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

Percentage Accurate: 77.9% → 92.2%

Time: 10.8s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.9% 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: 92.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+120} \lor \neg \left(t \leq 4 \cdot 10^{+156}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5e+120) (not (<= t 4e+156)))
   (+ x (/ y (/ t (- z a))))
   (+ x (fma (/ (- t z) (- a t)) y y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5e+120) || !(t <= 4e+156)) {
		tmp = x + (y / (t / (z - a)));
	} else {
		tmp = x + fma(((t - z) / (a - t)), y, y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5e+120) || !(t <= 4e+156))
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + fma(Float64(Float64(t - z) / Float64(a - t)), y, y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5e+120], N[Not[LessEqual[t, 4e+156]], $MachinePrecision]], N[(x + N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * y + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.00000000000000019e120 or 3.9999999999999999e156 < t

   1. Initial program 50.5%

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

      1. associate--l+ 59.1%

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

      2. sub-neg 59.1%

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

      3. distribute-frac-neg 59.1%

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

      4. distribute-rgt-neg-out 59.1%

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

      5. +-commutative 59.1%

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

      6. distribute-rgt-neg-out 59.1%

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

      7. distribute-lft-neg-in 59.1%

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

      8. associate-/l* 76.0%

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

      9. associate-/r/ 81.9%

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

      10. fma-def 81.8%

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

      11. sub-neg 81.8%

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

      12. distribute-neg-in 81.8%

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

      13. remove-double-neg 81.8%

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

      14. +-commutative 81.8%

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

      15. sub-neg 81.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in t around inf 70.4%

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

      1. neg-mul-1 70.4%

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

      2. associate-+r+ 81.7%

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

      3. neg-mul-1 81.7%

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

      4. distribute-rgt1-in 81.7%

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

      5. metadata-eval 81.7%

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

      6. mul0-lft 81.7%

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

      7. associate-/l* 97.6%

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

   6. Simplified 97.6%

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

   if -5.00000000000000019e120 < t < 3.9999999999999999e156

   1. Initial program 83.8%

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

      1. associate--l+ 84.3%

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

      2. sub-neg 84.3%

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

      3. distribute-frac-neg 84.3%

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

      4. distribute-rgt-neg-out 84.3%

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

      5. +-commutative 84.3%

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

      6. distribute-rgt-neg-out 84.3%

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

      7. distribute-lft-neg-in 84.3%

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

      8. associate-/l* 92.8%

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

      9. associate-/r/ 93.3%

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

      10. fma-def 93.3%

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

      11. sub-neg 93.3%

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

      12. distribute-neg-in 93.3%

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

      13. remove-double-neg 93.3%

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

      14. +-commutative 93.3%

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

      15. sub-neg 93.3%

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

   3. Simplified 93.3%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+120} \lor \neg \left(t \leq 4 \cdot 10^{+156}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)\\ \end{array} \]

Alternative 2: 78.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-211}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-16} \lor \neg \left(a \leq 4.6 \cdot 10^{+64}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- y (/ y (/ a z))))))
   (if (<= a -1.45e+31)
     t_1
     (if (<= a 1.45e-211)
       (+ x (/ y (/ t z)))
       (if (or (<= a 3.3e-16) (not (<= a 4.6e+64)))
         t_1
         (+ x (* y (/ z t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y - (y / (a / z)));
	double tmp;
	if (a <= -1.45e+31) {
		tmp = t_1;
	} else if (a <= 1.45e-211) {
		tmp = x + (y / (t / z));
	} else if ((a <= 3.3e-16) || !(a <= 4.6e+64)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + (y - (y / (a / z)))
    if (a <= (-1.45d+31)) then
        tmp = t_1
    else if (a <= 1.45d-211) then
        tmp = x + (y / (t / z))
    else if ((a <= 3.3d-16) .or. (.not. (a <= 4.6d+64))) then
        tmp = t_1
    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 t_1 = x + (y - (y / (a / z)));
	double tmp;
	if (a <= -1.45e+31) {
		tmp = t_1;
	} else if (a <= 1.45e-211) {
		tmp = x + (y / (t / z));
	} else if ((a <= 3.3e-16) || !(a <= 4.6e+64)) {
		tmp = t_1;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y - (y / (a / z)))
	tmp = 0
	if a <= -1.45e+31:
		tmp = t_1
	elif a <= 1.45e-211:
		tmp = x + (y / (t / z))
	elif (a <= 3.3e-16) or not (a <= 4.6e+64):
		tmp = t_1
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y - Float64(y / Float64(a / z))))
	tmp = 0.0
	if (a <= -1.45e+31)
		tmp = t_1;
	elseif (a <= 1.45e-211)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	elseif ((a <= 3.3e-16) || !(a <= 4.6e+64))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y - (y / (a / z)));
	tmp = 0.0;
	if (a <= -1.45e+31)
		tmp = t_1;
	elseif (a <= 1.45e-211)
		tmp = x + (y / (t / z));
	elseif ((a <= 3.3e-16) || ~((a <= 4.6e+64)))
		tmp = t_1;
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.45e+31], t$95$1, If[LessEqual[a, 1.45e-211], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 3.3e-16], N[Not[LessEqual[a, 4.6e+64]], $MachinePrecision]], t$95$1, N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.45e31 or 1.45000000000000007e-211 < a < 3.29999999999999988e-16 or 4.6e64 < a

