Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B

Percentage Accurate: 76.4% → 91.4%

Time: 12.1s

Alternatives: 14

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 76.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+149}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+145}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - a\right) \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9e+149)
   (- x (/ y (/ t (- a z))))
   (if (<= t 1.15e+145)
     (+ x (+ y (/ (- t z) (/ (- a t) y))))
     (+ x (* (- z a) (/ y t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9e+149) {
		tmp = x - (y / (t / (a - z)));
	} else if (t <= 1.15e+145) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} else {
		tmp = x + ((z - a) * (y / 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 (t <= (-9d+149)) then
        tmp = x - (y / (t / (a - z)))
    else if (t <= 1.15d+145) then
        tmp = x + (y + ((t - z) / ((a - t) / y)))
    else
        tmp = x + ((z - a) * (y / 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 (t <= -9e+149) {
		tmp = x - (y / (t / (a - z)));
	} else if (t <= 1.15e+145) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} else {
		tmp = x + ((z - a) * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9e+149:
		tmp = x - (y / (t / (a - z)))
	elif t <= 1.15e+145:
		tmp = x + (y + ((t - z) / ((a - t) / y)))
	else:
		tmp = x + ((z - a) * (y / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9e+149)
		tmp = Float64(x - Float64(y / Float64(t / Float64(a - z))));
	elseif (t <= 1.15e+145)
		tmp = Float64(x + Float64(y + Float64(Float64(t - z) / Float64(Float64(a - t) / y))));
	else
		tmp = Float64(x + Float64(Float64(z - a) * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9e+149)
		tmp = x - (y / (t / (a - z)));
	elseif (t <= 1.15e+145)
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	else
		tmp = x + ((z - a) * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9e+149], N[(x - N[(y / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+145], N[(x + N[(y + N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - a), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.99999999999999965e149

   1. Initial program 32.5%

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

      1. associate-*l/ 54.8%

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

   3. Simplified 54.8%

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

   4. Taylor expanded in t around -inf 69.2%

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

      1. +-commutative 69.2%

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

      2. mul-1-neg 69.2%

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

      3. unsub-neg 69.2%

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

      4. distribute-lft-out-- 69.7%

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

   6. Simplified 69.7%

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

      1. expm1-log1p-u 65.5%

         \[\leadsto x - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(a - z\right)}{t}\right)\right)} \]

      2. expm1-udef 50.7%

         \[\leadsto x - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - z\right)}{t}\right)} - 1\right)} \]

   8. Applied egg-rr 50.7%

      \[\leadsto x - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - z\right)}{t}\right)} - 1\right)} \]
   9. Step-by-step derivation

      1. expm1-def 65.5%

         \[\leadsto x - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(a - z\right)}{t}\right)\right)} \]

      2. expm1-log1p 69.7%

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

      3. associate-/l* 88.8%

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

   10. Simplified 88.8%

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

   if -8.99999999999999965e149 < t < 1.15e145

   1. Initial program 89.9%

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

      1. associate--l+ 91.9%

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

      2. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   if 1.15e145 < t

   1. Initial program 47.1%

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

      1. associate-*l/ 59.1%

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

   3. Simplified 59.1%

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

   4. Taylor expanded in y around 0 82.4%

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

   5. Taylor expanded in t around inf 78.7%

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

      1. mul-1-neg 78.7%

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

      2. neg-mul-1 78.7%

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

      3. +-commutative 78.7%

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

      4. sub-neg 78.7%

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

      5. associate-*r/ 89.1%

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

      6. distribute-lft-neg-in 89.1%

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

      7. sub-neg 89.1%

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

      8. +-commutative 89.1%

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

      9. distribute-neg-in 89.1%

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

      10. remove-double-neg 89.1%

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

      11. sub-neg 89.1%

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

   7. Simplified 89.1%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+149}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+145}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - a\right) \cdot \frac{y}{t}\\ \end{array} \]

