99.8%

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

      3. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{-266} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 3: 37.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{a - z}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+109}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+56}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z}\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+39}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.96 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-303}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ t (- a z)))))
   (if (<= z -9e+109)
     t
     (if (<= z -3.8e+56)
       (/ (* y (- t)) z)
       (if (<= z -4.9e+39)
         t
         (if (<= z -1.96e-16)
           x
           (if (<= z -2.5e-95)
             t_1
             (if (<= z -8.2e-139)
               x
               (if (<= z 1.3e-303) t_1 (if (<= z 3.9e+81) x t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / (a - z));
	double tmp;
	if (z <= -9e+109) {
		tmp = t;
	} else if (z <= -3.8e+56) {
		tmp = (y * -t) / z;
	} else if (z <= -4.9e+39) {
		tmp = t;
	} else if (z <= -1.96e-16) {
		tmp = x;
	} else if (z <= -2.5e-95) {
		tmp = t_1;
	} else if (z <= -8.2e-139) {
		tmp = x;
	} else if (z <= 1.3e-303) {
		tmp = t_1;
	} else if (z <= 3.9e+81) {
		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) :: t_1
    real(8) :: tmp
    t_1 = y * (t / (a - z))
    if (z <= (-9d+109)) then
        tmp = t
    else if (z <= (-3.8d+56)) then
        tmp = (y * -t) / z
    else if (z <= (-4.9d+39)) then
        tmp = t
    else if (z <= (-1.96d-16)) then
        tmp = x
    else if (z <= (-2.5d-95)) then
        tmp = t_1
    else if (z <= (-8.2d-139)) then
        tmp = x
    else if (z <= 1.3d-303) then
        tmp = t_1
    else if (z <= 3.9d+81) 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 t_1 = y * (t / (a - z));
	double tmp;
	if (z <= -9e+109) {
		tmp = t;
	} else if (z <= -3.8e+56) {
		tmp = (y * -t) / z;
	} else if (z <= -4.9e+39) {
		tmp = t;
	} else if (z <= -1.96e-16) {
		tmp = x;
	} else if (z <= -2.5e-95) {
		tmp = t_1;
	} else if (z <= -8.2e-139) {
		tmp = x;
	} else if (z <= 1.3e-303) {
		tmp = t_1;
	} else if (z <= 3.9e+81) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (t / (a - z))
	tmp = 0
	if z <= -9e+109:
		tmp = t
	elif z <= -3.8e+56:
		tmp = (y * -t) / z
	elif z <= -4.9e+39:
		tmp = t
	elif z <= -1.96e-16:
		tmp = x
	elif z <= -2.5e-95:
		tmp = t_1
	elif z <= -8.2e-139:
		tmp = x
	elif z <= 1.3e-303:
		tmp = t_1
	elif z <= 3.9e+81:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / Float64(a - z)))
	tmp = 0.0
	if (z <= -9e+109)
		tmp = t;
	elseif (z <= -3.8e+56)
		tmp = Float64(Float64(y * Float64(-t)) / z);
	elseif (z <= -4.9e+39)
		tmp = t;
	elseif (z <= -1.96e-16)
		tmp = x;
	elseif (z <= -2.5e-95)
		tmp = t_1;
	elseif (z <= -8.2e-139)
		tmp = x;
	elseif (z <= 1.3e-303)
		tmp = t_1;
	elseif (z <= 3.9e+81)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (t / (a - z));
	tmp = 0.0;
	if (z <= -9e+109)
		tmp = t;
	elseif (z <= -3.8e+56)
		tmp = (y * -t) / z;
	elseif (z <= -4.9e+39)
		tmp = t;
	elseif (z <= -1.96e-16)
		tmp = x;
	elseif (z <= -2.5e-95)
		tmp = t_1;
	elseif (z <= -8.2e-139)
		tmp = x;
	elseif (z <= 1.3e-303)
		tmp = t_1;
	elseif (z <= 3.9e+81)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+109], t, If[LessEqual[z, -3.8e+56], N[(N[(y * (-t)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -4.9e+39], t, If[LessEqual[z, -1.96e-16], x, If[LessEqual[z, -2.5e-95], t$95$1, If[LessEqual[z, -8.2e-139], x, If[LessEqual[z, 1.3e-303], t$95$1, If[LessEqual[z, 3.9e+81], x, t]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.9999999999999992e109 or -3.79999999999999996e56 < z < -4.89999999999999987e39 or 3.9000000000000001e81 < z

   1. Initial program 31.6%

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

      1. associate-*l/ 65.5%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in z around inf 58.8%

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

   if -8.9999999999999992e109 < z < -3.79999999999999996e56

   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/ 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in y around -inf 72.1%

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

   5. Taylor expanded in t around inf 60.6%

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

      1. *-commutative 60.6%

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

      2. associate-*r/ 60.5%

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

   7. Simplified 60.5%

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

   8. Taylor expanded in a around 0 61.0%

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

      1. *-commutative 61.0%

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

      2. associate-*r/ 61.0%

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

      3. mul-1-neg 61.0%

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

      4. distribute-rgt-neg-out 61.0%

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

   10. Simplified 61.0%

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

   if -4.89999999999999987e39 < z < -1.96000000000000005e-16 or -2.4999999999999999e-95 < z < -8.20000000000000028e-139 or 1.30000000000000002e-303 < z < 3.9000000000000001e81

   1. Initial program 83.2%

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

      1. associate-*l/ 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in a around inf 42.9%

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

   if -1.96000000000000005e-16 < z < -2.4999999999999999e-95 or -8.20000000000000028e-139 < z < 1.30000000000000002e-303

   1. Initial program 88.5%

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

      1. associate-*l/ 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in y around -inf 61.1%