   1. Initial program 76.6%

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

      1. associate--l+ 77.5%

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

      2. associate-/l* 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in t around 0 77.9%

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

      1. associate-/l* 88.0%

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

   6. Simplified 88.0%

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

   if -1.45e31 < a < 1.45000000000000007e-211

   1. Initial program 69.6%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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* 82.0%

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

   3. Simplified 82.0%

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

   4. Taylor expanded in z around inf 89.9%

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

      1. mul-1-neg 89.9%

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

      2. associate-*l/ 93.0%

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

      3. *-commutative 93.0%

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

      4. distribute-rgt-neg-in 93.0%

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

      5. distribute-frac-neg 93.0%

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

   6. Simplified 93.0%

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

   7. Taylor expanded in a around 0 85.3%

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

      1. associate-/l* 89.6%

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

   9. Simplified 89.6%

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

   if 3.29999999999999988e-16 < a < 4.6e64

   1. Initial program 57.5%

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

      1. associate--l+ 63.2%

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

      2. associate-/l* 75.8%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in z around inf 70.2%

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

      1. mul-1-neg 70.2%

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

      2. associate-*l/ 82.0%

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

      3. *-commutative 82.0%

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

      4. distribute-rgt-neg-in 82.0%

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

      5. distribute-frac-neg 82.0%

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

   6. Simplified 82.0%

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

      1. associate-*r/ 70.2%

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

      2. frac-2neg 70.2%

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

      3. add-sqr-sqrt 25.2%

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

      4. sqrt-unprod 57.8%

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

      5. sqr-neg 57.8%

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

      6. sqrt-unprod 44.5%

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

      7. add-sqr-sqrt 57.4%

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

      8. *-commutative 57.4%

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

      9. distribute-lft-neg-in 57.4%

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

      10. add-sqr-sqrt 12.9%

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

      11. sqrt-unprod 52.4%

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

      12. sqr-neg 52.4%

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

      13. sqrt-unprod 44.9%

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

      14. add-sqr-sqrt 70.2%

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

      15. *-commutative 70.2%

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

      16. sub-neg 70.2%

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

      17. distribute-neg-in 70.2%

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

      18. remove-double-neg 70.2%

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

   8. Applied egg-rr 70.2%

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

      1. associate-/l* 81.7%

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

      2. +-commutative 81.7%

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

      3. unsub-neg 81.7%

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

   10. Simplified 81.7%

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

   11. Taylor expanded in t around inf 70.2%

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

       1. associate-*r/ 87.7%

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

   13. Simplified 87.7%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+31}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-211}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-16} \lor \neg \left(a \leq 4.6 \cdot 10^{+64}\right):\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 3: 92.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+122} \lor \neg \left(t \leq 2.5 \cdot 10^{+158}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.15e+122) (not (<= t 2.5e+158)))
   (+ x (/ y (/ t (- z a))))
   (+ x (+ y (/ (- t z) (/ (- a t) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.15e+122) || !(t <= 2.5e+158)) {
		tmp = x + (y / (t / (z - a)));
	} 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) :: tmp
    if ((t <= (-1.15d+122)) .or. (.not. (t <= 2.5d+158))) then
        tmp = x + (y / (t / (z - a)))
    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 tmp;
	if ((t <= -1.15e+122) || !(t <= 2.5e+158)) {
