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

Percentage Accurate: 77.2% → 90.8%

Time: 14.3s

Alternatives: 13

Speedup: 0.7×

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: 77.2% 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: 90.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+165} \lor \neg \left(t \leq 3.8 \cdot 10^{+36}\right):\\ \;\;\;\;x + \left(y \cdot \frac{z}{t} - a \cdot \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \frac{y}{a - t} \cdot \left(t - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.5e+165) (not (<= t 3.8e+36)))
   (+ x (- (* y (/ z t)) (* a (/ y t))))
   (+ x (+ y (* (/ y (- a t)) (- t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.5e+165) || !(t <= 3.8e+36)) {
		tmp = x + ((y * (z / t)) - (a * (y / t)));
	} else {
		tmp = x + (y + ((y / (a - t)) * (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 ((t <= (-2.5d+165)) .or. (.not. (t <= 3.8d+36))) then
        tmp = x + ((y * (z / t)) - (a * (y / t)))
    else
        tmp = x + (y + ((y / (a - t)) * (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 ((t <= -2.5e+165) || !(t <= 3.8e+36)) {
		tmp = x + ((y * (z / t)) - (a * (y / t)));
	} else {
		tmp = x + (y + ((y / (a - t)) * (t - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.5e+165) or not (t <= 3.8e+36):
		tmp = x + ((y * (z / t)) - (a * (y / t)))
	else:
		tmp = x + (y + ((y / (a - t)) * (t - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.5e+165) || !(t <= 3.8e+36))
		tmp = Float64(x + Float64(Float64(y * Float64(z / t)) - Float64(a * Float64(y / t))));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(y / Float64(a - t)) * Float64(t - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.5e+165) || ~((t <= 3.8e+36)))
		tmp = x + ((y * (z / t)) - (a * (y / t)));
	else
		tmp = x + (y + ((y / (a - t)) * (t - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.5e+165], N[Not[LessEqual[t, 3.8e+36]], $MachinePrecision]], N[(x + N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.49999999999999985e165 or 3.80000000000000025e36 < t

   1. Initial program 52.5%

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

      1. sub-neg 52.5%

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

      2. +-commutative 52.5%

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

      3. distribute-frac-neg 52.5%

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

      4. distribute-rgt-neg-out 52.5%

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

      5. associate-/l* 66.4%

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

      6. fma-define 66.7%

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

      7. distribute-frac-neg 66.7%

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

      8. distribute-neg-frac2 66.7%

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

      9. sub-neg 66.7%

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

      10. distribute-neg-in 66.7%

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

      11. remove-double-neg 66.7%

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

      12. +-commutative 66.7%

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

      13. sub-neg 66.7%

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

   3. Simplified 66.7%

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

   5. Taylor expanded in t around inf 73.4%

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

      1. associate--l+ 73.4%

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

      2. neg-mul-1 73.4%

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

      3. associate-+r+ 80.9%

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

      4. neg-mul-1 80.9%

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

      5. distribute-rgt1-in 80.9%

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

      6. metadata-eval 80.9%

         \[\leadsto x + \left(\left(\color{blue}{0} \cdot y + \frac{y \cdot z}{t}\right) - \frac{a \cdot y}{t}\right) \]

      7. mul0-lft 80.9%

         \[\leadsto x + \left(\left(\color{blue}{0} + \frac{y \cdot z}{t}\right) - \frac{a \cdot y}{t}\right) \]

      8. associate-/l* 84.2%

         \[\leadsto x + \left(\left(0 + \color{blue}{y \cdot \frac{z}{t}}\right) - \frac{a \cdot y}{t}\right) \]

      9. associate-/l* 93.7%

         \[\leadsto x + \left(\left(0 + y \cdot \frac{z}{t}\right) - \color{blue}{a \cdot \frac{y}{t}}\right) \]