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

   5. Taylor expanded in t around inf 46.1%

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

      1. *-commutative 46.1%

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

      2. associate-*r/ 52.4%

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

   7. Simplified 52.4%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+109}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+56}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z}\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+39}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.96 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-95}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-303}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 50.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+110}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+55}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{t}{\frac{-a}{z}}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+19}:\\ \;\;\;\;\frac{-x}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-307}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+81}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.15e+110)
   t
   (if (<= z -3.3e+55)
     (/ (* y (- t)) z)
     (if (<= z -1.15e+29)
       (+ x (/ t (/ (- a) z)))
       (if (<= z -5e+19)
         (/ (- x) (/ (- a z) y))
         (if (<= z 7.5e-307)
           (+ x (* t (/ y a)))
           (if (<= z 2.5e+81) (- x (* x (/ y a))) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+110) {
		tmp = t;
	} else if (z <= -3.3e+55) {
		tmp = (y * -t) / z;
	} else if (z <= -1.15e+29) {
		tmp = x + (t / (-a / z));
	} else if (z <= -5e+19) {
		tmp = -x / ((a - z) / y);
	} else if (z <= 7.5e-307) {
		tmp = x + (t * (y / a));
	} else if (z <= 2.5e+81) {
		tmp = x - (x * (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 <= (-1.15d+110)) then
        tmp = t
    else if (z <= (-3.3d+55)) then
        tmp = (y * -t) / z
    else if (z <= (-1.15d+29)) then
        tmp = x + (t / (-a / z))
    else if (z <= (-5d+19)) then
        tmp = -x / ((a - z) / y)
    else if (z <= 7.5d-307) then
        tmp = x + (t * (y / a))
    else if (z <= 2.5d+81) then
        tmp = x - (x * (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 <= -1.15e+110) {
		tmp = t;
	} else if (z <= -3.3e+55) {
		tmp = (y * -t) / z;
	} else if (z <= -1.15e+29) {
		tmp = x + (t / (-a / z));
	} else if (z <= -5e+19) {
		tmp = -x / ((a - z) / y);
	} else if (z <= 7.5e-307) {
		tmp = x + (t * (y / a));
	} else if (z <= 2.5e+81) {
		tmp = x - (x * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.15e+110:
		tmp = t
	elif z <= -3.3e+55:
		tmp = (y * -t) / z
	elif z <= -1.15e+29:
		tmp = x + (t / (-a / z))
	elif z <= -5e+19:
		tmp = -x / ((a - z) / y)
	elif z <= 7.5e-307:
		tmp = x + (t * (y / a))
	elif z <= 2.5e+81:
		tmp = x - (x * (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.15e+110)
		tmp = t;
	elseif (z <= -3.3e+55)
		tmp = Float64(Float64(y * Float64(-t)) / z);
	elseif (z <= -1.15e+29)
		tmp = Float64(x + Float64(t / Float64(Float64(-a) / z)));
	elseif (z <= -5e+19)
		tmp = Float64(Float64(-x) / Float64(Float64(a - z) / y));
	elseif (z <= 7.5e-307)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 2.5e+81)
		tmp = Float64(x - Float64(x * 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 <= -1.15e+110)
		tmp = t;
	elseif (z <= -3.3e+55)
		tmp = (y * -t) / z;
	elseif (z <= -1.15e+29)
		tmp = x + (t / (-a / z));
	elseif (z <= -5e+19)
		tmp = -x / ((a - z) / y);
	elseif (z <= 7.5e-307)
		tmp = x + (t * (y / a));
	elseif (z <= 2.5e+81)
		tmp = x - (x * (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.15e+110], t, If[LessEqual[z, -3.3e+55], N[(N[(y * (-t)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -1.15e+29], N[(x + N[(t / N[((-a) / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5e+19], N[((-x) / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e-307], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+81], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.15e110 or 2.4999999999999999e81 < z

   1. Initial program 31.5%

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

      1. associate-*l/ 65.4%

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

   3. Simplified 65.4%

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

   4. Taylor expanded in z around inf 58.5%

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

   if -1.15e110 < z < -3.3e55

   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/ 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in y around -inf 72.1%

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

   5. Taylor expanded in t around inf 60.6%

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

      1. *-commutative 60.6%

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

      2. associate-*r/ 60.5%

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

   7. Simplified 60.5%

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

   8. Taylor expanded in a around 0 61.0%

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

      1. *-commutative 61.0%

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

      2. associate-*r/ 61.0%

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

      3. mul-1-neg 61.0%

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

      4. distribute-rgt-neg-out 61.0%

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

   10. Simplified 61.0%

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

   if -3.3e55 < z < -1.1500000000000001e29

   1. Initial program 52.6%

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

      1. associate-/l* 83.1%

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

   3. Simplified 83.1%

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

   4. Taylor expanded in t around inf 76.0%

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

   5. Taylor expanded in a around inf 42.8%

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

      1. associate-/l* 58.6%

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

   7. Simplified 58.6%

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

   8. Taylor expanded in y around 0 58.6%

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

      1. associate-*r/ 58.6%

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

      2. neg-mul-1 58.6%

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

   10. Simplified 58.6%

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

   if -1.1500000000000001e29 < z < -5e19

   1. Initial program 28.7%

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

      1. associate-*l/ 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in y around -inf 53.6%

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

   5. Taylor expanded in t around 0 51.1%

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

      1. associate-/l* 75.2%

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

      2. associate-*r/ 75.2%

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

      3. neg-mul-1 75.2%

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

   7. Simplified 75.2%

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

   if -5e19 < z < 7.5000000000000006e-307

   1. Initial program 86.5%

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

      1. associate-*l/ 89.4%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in z around 0 68.2%

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

      1. associate-/l* 74.3%

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

      2. associate-/r/ 74.1%

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

   6. Simplified 74.1%

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

   7. Taylor expanded in t around inf 61.8%

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

      1. associate-*r/ 66.2%

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

   9. Simplified 66.2%

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

   if 7.5000000000000006e-307 < z < 2.4999999999999999e81

   1. Initial program 86.6%

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

      1. associate-*l/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in z around 0 73.6%

