Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A

Percentage Accurate: 85.0% → 90.2%

Time: 11.2s

Alternatives: 13

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

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 - (a * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - (a * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+87}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+115}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} + \frac{-1}{a \cdot \frac{z}{x - y \cdot \frac{t}{a}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.9e+87)
   (/ y (- a (/ t z)))
   (if (<= z 6e+115)
     (/ (- x (* z y)) (- t (* z a)))
     (+ (/ y a) (/ -1.0 (* a (/ z (- x (* y (/ t a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.9e+87) {
		tmp = y / (a - (t / z));
	} else if (z <= 6e+115) {
		tmp = (x - (z * y)) / (t - (z * a));
	} else {
		tmp = (y / a) + (-1.0 / (a * (z / (x - (y * (t / 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 <= (-2.9d+87)) then
        tmp = y / (a - (t / z))
    else if (z <= 6d+115) then
        tmp = (x - (z * y)) / (t - (z * a))
    else
        tmp = (y / a) + ((-1.0d0) / (a * (z / (x - (y * (t / 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 <= -2.9e+87) {
		tmp = y / (a - (t / z));
	} else if (z <= 6e+115) {
		tmp = (x - (z * y)) / (t - (z * a));
	} else {
		tmp = (y / a) + (-1.0 / (a * (z / (x - (y * (t / a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.9e+87:
		tmp = y / (a - (t / z))
	elif z <= 6e+115:
		tmp = (x - (z * y)) / (t - (z * a))
	else:
		tmp = (y / a) + (-1.0 / (a * (z / (x - (y * (t / a))))))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.9e+87)
		tmp = Float64(y / Float64(a - Float64(t / z)));
	elseif (z <= 6e+115)
		tmp = Float64(Float64(x - Float64(z * y)) / Float64(t - Float64(z * a)));
	else
		tmp = Float64(Float64(y / a) + Float64(-1.0 / Float64(a * Float64(z / Float64(x - Float64(y * Float64(t / a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.9e+87)
		tmp = y / (a - (t / z));
	elseif (z <= 6e+115)
		tmp = (x - (z * y)) / (t - (z * a));
	else
		tmp = (y / a) + (-1.0 / (a * (z / (x - (y * (t / a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.9e+87], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+115], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] + N[(-1.0 / N[(a * N[(z / N[(x - N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8999999999999998e87

   1. Initial program 49.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 49.7%

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

      2. +-commutative 49.7%

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

      3. neg-sub0 49.7%

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

      4. associate-+l- 49.7%

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

      5. sub0-neg 49.7%

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

      6. neg-mul-1 49.7%

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

      7. sub-neg 49.7%

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

      8. +-commutative 49.7%

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

      9. neg-sub0 49.7%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 49.7%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 49.7%

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

      12. neg-mul-1 49.7%

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

      13. times-frac 49.7%

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

      14. metadata-eval 49.7%

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

      15. *-lft-identity 49.7%

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

      16. *-commutative 49.7%

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

   3. Simplified 49.7%

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

   4. Taylor expanded in y around inf 43.5%

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

      1. associate-/l* 58.0%

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

   6. Simplified 58.0%

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

   7. Taylor expanded in a around 0 88.0%

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

      1. mul-1-neg 88.0%

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

      2. unsub-neg 88.0%

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

   9. Simplified 88.0%

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

   if -2.8999999999999998e87 < z < 6.0000000000000001e115

   1. Initial program 95.7%

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

   if 6.0000000000000001e115 < z

   1. Initial program 46.4%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 46.4%

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

      2. +-commutative 46.4%

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

      3. neg-sub0 46.4%

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

      4. associate-+l- 46.4%

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

      5. sub0-neg 46.4%

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

      6. neg-mul-1 46.4%

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

      7. sub-neg 46.4%

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

      8. +-commutative 46.4%

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

      9. neg-sub0 46.4%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 46.4%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 46.4%

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

      12. neg-mul-1 46.4%

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

      13. times-frac 46.4%

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

      14. metadata-eval 46.4%

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

      15. *-lft-identity 46.4%

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

      16. *-commutative 46.4%

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

   3. Simplified 46.4%

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

   4. Taylor expanded in z around inf 62.6%

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

      1. mul-1-neg 62.6%

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

      2. +-commutative 62.6%

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

      3. associate--l+ 62.6%

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

      4. associate-/r* 74.9%

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

      5. distribute-neg-frac 74.9%

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

      6. mul-1-neg 74.9%

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

      7. associate-/r* 74.9%

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

      8. associate-*r/ 74.9%

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

      9. div-sub 74.9%

         \[\leadsto \frac{y}{a} + \color{blue}{\frac{-1 \cdot \frac{x}{a} - -1 \cdot \frac{y \cdot t}{{a}^{2}}}{z}} \]

      10. distribute-lft-out-- 74.9%

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

      11. associate-*r/ 74.9%

          \[\leadsto \frac{y}{a} + \color{blue}{-1 \cdot \frac{\frac{x}{a} - \frac{y \cdot t}{{a}^{2}}}{z}} \]

   6. Simplified 77.6%

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

      1. clear-num 77.4%

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

      2. inv-pow 77.4%

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

      3. associate-*l/ 82.6%

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

      4. sub-div 82.6%

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

   8. Applied egg-rr 82.6%

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

      1. unpow-1 82.6%

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

      2. associate-/r/ 89.5%

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

   10. Simplified 89.5%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+87}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+115}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} + \frac{-1}{a \cdot \frac{z}{x - y \cdot \frac{t}{a}}}\\ \end{array} \]