Alternative 2: 75.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y \cdot z}{a}\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{+73}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-146}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+70}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* y z) a))))
   (if (<= a -3.8e+73)
     (+ y x)
     (if (<= a -9.5e-83)
       t_1
       (if (<= a 6.6e-146)
         (+ x (* y (/ z t)))
         (if (<= a 9.2e+48)
           t_1
           (if (<= a 2.2e+70) (+ x (* z (/ y t))) (+ y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y * z) / a);
	double tmp;
	if (a <= -3.8e+73) {
		tmp = y + x;
	} else if (a <= -9.5e-83) {
		tmp = t_1;
	} else if (a <= 6.6e-146) {
		tmp = x + (y * (z / t));
	} else if (a <= 9.2e+48) {
		tmp = t_1;
	} else if (a <= 2.2e+70) {
		tmp = x + (z * (y / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y * z) / a)
    if (a <= (-3.8d+73)) then
        tmp = y + x
    else if (a <= (-9.5d-83)) then
        tmp = t_1
    else if (a <= 6.6d-146) then
        tmp = x + (y * (z / t))
    else if (a <= 9.2d+48) then
        tmp = t_1
    else if (a <= 2.2d+70) then
        tmp = x + (z * (y / t))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y * z) / a);
	double tmp;
	if (a <= -3.8e+73) {
		tmp = y + x;
	} else if (a <= -9.5e-83) {
		tmp = t_1;
	} else if (a <= 6.6e-146) {
		tmp = x + (y * (z / t));
	} else if (a <= 9.2e+48) {
		tmp = t_1;
	} else if (a <= 2.2e+70) {
		tmp = x + (z * (y / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y * z) / a)
	tmp = 0
	if a <= -3.8e+73:
		tmp = y + x
	elif a <= -9.5e-83:
		tmp = t_1
	elif a <= 6.6e-146:
		tmp = x + (y * (z / t))
	elif a <= 9.2e+48:
		tmp = t_1
	elif a <= 2.2e+70:
		tmp = x + (z * (y / t))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y * z) / a))
	tmp = 0.0
	if (a <= -3.8e+73)
		tmp = Float64(y + x);
	elseif (a <= -9.5e-83)
		tmp = t_1;
	elseif (a <= 6.6e-146)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (a <= 9.2e+48)
		tmp = t_1;
	elseif (a <= 2.2e+70)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y * z) / a);
	tmp = 0.0;
	if (a <= -3.8e+73)
		tmp = y + x;
	elseif (a <= -9.5e-83)
		tmp = t_1;
	elseif (a <= 6.6e-146)
		tmp = x + (y * (z / t));
	elseif (a <= 9.2e+48)
		tmp = t_1;
	elseif (a <= 2.2e+70)
		tmp = x + (z * (y / t));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.8e+73], N[(y + x), $MachinePrecision], If[LessEqual[a, -9.5e-83], t$95$1, If[LessEqual[a, 6.6e-146], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.2e+48], t$95$1, If[LessEqual[a, 2.2e+70], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.80000000000000022e73 or 2.20000000000000001e70 < a

   1. Initial program 73.2%

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

      1. associate-*l/ 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in a around inf 81.9%

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

   if -3.80000000000000022e73 < a < -9.50000000000000051e-83 or 6.6e-146 < a < 9.2000000000000001e48

   1. Initial program 79.1%

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

      1. associate--l+ 80.4%

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

      2. sub-neg 80.4%

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

      3. +-commutative 80.4%

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

      4. associate-/l* 84.5%

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

      5. distribute-neg-frac 84.5%

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

      6. associate-/r/ 80.4%

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

      7. fma-def 80.4%

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

      8. sub-neg 80.4%

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

      9. +-commutative 80.4%

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

      10. distribute-neg-in 80.4%

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

      11. unsub-neg 80.4%

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

      12. remove-double-neg 80.4%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in z around inf 84.4%

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

      1. associate-*r/ 84.4%

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

      2. associate-*r* 84.4%

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

      3. neg-mul-1 84.4%

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

   6. Simplified 84.4%

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

   7. Taylor expanded in a around inf 74.1%

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

      1. associate-*r/ 74.1%

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

      2. mul-1-neg 74.1%

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

   9. Simplified 74.1%

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

   if -9.50000000000000051e-83 < a < 6.6e-146

   1. Initial program 82.5%

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

      1. associate-*l/ 82.5%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in y around 0 95.6%

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

   5. Taylor expanded in a around 0 86.9%

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

   if 9.2000000000000001e48 < a < 2.20000000000000001e70

   1. Initial program 65.4%

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

      1. associate-*l/ 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in y around 0 87.4%

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

   5. Taylor expanded in a around 0 64.2%

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

      1. associate-/l* 74.4%

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

   7. Simplified 74.4%

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

      1. associate-/r/ 74.7%

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

   9. Applied egg-rr 74.7%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+73}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-83}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-146}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+48}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+70}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 3: 91.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+150}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+152}:\\ \;\;\;\;x + y \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - a\right) \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.1e+150)
   (- x (/ y (/ t (- a z))))
   (if (<= t 3.2e+152)
     (+ x (* y (+ (/ (- t z) (- a t)) 1.0)))
     (+ x (* (- z a) (/ y t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.1e+150) {
		tmp = x - (y / (t / (a - z)));
	} else if (t <= 3.2e+152) {
		tmp = x + (y * (((t - z) / (a - t)) + 1.0));
	} else {
		tmp = x + ((z - a) * (y / 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 (t <= (-1.1d+150)) then
        tmp = x - (y / (t / (a - z)))
    else if (t <= 3.2d+152) then
        tmp = x + (y * (((t - z) / (a - t)) + 1.0d0))
    else
        tmp = x + ((z - a) * (y / 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 (t <= -1.1e+150) {
		tmp = x - (y / (t / (a - z)));
	} else if (t <= 3.2e+152) {
		tmp = x + (y * (((t - z) / (a - t)) + 1.0));
	} else {
		tmp = x + ((z - a) * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.1e+150:
		tmp = x - (y / (t / (a - z)))
	elif t <= 3.2e+152:
		tmp = x + (y * (((t - z) / (a - t)) + 1.0))
	else:
		tmp = x + ((z - a) * (y / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.1e+150)
		tmp = Float64(x - Float64(y / Float64(t / Float64(a - z))));
	elseif (t <= 3.2e+152)
		tmp = Float64(x + Float64(y * Float64(Float64(Float64(t - z) / Float64(a - t)) + 1.0)));
	else
		tmp = Float64(x + Float64(Float64(z - a) * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.1e+150)
		tmp = x - (y / (t / (a - z)));
	elseif (t <= 3.2e+152)
		tmp = x + (y * (((t - z) / (a - t)) + 1.0));
	else
		tmp = x + ((z - a) * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.1e+150], N[(x - N[(y / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+152], N[(x + N[(y * N[(N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - a), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1e150