   7. Simplified 93.7%

      \[\leadsto \color{blue}{x + \left(\left(0 + y \cdot \frac{z}{t}\right) - a \cdot \frac{y}{t}\right)} \]

   if -2.49999999999999985e165 < t < 3.80000000000000025e36

   1. Initial program 90.1%

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

      1. associate--l+ 91.4%

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

      2. associate-/l* 92.0%

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

   3. Simplified 92.0%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+165} \lor \neg \left(t \leq 3.8 \cdot 10^{+36}\right):\\ \;\;\;\;x + \left(y \cdot \frac{z}{t} - a \cdot \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \frac{y}{a - t} \cdot \left(t - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-225} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \left(y + \frac{y}{a - t} \cdot \left(t - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z - y \cdot a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (+ x y) (/ (* y (- t z)) (- a t)))))
   (if (or (<= t_1 -2e-225) (not (<= t_1 0.0)))
     (+ x (+ y (* (/ y (- a t)) (- t z))))
     (+ x (/ (- (* y z) (* y a)) t)))))

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-225) || !(t_1 <= 0.0)) {
		tmp = x + (y + ((y / (a - t)) * (t - z)));
	} 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 = (x + y) + ((y * (t - z)) / (a - t))
    if ((t_1 <= (-2d-225)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + (y + ((y / (a - t)) * (t - z)))
    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 = (x + y) + ((y * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -2e-225) || !(t_1 <= 0.0)) {
		tmp = x + (y + ((y / (a - t)) * (t - z)));
	} else {
		tmp = x + (((y * z) - (y * a)) / t);
	}
	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-225) or not (t_1 <= 0.0):
		tmp = x + (y + ((y / (a - t)) * (t - z)))
	else:
		tmp = x + (((y * z) - (y * a)) / t)
	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-225) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(y + Float64(Float64(y / Float64(a - t)) * Float64(t - z))));
	else
		tmp = Float64(x + Float64(Float64(Float64(y * z) - Float64(y * a)) / t));
	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-225) || ~((t_1 <= 0.0)))
		tmp = x + (y + ((y / (a - t)) * (t - z)));
	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[(N[(x + y), $MachinePrecision] + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-225], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(y + N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(y * z), $MachinePrecision] - N[(y * a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -1.9999999999999999e-225 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 84.4%

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

      1. associate--l+ 85.1%

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

      2. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

   if -1.9999999999999999e-225 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 3.9%

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

      1. associate-*r/ 4.0%

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

      2. add-cube-cbrt 4.4%

         \[\leadsto \left(x + y\right) - \color{blue}{\left(\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}\right)} \cdot \frac{y}{a - t} \]

      3. associate-*l* 4.3%

         \[\leadsto \left(x + y\right) - \color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \left(\sqrt[3]{z - t} \cdot \frac{y}{a - t}\right)} \]

      4. pow2 4.3%

         \[\leadsto \left(x + y\right) - \color{blue}{{\left(\sqrt[3]{z - t}\right)}^{2}} \cdot \left(\sqrt[3]{z - t} \cdot \frac{y}{a - t}\right) \]

   4. Applied egg-rr 4.3%

      \[\leadsto \left(x + y\right) - \color{blue}{{\left(\sqrt[3]{z - t}\right)}^{2} \cdot \left(\sqrt[3]{z - t} \cdot \frac{y}{a - t}\right)} \]

