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

Percentage Accurate: 76.6% → 94.0%

Time: 15.9s

Alternatives: 16

Speedup: 0.8×

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: 76.6% 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: 94.0% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.7%

   \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
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* 87.1%

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

3. Simplified 87.1%

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

5. Taylor expanded in y around 0 95.7%

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

6. Final simplification 95.7%

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

Alternative 2: 92.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-275}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (+ x y) (/ (* y (- t z)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (- x (* z (/ y (- a t))))
     (if (<= t_1 -2e-275)
       t_1
       (if (<= t_1 0.0)
         (- x (/ y (/ t (- a z))))
         (+ x (+ y (/ (- t z) (/ (- a t) y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) + ((y * (t - z)) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x - (z * (y / (a - t)));
	} else if (t_1 <= -2e-275) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = x - (y / (t / (a - z)));
	} else {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) + ((y * (t - z)) / (a - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x - (z * (y / (a - t)));
	} else if (t_1 <= -2e-275) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = x - (y / (t / (a - z)));
	} else {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) + ((y * (t - z)) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x - (z * (y / (a - t)))
	elif t_1 <= -2e-275:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = x - (y / (t / (a - z)))
	else:
		tmp = x + (y + ((t - z) / ((a - t) / y)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) + Float64(Float64(y * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x - Float64(z * Float64(y / Float64(a - t))));
	elseif (t_1 <= -2e-275)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(x - Float64(y / Float64(t / Float64(a - z))));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(t - z) / Float64(Float64(a - t) / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) + ((y * (t - z)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x - (z * (y / (a - t)));
	elseif (t_1 <= -2e-275)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = x - (y / (t / (a - z)));
	else
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	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[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-275], t$95$1, If[LessEqual[t$95$1, 0.0], N[(x - N[(y / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -inf.0

   1. Initial program 50.3%

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

      1. associate--l+ 50.3%

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

      2. associate-/l* 83.0%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in z around inf 54.4%

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

      1. associate-*r/ 54.4%

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

      2. associate-*r* 54.4%

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

      3. neg-mul-1 54.4%

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

   7. Simplified 54.4%

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

   8. Taylor expanded in x around 0 54.4%

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

      1. mul-1-neg 54.4%

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

      2. sub-neg 54.4%

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

      3. *-commutative 54.4%

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

      4. associate-*r/ 87.1%

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

   10. Simplified 87.1%

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

   if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -1.99999999999999987e-275

   1. Initial program 98.0%

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

   if -1.99999999999999987e-275 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 4.2%

