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

Percentage Accurate: 76.8% → 89.9%

Time: 16.2s

Alternatives: 16

Speedup: 1.0×

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: 76.8% 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: 89.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-161}:\\ \;\;\;\;x + \left(y - \frac{z - t}{\frac{a - t}{y}}\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;x - y \cdot \left(\frac{z}{a - t} + \frac{a}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + y \cdot \frac{t - z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* y (- z t)) (- a t)))))
   (if (<= t_1 -2e-161)
     (+ x (- y (/ (- z t) (/ (- a t) y))))
     (if (<= t_1 0.0)
       (- x (* y (+ (/ z (- a t)) (/ a t))))
       (+ (+ x y) (* y (/ (- t z) (- a t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - ((y * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -2e-161) {
		tmp = x + (y - ((z - t) / ((a - t) / y)));
	} else if (t_1 <= 0.0) {
		tmp = x - (y * ((z / (a - t)) + (a / t)));
	} else {
		tmp = (x + y) + (y * ((t - z) / (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) :: t_1
    real(8) :: tmp
    t_1 = (x + y) - ((y * (z - t)) / (a - t))
    if (t_1 <= (-2d-161)) then
        tmp = x + (y - ((z - t) / ((a - t) / y)))
    else if (t_1 <= 0.0d0) then
        tmp = x - (y * ((z / (a - t)) + (a / t)))
    else
        tmp = (x + y) + (y * ((t - z) / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - ((y * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -2e-161) {
		tmp = x + (y - ((z - t) / ((a - t) / y)));
	} else if (t_1 <= 0.0) {
		tmp = x - (y * ((z / (a - t)) + (a / t)));
	} else {
		tmp = (x + y) + (y * ((t - z) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - ((y * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -2e-161:
		tmp = x + (y - ((z - t) / ((a - t) / y)))
	elif t_1 <= 0.0:
		tmp = x - (y * ((z / (a - t)) + (a / t)))
	else:
		tmp = (x + y) + (y * ((t - z) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(y * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -2e-161)
		tmp = Float64(x + Float64(y - Float64(Float64(z - t) / Float64(Float64(a - t) / y))));
	elseif (t_1 <= 0.0)
		tmp = Float64(x - Float64(y * Float64(Float64(z / Float64(a - t)) + Float64(a / t))));
	else
		tmp = Float64(Float64(x + y) + Float64(y * Float64(Float64(t - z) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - ((y * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -2e-161)
		tmp = x + (y - ((z - t) / ((a - t) / y)));
	elseif (t_1 <= 0.0)
		tmp = x - (y * ((z / (a - t)) + (a / t)));
	else
		tmp = (x + y) + (y * ((t - z) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-161], N[(x + N[(y - N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(x - N[(y * N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] + N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(y * N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -2.00000000000000006e-161

   1. Initial program 86.6%

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

      1. associate--l+ 86.7%

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

      2. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   if -2.00000000000000006e-161 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 26.5%

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

      1. associate--l+ 58.9%

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

      2. associate-/l* 48.7%

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

   3. Simplified 48.7%

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

   4. Taylor expanded in y around 0 78.6%

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

   5. Taylor expanded in t around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

   7. Simplified 100.0%

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

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

   1. Initial program 87.0%

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

      1. associate--l+ 87.0%

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

      2. associate-/l* 92.6%

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

   3. Simplified 92.6%

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

      1. associate-+r- 91.0%

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

      2. +-commutative 91.0%

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

      3. associate-/r/ 94.1%

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

   5. Applied egg-rr 94.1%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-161}:\\ \;\;\;\;x + \left(y - \frac{z - t}{\frac{a - t}{y}}\right)\\ \mathbf{elif}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;x - y \cdot \left(\frac{z}{a - t} + \frac{a}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + y \cdot \frac{t - z}{a - t}\\ \end{array} \]

Alternative 2: 91.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-222} \lor \neg \left(t_1 \leq 2 \cdot 10^{-173}\right):\\ \;\;\;\;x + \left(y - \frac{z - t}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* y (- z t)) (- a t)))))
   (if (or (<= t_1 -5e-222) (not (<= t_1 2e-173)))
     (+ x (- y (/ (- z t) (/ (- a t) y))))
     (+ x (/ (* y (- z a)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - ((y * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -5e-222) || !(t_1 <= 2e-173)) {
		tmp = x + (y - ((z - t) / ((a - t) / y)));
	} else {
		tmp = x + ((y * (z - 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) :: t_1
    real(8) :: tmp
    t_1 = (x + y) - ((y * (z - t)) / (a - t))
    if ((t_1 <= (-5d-222)) .or. (.not. (t_1 <= 2d-173))) then
        tmp = x + (y - ((z - t) / ((a - t) / y)))
    else
        tmp = x + ((y * (z - a)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - ((y * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -5e-222) || !(t_1 <= 2e-173)) {
		tmp = x + (y - ((z - t) / ((a - t) / y)));
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - ((y * (z - t)) / (a - t))
	tmp = 0
	if (t_1 <= -5e-222) or not (t_1 <= 2e-173):
		tmp = x + (y - ((z - t) / ((a - t) / y)))
	else:
		tmp = x + ((y * (z - a)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(y * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -5e-222) || !(t_1 <= 2e-173))
		tmp = Float64(x + Float64(y - Float64(Float64(z - t) / Float64(Float64(a - t) / y))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - ((y * (z - t)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -5e-222) || ~((t_1 <= 2e-173)))
		tmp = x + (y - ((z - t) / ((a - t) / y)));
	else
		tmp = x + ((y * (z - a)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-222], N[Not[LessEqual[t$95$1, 2e-173]], $MachinePrecision]], N[(x + N[(y - N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -5.00000000000000008e-222 or 2.0000000000000001e-173 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 86.8%

