Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A

Percentage Accurate: 85.8% → 99.6%

Time: 10.9s

Alternatives: 20

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ t_2 := \frac{t\_1}{z - a}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a - z}{y}}{z - t}}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+288}:\\ \;\;\;\;x - \frac{t\_1}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))) (t_2 (/ t_1 (- z a))))
   (if (<= t_2 (- INFINITY))
     (- x (/ 1.0 (/ (/ (- a z) y) (- z t))))
     (if (<= t_2 5e+288)
       (- x (/ t_1 (- a z)))
       (+ x (/ (- z t) (/ (- z a) y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double t_2 = t_1 / (z - a);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = x - (1.0 / (((a - z) / y) / (z - t)));
	} else if (t_2 <= 5e+288) {
		tmp = x - (t_1 / (a - z));
	} else {
		tmp = x + ((z - t) / ((z - a) / y));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double t_2 = t_1 / (z - a);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = x - (1.0 / (((a - z) / y) / (z - t)));
	} else if (t_2 <= 5e+288) {
		tmp = x - (t_1 / (a - z));
	} else {
		tmp = x + ((z - t) / ((z - a) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	t_2 = t_1 / (z - a)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = x - (1.0 / (((a - z) / y) / (z - t)))
	elif t_2 <= 5e+288:
		tmp = x - (t_1 / (a - z))
	else:
		tmp = x + ((z - t) / ((z - a) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	t_2 = Float64(t_1 / Float64(z - a))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(x - Float64(1.0 / Float64(Float64(Float64(a - z) / y) / Float64(z - t))));
	elseif (t_2 <= 5e+288)
		tmp = Float64(x - Float64(t_1 / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(z - a) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z - t);
	t_2 = t_1 / (z - a);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = x - (1.0 / (((a - z) / y) / (z - t)));
	elseif (t_2 <= 5e+288)
		tmp = x - (t_1 / (a - z));
	else
		tmp = x + ((z - t) / ((z - a) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(x - N[(1.0 / N[(N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+288], N[(x - N[(t$95$1 / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 52.8%

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

      1. clear-num 52.8%

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

      2. inv-pow 52.8%

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

   4. Applied egg-rr 52.8%

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

      1. unpow-1 52.8%

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

      2. associate-/r* 99.9%

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

   6. Simplified 99.9%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 5.0000000000000003e288

   1. Initial program 99.5%

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

   if 5.0000000000000003e288 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 36.2%

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

      1. clear-num 36.2%

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

      2. inv-pow 36.2%

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

   4. Applied egg-rr 36.2%

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

      1. unpow-1 36.2%

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

      2. associate-/r* 99.8%

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

   6. Simplified 99.8%

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

      1. clear-num 99.9%

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

      2. add-cube-cbrt 99.1%

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

      3. *-un-lft-identity 99.1%

         \[\leadsto x + \frac{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}{\color{blue}{1 \cdot \frac{z - a}{y}}} \]

      4. times-frac 99.0%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}}} \]

      5. pow2 99.0%

         \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{z - t}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}} \]

   8. Applied egg-rr 99.0%

      \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}}} \]
   9. Step-by-step derivation

      1. times-frac 99.1%

         \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2} \cdot \sqrt[3]{z - t}}{1 \cdot \frac{z - a}{y}}} \]

      2. unpow2 99.1%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right)} \cdot \sqrt[3]{z - t}}{1 \cdot \frac{z - a}{y}} \]

      3. rem-3cbrt-lft 99.9%

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

      4. *-lft-identity 99.9%

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

   10. Simplified 99.9%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a - z}{y}}{z - t}}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq 5 \cdot 10^{+288}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.2% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 86.1%

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

   1. +-commutative 86.1%

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

   2. associate-/l* 97.7%

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

   3. fma-define 97.7%

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

3. Simplified 97.7%

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

5. Final simplification 97.7%

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

Alternative 3: 74.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+113}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-5}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-82}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+36}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ t (/ a y)))))
   (if (<= z -1.2e+113)
     (+ y x)
     (if (<= z -7.5e-5)
       (- x (* t (/ y z)))
       (if (<= z -5.2e-56)
         t_1
         (if (<= z -6.4e-82)
           (/ (* y t) (- a z))
           (if (<= z 4e-157)
             t_1
             (if (<= z 2e-70)
               (* y (/ t (- a z)))
               (if (<= z 2.8e+36) (+ x (* t (/ y a))) (+ y x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / (a / y));
	double tmp;
	if (z <= -1.2e+113) {
		tmp = y + x;
	} else if (z <= -7.5e-5) {
		tmp = x - (t * (y / z));
	} else if (z <= -5.2e-56) {
		tmp = t_1;
	} else if (z <= -6.4e-82) {
		tmp = (y * t) / (a - z);
	} else if (z <= 4e-157) {
		tmp = t_1;
	} else if (z <= 2e-70) {
		tmp = y * (t / (a - z));
	} else if (z <= 2.8e+36) {
		tmp = x + (t * (y / a));
	} else {
		tmp = y + 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) :: t_1
    real(8) :: tmp
    t_1 = x + (t / (a / y))
    if (z <= (-1.2d+113)) then
        tmp = y + x
    else if (z <= (-7.5d-5)) then
        tmp = x - (t * (y / z))
    else if (z <= (-5.2d-56)) then
        tmp = t_1
    else if (z <= (-6.4d-82)) then
        tmp = (y * t) / (a - z)
    else if (z <= 4d-157) then
        tmp = t_1
    else if (z <= 2d-70) then
        tmp = y * (t / (a - z))
    else if (z <= 2.8d+36) then
        tmp = x + (t * (y / a))
    else
        tmp = y + x
    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 + (t / (a / y));
	double tmp;
	if (z <= -1.2e+113) {
		tmp = y + x;
	} else if (z <= -7.5e-5) {
		tmp = x - (t * (y / z));
	} else if (z <= -5.2e-56) {
		tmp = t_1;
	} else if (z <= -6.4e-82) {
		tmp = (y * t) / (a - z);
	} else if (z <= 4e-157) {
		tmp = t_1;
	} else if (z <= 2e-70) {
		tmp = y * (t / (a - z));
	} else if (z <= 2.8e+36) {
		tmp = x + (t * (y / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t / (a / y))
	tmp = 0
	if z <= -1.2e+113:
		tmp = y + x
	elif z <= -7.5e-5:
		tmp = x - (t * (y / z))
	elif z <= -5.2e-56:
		tmp = t_1
	elif z <= -6.4e-82:
		tmp = (y * t) / (a - z)
	elif z <= 4e-157:
		tmp = t_1
	elif z <= 2e-70:
		tmp = y * (t / (a - z))
	elif z <= 2.8e+36:
		tmp = x + (t * (y / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t / Float64(a / y)))
	tmp = 0.0
	if (z <= -1.2e+113)
		tmp = Float64(y + x);
	elseif (z <= -7.5e-5)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= -5.2e-56)
		tmp = t_1;
	elseif (z <= -6.4e-82)
		tmp = Float64(Float64(y * t) / Float64(a - z));
	elseif (z <= 4e-157)
		tmp = t_1;
	elseif (z <= 2e-70)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (z <= 2.8e+36)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t / (a / y));
	tmp = 0.0;
	if (z <= -1.2e+113)
		tmp = y + x;
	elseif (z <= -7.5e-5)
		tmp = x - (t * (y / z));
	elseif (z <= -5.2e-56)
		tmp = t_1;
	elseif (z <= -6.4e-82)
		tmp = (y * t) / (a - z);
	elseif (z <= 4e-157)
		tmp = t_1;
	elseif (z <= 2e-70)
		tmp = y * (t / (a - z));
	elseif (z <= 2.8e+36)
		tmp = x + (t * (y / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+113], N[(y + x), $MachinePrecision], If[LessEqual[z, -7.5e-5], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.2e-56], t$95$1, If[LessEqual[z, -6.4e-82], N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e-157], t$95$1, If[LessEqual[z, 2e-70], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+36], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.19999999999999992e113 or 2.8000000000000001e36 < z