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

      1. *-commutative 4.2%

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

      2. associate-/l* 4.2%

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

      3. associate-/r/ 4.3%

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

   3. Simplified 4.3%

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

      1. clear-num 4.5%

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

      2. inv-pow 4.5%

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

   6. Applied egg-rr 4.5%

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

      1. unpow-1 4.5%

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

   8. Simplified 4.5%

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

   9. Taylor expanded in t around -inf 99.6%

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

       1. mul-1-neg 99.6%

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

       2. unsub-neg 99.6%

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

       3. *-commutative 99.6%

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

       4. cancel-sign-sub-inv 99.6%

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

       5. mul-1-neg 99.6%

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

       6. distribute-rgt-in 99.6%

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

       7. associate-/l* 99.8%

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

       8. mul-1-neg 99.8%

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

       9. sub-neg 99.8%

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

   11. Simplified 99.8%

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

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

   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+ 86.6%

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

      2. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq -\infty:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq -2 \cdot 10^{-275}:\\ \;\;\;\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-275}:\\ \;\;\;\;\left(x + y\right) - \frac{\frac{z - t}{a - t}}{\frac{1}{y}}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (+ x y) (/ (* y (- t z)) (- a t)))))
   (if (<= t_1 -2e-275)
     (- (+ x y) (/ (/ (- z t) (- a t)) (/ 1.0 y)))
     (if (<= t_1 0.0)
       (- x (/ y (/ t (- a z))))
       (+ x (+ y (/ (- t z) (/ (- a t) y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) + ((y * (t - z)) / (a - t));
	double tmp;
	if (t_1 <= -2e-275) {
		tmp = (x + y) - (((z - t) / (a - t)) / (1.0 / y));
	} else if (t_1 <= 0.0) {
		tmp = x - (y / (t / (a - z)));
	} else {
		tmp = x + (y + ((t - z) / ((a - t) / 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) + ((y * (t - z)) / (a - t))
    if (t_1 <= (-2d-275)) then
        tmp = (x + y) - (((z - t) / (a - t)) / (1.0d0 / y))
    else if (t_1 <= 0.0d0) then
        tmp = x - (y / (t / (a - z)))
    else
        tmp = x + (y + ((t - z) / ((a - t) / 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) + ((y * (t - z)) / (a - t));
	double tmp;
	if (t_1 <= -2e-275) {
		tmp = (x + y) - (((z - t) / (a - t)) / (1.0 / y));
	} else if (t_1 <= 0.0) {
		tmp = x - (y / (t / (a - z)));
	} else {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) + ((y * (t - z)) / (a - t))
	tmp = 0
	if t_1 <= -2e-275:
		tmp = (x + y) - (((z - t) / (a - t)) / (1.0 / y))
	elif t_1 <= 0.0:
		tmp = x - (y / (t / (a - z)))
	else:
		tmp = x + (y + ((t - z) / ((a - t) / y)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) + Float64(Float64(y * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -2e-275)
		tmp = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) / Float64(a - t)) / Float64(1.0 / y)));
	elseif (t_1 <= 0.0)
		tmp = Float64(x - Float64(y / Float64(t / Float64(a - z))));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(t - z) / Float64(Float64(a - t) / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) + ((y * (t - z)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -2e-275)
		tmp = (x + y) - (((z - t) / (a - t)) / (1.0 / y));
	elseif (t_1 <= 0.0)
		tmp = x - (y / (t / (a - z)));
	else
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	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[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-275], N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] / N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(x - N[(y / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $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))) < -1.99999999999999987e-275

   1. Initial program 88.5%

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

      1. *-commutative 88.5%

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

      2. associate-/l* 93.8%

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

      3. associate-/r/ 91.0%

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

   3. Simplified 91.0%

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

      1. associate-*l/ 88.5%

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

      2. *-commutative 88.5%

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

      3. associate-/l* 91.0%

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

      4. div-inv 90.9%

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

      5. associate-/r* 92.6%

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

   6. Applied egg-rr 92.6%

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

   if -1.99999999999999987e-275 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 4.2%