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

      1. associate--l+ 86.8%

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

      2. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

   if -5.00000000000000008e-222 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 2.0000000000000001e-173

   1. Initial program 20.9%

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

      1. associate--l+ 56.6%

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

      2. associate-/l* 36.8%

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

   3. Simplified 36.8%

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

   4. Taylor expanded in y around 0 76.4%

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

      1. clear-num 76.4%

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

      2. inv-pow 76.4%

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

   6. Applied egg-rr 76.4%

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

      1. unpow-1 76.4%

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

   8. Simplified 76.4%

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

   9. Taylor expanded in t around inf 96.4%

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

       1. mul-1-neg 96.4%

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

       2. mul-1-neg 96.4%

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

       3. sub-neg 96.4%

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

   11. Simplified 96.4%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-222} \lor \neg \left(\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq 2 \cdot 10^{-173}\right):\\ \;\;\;\;x + \left(y - \frac{z - t}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \]

Alternative 3: 90.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-222}:\\ \;\;\;\;x + \left(y - \frac{z - t}{\frac{a - t}{y}}\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + y \cdot \frac{t - z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* y (- z t)) (- a t)))))
   (if (<= t_1 -5e-222)
     (+ x (- y (/ (- z t) (/ (- a t) y))))
     (if (<= t_1 0.0)
       (+ x (/ (* y (- z a)) t))
       (+ (+ x y) (* y (/ (- t z) (- a t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - ((y * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -5e-222) {
		tmp = x + (y - ((z - t) / ((a - t) / y)));
	} else if (t_1 <= 0.0) {
		tmp = x + ((y * (z - a)) / t);
	} else {
		tmp = (x + y) + (y * ((t - z) / (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) :: t_1
    real(8) :: tmp
    t_1 = (x + y) - ((y * (z - t)) / (a - t))
    if (t_1 <= (-5d-222)) then
        tmp = x + (y - ((z - t) / ((a - t) / y)))
    else if (t_1 <= 0.0d0) then
        tmp = x + ((y * (z - a)) / t)
    else
        tmp = (x + y) + (y * ((t - z) / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - ((y * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -5e-222) {
		tmp = x + (y - ((z - t) / ((a - t) / y)));
	} else if (t_1 <= 0.0) {
		tmp = x + ((y * (z - a)) / t);
	} else {
		tmp = (x + y) + (y * ((t - z) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - ((y * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -5e-222:
		tmp = x + (y - ((z - t) / ((a - t) / y)))
	elif t_1 <= 0.0:
		tmp = x + ((y * (z - a)) / t)
	else:
		tmp = (x + y) + (y * ((t - z) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(y * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -5e-222)
		tmp = Float64(x + Float64(y - Float64(Float64(z - t) / Float64(Float64(a - t) / y))));
	elseif (t_1 <= 0.0)
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	else
		tmp = Float64(Float64(x + y) + Float64(y * Float64(Float64(t - z) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - ((y * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -5e-222)
		tmp = x + (y - ((z - t) / ((a - t) / y)));
	elseif (t_1 <= 0.0)
		tmp = x + ((y * (z - a)) / t);
	else
		tmp = (x + y) + (y * ((t - z) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-222], N[(x + N[(y - N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(y * N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -5.00000000000000008e-222

   1. Initial program 86.8%

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

      1. associate--l+ 86.8%

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

      2. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   if -5.00000000000000008e-222 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 11.9%

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

      1. associate--l+ 51.7%

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

      2. associate-/l* 36.9%

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

   3. Simplified 36.9%

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

   4. Taylor expanded in y around 0 73.7%

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

      1. clear-num 73.7%

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

      2. inv-pow 73.7%

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

   6. Applied egg-rr 73.7%

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

      1. unpow-1 73.7%

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

   8. Simplified 73.7%

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

   9. Taylor expanded in t around inf 99.8%

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

       1. mul-1-neg 99.8%

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

       2. mul-1-neg 99.8%

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

       3. sub-neg 99.8%

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

   11. Simplified 99.8%

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

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

   1. Initial program 87.0%

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

      1. associate--l+ 87.0%

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

      2. associate-/l* 92.6%

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

   3. Simplified 92.6%

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

      1. associate-+r- 91.0%

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

      2. +-commutative 91.0%

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

      3. associate-/r/ 94.1%

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

   5. Applied egg-rr 94.1%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-222}:\\ \;\;\;\;x + \left(y - \frac{z - t}{\frac{a - t}{y}}\right)\\ \mathbf{elif}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + y \cdot \frac{t - z}{a - t}\\ \end{array} \]

Alternative 4: 93.5% accurate, 0.7× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x + (y * (((1.0 / ((a - t) / t)) + 1.0) - (z / (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 * (((1.0d0 / ((a - t) / t)) + 1.0d0) - (z / (a - t))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.3%