   1. Initial program 75.9%

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

   3. Taylor expanded in z around inf 82.9%

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

      1. +-commutative 82.9%

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

   5. Simplified 82.9%

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

   if -1.19999999999999992e113 < z < -7.49999999999999934e-5

   1. Initial program 86.8%

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

   3. Taylor expanded in a around 0 68.9%

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

      1. +-commutative 68.9%

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

      2. associate-/l* 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in z around 0 65.9%

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

      1. associate-*r/ 65.9%

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

      2. neg-mul-1 65.9%

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

      3. distribute-lft-neg-in 65.9%

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

   8. Simplified 65.9%

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

   9. Taylor expanded in t around 0 65.9%

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

       1. neg-mul-1 65.9%

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

       2. sub-neg 65.9%

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

       3. associate-*r/ 66.1%

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

   11. Simplified 66.1%

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

   if -7.49999999999999934e-5 < z < -5.19999999999999994e-56 or -6.4000000000000002e-82 < z < 3.99999999999999977e-157

   1. Initial program 92.3%

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

   3. Taylor expanded in z around 0 83.7%

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

      1. +-commutative 83.7%

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

      2. associate-/l* 87.6%

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

   5. Simplified 87.6%

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

      1. clear-num 87.7%

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

      2. un-div-inv 89.0%

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

   7. Applied egg-rr 89.0%

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

   if -5.19999999999999994e-56 < z < -6.4000000000000002e-82

   1. Initial program 99.5%

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

   3. Taylor expanded in y around inf 67.9%

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

      1. associate--l+ 67.9%

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

      2. div-sub 67.9%

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

   5. Simplified 67.9%

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

   6. Taylor expanded in t around inf 52.1%

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

      1. associate-*r/ 52.1%

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

      2. neg-mul-1 52.1%

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

   8. Simplified 52.1%

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

      1. associate-*r/ 73.2%

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

      2. frac-2neg 73.2%

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

      3. add-sqr-sqrt 44.8%

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

      4. sqrt-unprod 24.0%

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

      5. sqr-neg 24.0%

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

      6. sqrt-unprod 0.2%

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

      7. add-sqr-sqrt 1.5%

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

      8. distribute-rgt-neg-out 1.5%

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

      9. add-sqr-sqrt 1.2%

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

      10. sqrt-unprod 29.4%

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

      11. sqr-neg 29.4%

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

      12. sqrt-unprod 28.3%

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

      13. add-sqr-sqrt 73.2%

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

   10. Applied egg-rr 73.2%

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

   if 3.99999999999999977e-157 < z < 1.99999999999999999e-70

   1. Initial program 91.5%

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

   3. Taylor expanded in y around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. div-sub 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in t around inf 81.9%

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

      1. associate-*r/ 81.9%

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

      2. neg-mul-1 81.9%

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

   8. Simplified 81.9%

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

   if 1.99999999999999999e-70 < z < 2.8000000000000001e36

   1. Initial program 95.6%

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

   3. Taylor expanded in z around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-/l* 76.3%

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

   5. Simplified 76.3%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a} + x} \]
3. Recombined 6 regimes into one program.

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+113}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-5}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-56}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-82}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-157}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+36}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+112}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-10}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-56}:\\ \;\;\;\;y \cdot \left(\frac{x}{y} + \frac{t}{a}\right)\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-82}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-157}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 10^{-70}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+37}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.9e+112)
   (+ y x)
   (if (<= z -6.6e-10)
     (- x (* t (/ y z)))
     (if (<= z -5.2e-56)
       (* y (+ (/ x y) (/ t a)))
       (if (<= z -6.4e-82)
         (/ (* y t) (- a z))
         (if (<= z 4e-157)
           (+ x (/ t (/ a y)))
           (if (<= z 1e-70)
             (* y (/ t (- a z)))
             (if (<= z 1.5e+37) (+ x (* t (/ y a))) (+ y x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e+112) {
		tmp = y + x;
	} else if (z <= -6.6e-10) {
		tmp = x - (t * (y / z));
	} else if (z <= -5.2e-56) {
		tmp = y * ((x / y) + (t / a));
	} else if (z <= -6.4e-82) {
		tmp = (y * t) / (a - z);
	} else if (z <= 4e-157) {
		tmp = x + (t / (a / y));
	} else if (z <= 1e-70) {
		tmp = y * (t / (a - z));
	} else if (z <= 1.5e+37) {
		tmp = x + (t * (y / a));
	} else {
		tmp = y + 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 (z <= (-1.9d+112)) then
        tmp = y + x
    else if (z <= (-6.6d-10)) then
        tmp = x - (t * (y / z))
    else if (z <= (-5.2d-56)) then
        tmp = y * ((x / y) + (t / a))
    else if (z <= (-6.4d-82)) then
        tmp = (y * t) / (a - z)
    else if (z <= 4d-157) then
        tmp = x + (t / (a / y))
    else if (z <= 1d-70) then
        tmp = y * (t / (a - z))
    else if (z <= 1.5d+37) then
        tmp = x + (t * (y / a))
    else
        tmp = y + 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 (z <= -1.9e+112) {
		tmp = y + x;
	} else if (z <= -6.6e-10) {
		tmp = x - (t * (y / z));
	} else if (z <= -5.2e-56) {
		tmp = y * ((x / y) + (t / a));
	} else if (z <= -6.4e-82) {
		tmp = (y * t) / (a - z);
	} else if (z <= 4e-157) {
		tmp = x + (t / (a / y));
	} else if (z <= 1e-70) {
		tmp = y * (t / (a - z));
	} else if (z <= 1.5e+37) {
		tmp = x + (t * (y / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.9e+112:
		tmp = y + x
	elif z <= -6.6e-10:
		tmp = x - (t * (y / z))
	elif z <= -5.2e-56:
		tmp = y * ((x / y) + (t / a))
	elif z <= -6.4e-82:
		tmp = (y * t) / (a - z)
	elif z <= 4e-157:
		tmp = x + (t / (a / y))
	elif z <= 1e-70:
		tmp = y * (t / (a - z))
	elif z <= 1.5e+37:
		tmp = x + (t * (y / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.9e+112)
		tmp = Float64(y + x);
	elseif (z <= -6.6e-10)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= -5.2e-56)
		tmp = Float64(y * Float64(Float64(x / y) + Float64(t / a)));
	elseif (z <= -6.4e-82)
		tmp = Float64(Float64(y * t) / Float64(a - z));
	elseif (z <= 4e-157)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 1e-70)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (z <= 1.5e+37)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.9e+112)
		tmp = y + x;
	elseif (z <= -6.6e-10)
		tmp = x - (t * (y / z));
	elseif (z <= -5.2e-56)
		tmp = y * ((x / y) + (t / a));
	elseif (z <= -6.4e-82)
		tmp = (y * t) / (a - z);
	elseif (z <= 4e-157)
		tmp = x + (t / (a / y));
	elseif (z <= 1e-70)
		tmp = y * (t / (a - z));
	elseif (z <= 1.5e+37)
		tmp = x + (t * (y / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.9e+112], N[(y + x), $MachinePrecision], If[LessEqual[z, -6.6e-10], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.2e-56], N[(y * N[(N[(x / y), $MachinePrecision] + N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.4e-82], N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e-157], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-70], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+37], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -1.90000000000000004e112 or 1.50000000000000011e37 < z

   1. Initial program 75.9%

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

   3. Taylor expanded in z around inf 82.9%

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

      1. +-commutative 82.9%

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

   5. Simplified 82.9%

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

   if -1.90000000000000004e112 < z < -6.6e-10

   1. Initial program 86.8%

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

   3. Taylor expanded in a around 0 68.9%

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

      1. +-commutative 68.9%

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

      2. associate-/l* 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in z around 0 65.9%