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

      1. *-commutative 4.2%

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

      2. associate-/l* 4.2%

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

      3. associate-/r/ 4.3%

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

   3. Simplified 4.3%

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

      1. clear-num 4.5%

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

      2. inv-pow 4.5%

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

   6. Applied egg-rr 4.5%

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

      1. unpow-1 4.5%

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

   8. Simplified 4.5%

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

   9. Taylor expanded in t around -inf 99.6%

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

       1. mul-1-neg 99.6%

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

       2. unsub-neg 99.6%

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

       3. *-commutative 99.6%

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

       4. cancel-sign-sub-inv 99.6%

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

       5. mul-1-neg 99.6%

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

       6. distribute-rgt-in 99.6%

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

       7. associate-/l* 99.8%

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

       8. mul-1-neg 99.8%

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

       9. sub-neg 99.8%

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

   11. Simplified 99.8%

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

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

   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+ 86.6%

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

      2. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq -2 \cdot 10^{-275}:\\ \;\;\;\;\left(x + y\right) - \frac{\frac{z - t}{a - t}}{\frac{1}{y}}\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{a - t}\\ \mathbf{if}\;a \leq -1.95 \cdot 10^{-78}:\\ \;\;\;\;x + y \cdot \left(1 - t\_1\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+39}:\\ \;\;\;\;x - y \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ z (- a t))))
   (if (<= a -1.95e-78)
     (+ x (* y (- 1.0 t_1)))
     (if (<= a 2.4e+39)
       (- x (* y t_1))
       (+ x (+ y (/ (- t z) (/ (- a t) y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z / (a - t);
	double tmp;
	if (a <= -1.95e-78) {
		tmp = x + (y * (1.0 - t_1));
	} else if (a <= 2.4e+39) {
		tmp = x - (y * t_1);
	} else {
		tmp = x + (y + ((t - z) / ((a - t) / 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 = z / (a - t)
    if (a <= (-1.95d-78)) then
        tmp = x + (y * (1.0d0 - t_1))
    else if (a <= 2.4d+39) then
        tmp = x - (y * t_1)
    else
        tmp = x + (y + ((t - z) / ((a - t) / 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 = z / (a - t);
	double tmp;
	if (a <= -1.95e-78) {
		tmp = x + (y * (1.0 - t_1));
	} else if (a <= 2.4e+39) {
		tmp = x - (y * t_1);
	} else {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z / (a - t)
	tmp = 0
	if a <= -1.95e-78:
		tmp = x + (y * (1.0 - t_1))
	elif a <= 2.4e+39:
		tmp = x - (y * t_1)
	else:
		tmp = x + (y + ((t - z) / ((a - t) / y)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z / Float64(a - t))
	tmp = 0.0
	if (a <= -1.95e-78)
		tmp = Float64(x + Float64(y * Float64(1.0 - t_1)));
	elseif (a <= 2.4e+39)
		tmp = Float64(x - Float64(y * t_1));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(t - z) / Float64(Float64(a - t) / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z / (a - t);
	tmp = 0.0;
	if (a <= -1.95e-78)
		tmp = x + (y * (1.0 - t_1));
	elseif (a <= 2.4e+39)
		tmp = x - (y * t_1);
	else
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.95e-78], N[(x + N[(y * N[(1.0 - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e+39], N[(x - N[(y * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.9500000000000001e-78

   1. Initial program 90.5%

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

      1. associate--l+ 91.7%

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

      2. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in y around 0 99.9%

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

   6. Taylor expanded in t around 0 95.5%

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

   if -1.9500000000000001e-78 < a < 2.4000000000000001e39

   1. Initial program 70.5%

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

      1. associate--l+ 78.8%

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

      2. associate-/l* 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in y around 0 91.8%

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

   6. Taylor expanded in t around inf 90.4%

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

   if 2.4000000000000001e39 < a

   1. Initial program 84.0%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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* 96.2%

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

   3. Simplified 96.2%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{-78}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{a - t}\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+39}:\\ \;\;\;\;x - y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{-78} \lor \neg \left(a \leq 4.8 \cdot 10^{+96}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7.6e-78) (not (<= a 4.8e+96)))
   (+ x (* y (- 1.0 (/ z (- a t)))))
   (- x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.6e-78) || !(a <= 4.8e+96)) {
		tmp = x + (y * (1.0 - (z / (a - t))));
	} 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 <= (-7.6d-78)) .or. (.not. (a <= 4.8d+96))) then
        tmp = x + (y * (1.0d0 - (z / (a - t))))
    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 <= -7.6e-78) || !(a <= 4.8e+96)) {
		tmp = x + (y * (1.0 - (z / (a - t))));
	} else {
		tmp = x - (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7.6e-78) or not (a <= 4.8e+96):
		tmp = x + (y * (1.0 - (z / (a - t))))
	else:
		tmp = x - (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7.6e-78) || !(a <= 4.8e+96))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(z / Float64(a - t)))));
	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 <= -7.6e-78) || ~((a <= 4.8e+96)))
		tmp = x + (y * (1.0 - (z / (a - t))));
	else
		tmp = x - (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7.6e-78], N[Not[LessEqual[a, 4.8e+96]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.5999999999999998e-78 or 4.79999999999999986e96 < a