Alternative 2: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{z \cdot a - t}\\ t_2 := a - \frac{t}{z}\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{-17}:\\ \;\;\;\;\frac{y}{t_2}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-36}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+93}:\\ \;\;\;\;\frac{1}{\frac{t_2}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x) (- (* z a) t))) (t_2 (- a (/ t z))))
   (if (<= z -5.4e-17)
     (/ y t_2)
     (if (<= z -9e-119)
       t_1
       (if (<= z 4.6e-36)
         (/ (- x (* z y)) t)
         (if (<= z 3.3e+25)
           t_1
           (if (<= z 1.6e+93) (/ 1.0 (/ t_2 y)) (/ (- y (/ x z)) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -x / ((z * a) - t);
	double t_2 = a - (t / z);
	double tmp;
	if (z <= -5.4e-17) {
		tmp = y / t_2;
	} else if (z <= -9e-119) {
		tmp = t_1;
	} else if (z <= 4.6e-36) {
		tmp = (x - (z * y)) / t;
	} else if (z <= 3.3e+25) {
		tmp = t_1;
	} else if (z <= 1.6e+93) {
		tmp = 1.0 / (t_2 / y);
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -x / ((z * a) - t)
    t_2 = a - (t / z)
    if (z <= (-5.4d-17)) then
        tmp = y / t_2
    else if (z <= (-9d-119)) then
        tmp = t_1
    else if (z <= 4.6d-36) then
        tmp = (x - (z * y)) / t
    else if (z <= 3.3d+25) then
        tmp = t_1
    else if (z <= 1.6d+93) then
        tmp = 1.0d0 / (t_2 / y)
    else
        tmp = (y - (x / z)) / a
    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 * a) - t);
	double t_2 = a - (t / z);
	double tmp;
	if (z <= -5.4e-17) {
		tmp = y / t_2;
	} else if (z <= -9e-119) {
		tmp = t_1;
	} else if (z <= 4.6e-36) {
		tmp = (x - (z * y)) / t;
	} else if (z <= 3.3e+25) {
		tmp = t_1;
	} else if (z <= 1.6e+93) {
		tmp = 1.0 / (t_2 / y);
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -x / ((z * a) - t)
	t_2 = a - (t / z)
	tmp = 0
	if z <= -5.4e-17:
		tmp = y / t_2
	elif z <= -9e-119:
		tmp = t_1
	elif z <= 4.6e-36:
		tmp = (x - (z * y)) / t
	elif z <= 3.3e+25:
		tmp = t_1
	elif z <= 1.6e+93:
		tmp = 1.0 / (t_2 / y)
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-x) / Float64(Float64(z * a) - t))
	t_2 = Float64(a - Float64(t / z))
	tmp = 0.0
	if (z <= -5.4e-17)
		tmp = Float64(y / t_2);
	elseif (z <= -9e-119)
		tmp = t_1;
	elseif (z <= 4.6e-36)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	elseif (z <= 3.3e+25)
		tmp = t_1;
	elseif (z <= 1.6e+93)
		tmp = Float64(1.0 / Float64(t_2 / y));
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -x / ((z * a) - t);
	t_2 = a - (t / z);
	tmp = 0.0;
	if (z <= -5.4e-17)
		tmp = y / t_2;
	elseif (z <= -9e-119)
		tmp = t_1;
	elseif (z <= 4.6e-36)
		tmp = (x - (z * y)) / t;
	elseif (z <= 3.3e+25)
		tmp = t_1;
	elseif (z <= 1.6e+93)
		tmp = 1.0 / (t_2 / y);
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-x) / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4e-17], N[(y / t$95$2), $MachinePrecision], If[LessEqual[z, -9e-119], t$95$1, If[LessEqual[z, 4.6e-36], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 3.3e+25], t$95$1, If[LessEqual[z, 1.6e+93], N[(1.0 / N[(t$95$2 / y), $MachinePrecision]), $MachinePrecision], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.4000000000000002e-17

   1. Initial program 62.3%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 62.3%

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

      2. +-commutative 62.3%

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

      3. neg-sub0 62.3%

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

      4. associate-+l- 62.3%

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

      5. sub0-neg 62.3%

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

      6. neg-mul-1 62.3%

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

      7. sub-neg 62.3%

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

      8. +-commutative 62.3%

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

      9. neg-sub0 62.3%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 62.3%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 62.3%

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

      12. neg-mul-1 62.3%

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

      13. times-frac 62.3%

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

      14. metadata-eval 62.3%

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

      15. *-lft-identity 62.3%

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

      16. *-commutative 62.3%

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

   3. Simplified 62.3%

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

   4. Taylor expanded in y around inf 50.4%

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

      1. associate-/l* 60.8%

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

   6. Simplified 60.8%

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

   7. Taylor expanded in a around 0 83.7%

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

      1. mul-1-neg 83.7%

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

      2. unsub-neg 83.7%

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

   9. Simplified 83.7%

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

   if -5.4000000000000002e-17 < z < -9.0000000000000005e-119 or 4.59999999999999993e-36 < z < 3.3000000000000001e25

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. neg-sub0 99.8%

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

      4. associate-+l- 99.8%

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

      5. sub0-neg 99.8%

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

      6. neg-mul-1 99.8%

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

      7. sub-neg 99.8%

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

      8. +-commutative 99.8%

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

      9. neg-sub0 99.8%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 99.8%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 99.8%

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

      12. neg-mul-1 99.8%

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

      13. times-frac 99.8%

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

      14. metadata-eval 99.8%

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

      15. *-lft-identity 99.8%

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

      16. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 79.5%

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

      1. neg-mul-1 79.5%

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

   6. Simplified 79.5%

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

   if -9.0000000000000005e-119 < z < 4.59999999999999993e-36

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. neg-sub0 99.8%

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

      4. associate-+l- 99.8%

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

      5. sub0-neg 99.8%

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

      6. neg-mul-1 99.8%

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

      7. sub-neg 99.8%

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

      8. +-commutative 99.8%

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

      9. neg-sub0 99.8%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 99.8%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 99.8%

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

      12. neg-mul-1 99.8%

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

      13. times-frac 99.8%

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

      14. metadata-eval 99.8%

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

      15. *-lft-identity 99.8%

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

      16. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 83.8%

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

      1. associate-*r/ 83.8%

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

      2. neg-mul-1 83.8%

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

      3. neg-sub0 83.8%

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

      4. sub-neg 83.8%

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

      5. +-commutative 83.8%

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

      6. associate--r+ 83.8%

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

      7. neg-sub0 83.8%

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

      8. remove-double-neg 83.8%

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

      9. *-commutative 83.8%

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

   6. Simplified 83.8%

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

   if 3.3000000000000001e25 < z < 1.6000000000000001e93

   1. Initial program 70.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 70.8%

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

      2. +-commutative 70.8%

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

      3. neg-sub0 70.8%

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

      4. associate-+l- 70.8%

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

      5. sub0-neg 70.8%

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

      6. neg-mul-1 70.8%

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

      7. sub-neg 70.8%

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

      8. +-commutative 70.8%

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

      9. neg-sub0 70.8%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 70.8%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 70.8%

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

      12. neg-mul-1 70.8%

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

      13. times-frac 70.8%

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

      14. metadata-eval 70.8%

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

      15. *-lft-identity 70.8%

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

      16. *-commutative 70.8%

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

   3. Simplified 70.8%

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

   4. Taylor expanded in y around inf 51.6%

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

      1. associate-/l* 70.8%

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

   6. Simplified 70.8%

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

   7. Taylor expanded in a around 0 75.7%

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

      1. mul-1-neg 75.7%

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

      2. unsub-neg 75.7%

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

   9. Simplified 75.7%

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

       1. clear-num 75.7%

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

       2. inv-pow 75.7%

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

   11. Applied egg-rr 75.7%

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

       1. unpow-1 75.7%

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

   13. Simplified 75.7%

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

   if 1.6000000000000001e93 < z

   1. Initial program 50.2%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 50.2%

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

      2. +-commutative 50.2%

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

      3. neg-sub0 50.2%

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

      4. associate-+l- 50.2%

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

      5. sub0-neg 50.2%

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

      6. neg-mul-1 50.2%

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

      7. sub-neg 50.2%

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

      8. +-commutative 50.2%

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

      9. neg-sub0 50.2%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 50.2%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 50.2%

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

      12. neg-mul-1 50.2%

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

      13. times-frac 50.2%

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

      14. metadata-eval 50.2%

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

      15. *-lft-identity 50.2%

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

      16. *-commutative 50.2%

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

   3. Simplified 50.2%

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

   4. Taylor expanded in z around inf 62.8%

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

      1. mul-1-neg 62.8%

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

      2. +-commutative 62.8%

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

      3. associate--l+ 62.8%

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

      4. associate-/r* 74.3%

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

      5. distribute-neg-frac 74.3%

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

      6. mul-1-neg 74.3%

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

      7. associate-/r* 74.4%

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

      8. associate-*r/ 74.4%

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

      9. div-sub 74.4%

         \[\leadsto \frac{y}{a} + \color{blue}{\frac{-1 \cdot \frac{x}{a} - -1 \cdot \frac{y \cdot t}{{a}^{2}}}{z}} \]