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

      1. associate-/l* 76.8%

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

      2. associate-/r/ 77.9%

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

   6. Simplified 77.9%

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

   7. Taylor expanded in t around 0 65.6%

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

      1. mul-1-neg 65.6%

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

      2. *-commutative 65.6%

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

      3. associate-*l/ 68.8%

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

      4. distribute-rgt-neg-out 68.8%

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

   9. Simplified 68.8%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+110}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+55}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{t}{\frac{-a}{z}}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+19}:\\ \;\;\;\;\frac{-x}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-307}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+81}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 51.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ t_2 := x - x \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -5.3 \cdot 10^{+112}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -24000000000:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-306}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{+82}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))) (t_2 (- x (* x (/ y a)))))
   (if (<= z -5.3e+112)
     t
     (if (<= z -24000000000.0)
       (/ (- y) (/ z (- t x)))
       (if (<= z -4e-67)
         t_1
         (if (<= z -5.4e-110)
           t_2
           (if (<= z 1.32e-306) t_1 (if (<= z 1e+82) t_2 t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double t_2 = x - (x * (y / a));
	double tmp;
	if (z <= -5.3e+112) {
		tmp = t;
	} else if (z <= -24000000000.0) {
		tmp = -y / (z / (t - x));
	} else if (z <= -4e-67) {
		tmp = t_1;
	} else if (z <= -5.4e-110) {
		tmp = t_2;
	} else if (z <= 1.32e-306) {
		tmp = t_1;
	} else if (z <= 1e+82) {
		tmp = t_2;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (t * (y / a))
    t_2 = x - (x * (y / a))
    if (z <= (-5.3d+112)) then
        tmp = t
    else if (z <= (-24000000000.0d0)) then
        tmp = -y / (z / (t - x))
    else if (z <= (-4d-67)) then
        tmp = t_1
    else if (z <= (-5.4d-110)) then
        tmp = t_2
    else if (z <= 1.32d-306) then
        tmp = t_1
    else if (z <= 1d+82) then
        tmp = t_2
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double t_2 = x - (x * (y / a));
	double tmp;
	if (z <= -5.3e+112) {
		tmp = t;
	} else if (z <= -24000000000.0) {
		tmp = -y / (z / (t - x));
	} else if (z <= -4e-67) {
		tmp = t_1;
	} else if (z <= -5.4e-110) {
		tmp = t_2;
	} else if (z <= 1.32e-306) {
		tmp = t_1;
	} else if (z <= 1e+82) {
		tmp = t_2;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	t_2 = x - (x * (y / a))
	tmp = 0
	if z <= -5.3e+112:
		tmp = t
	elif z <= -24000000000.0:
		tmp = -y / (z / (t - x))
	elif z <= -4e-67:
		tmp = t_1
	elif z <= -5.4e-110:
		tmp = t_2
	elif z <= 1.32e-306:
		tmp = t_1
	elif z <= 1e+82:
		tmp = t_2
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	t_2 = Float64(x - Float64(x * Float64(y / a)))
	tmp = 0.0
	if (z <= -5.3e+112)
		tmp = t;
	elseif (z <= -24000000000.0)
		tmp = Float64(Float64(-y) / Float64(z / Float64(t - x)));
	elseif (z <= -4e-67)
		tmp = t_1;
	elseif (z <= -5.4e-110)
		tmp = t_2;
	elseif (z <= 1.32e-306)
		tmp = t_1;
	elseif (z <= 1e+82)
		tmp = t_2;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	t_2 = x - (x * (y / a));
	tmp = 0.0;
	if (z <= -5.3e+112)
		tmp = t;
	elseif (z <= -24000000000.0)
		tmp = -y / (z / (t - x));
	elseif (z <= -4e-67)
		tmp = t_1;
	elseif (z <= -5.4e-110)
		tmp = t_2;
	elseif (z <= 1.32e-306)
		tmp = t_1;
	elseif (z <= 1e+82)
		tmp = t_2;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.3e+112], t, If[LessEqual[z, -24000000000.0], N[((-y) / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4e-67], t$95$1, If[LessEqual[z, -5.4e-110], t$95$2, If[LessEqual[z, 1.32e-306], t$95$1, If[LessEqual[z, 1e+82], t$95$2, t]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.30000000000000018e112 or 9.9999999999999996e81 < z

   1. Initial program 31.5%

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

      1. associate-*l/ 65.4%

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

   3. Simplified 65.4%

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

   4. Taylor expanded in z around inf 58.5%

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

   if -5.30000000000000018e112 < z < -2.4e10

   1. Initial program 60.9%

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

      1. associate-*l/ 82.2%

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

   3. Simplified 82.2%

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

   4. Taylor expanded in y around -inf 48.5%

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

   5. Taylor expanded in a around 0 44.9%

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

      1. associate-/l* 53.0%

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

      2. associate-*r/ 53.0%

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

      3. neg-mul-1 53.0%

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

   7. Simplified 53.0%

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

   if -2.4e10 < z < -3.99999999999999977e-67 or -5.3999999999999996e-110 < z < 1.32e-306

   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/ 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in z around 0 80.5%

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

      1. associate-/l* 86.7%

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

      2. associate-/r/ 86.4%

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

   6. Simplified 86.4%

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

   7. Taylor expanded in t around inf 78.3%

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

      1. associate-*r/ 84.3%

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

   9. Simplified 84.3%

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

   if -3.99999999999999977e-67 < z < -5.3999999999999996e-110 or 1.32e-306 < z < 9.9999999999999996e81

   1. Initial program 87.6%

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

      1. associate-*l/ 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in z around 0 68.8%

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

      1. associate-/l* 72.5%

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

      2. associate-/r/ 73.4%

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

   6. Simplified 73.4%

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

   7. Taylor expanded in t around 0 62.8%

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

      1. mul-1-neg 62.8%

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

      2. *-commutative 62.8%

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

      3. associate-*l/ 67.4%

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

      4. distribute-rgt-neg-out 67.4%

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

   9. Simplified 67.4%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+112}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -24000000000:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-67}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-110}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-306}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 10^{+82}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6: 57.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -1.18 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-306}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= z -1.18e+36)
     t_2
     (if (<= z -1.75e-16)
       t_1
       (if (<= z -4.4e-91)
         t_2
         (if (<= z 1.3e-306)
           (+ x (* t (/ y a)))
           (if (<= z 1.1e+65) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.18e+36) {
		tmp = t_2;
	} else if (z <= -1.75e-16) {
		tmp = t_1;
	} else if (z <= -4.4e-91) {
		tmp = t_2;
	} else if (z <= 1.3e-306) {
		tmp = x + (t * (y / a));
	} else if (z <= 1.1e+65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (x * (y / a))
    t_2 = t * ((y - z) / (a - z))
    if (z <= (-1.18d+36)) then
        tmp = t_2
    else if (z <= (-1.75d-16)) then
        tmp = t_1
    else if (z <= (-4.4d-91)) then
        tmp = t_2
    else if (z <= 1.3d-306) then
        tmp = x + (t * (y / a))
    else if (z <= 1.1d+65) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.18e+36) {
		tmp = t_2;
	} else if (z <= -1.75e-16) {
		tmp = t_1;
	} else if (z <= -4.4e-91) {
		tmp = t_2;
	} else if (z <= 1.3e-306) {
		tmp = x + (t * (y / a));
	} else if (z <= 1.1e+65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (y / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -1.18e+36:
		tmp = t_2
	elif z <= -1.75e-16:
		tmp = t_1
	elif z <= -4.4e-91:
		tmp = t_2
	elif z <= 1.3e-306:
		tmp = x + (t * (y / a))
	elif z <= 1.1e+65:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.18e+36)
		tmp = t_2;
	elseif (z <= -1.75e-16)
		tmp = t_1;
	elseif (z <= -4.4e-91)
		tmp = t_2;
	elseif (z <= 1.3e-306)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 1.1e+65)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (y / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -1.18e+36)
		tmp = t_2;
	elseif (z <= -1.75e-16)
		tmp = t_1;
	elseif (z <= -4.4e-91)
		tmp = t_2;
	elseif (z <= 1.3e-306)
		tmp = x + (t * (y / a));
	elseif (z <= 1.1e+65)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.18e+36], t$95$2, If[LessEqual[z, -1.75e-16], t$95$1, If[LessEqual[z, -4.4e-91], t$95$2, If[LessEqual[z, 1.3e-306], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+65], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.17999999999999997e36 or -1.75000000000000009e-16 < z < -4.4000000000000002e-91 or 1.0999999999999999e65 < z

