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

Percentage Accurate: 77.0% → 87.7%

Time: 14.7s

Alternatives: 17

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.0% 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: 87.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+118} \lor \neg \left(t \leq 7 \cdot 10^{+37}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \frac{-1}{\frac{a - t}{y \cdot \left(z - t\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.05e+118) (not (<= t 7e+37)))
   (+ x (/ y (/ t (- z a))))
   (+ (+ x y) (/ -1.0 (/ (- a t) (* y (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e+118) || !(t <= 7e+37)) {
		tmp = x + (y / (t / (z - a)));
	} else {
		tmp = (x + y) + (-1.0 / ((a - t) / (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 ((t <= (-1.05d+118)) .or. (.not. (t <= 7d+37))) then
        tmp = x + (y / (t / (z - a)))
    else
        tmp = (x + y) + ((-1.0d0) / ((a - t) / (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 ((t <= -1.05e+118) || !(t <= 7e+37)) {
		tmp = x + (y / (t / (z - a)));
	} else {
		tmp = (x + y) + (-1.0 / ((a - t) / (y * (z - t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.05e+118) or not (t <= 7e+37):
		tmp = x + (y / (t / (z - a)))
	else:
		tmp = (x + y) + (-1.0 / ((a - t) / (y * (z - t))))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.05e+118) || !(t <= 7e+37))
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - a))));
	else
		tmp = Float64(Float64(x + y) + Float64(-1.0 / Float64(Float64(a - t) / Float64(y * Float64(z - t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.05e+118) || ~((t <= 7e+37)))
		tmp = x + (y / (t / (z - a)));
	else
		tmp = (x + y) + (-1.0 / ((a - t) / (y * (z - t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.05e+118], N[Not[LessEqual[t, 7e+37]], $MachinePrecision]], N[(x + N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(-1.0 / N[(N[(a - t), $MachinePrecision] / N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e118 or 7e37 < t

   1. Initial program 46.4%

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

      1. sub-neg 46.4%

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

      2. distribute-frac-neg 46.4%

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

      3. distribute-rgt-neg-out 46.4%

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

      4. +-commutative 46.4%

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

      5. associate-*l/ 59.6%

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

      6. distribute-rgt-neg-in 59.6%

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

      7. distribute-lft-neg-in 59.6%

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

      8. distribute-frac-neg 59.6%

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

      9. fma-def 59.6%

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

      10. sub-neg 59.6%

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

      11. distribute-neg-in 59.6%

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

      12. remove-double-neg 59.6%

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

      13. +-commutative 59.6%

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

      14. sub-neg 59.6%

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

   3. Simplified 59.6%

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

   5. Taylor expanded in t around inf 61.7%

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

      1. associate-+r+ 81.3%

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

      2. distribute-rgt1-in 81.3%

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

      3. metadata-eval 81.3%

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

      4. mul0-lft 81.3%

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

      5. associate-/l* 92.2%

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

   7. Simplified 92.2%

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

   if -1.05e118 < t < 7e37

   1. Initial program 93.2%

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

      1. associate-*l/ 92.6%

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

   3. Simplified 92.6%

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

      1. associate-*l/ 93.2%

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

      2. clear-num 93.4%

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

      3. *-commutative 93.4%

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

   6. Applied egg-rr 93.4%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{1}{\frac{a - t}{y \cdot \left(z - t\right)}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+118} \lor \neg \left(t \leq 7 \cdot 10^{+37}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \frac{-1}{\frac{a - t}{y \cdot \left(z - t\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 62.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-\frac{y}{a - t}\right)\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{+112}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-22}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-235}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-12}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (- (/ y (- a t))))))
   (if (<= a -9.5e+112)
     (+ x y)
     (if (<= a -1.9e+77)
       (* y (- 1.0 (/ z a)))
       (if (<= a -1.7e-22)
         (+ x y)
         (if (<= a -1.5e-210)
           t_1
           (if (<= a -1e-235)
             (- x (/ y (/ t a)))
             (if (<= a 2e-299)
               t_1
               (if (<= a 2.3e-12) (- x (/ (* y a) t)) (+ x y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * -(y / (a - t));
	double tmp;
	if (a <= -9.5e+112) {
		tmp = x + y;
	} else if (a <= -1.9e+77) {
		tmp = y * (1.0 - (z / a));
	} else if (a <= -1.7e-22) {
		tmp = x + y;
	} else if (a <= -1.5e-210) {
		tmp = t_1;
	} else if (a <= -1e-235) {
		tmp = x - (y / (t / a));
	} else if (a <= 2e-299) {
		tmp = t_1;
	} else if (a <= 2.3e-12) {
		tmp = x - ((y * a) / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -(y / (a - t))
    if (a <= (-9.5d+112)) then
        tmp = x + y
    else if (a <= (-1.9d+77)) then
        tmp = y * (1.0d0 - (z / a))
    else if (a <= (-1.7d-22)) then
        tmp = x + y
    else if (a <= (-1.5d-210)) then
        tmp = t_1
    else if (a <= (-1d-235)) then
        tmp = x - (y / (t / a))
    else if (a <= 2d-299) then
        tmp = t_1
    else if (a <= 2.3d-12) then
        tmp = x - ((y * a) / t)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * -(y / (a - t));
	double tmp;
	if (a <= -9.5e+112) {
		tmp = x + y;
	} else if (a <= -1.9e+77) {
		tmp = y * (1.0 - (z / a));
	} else if (a <= -1.7e-22) {
		tmp = x + y;
	} else if (a <= -1.5e-210) {
		tmp = t_1;
	} else if (a <= -1e-235) {
		tmp = x - (y / (t / a));
	} else if (a <= 2e-299) {
		tmp = t_1;
	} else if (a <= 2.3e-12) {
		tmp = x - ((y * a) / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * -(y / (a - t))
	tmp = 0
	if a <= -9.5e+112:
		tmp = x + y
	elif a <= -1.9e+77:
		tmp = y * (1.0 - (z / a))
	elif a <= -1.7e-22:
		tmp = x + y
	elif a <= -1.5e-210:
		tmp = t_1
	elif a <= -1e-235:
		tmp = x - (y / (t / a))
	elif a <= 2e-299:
		tmp = t_1
	elif a <= 2.3e-12:
		tmp = x - ((y * a) / t)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(-Float64(y / Float64(a - t))))
	tmp = 0.0
	if (a <= -9.5e+112)
		tmp = Float64(x + y);
	elseif (a <= -1.9e+77)
		tmp = Float64(y * Float64(1.0 - Float64(z / a)));
	elseif (a <= -1.7e-22)
		tmp = Float64(x + y);
	elseif (a <= -1.5e-210)
		tmp = t_1;
	elseif (a <= -1e-235)
		tmp = Float64(x - Float64(y / Float64(t / a)));
	elseif (a <= 2e-299)
		tmp = t_1;
	elseif (a <= 2.3e-12)
		tmp = Float64(x - Float64(Float64(y * a) / t));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * -(y / (a - t));
	tmp = 0.0;
	if (a <= -9.5e+112)
		tmp = x + y;
	elseif (a <= -1.9e+77)
		tmp = y * (1.0 - (z / a));
	elseif (a <= -1.7e-22)
		tmp = x + y;
	elseif (a <= -1.5e-210)
		tmp = t_1;
	elseif (a <= -1e-235)
		tmp = x - (y / (t / a));
	elseif (a <= 2e-299)
		tmp = t_1;
	elseif (a <= 2.3e-12)
		tmp = x - ((y * a) / t);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * (-N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[a, -9.5e+112], N[(x + y), $MachinePrecision], If[LessEqual[a, -1.9e+77], N[(y * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.7e-22], N[(x + y), $MachinePrecision], If[LessEqual[a, -1.5e-210], t$95$1, If[LessEqual[a, -1e-235], N[(x - N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2e-299], t$95$1, If[LessEqual[a, 2.3e-12], N[(x - N[(N[(y * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -9.5000000000000008e112 or -1.9000000000000001e77 < a < -1.6999999999999999e-22 or 2.29999999999999989e-12 < a