   5. Taylor expanded in t around inf 99.6%

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

      1. associate--l+ 99.6%

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

      2. associate-*r/ 99.6%

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

      3. associate-*r/ 99.6%

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

      4. div-sub 99.6%

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

      5. distribute-lft-out-- 99.6%

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

      6. associate-*r/ 99.6%

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

      7. mul-1-neg 99.6%

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

      8. *-commutative 99.6%

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

   7. Simplified 99.6%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq -2 \cdot 10^{-225} \lor \neg \left(\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq 0\right):\\ \;\;\;\;x + \left(y + \frac{y}{a - t} \cdot \left(t - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z - y \cdot a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+54}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-12}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -3.35 \cdot 10^{-49} \lor \neg \left(a \leq 3.5 \cdot 10^{+20}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.15e+54)
   (+ x y)
   (if (<= a -4.2e-12)
     (- x (* y (/ z a)))
     (if (or (<= a -3.35e-49) (not (<= a 3.5e+20)))
       (+ x y)
       (+ x (/ (* y z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.15e+54) {
		tmp = x + y;
	} else if (a <= -4.2e-12) {
		tmp = x - (y * (z / a));
	} else if ((a <= -3.35e-49) || !(a <= 3.5e+20)) {
		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 <= (-1.15d+54)) then
        tmp = x + y
    else if (a <= (-4.2d-12)) then
        tmp = x - (y * (z / a))
    else if ((a <= (-3.35d-49)) .or. (.not. (a <= 3.5d+20))) 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 <= -1.15e+54) {
		tmp = x + y;
	} else if (a <= -4.2e-12) {
		tmp = x - (y * (z / a));
	} else if ((a <= -3.35e-49) || !(a <= 3.5e+20)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.15e+54:
		tmp = x + y
	elif a <= -4.2e-12:
		tmp = x - (y * (z / a))
	elif (a <= -3.35e-49) or not (a <= 3.5e+20):
		tmp = x + y
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.15e+54)
		tmp = Float64(x + y);
	elseif (a <= -4.2e-12)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	elseif ((a <= -3.35e-49) || !(a <= 3.5e+20))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.15e+54)
		tmp = x + y;
	elseif (a <= -4.2e-12)
		tmp = x - (y * (z / a));
	elseif ((a <= -3.35e-49) || ~((a <= 3.5e+20)))
		tmp = x + y;
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.15e+54], N[(x + y), $MachinePrecision], If[LessEqual[a, -4.2e-12], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -3.35e-49], N[Not[LessEqual[a, 3.5e+20]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.14999999999999997e54 or -4.19999999999999988e-12 < a < -3.35e-49 or 3.5e20 < a

   1. Initial program 78.6%

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

   3. Taylor expanded in a around inf 78.6%

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

      1. +-commutative 78.6%

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

   5. Simplified 78.6%

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

   if -1.14999999999999997e54 < a < -4.19999999999999988e-12

   1. Initial program 69.8%

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

      1. associate--l+ 76.3%

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

      2. associate-/l* 76.1%

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

   3. Simplified 76.1%

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

   5. Taylor expanded in z around inf 76.5%

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

      1. associate-*r/ 76.5%

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

      2. associate-*r* 76.5%

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

      3. neg-mul-1 76.5%

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

   7. Simplified 76.5%

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

   8. Taylor expanded in a around inf 64.1%

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

      1. associate-*r/ 64.1%

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

      2. neg-mul-1 64.1%

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

      3. unsub-neg 64.1%

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

   10. Simplified 64.1%

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

   if -3.35e-49 < a < 3.5e20

   1. Initial program 77.4%

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

      1. associate--l+ 82.5%

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

      2. associate-/l* 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in z around inf 90.6%