   1. Initial program 46.1%

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

      1. associate-*l/ 72.2%

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

   3. Simplified 72.2%

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

   4. Taylor expanded in x around 0 47.9%

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

      1. associate-*r/ 66.6%

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

   6. Simplified 66.6%

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

   if -1.17999999999999997e36 < z < -1.75000000000000009e-16 or 1.3e-306 < z < 1.0999999999999999e65

   1. Initial program 83.9%

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

      1. associate-*l/ 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in z around 0 72.2%

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

      1. associate-/l* 77.0%

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

      2. associate-/r/ 78.1%

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

   6. Simplified 78.1%

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

   7. Taylor expanded in t around 0 64.0%

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

      1. mul-1-neg 64.0%

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

      2. *-commutative 64.0%

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

      3. associate-*l/ 68.9%

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

      4. distribute-rgt-neg-out 68.9%

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

   9. Simplified 68.9%

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

   if -4.4000000000000002e-91 < z < 1.3e-306

   1. Initial program 82.1%

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

      1. associate-*l/ 86.6%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in z around 0 72.2%

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

      1. associate-/l* 84.6%

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

      2. associate-/r/ 81.7%

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

   6. Simplified 81.7%

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

   7. Taylor expanded in t around inf 72.1%

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

      1. associate-*r/ 79.2%

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

   9. Simplified 79.2%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{+36}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-16}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-91}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-306}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+65}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 7: 37.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+39}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-64}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-89}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-140}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-305}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.2e+39)
   t
   (if (<= z -1.55e-17)
     x
     (if (<= z -1.08e-64)
       (* t (/ y a))
       (if (<= z -6.2e-89)
         (/ (- x) (/ a y))
         (if (<= z -5.5e-140)
           x
           (if (<= z 1.15e-305) (* y (/ t a)) (if (<= z 6.2e+81) x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.2e+39) {
		tmp = t;
	} else if (z <= -1.55e-17) {
		tmp = x;
	} else if (z <= -1.08e-64) {
		tmp = t * (y / a);
	} else if (z <= -6.2e-89) {
		tmp = -x / (a / y);
	} else if (z <= -5.5e-140) {
		tmp = x;
	} else if (z <= 1.15e-305) {
		tmp = y * (t / a);
	} else if (z <= 6.2e+81) {
		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 <= (-6.2d+39)) then
        tmp = t
    else if (z <= (-1.55d-17)) then
        tmp = x
    else if (z <= (-1.08d-64)) then
        tmp = t * (y / a)
    else if (z <= (-6.2d-89)) then
        tmp = -x / (a / y)
    else if (z <= (-5.5d-140)) then
        tmp = x
    else if (z <= 1.15d-305) then
        tmp = y * (t / a)
    else if (z <= 6.2d+81) 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 <= -6.2e+39) {
		tmp = t;
	} else if (z <= -1.55e-17) {
		tmp = x;
	} else if (z <= -1.08e-64) {
		tmp = t * (y / a);
	} else if (z <= -6.2e-89) {
		tmp = -x / (a / y);
	} else if (z <= -5.5e-140) {
		tmp = x;
	} else if (z <= 1.15e-305) {
		tmp = y * (t / a);
	} else if (z <= 6.2e+81) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.2e+39:
		tmp = t
	elif z <= -1.55e-17:
		tmp = x
	elif z <= -1.08e-64:
		tmp = t * (y / a)
	elif z <= -6.2e-89:
		tmp = -x / (a / y)
	elif z <= -5.5e-140:
		tmp = x
	elif z <= 1.15e-305:
		tmp = y * (t / a)
	elif z <= 6.2e+81:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.2e+39)
		tmp = t;
	elseif (z <= -1.55e-17)
		tmp = x;
	elseif (z <= -1.08e-64)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= -6.2e-89)
		tmp = Float64(Float64(-x) / Float64(a / y));
	elseif (z <= -5.5e-140)
		tmp = x;
	elseif (z <= 1.15e-305)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 6.2e+81)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.2e+39)
		tmp = t;
	elseif (z <= -1.55e-17)
		tmp = x;
	elseif (z <= -1.08e-64)
		tmp = t * (y / a);
	elseif (z <= -6.2e-89)
		tmp = -x / (a / y);
	elseif (z <= -5.5e-140)
		tmp = x;
	elseif (z <= 1.15e-305)
		tmp = y * (t / a);
	elseif (z <= 6.2e+81)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.2e+39], t, If[LessEqual[z, -1.55e-17], x, If[LessEqual[z, -1.08e-64], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.2e-89], N[((-x) / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.5e-140], x, If[LessEqual[z, 1.15e-305], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+81], x, t]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.2000000000000005e39 or 6.2e81 < z

   1. Initial program 36.5%

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

      1. associate-*l/ 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in z around inf 54.3%

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

   if -6.2000000000000005e39 < z < -1.5499999999999999e-17 or -6.19999999999999993e-89 < z < -5.50000000000000026e-140 or 1.15e-305 < z < 6.2e81

   1. Initial program 83.5%

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

      1. associate-*l/ 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in a around inf 42.2%

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

   if -1.5499999999999999e-17 < z < -1.0799999999999999e-64

   1. Initial program 94.4%

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

      1. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in y around -inf 52.2%

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

   5. Taylor expanded in t around inf 40.3%

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

      1. *-commutative 40.3%

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

      2. associate-*r/ 28.6%

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

   7. Simplified 28.6%

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

   8. Taylor expanded in a around inf 28.1%

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

   9. Taylor expanded in y around 0 39.8%

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

       1. associate-*r/ 39.8%

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

   11. Simplified 39.8%

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

   if -1.0799999999999999e-64 < z < -6.19999999999999993e-89

   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/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around -inf 87.5%