      10. distribute-lft-out-- 74.4%

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

      11. associate-*r/ 74.4%

          \[\leadsto \frac{y}{a} + \color{blue}{-1 \cdot \frac{\frac{x}{a} - \frac{y \cdot t}{{a}^{2}}}{z}} \]

   6. Simplified 76.8%

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

   7. Taylor expanded in a around inf 87.6%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-17}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-119}:\\ \;\;\;\;\frac{-x}{z \cdot a - t}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-36}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+25}:\\ \;\;\;\;\frac{-x}{z \cdot a - t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+93}:\\ \;\;\;\;\frac{1}{\frac{a - \frac{t}{z}}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 3: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{z \cdot a - t}\\ t_2 := \frac{y}{a - \frac{t}{z}}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{-17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-36}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+93}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x) (- (* z a) t))) (t_2 (/ y (- a (/ t z)))))
   (if (<= z -5.2e-17)
     t_2
     (if (<= z -4.6e-119)
       t_1
       (if (<= z 5e-36)
         (/ (- x (* z y)) t)
         (if (<= z 1.9e+24)
           t_1
           (if (<= z 1.9e+93) t_2 (/ (- y (/ x z)) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -x / ((z * a) - t);
	double t_2 = y / (a - (t / z));
	double tmp;
	if (z <= -5.2e-17) {
		tmp = t_2;
	} else if (z <= -4.6e-119) {
		tmp = t_1;
	} else if (z <= 5e-36) {
		tmp = (x - (z * y)) / t;
	} else if (z <= 1.9e+24) {
		tmp = t_1;
	} else if (z <= 1.9e+93) {
		tmp = t_2;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -x / ((z * a) - t)
    t_2 = y / (a - (t / z))
    if (z <= (-5.2d-17)) then
        tmp = t_2
    else if (z <= (-4.6d-119)) then
        tmp = t_1
    else if (z <= 5d-36) then
        tmp = (x - (z * y)) / t
    else if (z <= 1.9d+24) then
        tmp = t_1
    else if (z <= 1.9d+93) then
        tmp = t_2
    else
        tmp = (y - (x / z)) / a
    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 * a) - t);
	double t_2 = y / (a - (t / z));
	double tmp;
	if (z <= -5.2e-17) {
		tmp = t_2;
	} else if (z <= -4.6e-119) {
		tmp = t_1;
	} else if (z <= 5e-36) {
		tmp = (x - (z * y)) / t;
	} else if (z <= 1.9e+24) {
		tmp = t_1;
	} else if (z <= 1.9e+93) {
		tmp = t_2;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -x / ((z * a) - t)
	t_2 = y / (a - (t / z))
	tmp = 0
	if z <= -5.2e-17:
		tmp = t_2
	elif z <= -4.6e-119:
		tmp = t_1
	elif z <= 5e-36:
		tmp = (x - (z * y)) / t
	elif z <= 1.9e+24:
		tmp = t_1
	elif z <= 1.9e+93:
		tmp = t_2
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-x) / Float64(Float64(z * a) - t))
	t_2 = Float64(y / Float64(a - Float64(t / z)))
	tmp = 0.0
	if (z <= -5.2e-17)
		tmp = t_2;
	elseif (z <= -4.6e-119)
		tmp = t_1;
	elseif (z <= 5e-36)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	elseif (z <= 1.9e+24)
		tmp = t_1;
	elseif (z <= 1.9e+93)
		tmp = t_2;
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -x / ((z * a) - t);
	t_2 = y / (a - (t / z));
	tmp = 0.0;
	if (z <= -5.2e-17)
		tmp = t_2;
	elseif (z <= -4.6e-119)
		tmp = t_1;
	elseif (z <= 5e-36)
		tmp = (x - (z * y)) / t;
	elseif (z <= 1.9e+24)
		tmp = t_1;
	elseif (z <= 1.9e+93)
		tmp = t_2;
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-x) / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e-17], t$95$2, If[LessEqual[z, -4.6e-119], t$95$1, If[LessEqual[z, 5e-36], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.9e+24], t$95$1, If[LessEqual[z, 1.9e+93], t$95$2, N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.20000000000000006e-17 or 1.90000000000000008e24 < z < 1.8999999999999999e93

   1. Initial program 64.3%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 64.3%

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

      2. +-commutative 64.3%

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

      3. neg-sub0 64.3%

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

      4. associate-+l- 64.3%

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

      5. sub0-neg 64.3%

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

      6. neg-mul-1 64.3%

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

      7. sub-neg 64.3%

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

      8. +-commutative 64.3%

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

      9. neg-sub0 64.3%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 64.3%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 64.3%

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

      12. neg-mul-1 64.3%

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

      13. times-frac 64.3%

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

      14. metadata-eval 64.3%

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

      15. *-lft-identity 64.3%

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

      16. *-commutative 64.3%

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

   3. Simplified 64.3%

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

   4. Taylor expanded in y around inf 50.7%

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

      1. associate-/l* 63.1%

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

   6. Simplified 63.1%

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

   7. Taylor expanded in a around 0 81.8%

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

      1. mul-1-neg 81.8%

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

      2. unsub-neg 81.8%

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

   9. Simplified 81.8%

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

   if -5.20000000000000006e-17 < z < -4.59999999999999987e-119 or 5.00000000000000004e-36 < z < 1.90000000000000008e24

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. neg-sub0 99.8%

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

      4. associate-+l- 99.8%

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

      5. sub0-neg 99.8%

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

      6. neg-mul-1 99.8%

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

      7. sub-neg 99.8%

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

      8. +-commutative 99.8%

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

      9. neg-sub0 99.8%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 99.8%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 99.8%

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

      12. neg-mul-1 99.8%

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

      13. times-frac 99.8%

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

      14. metadata-eval 99.8%

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

      15. *-lft-identity 99.8%

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

      16. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 79.5%

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

      1. neg-mul-1 79.5%

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

   6. Simplified 79.5%

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

   if -4.59999999999999987e-119 < z < 5.00000000000000004e-36

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. neg-sub0 99.8%

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

      4. associate-+l- 99.8%

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

      5. sub0-neg 99.8%

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

      6. neg-mul-1 99.8%

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

      7. sub-neg 99.8%

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

      8. +-commutative 99.8%

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

      9. neg-sub0 99.8%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 99.8%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 99.8%

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

      12. neg-mul-1 99.8%

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

      13. times-frac 99.8%

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

      14. metadata-eval 99.8%

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

      15. *-lft-identity 99.8%

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

      16. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 83.8%

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

      1. associate-*r/ 83.8%

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

      2. neg-mul-1 83.8%

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

      3. neg-sub0 83.8%

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

      4. sub-neg 83.8%

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

      5. +-commutative 83.8%

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

      6. associate--r+ 83.8%

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

      7. neg-sub0 83.8%

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

      8. remove-double-neg 83.8%

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

      9. *-commutative 83.8%

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

   6. Simplified 83.8%

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

   if 1.8999999999999999e93 < z

   1. Initial program 50.2%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 50.2%

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

      2. +-commutative 50.2%

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

      3. neg-sub0 50.2%

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

      4. associate-+l- 50.2%

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

      5. sub0-neg 50.2%

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

      6. neg-mul-1 50.2%

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

      7. sub-neg 50.2%

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

      8. +-commutative 50.2%

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

      9. neg-sub0 50.2%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 50.2%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 50.2%