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

      1. associate-*r/ 65.9%

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

      2. neg-mul-1 65.9%

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

      3. distribute-lft-neg-in 65.9%

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

   8. Simplified 65.9%

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

   9. Taylor expanded in t around 0 65.9%

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

       1. neg-mul-1 65.9%

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

       2. sub-neg 65.9%

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

       3. associate-*r/ 66.1%

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

   11. Simplified 66.1%

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

   if -6.6e-10 < z < -5.19999999999999994e-56

   1. Initial program 84.2%

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

   3. Taylor expanded in z around 0 67.6%

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

      1. +-commutative 67.6%

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

      2. associate-/l* 83.1%

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

   5. Simplified 83.1%

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

   6. Taylor expanded in y around inf 83.4%

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

      1. +-commutative 83.4%

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

   8. Simplified 83.4%

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

   if -5.19999999999999994e-56 < z < -6.4000000000000002e-82

   1. Initial program 99.5%

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

   3. Taylor expanded in y around inf 67.9%

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

      1. associate--l+ 67.9%

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

      2. div-sub 67.9%

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

   5. Simplified 67.9%

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

   6. Taylor expanded in t around inf 52.1%

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

      1. associate-*r/ 52.1%

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

      2. neg-mul-1 52.1%

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

   8. Simplified 52.1%

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

      1. associate-*r/ 73.2%

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

      2. frac-2neg 73.2%

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

      3. add-sqr-sqrt 44.8%

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

      4. sqrt-unprod 24.0%

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

      5. sqr-neg 24.0%

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

      6. sqrt-unprod 0.2%

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

      7. add-sqr-sqrt 1.5%

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

      8. distribute-rgt-neg-out 1.5%

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

      9. add-sqr-sqrt 1.2%

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

      10. sqrt-unprod 29.4%

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

      11. sqr-neg 29.4%

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

      12. sqrt-unprod 28.3%

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

      13. add-sqr-sqrt 73.2%

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

   10. Applied egg-rr 73.2%

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

   if -6.4000000000000002e-82 < z < 3.99999999999999977e-157

   1. Initial program 92.9%

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

   3. Taylor expanded in z around 0 84.8%

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

      1. +-commutative 84.8%

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

      2. associate-/l* 87.9%

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

   5. Simplified 87.9%

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

      1. clear-num 88.0%

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

      2. un-div-inv 89.4%

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

   7. Applied egg-rr 89.4%

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

   if 3.99999999999999977e-157 < z < 9.99999999999999996e-71

   1. Initial program 91.5%

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

   3. Taylor expanded in y around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. div-sub 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in t around inf 81.9%

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

      1. associate-*r/ 81.9%

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

      2. neg-mul-1 81.9%

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

   8. Simplified 81.9%

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

   if 9.99999999999999996e-71 < z < 1.50000000000000011e37

   1. Initial program 95.6%

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

   3. Taylor expanded in z around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-/l* 76.3%

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

   5. Simplified 76.3%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a} + x} \]
3. Recombined 7 regimes into one program.

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+112}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-10}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-56}:\\ \;\;\;\;y \cdot \left(\frac{x}{y} + \frac{t}{a}\right)\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-82}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-157}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 10^{-70}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+37}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+46}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-78}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-97}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-157}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 10^{-70}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+37}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.4e+46)
   (+ y x)
   (if (<= z -1.02e-78)
     (* (- z t) (/ y (- z a)))
     (if (<= z -7.5e-97)
       (- x (* t (/ y z)))
       (if (<= z 4e-157)
         (+ x (/ t (/ a y)))
         (if (<= z 1e-70)
           (* y (/ t (- a z)))
           (if (<= z 1.16e+37) (+ x (* t (/ y a))) (+ y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.4e+46) {
		tmp = y + x;
	} else if (z <= -1.02e-78) {
		tmp = (z - t) * (y / (z - a));
	} else if (z <= -7.5e-97) {
		tmp = x - (t * (y / z));
	} else if (z <= 4e-157) {
		tmp = x + (t / (a / y));
	} else if (z <= 1e-70) {
		tmp = y * (t / (a - z));
	} else if (z <= 1.16e+37) {
		tmp = x + (t * (y / a));
	} else {
		tmp = y + 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 (z <= (-4.4d+46)) then
        tmp = y + x
    else if (z <= (-1.02d-78)) then
        tmp = (z - t) * (y / (z - a))
    else if (z <= (-7.5d-97)) then
        tmp = x - (t * (y / z))
    else if (z <= 4d-157) then
        tmp = x + (t / (a / y))
    else if (z <= 1d-70) then
        tmp = y * (t / (a - z))
    else if (z <= 1.16d+37) then
        tmp = x + (t * (y / a))
    else
        tmp = y + 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 (z <= -4.4e+46) {
		tmp = y + x;
	} else if (z <= -1.02e-78) {
		tmp = (z - t) * (y / (z - a));
	} else if (z <= -7.5e-97) {
		tmp = x - (t * (y / z));
	} else if (z <= 4e-157) {
		tmp = x + (t / (a / y));
	} else if (z <= 1e-70) {
		tmp = y * (t / (a - z));
	} else if (z <= 1.16e+37) {
		tmp = x + (t * (y / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.4e+46:
		tmp = y + x
	elif z <= -1.02e-78:
		tmp = (z - t) * (y / (z - a))
	elif z <= -7.5e-97:
		tmp = x - (t * (y / z))
	elif z <= 4e-157:
		tmp = x + (t / (a / y))
	elif z <= 1e-70:
		tmp = y * (t / (a - z))
	elif z <= 1.16e+37:
		tmp = x + (t * (y / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.4e+46)
		tmp = Float64(y + x);
	elseif (z <= -1.02e-78)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(z - a)));
	elseif (z <= -7.5e-97)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 4e-157)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 1e-70)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (z <= 1.16e+37)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.4e+46)
		tmp = y + x;
	elseif (z <= -1.02e-78)
		tmp = (z - t) * (y / (z - a));
	elseif (z <= -7.5e-97)
		tmp = x - (t * (y / z));
	elseif (z <= 4e-157)
		tmp = x + (t / (a / y));
	elseif (z <= 1e-70)
		tmp = y * (t / (a - z));
	elseif (z <= 1.16e+37)
		tmp = x + (t * (y / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.4e+46], N[(y + x), $MachinePrecision], If[LessEqual[z, -1.02e-78], N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.5e-97], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e-157], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-70], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.16e+37], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -4.4000000000000001e46 or 1.16e37 < z

   1. Initial program 78.0%

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

   3. Taylor expanded in z around inf 80.0%

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

      1. +-commutative 80.0%

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

   5. Simplified 80.0%

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

   if -4.4000000000000001e46 < z < -1.02e-78

   1. Initial program 85.6%

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

   3. Taylor expanded in x around 0 56.6%

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

      1. associate-*l/ 70.9%

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

   5. Simplified 70.9%

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

   if -1.02e-78 < z < -7.5e-97

   1. Initial program 99.6%

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

   3. Taylor expanded in a around 0 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-/l* 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around 0 99.6%

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

      1. associate-*r/ 99.6%

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

      2. neg-mul-1 99.6%

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

      3. distribute-lft-neg-in 99.6%

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

   8. Simplified 99.6%

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

   9. Taylor expanded in t around 0 99.6%

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

       1. neg-mul-1 99.6%

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

       2. sub-neg 99.6%

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

       3. associate-*r/ 100.0%

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

   11. Simplified 100.0%

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

   if -7.5e-97 < z < 3.99999999999999977e-157

   1. Initial program 92.5%

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

   3. Taylor expanded in z around 0 84.1%

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

      1. +-commutative 84.1%

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

      2. associate-/l* 87.3%

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

   5. Simplified 87.3%

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

      1. clear-num 87.4%

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

      2. un-div-inv 88.9%

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

   7. Applied egg-rr 88.9%

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

   if 3.99999999999999977e-157 < z < 9.99999999999999996e-71

   1. Initial program 91.5%

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

   3. Taylor expanded in y around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. div-sub 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in t around inf 81.9%

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

      1. associate-*r/ 81.9%

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

      2. neg-mul-1 81.9%

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

   8. Simplified 81.9%

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

   if 9.99999999999999996e-71 < z < 1.16e37

   1. Initial program 95.6%

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

   3. Taylor expanded in z around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-/l* 76.3%

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

   5. Simplified 76.3%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a} + x} \]
3. Recombined 6 regimes into one program.