   1. Initial program 32.5%

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

      1. associate-*l/ 54.8%

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

   3. Simplified 54.8%

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

   4. Taylor expanded in t around -inf 69.2%

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

      1. +-commutative 69.2%

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

      2. mul-1-neg 69.2%

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

      3. unsub-neg 69.2%

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

      4. distribute-lft-out-- 69.7%

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

   6. Simplified 69.7%

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

      1. expm1-log1p-u 65.5%

         \[\leadsto x - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(a - z\right)}{t}\right)\right)} \]

      2. expm1-udef 50.7%

         \[\leadsto x - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - z\right)}{t}\right)} - 1\right)} \]

   8. Applied egg-rr 50.7%

      \[\leadsto x - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - z\right)}{t}\right)} - 1\right)} \]
   9. Step-by-step derivation

      1. expm1-def 65.5%

         \[\leadsto x - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(a - z\right)}{t}\right)\right)} \]

      2. expm1-log1p 69.7%

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

      3. associate-/l* 88.8%

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

   10. Simplified 88.8%

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

   if -1.1e150 < t < 3.20000000000000005e152

   1. Initial program 89.9%

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

      1. associate--l+ 91.9%

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

      2. sub-neg 91.9%

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

      3. +-commutative 91.9%

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

      4. associate-/l* 95.9%

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

      5. distribute-neg-frac 95.9%

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

      6. associate-/r/ 94.8%

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

      7. fma-def 94.8%

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

      8. sub-neg 94.8%

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

      9. +-commutative 94.8%

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

      10. distribute-neg-in 94.8%

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

      11. unsub-neg 94.8%

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

      12. remove-double-neg 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in y around 0 95.8%

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

      1. associate--l+ 94.7%

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

      2. div-sub 94.7%

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

   6. Simplified 94.7%

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

   if 3.20000000000000005e152 < t

   1. Initial program 47.1%

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

      1. associate-*l/ 59.1%

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

   3. Simplified 59.1%

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

   4. Taylor expanded in y around 0 82.4%

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

   5. Taylor expanded in t around inf 78.7%

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

      1. mul-1-neg 78.7%

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

      2. neg-mul-1 78.7%

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

      3. +-commutative 78.7%

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

      4. sub-neg 78.7%

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

      5. associate-*r/ 89.1%

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

      6. distribute-lft-neg-in 89.1%

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

      7. sub-neg 89.1%

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

      8. +-commutative 89.1%

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

      9. distribute-neg-in 89.1%

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

      10. remove-double-neg 89.1%

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

      11. sub-neg 89.1%

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

   7. Simplified 89.1%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+150}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+152}:\\ \;\;\;\;x + y \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - a\right) \cdot \frac{y}{t}\\ \end{array} \]

Alternative 4: 93.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ y \cdot \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) + x \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (* y (- (+ (/ t (- a t)) 1.0) (/ z (- a t)))) x))

C

double code(double x, double y, double z, double t, double a) {
	return (y * (((t / (a - t)) + 1.0) - (z / (a - t)))) + x;
}

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 = (y * (((t / (a - t)) + 1.0d0) - (z / (a - t)))) + x
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (y * (((t / (a - t)) + 1.0) - (z / (a - t)))) + x;
}

Python

def code(x, y, z, t, a):
	return (y * (((t / (a - t)) + 1.0) - (z / (a - t)))) + x

Julia

function code(x, y, z, t, a)
	return Float64(Float64(y * Float64(Float64(Float64(t / Float64(a - t)) + 1.0) - Float64(z / Float64(a - t)))) + x)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (y * (((t / (a - t)) + 1.0) - (z / (a - t)))) + x;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(y * N[(N[(N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] - N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 77.1%