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

      1. associate-*r/ 90.6%

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

      2. associate-*r* 90.6%

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

      3. neg-mul-1 90.6%

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

   7. Simplified 90.6%

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

   8. Taylor expanded in a around 0 83.5%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+54}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-12}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -3.35 \cdot 10^{-49} \lor \neg \left(a \leq 3.5 \cdot 10^{+20}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t - a}\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{+183}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+77}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -0.061:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+202}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- t a)))))
   (if (<= y -1.95e+183)
     t_1
     (if (<= y -6.5e+77)
       (+ x y)
       (if (<= y -0.061)
         t_1
         (if (<= y 2.9e+202) (+ x y) (* y (/ (- z a) t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (t - a));
	double tmp;
	if (y <= -1.95e+183) {
		tmp = t_1;
	} else if (y <= -6.5e+77) {
		tmp = x + y;
	} else if (y <= -0.061) {
		tmp = t_1;
	} else if (y <= 2.9e+202) {
		tmp = x + y;
	} else {
		tmp = y * ((z - a) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / (t - a))
    if (y <= (-1.95d+183)) then
        tmp = t_1
    else if (y <= (-6.5d+77)) then
        tmp = x + y
    else if (y <= (-0.061d0)) then
        tmp = t_1
    else if (y <= 2.9d+202) then
        tmp = x + y
    else
        tmp = y * ((z - a) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (t - a));
	double tmp;
	if (y <= -1.95e+183) {
		tmp = t_1;
	} else if (y <= -6.5e+77) {
		tmp = x + y;
	} else if (y <= -0.061) {
		tmp = t_1;
	} else if (y <= 2.9e+202) {
		tmp = x + y;
	} else {
		tmp = y * ((z - a) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (t - a))
	tmp = 0
	if y <= -1.95e+183:
		tmp = t_1
	elif y <= -6.5e+77:
		tmp = x + y
	elif y <= -0.061:
		tmp = t_1
	elif y <= 2.9e+202:
		tmp = x + y
	else:
		tmp = y * ((z - a) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(t - a)))
	tmp = 0.0
	if (y <= -1.95e+183)
		tmp = t_1;
	elseif (y <= -6.5e+77)
		tmp = Float64(x + y);
	elseif (y <= -0.061)
		tmp = t_1;
	elseif (y <= 2.9e+202)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(Float64(z - a) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (t - a));
	tmp = 0.0;
	if (y <= -1.95e+183)
		tmp = t_1;
	elseif (y <= -6.5e+77)
		tmp = x + y;
	elseif (y <= -0.061)
		tmp = t_1;
	elseif (y <= 2.9e+202)
		tmp = x + y;
	else
		tmp = y * ((z - a) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.95e+183], t$95$1, If[LessEqual[y, -6.5e+77], N[(x + y), $MachinePrecision], If[LessEqual[y, -0.061], t$95$1, If[LessEqual[y, 2.9e+202], N[(x + y), $MachinePrecision], N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9499999999999999e183 or -6.5e77 < y < -0.060999999999999999

   1. Initial program 61.4%

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

      1. sub-neg 61.4%

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

      2. +-commutative 61.4%

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

      3. distribute-frac-neg 61.4%

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

      4. distribute-rgt-neg-out 61.4%

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

      5. associate-/l* 72.2%

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

      6. fma-define 72.4%

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

      7. distribute-frac-neg 72.4%

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

      8. distribute-neg-frac2 72.4%

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

      9. sub-neg 72.4%

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

      10. distribute-neg-in 72.4%

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

      11. remove-double-neg 72.4%

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

      12. +-commutative 72.4%

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

      13. sub-neg 72.4%

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

   3. Simplified 72.4%

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

   5. Taylor expanded in z around inf 51.2%

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

      1. associate-/l* 57.7%

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

   7. Simplified 57.7%

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

   if -1.9499999999999999e183 < y < -6.5e77 or -0.060999999999999999 < y < 2.8999999999999999e202