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

   5. Taylor expanded in t around 0 38.5%

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

      1. associate-*r/ 38.5%

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

      2. mul-1-neg 38.5%

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

      3. distribute-lft-neg-out 38.5%

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

      4. *-commutative 38.5%

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

   7. Simplified 38.5%

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

   8. Taylor expanded in a around inf 51.1%

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

      1. mul-1-neg 51.1%

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

      2. associate-/l* 51.1%

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

   10. Simplified 51.1%

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

   if -5.50000000000000026e-140 < z < 1.15e-305

   1. Initial program 82.5%

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

      1. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in y around -inf 56.7%

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

   5. Taylor expanded in t around inf 49.5%

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

      1. *-commutative 49.5%

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

      2. associate-*r/ 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in a around inf 63.3%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+39}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-64}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-89}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-140}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-305}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 57.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-96}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-307}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+64}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -2.3e+39)
     t_1
     (if (<= z -6e-96)
       (* y (/ (- t x) (- a z)))
       (if (<= z 1.05e-307)
         (+ x (* t (/ y a)))
         (if (<= z 1.25e+64) (- x (* x (/ y a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2.3e+39) {
		tmp = t_1;
	} else if (z <= -6e-96) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.05e-307) {
		tmp = x + (t * (y / a));
	} else if (z <= 1.25e+64) {
		tmp = x - (x * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-2.3d+39)) then
        tmp = t_1
    else if (z <= (-6d-96)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 1.05d-307) then
        tmp = x + (t * (y / a))
    else if (z <= 1.25d+64) then
        tmp = x - (x * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2.3e+39) {
		tmp = t_1;
	} else if (z <= -6e-96) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.05e-307) {
		tmp = x + (t * (y / a));
	} else if (z <= 1.25e+64) {
		tmp = x - (x * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -2.3e+39:
		tmp = t_1
	elif z <= -6e-96:
		tmp = y * ((t - x) / (a - z))
	elif z <= 1.05e-307:
		tmp = x + (t * (y / a))
	elif z <= 1.25e+64:
		tmp = x - (x * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -2.3e+39)
		tmp = t_1;
	elseif (z <= -6e-96)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 1.05e-307)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 1.25e+64)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -2.3e+39)
		tmp = t_1;
	elseif (z <= -6e-96)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 1.05e-307)
		tmp = x + (t * (y / a));
	elseif (z <= 1.25e+64)
		tmp = x - (x * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e+39], t$95$1, If[LessEqual[z, -6e-96], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-307], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+64], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.30000000000000012e39 or 1.25e64 < z

   1. Initial program 37.9%

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

      1. associate-*l/ 68.2%

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

   3. Simplified 68.2%

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

   4. Taylor expanded in x around 0 45.9%

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

      1. associate-*r/ 67.6%

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

   6. Simplified 67.6%

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

   if -2.30000000000000012e39 < z < -6e-96

   1. Initial program 83.1%

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

      1. associate-*l/ 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in y around inf 57.0%

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

      1. div-sub 57.0%

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

   6. Simplified 57.0%

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

   if -6e-96 < z < 1.0500000000000001e-307

   1. Initial program 81.7%

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

      1. associate-*l/ 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in z around 0 74.0%

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

      1. associate-/l* 86.7%

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

      2. associate-/r/ 83.7%

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

   6. Simplified 83.7%

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

   7. Taylor expanded in t around inf 73.9%

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

      1. associate-*r/ 81.1%

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

   9. Simplified 81.1%

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

   if 1.0500000000000001e-307 < z < 1.25e64

   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/ 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in z around 0 75.8%

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

      1. associate-/l* 79.2%

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

      2. associate-/r/ 80.4%

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

   6. Simplified 80.4%

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

   7. Taylor expanded in t around 0 67.5%

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

      1. mul-1-neg 67.5%

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

      2. *-commutative 67.5%

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

      3. associate-*l/ 70.8%

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

      4. distribute-rgt-neg-out 70.8%

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

   9. Simplified 70.8%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+39}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-96}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-307}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+64}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 9: 37.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+110}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{+51}:\\ \;\;\;\;\frac{y}{\frac{z}{-t}}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-142}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-306}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.05e+110)
   t
   (if (<= z -5.1e+51)
     (/ y (/ z (- t)))
     (if (<= z -4.2e+37)
       t
       (if (<= z -1.15e-142)
         x
         (if (<= z 1.7e-306) (* y (/ t a)) (if (<= z 5.5e+81) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+110) {
		tmp = t;
	} else if (z <= -5.1e+51) {
		tmp = y / (z / -t);
	} else if (z <= -4.2e+37) {
		tmp = t;
	} else if (z <= -1.15e-142) {
		tmp = x;
	} else if (z <= 1.7e-306) {
		tmp = y * (t / a);
	} else if (z <= 5.5e+81) {
		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 <= (-1.05d+110)) then
        tmp = t
    else if (z <= (-5.1d+51)) then
        tmp = y / (z / -t)
    else if (z <= (-4.2d+37)) then
        tmp = t
    else if (z <= (-1.15d-142)) then
        tmp = x
    else if (z <= 1.7d-306) then
        tmp = y * (t / a)
    else if (z <= 5.5d+81) 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 <= -1.05e+110) {
		tmp = t;
	} else if (z <= -5.1e+51) {
		tmp = y / (z / -t);
	} else if (z <= -4.2e+37) {
		tmp = t;
	} else if (z <= -1.15e-142) {
		tmp = x;
	} else if (z <= 1.7e-306) {
		tmp = y * (t / a);
	} else if (z <= 5.5e+81) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.05e+110:
		tmp = t
	elif z <= -5.1e+51:
		tmp = y / (z / -t)
	elif z <= -4.2e+37:
		tmp = t
	elif z <= -1.15e-142:
		tmp = x
	elif z <= 1.7e-306:
		tmp = y * (t / a)
	elif z <= 5.5e+81:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.05e+110)
		tmp = t;
	elseif (z <= -5.1e+51)
		tmp = Float64(y / Float64(z / Float64(-t)));
	elseif (z <= -4.2e+37)
		tmp = t;
	elseif (z <= -1.15e-142)
		tmp = x;
	elseif (z <= 1.7e-306)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 5.5e+81)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.05e+110)
		tmp = t;
	elseif (z <= -5.1e+51)
		tmp = y / (z / -t);
	elseif (z <= -4.2e+37)
		tmp = t;
	elseif (z <= -1.15e-142)
		tmp = x;
	elseif (z <= 1.7e-306)
		tmp = y * (t / a);
	elseif (z <= 5.5e+81)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.05e+110], t, If[LessEqual[z, -5.1e+51], N[(y / N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.2e+37], t, If[LessEqual[z, -1.15e-142], x, If[LessEqual[z, 1.7e-306], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+81], x, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.05000000000000007e110 or -5.1000000000000001e51 < z < -4.2000000000000002e37 or 5.5000000000000003e81 < z

   1. Initial program 31.6%

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

      1. associate-*l/ 65.5%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in z around inf 58.8%

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

   if -1.05000000000000007e110 < z < -5.1000000000000001e51

   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/ 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in y around -inf 72.1%