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

   1. associate-*l/ 83.5%

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

3. Simplified 83.5%

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

4. Taylor expanded in y around 0 91.9%

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

5. Final simplification 91.9%

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

Alternative 5: 86.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+152}:\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{+73}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{t}{a - t} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.75e+152)
   (+ y (- x (/ y (/ a z))))
   (if (<= a 9.8e+73)
     (- x (* z (/ y (- a t))))
     (+ x (* y (+ (/ t (- a t)) 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.75e+152) {
		tmp = y + (x - (y / (a / z)));
	} else if (a <= 9.8e+73) {
		tmp = x - (z * (y / (a - t)));
	} else {
		tmp = x + (y * ((t / (a - t)) + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.75d+152)) then
        tmp = y + (x - (y / (a / z)))
    else if (a <= 9.8d+73) then
        tmp = x - (z * (y / (a - t)))
    else
        tmp = x + (y * ((t / (a - t)) + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.75e+152) {
		tmp = y + (x - (y / (a / z)));
	} else if (a <= 9.8e+73) {
		tmp = x - (z * (y / (a - t)));
	} else {
		tmp = x + (y * ((t / (a - t)) + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.75e+152:
		tmp = y + (x - (y / (a / z)))
	elif a <= 9.8e+73:
		tmp = x - (z * (y / (a - t)))
	else:
		tmp = x + (y * ((t / (a - t)) + 1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.75e+152)
		tmp = Float64(y + Float64(x - Float64(y / Float64(a / z))));
	elseif (a <= 9.8e+73)
		tmp = Float64(x - Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t / Float64(a - t)) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.75e+152)
		tmp = y + (x - (y / (a / z)));
	elseif (a <= 9.8e+73)
		tmp = x - (z * (y / (a - t)));
	else
		tmp = x + (y * ((t / (a - t)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.75e+152], N[(y + N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.8e+73], N[(x - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.74999999999999991e152

   1. Initial program 74.9%

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

      1. associate-*l/ 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in t around 0 82.1%

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

      1. associate--l+ 82.1%

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

      2. associate-/l* 90.2%

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

   6. Simplified 90.2%

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

   if -1.74999999999999991e152 < a < 9.7999999999999998e73

   1. Initial program 78.3%

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

      1. associate--l+ 83.0%

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

      2. sub-neg 83.0%

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

      3. +-commutative 83.0%

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

      4. associate-/l* 85.8%

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

      5. distribute-neg-frac 85.8%

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

      6. associate-/r/ 85.9%

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

      7. fma-def 85.9%

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

      8. sub-neg 85.9%

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

      9. +-commutative 85.9%

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

      10. distribute-neg-in 85.9%

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

      11. unsub-neg 85.9%

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

      12. remove-double-neg 85.9%

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

   3. Simplified 85.9%

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

   4. Taylor expanded in z around inf 85.5%

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

      1. mul-1-neg 85.5%

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

      2. *-commutative 85.5%

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

      3. associate-*r/ 86.9%

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

      4. distribute-lft-neg-in 86.9%

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

   6. Simplified 86.9%

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

   if 9.7999999999999998e73 < a

   1. Initial program 75.0%

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

      1. associate-*l/ 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in y around 0 94.5%

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

   5. Taylor expanded in z around 0 89.2%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+152}:\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{+73}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{t}{a - t} + 1\right)\\ \end{array} \]

Alternative 6: 88.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.52 \cdot 10^{+140}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+141}:\\ \;\;\;\;\left(y + x\right) - y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - a\right) \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.52e+140)
   (- x (/ y (/ t (- a z))))
   (if (<= t 4.4e+141)
     (- (+ y x) (* y (/ z (- a t))))
     (+ x (* (- z a) (/ y t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.52e+140) {
		tmp = x - (y / (t / (a - z)));
	} else if (t <= 4.4e+141) {
		tmp = (y + x) - (y * (z / (a - t)));
	} else {
		tmp = x + ((z - a) * (y / 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 (t <= (-1.52d+140)) then
        tmp = x - (y / (t / (a - z)))
    else if (t <= 4.4d+141) then
        tmp = (y + x) - (y * (z / (a - t)))
    else
        tmp = x + ((z - a) * (y / 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 (t <= -1.52e+140) {
		tmp = x - (y / (t / (a - z)));
	} else if (t <= 4.4e+141) {
		tmp = (y + x) - (y * (z / (a - t)));
	} else {
		tmp = x + ((z - a) * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.52e+140:
		tmp = x - (y / (t / (a - z)))
	elif t <= 4.4e+141:
		tmp = (y + x) - (y * (z / (a - t)))
	else:
		tmp = x + ((z - a) * (y / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.52e+140)
		tmp = Float64(x - Float64(y / Float64(t / Float64(a - z))));
	elseif (t <= 4.4e+141)
		tmp = Float64(Float64(y + x) - Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(x + Float64(Float64(z - a) * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.52e+140)
		tmp = x - (y / (t / (a - z)));
	elseif (t <= 4.4e+141)
		tmp = (y + x) - (y * (z / (a - t)));
	else
		tmp = x + ((z - a) * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.52e+140], N[(x - N[(y / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e+141], N[(N[(y + x), $MachinePrecision] - N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - a), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.52e140

   1. Initial program 33.6%

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

      1. associate-*l/ 54.6%

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

   3. Simplified 54.6%

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

   4. Taylor expanded in t around -inf 68.1%

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

      1. +-commutative 68.1%

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

      2. mul-1-neg 68.1%

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

      3. unsub-neg 68.1%

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

      4. distribute-lft-out-- 68.6%

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

   6. Simplified 68.6%

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

      1. expm1-log1p-u 64.4%

         \[\leadsto x - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(a - z\right)}{t}\right)\right)} \]