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

      12. neg-mul-1 50.2%

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

      13. times-frac 50.2%

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

      14. metadata-eval 50.2%

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

      15. *-lft-identity 50.2%

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

      16. *-commutative 50.2%

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

   3. Simplified 50.2%

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

   4. Taylor expanded in z around inf 62.8%

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

      1. mul-1-neg 62.8%

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

      2. +-commutative 62.8%

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

      3. associate--l+ 62.8%

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

      4. associate-/r* 74.3%

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

      5. distribute-neg-frac 74.3%

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

      6. mul-1-neg 74.3%

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

      7. associate-/r* 74.4%

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

      8. associate-*r/ 74.4%

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

      9. div-sub 74.4%

         \[\leadsto \frac{y}{a} + \color{blue}{\frac{-1 \cdot \frac{x}{a} - -1 \cdot \frac{y \cdot t}{{a}^{2}}}{z}} \]

      10. distribute-lft-out-- 74.4%

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

      11. associate-*r/ 74.4%

          \[\leadsto \frac{y}{a} + \color{blue}{-1 \cdot \frac{\frac{x}{a} - \frac{y \cdot t}{{a}^{2}}}{z}} \]

   6. Simplified 76.8%

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

   7. Taylor expanded in a around inf 87.6%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-17}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-119}:\\ \;\;\;\;\frac{-x}{z \cdot a - t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-36}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+24}:\\ \;\;\;\;\frac{-x}{z \cdot a - t}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+93}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 4: 53.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+91}:\\ \;\;\;\;\frac{y}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+160}:\\ \;\;\;\;\frac{\frac{-x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e-33)
   (/ y a)
   (if (<= z 3.5e-32)
     (/ x t)
     (if (<= z 9.5e+58)
       (/ (- x) (* z a))
       (if (<= z 4.2e+91)
         (/ y (/ (- t) z))
         (if (<= z 4.6e+160) (/ (/ (- x) z) a) (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e-33) {
		tmp = y / a;
	} else if (z <= 3.5e-32) {
		tmp = x / t;
	} else if (z <= 9.5e+58) {
		tmp = -x / (z * a);
	} else if (z <= 4.2e+91) {
		tmp = y / (-t / z);
	} else if (z <= 4.6e+160) {
		tmp = (-x / z) / a;
	} else {
		tmp = 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 <= (-1.8d-33)) then
        tmp = y / a
    else if (z <= 3.5d-32) then
        tmp = x / t
    else if (z <= 9.5d+58) then
        tmp = -x / (z * a)
    else if (z <= 4.2d+91) then
        tmp = y / (-t / z)
    else if (z <= 4.6d+160) then
        tmp = (-x / z) / a
    else
        tmp = 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 <= -1.8e-33) {
		tmp = y / a;
	} else if (z <= 3.5e-32) {
		tmp = x / t;
	} else if (z <= 9.5e+58) {
		tmp = -x / (z * a);
	} else if (z <= 4.2e+91) {
		tmp = y / (-t / z);
	} else if (z <= 4.6e+160) {
		tmp = (-x / z) / a;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.8e-33:
		tmp = y / a
	elif z <= 3.5e-32:
		tmp = x / t
	elif z <= 9.5e+58:
		tmp = -x / (z * a)
	elif z <= 4.2e+91:
		tmp = y / (-t / z)
	elif z <= 4.6e+160:
		tmp = (-x / z) / a
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e-33)
		tmp = Float64(y / a);
	elseif (z <= 3.5e-32)
		tmp = Float64(x / t);
	elseif (z <= 9.5e+58)
		tmp = Float64(Float64(-x) / Float64(z * a));
	elseif (z <= 4.2e+91)
		tmp = Float64(y / Float64(Float64(-t) / z));
	elseif (z <= 4.6e+160)
		tmp = Float64(Float64(Float64(-x) / z) / a);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.8e-33)
		tmp = y / a;
	elseif (z <= 3.5e-32)
		tmp = x / t;
	elseif (z <= 9.5e+58)
		tmp = -x / (z * a);
	elseif (z <= 4.2e+91)
		tmp = y / (-t / z);
	elseif (z <= 4.6e+160)
		tmp = (-x / z) / a;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e-33], N[(y / a), $MachinePrecision], If[LessEqual[z, 3.5e-32], N[(x / t), $MachinePrecision], If[LessEqual[z, 9.5e+58], N[((-x) / N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+91], N[(y / N[((-t) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+160], N[(N[((-x) / z), $MachinePrecision] / a), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.80000000000000017e-33 or 4.59999999999999975e160 < z

   1. Initial program 58.1%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 58.1%

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

      2. +-commutative 58.1%

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

      3. neg-sub0 58.1%

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

      4. associate-+l- 58.1%

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

      5. sub0-neg 58.1%

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

      6. neg-mul-1 58.1%

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

      7. sub-neg 58.1%

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

      8. +-commutative 58.1%

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

      9. neg-sub0 58.1%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 58.1%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 58.1%

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

      12. neg-mul-1 58.1%

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

      13. times-frac 58.1%

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

      14. metadata-eval 58.1%

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

      15. *-lft-identity 58.1%

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

      16. *-commutative 58.1%

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

   3. Simplified 58.1%

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

   4. Taylor expanded in z around inf 67.9%

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

   if -1.80000000000000017e-33 < z < 3.4999999999999999e-32

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. neg-sub0 99.8%

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

      4. associate-+l- 99.8%

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

      5. sub0-neg 99.8%

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

      6. neg-mul-1 99.8%

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

      7. sub-neg 99.8%

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

      8. +-commutative 99.8%

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

      9. neg-sub0 99.8%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 99.8%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 99.8%

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

      12. neg-mul-1 99.8%

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

      13. times-frac 99.8%

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

      14. metadata-eval 99.8%

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

      15. *-lft-identity 99.8%

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

      16. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 60.8%

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

   if 3.4999999999999999e-32 < z < 9.5000000000000002e58

   1. Initial program 87.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 87.6%

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

      2. +-commutative 87.6%

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

      3. neg-sub0 87.6%

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

      4. associate-+l- 87.6%

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

      5. sub0-neg 87.6%

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

      6. neg-mul-1 87.6%

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

      7. sub-neg 87.6%

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

      8. +-commutative 87.6%

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

      9. neg-sub0 87.6%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 87.6%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 87.6%

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

      12. neg-mul-1 87.6%

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

      13. times-frac 87.6%

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

      14. metadata-eval 87.6%

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

      15. *-lft-identity 87.6%

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

      16. *-commutative 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in z around inf 62.6%