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

   5. Taylor expanded in t around inf 60.6%

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

      1. *-commutative 60.6%

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

      2. associate-*r/ 60.5%

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

   7. Simplified 60.5%

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

   8. Taylor expanded in a around 0 61.0%

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

      1. *-commutative 61.0%

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

      2. associate-*r/ 61.0%

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

      3. mul-1-neg 61.0%

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

      4. distribute-rgt-neg-out 61.0%

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

      5. associate-/l* 60.8%

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

   10. Simplified 60.8%

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

   if -4.2000000000000002e37 < z < -1.15000000000000001e-142 or 1.6999999999999999e-306 < z < 5.5000000000000003e81

   1. Initial program 85.2%

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

      1. associate-*l/ 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in a around inf 38.8%

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

   if -1.15000000000000001e-142 < z < 1.6999999999999999e-306

   1. Initial program 82.5%

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

      1. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in y around -inf 56.7%

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

   5. Taylor expanded in t around inf 49.5%

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

      1. *-commutative 49.5%

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

      2. associate-*r/ 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in a around inf 63.3%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+110}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{+51}:\\ \;\;\;\;\frac{y}{\frac{z}{-t}}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-142}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-306}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10: 37.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+110}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+56}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-137}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-306}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 7.9 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.9e+110)
   t
   (if (<= z -3.6e+56)
     (/ (* y (- t)) z)
     (if (<= z -8e+38)
       t
       (if (<= z -4.5e-137)
         x
         (if (<= z 4.7e-306) (* y (/ t a)) (if (<= z 7.9e+80) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.9e+110) {
		tmp = t;
	} else if (z <= -3.6e+56) {
		tmp = (y * -t) / z;
	} else if (z <= -8e+38) {
		tmp = t;
	} else if (z <= -4.5e-137) {
		tmp = x;
	} else if (z <= 4.7e-306) {
		tmp = y * (t / a);
	} else if (z <= 7.9e+80) {
		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 <= (-5.9d+110)) then
        tmp = t
    else if (z <= (-3.6d+56)) then
        tmp = (y * -t) / z
    else if (z <= (-8d+38)) then
        tmp = t
    else if (z <= (-4.5d-137)) then
        tmp = x
    else if (z <= 4.7d-306) then
        tmp = y * (t / a)
    else if (z <= 7.9d+80) 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 <= -5.9e+110) {
		tmp = t;
	} else if (z <= -3.6e+56) {
		tmp = (y * -t) / z;
	} else if (z <= -8e+38) {
		tmp = t;
	} else if (z <= -4.5e-137) {
		tmp = x;
	} else if (z <= 4.7e-306) {
		tmp = y * (t / a);
	} else if (z <= 7.9e+80) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.9e+110:
		tmp = t
	elif z <= -3.6e+56:
		tmp = (y * -t) / z
	elif z <= -8e+38:
		tmp = t
	elif z <= -4.5e-137:
		tmp = x
	elif z <= 4.7e-306:
		tmp = y * (t / a)
	elif z <= 7.9e+80:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.9e+110)
		tmp = t;
	elseif (z <= -3.6e+56)
		tmp = Float64(Float64(y * Float64(-t)) / z);
	elseif (z <= -8e+38)
		tmp = t;
	elseif (z <= -4.5e-137)
		tmp = x;
	elseif (z <= 4.7e-306)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 7.9e+80)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.9e+110)
		tmp = t;
	elseif (z <= -3.6e+56)
		tmp = (y * -t) / z;
	elseif (z <= -8e+38)
		tmp = t;
	elseif (z <= -4.5e-137)
		tmp = x;
	elseif (z <= 4.7e-306)
		tmp = y * (t / a);
	elseif (z <= 7.9e+80)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.9e+110], t, If[LessEqual[z, -3.6e+56], N[(N[(y * (-t)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -8e+38], t, If[LessEqual[z, -4.5e-137], x, If[LessEqual[z, 4.7e-306], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.9e+80], x, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.8999999999999997e110 or -3.59999999999999998e56 < z < -7.99999999999999982e38 or 7.89999999999999999e80 < z

   1. Initial program 31.6%

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

      1. associate-*l/ 65.5%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in z around inf 58.8%

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

   if -5.8999999999999997e110 < z < -3.59999999999999998e56

   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/ 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in y around -inf 72.1%

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

   5. Taylor expanded in t around inf 60.6%

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

      1. *-commutative 60.6%

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

      2. associate-*r/ 60.5%

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

   7. Simplified 60.5%

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

   8. Taylor expanded in a around 0 61.0%

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

      1. *-commutative 61.0%

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

      2. associate-*r/ 61.0%

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

      3. mul-1-neg 61.0%

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

      4. distribute-rgt-neg-out 61.0%

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

   10. Simplified 61.0%

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

   if -7.99999999999999982e38 < z < -4.4999999999999997e-137 or 4.7000000000000001e-306 < z < 7.89999999999999999e80

   1. Initial program 85.2%

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

      1. associate-*l/ 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in a around inf 38.8%

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

   if -4.4999999999999997e-137 < z < 4.7000000000000001e-306

   1. Initial program 82.5%

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

      1. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in y around -inf 56.7%

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

   5. Taylor expanded in t around inf 49.5%

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

      1. *-commutative 49.5%

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

      2. associate-*r/ 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in a around inf 63.3%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+110}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+56}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-137}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-306}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 7.9 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11: 73.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+114} \lor \neg \left(z \leq 1.15 \cdot 10^{+68}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.95e+114) (not (<= z 1.15e+68)))
   (* t (/ (- y z) (- a z)))
   (+ x (* (- t x) (/ y (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.95e+114) || !(z <= 1.15e+68)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) * (y / (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 <= (-1.95d+114)) .or. (.not. (z <= 1.15d+68))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + ((t - x) * (y / (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 <= -1.95e+114) || !(z <= 1.15e+68)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.95e+114) or not (z <= 1.15e+68):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + ((t - x) * (y / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.95e+114) || !(z <= 1.15e+68))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.95e+114) || ~((z <= 1.15e+68)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + ((t - x) * (y / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.95e+114], N[Not[LessEqual[z, 1.15e+68]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e114 or 1.15e68 < z

   1. Initial program 33.7%

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

      1. associate-*l/ 65.5%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in x around 0 43.0%