      2. expm1-udef 50.4%

         \[\leadsto x - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - z\right)}{t}\right)} - 1\right)} \]

   8. Applied egg-rr 50.4%

      \[\leadsto x - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - z\right)}{t}\right)} - 1\right)} \]
   9. Step-by-step derivation

      1. expm1-def 64.4%

         \[\leadsto x - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(a - z\right)}{t}\right)\right)} \]

      2. expm1-log1p 68.6%

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

      3. associate-/l* 86.7%

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

   10. Simplified 86.7%

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

   if -1.52e140 < t < 4.4e141

   1. Initial program 90.3%

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

      1. associate-*l/ 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in z around inf 91.8%

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

   if 4.4e141 < t

   1. Initial program 47.1%

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

      1. associate-*l/ 59.1%

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

   3. Simplified 59.1%

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

   4. Taylor expanded in y around 0 82.4%

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

   5. Taylor expanded in t around inf 78.7%

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

      1. mul-1-neg 78.7%

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

      2. neg-mul-1 78.7%

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

      3. +-commutative 78.7%

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

      4. sub-neg 78.7%

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

      5. associate-*r/ 89.1%

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

      6. distribute-lft-neg-in 89.1%

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

      7. sub-neg 89.1%

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

      8. +-commutative 89.1%

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

      9. distribute-neg-in 89.1%

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

      10. remove-double-neg 89.1%

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

      11. sub-neg 89.1%

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

   7. Simplified 89.1%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.52 \cdot 10^{+140}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+141}:\\ \;\;\;\;\left(y + x\right) - y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - a\right) \cdot \frac{y}{t}\\ \end{array} \]

Alternative 7: 76.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+178}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-14}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 10^{+72}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.2e+178)
   (+ y x)
   (if (<= a -4.9e-14)
     (- x (/ y (/ a z)))
     (if (<= a 1e+72) (+ x (* y (/ z t))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.2e+178) {
		tmp = y + x;
	} else if (a <= -4.9e-14) {
		tmp = x - (y / (a / z));
	} else if (a <= 1e+72) {
		tmp = x + (y * (z / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.2d+178)) then
        tmp = y + x
    else if (a <= (-4.9d-14)) then
        tmp = x - (y / (a / z))
    else if (a <= 1d+72) then
        tmp = x + (y * (z / t))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.2e+178) {
		tmp = y + x;
	} else if (a <= -4.9e-14) {
		tmp = x - (y / (a / z));
	} else if (a <= 1e+72) {
		tmp = x + (y * (z / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.2e+178:
		tmp = y + x
	elif a <= -4.9e-14:
		tmp = x - (y / (a / z))
	elif a <= 1e+72:
		tmp = x + (y * (z / t))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.2e+178)
		tmp = Float64(y + x);
	elseif (a <= -4.9e-14)
		tmp = Float64(x - Float64(y / Float64(a / z)));
	elseif (a <= 1e+72)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.2e+178)
		tmp = y + x;
	elseif (a <= -4.9e-14)
		tmp = x - (y / (a / z));
	elseif (a <= 1e+72)
		tmp = x + (y * (z / t));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.2e+178], N[(y + x), $MachinePrecision], If[LessEqual[a, -4.9e-14], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e+72], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.2000000000000001e178 or 9.99999999999999944e71 < a

   1. Initial program 75.2%

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

      1. associate-*l/ 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in a around inf 87.9%

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

   if -5.2000000000000001e178 < a < -4.89999999999999995e-14

   1. Initial program 70.6%

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

      1. associate--l+ 70.6%

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

      2. sub-neg 70.6%

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

      3. +-commutative 70.6%

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

      4. associate-/l* 82.6%

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

      5. distribute-neg-frac 82.6%

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

      6. associate-/r/ 83.2%

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

      7. fma-def 83.2%

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

      8. sub-neg 83.2%

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

      9. +-commutative 83.2%

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

      10. distribute-neg-in 83.2%

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

      11. unsub-neg 83.2%

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

      12. remove-double-neg 83.2%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in z around inf 71.3%