		tmp = x + (y / (t / (z - a)));
	} else {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.15e+122) or not (t <= 2.5e+158):
		tmp = x + (y / (t / (z - a)))
	else:
		tmp = x + (y + ((t - z) / ((a - t) / y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.15e+122) || !(t <= 2.5e+158))
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - a))));
	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)
	tmp = 0.0;
	if ((t <= -1.15e+122) || ~((t <= 2.5e+158)))
		tmp = x + (y / (t / (z - a)));
	else
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.15e+122], N[Not[LessEqual[t, 2.5e+158]], $MachinePrecision]], N[(x + N[(y / N[(t / N[(z - a), $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 2 regimes

2. if t < -1.15e122 or 2.4999999999999998e158 < t

   1. Initial program 50.5%

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

      1. associate--l+ 59.1%

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

      2. sub-neg 59.1%

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

      3. distribute-frac-neg 59.1%

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

      4. distribute-rgt-neg-out 59.1%

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

      5. +-commutative 59.1%

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

      6. distribute-rgt-neg-out 59.1%

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

      7. distribute-lft-neg-in 59.1%

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

      8. associate-/l* 76.0%

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

      9. associate-/r/ 81.9%

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

      10. fma-def 81.8%

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

      11. sub-neg 81.8%

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

      12. distribute-neg-in 81.8%

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

      13. remove-double-neg 81.8%

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

      14. +-commutative 81.8%

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

      15. sub-neg 81.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in t around inf 70.4%

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

      1. neg-mul-1 70.4%

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

      2. associate-+r+ 81.7%

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

      3. neg-mul-1 81.7%

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

      4. distribute-rgt1-in 81.7%

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

      5. metadata-eval 81.7%

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

      6. mul0-lft 81.7%

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

      7. associate-/l* 97.6%

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

   6. Simplified 97.6%

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

   if -1.15e122 < t < 2.4999999999999998e158

   1. Initial program 83.8%

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

      1. associate--l+ 84.3%

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

      2. associate-/l* 92.8%

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

   3. Simplified 92.8%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+122} \lor \neg \left(t \leq 2.5 \cdot 10^{+158}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \end{array} \]

Alternative 4: 76.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+128}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{+30}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+101}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e+128)
   (+ x y)
   (if (<= a -1.85e+30)
     (- x (* z (/ y a)))
     (if (<= a 2.3e+101) (+ x (/ y (/ t z))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+128) {
		tmp = x + y;
	} else if (a <= -1.85e+30) {
		tmp = x - (z * (y / a));
	} else if (a <= 2.3e+101) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9.5d+128)) then
        tmp = x + y
    else if (a <= (-1.85d+30)) then
        tmp = x - (z * (y / a))
    else if (a <= 2.3d+101) then
        tmp = x + (y / (t / z))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+128) {
		tmp = x + y;
	} else if (a <= -1.85e+30) {
		tmp = x - (z * (y / a));
	} else if (a <= 2.3e+101) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.5e+128:
		tmp = x + y
	elif a <= -1.85e+30:
		tmp = x - (z * (y / a))
	elif a <= 2.3e+101:
		tmp = x + (y / (t / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e+128)
		tmp = Float64(x + y);
	elseif (a <= -1.85e+30)
		tmp = Float64(x - Float64(z * Float64(y / a)));
	elseif (a <= 2.3e+101)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.5e+128)
		tmp = x + y;
	elseif (a <= -1.85e+30)
		tmp = x - (z * (y / a));
	elseif (a <= 2.3e+101)
		tmp = x + (y / (t / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e+128], N[(x + y), $MachinePrecision], If[LessEqual[a, -1.85e+30], N[(x - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e+101], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.50000000000000014e128 or 2.3000000000000001e101 < a

   1. Initial program 71.4%

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

      1. +-commutative 71.4%

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

      2. associate--l+ 71.4%

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

      3. *-commutative 71.4%

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

      4. associate-/l* 90.8%

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

      5. associate-/r/ 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in a around inf 79.4%