   1. Initial program 87.1%

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

      1. associate--l+ 87.9%

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

      2. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in y around 0 99.1%

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

   6. Taylor expanded in t around 0 94.8%

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

   if -7.5999999999999998e-78 < a < 4.79999999999999986e96

   1. Initial program 72.6%

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

      1. associate--l+ 80.3%

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

      2. associate-/l* 79.9%

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

   3. Simplified 79.9%

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

   5. Taylor expanded in z around inf 90.3%

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

      1. associate-*r/ 90.3%

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

      2. associate-*r* 90.3%

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

      3. neg-mul-1 90.3%

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

   7. Simplified 90.3%

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

   8. Taylor expanded in x around 0 90.3%

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

      1. mul-1-neg 90.3%

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

      2. sub-neg 90.3%

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

      3. *-commutative 90.3%

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

      4. associate-*r/ 90.8%

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

   10. Simplified 90.8%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{-78} \lor \neg \left(a \leq 4.8 \cdot 10^{+96}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{a - t}\\ \mathbf{if}\;a \leq -7.6 \cdot 10^{-78}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{a - t}\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+98}:\\ \;\;\;\;x - t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y (- a t)))))
   (if (<= a -7.6e-78)
     (+ x (* y (- 1.0 (/ z (- a t)))))
     (if (<= a 4.2e+98) (- x t_1) (+ x (- y t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / (a - t));
	double tmp;
	if (a <= -7.6e-78) {
		tmp = x + (y * (1.0 - (z / (a - t))));
	} else if (a <= 4.2e+98) {
		tmp = x - t_1;
	} else {
		tmp = x + (y - 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 = z * (y / (a - t))
    if (a <= (-7.6d-78)) then
        tmp = x + (y * (1.0d0 - (z / (a - t))))
    else if (a <= 4.2d+98) then
        tmp = x - t_1
    else
        tmp = x + (y - 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 = z * (y / (a - t));
	double tmp;
	if (a <= -7.6e-78) {
		tmp = x + (y * (1.0 - (z / (a - t))));
	} else if (a <= 4.2e+98) {
		tmp = x - t_1;
	} else {
		tmp = x + (y - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / (a - t))
	tmp = 0
	if a <= -7.6e-78:
		tmp = x + (y * (1.0 - (z / (a - t))))
	elif a <= 4.2e+98:
		tmp = x - t_1
	else:
		tmp = x + (y - t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / Float64(a - t)))
	tmp = 0.0
	if (a <= -7.6e-78)
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(z / Float64(a - t)))));
	elseif (a <= 4.2e+98)
		tmp = Float64(x - t_1);
	else
		tmp = Float64(x + Float64(y - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / (a - t));
	tmp = 0.0;
	if (a <= -7.6e-78)
		tmp = x + (y * (1.0 - (z / (a - t))));
	elseif (a <= 4.2e+98)
		tmp = x - t_1;
	else
		tmp = x + (y - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.6e-78], N[(x + N[(y * N[(1.0 - N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e+98], N[(x - t$95$1), $MachinePrecision], N[(x + N[(y - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.5999999999999998e-78