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

   1. associate--l+ 83.4%

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

   2. associate-/l* 88.9%

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

3. Simplified 88.9%

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

4. Taylor expanded in y around 0 94.0%

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

   1. clear-num 94.0%

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

   2. inv-pow 94.0%

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

6. Applied egg-rr 94.0%

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

   1. unpow-1 94.0%

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

8. Simplified 94.0%

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

9. Final simplification 94.0%

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

Alternative 5: 73.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{+116}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -450000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+199}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ t z)))))
   (if (<= a -4.8e+116)
     (+ x y)
     (if (<= a -2e+79)
       t_1
       (if (<= a -450000.0)
         (+ x y)
         (if (<= a 4.3e-110)
           t_1
           (if (<= a 8.5e+199) (- x (/ y (/ a z))) (+ x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (t / z));
	double tmp;
	if (a <= -4.8e+116) {
		tmp = x + y;
	} else if (a <= -2e+79) {
		tmp = t_1;
	} else if (a <= -450000.0) {
		tmp = x + y;
	} else if (a <= 4.3e-110) {
		tmp = t_1;
	} else if (a <= 8.5e+199) {
		tmp = x - (y / (a / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (t / z))
    if (a <= (-4.8d+116)) then
        tmp = x + y
    else if (a <= (-2d+79)) then
        tmp = t_1
    else if (a <= (-450000.0d0)) then
        tmp = x + y
    else if (a <= 4.3d-110) then
        tmp = t_1
    else if (a <= 8.5d+199) then
        tmp = x - (y / (a / z))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (t / z));
	double tmp;
	if (a <= -4.8e+116) {
		tmp = x + y;
	} else if (a <= -2e+79) {
		tmp = t_1;
	} else if (a <= -450000.0) {
		tmp = x + y;
	} else if (a <= 4.3e-110) {
		tmp = t_1;
	} else if (a <= 8.5e+199) {
		tmp = x - (y / (a / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (t / z))
	tmp = 0
	if a <= -4.8e+116:
		tmp = x + y
	elif a <= -2e+79:
		tmp = t_1
	elif a <= -450000.0:
		tmp = x + y
	elif a <= 4.3e-110:
		tmp = t_1
	elif a <= 8.5e+199:
		tmp = x - (y / (a / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(t / z)))
	tmp = 0.0
	if (a <= -4.8e+116)
		tmp = Float64(x + y);
	elseif (a <= -2e+79)
		tmp = t_1;
	elseif (a <= -450000.0)
		tmp = Float64(x + y);
	elseif (a <= 4.3e-110)
		tmp = t_1;
	elseif (a <= 8.5e+199)
		tmp = Float64(x - Float64(y / Float64(a / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (t / z));
	tmp = 0.0;
	if (a <= -4.8e+116)
		tmp = x + y;
	elseif (a <= -2e+79)
		tmp = t_1;
	elseif (a <= -450000.0)
		tmp = x + y;
	elseif (a <= 4.3e-110)
		tmp = t_1;
	elseif (a <= 8.5e+199)
		tmp = x - (y / (a / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.8e+116], N[(x + y), $MachinePrecision], If[LessEqual[a, -2e+79], t$95$1, If[LessEqual[a, -450000.0], N[(x + y), $MachinePrecision], If[LessEqual[a, 4.3e-110], t$95$1, If[LessEqual[a, 8.5e+199], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.8000000000000001e116 or -1.99999999999999993e79 < a < -4.5e5 or 8.49999999999999923e199 < a

   1. Initial program 84.7%

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

      1. associate--l+ 87.2%

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

      2. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in a around inf 83.3%

      \[\leadsto \color{blue}{x + y} \]
   5. Step-by-step derivation

      1. +-commutative 83.3%

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

   6. Simplified 83.3%

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

   if -4.8000000000000001e116 < a < -1.99999999999999993e79 or -4.5e5 < a < 4.30000000000000025e-110

   1. Initial program 74.6%

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

      1. associate--l+ 80.1%

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

      2. associate-/l* 84.0%

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

   3. Simplified 84.0%

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

   4. Taylor expanded in y around 0 92.6%

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

   5. Taylor expanded in a around 0 81.4%

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

      1. +-commutative 81.4%

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

      2. associate-/l* 84.0%

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

   7. Simplified 84.0%

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

   if 4.30000000000000025e-110 < a < 8.49999999999999923e199

   1. Initial program 81.6%

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

      1. associate--l+ 84.8%

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

      2. associate-/l* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in z around inf 77.2%