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

      1. +-commutative 79.4%

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

   6. Simplified 79.4%

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

   if -9.50000000000000014e128 < a < -1.85000000000000008e30

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 96.6%

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

      1. mul-1-neg 96.6%

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

      2. associate-*l/ 96.6%

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

      3. *-commutative 96.6%

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

      4. distribute-rgt-neg-in 96.6%

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

      5. distribute-frac-neg 96.6%

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

   6. Simplified 96.6%

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

   7. Taylor expanded in a around inf 96.6%

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

      1. mul-1-neg 96.6%

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

      2. distribute-neg-frac 96.6%

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

   9. Simplified 96.6%

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

       1. *-commutative 96.6%

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

       2. add-sqr-sqrt 45.0%

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

       3. sqrt-unprod 75.3%

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

       4. sqr-neg 75.3%

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

       5. sqrt-unprod 33.8%

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

       6. add-sqr-sqrt 68.8%

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

       7. cancel-sign-sub 68.8%

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

       8. distribute-frac-neg 68.8%

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

       9. *-commutative 68.8%

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

       10. add-sqr-sqrt 35.0%

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

       11. sqrt-unprod 81.6%

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

       12. sqr-neg 81.6%

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

       13. sqrt-unprod 51.5%

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

       14. add-sqr-sqrt 96.6%

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

   11. Applied egg-rr 96.6%

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

   if -1.85000000000000008e30 < a < 2.3000000000000001e101

   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+ 75.8%

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

      2. associate-/l* 83.2%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in z around inf 83.7%

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

      1. mul-1-neg 83.7%

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

      2. associate-*l/ 88.8%

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

      3. *-commutative 88.8%

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

      4. distribute-rgt-neg-in 88.8%

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

      5. distribute-frac-neg 88.8%

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

   6. Simplified 88.8%

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

   7. Taylor expanded in a around 0 76.2%

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

      1. associate-/l* 81.5%

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

   9. Simplified 81.5%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+128}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{+30}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+101}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5: 76.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.8 \cdot 10^{+128}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{+29}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+101}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.8e+128)
   (+ x y)
   (if (<= a -2.7e+29)
     (- x (* y (/ z a)))
     (if (<= a 1.9e+101) (+ x (/ y (/ t z))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.8e+128) {
		tmp = x + y;
	} else if (a <= -2.7e+29) {
		tmp = x - (y * (z / a));
	} else if (a <= 1.9e+101) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9.8d+128)) then
        tmp = x + y
    else if (a <= (-2.7d+29)) then
        tmp = x - (y * (z / a))
    else if (a <= 1.9d+101) then
        tmp = x + (y / (t / z))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.8e+128) {
		tmp = x + y;
	} else if (a <= -2.7e+29) {
		tmp = x - (y * (z / a));
	} else if (a <= 1.9e+101) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.8e+128:
		tmp = x + y
	elif a <= -2.7e+29:
		tmp = x - (y * (z / a))
	elif a <= 1.9e+101:
		tmp = x + (y / (t / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.8e+128)
		tmp = Float64(x + y);
	elseif (a <= -2.7e+29)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	elseif (a <= 1.9e+101)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.8e+128)
		tmp = x + y;
	elseif (a <= -2.7e+29)
		tmp = x - (y * (z / a));
	elseif (a <= 1.9e+101)
		tmp = x + (y / (t / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.8e+128], N[(x + y), $MachinePrecision], If[LessEqual[a, -2.7e+29], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e+101], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.80000000000000035e128 or 1.8999999999999999e101 < a

   1. Initial program 71.4%

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

      1. +-commutative 71.4%

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

      2. associate--l+ 71.4%

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

      3. *-commutative 71.4%

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

      4. associate-/l* 90.8%

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

      5. associate-/r/ 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in a around inf 79.4%

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

      1. +-commutative 79.4%

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

   6. Simplified 79.4%

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

   if -9.80000000000000035e128 < a < -2.7e29

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 96.6%

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

      1. mul-1-neg 96.6%

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

      2. associate-*l/ 96.6%

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

      3. *-commutative 96.6%

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

      4. distribute-rgt-neg-in 96.6%

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

      5. distribute-frac-neg 96.6%

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

   6. Simplified 96.6%

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

   7. Taylor expanded in a around inf 96.6%

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

      1. associate-*r/ 96.6%

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

      2. *-commutative 96.6%

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

      3. neg-mul-1 96.6%

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

      4. *-commutative 96.6%

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

      5. distribute-rgt-neg-in 96.6%

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

      6. associate-*r/ 96.6%

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

   9. Simplified 96.6%

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

   if -2.7e29 < a < 1.8999999999999999e101

   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+ 75.8%

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

      2. associate-/l* 83.2%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in z around inf 83.7%