   1. Initial program 90.5%

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

      1. associate--l+ 91.7%

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

      2. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in y around 0 99.9%

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

   6. Taylor expanded in t around 0 95.5%

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

   if -7.5999999999999998e-78 < a < 4.20000000000000008e98

   1. Initial program 72.6%

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

      1. associate--l+ 80.3%

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

      2. associate-/l* 79.9%

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

   3. Simplified 79.9%

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

   5. Taylor expanded in z around inf 90.3%

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

      1. associate-*r/ 90.3%

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

      2. associate-*r* 90.3%

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

      3. neg-mul-1 90.3%

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

   7. Simplified 90.3%

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

   8. Taylor expanded in x around 0 90.3%

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

      1. mul-1-neg 90.3%

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

      2. sub-neg 90.3%

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

      3. *-commutative 90.3%

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

      4. associate-*r/ 90.8%

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

   10. Simplified 90.8%

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

   if 4.20000000000000008e98 < a

   1. Initial program 80.8%

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

      1. associate--l+ 80.8%

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

      2. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in z around inf 82.9%

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

      1. associate-*l/ 93.5%

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

      2. *-commutative 93.5%

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

   7. Simplified 93.5%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{-78}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{a - t}\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+98}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z \cdot \frac{y}{a - t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{a - t}\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{-78}:\\ \;\;\;\;x + y \cdot \left(1 - t\_1\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+96}:\\ \;\;\;\;x - y \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z \cdot \frac{y}{a - t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ z (- a t))))
   (if (<= a -6.5e-78)
     (+ x (* y (- 1.0 t_1)))
     (if (<= a 8.2e+96) (- x (* y t_1)) (+ x (- y (* z (/ y (- a t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z / (a - t);
	double tmp;
	if (a <= -6.5e-78) {
		tmp = x + (y * (1.0 - t_1));
	} else if (a <= 8.2e+96) {
		tmp = x - (y * t_1);
	} else {
		tmp = x + (y - (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) :: t_1
    real(8) :: tmp
    t_1 = z / (a - t)
    if (a <= (-6.5d-78)) then
        tmp = x + (y * (1.0d0 - t_1))
    else if (a <= 8.2d+96) then
        tmp = x - (y * t_1)
    else
        tmp = x + (y - (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 t_1 = z / (a - t);
	double tmp;
	if (a <= -6.5e-78) {
		tmp = x + (y * (1.0 - t_1));
	} else if (a <= 8.2e+96) {
		tmp = x - (y * t_1);
	} else {
		tmp = x + (y - (z * (y / (a - t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z / (a - t)
	tmp = 0
	if a <= -6.5e-78:
		tmp = x + (y * (1.0 - t_1))
	elif a <= 8.2e+96:
		tmp = x - (y * t_1)
	else:
		tmp = x + (y - (z * (y / (a - t))))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z / Float64(a - t))
	tmp = 0.0
	if (a <= -6.5e-78)
		tmp = Float64(x + Float64(y * Float64(1.0 - t_1)));
	elseif (a <= 8.2e+96)
		tmp = Float64(x - Float64(y * t_1));
	else
		tmp = Float64(x + Float64(y - Float64(z * Float64(y / Float64(a - t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z / (a - t);
	tmp = 0.0;
	if (a <= -6.5e-78)
		tmp = x + (y * (1.0 - t_1));
	elseif (a <= 8.2e+96)
		tmp = x - (y * t_1);
	else
		tmp = x + (y - (z * (y / (a - t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.5e-78], N[(x + N[(y * N[(1.0 - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e+96], N[(x - N[(y * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(y - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.5000000000000003e-78

   1. Initial program 90.5%

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

      1. associate--l+ 91.7%

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

      2. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in y around 0 99.9%

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

   6. Taylor expanded in t around 0 95.5%

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

   if -6.5000000000000003e-78 < a < 8.19999999999999996e96

   1. Initial program 72.6%

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

      1. associate--l+ 80.3%

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

      2. associate-/l* 79.9%

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

   3. Simplified 79.9%

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

   5. Taylor expanded in y around 0 92.3%

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

   6. Taylor expanded in t around inf 91.1%

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

   if 8.19999999999999996e96 < a

   1. Initial program 80.8%

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

      1. associate--l+ 80.8%

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

      2. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in z around inf 82.9%

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

      1. associate-*l/ 93.5%

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

      2. *-commutative 93.5%

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

   7. Simplified 93.5%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-78}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{a - t}\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+96}:\\ \;\;\;\;x - y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z \cdot \frac{y}{a - t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+28} \lor \neg \left(a \leq 2.1 \cdot 10^{+121}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.2e+28) (not (<= a 2.1e+121)))
   (+ x y)
   (- x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.2e+28) || !(a <= 2.1e+121)) {
		tmp = x + y;
	} 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 <= (-3.2d+28)) .or. (.not. (a <= 2.1d+121))) then
        tmp = x + y
    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 <= -3.2e+28) || !(a <= 2.1e+121)) {
		tmp = x + y;
	} else {
		tmp = x - (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.2e+28) or not (a <= 2.1e+121):
		tmp = x + y
	else:
		tmp = x - (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.2e+28) || !(a <= 2.1e+121))
		tmp = Float64(x + y);
	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 <= -3.2e+28) || ~((a <= 2.1e+121)))
		tmp = x + y;
	else
		tmp = x - (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.2e+28], N[Not[LessEqual[a, 2.1e+121]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.2e28 or 2.1000000000000002e121 < a

   1. Initial program 87.4%

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

      1. *-commutative 87.4%

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

      2. associate-/l* 98.1%

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

      3. associate-/r/ 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in a around inf 88.4%

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

      1. +-commutative 88.4%

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

   7. Simplified 88.4%

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

   if -3.2e28 < a < 2.1000000000000002e121

   1. Initial program 74.3%

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

      1. associate--l+ 81.7%

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

      2. associate-/l* 81.2%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in z around inf 89.7%