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

      1. associate-*r/ 77.2%

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

      2. associate-*r* 77.2%

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

      3. neg-mul-1 77.2%

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

   6. Simplified 77.2%

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

   7. Taylor expanded in a around inf 72.8%

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

      1. mul-1-neg 72.8%

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

      2. unsub-neg 72.8%

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

      3. associate-/l* 75.7%

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

   9. Simplified 75.7%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+116}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2 \cdot 10^{+79}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq -450000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-110}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+199}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6: 83.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+157}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{+56}:\\ \;\;\;\;x - y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{+45}:\\ \;\;\;\;y + \frac{t}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+107}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.5e+157)
   (+ x y)
   (if (<= a -4.6e+56)
     (- x (* y (/ z (- a t))))
     (if (<= a -2.6e+45)
       (+ y (/ t (/ (- a t) y)))
       (if (<= a 4.4e+107) (- x (* z (/ y (- a t)))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.5e+157) {
		tmp = x + y;
	} else if (a <= -4.6e+56) {
		tmp = x - (y * (z / (a - t)));
	} else if (a <= -2.6e+45) {
		tmp = y + (t / ((a - t) / y));
	} else if (a <= 4.4e+107) {
		tmp = x - (z * (y / (a - t)));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.5d+157)) then
        tmp = x + y
    else if (a <= (-4.6d+56)) then
        tmp = x - (y * (z / (a - t)))
    else if (a <= (-2.6d+45)) then
        tmp = y + (t / ((a - t) / y))
    else if (a <= 4.4d+107) then
        tmp = x - (z * (y / (a - t)))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.5e+157) {
		tmp = x + y;
	} else if (a <= -4.6e+56) {
		tmp = x - (y * (z / (a - t)));
	} else if (a <= -2.6e+45) {
		tmp = y + (t / ((a - t) / y));
	} else if (a <= 4.4e+107) {
		tmp = x - (z * (y / (a - t)));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.5e+157:
		tmp = x + y
	elif a <= -4.6e+56:
		tmp = x - (y * (z / (a - t)))
	elif a <= -2.6e+45:
		tmp = y + (t / ((a - t) / y))
	elif a <= 4.4e+107:
		tmp = x - (z * (y / (a - t)))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.5e+157)
		tmp = Float64(x + y);
	elseif (a <= -4.6e+56)
		tmp = Float64(x - Float64(y * Float64(z / Float64(a - t))));
	elseif (a <= -2.6e+45)
		tmp = Float64(y + Float64(t / Float64(Float64(a - t) / y)));
	elseif (a <= 4.4e+107)
		tmp = Float64(x - Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.5e+157)
		tmp = x + y;
	elseif (a <= -4.6e+56)
		tmp = x - (y * (z / (a - t)));
	elseif (a <= -2.6e+45)
		tmp = y + (t / ((a - t) / y));
	elseif (a <= 4.4e+107)
		tmp = x - (z * (y / (a - t)));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.5e+157], N[(x + y), $MachinePrecision], If[LessEqual[a, -4.6e+56], N[(x - N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.6e+45], N[(y + N[(t / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.4e+107], N[(x - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.49999999999999988e157 or 4.4e107 < a

   1. Initial program 82.3%

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

      1. associate--l+ 82.3%

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

      2. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in a around inf 83.1%

      \[\leadsto \color{blue}{x + y} \]
   5. Step-by-step derivation

      1. +-commutative 83.1%

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

   6. Simplified 83.1%

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

   if -2.49999999999999988e157 < a < -4.60000000000000029e56

   1. Initial program 81.1%

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

      1. associate--l+ 83.9%

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

      2. associate-/l* 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in z around inf 79.7%

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

      1. associate-*r/ 79.7%

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

      2. associate-*r* 79.7%

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

      3. neg-mul-1 79.7%

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

   6. Simplified 79.7%

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

   7. Taylor expanded in x around 0 79.7%

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

      1. mul-1-neg 79.7%

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

      2. sub-neg 79.7%

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

      3. associate-*r/ 82.6%

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

   9. Simplified 82.6%

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

   if -4.60000000000000029e56 < a < -2.60000000000000007e45

   1. Initial program 84.6%

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

      1. associate--l+ 84.6%

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

      2. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 84.6%

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

   5. Taylor expanded in z around 0 68.3%

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

      1. sub-neg 68.3%

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

      2. mul-1-neg 68.3%

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

      3. remove-double-neg 68.3%

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

      4. associate-/l* 83.5%

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

   7. Simplified 83.5%

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

   if -2.60000000000000007e45 < a < 4.4e107

   1. Initial program 77.6%

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

      1. associate--l+ 83.6%

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

      2. associate-/l* 87.7%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in z around inf 86.7%

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

      1. associate-*r/ 86.7%

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

      2. associate-*r* 86.7%

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

      3. neg-mul-1 86.7%

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

   6. Simplified 86.7%

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

   7. Taylor expanded in x around 0 86.7%

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

      1. mul-1-neg 86.7%

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

      2. sub-neg 86.7%

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

      3. associate-*r/ 89.4%

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

   9. Simplified 89.4%

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

   10. Taylor expanded in y around 0 86.7%

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

       1. associate-*l/ 90.8%

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

       2. *-commutative 90.8%

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

   12. Simplified 90.8%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+157}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{+56}:\\ \;\;\;\;x - y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{+45}:\\ \;\;\;\;y + \frac{t}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+107}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7: 83.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+158}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{+56}:\\ \;\;\;\;x - y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{+45}:\\ \;\;\;\;y + \frac{t}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+105}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e+158)
   (+ x y)
   (if (<= a -4.6e+56)
     (- x (* y (/ z (- a t))))
     (if (<= a -2.6e+45)
       (+ y (/ t (/ (- a t) y)))
       (if (<= a 4.1e+105)
         (- x (* z (/ y (- a t))))
         (- (+ x y) (/ (* y z) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+158) {
		tmp = x + y;
	} else if (a <= -4.6e+56) {
		tmp = x - (y * (z / (a - t)));
	} else if (a <= -2.6e+45) {
		tmp = y + (t / ((a - t) / y));
	} else if (a <= 4.1e+105) {
		tmp = x - (z * (y / (a - t)));
	} else {
		tmp = (x + y) - ((y * z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9.5d+158)) then
        tmp = x + y
    else if (a <= (-4.6d+56)) then
        tmp = x - (y * (z / (a - t)))
    else if (a <= (-2.6d+45)) then
        tmp = y + (t / ((a - t) / y))
    else if (a <= 4.1d+105) then
        tmp = x - (z * (y / (a - t)))
    else
        tmp = (x + y) - ((y * z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+158) {
		tmp = x + y;
	} else if (a <= -4.6e+56) {
		tmp = x - (y * (z / (a - t)));
	} else if (a <= -2.6e+45) {
		tmp = y + (t / ((a - t) / y));
	} else if (a <= 4.1e+105) {
		tmp = x - (z * (y / (a - t)));
	} else {
		tmp = (x + y) - ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.5e+158:
		tmp = x + y
	elif a <= -4.6e+56:
		tmp = x - (y * (z / (a - t)))
	elif a <= -2.6e+45:
		tmp = y + (t / ((a - t) / y))
	elif a <= 4.1e+105:
		tmp = x - (z * (y / (a - t)))
	else:
		tmp = (x + y) - ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e+158)
		tmp = Float64(x + y);
	elseif (a <= -4.6e+56)
		tmp = Float64(x - Float64(y * Float64(z / Float64(a - t))));
	elseif (a <= -2.6e+45)
		tmp = Float64(y + Float64(t / Float64(Float64(a - t) / y)));
	elseif (a <= 4.1e+105)
		tmp = Float64(x - Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(Float64(x + y) - Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.5e+158)
		tmp = x + y;
	elseif (a <= -4.6e+56)
		tmp = x - (y * (z / (a - t)));
	elseif (a <= -2.6e+45)
		tmp = y + (t / ((a - t) / y));
	elseif (a <= 4.1e+105)
		tmp = x - (z * (y / (a - t)));
	else
		tmp = (x + y) - ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e+158], N[(x + y), $MachinePrecision], If[LessEqual[a, -4.6e+56], N[(x - N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.6e+45], N[(y + N[(t / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.1e+105], N[(x - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -9.49999999999999913e158