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

      1. associate-*r/ 71.3%

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

      2. associate-*r* 71.3%

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

      3. neg-mul-1 71.3%

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

   6. Simplified 71.3%

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

   7. Taylor expanded in a around inf 70.2%

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

      1. mul-1-neg 70.2%

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

      2. associate-/l* 72.6%

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

      3. distribute-neg-frac 72.6%

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

   9. Simplified 72.6%

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

   if -4.89999999999999995e-14 < a < 9.99999999999999944e71

   1. Initial program 80.2%

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

      1. associate-*l/ 77.8%

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

   3. Simplified 77.8%

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

   4. Taylor expanded in y around 0 91.1%

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

   5. Taylor expanded in a around 0 74.2%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+178}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-14}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 10^{+72}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 8: 82.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-47} \lor \neg \left(t \leq 3.85 \cdot 10^{+77}\right):\\ \;\;\;\;x + \left(z - a\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.65e-47) (not (<= t 3.85e+77)))
   (+ x (* (- z a) (/ y t)))
   (+ y (- x (/ y (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.65e-47) || !(t <= 3.85e+77)) {
		tmp = x + ((z - a) * (y / t));
	} else {
		tmp = y + (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 ((t <= (-1.65d-47)) .or. (.not. (t <= 3.85d+77))) then
        tmp = x + ((z - a) * (y / t))
    else
        tmp = y + (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 ((t <= -1.65e-47) || !(t <= 3.85e+77)) {
		tmp = x + ((z - a) * (y / t));
	} else {
		tmp = y + (x - (y / (a / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.65e-47) or not (t <= 3.85e+77):
		tmp = x + ((z - a) * (y / t))
	else:
		tmp = y + (x - (y / (a / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.65e-47) || !(t <= 3.85e+77))
		tmp = Float64(x + Float64(Float64(z - a) * Float64(y / t)));
	else
		tmp = Float64(y + Float64(x - Float64(y / Float64(a / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.65e-47) || ~((t <= 3.85e+77)))
		tmp = x + ((z - a) * (y / t));
	else
		tmp = y + (x - (y / (a / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.65e-47], N[Not[LessEqual[t, 3.85e+77]], $MachinePrecision]], N[(x + N[(N[(z - a), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.65000000000000002e-47 or 3.8499999999999999e77 < t

   1. Initial program 56.8%

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

      1. associate-*l/ 70.8%

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

   3. Simplified 70.8%

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

   4. Taylor expanded in y around 0 87.5%

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

   5. Taylor expanded in t around inf 75.0%

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

      1. mul-1-neg 75.0%

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

      2. neg-mul-1 75.0%

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

      3. +-commutative 75.0%

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

      4. sub-neg 75.0%

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

      5. associate-*r/ 81.0%

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

      6. distribute-lft-neg-in 81.0%

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

      7. sub-neg 81.0%

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

      8. +-commutative 81.0%

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

      9. distribute-neg-in 81.0%

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

      10. remove-double-neg 81.0%

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

      11. sub-neg 81.0%

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

   7. Simplified 81.0%

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

   if -1.65000000000000002e-47 < t < 3.8499999999999999e77

   1. Initial program 94.4%

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

      1. associate-*l/ 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in t around 0 85.3%

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

      1. associate--l+ 85.3%

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

      2. associate-/l* 85.4%

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

   6. Simplified 85.4%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-47} \lor \neg \left(t \leq 3.85 \cdot 10^{+77}\right):\\ \;\;\;\;x + \left(z - a\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \end{array} \]

Alternative 9: 87.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+152} \lor \neg \left(a \leq 4.4 \cdot 10^{+73}\right):\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.75e+152) (not (<= a 4.4e+73)))
   (+ y (- x (/ y (/ a z))))
   (- x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.75e+152) || !(a <= 4.4e+73)) {
		tmp = y + (x - (y / (a / z)));
	} else {
		tmp = x - (z * (y / (a - 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 ((a <= (-1.75d+152)) .or. (.not. (a <= 4.4d+73))) then
        tmp = y + (x - (y / (a / z)))
    else
        tmp = x - (z * (y / (a - 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 ((a <= -1.75e+152) || !(a <= 4.4e+73)) {
		tmp = y + (x - (y / (a / z)));
	} else {
		tmp = x - (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.75e+152) or not (a <= 4.4e+73):
		tmp = y + (x - (y / (a / z)))
	else:
		tmp = x - (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.75e+152) || !(a <= 4.4e+73))
		tmp = Float64(y + Float64(x - Float64(y / Float64(a / z))));
	else
		tmp = Float64(x - Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.75e+152) || ~((a <= 4.4e+73)))
		tmp = y + (x - (y / (a / z)));
	else
		tmp = x - (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.75e+152], N[Not[LessEqual[a, 4.4e+73]], $MachinePrecision]], N[(y + N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.74999999999999991e152 or 4.4e73 < a

   1. Initial program 74.9%

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

      1. associate-*l/ 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in t around 0 81.1%