   1. Initial program 83.1%

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

      1. associate-*l/ 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in a around inf 84.3%

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

      1. +-commutative 84.3%

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

   7. Simplified 84.3%

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

   if -9.5000000000000008e112 < a < -1.9000000000000001e77

   1. Initial program 99.8%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 99.8%

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

      1. sub-neg 99.8%

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

      2. associate-*r/ 100.0%

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

      3. *-rgt-identity 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. distribute-frac-neg 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. distribute-frac-neg 100.0%

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

      8. sub-neg 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in t around 0 85.7%

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

   if -1.6999999999999999e-22 < a < -1.5000000000000001e-210 or -9.9999999999999996e-236 < a < 1.99999999999999998e-299

   1. Initial program 70.6%

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

      1. associate-*l/ 73.8%

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

   3. Simplified 73.8%

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

   5. Taylor expanded in z around inf 70.1%

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

      1. associate-/l* 71.6%

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

   7. Simplified 71.6%

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

      1. div-sub 71.5%

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

   9. Applied egg-rr 71.5%

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

   10. Taylor expanded in z around inf 60.3%

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

       1. mul-1-neg 60.3%

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

       2. associate-/l* 63.6%

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

       3. distribute-frac-neg 63.6%

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

   12. Simplified 63.6%

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

       1. add-sqr-sqrt 30.4%

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

       2. sqrt-unprod 30.1%

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

       3. sqr-neg 30.1%

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

       4. sqrt-unprod 1.0%

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

       5. sub-div 1.2%

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

       6. add-sqr-sqrt 1.9%

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

       7. frac-2neg 1.9%

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

       8. distribute-frac-neg 1.9%

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

       9. remove-double-neg 1.9%

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

       10. frac-2neg 1.9%

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

       11. sub-div 1.8%

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

       12. associate-/r/ 1.8%

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

       13. *-commutative 1.8%

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

       14. add-sqr-sqrt 0.7%

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

       15. sqrt-unprod 29.1%

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

       16. sqr-neg 29.1%

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

       17. sqrt-unprod 34.8%

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

       18. add-sqr-sqrt 67.1%

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

   14. Applied egg-rr 67.1%

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

   if -1.5000000000000001e-210 < a < -9.9999999999999996e-236

   1. Initial program 65.4%

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

      1. associate-*l/ 65.7%

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

   3. Simplified 65.7%

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

   5. Taylor expanded in t around -inf 77.0%

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

      1. mul-1-neg 77.0%

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

      2. unsub-neg 77.0%

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

      3. *-commutative 77.0%

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

   7. Simplified 77.0%

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

   8. Taylor expanded in a around inf 67.1%

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

      1. *-commutative 67.1%

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

      2. associate-/l* 67.1%

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

   10. Simplified 67.1%

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

   if 1.99999999999999998e-299 < a < 2.29999999999999989e-12

   1. Initial program 69.5%

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

      1. associate-*l/ 68.0%

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

   3. Simplified 68.0%

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

   5. Taylor expanded in t around -inf 86.3%

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

      1. mul-1-neg 86.3%

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

      2. unsub-neg 86.3%

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

      3. *-commutative 86.3%

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

   7. Simplified 86.3%

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

   8. Taylor expanded in a around inf 63.2%

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

      1. *-commutative 63.2%

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

   10. Simplified 63.2%

       \[\leadsto x - \color{blue}{\frac{y \cdot a}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+112}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-22}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-210}:\\ \;\;\;\;z \cdot \left(-\frac{y}{a - t}\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-235}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-299}:\\ \;\;\;\;z \cdot \left(-\frac{y}{a - t}\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-12}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+112}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-22} \lor \neg \left(a \leq 2.45 \cdot 10^{-11}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e+112)