   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+ 73.2%

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

      2. associate-/l* 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in a around inf 88.3%

      \[\leadsto \color{blue}{x + y} \]
   5. Step-by-step derivation

      1. +-commutative 88.3%

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

   6. Simplified 88.3%

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

   if -9.49999999999999913e158 < a < -4.60000000000000029e56

   1. Initial program 81.1%

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

      1. associate--l+ 83.9%

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

      2. associate-/l* 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in z around inf 79.7%

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

      1. associate-*r/ 79.7%

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

      2. associate-*r* 79.7%

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

      3. neg-mul-1 79.7%

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

   6. Simplified 79.7%

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

   7. Taylor expanded in x around 0 79.7%

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

      1. mul-1-neg 79.7%

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

      2. sub-neg 79.7%

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

      3. associate-*r/ 82.6%

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

   9. Simplified 82.6%

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

   if -4.60000000000000029e56 < a < -2.60000000000000007e45

   1. Initial program 84.6%

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

      1. associate--l+ 84.6%

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

      2. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 84.6%

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

   5. Taylor expanded in z around 0 68.3%

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

      1. sub-neg 68.3%

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

      2. mul-1-neg 68.3%

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

      3. remove-double-neg 68.3%

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

      4. associate-/l* 83.5%

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

   7. Simplified 83.5%

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

   if -2.60000000000000007e45 < a < 4.1000000000000002e105

   1. Initial program 77.6%

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

      1. associate--l+ 83.6%

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

      2. associate-/l* 87.7%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in z around inf 86.7%

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

      1. associate-*r/ 86.7%

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

      2. associate-*r* 86.7%

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

      3. neg-mul-1 86.7%

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

   6. Simplified 86.7%

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

   7. Taylor expanded in x around 0 86.7%

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

      1. mul-1-neg 86.7%

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

      2. sub-neg 86.7%

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

      3. associate-*r/ 89.4%

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

   9. Simplified 89.4%

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

   10. Taylor expanded in y around 0 86.7%

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

       1. associate-*l/ 90.8%

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

       2. *-commutative 90.8%

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

   12. Simplified 90.8%

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

   if 4.1000000000000002e105 < a

   1. Initial program 93.0%

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

      1. associate--l+ 93.0%

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

      2. associate-/l* 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in t around 0 93.2%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+158}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{+56}:\\ \;\;\;\;x - y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{+45}:\\ \;\;\;\;y + \frac{t}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+105}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot z}{a}\\ \end{array} \]

Alternative 8: 93.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x + (y * (((t / (a - t)) + 1.0) - (z / (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 * (((t / (a - t)) + 1.0d0) - (z / (a - t))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.3%

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

   1. associate--l+ 83.4%

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

   2. associate-/l* 88.9%

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

3. Simplified 88.9%

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

4. Taylor expanded in y around 0 94.0%

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

5. Final simplification 94.0%

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

Alternative 9: 75.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.7 \cdot 10^{+116} \lor \neg \left(a \leq -3.2 \cdot 10^{+79} \lor \neg \left(a \leq -3900\right) \land a \leq 3.7 \cdot 10^{-19}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.7e+116)
         (not (or (<= a -3.2e+79) (and (not (<= a -3900.0)) (<= a 3.7e-19)))))
   (+ x y)
   (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.7e+116) || !((a <= -3.2e+79) || (!(a <= -3900.0) && (a <= 3.7e-19)))) {
		tmp = x + y;
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-5.7d+116)) .or. (.not. (a <= (-3.2d+79)) .or. (.not. (a <= (-3900.0d0))) .and. (a <= 3.7d-19))) then
        tmp = x + y
    else
        tmp = x + (y / (t / 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 ((a <= -5.7e+116) || !((a <= -3.2e+79) || (!(a <= -3900.0) && (a <= 3.7e-19)))) {
		tmp = x + y;
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.7e+116) or not ((a <= -3.2e+79) or (not (a <= -3900.0) and (a <= 3.7e-19))):
		tmp = x + y
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.7e+116) || !((a <= -3.2e+79) || (!(a <= -3900.0) && (a <= 3.7e-19))))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.7e+116) || ~(((a <= -3.2e+79) || (~((a <= -3900.0)) && (a <= 3.7e-19)))))
		tmp = x + y;
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.7e+116], N[Not[Or[LessEqual[a, -3.2e+79], And[N[Not[LessEqual[a, -3900.0]], $MachinePrecision], LessEqual[a, 3.7e-19]]]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.69999999999999983e116 or -3.20000000000000003e79 < a < -3900 or 3.70000000000000005e-19 < a