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

      1. mul-1-neg 83.7%

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

      2. associate-*l/ 88.8%

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

      3. *-commutative 88.8%

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

      4. distribute-rgt-neg-in 88.8%

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

      5. distribute-frac-neg 88.8%

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

   6. Simplified 88.8%

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

   7. Taylor expanded in a around 0 76.2%

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

      1. associate-/l* 81.5%

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

   9. Simplified 81.5%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.8 \cdot 10^{+128}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{+29}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+101}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6: 87.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+139} \lor \neg \left(a \leq 1.46 \cdot 10^{+65}\right):\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t - a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.6e+139) (not (<= a 1.46e+65)))
   (+ x (- y (/ y (/ a z))))
   (+ x (/ z (/ (- t a) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.6e+139) || !(a <= 1.46e+65)) {
		tmp = x + (y - (y / (a / z)));
	} else {
		tmp = x + (z / ((t - a) / 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 <= (-2.6d+139)) .or. (.not. (a <= 1.46d+65))) then
        tmp = x + (y - (y / (a / z)))
    else
        tmp = x + (z / ((t - a) / 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 <= -2.6e+139) || !(a <= 1.46e+65)) {
		tmp = x + (y - (y / (a / z)));
	} else {
		tmp = x + (z / ((t - a) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.6e+139) or not (a <= 1.46e+65):
		tmp = x + (y - (y / (a / z)))
	else:
		tmp = x + (z / ((t - a) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.6e+139) || !(a <= 1.46e+65))
		tmp = Float64(x + Float64(y - Float64(y / Float64(a / z))));
	else
		tmp = Float64(x + Float64(z / Float64(Float64(t - a) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.6e+139) || ~((a <= 1.46e+65)))
		tmp = x + (y - (y / (a / z)));
	else
		tmp = x + (z / ((t - a) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.6e+139], N[Not[LessEqual[a, 1.46e+65]], $MachinePrecision]], N[(x + N[(y - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.60000000000000022e139 or 1.45999999999999999e65 < a

   1. Initial program 71.4%

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

      1. associate--l+ 71.9%

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

      2. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in t around 0 74.5%

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

      1. associate-/l* 92.1%

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

   6. Simplified 92.1%

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

   if -2.60000000000000022e139 < a < 1.45999999999999999e65

   1. Initial program 74.0%

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

      1. associate--l+ 78.5%

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

      2. associate-/l* 83.4%

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

   3. Simplified 83.4%

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

   4. Taylor expanded in z around inf 86.2%

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

      1. mul-1-neg 86.2%

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

      2. associate-*l/ 89.1%

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

      3. *-commutative 89.1%

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

      4. distribute-rgt-neg-in 89.1%

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

      5. distribute-frac-neg 89.1%

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

   6. Simplified 89.1%

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

      1. associate-*r/ 86.2%

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

      2. frac-2neg 86.2%

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

      3. add-sqr-sqrt 41.3%

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

      4. sqrt-unprod 67.3%

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

      5. sqr-neg 67.3%

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

      6. sqrt-unprod 30.9%

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

      7. add-sqr-sqrt 55.5%

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

      8. *-commutative 55.5%

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

      9. distribute-lft-neg-in 55.5%

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

      10. add-sqr-sqrt 24.6%

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

      11. sqrt-unprod 64.2%

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

      12. sqr-neg 64.2%

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

      13. sqrt-unprod 44.7%

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

      14. add-sqr-sqrt 86.2%

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

      15. *-commutative 86.2%

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

      16. sub-neg 86.2%

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

      17. distribute-neg-in 86.2%

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

      18. remove-double-neg 86.2%

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

   8. Applied egg-rr 86.2%

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

      1. associate-/l* 89.1%

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

      2. +-commutative 89.1%

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

      3. unsub-neg 89.1%

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

   10. Simplified 89.1%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+139} \lor \neg \left(a \leq 1.46 \cdot 10^{+65}\right):\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t - a}{y}}\\ \end{array} \]