   (+ x y)
   (if (<= a -1.9e+77)
     (* y (- 1.0 (/ z a)))
     (if (or (<= a -3.5e-22) (not (<= a 2.45e-11)))
       (+ x y)
       (+ x (/ (* y z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+112) {
		tmp = x + y;
	} else if (a <= -1.9e+77) {
		tmp = y * (1.0 - (z / a));
	} else if ((a <= -3.5e-22) || !(a <= 2.45e-11)) {
		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 <= (-9.5d+112)) then
        tmp = x + y
    else if (a <= (-1.9d+77)) then
        tmp = y * (1.0d0 - (z / a))
    else if ((a <= (-3.5d-22)) .or. (.not. (a <= 2.45d-11))) 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 <= -9.5e+112) {
		tmp = x + y;
	} else if (a <= -1.9e+77) {
		tmp = y * (1.0 - (z / a));
	} else if ((a <= -3.5e-22) || !(a <= 2.45e-11)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.5e+112:
		tmp = x + y
	elif a <= -1.9e+77:
		tmp = y * (1.0 - (z / a))
	elif (a <= -3.5e-22) or not (a <= 2.45e-11):
		tmp = x + y
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e+112)
		tmp = Float64(x + y);
	elseif (a <= -1.9e+77)
		tmp = Float64(y * Float64(1.0 - Float64(z / a)));
	elseif ((a <= -3.5e-22) || !(a <= 2.45e-11))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.5e+112)
		tmp = x + y;
	elseif (a <= -1.9e+77)
		tmp = y * (1.0 - (z / a));
	elseif ((a <= -3.5e-22) || ~((a <= 2.45e-11)))
		tmp = x + y;
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e+112], N[(x + y), $MachinePrecision], If[LessEqual[a, -1.9e+77], N[(y * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -3.5e-22], N[Not[LessEqual[a, 2.45e-11]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.5000000000000008e112 or -1.9000000000000001e77 < a < -3.50000000000000005e-22 or 2.4499999999999999e-11 < a

   1. Initial program 83.1%

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

      1. associate-*l/ 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in a around inf 84.3%

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

      1. +-commutative 84.3%

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

   7. Simplified 84.3%

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

   if -9.5000000000000008e112 < a < -1.9000000000000001e77

   1. Initial program 99.8%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 99.8%

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

      1. sub-neg 99.8%

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

      2. associate-*r/ 100.0%

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

      3. *-rgt-identity 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. distribute-frac-neg 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. distribute-frac-neg 100.0%

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

      8. sub-neg 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in t around 0 85.7%

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

   if -3.50000000000000005e-22 < a < 2.4499999999999999e-11

   1. Initial program 69.8%

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

      1. associate-*l/ 70.6%

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

   3. Simplified 70.6%

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

   5. Taylor expanded in t around -inf 79.2%

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

      1. mul-1-neg 79.2%

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

      2. unsub-neg 79.2%

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

      3. *-commutative 79.2%

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

   7. Simplified 79.2%

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

   8. Taylor expanded in a around 0 76.9%

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

      1. mul-1-neg 76.9%

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

      2. distribute-rgt-neg-in 76.9%

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

   10. Simplified 76.9%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+112}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-22} \lor \neg \left(a \leq 2.45 \cdot 10^{-11}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+112}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{+77}:\\ \;\;\;\;y - z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-22} \lor \neg \left(a \leq 4.6 \cdot 10^{-11}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e+112)
   (+ x y)
   (if (<= a -1.9e+77)
     (- y (* z (/ y (- a t))))
     (if (or (<= a -3.7e-22) (not (<= a 4.6e-11)))
       (+ x y)
       (+ x (/ (* y z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+112) {
		tmp = x + y;
	} else if (a <= -1.9e+77) {
		tmp = y - (z * (y / (a - t)));
	} else if ((a <= -3.7e-22) || !(a <= 4.6e-11)) {
		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 <= (-9.5d+112)) then
        tmp = x + y
    else if (a <= (-1.9d+77)) then
        tmp = y - (z * (y / (a - t)))
    else if ((a <= (-3.7d-22)) .or. (.not. (a <= 4.6d-11))) 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 <= -9.5e+112) {
		tmp = x + y;
	} else if (a <= -1.9e+77) {
		tmp = y - (z * (y / (a - t)));
	} else if ((a <= -3.7e-22) || !(a <= 4.6e-11)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.5e+112:
		tmp = x + y
	elif a <= -1.9e+77:
		tmp = y - (z * (y / (a - t)))
	elif (a <= -3.7e-22) or not (a <= 4.6e-11):
		tmp = x + y
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e+112)
		tmp = Float64(x + y);
	elseif (a <= -1.9e+77)
		tmp = Float64(y - Float64(z * Float64(y / Float64(a - t))));
	elseif ((a <= -3.7e-22) || !(a <= 4.6e-11))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.5e+112)
		tmp = x + y;
	elseif (a <= -1.9e+77)
		tmp = y - (z * (y / (a - t)));
	elseif ((a <= -3.7e-22) || ~((a <= 4.6e-11)))
		tmp = x + y;
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e+112], N[(x + y), $MachinePrecision], If[LessEqual[a, -1.9e+77], N[(y - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -3.7e-22], N[Not[LessEqual[a, 4.6e-11]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.5000000000000008e112 or -1.9000000000000001e77 < a < -3.7e-22 or 4.60000000000000027e-11 < a

   1. Initial program 83.1%

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

      1. associate-*l/ 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in a around inf 84.3%