   1. Initial program 83.7%

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

   3. Taylor expanded in a around inf 71.9%

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

      1. +-commutative 71.9%

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

   5. Simplified 71.9%

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

   if 2.8999999999999999e202 < y

   1. Initial program 53.9%

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

      1. sub-neg 53.9%

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

      2. +-commutative 53.9%

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

      3. distribute-frac-neg 53.9%

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

      4. distribute-rgt-neg-out 53.9%

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

      5. associate-/l* 54.0%

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

      6. fma-define 54.6%

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

      7. distribute-frac-neg 54.6%

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

      8. distribute-neg-frac2 54.6%

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

      9. sub-neg 54.6%

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

      10. distribute-neg-in 54.6%

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

      11. remove-double-neg 54.6%

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

      12. +-commutative 54.6%

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

      13. sub-neg 54.6%

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

   3. Simplified 54.6%

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

   5. Taylor expanded in y around inf 58.0%

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

      1. associate--l+ 58.0%

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

      2. div-sub 58.0%

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

   7. Simplified 58.0%

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

   8. Taylor expanded in t around inf 67.9%

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

      1. mul-1-neg 67.9%

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

      2. sub-neg 67.9%

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

   10. Simplified 67.9%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+183}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+77}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -0.061:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+202}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{-49} \lor \neg \left(a \leq 4.15 \cdot 10^{-38}\right):\\ \;\;\;\;x + \left(y - y \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.8e-49) (not (<= a 4.15e-38)))
   (+ x (- y (* y (/ z a))))
   (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.8e-49) || !(a <= 4.15e-38)) {
		tmp = x + (y - (y * (z / a)));
	} 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 <= (-3.8d-49)) .or. (.not. (a <= 4.15d-38))) then
        tmp = x + (y - (y * (z / a)))
    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 <= -3.8e-49) || !(a <= 4.15e-38)) {
		tmp = x + (y - (y * (z / a)));
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.8e-49) or not (a <= 4.15e-38):
		tmp = x + (y - (y * (z / a)))
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.8e-49) || !(a <= 4.15e-38))
		tmp = Float64(x + Float64(y - Float64(y * Float64(z / a))));
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.8e-49) || ~((a <= 4.15e-38)))
		tmp = x + (y - (y * (z / a)));
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.8e-49], N[Not[LessEqual[a, 4.15e-38]], $MachinePrecision]], N[(x + N[(y - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.7999999999999997e-49 or 4.1499999999999998e-38 < a

   1. Initial program 77.7%

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

   3. Taylor expanded in t around 0 76.6%

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

      1. sub-neg 76.6%

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

      2. associate-+r+ 76.6%

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

      3. mul-1-neg 76.6%

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

      4. +-commutative 76.6%

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

      5. mul-1-neg 76.6%

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

      6. sub-neg 76.6%

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

      7. associate-/l* 80.6%

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

   5. Simplified 80.6%

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

   if -3.7999999999999997e-49 < a < 4.1499999999999998e-38

   1. Initial program 77.1%

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

      1. associate--l+ 81.6%

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

      2. associate-/l* 82.2%

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

   3. Simplified 82.2%

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

   5. Taylor expanded in z around inf 93.6%

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

      1. associate-*r/ 93.6%

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

      2. associate-*r* 93.6%

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

      3. neg-mul-1 93.6%

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

   7. Simplified 93.6%

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

   8. Taylor expanded in a around 0 87.3%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{-49} \lor \neg \left(a \leq 4.15 \cdot 10^{-38}\right):\\ \;\;\;\;x + \left(y - y \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -620000000 \lor \neg \left(a \leq 13600000000\right):\\ \;\;\;\;x + \left(y - y \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -620000000.0) (not (<= a 13600000000.0)))
   (+ x (- y (* y (/ z a))))
   (- x (/ (* y z) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -620000000.0) || !(a <= 13600000000.0)) {
		tmp = x + (y - (y * (z / a)));
	} else {
		tmp = x - ((y * z) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-620000000.0d0)) .or. (.not. (a <= 13600000000.0d0))) then
        tmp = x + (y - (y * (z / a)))
    else
        tmp = x - ((y * z) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -620000000.0) || !(a <= 13600000000.0)) {
		tmp = x + (y - (y * (z / a)));
	} else {
		tmp = x - ((y * z) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -620000000.0) or not (a <= 13600000000.0):
		tmp = x + (y - (y * (z / a)))
	else:
		tmp = x - ((y * z) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -620000000.0) || !(a <= 13600000000.0))
		tmp = Float64(x + Float64(y - Float64(y * Float64(z / a))));
	else
		tmp = Float64(x - Float64(Float64(y * z) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -620000000.0) || ~((a <= 13600000000.0)))
		tmp = x + (y - (y * (z / a)));
	else
		tmp = x - ((y * z) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -620000000.0], N[Not[LessEqual[a, 13600000000.0]], $MachinePrecision]], N[(x + N[(y - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.2e8 or 1.36e10 < a