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

      1. associate--l+ 81.1%

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

      2. associate-/l* 88.6%

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

   6. Simplified 88.6%

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

   if -1.74999999999999991e152 < a < 4.4e73

   1. Initial program 78.3%

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

      1. associate--l+ 83.0%

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

      2. sub-neg 83.0%

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

      3. +-commutative 83.0%

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

      4. associate-/l* 85.8%

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

      5. distribute-neg-frac 85.8%

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

      6. associate-/r/ 85.9%

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

      7. fma-def 85.9%

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

      8. sub-neg 85.9%

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

      9. +-commutative 85.9%

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

      10. distribute-neg-in 85.9%

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

      11. unsub-neg 85.9%

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

      12. remove-double-neg 85.9%

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

   3. Simplified 85.9%

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

   4. Taylor expanded in z around inf 85.5%

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

      1. mul-1-neg 85.5%

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

      2. *-commutative 85.5%

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

      3. associate-*r/ 86.9%

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

      4. distribute-lft-neg-in 86.9%

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

   6. Simplified 86.9%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+152} \lor \neg \left(a \leq 4.4 \cdot 10^{+73}\right):\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 10: 79.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-47}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+77}:\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.8e-47)
   (+ x (* y (/ z t)))
   (if (<= t 2.7e+77) (+ y (- x (/ y (/ a z)))) (+ x (* z (/ y t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.8e-47) {
		tmp = x + (y * (z / t));
	} else if (t <= 2.7e+77) {
		tmp = y + (x - (y / (a / z)));
	} else {
		tmp = x + (z * (y / 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 (t <= (-3.8d-47)) then
        tmp = x + (y * (z / t))
    else if (t <= 2.7d+77) then
        tmp = y + (x - (y / (a / z)))
    else
        tmp = x + (z * (y / 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 (t <= -3.8e-47) {
		tmp = x + (y * (z / t));
	} else if (t <= 2.7e+77) {
		tmp = y + (x - (y / (a / z)));
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.8e-47:
		tmp = x + (y * (z / t))
	elif t <= 2.7e+77:
		tmp = y + (x - (y / (a / z)))
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.8e-47)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (t <= 2.7e+77)
		tmp = Float64(y + Float64(x - Float64(y / Float64(a / z))));
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.8e-47)
		tmp = x + (y * (z / t));
	elseif (t <= 2.7e+77)
		tmp = y + (x - (y / (a / z)));
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.8e-47], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e+77], N[(y + N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.80000000000000015e-47

   1. Initial program 57.4%

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

      1. associate-*l/ 72.2%

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

   3. Simplified 72.2%

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

   4. Taylor expanded in y around 0 87.5%

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

   5. Taylor expanded in a around 0 71.9%

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

   if -3.80000000000000015e-47 < t < 2.6999999999999998e77

   1. Initial program 94.4%

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

      1. associate-*l/ 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in t around 0 85.3%

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

      1. associate--l+ 85.3%

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

      2. associate-/l* 85.4%

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

   6. Simplified 85.4%

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

   if 2.6999999999999998e77 < t

   1. Initial program 55.7%

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

      1. associate-*l/ 68.5%

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

   3. Simplified 68.5%

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

   4. Taylor expanded in y around 0 87.6%

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

   5. Taylor expanded in a around 0 71.3%

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

      1. associate-/l* 72.7%

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

   7. Simplified 72.7%

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

      1. associate-/r/ 72.7%

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

   9. Applied egg-rr 72.7%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-47}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+77}:\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 11: 82.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-47}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+77}:\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - a\right) \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.8e-47)
   (- x (/ y (/ t (- a z))))
   (if (<= t 3.2e+77) (+ y (- x (/ y (/ a z)))) (+ x (* (- z a) (/ y t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.8e-47) {
		tmp = x - (y / (t / (a - z)));
	} else if (t <= 3.2e+77) {
		tmp = y + (x - (y / (a / z)));
	} else {
		tmp = x + ((z - a) * (y / 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 (t <= (-3.8d-47)) then
        tmp = x - (y / (t / (a - z)))
    else if (t <= 3.2d+77) then
        tmp = y + (x - (y / (a / z)))
    else
        tmp = x + ((z - a) * (y / 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 (t <= -3.8e-47) {
		tmp = x - (y / (t / (a - z)));
	} else if (t <= 3.2e+77) {
		tmp = y + (x - (y / (a / z)));
	} else {
		tmp = x + ((z - a) * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.8e-47:
		tmp = x - (y / (t / (a - z)))
	elif t <= 3.2e+77:
		tmp = y + (x - (y / (a / z)))
	else:
		tmp = x + ((z - a) * (y / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.8e-47)
		tmp = Float64(x - Float64(y / Float64(t / Float64(a - z))));
	elseif (t <= 3.2e+77)
		tmp = Float64(y + Float64(x - Float64(y / Float64(a / z))));
	else
		tmp = Float64(x + Float64(Float64(z - a) * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.8e-47)
		tmp = x - (y / (t / (a - z)));
	elseif (t <= 3.2e+77)
		tmp = y + (x - (y / (a / z)));
	else
		tmp = x + ((z - a) * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.8e-47], N[(x - N[(y / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+77], N[(y + N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - a), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.80000000000000015e-47

   1. Initial program 57.4%

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

      1. associate-*l/ 72.2%

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

   3. Simplified 72.2%

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

   4. Taylor expanded in t around -inf 72.8%

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

      1. +-commutative 72.8%

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

      2. mul-1-neg 72.8%

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

      3. unsub-neg 72.8%

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

      4. distribute-lft-out-- 73.0%

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

   6. Simplified 73.0%

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

      1. expm1-log1p-u 51.8%

         \[\leadsto x - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(a - z\right)}{t}\right)\right)} \]

      2. expm1-udef 43.7%

         \[\leadsto x - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - z\right)}{t}\right)} - 1\right)} \]