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

      1. +-commutative 84.3%

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

   7. Simplified 84.3%

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

   if -9.5000000000000008e112 < a < -1.9000000000000001e77

   1. Initial program 99.8%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. associate-/l* 99.8%

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

   7. Simplified 99.8%

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

      1. div-sub 99.8%

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

   9. Applied egg-rr 99.8%

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

   10. Taylor expanded in x around 0 99.8%

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

       1. div-sub 99.8%

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

       2. associate-/l* 99.8%

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

       3. associate-*l/ 99.6%

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

       4. *-commutative 99.6%

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

   12. Simplified 99.6%

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

   if -3.7e-22 < a < 4.60000000000000027e-11

   1. Initial program 69.8%

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

      1. associate-*l/ 70.6%

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

   3. Simplified 70.6%

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

   5. Taylor expanded in t around -inf 79.2%

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

      1. mul-1-neg 79.2%

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

      2. unsub-neg 79.2%

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

      3. *-commutative 79.2%

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

   7. Simplified 79.2%

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

   8. Taylor expanded in a around 0 76.9%

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

      1. mul-1-neg 76.9%

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

      2. distribute-rgt-neg-in 76.9%

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

   10. Simplified 76.9%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+112}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{+77}:\\ \;\;\;\;y - z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-22} \lor \neg \left(a \leq 4.6 \cdot 10^{-11}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{\frac{t}{a}}\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 10^{-108}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-99}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+42}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ y (/ t a)))))
   (if (<= t -1.3e+152)
     t_1
     (if (<= t 1e-108)
       (+ x y)
       (if (<= t 3.4e-99) (/ z (/ t y)) (if (<= t 1.15e+42) (+ x y) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (t / a));
	double tmp;
	if (t <= -1.3e+152) {
		tmp = t_1;
	} else if (t <= 1e-108) {
		tmp = x + y;
	} else if (t <= 3.4e-99) {
		tmp = z / (t / y);
	} else if (t <= 1.15e+42) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y / (t / a))
    if (t <= (-1.3d+152)) then
        tmp = t_1
    else if (t <= 1d-108) then
        tmp = x + y
    else if (t <= 3.4d-99) then
        tmp = z / (t / y)
    else if (t <= 1.15d+42) then
        tmp = x + y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (t / a));
	double tmp;
	if (t <= -1.3e+152) {
		tmp = t_1;
	} else if (t <= 1e-108) {
		tmp = x + y;
	} else if (t <= 3.4e-99) {
		tmp = z / (t / y);
	} else if (t <= 1.15e+42) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y / (t / a))
	tmp = 0
	if t <= -1.3e+152:
		tmp = t_1
	elif t <= 1e-108:
		tmp = x + y
	elif t <= 3.4e-99:
		tmp = z / (t / y)
	elif t <= 1.15e+42:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y / Float64(t / a)))
	tmp = 0.0
	if (t <= -1.3e+152)
		tmp = t_1;
	elseif (t <= 1e-108)
		tmp = Float64(x + y);
	elseif (t <= 3.4e-99)
		tmp = Float64(z / Float64(t / y));
	elseif (t <= 1.15e+42)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y / (t / a));
	tmp = 0.0;
	if (t <= -1.3e+152)
		tmp = t_1;
	elseif (t <= 1e-108)
		tmp = x + y;
	elseif (t <= 3.4e-99)
		tmp = z / (t / y);
	elseif (t <= 1.15e+42)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.3e+152], t$95$1, If[LessEqual[t, 1e-108], N[(x + y), $MachinePrecision], If[LessEqual[t, 3.4e-99], N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+42], N[(x + y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.3e152 or 1.15e42 < t

   1. Initial program 46.6%

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

      1. associate-*l/ 59.7%

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

   3. Simplified 59.7%

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

   5. Taylor expanded in t around -inf 81.0%

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

      1. mul-1-neg 81.0%

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

      2. unsub-neg 81.0%

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

      3. *-commutative 81.0%

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

   7. Simplified 81.0%

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

   8. Taylor expanded in a around inf 71.5%

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

      1. *-commutative 71.5%

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

      2. associate-/l* 75.1%

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

   10. Simplified 75.1%

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

   if -1.3e152 < t < 1.00000000000000004e-108 or 3.40000000000000007e-99 < t < 1.15e42

   1. Initial program 91.5%

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

      1. associate-*l/ 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in a around inf 65.0%

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

      1. +-commutative 65.0%

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

   7. Simplified 65.0%

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

   if 1.00000000000000004e-108 < t < 3.40000000000000007e-99

   1. Initial program 86.1%

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

      1. associate-*l/ 85.8%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in x around 0 72.1%

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

      1. sub-neg 72.1%

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

      2. associate-*r/ 71.9%

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

      3. *-rgt-identity 71.9%

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

      4. distribute-rgt-neg-in 71.9%

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

      5. distribute-frac-neg 71.9%

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

      6. distribute-lft-in 71.9%

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

      7. distribute-frac-neg 71.9%

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

      8. sub-neg 71.9%

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

   7. Simplified 71.9%

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

   8. Taylor expanded in a around 0 72.6%

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

      1. div-inv 72.6%

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

      2. add-sqr-sqrt 28.9%

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

      3. sqrt-unprod 29.4%

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

      4. sqr-neg 29.4%

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

      5. sqrt-unprod 0.3%

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

      6. add-sqr-sqrt 1.6%

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

      7. associate-*l* 1.6%

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

      8. div-inv 1.6%

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

      9. *-commutative 1.6%

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

      10. associate-/l* 1.6%

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

      11. add-sqr-sqrt 0.3%

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

      12. sqrt-unprod 29.4%

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

      13. sqr-neg 29.4%

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

      14. sqrt-unprod 28.9%

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

      15. add-sqr-sqrt 72.6%

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

   10. Applied egg-rr 72.6%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+152}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \mathbf{elif}\;t \leq 10^{-108}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-99}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+42}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+118} \lor \neg \left(t \leq 6.6 \cdot 10^{+37}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + y \cdot \frac{t - z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.15e+118) (not (<= t 6.6e+37)))
   (+ x (/ y (/ t (- z a))))
   (+ (+ x y) (* y (/ (- t z) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.15e+118) || !(t <= 6.6e+37)) {
		tmp = x + (y / (t / (z - a)));
	} else {
		tmp = (x + y) + (y * ((t - z) / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.15d+118)) .or. (.not. (t <= 6.6d+37))) then
        tmp = x + (y / (t / (z - a)))
    else
        tmp = (x + y) + (y * ((t - z) / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.15e+118) || !(t <= 6.6e+37)) {
		tmp = x + (y / (t / (z - a)));
	} else {
		tmp = (x + y) + (y * ((t - z) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.15e+118) or not (t <= 6.6e+37):
		tmp = x + (y / (t / (z - a)))
	else:
		tmp = (x + y) + (y * ((t - z) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.15e+118) || !(t <= 6.6e+37))
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - a))));
	else
		tmp = Float64(Float64(x + y) + Float64(y * Float64(Float64(t - z) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.15e+118) || ~((t <= 6.6e+37)))
		tmp = x + (y / (t / (z - a)));
	else
		tmp = (x + y) + (y * ((t - z) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.15e+118], N[Not[LessEqual[t, 6.6e+37]], $MachinePrecision]], N[(x + N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(y * N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.15000000000000008e118 or 6.6000000000000002e37 < t