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

      1. associate-*r/ 67.0%

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

   6. Simplified 67.0%

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

   if -1.95e114 < z < 1.15e68

   1. Initial program 83.4%

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

      1. associate-*l/ 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in y around inf 82.4%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+114} \lor \neg \left(z \leq 1.15 \cdot 10^{+68}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 12: 80.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+38} \lor \neg \left(z \leq 4.6 \cdot 10^{+36}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.1e+38) (not (<= z 4.6e+36)))
   (+ t (/ (- x t) (/ z (- y a))))
   (+ x (* (- t x) (/ y (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.1e+38) || !(z <= 4.6e+36)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((t - x) * (y / (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 <= (-1.1d+38)) .or. (.not. (z <= 4.6d+36))) then
        tmp = t + ((x - t) / (z / (y - a)))
    else
        tmp = x + ((t - x) * (y / (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 <= -1.1e+38) || !(z <= 4.6e+36)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((t - x) * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.1e+38) or not (z <= 4.6e+36):
		tmp = t + ((x - t) / (z / (y - a)))
	else:
		tmp = x + ((t - x) * (y / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.1e+38) || !(z <= 4.6e+36))
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.1e+38) || ~((z <= 4.6e+36)))
		tmp = t + ((x - t) / (z / (y - a)));
	else
		tmp = x + ((t - x) * (y / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.1e+38], N[Not[LessEqual[z, 4.6e+36]], $MachinePrecision]], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.10000000000000003e38 or 4.59999999999999993e36 < z

   1. Initial program 37.6%

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

      1. associate-*l/ 66.7%

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

   3. Simplified 66.7%

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

   4. Taylor expanded in z around -inf 62.8%

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

      1. mul-1-neg 62.8%

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

      2. distribute-rgt-out-- 63.0%

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

      3. associate-/l* 83.0%

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

   6. Simplified 83.0%

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

   if -1.10000000000000003e38 < z < 4.59999999999999993e36

   1. Initial program 86.5%

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

      1. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in y around inf 84.9%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+38} \lor \neg \left(z \leq 4.6 \cdot 10^{+36}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 13: 51.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+116}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-307}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.82 \cdot 10^{+81}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.8e+116)
   t
   (if (<= z 4.5e-307)
     (+ x (* t (/ y a)))
     (if (<= z 1.82e+81) (- x (* x (/ y a))) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.8e+116) {
		tmp = t;
	} else if (z <= 4.5e-307) {
		tmp = x + (t * (y / a));
	} else if (z <= 1.82e+81) {
		tmp = x - (x * (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 <= (-5.8d+116)) then
        tmp = t
    else if (z <= 4.5d-307) then
        tmp = x + (t * (y / a))
    else if (z <= 1.82d+81) then
        tmp = x - (x * (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 <= -5.8e+116) {
		tmp = t;
	} else if (z <= 4.5e-307) {
		tmp = x + (t * (y / a));
	} else if (z <= 1.82e+81) {
		tmp = x - (x * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.8e+116:
		tmp = t
	elif z <= 4.5e-307:
		tmp = x + (t * (y / a))
	elif z <= 1.82e+81:
		tmp = x - (x * (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.8e+116)
		tmp = t;
	elseif (z <= 4.5e-307)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 1.82e+81)
		tmp = Float64(x - Float64(x * 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 <= -5.8e+116)
		tmp = t;
	elseif (z <= 4.5e-307)
		tmp = x + (t * (y / a));
	elseif (z <= 1.82e+81)
		tmp = x - (x * (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.8e+116], t, If[LessEqual[z, 4.5e-307], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.82e+81], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8000000000000003e116 or 1.82000000000000003e81 < z

   1. Initial program 31.8%

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

      1. associate-*l/ 65.0%

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

   3. Simplified 65.0%

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

   4. Taylor expanded in z around inf 59.1%

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

   if -5.8000000000000003e116 < z < 4.49999999999999989e-307

   1. Initial program 79.5%

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

      1. associate-*l/ 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in z around 0 59.7%

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

      1. associate-/l* 67.6%

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

      2. associate-/r/ 67.6%

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

   6. Simplified 67.6%

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

   7. Taylor expanded in t around inf 53.9%

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

      1. associate-*r/ 58.3%

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

   9. Simplified 58.3%

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

   if 4.49999999999999989e-307 < z < 1.82000000000000003e81

   1. Initial program 86.6%

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

      1. associate-*l/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in z around 0 73.6%

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

      1. associate-/l* 76.8%

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

      2. associate-/r/ 77.9%

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

   6. Simplified 77.9%

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

   7. Taylor expanded in t around 0 65.6%

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

      1. mul-1-neg 65.6%

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

      2. *-commutative 65.6%

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

      3. associate-*l/ 68.8%

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

      4. distribute-rgt-neg-out 68.8%

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

   9. Simplified 68.8%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+116}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-307}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.82 \cdot 10^{+81}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 66.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+38} \lor \neg \left(z \leq 3.6 \cdot 10^{+64}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.2e+38) (not (<= z 3.6e+64)))
   (* t (/ (- y z) (- a z)))
   (+ x (* (- t x) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.2e+38) || !(z <= 3.6e+64)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - 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) :: tmp
    if ((z <= (-6.2d+38)) .or. (.not. (z <= 3.6d+64))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + ((t - 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 tmp;
	if ((z <= -6.2e+38) || !(z <= 3.6e+64)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.2e+38) or not (z <= 3.6e+64):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + ((t - x) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.2e+38) || !(z <= 3.6e+64))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.2e+38) || ~((z <= 3.6e+64)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + ((t - x) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.2e+38], N[Not[LessEqual[z, 3.6e+64]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.20000000000000035e38 or 3.60000000000000014e64 < z

   1. Initial program 37.9%

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

      1. associate-*l/ 68.2%

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

   3. Simplified 68.2%

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

   4. Taylor expanded in x around 0 45.9%

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

      1. associate-*r/ 67.6%

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

   6. Simplified 67.6%

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

   if -6.20000000000000035e38 < z < 3.60000000000000014e64

   1. Initial program 85.0%

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

      1. associate-*l/ 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in z around 0 70.8%

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

      1. associate-/l* 76.3%

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

      2. associate-/r/ 76.9%

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

   6. Simplified 76.9%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+38} \lor \neg \left(z \leq 3.6 \cdot 10^{+64}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 15: 38.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-303}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+82}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e+37)
   t
   (if (<= z -3.5e-139)
     x
     (if (<= z 5e-303) (* t (/ y a)) (if (<= z 1.1e+82) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+37) {
		tmp = t;
	} else if (z <= -3.5e-139) {
		tmp = x;
	} else if (z <= 5e-303) {
		tmp = t * (y / a);
	} else if (z <= 1.1e+82) {
		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 <= (-6.5d+37)) then
        tmp = t
    else if (z <= (-3.5d-139)) then
        tmp = x
    else if (z <= 5d-303) then
        tmp = t * (y / a)
    else if (z <= 1.1d+82) 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 <= -6.5e+37) {
		tmp = t;
	} else if (z <= -3.5e-139) {
		tmp = x;
	} else if (z <= 5e-303) {
		tmp = t * (y / a);
	} else if (z <= 1.1e+82) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e+37:
		tmp = t
	elif z <= -3.5e-139:
		tmp = x
	elif z <= 5e-303:
		tmp = t * (y / a)
	elif z <= 1.1e+82:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e+37)
		tmp = t;
	elseif (z <= -3.5e-139)
		tmp = x;
	elseif (z <= 5e-303)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 1.1e+82)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.5e+37)
		tmp = t;
	elseif (z <= -3.5e-139)
		tmp = x;
	elseif (z <= 5e-303)
		tmp = t * (y / a);
	elseif (z <= 1.1e+82)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e+37], t, If[LessEqual[z, -3.5e-139], x, If[LessEqual[z, 5e-303], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+82], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.4999999999999998e37 or 1.1000000000000001e82 < z