Alternative 7: 87.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.04 \cdot 10^{+139} \lor \neg \left(a \leq 1.5 \cdot 10^{+101}\right):\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.04e+139) (not (<= a 1.5e+101)))
   (+ 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 <= -1.04e+139) || !(a <= 1.5e+101)) {
		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 <= (-1.04d+139)) .or. (.not. (a <= 1.5d+101))) 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 <= -1.04e+139) || !(a <= 1.5e+101)) {
		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 <= -1.04e+139) or not (a <= 1.5e+101):
		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 <= -1.04e+139) || !(a <= 1.5e+101))
		tmp = Float64(x + Float64(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 <= -1.04e+139) || ~((a <= 1.5e+101)))
		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, -1.04e+139], N[Not[LessEqual[a, 1.5e+101]], $MachinePrecision]], N[(x + N[(y - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.04e139 or 1.49999999999999997e101 < a

   1. Initial program 73.2%

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

      1. associate--l+ 73.7%

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

      2. associate-/l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in t around 0 76.6%

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

      1. associate-/l* 92.9%

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

   6. Simplified 92.9%

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

   if -1.04e139 < a < 1.49999999999999997e101

   1. Initial program 73.0%

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

      1. associate--l+ 77.5%

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

      2. associate-/l* 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in z around inf 84.3%

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

      1. mul-1-neg 84.3%

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

      2. associate-*l/ 88.8%

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

      3. *-commutative 88.8%

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

      4. distribute-rgt-neg-in 88.8%

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

      5. distribute-frac-neg 88.8%

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

   6. Simplified 88.8%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.04 \cdot 10^{+139} \lor \neg \left(a \leq 1.5 \cdot 10^{+101}\right):\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 8: 59.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+82} \lor \neg \left(y \leq 10^{+117}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3.8e+82) (not (<= y 1e+117))) (* y (- 1.0 (/ z a))) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.8e+82) || !(y <= 1e+117)) {
		tmp = y * (1.0 - (z / a));
	} 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 ((y <= (-3.8d+82)) .or. (.not. (y <= 1d+117))) then
        tmp = y * (1.0d0 - (z / a))
    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 ((y <= -3.8e+82) || !(y <= 1e+117)) {
		tmp = y * (1.0 - (z / a));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3.8e+82) or not (y <= 1e+117):
		tmp = y * (1.0 - (z / a))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3.8e+82) || !(y <= 1e+117))
		tmp = Float64(y * Float64(1.0 - Float64(z / a)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -3.8e+82) || ~((y <= 1e+117)))
		tmp = y * (1.0 - (z / a));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3.8e+82], N[Not[LessEqual[y, 1e+117]], $MachinePrecision]], N[(y * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.80000000000000033e82 or 1.00000000000000005e117 < y

   1. Initial program 52.1%

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

      1. +-commutative 52.1%

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

      2. associate--l+ 52.1%

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

      3. *-commutative 52.1%

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

      4. associate-/l* 78.4%

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

      5. associate-/r/ 75.5%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in t around 0 53.9%

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

   5. Taylor expanded in x around 0 46.0%

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

      1. associate-*r/ 59.7%

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

      2. *-commutative 59.7%

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

      3. cancel-sign-sub-inv 59.7%

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

      4. *-lft-identity 59.7%

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

      5. mul-1-neg 59.7%

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

      6. distribute-rgt-in 59.7%

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

      7. mul-1-neg 59.7%

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

      8. sub-neg 59.7%

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

   7. Simplified 59.7%

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

   if -3.80000000000000033e82 < y < 1.00000000000000005e117

   1. Initial program 85.2%

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

      1. +-commutative 85.2%

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

      2. associate--l+ 85.2%

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

      3. *-commutative 85.2%

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

      4. associate-/l* 88.0%

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

      5. associate-/r/ 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in y around 0 73.4%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+82} \lor \neg \left(y \leq 10^{+117}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 76.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+75} \lor \neg \left(a \leq 2.32 \cdot 10^{+101}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.7e+75) (not (<= a 2.32e+101))) (+ x y) (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.7e+75) || !(a <= 2.32e+101)) {
		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 <= (-2.7d+75)) .or. (.not. (a <= 2.32d+101))) 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 <= -2.7e+75) || !(a <= 2.32e+101)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.7e+75) or not (a <= 2.32e+101):
		tmp = x + y
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.7e+75) || !(a <= 2.32e+101))
		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 <= -2.7e+75) || ~((a <= 2.32e+101)))
		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, -2.7e+75], N[Not[LessEqual[a, 2.32e+101]], $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 < -2.69999999999999998e75 or 2.32e101 < a