   1. Initial program 46.4%

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

      1. sub-neg 46.4%

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

      2. distribute-frac-neg 46.4%

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

      3. distribute-rgt-neg-out 46.4%

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

      4. +-commutative 46.4%

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

      5. associate-*l/ 59.6%

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

      6. distribute-rgt-neg-in 59.6%

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

      7. distribute-lft-neg-in 59.6%

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

      8. distribute-frac-neg 59.6%

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

      9. fma-def 59.6%

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

      10. sub-neg 59.6%

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

      11. distribute-neg-in 59.6%

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

      12. remove-double-neg 59.6%

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

      13. +-commutative 59.6%

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

      14. sub-neg 59.6%

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

   3. Simplified 59.6%

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

   5. Taylor expanded in t around inf 61.7%

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

      1. associate-+r+ 81.3%

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

      2. distribute-rgt1-in 81.3%

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

      3. metadata-eval 81.3%

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

      4. mul0-lft 81.3%

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

      5. associate-/l* 92.2%

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

   7. Simplified 92.2%

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

   if -1.15000000000000008e118 < t < 6.6000000000000002e37

   1. Initial program 93.2%

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

      1. associate-*l/ 92.6%

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

   3. Simplified 92.6%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+118} \lor \neg \left(t \leq 6.6 \cdot 10^{+37}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + y \cdot \frac{t - z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+118} \lor \neg \left(t \leq 2.35 \cdot 10^{+32}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.15e+118) (not (<= t 2.35e+32)))
   (+ x (/ y (/ t (- z a))))
   (+ (+ x y) (/ (* y (- t z)) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.15e+118) || !(t <= 2.35e+32)) {
		tmp = x + (y / (t / (z - a)));
	} else {
		tmp = (x + y) + ((y * (t - z)) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.15d+118)) .or. (.not. (t <= 2.35d+32))) then
        tmp = x + (y / (t / (z - a)))
    else
        tmp = (x + y) + ((y * (t - z)) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.15e+118) || !(t <= 2.35e+32)) {
		tmp = x + (y / (t / (z - a)));
	} else {
		tmp = (x + y) + ((y * (t - z)) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.15e+118) or not (t <= 2.35e+32):
		tmp = x + (y / (t / (z - a)))
	else:
		tmp = (x + y) + ((y * (t - z)) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.15e+118) || !(t <= 2.35e+32))
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - a))));
	else
		tmp = Float64(Float64(x + y) + Float64(Float64(y * Float64(t - z)) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.15e+118) || ~((t <= 2.35e+32)))
		tmp = x + (y / (t / (z - a)));
	else
		tmp = (x + y) + ((y * (t - z)) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.15e+118], N[Not[LessEqual[t, 2.35e+32]], $MachinePrecision]], N[(x + N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.15000000000000008e118 or 2.35000000000000012e32 < t

   1. Initial program 46.4%

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

      1. sub-neg 46.4%

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

      2. distribute-frac-neg 46.4%

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

      3. distribute-rgt-neg-out 46.4%

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

      4. +-commutative 46.4%

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

      5. associate-*l/ 59.6%

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

      6. distribute-rgt-neg-in 59.6%

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

      7. distribute-lft-neg-in 59.6%

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

      8. distribute-frac-neg 59.6%

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

      9. fma-def 59.6%

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

      10. sub-neg 59.6%

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

      11. distribute-neg-in 59.6%

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

      12. remove-double-neg 59.6%

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

      13. +-commutative 59.6%

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

      14. sub-neg 59.6%

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

   3. Simplified 59.6%

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

   5. Taylor expanded in t around inf 61.7%

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

      1. associate-+r+ 81.3%

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

      2. distribute-rgt1-in 81.3%

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

      3. metadata-eval 81.3%

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

      4. mul0-lft 81.3%

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

      5. associate-/l* 92.2%

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

   7. Simplified 92.2%

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

   if -1.15000000000000008e118 < t < 2.35000000000000012e32

   1. Initial program 93.2%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+118} \lor \neg \left(t \leq 2.35 \cdot 10^{+32}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+118} \lor \neg \left(t \leq 4.4 \cdot 10^{+32}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.15e+118) (not (<= t 4.4e+32)))
   (+ x (/ y (/ t (- z a))))
   (- (+ x y) (/ y (/ (- a t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.15e+118) || !(t <= 4.4e+32)) {
		tmp = x + (y / (t / (z - a)));
	} else {
		tmp = (x + y) - (y / ((a - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.15d+118)) .or. (.not. (t <= 4.4d+32))) then
        tmp = x + (y / (t / (z - a)))
    else
        tmp = (x + y) - (y / ((a - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.15e+118) || !(t <= 4.4e+32)) {
		tmp = x + (y / (t / (z - a)));
	} else {
		tmp = (x + y) - (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.15e+118) or not (t <= 4.4e+32):
		tmp = x + (y / (t / (z - a)))
	else:
		tmp = (x + y) - (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.15e+118) || !(t <= 4.4e+32))
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - a))));
	else
		tmp = Float64(Float64(x + y) - Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.15e+118) || ~((t <= 4.4e+32)))
		tmp = x + (y / (t / (z - a)));
	else
		tmp = (x + y) - (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.15e+118], N[Not[LessEqual[t, 4.4e+32]], $MachinePrecision]], N[(x + N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.15000000000000008e118 or 4.40000000000000002e32 < t