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+46}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-78}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-97}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-157}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 10^{-70}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+37}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ t_2 := \frac{t\_1}{z - a}\\ \mathbf{if}\;t\_2 \leq -\infty \lor \neg \left(t\_2 \leq 5 \cdot 10^{+288}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t\_1}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))) (t_2 (/ t_1 (- z a))))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 5e+288)))
     (* (- z t) (/ y (- z a)))
     (- x (/ t_1 (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double t_2 = t_1 / (z - a);
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 5e+288)) {
		tmp = (z - t) * (y / (z - a));
	} else {
		tmp = x - (t_1 / (a - z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double t_2 = t_1 / (z - a);
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 5e+288)) {
		tmp = (z - t) * (y / (z - a));
	} else {
		tmp = x - (t_1 / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	t_2 = t_1 / (z - a)
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 5e+288):
		tmp = (z - t) * (y / (z - a))
	else:
		tmp = x - (t_1 / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	t_2 = Float64(t_1 / Float64(z - a))
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 5e+288))
		tmp = Float64(Float64(z - t) * Float64(y / Float64(z - a)));
	else
		tmp = Float64(x - Float64(t_1 / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z - t);
	t_2 = t_1 / (z - a);
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 5e+288)))
		tmp = (z - t) * (y / (z - a));
	else
		tmp = x - (t_1 / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 5e+288]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t$95$1 / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -inf.0 or 5.0000000000000003e288 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 43.3%

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

   3. Taylor expanded in x around 0 43.3%

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

      1. associate-*l/ 84.6%

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

   5. Simplified 84.6%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 5.0000000000000003e288

   1. Initial program 99.5%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 5 \cdot 10^{+288}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ t_2 := \frac{t\_1}{z - a}\\ \mathbf{if}\;t\_2 \leq -\infty \lor \neg \left(t\_2 \leq 5 \cdot 10^{+288}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t\_1}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))) (t_2 (/ t_1 (- z a))))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 5e+288)))
     (+ x (/ (- z t) (/ (- z a) y)))
     (- x (/ t_1 (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double t_2 = t_1 / (z - a);
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 5e+288)) {
		tmp = x + ((z - t) / ((z - a) / y));
	} else {
		tmp = x - (t_1 / (a - z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double t_2 = t_1 / (z - a);
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 5e+288)) {
		tmp = x + ((z - t) / ((z - a) / y));
	} else {
		tmp = x - (t_1 / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	t_2 = t_1 / (z - a)
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 5e+288):
		tmp = x + ((z - t) / ((z - a) / y))
	else:
		tmp = x - (t_1 / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	t_2 = Float64(t_1 / Float64(z - a))
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 5e+288))
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(z - a) / y)));
	else
		tmp = Float64(x - Float64(t_1 / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z - t);
	t_2 = t_1 / (z - a);
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 5e+288)))
		tmp = x + ((z - t) / ((z - a) / y));
	else
		tmp = x - (t_1 / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 5e+288]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t$95$1 / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -inf.0 or 5.0000000000000003e288 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 43.3%

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

      1. clear-num 43.3%

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

      2. inv-pow 43.3%

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

   4. Applied egg-rr 43.3%

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

      1. unpow-1 43.3%

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

      2. associate-/r* 99.8%

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

   6. Simplified 99.8%

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

      1. clear-num 99.9%

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

      2. add-cube-cbrt 99.2%

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

      3. *-un-lft-identity 99.2%

         \[\leadsto x + \frac{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}{\color{blue}{1 \cdot \frac{z - a}{y}}} \]

      4. times-frac 99.2%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}}} \]

      5. pow2 99.2%

         \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{z - t}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}} \]

   8. Applied egg-rr 99.2%

      \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}}} \]
   9. Step-by-step derivation

      1. times-frac 99.2%

         \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2} \cdot \sqrt[3]{z - t}}{1 \cdot \frac{z - a}{y}}} \]

      2. unpow2 99.2%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right)} \cdot \sqrt[3]{z - t}}{1 \cdot \frac{z - a}{y}} \]

      3. rem-3cbrt-lft 99.9%

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

      4. *-lft-identity 99.9%

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

   10. Simplified 99.9%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 5.0000000000000003e288

   1. Initial program 99.5%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 5 \cdot 10^{+288}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ t_2 := \frac{t\_1}{z - a}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;y \cdot \left(\frac{z - t}{z - a} + \frac{x}{y}\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+288}:\\ \;\;\;\;x - \frac{t\_1}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))) (t_2 (/ t_1 (- z a))))
   (if (<= t_2 (- INFINITY))
     (* y (+ (/ (- z t) (- z a)) (/ x y)))
     (if (<= t_2 5e+288)
       (- x (/ t_1 (- a z)))
       (+ x (/ (- z t) (/ (- z a) y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double t_2 = t_1 / (z - a);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = y * (((z - t) / (z - a)) + (x / y));
	} else if (t_2 <= 5e+288) {
		tmp = x - (t_1 / (a - z));
	} else {
		tmp = x + ((z - t) / ((z - a) / y));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double t_2 = t_1 / (z - a);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (((z - t) / (z - a)) + (x / y));
	} else if (t_2 <= 5e+288) {
		tmp = x - (t_1 / (a - z));
	} else {
		tmp = x + ((z - t) / ((z - a) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	t_2 = t_1 / (z - a)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = y * (((z - t) / (z - a)) + (x / y))
	elif t_2 <= 5e+288:
		tmp = x - (t_1 / (a - z))
	else:
		tmp = x + ((z - t) / ((z - a) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	t_2 = Float64(t_1 / Float64(z - a))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(y * Float64(Float64(Float64(z - t) / Float64(z - a)) + Float64(x / y)));
	elseif (t_2 <= 5e+288)
		tmp = Float64(x - Float64(t_1 / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(z - a) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z - t);
	t_2 = t_1 / (z - a);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = y * (((z - t) / (z - a)) + (x / y));
	elseif (t_2 <= 5e+288)
		tmp = x - (t_1 / (a - z));
	else
		tmp = x + ((z - t) / ((z - a) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(y * N[(N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+288], N[(x - N[(t$95$1 / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 52.8%

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

   3. Taylor expanded in y around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. div-sub 99.9%

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

   5. Simplified 99.9%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 5.0000000000000003e288

   1. Initial program 99.5%

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

   if 5.0000000000000003e288 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 36.2%

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

      1. clear-num 36.2%

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

      2. inv-pow 36.2%

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

   4. Applied egg-rr 36.2%

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

      1. unpow-1 36.2%

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

      2. associate-/r* 99.8%

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

   6. Simplified 99.8%

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

      1. clear-num 99.9%

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

      2. add-cube-cbrt 99.1%

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

      3. *-un-lft-identity 99.1%

         \[\leadsto x + \frac{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}{\color{blue}{1 \cdot \frac{z - a}{y}}} \]

      4. times-frac 99.0%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}}} \]

      5. pow2 99.0%

         \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{z - t}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}} \]

   8. Applied egg-rr 99.0%

      \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}}} \]
   9. Step-by-step derivation

      1. times-frac 99.1%

         \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2} \cdot \sqrt[3]{z - t}}{1 \cdot \frac{z - a}{y}}} \]

      2. unpow2 99.1%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right)} \cdot \sqrt[3]{z - t}}{1 \cdot \frac{z - a}{y}} \]