   1. Initial program 74.4%

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

      1. +-commutative 74.4%

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

      2. associate--l+ 74.4%

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

      3. *-commutative 74.4%

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

      4. associate-/l* 91.8%

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

      5. associate-/r/ 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in a around inf 77.8%

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

      1. +-commutative 77.8%

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

   6. Simplified 77.8%

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

   if -2.69999999999999998e75 < a < 2.32e101

   1. Initial program 72.2%

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

      1. associate--l+ 77.2%

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

      2. associate-/l* 84.2%

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

   3. Simplified 84.2%

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

   4. Taylor expanded in z around inf 84.7%

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

      1. mul-1-neg 84.7%

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

      2. associate-*l/ 89.4%

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

      3. *-commutative 89.4%

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

      4. distribute-rgt-neg-in 89.4%

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

      5. distribute-frac-neg 89.4%

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

   6. Simplified 89.4%

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

      1. associate-*r/ 84.7%

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

      2. frac-2neg 84.7%

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

      3. add-sqr-sqrt 40.3%

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

      4. sqrt-unprod 66.1%

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

      5. sqr-neg 66.1%

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

      6. sqrt-unprod 30.8%

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

      7. add-sqr-sqrt 54.6%

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

      8. *-commutative 54.6%

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

      9. distribute-lft-neg-in 54.6%

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

      10. add-sqr-sqrt 23.8%

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

      11. sqrt-unprod 63.0%

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

      12. sqr-neg 63.0%

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

      13. sqrt-unprod 44.3%

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

      14. add-sqr-sqrt 84.7%

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

      15. *-commutative 84.7%

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

      16. sub-neg 84.7%

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

      17. distribute-neg-in 84.7%

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

      18. remove-double-neg 84.7%

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

   8. Applied egg-rr 84.7%

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

      1. associate-/l* 89.4%

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

      2. +-commutative 89.4%

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

      3. unsub-neg 89.4%

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

   10. Simplified 89.4%

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

   11. Taylor expanded in t around inf 76.4%

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

       1. associate-*r/ 81.2%

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

   13. Simplified 81.2%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+75} \lor \neg \left(a \leq 2.32 \cdot 10^{+101}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 10: 76.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+75} \lor \neg \left(a \leq 2.65 \cdot 10^{+101}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7.2e+75) (not (<= a 2.65e+101))) (+ x y) (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.2e+75) || !(a <= 2.65e+101)) {
		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 <= (-7.2d+75)) .or. (.not. (a <= 2.65d+101))) 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 <= -7.2e+75) || !(a <= 2.65e+101)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7.2e+75) or not (a <= 2.65e+101):
		tmp = x + y
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7.2e+75) || !(a <= 2.65e+101))
		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 <= -7.2e+75) || ~((a <= 2.65e+101)))
		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, -7.2e+75], N[Not[LessEqual[a, 2.65e+101]], $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 < -7.2e75 or 2.65000000000000003e101 < a

   1. Initial program 74.4%

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

      1. +-commutative 74.4%

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

      2. associate--l+ 74.4%

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

      3. *-commutative 74.4%

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

      4. associate-/l* 91.8%

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

      5. associate-/r/ 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in a around inf 77.8%