   1. Initial program 36.5%

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

      1. associate-*l/ 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in z around inf 54.3%

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

   if -6.4999999999999998e37 < z < -3.50000000000000001e-139 or 4.9999999999999998e-303 < z < 1.1000000000000001e82

   1. Initial program 85.2%

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

      1. associate-*l/ 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in a around inf 38.8%

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

   if -3.50000000000000001e-139 < z < 4.9999999999999998e-303

   1. Initial program 82.5%

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

      1. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in y around -inf 56.7%

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

   5. Taylor expanded in t around inf 49.5%

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

      1. *-commutative 49.5%

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

      2. associate-*r/ 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in a around inf 63.3%

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

   9. Taylor expanded in y around 0 49.5%

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

       1. associate-*r/ 59.3%

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

   11. Simplified 59.3%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-303}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+82}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 16: 38.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-141}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-302}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+82}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.52e+38)
   t
   (if (<= z -2.55e-141)
     x
     (if (<= z 1.25e-302) (* y (/ t a)) (if (<= z 1.02e+82) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.52e+38) {
		tmp = t;
	} else if (z <= -2.55e-141) {
		tmp = x;
	} else if (z <= 1.25e-302) {
		tmp = y * (t / a);
	} else if (z <= 1.02e+82) {
		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 <= (-1.52d+38)) then
        tmp = t
    else if (z <= (-2.55d-141)) then
        tmp = x
    else if (z <= 1.25d-302) then
        tmp = y * (t / a)
    else if (z <= 1.02d+82) 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 <= -1.52e+38) {
		tmp = t;
	} else if (z <= -2.55e-141) {
		tmp = x;
	} else if (z <= 1.25e-302) {
		tmp = y * (t / a);
	} else if (z <= 1.02e+82) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.52e+38:
		tmp = t
	elif z <= -2.55e-141:
		tmp = x
	elif z <= 1.25e-302:
		tmp = y * (t / a)
	elif z <= 1.02e+82:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.52e+38)
		tmp = t;
	elseif (z <= -2.55e-141)
		tmp = x;
	elseif (z <= 1.25e-302)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 1.02e+82)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.52e+38)
		tmp = t;
	elseif (z <= -2.55e-141)
		tmp = x;
	elseif (z <= 1.25e-302)
		tmp = y * (t / a);
	elseif (z <= 1.02e+82)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.52e+38], t, If[LessEqual[z, -2.55e-141], x, If[LessEqual[z, 1.25e-302], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e+82], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.51999999999999996e38 or 1.0200000000000001e82 < z

   1. Initial program 36.5%

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

      1. associate-*l/ 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in z around inf 54.3%

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

   if -1.51999999999999996e38 < z < -2.54999999999999989e-141 or 1.25000000000000008e-302 < z < 1.0200000000000001e82

   1. Initial program 85.2%

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

      1. associate-*l/ 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in a around inf 38.8%

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

   if -2.54999999999999989e-141 < z < 1.25000000000000008e-302

   1. Initial program 82.5%

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

      1. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in y around -inf 56.7%

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

   5. Taylor expanded in t around inf 49.5%

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

      1. *-commutative 49.5%

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

      2. associate-*r/ 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in a around inf 63.3%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-141}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-302}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+82}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 17: 52.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+113}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+81}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e+113) t (if (<= z 1.2e+81) (+ x (* t (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+113) {
		tmp = t;
	} else if (z <= 1.2e+81) {
		tmp = x + (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 <= (-2.4d+113)) then
        tmp = t
    else if (z <= 1.2d+81) then
        tmp = x + (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 <= -2.4e+113) {
		tmp = t;
	} else if (z <= 1.2e+81) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e+113:
		tmp = t
	elif z <= 1.2e+81:
		tmp = x + (t * (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e+113)
		tmp = t;
	elseif (z <= 1.2e+81)
		tmp = Float64(x + 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 <= -2.4e+113)
		tmp = t;
	elseif (z <= 1.2e+81)
		tmp = x + (t * (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e+113], t, If[LessEqual[z, 1.2e+81], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -2.39999999999999983e113 or 1.19999999999999995e81 < z

   1. Initial program 31.8%

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

      1. associate-*l/ 65.0%

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

   3. Simplified 65.0%

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

   4. Taylor expanded in z around inf 59.1%

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

   if -2.39999999999999983e113 < z < 1.19999999999999995e81

   1. Initial program 83.2%

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

      1. associate-*l/ 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in z around 0 66.9%

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

      1. associate-/l* 72.4%

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

      2. associate-/r/ 72.9%

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

   6. Simplified 72.9%

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

   7. Taylor expanded in t around inf 52.7%

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

      1. associate-*r/ 55.9%

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

   9. Simplified 55.9%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+113}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+81}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 18: 38.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.7e+38) t (if (<= z 3.05e+81) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.7e+38) {
		tmp = t;
	} else if (z <= 3.05e+81) {
		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 <= (-1.7d+38)) then
        tmp = t
    else if (z <= 3.05d+81) 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 <= -1.7e+38) {
		tmp = t;
	} else if (z <= 3.05e+81) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.7e+38:
		tmp = t
	elif z <= 3.05e+81:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.7e+38)
		tmp = t;
	elseif (z <= 3.05e+81)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.7e+38)
		tmp = t;
	elseif (z <= 3.05e+81)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.7e+38], t, If[LessEqual[z, 3.05e+81], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.69999999999999998e38 or 3.05000000000000019e81 < z

   1. Initial program 36.5%

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

      1. associate-*l/ 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in z around inf 54.3%

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

   if -1.69999999999999998e38 < z < 3.05000000000000019e81

   1. Initial program 84.8%

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

      1. associate-*l/ 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in a around inf 37.5%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19: 25.4% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 65.5%

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

   1. associate-*l/ 81.3%

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

3. Simplified 81.3%

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

4. Taylor expanded in z around inf 26.8%

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

5. Final simplification 26.8%

   \[\leadsto t \]

Developer target: 83.4% accurate, 0.8× 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 2023301 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (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))))