      3. rem-3cbrt-lft 99.9%

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

      4. *-lft-identity 99.9%

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

   10. Simplified 99.9%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty:\\ \;\;\;\;y \cdot \left(\frac{z - t}{z - a} + \frac{x}{y}\right)\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq 5 \cdot 10^{+288}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - t}{\frac{z}{y}}\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.5 \cdot 10^{-13}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-111}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z t) (/ z y)))) (t_2 (+ x (* t (/ y a)))))
   (if (<= a -1.5e-13)
     t_2
     (if (<= a -6.2e-65)
       t_1
       (if (<= a -1.05e-111)
         (+ x (/ (* y t) a))
         (if (<= a 1.6e-32) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) / (z / y));
	double t_2 = x + (t * (y / a));
	double tmp;
	if (a <= -1.5e-13) {
		tmp = t_2;
	} else if (a <= -6.2e-65) {
		tmp = t_1;
	} else if (a <= -1.05e-111) {
		tmp = x + ((y * t) / a);
	} else if (a <= 1.6e-32) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = x + ((z - t) / (z / y))
    t_2 = x + (t * (y / a))
    if (a <= (-1.5d-13)) then
        tmp = t_2
    else if (a <= (-6.2d-65)) then
        tmp = t_1
    else if (a <= (-1.05d-111)) then
        tmp = x + ((y * t) / a)
    else if (a <= 1.6d-32) then
        tmp = t_1
    else
        tmp = t_2
    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 + ((z - t) / (z / y));
	double t_2 = x + (t * (y / a));
	double tmp;
	if (a <= -1.5e-13) {
		tmp = t_2;
	} else if (a <= -6.2e-65) {
		tmp = t_1;
	} else if (a <= -1.05e-111) {
		tmp = x + ((y * t) / a);
	} else if (a <= 1.6e-32) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) / (z / y))
	t_2 = x + (t * (y / a))
	tmp = 0
	if a <= -1.5e-13:
		tmp = t_2
	elif a <= -6.2e-65:
		tmp = t_1
	elif a <= -1.05e-111:
		tmp = x + ((y * t) / a)
	elif a <= 1.6e-32:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) / Float64(z / y)))
	t_2 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (a <= -1.5e-13)
		tmp = t_2;
	elseif (a <= -6.2e-65)
		tmp = t_1;
	elseif (a <= -1.05e-111)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= 1.6e-32)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) / (z / y));
	t_2 = x + (t * (y / a));
	tmp = 0.0;
	if (a <= -1.5e-13)
		tmp = t_2;
	elseif (a <= -6.2e-65)
		tmp = t_1;
	elseif (a <= -1.05e-111)
		tmp = x + ((y * t) / a);
	elseif (a <= 1.6e-32)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.5e-13], t$95$2, If[LessEqual[a, -6.2e-65], t$95$1, If[LessEqual[a, -1.05e-111], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e-32], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.49999999999999992e-13 or 1.6000000000000001e-32 < a

   1. Initial program 86.6%

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

   3. Taylor expanded in z around 0 74.8%

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

      1. +-commutative 74.8%

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

      2. associate-/l* 83.2%

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

   5. Simplified 83.2%

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

   if -1.49999999999999992e-13 < a < -6.20000000000000032e-65 or -1.0499999999999999e-111 < a < 1.6000000000000001e-32

   1. Initial program 84.4%

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

      1. clear-num 84.4%

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

      2. inv-pow 84.4%

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

   4. Applied egg-rr 84.4%

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

      1. unpow-1 84.4%

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

      2. associate-/r* 93.6%

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

   6. Simplified 93.6%

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

      1. clear-num 93.6%

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

      2. add-cube-cbrt 92.9%

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

      3. *-un-lft-identity 92.9%

         \[\leadsto x + \frac{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}{\color{blue}{1 \cdot \frac{z - a}{y}}} \]

      4. times-frac 92.9%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}}} \]

      5. pow2 92.9%

         \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{z - t}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}} \]

   8. Applied egg-rr 92.9%

      \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}}} \]
   9. Step-by-step derivation

      1. times-frac 92.9%

         \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2} \cdot \sqrt[3]{z - t}}{1 \cdot \frac{z - a}{y}}} \]

      2. unpow2 92.9%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right)} \cdot \sqrt[3]{z - t}}{1 \cdot \frac{z - a}{y}} \]

      3. rem-3cbrt-lft 93.6%

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

      4. *-lft-identity 93.6%

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

   10. Simplified 93.6%

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

   11. Taylor expanded in z around inf 84.2%

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

   if -6.20000000000000032e-65 < a < -1.0499999999999999e-111

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 86.8%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-13}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-111}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-32}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 78.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.16 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-112}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-31}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= a -1.16e-10)
     t_1
     (if (<= a -5e-65)
       (+ x (/ (- z t) (/ z y)))
       (if (<= a -6.8e-112)
         (+ x (/ (* y t) a))
         (if (<= a 1.1e-31) (+ x (* y (/ (- z t) z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (a <= -1.16e-10) {
		tmp = t_1;
	} else if (a <= -5e-65) {
		tmp = x + ((z - t) / (z / y));
	} else if (a <= -6.8e-112) {
		tmp = x + ((y * t) / a);
	} else if (a <= 1.1e-31) {
		tmp = x + (y * ((z - t) / z));
	} 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 + (t * (y / a))
    if (a <= (-1.16d-10)) then
        tmp = t_1
    else if (a <= (-5d-65)) then
        tmp = x + ((z - t) / (z / y))
    else if (a <= (-6.8d-112)) then
        tmp = x + ((y * t) / a)
    else if (a <= 1.1d-31) then
        tmp = x + (y * ((z - t) / z))
    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 + (t * (y / a));
	double tmp;
	if (a <= -1.16e-10) {
		tmp = t_1;
	} else if (a <= -5e-65) {
		tmp = x + ((z - t) / (z / y));
	} else if (a <= -6.8e-112) {
		tmp = x + ((y * t) / a);
	} else if (a <= 1.1e-31) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if a <= -1.16e-10:
		tmp = t_1
	elif a <= -5e-65:
		tmp = x + ((z - t) / (z / y))
	elif a <= -6.8e-112:
		tmp = x + ((y * t) / a)
	elif a <= 1.1e-31:
		tmp = x + (y * ((z - t) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (a <= -1.16e-10)
		tmp = t_1;
	elseif (a <= -5e-65)
		tmp = Float64(x + Float64(Float64(z - t) / Float64(z / y)));
	elseif (a <= -6.8e-112)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= 1.1e-31)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (a <= -1.16e-10)
		tmp = t_1;
	elseif (a <= -5e-65)
		tmp = x + ((z - t) / (z / y));
	elseif (a <= -6.8e-112)
		tmp = x + ((y * t) / a);
	elseif (a <= 1.1e-31)
		tmp = x + (y * ((z - t) / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.16e-10], t$95$1, If[LessEqual[a, -5e-65], N[(x + N[(N[(z - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.8e-112], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.1e-31], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.16e-10 or 1.10000000000000005e-31 < a

   1. Initial program 86.6%

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

   3. Taylor expanded in z around 0 74.8%

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

      1. +-commutative 74.8%

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

      2. associate-/l* 83.2%

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

   5. Simplified 83.2%

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

   if -1.16e-10 < a < -4.99999999999999983e-65

   1. Initial program 74.9%

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

      1. clear-num 74.9%

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

      2. inv-pow 74.9%

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

   4. Applied egg-rr 74.9%

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

      1. unpow-1 74.9%

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

      2. associate-/r* 99.8%

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

   6. Simplified 99.8%

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

      1. clear-num 99.9%

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

      2. add-cube-cbrt 98.9%

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

      3. *-un-lft-identity 98.9%

         \[\leadsto x + \frac{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}{\color{blue}{1 \cdot \frac{z - a}{y}}} \]

      4. times-frac 98.9%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}}} \]

      5. pow2 98.9%

         \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{z - t}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}} \]

   8. Applied egg-rr 98.9%

      \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}}} \]
   9. Step-by-step derivation

      1. times-frac 98.9%

         \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2} \cdot \sqrt[3]{z - t}}{1 \cdot \frac{z - a}{y}}} \]

      2. unpow2 98.9%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right)} \cdot \sqrt[3]{z - t}}{1 \cdot \frac{z - a}{y}} \]