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

      1. associate-*r/ 89.7%

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

      2. associate-*r* 89.7%

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

      3. neg-mul-1 89.7%

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

   7. Simplified 89.7%

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

   8. Taylor expanded in x around 0 89.7%

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

      1. mul-1-neg 89.7%

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

      2. sub-neg 89.7%

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

      3. *-commutative 89.7%

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

      4. associate-*r/ 90.1%

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

   10. Simplified 90.1%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+28} \lor \neg \left(a \leq 2.1 \cdot 10^{+121}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.18 \cdot 10^{+24} \lor \neg \left(a \leq 1.76 \cdot 10^{+121}\right):\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.18e+24) (not (<= a 1.76e+121)))
   (- (+ 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 <= -1.18e+24) || !(a <= 1.76e+121)) {
		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 <= (-1.18d+24)) .or. (.not. (a <= 1.76d+121))) 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 <= -1.18e+24) || !(a <= 1.76e+121)) {
		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 <= -1.18e+24) or not (a <= 1.76e+121):
		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 <= -1.18e+24) || !(a <= 1.76e+121))
		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 <= -1.18e+24) || ~((a <= 1.76e+121)))
		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, -1.18e+24], N[Not[LessEqual[a, 1.76e+121]], $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 < -1.17999999999999997e24 or 1.7600000000000001e121 < a

   1. Initial program 87.4%

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

      1. *-commutative 87.4%

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

      2. associate-/l* 98.1%

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

      3. associate-/r/ 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in t around 0 90.0%

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

      1. +-commutative 90.0%

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

      2. associate-/l* 95.3%

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

   7. Simplified 95.3%

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

   if -1.17999999999999997e24 < a < 1.7600000000000001e121

   1. Initial program 74.3%

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

      1. associate--l+ 81.7%

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

      2. associate-/l* 81.2%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in z around inf 89.7%

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

      1. associate-*r/ 89.7%

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

      2. associate-*r* 89.7%

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

      3. neg-mul-1 89.7%

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

   7. Simplified 89.7%

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

   8. Taylor expanded in x around 0 89.7%

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

      1. mul-1-neg 89.7%

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

      2. sub-neg 89.7%

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

      3. *-commutative 89.7%

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

      4. associate-*r/ 90.1%

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

   10. Simplified 90.1%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.18 \cdot 10^{+24} \lor \neg \left(a \leq 1.76 \cdot 10^{+121}\right):\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+27}:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+125}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.7e+27)
   (- (+ x y) (/ (* y z) a))
   (if (<= a 1.6e+125) (- x (* z (/ y (- a t)))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.7e+27) {
		tmp = (x + y) - ((y * z) / a);
	} else if (a <= 1.6e+125) {
		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 <= (-1.7d+27)) then
        tmp = (x + y) - ((y * z) / a)
    else if (a <= 1.6d+125) 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 <= -1.7e+27) {
		tmp = (x + y) - ((y * z) / a);
	} else if (a <= 1.6e+125) {
		tmp = x - (z * (y / (a - t)));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.7e+27:
		tmp = (x + y) - ((y * z) / a)
	elif a <= 1.6e+125:
		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 <= -1.7e+27)
		tmp = Float64(Float64(x + y) - Float64(Float64(y * z) / a));
	elseif (a <= 1.6e+125)
		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 <= -1.7e+27)
		tmp = (x + y) - ((y * z) / a);
	elseif (a <= 1.6e+125)
		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, -1.7e+27], N[(N[(x + y), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+125], N[(x - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.7e27

   1. Initial program 92.8%

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

      1. *-commutative 92.8%

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

      2. associate-/l* 100.0%

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

      3. associate-/r/ 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in t around 0 95.6%

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

   if -1.7e27 < a < 1.59999999999999992e125

   1. Initial program 74.3%

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

      1. associate--l+ 81.7%

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

      2. associate-/l* 81.2%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in z around inf 89.7%

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

      1. associate-*r/ 89.7%

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

      2. associate-*r* 89.7%

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

      3. neg-mul-1 89.7%

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

   7. Simplified 89.7%

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

   8. Taylor expanded in x around 0 89.7%

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

      1. mul-1-neg 89.7%

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

      2. sub-neg 89.7%

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

      3. *-commutative 89.7%

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

      4. associate-*r/ 90.1%

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

   10. Simplified 90.1%

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

   if 1.59999999999999992e125 < a

   1. Initial program 77.7%

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

      1. *-commutative 77.7%

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

      2. associate-/l* 94.7%

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

      3. associate-/r/ 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in a around inf 87.6%