   1. Initial program 46.4%

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

      1. sub-neg 46.4%

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

      2. distribute-frac-neg 46.4%

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

      3. distribute-rgt-neg-out 46.4%

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

      4. +-commutative 46.4%

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

      5. associate-*l/ 59.6%

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

      6. distribute-rgt-neg-in 59.6%

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

      7. distribute-lft-neg-in 59.6%

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

      8. distribute-frac-neg 59.6%

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

      9. fma-def 59.6%

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

      10. sub-neg 59.6%

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

      11. distribute-neg-in 59.6%

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

      12. remove-double-neg 59.6%

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

      13. +-commutative 59.6%

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

      14. sub-neg 59.6%

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

   3. Simplified 59.6%

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

   5. Taylor expanded in t around inf 61.7%

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

      1. associate-+r+ 81.3%

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

      2. distribute-rgt1-in 81.3%

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

      3. metadata-eval 81.3%

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

      4. mul0-lft 81.3%

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

      5. associate-/l* 92.2%

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

   7. Simplified 92.2%

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

   if -1.15000000000000008e118 < t < 4.40000000000000002e32

   1. Initial program 93.2%

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

      1. associate-*l/ 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in z around inf 92.1%

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

      1. associate-/l* 91.6%

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

   7. Simplified 91.6%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+118} \lor \neg \left(t \leq 4.4 \cdot 10^{+32}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a - t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{-114} \lor \neg \left(a \leq 2.15 \cdot 10^{-80}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.2e-114) (not (<= a 2.15e-80)))
   (- (+ x y) (* y (/ z a)))
   (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.2e-114) || !(a <= 2.15e-80)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-5.2d-114)) .or. (.not. (a <= 2.15d-80))) then
        tmp = (x + y) - (y * (z / a))
    else
        tmp = x + ((y * z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.2e-114) || !(a <= 2.15e-80)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.2e-114) or not (a <= 2.15e-80):
		tmp = (x + y) - (y * (z / a))
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.2e-114) || !(a <= 2.15e-80))
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.2e-114) || ~((a <= 2.15e-80)))
		tmp = (x + y) - (y * (z / a));
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.2e-114], N[Not[LessEqual[a, 2.15e-80]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.20000000000000026e-114 or 2.1500000000000001e-80 < a

   1. Initial program 84.7%

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

      1. associate-*l/ 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in t around 0 85.7%

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

   if -5.20000000000000026e-114 < a < 2.1500000000000001e-80

   1. Initial program 63.5%

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

      1. associate-*l/ 65.6%

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

   3. Simplified 65.6%

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

   5. Taylor expanded in t around -inf 85.7%

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

      1. mul-1-neg 85.7%

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

      2. unsub-neg 85.7%

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

      3. *-commutative 85.7%

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

   7. Simplified 85.7%

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

   8. Taylor expanded in a around 0 83.4%

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

      1. mul-1-neg 83.4%

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

      2. distribute-rgt-neg-in 83.4%

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

   10. Simplified 83.4%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{-114} \lor \neg \left(a \leq 2.15 \cdot 10^{-80}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.56 \cdot 10^{-111} \lor \neg \left(a \leq 1.75 \cdot 10^{-82}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.56e-111) (not (<= a 1.75e-82)))
   (- (+ x y) (* y (/ z a)))
   (+ x (/ y (/ t (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.56e-111) || !(a <= 1.75e-82)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x + (y / (t / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.56d-111)) .or. (.not. (a <= 1.75d-82))) then
        tmp = (x + y) - (y * (z / a))
    else
        tmp = x + (y / (t / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.56e-111) || !(a <= 1.75e-82)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x + (y / (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.56e-111) or not (a <= 1.75e-82):
		tmp = (x + y) - (y * (z / a))
	else:
		tmp = x + (y / (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.56e-111) || !(a <= 1.75e-82))
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.56e-111) || ~((a <= 1.75e-82)))
		tmp = (x + y) - (y * (z / a));
	else
		tmp = x + (y / (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.56e-111], N[Not[LessEqual[a, 1.75e-82]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.56e-111 or 1.7499999999999999e-82 < a

   1. Initial program 84.7%

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

      1. associate-*l/ 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in t around 0 85.7%

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

   if -1.56e-111 < a < 1.7499999999999999e-82

   1. Initial program 63.5%

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

      1. sub-neg 63.5%

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

      2. distribute-frac-neg 63.5%

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

      3. distribute-rgt-neg-out 63.5%

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

      4. +-commutative 63.5%

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

      5. associate-*l/ 65.6%

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

      6. distribute-rgt-neg-in 65.6%

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

      7. distribute-lft-neg-in 65.6%

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

      8. distribute-frac-neg 65.6%

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

      9. fma-def 65.6%

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

      10. sub-neg 65.6%

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

      11. distribute-neg-in 65.6%

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

      12. remove-double-neg 65.6%

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

      13. +-commutative 65.6%

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

      14. sub-neg 65.6%

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

   3. Simplified 65.6%

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

   5. Taylor expanded in t around inf 70.0%

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

      1. associate-+r+ 85.7%

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

      2. distribute-rgt1-in 85.7%

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

      3. metadata-eval 85.7%

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

      4. mul0-lft 85.7%

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

      5. associate-/l* 90.8%

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

   7. Simplified 90.8%

      \[\leadsto \color{blue}{x + \left(0 + \frac{y}{\frac{t}{z - a}}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.56 \cdot 10^{-111} \lor \neg \left(a \leq 1.75 \cdot 10^{-82}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-83}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-216}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.65e-83)
   (+ x y)
   (if (<= a 1.75e-216) (* y (/ z t)) (if (<= a 2.6e-13) x (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.65e-83) {
		tmp = x + y;
	} else if (a <= 1.75e-216) {
		tmp = y * (z / t);
	} else if (a <= 2.6e-13) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.65d-83)) then
        tmp = x + y
    else if (a <= 1.75d-216) then
        tmp = y * (z / t)
    else if (a <= 2.6d-13) then
        tmp = x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.65e-83) {
		tmp = x + y;
	} else if (a <= 1.75e-216) {
		tmp = y * (z / t);
	} else if (a <= 2.6e-13) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.65e-83:
		tmp = x + y
	elif a <= 1.75e-216:
		tmp = y * (z / t)
	elif a <= 2.6e-13:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.65e-83)
		tmp = Float64(x + y);
	elseif (a <= 1.75e-216)
		tmp = Float64(y * Float64(z / t));
	elseif (a <= 2.6e-13)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.65e-83)
		tmp = x + y;
	elseif (a <= 1.75e-216)
		tmp = y * (z / t);
	elseif (a <= 2.6e-13)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.65e-83], N[(x + y), $MachinePrecision], If[LessEqual[a, 1.75e-216], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e-13], x, N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.65e-83 or 2.6e-13 < a