      3. rem-3cbrt-lft 99.9%

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

      4. *-lft-identity 99.9%

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

   10. Simplified 99.9%

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

   11. Taylor expanded in z around inf 83.9%

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

   if -4.99999999999999983e-65 < a < -6.7999999999999996e-112

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 86.8%

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

   if -6.7999999999999996e-112 < a < 1.10000000000000005e-31

   1. Initial program 85.9%

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

   3. Taylor expanded in a around 0 76.6%

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

      1. +-commutative 76.6%

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

      2. associate-/l* 87.2%

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

   5. Simplified 87.2%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.16 \cdot 10^{-10}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-112}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-31}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 78.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{y}}{t}}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-111}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-32}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.12e-13)
   (+ x (/ 1.0 (/ (/ a y) t)))
   (if (<= a -1.8e-64)
     (+ x (/ (- z t) (/ z y)))
     (if (<= a -1.1e-111)
       (+ x (/ (* y t) a))
       (if (<= a 3.5e-32) (+ x (* y (/ (- z t) z))) (+ x (* t (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.12e-13) {
		tmp = x + (1.0 / ((a / y) / t));
	} else if (a <= -1.8e-64) {
		tmp = x + ((z - t) / (z / y));
	} else if (a <= -1.1e-111) {
		tmp = x + ((y * t) / a);
	} else if (a <= 3.5e-32) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + (t * (y / 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 <= (-1.12d-13)) then
        tmp = x + (1.0d0 / ((a / y) / t))
    else if (a <= (-1.8d-64)) then
        tmp = x + ((z - t) / (z / y))
    else if (a <= (-1.1d-111)) then
        tmp = x + ((y * t) / a)
    else if (a <= 3.5d-32) then
        tmp = x + (y * ((z - t) / z))
    else
        tmp = x + (t * (y / 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 <= -1.12e-13) {
		tmp = x + (1.0 / ((a / y) / t));
	} else if (a <= -1.8e-64) {
		tmp = x + ((z - t) / (z / y));
	} else if (a <= -1.1e-111) {
		tmp = x + ((y * t) / a);
	} else if (a <= 3.5e-32) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.12e-13:
		tmp = x + (1.0 / ((a / y) / t))
	elif a <= -1.8e-64:
		tmp = x + ((z - t) / (z / y))
	elif a <= -1.1e-111:
		tmp = x + ((y * t) / a)
	elif a <= 3.5e-32:
		tmp = x + (y * ((z - t) / z))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.12e-13)
		tmp = Float64(x + Float64(1.0 / Float64(Float64(a / y) / t)));
	elseif (a <= -1.8e-64)
		tmp = Float64(x + Float64(Float64(z - t) / Float64(z / y)));
	elseif (a <= -1.1e-111)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= 3.5e-32)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.12e-13)
		tmp = x + (1.0 / ((a / y) / t));
	elseif (a <= -1.8e-64)
		tmp = x + ((z - t) / (z / y));
	elseif (a <= -1.1e-111)
		tmp = x + ((y * t) / a);
	elseif (a <= 3.5e-32)
		tmp = x + (y * ((z - t) / z));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.12e-13], N[(x + N[(1.0 / N[(N[(a / y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.8e-64], N[(x + N[(N[(z - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.1e-111], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e-32], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.12e-13

   1. Initial program 84.8%

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

   3. Taylor expanded in z around 0 70.1%

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

      1. +-commutative 70.1%

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

      2. associate-/l* 82.0%

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

   5. Simplified 82.0%

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

      1. clear-num 82.0%

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

      2. un-div-inv 82.0%

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

   7. Applied egg-rr 82.0%

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

      1. clear-num 82.0%

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

      2. inv-pow 82.0%

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

   9. Applied egg-rr 82.0%

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

       1. unpow-1 82.0%

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

   11. Simplified 82.0%

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

   if -1.12e-13 < a < -1.7999999999999999e-64

   1. Initial program 74.9%

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

      1. clear-num 74.9%

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

      2. inv-pow 74.9%

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

   4. Applied egg-rr 74.9%

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

      1. unpow-1 74.9%

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

      2. associate-/r* 99.8%

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

   6. Simplified 99.8%

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

      1. clear-num 99.9%

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

      2. add-cube-cbrt 98.9%

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

      3. *-un-lft-identity 98.9%

         \[\leadsto x + \frac{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}{\color{blue}{1 \cdot \frac{z - a}{y}}} \]

      4. times-frac 98.9%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}}} \]

      5. pow2 98.9%

         \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{z - t}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}} \]

   8. Applied egg-rr 98.9%

      \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}}} \]
   9. Step-by-step derivation

      1. times-frac 98.9%

         \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2} \cdot \sqrt[3]{z - t}}{1 \cdot \frac{z - a}{y}}} \]

      2. unpow2 98.9%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right)} \cdot \sqrt[3]{z - t}}{1 \cdot \frac{z - a}{y}} \]

      3. rem-3cbrt-lft 99.9%

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

      4. *-lft-identity 99.9%

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

   10. Simplified 99.9%

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

   11. Taylor expanded in z around inf 83.9%

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

   if -1.7999999999999999e-64 < a < -1.1e-111

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 86.8%

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

   if -1.1e-111 < a < 3.4999999999999999e-32

   1. Initial program 85.9%

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

   3. Taylor expanded in a around 0 76.6%

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

      1. +-commutative 76.6%

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

      2. associate-/l* 87.2%

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

   5. Simplified 87.2%

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

   if 3.4999999999999999e-32 < a

   1. Initial program 88.1%

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

   3. Taylor expanded in z around 0 78.8%

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

      1. +-commutative 78.8%

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

      2. associate-/l* 84.2%

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

   5. Simplified 84.2%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{y}}{t}}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-111}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-32}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 81.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{z - t}{a}\\ \mathbf{if}\;a \leq -6.8 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-112}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-31}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- z t) a)))))
   (if (<= a -6.8e-8)
     t_1
     (if (<= a -2.4e-65)
       (+ x (/ (- z t) (/ z y)))
       (if (<= a -6.8e-112)
         (+ x (/ (* y t) a))
         (if (<= a 4.6e-31) (+ x (* y (/ (- z t) z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((z - t) / a));
	double tmp;
	if (a <= -6.8e-8) {
		tmp = t_1;
	} else if (a <= -2.4e-65) {
		tmp = x + ((z - t) / (z / y));
	} else if (a <= -6.8e-112) {
		tmp = x + ((y * t) / a);
	} else if (a <= 4.6e-31) {
		tmp = x + (y * ((z - t) / z));
	} 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 * ((z - t) / a))
    if (a <= (-6.8d-8)) then
        tmp = t_1
    else if (a <= (-2.4d-65)) then
        tmp = x + ((z - t) / (z / y))
    else if (a <= (-6.8d-112)) then
        tmp = x + ((y * t) / a)
    else if (a <= 4.6d-31) then
        tmp = x + (y * ((z - t) / z))
    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 * ((z - t) / a));
	double tmp;
	if (a <= -6.8e-8) {
		tmp = t_1;
	} else if (a <= -2.4e-65) {
		tmp = x + ((z - t) / (z / y));
	} else if (a <= -6.8e-112) {
		tmp = x + ((y * t) / a);
	} else if (a <= 4.6e-31) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((z - t) / a))
	tmp = 0
	if a <= -6.8e-8:
		tmp = t_1
	elif a <= -2.4e-65:
		tmp = x + ((z - t) / (z / y))
	elif a <= -6.8e-112:
		tmp = x + ((y * t) / a)
	elif a <= 4.6e-31:
		tmp = x + (y * ((z - t) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(Float64(z - t) / a)))
	tmp = 0.0
	if (a <= -6.8e-8)
		tmp = t_1;
	elseif (a <= -2.4e-65)
		tmp = Float64(x + Float64(Float64(z - t) / Float64(z / y)));
	elseif (a <= -6.8e-112)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= 4.6e-31)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * ((z - t) / a));
	tmp = 0.0;
	if (a <= -6.8e-8)
		tmp = t_1;
	elseif (a <= -2.4e-65)
		tmp = x + ((z - t) / (z / y));
	elseif (a <= -6.8e-112)
		tmp = x + ((y * t) / a);
	elseif (a <= 4.6e-31)
		tmp = x + (y * ((z - t) / z));
	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[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.8e-8], t$95$1, If[LessEqual[a, -2.4e-65], N[(x + N[(N[(z - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.8e-112], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.6e-31], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.8e-8 or 4.5999999999999997e-31 < a

   1. Initial program 86.6%

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

   3. Taylor expanded in a around inf 76.6%

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

      1. mul-1-neg 76.6%

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

      2. unsub-neg 76.6%

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

      3. associate-/l* 85.7%

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

   5. Simplified 85.7%

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

   if -6.8e-8 < a < -2.4000000000000002e-65

   1. Initial program 74.9%

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

      1. clear-num 74.9%

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

      2. inv-pow 74.9%

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

   4. Applied egg-rr 74.9%

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

      1. unpow-1 74.9%

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

      2. associate-/r* 99.8%

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

   6. Simplified 99.8%

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

      1. clear-num 99.9%

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

      2. add-cube-cbrt 98.9%

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

      3. *-un-lft-identity 98.9%

         \[\leadsto x + \frac{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}{\color{blue}{1 \cdot \frac{z - a}{y}}} \]

      4. times-frac 98.9%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}}} \]

      5. pow2 98.9%

         \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{z - t}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}} \]