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

      1. +-commutative 87.6%

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

   7. Simplified 87.6%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+27}:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+125}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 77.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+20} \lor \neg \left(a \leq 5.2 \cdot 10^{+41}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.1e+20) (not (<= a 5.2e+41))) (+ x y) (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.1e+20) || !(a <= 5.2e+41)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.1d+20)) .or. (.not. (a <= 5.2d+41))) then
        tmp = x + y
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.1e+20) || !(a <= 5.2e+41)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.1e+20) or not (a <= 5.2e+41):
		tmp = x + y
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.1e+20) || !(a <= 5.2e+41))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.1e+20) || ~((a <= 5.2e+41)))
		tmp = x + y;
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.1e+20], N[Not[LessEqual[a, 5.2e+41]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.1e20 or 5.2000000000000001e41 < a

   1. Initial program 89.1%

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

      1. *-commutative 89.1%

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

      2. associate-/l* 98.3%

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

      3. associate-/r/ 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in a around inf 86.6%

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

      1. +-commutative 86.6%

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

   7. Simplified 86.6%

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

   if -1.1e20 < a < 5.2000000000000001e41

   1. Initial program 71.2%

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

      1. associate--l+ 79.5%

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

      2. associate-/l* 79.0%

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

   3. Simplified 79.0%

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

   5. Taylor expanded in y around 0 92.6%

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

   6. Taylor expanded in t around inf 89.0%

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

      1. associate-*r/ 89.0%

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

      2. neg-mul-1 89.0%

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

   8. Simplified 89.0%

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

   9. Taylor expanded in a around 0 77.7%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+20} \lor \neg \left(a \leq 5.2 \cdot 10^{+41}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 77.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{+21} \lor \neg \left(a \leq 2.5 \cdot 10^{+39}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.85e+21) (not (<= a 2.5e+39))) (+ x y) (+ x (* z (/ y t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.85e+21) || !(a <= 2.5e+39)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.85d+21)) .or. (.not. (a <= 2.5d+39))) then
        tmp = x + y
    else
        tmp = x + (z * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.85e+21) || !(a <= 2.5e+39)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.85e+21) or not (a <= 2.5e+39):
		tmp = x + y
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.85e+21) || !(a <= 2.5e+39))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.85e+21) || ~((a <= 2.5e+39)))
		tmp = x + y;
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.85e+21], N[Not[LessEqual[a, 2.5e+39]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.85e21 or 2.50000000000000008e39 < a

   1. Initial program 89.1%

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

      1. *-commutative 89.1%

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

      2. associate-/l* 98.3%

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

      3. associate-/r/ 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in a around inf 86.6%

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

      1. +-commutative 86.6%

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

   7. Simplified 86.6%

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

   if -1.85e21 < a < 2.50000000000000008e39

   1. Initial program 71.2%

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

      1. associate--l+ 79.5%

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

      2. associate-/l* 79.0%

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

   3. Simplified 79.0%

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

   5. Taylor expanded in z around inf 88.4%

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

      1. associate-*r/ 88.4%

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

      2. associate-*r* 88.4%

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

      3. neg-mul-1 88.4%

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

   7. Simplified 88.4%

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

   8. Taylor expanded in x around 0 88.4%

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

      1. mul-1-neg 88.4%

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

      2. sub-neg 88.4%

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

      3. *-commutative 88.4%

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

      4. associate-*r/ 88.9%

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

   10. Simplified 88.9%

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

       1. clear-num 88.8%

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

       2. un-div-inv 88.9%

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

   12. Applied egg-rr 88.9%

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

   13. Taylor expanded in a around 0 77.5%

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

       1. sub-neg 77.5%

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

       2. mul-1-neg 77.5%

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

       3. associate-/l* 78.2%

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

       4. remove-double-neg 78.2%

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

       5. associate-/r/ 78.0%

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

   15. Simplified 78.0%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{+21} \lor \neg \left(a \leq 2.5 \cdot 10^{+39}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 77.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+20} \lor \neg \left(a \leq 6.2 \cdot 10^{+39}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -9.5e+20) (not (<= a 6.2e+39))) (+ x y) (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -9.5e+20) || !(a <= 6.2e+39)) {
		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 <= (-9.5d+20)) .or. (.not. (a <= 6.2d+39))) 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 <= -9.5e+20) || !(a <= 6.2e+39)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -9.5e+20) or not (a <= 6.2e+39):
		tmp = x + y
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -9.5e+20) || !(a <= 6.2e+39))
		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 <= -9.5e+20) || ~((a <= 6.2e+39)))
		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, -9.5e+20], N[Not[LessEqual[a, 6.2e+39]], $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 < -9.5e20 or 6.2000000000000005e39 < a