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

      1. mul-1-neg 62.6%

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

      2. +-commutative 62.6%

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

      3. associate--l+ 62.6%

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

      4. associate-/r* 62.7%

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

      5. distribute-neg-frac 62.7%

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

      6. mul-1-neg 62.7%

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

      7. associate-/r* 62.7%

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

      8. associate-*r/ 62.7%

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

      9. div-sub 62.7%

         \[\leadsto \frac{y}{a} + \color{blue}{\frac{-1 \cdot \frac{x}{a} - -1 \cdot \frac{y \cdot t}{{a}^{2}}}{z}} \]

      10. distribute-lft-out-- 62.7%

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

      11. associate-*r/ 62.7%

          \[\leadsto \frac{y}{a} + \color{blue}{-1 \cdot \frac{\frac{x}{a} - \frac{y \cdot t}{{a}^{2}}}{z}} \]

   6. Simplified 71.0%

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

   7. Taylor expanded in y around 0 43.2%

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

      1. associate-*r/ 43.2%

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

      2. neg-mul-1 43.2%

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

   9. Simplified 43.2%

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

   if 9.5000000000000002e58 < z < 4.20000000000000015e91

   1. Initial program 67.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 67.8%

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

      2. +-commutative 67.8%

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

      3. neg-sub0 67.8%

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

      4. associate-+l- 67.8%

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

      5. sub0-neg 67.8%

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

      6. neg-mul-1 67.8%

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

      7. sub-neg 67.8%

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

      8. +-commutative 67.8%

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

      9. neg-sub0 67.8%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 67.8%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 67.8%

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

      12. neg-mul-1 67.8%

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

      13. times-frac 67.8%

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

      14. metadata-eval 67.8%

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

      15. *-lft-identity 67.8%

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

      16. *-commutative 67.8%

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

   3. Simplified 67.8%

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

   4. Taylor expanded in y around inf 57.1%

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

      1. associate-/l* 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in a around 0 78.4%

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

      1. associate-*r/ 78.4%

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

      2. neg-mul-1 78.4%

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

   9. Simplified 78.4%

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

   if 4.20000000000000015e91 < z < 4.59999999999999975e160

   1. Initial program 81.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 81.8%

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

      2. +-commutative 81.8%

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

      3. neg-sub0 81.8%

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

      4. associate-+l- 81.8%

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

      5. sub0-neg 81.8%

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

      6. neg-mul-1 81.8%

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

      7. sub-neg 81.8%

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

      8. +-commutative 81.8%

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

      9. neg-sub0 81.8%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 81.8%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 81.8%

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

      12. neg-mul-1 81.8%

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

      13. times-frac 81.8%

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

      14. metadata-eval 81.8%

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

      15. *-lft-identity 81.8%

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

      16. *-commutative 81.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in z around inf 69.6%

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

      1. mul-1-neg 69.6%

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

      2. +-commutative 69.6%

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

      3. associate--l+ 69.6%

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

      4. associate-/r* 71.1%

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

      5. distribute-neg-frac 71.1%

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

      6. mul-1-neg 71.1%

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

      7. associate-/r* 71.1%

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

      8. associate-*r/ 71.1%

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

      9. div-sub 71.1%

         \[\leadsto \frac{y}{a} + \color{blue}{\frac{-1 \cdot \frac{x}{a} - -1 \cdot \frac{y \cdot t}{{a}^{2}}}{z}} \]

      10. distribute-lft-out-- 71.1%

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

      11. associate-*r/ 71.1%

          \[\leadsto \frac{y}{a} + \color{blue}{-1 \cdot \frac{\frac{x}{a} - \frac{y \cdot t}{{a}^{2}}}{z}} \]

   6. Simplified 71.1%

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

   7. Taylor expanded in x around inf 71.9%

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

   8. Taylor expanded in y around 0 52.3%

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

      1. associate-*r/ 52.3%

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

      2. neg-mul-1 52.3%

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

      3. associate-/l/ 61.6%

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

      4. distribute-neg-frac 61.6%

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

   10. Simplified 61.6%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+91}:\\ \;\;\;\;\frac{y}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+160}:\\ \;\;\;\;\frac{\frac{-x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 5: 90.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+87}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+113}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.9e+87)
   (/ y (- a (/ t z)))
   (if (<= z 1.3e+113) (/ (- x (* z y)) (- t (* z a))) (/ (- y (/ x z)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.9e+87) {
		tmp = y / (a - (t / z));
	} else if (z <= 1.3e+113) {
		tmp = (x - (z * y)) / (t - (z * a));
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.9d+87)) then
        tmp = y / (a - (t / z))
    else if (z <= 1.3d+113) then
        tmp = (x - (z * y)) / (t - (z * a))
    else
        tmp = (y - (x / z)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.9e+87) {
		tmp = y / (a - (t / z));
	} else if (z <= 1.3e+113) {
		tmp = (x - (z * y)) / (t - (z * a));
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.9e+87:
		tmp = y / (a - (t / z))
	elif z <= 1.3e+113:
		tmp = (x - (z * y)) / (t - (z * a))
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.9e+87)
		tmp = Float64(y / Float64(a - Float64(t / z)));
	elseif (z <= 1.3e+113)
		tmp = Float64(Float64(x - Float64(z * y)) / Float64(t - Float64(z * a)));
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.9e+87)
		tmp = y / (a - (t / z));
	elseif (z <= 1.3e+113)
		tmp = (x - (z * y)) / (t - (z * a));
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.9e+87], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+113], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8999999999999997e87

   1. Initial program 49.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 49.7%

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

      2. +-commutative 49.7%

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

      3. neg-sub0 49.7%

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

      4. associate-+l- 49.7%

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

      5. sub0-neg 49.7%

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

      6. neg-mul-1 49.7%

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

      7. sub-neg 49.7%

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

      8. +-commutative 49.7%

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

      9. neg-sub0 49.7%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 49.7%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 49.7%

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

      12. neg-mul-1 49.7%

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

      13. times-frac 49.7%

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

      14. metadata-eval 49.7%

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

      15. *-lft-identity 49.7%

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

      16. *-commutative 49.7%

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

   3. Simplified 49.7%

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

   4. Taylor expanded in y around inf 43.5%

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

      1. associate-/l* 58.0%

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

   6. Simplified 58.0%

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

   7. Taylor expanded in a around 0 88.0%

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

      1. mul-1-neg 88.0%

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

      2. unsub-neg 88.0%

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

   9. Simplified 88.0%

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

   if -5.8999999999999997e87 < z < 1.3e113

   1. Initial program 95.7%

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

   if 1.3e113 < z

   1. Initial program 46.4%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 46.4%

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

      2. +-commutative 46.4%

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

      3. neg-sub0 46.4%

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

      4. associate-+l- 46.4%

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

      5. sub0-neg 46.4%

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

      6. neg-mul-1 46.4%

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

      7. sub-neg 46.4%

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

      8. +-commutative 46.4%

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

      9. neg-sub0 46.4%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 46.4%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 46.4%