   1. Initial program 78.9%

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

   3. Taylor expanded in t around 0 80.8%

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

      1. sub-neg 80.8%

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

      2. associate-+r+ 80.8%

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

      3. mul-1-neg 80.8%

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

      4. +-commutative 80.8%

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

      5. mul-1-neg 80.8%

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

      6. sub-neg 80.8%

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

      7. associate-/l* 85.7%

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

   5. Simplified 85.7%

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

   if -6.2e8 < a < 1.36e10

   1. Initial program 76.2%

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

      1. associate--l+ 82.1%

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

      2. associate-/l* 81.9%

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

   3. Simplified 81.9%

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

   5. Taylor expanded in z around inf 87.4%

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

      1. associate-*r/ 87.4%

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

      2. associate-*r* 87.4%

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

      3. neg-mul-1 87.4%

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

   7. Simplified 87.4%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -620000000 \lor \neg \left(a \leq 13600000000\right):\\ \;\;\;\;x + \left(y - y \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{-78}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-202}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.5e-78)
   (+ x y)
   (if (<= a -4.1e-196) (* y (/ z t)) (if (<= a 6e-202) x (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.5e-78) {
		tmp = x + y;
	} else if (a <= -4.1e-196) {
		tmp = y * (z / t);
	} else if (a <= 6e-202) {
		tmp = x;
	} 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 <= (-7.5d-78)) then
        tmp = x + y
    else if (a <= (-4.1d-196)) then
        tmp = y * (z / t)
    else if (a <= 6d-202) then
        tmp = x
    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 <= -7.5e-78) {
		tmp = x + y;
	} else if (a <= -4.1e-196) {
		tmp = y * (z / t);
	} else if (a <= 6e-202) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7.5e-78:
		tmp = x + y
	elif a <= -4.1e-196:
		tmp = y * (z / t)
	elif a <= 6e-202:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.5e-78)
		tmp = Float64(x + y);
	elseif (a <= -4.1e-196)
		tmp = Float64(y * Float64(z / t));
	elseif (a <= 6e-202)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7.5e-78)
		tmp = x + y;
	elseif (a <= -4.1e-196)
		tmp = y * (z / t);
	elseif (a <= 6e-202)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.5e-78], N[(x + y), $MachinePrecision], If[LessEqual[a, -4.1e-196], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e-202], x, N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.50000000000000041e-78 or 6.00000000000000022e-202 < a