   8. Applied egg-rr 43.7%

      \[\leadsto x - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot \left(a - z\right)}{t}\right)} - 1\right)} \]
   9. Step-by-step derivation

      1. expm1-def 51.8%

         \[\leadsto x - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(a - z\right)}{t}\right)\right)} \]

      2. expm1-log1p 73.0%

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

      3. associate-/l* 82.0%

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

   10. Simplified 82.0%

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

   if -3.80000000000000015e-47 < t < 3.2000000000000002e77

   1. Initial program 94.4%

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

      1. associate-*l/ 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in t around 0 85.3%

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

      1. associate--l+ 85.3%

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

      2. associate-/l* 85.4%

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

   6. Simplified 85.4%

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

   if 3.2000000000000002e77 < t

   1. Initial program 55.7%

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

      1. associate-*l/ 68.5%

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

   3. Simplified 68.5%

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

   4. Taylor expanded in y around 0 87.6%

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

   5. Taylor expanded in t around inf 78.2%

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

      1. mul-1-neg 78.2%

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

      2. neg-mul-1 78.2%

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

      3. +-commutative 78.2%

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

      4. sub-neg 78.2%

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

      5. associate-*r/ 85.5%

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

      6. distribute-lft-neg-in 85.5%

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

      7. sub-neg 85.5%

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

      8. +-commutative 85.5%

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

      9. distribute-neg-in 85.5%

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

      10. remove-double-neg 85.5%

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

      11. sub-neg 85.5%

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

   7. Simplified 85.5%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-47}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+77}:\\ \;\;\;\;y + \left(x - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - a\right) \cdot \frac{y}{t}\\ \end{array} \]

Alternative 12: 77.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+23}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+71}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.9e+23) (+ y x) (if (<= a 8.2e+71) (+ x (* y (/ z t))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.9e+23) {
		tmp = y + x;
	} else if (a <= 8.2e+71) {
		tmp = x + (y * (z / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.9d+23)) then
        tmp = y + x
    else if (a <= 8.2d+71) then
        tmp = x + (y * (z / t))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.9e+23) {
		tmp = y + x;
	} else if (a <= 8.2e+71) {
		tmp = x + (y * (z / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.9e+23:
		tmp = y + x
	elif a <= 8.2e+71:
		tmp = x + (y * (z / t))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.9e+23)
		tmp = Float64(y + x);
	elseif (a <= 8.2e+71)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.9e+23)
		tmp = y + x;
	elseif (a <= 8.2e+71)
		tmp = x + (y * (z / t));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.9e+23], N[(y + x), $MachinePrecision], If[LessEqual[a, 8.2e+71], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.89999999999999987e23 or 8.2000000000000004e71 < a

   1. Initial program 73.0%

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

      1. associate-*l/ 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in a around inf 79.8%

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

   if -1.89999999999999987e23 < a < 8.2000000000000004e71

   1. Initial program 80.5%

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

      1. associate-*l/ 78.7%

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

   3. Simplified 78.7%

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

   4. Taylor expanded in y around 0 91.5%

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

   5. Taylor expanded in a around 0 72.8%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+23}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+71}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 13: 61.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.08 \cdot 10^{+214}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= t 1.08e+214) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.08e+214) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= 1.08d+214) then
        tmp = y + x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.08e+214) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 1.08e+214:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 1.08e+214)
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 1.08e+214)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 1.08e+214], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < 1.08e214

   1. Initial program 80.4%

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

      1. associate-*l/ 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in a around inf 61.9%

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

   if 1.08e214 < t

   1. Initial program 46.2%

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

      1. associate-*l/ 57.0%

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

   3. Simplified 57.0%

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

   4. Taylor expanded in x around inf 64.9%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.08 \cdot 10^{+214}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 51.2% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.1%

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

   1. associate-*l/ 83.5%

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

3. Simplified 83.5%

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

4. Taylor expanded in x around inf 50.1%

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

5. Final simplification 50.1%

   \[\leadsto x \]

Developer target: 87.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t_2 < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (< t_2 -1.3664970889390727e-7)
     t_1
     (if (< t_2 1.4754293444577233e-239)
       (/ (- (* y (- a z)) (* x t)) (- a t))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y + x) - (((z - t) * (1.0d0 / (a - t))) * y)
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 < (-1.3664970889390727d-7)) then
        tmp = t_1
    else if (t_2 < 1.4754293444577233d-239) then
        tmp = ((y * (a - z)) - (x * t)) / (a - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 < -1.3664970889390727e-7:
		tmp = t_1
	elif t_2 < 1.4754293444577233e-239:
		tmp = ((y * (a - z)) - (x * t)) / (a - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) - Float64(Float64(Float64(z - t) * Float64(1.0 / Float64(a - t))) * y))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = Float64(Float64(Float64(y * Float64(a - z)) - Float64(x * t)) / Float64(a - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -1.3664970889390727e-7], t$95$1, If[Less[t$95$2, 1.4754293444577233e-239], N[(N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2023171 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-7) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y))))

  (- (+ x y) (/ (* (- z t) y) (- a t))))