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

      12. neg-mul-1 46.4%

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

      13. times-frac 46.4%

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

      14. metadata-eval 46.4%

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

      15. *-lft-identity 46.4%

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

      16. *-commutative 46.4%

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

   3. Simplified 46.4%

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

   4. Taylor expanded in z around inf 62.6%

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

      1. mul-1-neg 62.6%

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

      2. +-commutative 62.6%

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

      3. associate--l+ 62.6%

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

      4. associate-/r* 74.9%

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

      5. distribute-neg-frac 74.9%

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

      6. mul-1-neg 74.9%

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

      7. associate-/r* 74.9%

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

      8. associate-*r/ 74.9%

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

      9. div-sub 74.9%

         \[\leadsto \frac{y}{a} + \color{blue}{\frac{-1 \cdot \frac{x}{a} - -1 \cdot \frac{y \cdot t}{{a}^{2}}}{z}} \]

      10. distribute-lft-out-- 74.9%

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

      11. associate-*r/ 74.9%

          \[\leadsto \frac{y}{a} + \color{blue}{-1 \cdot \frac{\frac{x}{a} - \frac{y \cdot t}{{a}^{2}}}{z}} \]

   6. Simplified 77.6%

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

   7. Taylor expanded in a around inf 89.1%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+87}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+113}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 6: 55.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 56000000:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+58} \lor \neg \left(z \leq 3.7 \cdot 10^{+109}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{-t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.4e-33)
   (/ y a)
   (if (<= z 56000000.0)
     (/ x t)
     (if (or (<= z 1.35e+58) (not (<= z 3.7e+109)))
       (/ y a)
       (/ y (/ (- t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.4e-33) {
		tmp = y / a;
	} else if (z <= 56000000.0) {
		tmp = x / t;
	} else if ((z <= 1.35e+58) || !(z <= 3.7e+109)) {
		tmp = y / a;
	} else {
		tmp = y / (-t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.4d-33)) then
        tmp = y / a
    else if (z <= 56000000.0d0) then
        tmp = x / t
    else if ((z <= 1.35d+58) .or. (.not. (z <= 3.7d+109))) then
        tmp = y / a
    else
        tmp = y / (-t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.4e-33) {
		tmp = y / a;
	} else if (z <= 56000000.0) {
		tmp = x / t;
	} else if ((z <= 1.35e+58) || !(z <= 3.7e+109)) {
		tmp = y / a;
	} else {
		tmp = y / (-t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.4e-33:
		tmp = y / a
	elif z <= 56000000.0:
		tmp = x / t
	elif (z <= 1.35e+58) or not (z <= 3.7e+109):
		tmp = y / a
	else:
		tmp = y / (-t / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.4e-33)
		tmp = Float64(y / a);
	elseif (z <= 56000000.0)
		tmp = Float64(x / t);
	elseif ((z <= 1.35e+58) || !(z <= 3.7e+109))
		tmp = Float64(y / a);
	else
		tmp = Float64(y / Float64(Float64(-t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.4e-33)
		tmp = y / a;
	elseif (z <= 56000000.0)
		tmp = x / t;
	elseif ((z <= 1.35e+58) || ~((z <= 3.7e+109)))
		tmp = y / a;
	else
		tmp = y / (-t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.4e-33], N[(y / a), $MachinePrecision], If[LessEqual[z, 56000000.0], N[(x / t), $MachinePrecision], If[Or[LessEqual[z, 1.35e+58], N[Not[LessEqual[z, 3.7e+109]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(y / N[((-t) / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4e-33 or 5.6e7 < z < 1.3500000000000001e58 or 3.7000000000000002e109 < z

   1. Initial program 61.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 61.6%

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

      2. +-commutative 61.6%

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

      3. neg-sub0 61.6%

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

      4. associate-+l- 61.6%

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

      5. sub0-neg 61.6%

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

      6. neg-mul-1 61.6%

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

      7. sub-neg 61.6%

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

      8. +-commutative 61.6%

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

      9. neg-sub0 61.6%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 61.6%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 61.6%

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

      12. neg-mul-1 61.6%

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

      13. times-frac 61.6%

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

      14. metadata-eval 61.6%

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

      15. *-lft-identity 61.6%

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

      16. *-commutative 61.6%

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

   3. Simplified 61.6%

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

   4. Taylor expanded in z around inf 63.9%

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

   if -1.4e-33 < z < 5.6e7

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. neg-sub0 99.8%

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

      4. associate-+l- 99.8%

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

      5. sub0-neg 99.8%

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

      6. neg-mul-1 99.8%

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

      7. sub-neg 99.8%

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

      8. +-commutative 99.8%

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

      9. neg-sub0 99.8%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 99.8%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 99.8%

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

      12. neg-mul-1 99.8%

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

      13. times-frac 99.8%

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

      14. metadata-eval 99.8%

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

      15. *-lft-identity 99.8%

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

      16. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 58.0%

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

   if 1.3500000000000001e58 < z < 3.7000000000000002e109

   1. Initial program 75.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 75.7%

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

      2. +-commutative 75.7%

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

      3. neg-sub0 75.7%

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

      4. associate-+l- 75.7%

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

      5. sub0-neg 75.7%

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

      6. neg-mul-1 75.7%

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

      7. sub-neg 75.7%

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

      8. +-commutative 75.7%

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

      9. neg-sub0 75.7%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 75.7%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 75.7%

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

      12. neg-mul-1 75.7%

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

      13. times-frac 75.7%

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

      14. metadata-eval 75.7%

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

      15. *-lft-identity 75.7%

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

      16. *-commutative 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in y around inf 43.8%

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

      1. associate-/l* 59.7%

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

   6. Simplified 59.7%

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

   7. Taylor expanded in a around 0 60.6%

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

      1. associate-*r/ 60.6%

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

      2. neg-mul-1 60.6%

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

   9. Simplified 60.6%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 56000000:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+58} \lor \neg \left(z \leq 3.7 \cdot 10^{+109}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{-t}{z}}\\ \end{array} \]

Alternative 7: 54.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1050000000:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+58}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+109}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.1e-33)
   (/ y a)
   (if (<= z 1050000000.0)
     (/ x t)
     (if (<= z 3.6e+58)
       (/ y a)
       (if (<= z 3.7e+109) (* z (/ (- y) t)) (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.1e-33) {
		tmp = y / a;
	} else if (z <= 1050000000.0) {
		tmp = x / t;
	} else if (z <= 3.6e+58) {
		tmp = y / a;
	} else if (z <= 3.7e+109) {
		tmp = z * (-y / t);
	} else {
		tmp = 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 <= (-5.1d-33)) then
        tmp = y / a
    else if (z <= 1050000000.0d0) then
        tmp = x / t
    else if (z <= 3.6d+58) then
        tmp = y / a
    else if (z <= 3.7d+109) then
        tmp = z * (-y / t)
    else
        tmp = 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 <= -5.1e-33) {
		tmp = y / a;
	} else if (z <= 1050000000.0) {
		tmp = x / t;
	} else if (z <= 3.6e+58) {
		tmp = y / a;
	} else if (z <= 3.7e+109) {
		tmp = z * (-y / t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.1e-33:
		tmp = y / a
	elif z <= 1050000000.0:
		tmp = x / t
	elif z <= 3.6e+58:
		tmp = y / a
	elif z <= 3.7e+109:
		tmp = z * (-y / t)
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.1e-33)
		tmp = Float64(y / a);
	elseif (z <= 1050000000.0)
		tmp = Float64(x / t);
	elseif (z <= 3.6e+58)
		tmp = Float64(y / a);
	elseif (z <= 3.7e+109)
		tmp = Float64(z * Float64(Float64(-y) / t));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.1e-33)
		tmp = y / a;
	elseif (z <= 1050000000.0)
		tmp = x / t;
	elseif (z <= 3.6e+58)
		tmp = y / a;
	elseif (z <= 3.7e+109)
		tmp = z * (-y / t);
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.1e-33], N[(y / a), $MachinePrecision], If[LessEqual[z, 1050000000.0], N[(x / t), $MachinePrecision], If[LessEqual[z, 3.6e+58], N[(y / a), $MachinePrecision], If[LessEqual[z, 3.7e+109], N[(z * N[((-y) / t), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.10000000000000008e-33 or 1.05e9 < z < 3.59999999999999996e58 or 3.7000000000000002e109 < z