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

      1. +-commutative 77.8%

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

   6. Simplified 77.8%

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

   if -7.2e75 < a < 2.65000000000000003e101

   1. Initial program 72.2%

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

      1. associate--l+ 77.2%

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

      2. associate-/l* 84.2%

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

   3. Simplified 84.2%

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

   4. Taylor expanded in z around inf 84.7%

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

      1. mul-1-neg 84.7%

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

      2. associate-*l/ 89.4%

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

      3. *-commutative 89.4%

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

      4. distribute-rgt-neg-in 89.4%

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

      5. distribute-frac-neg 89.4%

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

   6. Simplified 89.4%

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

   7. Taylor expanded in a around 0 76.4%

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

      1. associate-/l* 81.3%

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

   9. Simplified 81.3%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+75} \lor \neg \left(a \leq 2.65 \cdot 10^{+101}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 11: 63.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+87} \lor \neg \left(a \leq 1.1 \cdot 10^{-129}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.8e+87) (not (<= a 1.1e-129))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.8e+87) || !(a <= 1.1e-129)) {
		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 <= (-5.8d+87)) .or. (.not. (a <= 1.1d-129))) 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 <= -5.8e+87) || !(a <= 1.1e-129)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.8e+87) or not (a <= 1.1e-129):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.8e+87) || !(a <= 1.1e-129))
		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 <= -5.8e+87) || ~((a <= 1.1e-129)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.8e+87], N[Not[LessEqual[a, 1.1e-129]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -5.7999999999999996e87 or 1.10000000000000001e-129 < a

   1. Initial program 70.9%

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

      1. +-commutative 70.9%

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

      2. associate--l+ 70.9%

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

      3. *-commutative 70.9%

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

      4. associate-/l* 89.1%

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

      5. associate-/r/ 87.9%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in a around inf 72.6%

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

      1. +-commutative 72.6%

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

   6. Simplified 72.6%

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

   if -5.7999999999999996e87 < a < 1.10000000000000001e-129

   1. Initial program 75.8%

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

      1. +-commutative 75.8%

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

      2. associate--l+ 75.8%

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

      3. *-commutative 75.8%

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

      4. associate-/l* 78.8%

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

      5. associate-/r/ 78.1%

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

   3. Simplified 78.1%

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

   4. Taylor expanded in y around 0 60.7%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+87} \lor \neg \left(a \leq 1.1 \cdot 10^{-129}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 53.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+148}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+162}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.8e+148) y (if (<= y 9e+162) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.8e+148) {
		tmp = y;
	} else if (y <= 9e+162) {
		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 <= (-1.8d+148)) then
        tmp = y
    else if (y <= 9d+162) 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 <= -1.8e+148) {
		tmp = y;
	} else if (y <= 9e+162) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.8e+148:
		tmp = y
	elif y <= 9e+162:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.8e+148)
		tmp = y;
	elseif (y <= 9e+162)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.8e+148)
		tmp = y;
	elseif (y <= 9e+162)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.8e+148], y, If[LessEqual[y, 9e+162], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -1.80000000000000003e148 or 8.99999999999999944e162 < y

   1. Initial program 45.2%

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

      1. +-commutative 45.2%

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

      2. associate--l+ 45.2%

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

      3. *-commutative 45.2%

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

      4. associate-/l* 72.4%

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

      5. associate-/r/ 69.7%

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

   3. Simplified 69.7%

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

   4. Taylor expanded in t around 0 49.3%

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

   5. Taylor expanded in x around 0 45.6%

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

      1. associate-*r/ 61.7%

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

      2. *-commutative 61.7%

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

      3. cancel-sign-sub-inv 61.7%

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

      4. *-lft-identity 61.7%

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

      5. mul-1-neg 61.7%

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

      6. distribute-rgt-in 61.7%

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

      7. mul-1-neg 61.7%

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

      8. sub-neg 61.7%

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

   7. Simplified 61.7%

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

   8. Taylor expanded in z around 0 36.4%

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

   if -1.80000000000000003e148 < y < 8.99999999999999944e162

   1. Initial program 82.2%

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

      1. +-commutative 82.2%

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

      2. associate--l+ 82.2%

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

      3. *-commutative 82.2%

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

      4. associate-/l* 88.4%

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

      5. associate-/r/ 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in y around 0 67.0%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+148}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+162}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 13: 51.2% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.1%

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

   1. +-commutative 73.1%

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

   2. associate--l+ 73.1%

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

   3. *-commutative 73.1%

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

   4. associate-/l* 84.5%

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

   5. associate-/r/ 83.5%

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

3. Simplified 83.5%

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

4. Taylor expanded in y around 0 53.5%

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

5. Final simplification 53.5%

   \[\leadsto x \]

Developer target: 87.6% 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 2023310 
(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))))