   1. Initial program 89.1%

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

      1. *-commutative 89.1%

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

      2. associate-/l* 98.3%

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

      3. associate-/r/ 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in a around inf 86.6%

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

      1. +-commutative 86.6%

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

   7. Simplified 86.6%

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

   if -9.5e20 < a < 6.2000000000000005e39

   1. Initial program 71.2%

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

      1. associate--l+ 79.5%

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

      2. associate-/l* 79.0%

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

   3. Simplified 79.0%

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

   5. Taylor expanded in z around inf 88.4%

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

      1. associate-*r/ 88.4%

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

      2. associate-*r* 88.4%

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

      3. neg-mul-1 88.4%

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

   7. Simplified 88.4%

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

   8. Taylor expanded in a around 0 77.5%

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

      1. +-commutative 77.5%

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

      2. associate-/l* 78.2%

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

   10. Simplified 78.2%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+20} \lor \neg \left(a \leq 6.2 \cdot 10^{+39}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 63.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-95} \lor \neg \left(a \leq 1.76 \cdot 10^{+121}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.9e-95) (not (<= a 1.76e+121))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.9e-95) || !(a <= 1.76e+121)) {
		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 <= (-1.9d-95)) .or. (.not. (a <= 1.76d+121))) 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 <= -1.9e-95) || !(a <= 1.76e+121)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.9e-95) or not (a <= 1.76e+121):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.9e-95) || !(a <= 1.76e+121))
		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 <= -1.9e-95) || ~((a <= 1.76e+121)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.9e-95], N[Not[LessEqual[a, 1.76e+121]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -1.8999999999999999e-95 or 1.7600000000000001e121 < a

   1. Initial program 86.1%

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

      1. *-commutative 86.1%

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

      2. associate-/l* 96.0%

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

      3. associate-/r/ 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in a around inf 83.2%

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

      1. +-commutative 83.2%

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

   7. Simplified 83.2%

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

   if -1.8999999999999999e-95 < a < 1.7600000000000001e121

   1. Initial program 73.8%

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

      1. *-commutative 73.8%

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

      2. associate-/l* 72.5%

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

      3. associate-/r/ 72.2%

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

   3. Simplified 72.2%

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

   5. Taylor expanded in x around inf 53.7%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-95} \lor \neg \left(a \leq 1.76 \cdot 10^{+121}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 53.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+227}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.6e+227) y (if (<= y 9.6e+146) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.6e+227) {
		tmp = y;
	} else if (y <= 9.6e+146) {
		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 <= (-1.6d+227)) then
        tmp = y
    else if (y <= 9.6d+146) 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 <= -1.6e+227) {
		tmp = y;
	} else if (y <= 9.6e+146) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.6e+227:
		tmp = y
	elif y <= 9.6e+146:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.6e+227)
		tmp = y;
	elseif (y <= 9.6e+146)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.6e+227)
		tmp = y;
	elseif (y <= 9.6e+146)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.6e+227], y, If[LessEqual[y, 9.6e+146], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -1.59999999999999994e227 or 9.6000000000000008e146 < y

   1. Initial program 54.1%

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

      1. *-commutative 54.1%

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

      2. associate-/l* 67.3%

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

      3. associate-/r/ 63.0%

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

   3. Simplified 63.0%

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

   5. Taylor expanded in x around 0 47.1%

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

   6. Taylor expanded in a around inf 38.0%

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

   if -1.59999999999999994e227 < y < 9.6000000000000008e146

   1. Initial program 84.8%

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

      1. *-commutative 84.8%

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

      2. associate-/l* 87.2%

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

      3. associate-/r/ 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in x around inf 61.4%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+227}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.8% 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 79.7%

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

   1. *-commutative 79.7%

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

   2. associate-/l* 83.9%

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

   3. associate-/r/ 82.6%

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

3. Simplified 82.6%

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

5. Taylor expanded in x around inf 53.6%

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

6. Final simplification 53.6%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 88.1% 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 2024034 
(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))))