   1. Initial program 84.9%

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

      1. associate-*l/ 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in a around inf 76.8%

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

      1. +-commutative 76.8%

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

   7. Simplified 76.8%

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

   if -1.65e-83 < a < 1.74999999999999991e-216

   1. Initial program 64.4%

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

      1. associate-*l/ 67.1%

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

   3. Simplified 67.1%

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

   5. Taylor expanded in x around 0 43.3%

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

      1. sub-neg 43.3%

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

      2. associate-*r/ 44.6%

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

      3. *-rgt-identity 44.6%

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

      4. distribute-rgt-neg-in 44.6%

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

      5. distribute-frac-neg 44.6%

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

      6. distribute-lft-in 44.6%

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

      7. distribute-frac-neg 44.6%

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

      8. sub-neg 44.6%

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

   7. Simplified 44.6%

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

   8. Taylor expanded in a around 0 53.0%

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

   if 1.74999999999999991e-216 < a < 2.6e-13

   1. Initial program 69.9%

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

      1. associate-*l/ 67.9%

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

   3. Simplified 67.9%

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

   5. Taylor expanded in x around inf 60.8%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-83}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-216}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-83}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-217}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.9e-83)
   (+ x y)
   (if (<= a 5.5e-217) (/ y (/ t z)) (if (<= a 4.4e-10) x (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.9e-83) {
		tmp = x + y;
	} else if (a <= 5.5e-217) {
		tmp = y / (t / z);
	} else if (a <= 4.4e-10) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.9d-83)) then
        tmp = x + y
    else if (a <= 5.5d-217) then
        tmp = y / (t / z)
    else if (a <= 4.4d-10) then
        tmp = x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.9e-83) {
		tmp = x + y;
	} else if (a <= 5.5e-217) {
		tmp = y / (t / z);
	} else if (a <= 4.4e-10) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.9e-83:
		tmp = x + y
	elif a <= 5.5e-217:
		tmp = y / (t / z)
	elif a <= 4.4e-10:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.9e-83)
		tmp = Float64(x + y);
	elseif (a <= 5.5e-217)
		tmp = Float64(y / Float64(t / z));
	elseif (a <= 4.4e-10)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.9e-83)
		tmp = x + y;
	elseif (a <= 5.5e-217)
		tmp = y / (t / z);
	elseif (a <= 4.4e-10)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.9e-83], N[(x + y), $MachinePrecision], If[LessEqual[a, 5.5e-217], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.4e-10], x, N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.8999999999999999e-83 or 4.3999999999999998e-10 < a

   1. Initial program 84.9%

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

      1. associate-*l/ 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in a around inf 76.8%

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

      1. +-commutative 76.8%

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

   7. Simplified 76.8%

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

   if -2.8999999999999999e-83 < a < 5.49999999999999975e-217

   1. Initial program 64.4%

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

      1. associate-*l/ 67.1%

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

   3. Simplified 67.1%

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

   5. Taylor expanded in z around inf 53.9%

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

      1. associate-*r/ 53.9%

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

      2. associate-*r* 53.9%

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

      3. neg-mul-1 53.9%

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

   7. Simplified 53.9%

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

   8. Taylor expanded in a around 0 47.5%

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

      1. associate-/l* 53.1%

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

   10. Simplified 53.1%

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

   if 5.49999999999999975e-217 < a < 4.3999999999999998e-10

   1. Initial program 69.9%

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

      1. associate-*l/ 67.9%

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

   3. Simplified 67.9%

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

   5. Taylor expanded in x around inf 60.8%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-83}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-217}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.65 \cdot 10^{-83}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-218}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;a \leq 0.00043:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.65e-83)
   (+ x y)
   (if (<= a 1.85e-218) (/ z (/ t y)) (if (<= a 0.00043) x (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.65e-83) {
		tmp = x + y;
	} else if (a <= 1.85e-218) {
		tmp = z / (t / y);
	} else if (a <= 0.00043) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.65d-83)) then
        tmp = x + y
    else if (a <= 1.85d-218) then
        tmp = z / (t / y)
    else if (a <= 0.00043d0) then
        tmp = x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.65e-83) {
		tmp = x + y;
	} else if (a <= 1.85e-218) {
		tmp = z / (t / y);
	} else if (a <= 0.00043) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.65e-83:
		tmp = x + y
	elif a <= 1.85e-218:
		tmp = z / (t / y)
	elif a <= 0.00043:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.65e-83)
		tmp = Float64(x + y);
	elseif (a <= 1.85e-218)
		tmp = Float64(z / Float64(t / y));
	elseif (a <= 0.00043)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.65e-83)
		tmp = x + y;
	elseif (a <= 1.85e-218)
		tmp = z / (t / y);
	elseif (a <= 0.00043)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.65e-83], N[(x + y), $MachinePrecision], If[LessEqual[a, 1.85e-218], N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.00043], x, N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.65e-83 or 4.29999999999999989e-4 < a

   1. Initial program 84.9%

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

      1. associate-*l/ 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in a around inf 76.8%