   1. Initial program 82.4%

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

      1. associate--l+ 84.8%

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

      2. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in a around inf 74.6%

      \[\leadsto \color{blue}{x + y} \]
   5. Step-by-step derivation

      1. +-commutative 74.6%

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

   6. Simplified 74.6%

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

   if -5.69999999999999983e116 < a < -3.20000000000000003e79 or -3900 < a < 3.70000000000000005e-19

   1. Initial program 76.5%

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

      1. associate--l+ 82.1%

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

      2. associate-/l* 85.5%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in y around 0 92.2%

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

   5. Taylor expanded in a around 0 80.4%

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

      1. +-commutative 80.4%

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

      2. associate-/l* 82.6%

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

   7. Simplified 82.6%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.7 \cdot 10^{+116} \lor \neg \left(a \leq -3.2 \cdot 10^{+79} \lor \neg \left(a \leq -3900\right) \land a \leq 3.7 \cdot 10^{-19}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 10: 59.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{-z}{a}\\ \mathbf{if}\;z \leq -9.4 \cdot 10^{+222}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-28}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-150}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+246}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z) a))))
   (if (<= z -9.4e+222)
     t_1
     (if (<= z -4.8e-28)
       (+ x y)
       (if (<= z -1.05e-150) x (if (<= z 9.2e+246) (+ x y) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (-z / a);
	double tmp;
	if (z <= -9.4e+222) {
		tmp = t_1;
	} else if (z <= -4.8e-28) {
		tmp = x + y;
	} else if (z <= -1.05e-150) {
		tmp = x;
	} else if (z <= 9.2e+246) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (-z / a)
    if (z <= (-9.4d+222)) then
        tmp = t_1
    else if (z <= (-4.8d-28)) then
        tmp = x + y
    else if (z <= (-1.05d-150)) then
        tmp = x
    else if (z <= 9.2d+246) then
        tmp = x + y
    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 * (-z / a);
	double tmp;
	if (z <= -9.4e+222) {
		tmp = t_1;
	} else if (z <= -4.8e-28) {
		tmp = x + y;
	} else if (z <= -1.05e-150) {
		tmp = x;
	} else if (z <= 9.2e+246) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (-z / a)
	tmp = 0
	if z <= -9.4e+222:
		tmp = t_1
	elif z <= -4.8e-28:
		tmp = x + y
	elif z <= -1.05e-150:
		tmp = x
	elif z <= 9.2e+246:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(-z) / a))
	tmp = 0.0
	if (z <= -9.4e+222)
		tmp = t_1;
	elseif (z <= -4.8e-28)
		tmp = Float64(x + y);
	elseif (z <= -1.05e-150)
		tmp = x;
	elseif (z <= 9.2e+246)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (-z / a);
	tmp = 0.0;
	if (z <= -9.4e+222)
		tmp = t_1;
	elseif (z <= -4.8e-28)
		tmp = x + y;
	elseif (z <= -1.05e-150)
		tmp = x;
	elseif (z <= 9.2e+246)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[((-z) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.4e+222], t$95$1, If[LessEqual[z, -4.8e-28], N[(x + y), $MachinePrecision], If[LessEqual[z, -1.05e-150], x, If[LessEqual[z, 9.2e+246], N[(x + y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.3999999999999998e222 or 9.20000000000000055e246 < z

   1. Initial program 81.6%

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

      1. associate--l+ 81.6%

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

      2. associate-/l* 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in x around 0 70.5%

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

   5. Taylor expanded in t around 0 43.7%

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

   6. Taylor expanded in z around inf 43.7%

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

      1. mul-1-neg 43.7%

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

      2. associate-*r/ 52.3%

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

      3. distribute-rgt-neg-in 52.3%

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

      4. mul-1-neg 52.3%

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

      5. associate-*r/ 52.3%

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

      6. mul-1-neg 52.3%

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

   8. Simplified 52.3%

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

   if -9.3999999999999998e222 < z < -4.8000000000000004e-28 or -1.0500000000000001e-150 < z < 9.20000000000000055e246

   1. Initial program 80.3%

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

      1. associate--l+ 84.0%

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

      2. associate-/l* 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in a around inf 67.3%

      \[\leadsto \color{blue}{x + y} \]
   5. Step-by-step derivation

      1. +-commutative 67.3%

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

   6. Simplified 67.3%

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

   if -4.8000000000000004e-28 < z < -1.0500000000000001e-150

   1. Initial program 71.8%

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

      1. associate--l+ 81.9%

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

      2. associate-/l* 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in x around inf 78.2%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{+222}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-28}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-150}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+246}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \end{array} \]