   1. Initial program 78.1%

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

   3. Taylor expanded in a around inf 68.6%

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

      1. +-commutative 68.6%

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

   5. Simplified 68.6%

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

   if -7.50000000000000041e-78 < a < -4.10000000000000021e-196

   1. Initial program 79.0%

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

      1. sub-neg 79.0%

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

      2. +-commutative 79.0%

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

      3. distribute-frac-neg 79.0%

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

      4. distribute-rgt-neg-out 79.0%

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

      5. associate-/l* 76.4%

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

      6. fma-define 76.2%

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

      7. distribute-frac-neg 76.2%

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

      8. distribute-neg-frac2 76.2%

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

      9. sub-neg 76.2%

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

      10. distribute-neg-in 76.2%

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

      11. remove-double-neg 76.2%

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

      12. +-commutative 76.2%

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

      13. sub-neg 76.2%

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

   3. Simplified 76.2%

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

   5. Taylor expanded in z around inf 68.7%

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

   6. Taylor expanded in t around inf 62.5%

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

      1. associate-/l* 62.3%

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

   8. Simplified 62.3%

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

   if -4.10000000000000021e-196 < a < 6.00000000000000022e-202

   1. Initial program 73.7%

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

   3. Taylor expanded in x around inf 58.3%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{-78}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-202}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-78}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-195}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-202}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7e-78)
   (+ x y)
   (if (<= a -1.2e-195) (/ (* y z) t) (if (<= a 7e-202) x (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7e-78) {
		tmp = x + y;
	} else if (a <= -1.2e-195) {
		tmp = (y * z) / t;
	} else if (a <= 7e-202) {
		tmp = x;
	} 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 <= (-7d-78)) then
        tmp = x + y
    else if (a <= (-1.2d-195)) then
        tmp = (y * z) / t
    else if (a <= 7d-202) then
        tmp = x
    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 <= -7e-78) {
		tmp = x + y;
	} else if (a <= -1.2e-195) {
		tmp = (y * z) / t;
	} else if (a <= 7e-202) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7e-78:
		tmp = x + y
	elif a <= -1.2e-195:
		tmp = (y * z) / t
	elif a <= 7e-202:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7e-78)
		tmp = Float64(x + y);
	elseif (a <= -1.2e-195)
		tmp = Float64(Float64(y * z) / t);
	elseif (a <= 7e-202)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7e-78)
		tmp = x + y;
	elseif (a <= -1.2e-195)
		tmp = (y * z) / t;
	elseif (a <= 7e-202)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7e-78], N[(x + y), $MachinePrecision], If[LessEqual[a, -1.2e-195], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 7e-202], x, N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.9999999999999999e-78 or 6.9999999999999998e-202 < a

   1. Initial program 78.1%

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

   3. Taylor expanded in a around inf 68.6%

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

      1. +-commutative 68.6%

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

   5. Simplified 68.6%

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

   if -6.9999999999999999e-78 < a < -1.2e-195

   1. Initial program 79.0%

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

      1. sub-neg 79.0%

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

      2. +-commutative 79.0%

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

      3. distribute-frac-neg 79.0%

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

      4. distribute-rgt-neg-out 79.0%

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

      5. associate-/l* 76.4%

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

      6. fma-define 76.2%

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

      7. distribute-frac-neg 76.2%

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

      8. distribute-neg-frac2 76.2%

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

      9. sub-neg 76.2%

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

      10. distribute-neg-in 76.2%

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

      11. remove-double-neg 76.2%

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

      12. +-commutative 76.2%

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

      13. sub-neg 76.2%

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

   3. Simplified 76.2%

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

   5. Taylor expanded in z around inf 68.7%

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

   6. Taylor expanded in t around inf 62.5%

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

   if -1.2e-195 < a < 6.9999999999999998e-202

   1. Initial program 73.7%

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

   3. Taylor expanded in x around inf 58.3%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-78}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-195}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-202}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.95 \cdot 10^{-74}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-202}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.95e-74)
   (+ x y)
   (if (<= a -8e-196) (* y (/ z (- t a))) (if (<= a 6.8e-202) x (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.95e-74) {
		tmp = x + y;
	} else if (a <= -8e-196) {
		tmp = y * (z / (t - a));
	} else if (a <= 6.8e-202) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.95d-74)) then
        tmp = x + y
    else if (a <= (-8d-196)) then
        tmp = y * (z / (t - a))
    else if (a <= 6.8d-202) then
        tmp = x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.95e-74) {
		tmp = x + y;
	} else if (a <= -8e-196) {
		tmp = y * (z / (t - a));
	} else if (a <= 6.8e-202) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.95e-74:
		tmp = x + y
	elif a <= -8e-196:
		tmp = y * (z / (t - a))
	elif a <= 6.8e-202:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.95e-74)
		tmp = Float64(x + y);
	elseif (a <= -8e-196)
		tmp = Float64(y * Float64(z / Float64(t - a)));
	elseif (a <= 6.8e-202)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.95e-74)
		tmp = x + y;
	elseif (a <= -8e-196)
		tmp = y * (z / (t - a));
	elseif (a <= 6.8e-202)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.95e-74], N[(x + y), $MachinePrecision], If[LessEqual[a, -8e-196], N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.8e-202], x, N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.94999999999999983e-74 or 6.80000000000000025e-202 < a