   8. Applied egg-rr 98.9%

      \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}}} \]
   9. Step-by-step derivation

      1. times-frac 98.9%

         \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2} \cdot \sqrt[3]{z - t}}{1 \cdot \frac{z - a}{y}}} \]

      2. unpow2 98.9%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right)} \cdot \sqrt[3]{z - t}}{1 \cdot \frac{z - a}{y}} \]

      3. rem-3cbrt-lft 99.9%

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

      4. *-lft-identity 99.9%

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

   10. Simplified 99.9%

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

   11. Taylor expanded in z around inf 83.9%

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

   if -2.4000000000000002e-65 < a < -6.7999999999999996e-112

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 86.8%

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

   if -6.7999999999999996e-112 < a < 4.5999999999999997e-31

   1. Initial program 85.9%

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

   3. Taylor expanded in a around 0 76.6%

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

      1. +-commutative 76.6%

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

      2. associate-/l* 87.2%

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

   5. Simplified 87.2%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{-8}:\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-112}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-31}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 72.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{-22}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{-70}:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))))
   (if (<= z -6.6e-22)
     (+ y x)
     (if (<= z 6.6e-157)
       t_1
       (if (<= z 1e-70) (* y (/ t (- z))) (if (<= z 1.95e+37) t_1 (+ y x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (z <= -6.6e-22) {
		tmp = y + x;
	} else if (z <= 6.6e-157) {
		tmp = t_1;
	} else if (z <= 1e-70) {
		tmp = y * (t / -z);
	} else if (z <= 1.95e+37) {
		tmp = t_1;
	} else {
		tmp = y + 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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    if (z <= (-6.6d-22)) then
        tmp = y + x
    else if (z <= 6.6d-157) then
        tmp = t_1
    else if (z <= 1d-70) then
        tmp = y * (t / -z)
    else if (z <= 1.95d+37) then
        tmp = t_1
    else
        tmp = y + x
    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 (z <= -6.6e-22) {
		tmp = y + x;
	} else if (z <= 6.6e-157) {
		tmp = t_1;
	} else if (z <= 1e-70) {
		tmp = y * (t / -z);
	} else if (z <= 1.95e+37) {
		tmp = t_1;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	tmp = 0
	if z <= -6.6e-22:
		tmp = y + x
	elif z <= 6.6e-157:
		tmp = t_1
	elif z <= 1e-70:
		tmp = y * (t / -z)
	elif z <= 1.95e+37:
		tmp = t_1
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (z <= -6.6e-22)
		tmp = Float64(y + x);
	elseif (z <= 6.6e-157)
		tmp = t_1;
	elseif (z <= 1e-70)
		tmp = Float64(y * Float64(t / Float64(-z)));
	elseif (z <= 1.95e+37)
		tmp = t_1;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	tmp = 0.0;
	if (z <= -6.6e-22)
		tmp = y + x;
	elseif (z <= 6.6e-157)
		tmp = t_1;
	elseif (z <= 1e-70)
		tmp = y * (t / -z);
	elseif (z <= 1.95e+37)
		tmp = t_1;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.6e-22], N[(y + x), $MachinePrecision], If[LessEqual[z, 6.6e-157], t$95$1, If[LessEqual[z, 1e-70], N[(y * N[(t / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e+37], t$95$1, N[(y + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.6000000000000002e-22 or 1.9499999999999999e37 < z

   1. Initial program 77.5%

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

   3. Taylor expanded in z around inf 76.1%

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

      1. +-commutative 76.1%

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

   5. Simplified 76.1%

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

   if -6.6000000000000002e-22 < z < 6.59999999999999998e-157 or 9.99999999999999996e-71 < z < 1.9499999999999999e37

   1. Initial program 94.1%

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

   3. Taylor expanded in z around 0 80.1%

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

   if 6.59999999999999998e-157 < z < 9.99999999999999996e-71

   1. Initial program 90.7%

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

   3. Taylor expanded in y around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. div-sub 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in t around inf 80.1%

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

      1. associate-*r/ 80.1%

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

      2. neg-mul-1 80.1%

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

   8. Simplified 80.1%

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

   9. Taylor expanded in z around inf 70.9%

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

       1. associate-*r/ 70.9%

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

       2. mul-1-neg 70.9%

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

   11. Simplified 70.9%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-22}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-157}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 10^{-70}:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+37}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 75.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+21}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-157}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 10^{-70}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+37}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.35e+21)
   (+ y x)
   (if (<= z 6.6e-157)
     (+ x (/ t (/ a y)))
     (if (<= z 1e-70)
       (- x (* t (/ y z)))
       (if (<= z 2.8e+37) (+ x (* t (/ y a))) (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.35e+21) {
		tmp = y + x;
	} else if (z <= 6.6e-157) {
		tmp = x + (t / (a / y));
	} else if (z <= 1e-70) {
		tmp = x - (t * (y / z));
	} else if (z <= 2.8e+37) {
		tmp = x + (t * (y / a));
	} else {
		tmp = y + 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 (z <= (-2.35d+21)) then
        tmp = y + x
    else if (z <= 6.6d-157) then
        tmp = x + (t / (a / y))
    else if (z <= 1d-70) then
        tmp = x - (t * (y / z))
    else if (z <= 2.8d+37) then
        tmp = x + (t * (y / a))
    else
        tmp = y + 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 (z <= -2.35e+21) {
		tmp = y + x;
	} else if (z <= 6.6e-157) {
		tmp = x + (t / (a / y));
	} else if (z <= 1e-70) {
		tmp = x - (t * (y / z));
	} else if (z <= 2.8e+37) {
		tmp = x + (t * (y / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.35e+21:
		tmp = y + x
	elif z <= 6.6e-157:
		tmp = x + (t / (a / y))
	elif z <= 1e-70:
		tmp = x - (t * (y / z))
	elif z <= 2.8e+37:
		tmp = x + (t * (y / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.35e+21)
		tmp = Float64(y + x);
	elseif (z <= 6.6e-157)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 1e-70)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 2.8e+37)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.35e+21)
		tmp = y + x;
	elseif (z <= 6.6e-157)
		tmp = x + (t / (a / y));
	elseif (z <= 1e-70)
		tmp = x - (t * (y / z));
	elseif (z <= 2.8e+37)
		tmp = x + (t * (y / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.35e+21], N[(y + x), $MachinePrecision], If[LessEqual[z, 6.6e-157], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-70], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+37], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.35e21 or 2.7999999999999998e37 < z