Alternative 11: 59.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+223}:\\ \;\;\;\;z \cdot \left(-\frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-27}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-151}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+250}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.5e+223)
   (* z (- (/ y a)))
   (if (<= z -1.32e-27)
     (+ x y)
     (if (<= z -6e-151) x (if (<= z 9.8e+250) (+ x y) (* y (/ (- z) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+223) {
		tmp = z * -(y / a);
	} else if (z <= -1.32e-27) {
		tmp = x + y;
	} else if (z <= -6e-151) {
		tmp = x;
	} else if (z <= 9.8e+250) {
		tmp = x + y;
	} else {
		tmp = y * (-z / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.5d+223)) then
        tmp = z * -(y / a)
    else if (z <= (-1.32d-27)) then
        tmp = x + y
    else if (z <= (-6d-151)) then
        tmp = x
    else if (z <= 9.8d+250) then
        tmp = x + y
    else
        tmp = y * (-z / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+223) {
		tmp = z * -(y / a);
	} else if (z <= -1.32e-27) {
		tmp = x + y;
	} else if (z <= -6e-151) {
		tmp = x;
	} else if (z <= 9.8e+250) {
		tmp = x + y;
	} else {
		tmp = y * (-z / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.5e+223:
		tmp = z * -(y / a)
	elif z <= -1.32e-27:
		tmp = x + y
	elif z <= -6e-151:
		tmp = x
	elif z <= 9.8e+250:
		tmp = x + y
	else:
		tmp = y * (-z / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.5e+223)
		tmp = Float64(z * Float64(-Float64(y / a)));
	elseif (z <= -1.32e-27)
		tmp = Float64(x + y);
	elseif (z <= -6e-151)
		tmp = x;
	elseif (z <= 9.8e+250)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(Float64(-z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.5e+223)
		tmp = z * -(y / a);
	elseif (z <= -1.32e-27)
		tmp = x + y;
	elseif (z <= -6e-151)
		tmp = x;
	elseif (z <= 9.8e+250)
		tmp = x + y;
	else
		tmp = y * (-z / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.5e+223], N[(z * (-N[(y / a), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, -1.32e-27], N[(x + y), $MachinePrecision], If[LessEqual[z, -6e-151], x, If[LessEqual[z, 9.8e+250], N[(x + y), $MachinePrecision], N[(y * N[((-z) / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.50000000000000001e223

   1. Initial program 86.1%

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

      1. associate--l+ 86.1%

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

      2. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in x around 0 67.1%

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

   5. Taylor expanded in t around 0 45.2%

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

      1. associate-/l* 53.5%

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

   7. Simplified 53.5%

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

   8. Taylor expanded in a around 0 45.2%

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

      1. associate-*l/ 56.2%

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

      2. *-commutative 56.2%

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

      3. associate-*r* 56.2%

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

      4. neg-mul-1 56.2%

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

   10. Simplified 56.2%

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

   if -1.50000000000000001e223 < z < -1.3200000000000001e-27 or -6e-151 < z < 9.79999999999999986e250

   1. Initial program 80.3%

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

      1. associate--l+ 84.0%

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

      2. associate-/l* 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in a around inf 67.3%

      \[\leadsto \color{blue}{x + y} \]
   5. Step-by-step derivation

      1. +-commutative 67.3%

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

   6. Simplified 67.3%

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

   if -1.3200000000000001e-27 < z < -6e-151

   1. Initial program 71.8%

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

      1. associate--l+ 81.9%

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

      2. associate-/l* 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in x around inf 78.2%

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

   if 9.79999999999999986e250 < z

   1. Initial program 75.1%

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

      1. associate--l+ 75.1%

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

      2. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 75.1%

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

   5. Taylor expanded in t around 0 41.7%

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

   6. Taylor expanded in z around inf 41.7%

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

      1. mul-1-neg 41.7%

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

      2. associate-*r/ 54.1%

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

      3. distribute-rgt-neg-in 54.1%

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

      4. mul-1-neg 54.1%

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

      5. associate-*r/ 54.1%

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

      6. mul-1-neg 54.1%

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

   8. Simplified 54.1%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+223}:\\ \;\;\;\;z \cdot \left(-\frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-27}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-151}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+250}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \end{array} \]

Alternative 12: 83.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+160} \lor \neg \left(a \leq 7.5 \cdot 10^{+199}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.3e+160) (not (<= a 7.5e+199)))
   (+ x y)
   (- x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.3e+160) || !(a <= 7.5e+199)) {
		tmp = x + y;
	} else {
		tmp = x - (y * (z / (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 <= (-2.3d+160)) .or. (.not. (a <= 7.5d+199))) then
        tmp = x + y
    else
        tmp = x - (y * (z / (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 <= -2.3e+160) || !(a <= 7.5e+199)) {
		tmp = x + y;
	} else {
		tmp = x - (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.3e+160) or not (a <= 7.5e+199):
		tmp = x + y
	else:
		tmp = x - (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.3e+160) || !(a <= 7.5e+199))
		tmp = Float64(x + y);
	else
		tmp = Float64(x - Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.3e+160) || ~((a <= 7.5e+199)))
		tmp = x + y;
	else
		tmp = x - (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.3e+160], N[Not[LessEqual[a, 7.5e+199]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x - N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.29999999999999987e160 or 7.49999999999999977e199 < a

   1. Initial program 79.9%

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

      1. associate--l+ 79.9%

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

      2. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in a around inf 91.2%

      \[\leadsto \color{blue}{x + y} \]
   5. Step-by-step derivation

      1. +-commutative 91.2%

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

   6. Simplified 91.2%

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

   if -2.29999999999999987e160 < a < 7.49999999999999977e199

   1. Initial program 79.2%

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

      1. associate--l+ 84.1%

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

      2. associate-/l* 87.5%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in z around inf 81.7%