   1. Initial program 78.1%

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

   3. Taylor expanded in a around inf 68.6%

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

      1. +-commutative 68.6%

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

   5. Simplified 68.6%

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

   if -2.94999999999999983e-74 < a < -8.0000000000000004e-196

   1. Initial program 79.0%

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

      1. sub-neg 79.0%

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

      2. +-commutative 79.0%

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

      3. distribute-frac-neg 79.0%

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

      4. distribute-rgt-neg-out 79.0%

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

      5. associate-/l* 76.4%

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

      6. fma-define 76.2%

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

      7. distribute-frac-neg 76.2%

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

      8. distribute-neg-frac2 76.2%

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

      9. sub-neg 76.2%

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

      10. distribute-neg-in 76.2%

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

      11. remove-double-neg 76.2%

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

      12. +-commutative 76.2%

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

      13. sub-neg 76.2%

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

   3. Simplified 76.2%

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

   5. Taylor expanded in z around inf 68.7%

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

      1. associate-/l* 65.4%

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

   7. Simplified 65.4%

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

   if -8.0000000000000004e-196 < a < 6.80000000000000025e-202

   1. Initial program 73.7%

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

   3. Taylor expanded in x around inf 58.3%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.95 \cdot 10^{-74}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-202}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -10000 \lor \neg \left(a \leq 3.5 \cdot 10^{+21}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -10000.0) (not (<= a 3.5e+21))) (+ x y) (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -10000.0) || !(a <= 3.5e+21)) {
		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 <= (-10000.0d0)) .or. (.not. (a <= 3.5d+21))) 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 <= -10000.0) || !(a <= 3.5e+21)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -10000.0) or not (a <= 3.5e+21):
		tmp = x + y
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -10000.0) || !(a <= 3.5e+21))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -10000.0) || ~((a <= 3.5e+21)))
		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, -10000.0], N[Not[LessEqual[a, 3.5e+21]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1e4 or 3.5e21 < a

   1. Initial program 78.9%

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

   3. Taylor expanded in a around inf 76.7%

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

      1. +-commutative 76.7%

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

   5. Simplified 76.7%

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

   if -1e4 < a < 3.5e21

   1. Initial program 76.2%

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

      1. associate--l+ 82.1%

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

      2. associate-/l* 81.9%

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

   3. Simplified 81.9%

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

   5. Taylor expanded in z around inf 87.4%

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

      1. associate-*r/ 87.4%

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

      2. associate-*r* 87.4%

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

      3. neg-mul-1 87.4%

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

   7. Simplified 87.4%

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

   8. Taylor expanded in a around 0 80.0%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -10000 \lor \neg \left(a \leq 3.5 \cdot 10^{+21}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-210}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-132}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -5.5e-210) x (if (<= x 2.6e-132) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5.5e-210) {
		tmp = x;
	} else if (x <= 2.6e-132) {
		tmp = 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 (x <= (-5.5d-210)) then
        tmp = x
    else if (x <= 2.6d-132) then
        tmp = 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 (x <= -5.5e-210) {
		tmp = x;
	} else if (x <= 2.6e-132) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -5.5e-210:
		tmp = x
	elif x <= 2.6e-132:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -5.5e-210)
		tmp = x;
	elseif (x <= 2.6e-132)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -5.5e-210)
		tmp = x;
	elseif (x <= 2.6e-132)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -5.5e-210], x, If[LessEqual[x, 2.6e-132], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.50000000000000024e-210 or 2.6000000000000001e-132 < x

   1. Initial program 79.2%

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

   3. Taylor expanded in x around inf 60.8%

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

   if -5.50000000000000024e-210 < x < 2.6000000000000001e-132

   1. Initial program 71.6%

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

   3. Taylor expanded in x around 0 64.3%

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

   4. Taylor expanded in t around 0 46.5%

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

      1. associate-/l* 49.6%

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

   6. Simplified 49.6%

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

   7. Taylor expanded in z around 0 37.4%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-210}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-132}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.0% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + y), $MachinePrecision]

Derivation

1. Initial program 77.5%

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

3. Taylor expanded in a around inf 60.2%

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

   1. +-commutative 60.2%

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

5. Simplified 60.2%

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

6. Final simplification 60.2%

   \[\leadsto x + y \]
7. Add Preprocessing

Alternative 13: 50.4% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.5%

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

3. Taylor expanded in x around inf 50.8%

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

4. Final simplification 50.8%

   \[\leadsto x \]
5. 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 2024046 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (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))))