   1. Initial program 61.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 61.6%

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

      2. +-commutative 61.6%

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

      3. neg-sub0 61.6%

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

      4. associate-+l- 61.6%

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

      5. sub0-neg 61.6%

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

      6. neg-mul-1 61.6%

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

      7. sub-neg 61.6%

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

      8. +-commutative 61.6%

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

      9. neg-sub0 61.6%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 61.6%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 61.6%

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

      12. neg-mul-1 61.6%

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

      13. times-frac 61.6%

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

      14. metadata-eval 61.6%

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

      15. *-lft-identity 61.6%

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

      16. *-commutative 61.6%

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

   3. Simplified 61.6%

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

   4. Taylor expanded in z around inf 63.9%

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

   if -5.10000000000000008e-33 < z < 1.05e9

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. neg-sub0 99.8%

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

      4. associate-+l- 99.8%

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

      5. sub0-neg 99.8%

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

      6. neg-mul-1 99.8%

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

      7. sub-neg 99.8%

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

      8. +-commutative 99.8%

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

      9. neg-sub0 99.8%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 99.8%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 99.8%

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

      12. neg-mul-1 99.8%

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

      13. times-frac 99.8%

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

      14. metadata-eval 99.8%

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

      15. *-lft-identity 99.8%

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

      16. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 58.0%

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

   if 3.59999999999999996e58 < z < 3.7000000000000002e109

   1. Initial program 75.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 75.7%

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

      2. +-commutative 75.7%

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

      3. neg-sub0 75.7%

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

      4. associate-+l- 75.7%

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

      5. sub0-neg 75.7%

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

      6. neg-mul-1 75.7%

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

      7. sub-neg 75.7%

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

      8. +-commutative 75.7%

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

      9. neg-sub0 75.7%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 75.7%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 75.7%

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

      12. neg-mul-1 75.7%

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

      13. times-frac 75.7%

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

      14. metadata-eval 75.7%

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

      15. *-lft-identity 75.7%

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

      16. *-commutative 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in y around inf 43.8%

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

      1. associate-/l* 59.7%

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

   6. Simplified 59.7%

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

      1. associate-/r/ 59.6%

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

      2. *-commutative 59.6%

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

   8. Applied egg-rr 59.6%

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

   9. Taylor expanded in z around 0 60.5%

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

       1. mul-1-neg 60.5%

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

       2. distribute-neg-frac 60.5%

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

   11. Simplified 60.5%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1050000000:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+58}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+109}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 8: 54.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+58}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+109}:\\ \;\;\;\;\frac{y}{\frac{-t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.2e-33)
   (/ y a)
   (if (<= z 2.45e-32)
     (/ x t)
     (if (<= z 4.6e+58)
       (/ (- x) (* z a))
       (if (<= z 5.4e+109) (/ y (/ (- t) z)) (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e-33) {
		tmp = y / a;
	} else if (z <= 2.45e-32) {
		tmp = x / t;
	} else if (z <= 4.6e+58) {
		tmp = -x / (z * a);
	} else if (z <= 5.4e+109) {
		tmp = y / (-t / z);
	} else {
		tmp = 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 <= (-1.2d-33)) then
        tmp = y / a
    else if (z <= 2.45d-32) then
        tmp = x / t
    else if (z <= 4.6d+58) then
        tmp = -x / (z * a)
    else if (z <= 5.4d+109) then
        tmp = y / (-t / z)
    else
        tmp = 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 <= -1.2e-33) {
		tmp = y / a;
	} else if (z <= 2.45e-32) {
		tmp = x / t;
	} else if (z <= 4.6e+58) {
		tmp = -x / (z * a);
	} else if (z <= 5.4e+109) {
		tmp = y / (-t / z);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.2e-33:
		tmp = y / a
	elif z <= 2.45e-32:
		tmp = x / t
	elif z <= 4.6e+58:
		tmp = -x / (z * a)
	elif z <= 5.4e+109:
		tmp = y / (-t / z)
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.2e-33)
		tmp = Float64(y / a);
	elseif (z <= 2.45e-32)
		tmp = Float64(x / t);
	elseif (z <= 4.6e+58)
		tmp = Float64(Float64(-x) / Float64(z * a));
	elseif (z <= 5.4e+109)
		tmp = Float64(y / Float64(Float64(-t) / z));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.2e-33)
		tmp = y / a;
	elseif (z <= 2.45e-32)
		tmp = x / t;
	elseif (z <= 4.6e+58)
		tmp = -x / (z * a);
	elseif (z <= 5.4e+109)
		tmp = y / (-t / z);
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.2e-33], N[(y / a), $MachinePrecision], If[LessEqual[z, 2.45e-32], N[(x / t), $MachinePrecision], If[LessEqual[z, 4.6e+58], N[((-x) / N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+109], N[(y / N[((-t) / z), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.2e-33 or 5.40000000000000003e109 < z

   1. Initial program 59.1%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 59.1%

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

      2. +-commutative 59.1%

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

      3. neg-sub0 59.1%

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

      4. associate-+l- 59.1%

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

      5. sub0-neg 59.1%

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

      6. neg-mul-1 59.1%

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

      7. sub-neg 59.1%

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

      8. +-commutative 59.1%

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

      9. neg-sub0 59.1%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 59.1%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 59.1%

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

      12. neg-mul-1 59.1%

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

      13. times-frac 59.1%

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

      14. metadata-eval 59.1%

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

      15. *-lft-identity 59.1%

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

      16. *-commutative 59.1%

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

   3. Simplified 59.1%

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

   4. Taylor expanded in z around inf 65.3%

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

   if -1.2e-33 < z < 2.4499999999999999e-32

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. neg-sub0 99.8%

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

      4. associate-+l- 99.8%

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

      5. sub0-neg 99.8%

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

      6. neg-mul-1 99.8%

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

      7. sub-neg 99.8%

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

      8. +-commutative 99.8%

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

      9. neg-sub0 99.8%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 99.8%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 99.8%

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

      12. neg-mul-1 99.8%

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

      13. times-frac 99.8%

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

      14. metadata-eval 99.8%

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

      15. *-lft-identity 99.8%

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

      16. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 60.8%

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

   if 2.4499999999999999e-32 < z < 4.60000000000000005e58

   1. Initial program 87.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 87.6%

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

      2. +-commutative 87.6%

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

      3. neg-sub0 87.6%

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

      4. associate-+l- 87.6%

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

      5. sub0-neg 87.6%

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

      6. neg-mul-1 87.6%

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

      7. sub-neg 87.6%

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

      8. +-commutative 87.6%

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

      9. neg-sub0 87.6%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 87.6%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 87.6%