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

      1. associate-*r/ 81.7%

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

      2. associate-*r* 81.7%

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

      3. neg-mul-1 81.7%

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

   6. Simplified 81.7%

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

   7. Taylor expanded in x around 0 81.7%

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

      1. mul-1-neg 81.7%

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

      2. sub-neg 81.7%

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

      3. associate-*r/ 84.6%

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

   9. Simplified 84.6%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+160} \lor \neg \left(a \leq 7.5 \cdot 10^{+199}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a - t}\\ \end{array} \]

Alternative 13: 87.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+20} \lor \neg \left(a \leq 5.2 \cdot 10^{+103}\right):\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.2e+20) (not (<= a 5.2e+103)))
   (- (+ x y) (/ 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 <= -2.2e+20) || !(a <= 5.2e+103)) {
		tmp = (x + y) - (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 <= (-2.2d+20)) .or. (.not. (a <= 5.2d+103))) then
        tmp = (x + y) - (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 <= -2.2e+20) || !(a <= 5.2e+103)) {
		tmp = (x + y) - (y / (a / z));
	} else {
		tmp = x - (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.2e+20) or not (a <= 5.2e+103):
		tmp = (x + y) - (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 <= -2.2e+20) || !(a <= 5.2e+103))
		tmp = Float64(Float64(x + y) - 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 <= -2.2e+20) || ~((a <= 5.2e+103)))
		tmp = (x + y) - (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, -2.2e+20], N[Not[LessEqual[a, 5.2e+103]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(y / N[(a / z), $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 < -2.2e20 or 5.2000000000000003e103 < a

   1. Initial program 83.4%

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

      1. associate--l+ 84.2%

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

      2. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in t around 0 81.9%

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

      1. +-commutative 81.9%

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

      2. associate-/l* 87.2%

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

   6. Simplified 87.2%

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

   if -2.2e20 < a < 5.2000000000000003e103

   1. Initial program 76.3%

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

      1. associate--l+ 82.7%

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

      2. associate-/l* 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in z around inf 86.7%

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

      1. associate-*r/ 86.7%

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

      2. associate-*r* 86.7%

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

      3. neg-mul-1 86.7%

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

   6. Simplified 86.7%

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

   7. Taylor expanded in x around 0 86.7%

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

      1. mul-1-neg 86.7%

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

      2. sub-neg 86.7%

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

      3. associate-*r/ 89.5%

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

   9. Simplified 89.5%

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

   10. Taylor expanded in y around 0 86.7%

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

       1. associate-*l/ 90.9%

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

       2. *-commutative 90.9%

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

   12. Simplified 90.9%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+20} \lor \neg \left(a \leq 5.2 \cdot 10^{+103}\right):\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 14: 61.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -850000000 \lor \neg \left(a \leq 7.5 \cdot 10^{+103}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -850000000.0) (not (<= a 7.5e+103))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -850000000.0) || !(a <= 7.5e+103)) {
		tmp = x + y;
	} 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 ((a <= (-850000000.0d0)) .or. (.not. (a <= 7.5d+103))) then
        tmp = x + y
    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 ((a <= -850000000.0) || !(a <= 7.5e+103)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -850000000.0) or not (a <= 7.5e+103):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -850000000.0) || !(a <= 7.5e+103))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -850000000.0) || ~((a <= 7.5e+103)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -850000000.0], N[Not[LessEqual[a, 7.5e+103]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -8.5e8 or 7.49999999999999922e103 < a

   1. Initial program 83.7%

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

      1. associate--l+ 84.5%

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

      2. associate-/l* 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in a around inf 75.1%

      \[\leadsto \color{blue}{x + y} \]
   5. Step-by-step derivation

      1. +-commutative 75.1%

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

   6. Simplified 75.1%

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

   if -8.5e8 < a < 7.49999999999999922e103

   1. Initial program 76.0%

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

      1. associate--l+ 82.5%

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

      2. associate-/l* 86.9%

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

   3. Simplified 86.9%

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

   4. Taylor expanded in x around inf 54.4%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -850000000 \lor \neg \left(a \leq 7.5 \cdot 10^{+103}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 51.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+91}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+244}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -9e+91) y (if (<= y 2.55e+244) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -9e+91) {
		tmp = y;
	} else if (y <= 2.55e+244) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-9d+91)) then
        tmp = y
    else if (y <= 2.55d+244) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -9e+91) {
		tmp = y;
	} else if (y <= 2.55e+244) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -9e+91:
		tmp = y
	elif y <= 2.55e+244:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -9e+91)
		tmp = y;
	elseif (y <= 2.55e+244)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -9e+91)
		tmp = y;
	elseif (y <= 2.55e+244)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -9e+91], y, If[LessEqual[y, 2.55e+244], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -9e91 or 2.54999999999999993e244 < y

   1. Initial program 69.0%

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

      1. associate--l+ 69.1%

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

      2. associate-/l* 85.4%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in x around 0 61.9%

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

   5. Taylor expanded in t around 0 59.6%

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

      1. associate-/l* 65.2%

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

   7. Simplified 65.2%

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

   8. Taylor expanded in a around inf 40.0%

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

   if -9e91 < y < 2.54999999999999993e244

   1. Initial program 82.0%

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

      1. associate--l+ 87.1%

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

      2. associate-/l* 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in x around inf 60.3%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+91}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+244}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 16: 49.4% 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 79.3%

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

   1. associate--l+ 83.4%

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

   2. associate-/l* 88.9%

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

3. Simplified 88.9%

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

4. Taylor expanded in x around inf 50.8%

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

5. Final simplification 50.8%

   \[\leadsto x \]

Developer target: 87.5% 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 2023308 
(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))))