   1. Initial program 77.9%

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

   3. Taylor expanded in z around inf 78.1%

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

      1. +-commutative 78.1%

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

   5. Simplified 78.1%

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

   if -2.35e21 < z < 6.59999999999999998e-157

   1. Initial program 92.4%

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

   3. Taylor expanded in z around 0 79.4%

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

      1. +-commutative 79.4%

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

      2. associate-/l* 82.9%

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

   5. Simplified 82.9%

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

      1. clear-num 82.9%

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

      2. un-div-inv 84.1%

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

   7. Applied egg-rr 84.1%

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

   if 6.59999999999999998e-157 < z < 9.99999999999999996e-71

   1. Initial program 90.7%

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

   3. Taylor expanded in a around 0 90.7%

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

      1. +-commutative 90.7%

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

      2. associate-/l* 90.7%

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

   5. Simplified 90.7%

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

   6. Taylor expanded in z around 0 80.7%

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

      1. associate-*r/ 80.7%

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

      2. neg-mul-1 80.7%

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

      3. distribute-lft-neg-in 80.7%

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

   8. Simplified 80.7%

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

   9. Taylor expanded in t around 0 80.7%

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

       1. neg-mul-1 80.7%

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

       2. sub-neg 80.7%

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

       3. associate-*r/ 80.7%

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

   11. Simplified 80.7%

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

   if 9.99999999999999996e-71 < z < 2.7999999999999998e37

   1. Initial program 95.6%

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

   3. Taylor expanded in z around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-/l* 76.3%

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

   5. Simplified 76.3%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+21}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-157}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 10^{-70}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+37}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 74.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+20}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-157}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 10^{-70}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+37}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.8e+20)
   (+ y x)
   (if (<= z 4e-157)
     (+ x (/ t (/ a y)))
     (if (<= z 1e-70)
       (* y (/ t (- a z)))
       (if (<= z 4.6e+37) (+ x (* t (/ y a))) (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.8e+20) {
		tmp = y + x;
	} else if (z <= 4e-157) {
		tmp = x + (t / (a / y));
	} else if (z <= 1e-70) {
		tmp = y * (t / (a - z));
	} else if (z <= 4.6e+37) {
		tmp = x + (t * (y / a));
	} else {
		tmp = y + 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 (z <= (-9.8d+20)) then
        tmp = y + x
    else if (z <= 4d-157) then
        tmp = x + (t / (a / y))
    else if (z <= 1d-70) then
        tmp = y * (t / (a - z))
    else if (z <= 4.6d+37) then
        tmp = x + (t * (y / a))
    else
        tmp = y + 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 (z <= -9.8e+20) {
		tmp = y + x;
	} else if (z <= 4e-157) {
		tmp = x + (t / (a / y));
	} else if (z <= 1e-70) {
		tmp = y * (t / (a - z));
	} else if (z <= 4.6e+37) {
		tmp = x + (t * (y / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.8e+20:
		tmp = y + x
	elif z <= 4e-157:
		tmp = x + (t / (a / y))
	elif z <= 1e-70:
		tmp = y * (t / (a - z))
	elif z <= 4.6e+37:
		tmp = x + (t * (y / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.8e+20)
		tmp = Float64(y + x);
	elseif (z <= 4e-157)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 1e-70)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (z <= 4.6e+37)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.8e+20)
		tmp = y + x;
	elseif (z <= 4e-157)
		tmp = x + (t / (a / y));
	elseif (z <= 1e-70)
		tmp = y * (t / (a - z));
	elseif (z <= 4.6e+37)
		tmp = x + (t * (y / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.8e+20], N[(y + x), $MachinePrecision], If[LessEqual[z, 4e-157], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-70], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+37], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.8e20 or 4.60000000000000005e37 < z

   1. Initial program 77.9%

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

   3. Taylor expanded in z around inf 78.1%

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

      1. +-commutative 78.1%

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

   5. Simplified 78.1%

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

   if -9.8e20 < z < 3.99999999999999977e-157

   1. Initial program 92.3%

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

   3. Taylor expanded in z around 0 79.2%

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

      1. +-commutative 79.2%

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

      2. associate-/l* 83.5%

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

   5. Simplified 83.5%

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

      1. clear-num 83.6%

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

      2. un-div-inv 84.8%

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

   7. Applied egg-rr 84.8%

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

   if 3.99999999999999977e-157 < z < 9.99999999999999996e-71

   1. Initial program 91.5%

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

   3. Taylor expanded in y around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. div-sub 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in t around inf 81.9%

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

      1. associate-*r/ 81.9%

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

      2. neg-mul-1 81.9%

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

   8. Simplified 81.9%

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

   if 9.99999999999999996e-71 < z < 4.60000000000000005e37

   1. Initial program 95.6%

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

   3. Taylor expanded in z around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-/l* 76.3%

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

   5. Simplified 76.3%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+20}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-157}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 10^{-70}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+37}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 77.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+20} \lor \neg \left(z \leq 8 \cdot 10^{+36}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.7e+20) (not (<= z 8e+36))) (+ y x) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.7e+20) || !(z <= 8e+36)) {
		tmp = y + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.7d+20)) .or. (.not. (z <= 8d+36))) then
        tmp = y + x
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.7e+20) || !(z <= 8e+36)) {
		tmp = y + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.7e+20) or not (z <= 8e+36):
		tmp = y + x
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.7e+20) || !(z <= 8e+36))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.7e+20) || ~((z <= 8e+36)))
		tmp = y + x;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.7e+20], N[Not[LessEqual[z, 8e+36]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7e20 or 8.00000000000000034e36 < z

   1. Initial program 77.9%

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

   3. Taylor expanded in z around inf 78.1%

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

      1. +-commutative 78.1%

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

   5. Simplified 78.1%

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

   if -3.7e20 < z < 8.00000000000000034e36

   1. Initial program 92.8%

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

   3. Taylor expanded in z around 0 74.1%

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

      1. +-commutative 74.1%

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

      2. associate-/l* 78.2%

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

   5. Simplified 78.2%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+20} \lor \neg \left(z \leq 8 \cdot 10^{+36}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 77.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+20} \lor \neg \left(z \leq 1.16 \cdot 10^{+37}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.8e+20) (not (<= z 1.16e+37))) (+ y x) (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.8e+20) || !(z <= 1.16e+37)) {
		tmp = y + x;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.8d+20)) .or. (.not. (z <= 1.16d+37))) then
        tmp = y + x
    else
        tmp = x + (t / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.8e+20) || !(z <= 1.16e+37)) {
		tmp = y + x;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.8e+20) or not (z <= 1.16e+37):
		tmp = y + x
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.8e+20) || !(z <= 1.16e+37))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.8e+20) || ~((z <= 1.16e+37)))
		tmp = y + x;
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.8e+20], N[Not[LessEqual[z, 1.16e+37]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8e20 or 1.16e37 < z

   1. Initial program 77.9%

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

   3. Taylor expanded in z around inf 78.1%

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

      1. +-commutative 78.1%

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

   5. Simplified 78.1%

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

   if -3.8e20 < z < 1.16e37

   1. Initial program 92.8%

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

   3. Taylor expanded in z around 0 74.1%

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

      1. +-commutative 74.1%

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

      2. associate-/l* 78.2%

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

   5. Simplified 78.2%

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

      1. clear-num 78.2%

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

      2. un-div-inv 79.1%

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

   7. Applied egg-rr 79.1%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+20} \lor \neg \left(z \leq 1.16 \cdot 10^{+37}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 62.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 23000000000:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9e+16) x (if (<= a 23000000000.0) (+ y x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9e+16) {
		tmp = x;
	} else if (a <= 23000000000.0) {
		tmp = y + x;
	} 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 <= (-9d+16)) then
        tmp = x
    else if (a <= 23000000000.0d0) then
        tmp = y + x
    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 <= -9e+16) {
		tmp = x;
	} else if (a <= 23000000000.0) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9e+16:
		tmp = x
	elif a <= 23000000000.0:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9e+16)
		tmp = x;
	elseif (a <= 23000000000.0)
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9e+16)
		tmp = x;
	elseif (a <= 23000000000.0)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9e+16], x, If[LessEqual[a, 23000000000.0], N[(y + x), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -9e16 or 2.3e10 < a

   1. Initial program 86.0%

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

   3. Taylor expanded in x around inf 60.4%

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

   if -9e16 < a < 2.3e10

   1. Initial program 86.3%

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

   3. Taylor expanded in z around inf 60.7%

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

      1. +-commutative 60.7%

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

   5. Simplified 60.7%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 23000000000:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 60.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{+165}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.38e+165) (* y (/ t a)) (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.38e+165) {
		tmp = y * (t / a);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.38d+165)) then
        tmp = y * (t / a)
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.38e+165) {
		tmp = y * (t / a);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.38e+165:
		tmp = y * (t / a)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.38e+165)
		tmp = Float64(y * Float64(t / a));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.38e+165)
		tmp = y * (t / a);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.38e+165], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.37999999999999997e165

   1. Initial program 81.9%

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

   3. Taylor expanded in y around inf 96.2%

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

      1. associate--l+ 96.2%

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

      2. div-sub 96.2%

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

   5. Simplified 96.2%

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

   6. Taylor expanded in t around inf 69.9%

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

      1. associate-*r/ 69.9%

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

      2. neg-mul-1 69.9%

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

   8. Simplified 69.9%

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

   9. Taylor expanded in z around 0 58.8%

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

   if -1.37999999999999997e165 < y

   1. Initial program 86.6%

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

   3. Taylor expanded in z around inf 60.2%

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

      1. +-commutative 60.2%

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

   5. Simplified 60.2%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{+165}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 50.8% accurate, 11.0× 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 86.1%

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

3. Taylor expanded in x around inf 48.8%

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

4. Final simplification 48.8%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 98.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{\frac{z - a}{z - t}} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024075 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (+ x (/ y (/ (- z a) (- z t))))

  (+ x (/ (* y (- z t)) (- z a))))