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

      1. +-commutative 76.8%

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

   7. Simplified 76.8%

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

   if -2.65e-83 < a < 1.8500000000000001e-218

   1. Initial program 64.4%

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

      1. associate-*l/ 67.1%

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

   3. Simplified 67.1%

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

   5. Taylor expanded in x around 0 43.3%

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

      1. sub-neg 43.3%

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

      2. associate-*r/ 44.6%

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

      3. *-rgt-identity 44.6%

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

      4. distribute-rgt-neg-in 44.6%

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

      5. distribute-frac-neg 44.6%

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

      6. distribute-lft-in 44.6%

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

      7. distribute-frac-neg 44.6%

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

      8. sub-neg 44.6%

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

   7. Simplified 44.6%

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

   8. Taylor expanded in a around 0 53.0%

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

      1. div-inv 53.0%

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

      2. add-sqr-sqrt 20.8%

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

      3. sqrt-unprod 12.3%

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

      4. sqr-neg 12.3%

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

      5. sqrt-unprod 1.1%

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

      6. add-sqr-sqrt 2.4%

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

      7. associate-*l* 2.5%

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

      8. div-inv 2.5%

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

      9. *-commutative 2.5%

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

      10. associate-/l* 2.4%

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

      11. add-sqr-sqrt 1.2%

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

      12. sqrt-unprod 12.0%

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

      13. sqr-neg 12.0%

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

      14. sqrt-unprod 19.7%

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

      15. add-sqr-sqrt 53.3%

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

   10. Applied egg-rr 53.3%

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

   if 1.8500000000000001e-218 < a < 4.29999999999999989e-4

   1. Initial program 69.9%

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

      1. associate-*l/ 67.9%

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

   3. Simplified 67.9%

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

   5. Taylor expanded in x around inf 60.8%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.65 \cdot 10^{-83}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-218}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;a \leq 0.00043:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 62.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+37} \lor \neg \left(y \leq 2.15 \cdot 10^{+218}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.75e+37) (not (<= y 2.15e+218)))
   (* y (- 1.0 (/ z a)))
   (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.75e+37) || !(y <= 2.15e+218)) {
		tmp = y * (1.0 - (z / a));
	} 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 ((y <= (-1.75d+37)) .or. (.not. (y <= 2.15d+218))) then
        tmp = y * (1.0d0 - (z / a))
    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 ((y <= -1.75e+37) || !(y <= 2.15e+218)) {
		tmp = y * (1.0 - (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.75e+37) or not (y <= 2.15e+218):
		tmp = y * (1.0 - (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.75e+37) || !(y <= 2.15e+218))
		tmp = Float64(y * Float64(1.0 - Float64(z / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.75e+37) || ~((y <= 2.15e+218)))
		tmp = y * (1.0 - (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.75e+37], N[Not[LessEqual[y, 2.15e+218]], $MachinePrecision]], N[(y * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.75e37 or 2.14999999999999993e218 < y

   1. Initial program 58.7%

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

      1. associate-*l/ 72.0%

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

   3. Simplified 72.0%

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

   5. Taylor expanded in x around 0 54.8%

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

      1. sub-neg 54.8%

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

      2. associate-*r/ 66.0%

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

      3. *-rgt-identity 66.0%

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

      4. distribute-rgt-neg-in 66.0%

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

      5. distribute-frac-neg 66.0%

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

      6. distribute-lft-in 66.0%

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

      7. distribute-frac-neg 66.0%

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

      8. sub-neg 66.0%

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

   7. Simplified 66.0%

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

   8. Taylor expanded in t around 0 56.8%

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

   if -1.75e37 < y < 2.14999999999999993e218

   1. Initial program 84.5%

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

      1. associate-*l/ 85.0%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in a around inf 67.8%

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

      1. +-commutative 67.8%

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

   7. Simplified 67.8%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+37} \lor \neg \left(y \leq 2.15 \cdot 10^{+218}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 64.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-80} \lor \neg \left(a \leq 1.35 \cdot 10^{-7}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.1e-80) (not (<= a 1.35e-7))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.1e-80) || !(a <= 1.35e-7)) {
		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 <= (-3.1d-80)) .or. (.not. (a <= 1.35d-7))) 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 <= -3.1e-80) || !(a <= 1.35e-7)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.1e-80) or not (a <= 1.35e-7):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.1e-80) || !(a <= 1.35e-7))
		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 <= -3.1e-80) || ~((a <= 1.35e-7)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.1e-80], N[Not[LessEqual[a, 1.35e-7]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -3.10000000000000016e-80 or 1.35000000000000004e-7 < a

   1. Initial program 84.8%

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

      1. associate-*l/ 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in a around inf 76.7%

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

      1. +-commutative 76.7%

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

   7. Simplified 76.7%

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

   if -3.10000000000000016e-80 < a < 1.35000000000000004e-7

   1. Initial program 66.8%

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

      1. associate-*l/ 67.7%

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

   3. Simplified 67.7%

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

   5. Taylor expanded in x around inf 47.0%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-80} \lor \neg \left(a \leq 1.35 \cdot 10^{-7}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 53.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+69}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+107}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.6e+69) y (if (<= y 2.1e+107) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.6e+69) {
		tmp = y;
	} else if (y <= 2.1e+107) {
		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 <= (-4.6d+69)) then
        tmp = y
    else if (y <= 2.1d+107) 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 <= -4.6e+69) {
		tmp = y;
	} else if (y <= 2.1e+107) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4.6e+69:
		tmp = y
	elif y <= 2.1e+107:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.6e+69)
		tmp = y;
	elseif (y <= 2.1e+107)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -4.6e+69)
		tmp = y;
	elseif (y <= 2.1e+107)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.6e+69], y, If[LessEqual[y, 2.1e+107], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -4.60000000000000033e69 or 2.1e107 < y

   1. Initial program 58.1%

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

      1. associate-*l/ 71.2%

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

   3. Simplified 71.2%

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

   5. Taylor expanded in x around 0 52.1%

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

      1. sub-neg 52.1%

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

      2. associate-*r/ 62.7%

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

      3. *-rgt-identity 62.7%

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

      4. distribute-rgt-neg-in 62.7%

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

      5. distribute-frac-neg 62.7%

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

      6. distribute-lft-in 62.7%

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

      7. distribute-frac-neg 62.7%

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

      8. sub-neg 62.7%

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

   7. Simplified 62.7%

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

   8. Taylor expanded in a around inf 32.7%

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

   if -4.60000000000000033e69 < y < 2.1e107

   1. Initial program 88.4%

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

      1. associate-*l/ 87.2%

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

   3. Simplified 87.2%

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

   5. Taylor expanded in x around inf 67.3%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+69}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+107}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.9% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.1%

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

   1. associate-*l/ 81.3%

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

3. Simplified 81.3%

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

5. Taylor expanded in x around inf 48.0%

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

6. Final simplification 48.0%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 88.2% 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 2024019 
(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))))