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

      12. neg-mul-1 87.6%

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

      13. times-frac 87.6%

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

      14. metadata-eval 87.6%

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

      15. *-lft-identity 87.6%

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

      16. *-commutative 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in z around inf 62.6%

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

      1. mul-1-neg 62.6%

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

      2. +-commutative 62.6%

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

      3. associate--l+ 62.6%

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

      4. associate-/r* 62.7%

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

      5. distribute-neg-frac 62.7%

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

      6. mul-1-neg 62.7%

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

      7. associate-/r* 62.7%

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

      8. associate-*r/ 62.7%

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

      9. div-sub 62.7%

         \[\leadsto \frac{y}{a} + \color{blue}{\frac{-1 \cdot \frac{x}{a} - -1 \cdot \frac{y \cdot t}{{a}^{2}}}{z}} \]

      10. distribute-lft-out-- 62.7%

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

      11. associate-*r/ 62.7%

          \[\leadsto \frac{y}{a} + \color{blue}{-1 \cdot \frac{\frac{x}{a} - \frac{y \cdot t}{{a}^{2}}}{z}} \]

   6. Simplified 71.0%

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

   7. Taylor expanded in y around 0 43.2%

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

      1. associate-*r/ 43.2%

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

      2. neg-mul-1 43.2%

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

   9. Simplified 43.2%

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

   if 4.60000000000000005e58 < z < 5.40000000000000003e109

   1. Initial program 75.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 75.7%

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

      2. +-commutative 75.7%

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

      3. neg-sub0 75.7%

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

      4. associate-+l- 75.7%

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

      5. sub0-neg 75.7%

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

      6. neg-mul-1 75.7%

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

      7. sub-neg 75.7%

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

      8. +-commutative 75.7%

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

      9. neg-sub0 75.7%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 75.7%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 75.7%

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

      12. neg-mul-1 75.7%

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

      13. times-frac 75.7%

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

      14. metadata-eval 75.7%

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

      15. *-lft-identity 75.7%

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

      16. *-commutative 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in y around inf 43.8%

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

      1. associate-/l* 59.7%

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

   6. Simplified 59.7%

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

   7. Taylor expanded in a around 0 60.6%

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

      1. associate-*r/ 60.6%

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

      2. neg-mul-1 60.6%

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

   9. Simplified 60.6%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+58}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+109}:\\ \;\;\;\;\frac{y}{\frac{-t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 9: 65.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-33} \lor \neg \left(z \leq 9.6 \cdot 10^{-24}\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.3e-33) (not (<= z 9.6e-24))) (/ y (- a (/ t z))) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.3e-33) || !(z <= 9.6e-24)) {
		tmp = y / (a - (t / z));
	} else {
		tmp = x / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.3d-33)) .or. (.not. (z <= 9.6d-24))) then
        tmp = y / (a - (t / z))
    else
        tmp = x / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.3e-33) || !(z <= 9.6e-24)) {
		tmp = y / (a - (t / z));
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.3e-33) or not (z <= 9.6e-24):
		tmp = y / (a - (t / z))
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.3e-33) || !(z <= 9.6e-24))
		tmp = Float64(y / Float64(a - Float64(t / z)));
	else
		tmp = Float64(x / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.3e-33) || ~((z <= 9.6e-24)))
		tmp = y / (a - (t / z));
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.3e-33], N[Not[LessEqual[z, 9.6e-24]], $MachinePrecision]], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.29999999999999986e-33 or 9.5999999999999993e-24 < z

   1. Initial program 64.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 64.6%

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

      2. +-commutative 64.6%

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

      3. neg-sub0 64.6%

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

      4. associate-+l- 64.6%

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

      5. sub0-neg 64.6%

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

      6. neg-mul-1 64.6%

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

      7. sub-neg 64.6%

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

      8. +-commutative 64.6%

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

      9. neg-sub0 64.6%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 64.6%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 64.6%

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

      12. neg-mul-1 64.6%

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

      13. times-frac 64.6%

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

      14. metadata-eval 64.6%

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

      15. *-lft-identity 64.6%

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

      16. *-commutative 64.6%

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

   3. Simplified 64.6%

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

   4. Taylor expanded in y around inf 46.0%

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

      1. associate-/l* 56.7%

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

   6. Simplified 56.7%

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

   7. Taylor expanded in a around 0 74.9%

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

      1. mul-1-neg 74.9%

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

      2. unsub-neg 74.9%

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

   9. Simplified 74.9%

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

   if -2.29999999999999986e-33 < z < 9.5999999999999993e-24

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. neg-sub0 99.8%

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

      4. associate-+l- 99.8%

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

      5. sub0-neg 99.8%

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

      6. neg-mul-1 99.8%

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

      7. sub-neg 99.8%

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

      8. +-commutative 99.8%

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

      9. neg-sub0 99.8%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 99.8%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 99.8%

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

      12. neg-mul-1 99.8%

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

      13. times-frac 99.8%

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

      14. metadata-eval 99.8%

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

      15. *-lft-identity 99.8%

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

      16. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 59.7%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-33} \lor \neg \left(z \leq 9.6 \cdot 10^{-24}\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]

Alternative 10: 73.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-31} \lor \neg \left(z \leq 58000000\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5e-31) (not (<= z 58000000.0)))
   (/ y (- a (/ t z)))
   (/ (- x (* z y)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5e-31) || !(z <= 58000000.0)) {
		tmp = y / (a - (t / z));
	} else {
		tmp = (x - (z * y)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5d-31)) .or. (.not. (z <= 58000000.0d0))) then
        tmp = y / (a - (t / z))
    else
        tmp = (x - (z * y)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5e-31) || !(z <= 58000000.0)) {
		tmp = y / (a - (t / z));
	} else {
		tmp = (x - (z * y)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5e-31) or not (z <= 58000000.0):
		tmp = y / (a - (t / z))
	else:
		tmp = (x - (z * y)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5e-31) || !(z <= 58000000.0))
		tmp = Float64(y / Float64(a - Float64(t / z)));
	else
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5e-31) || ~((z <= 58000000.0)))
		tmp = y / (a - (t / z));
	else
		tmp = (x - (z * y)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5e-31], N[Not[LessEqual[z, 58000000.0]], $MachinePrecision]], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5e-31 or 5.8e7 < z

   1. Initial program 62.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 62.6%

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

      2. +-commutative 62.6%

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

      3. neg-sub0 62.6%

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

      4. associate-+l- 62.6%

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

      5. sub0-neg 62.6%

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

      6. neg-mul-1 62.6%

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

      7. sub-neg 62.6%

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

      8. +-commutative 62.6%

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

      9. neg-sub0 62.6%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 62.6%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 62.6%

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

      12. neg-mul-1 62.6%

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

      13. times-frac 62.6%

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

      14. metadata-eval 62.6%

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

      15. *-lft-identity 62.6%

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

      16. *-commutative 62.6%

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

   3. Simplified 62.6%

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

   4. Taylor expanded in y around inf 45.7%

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

      1. associate-/l* 57.0%

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

   6. Simplified 57.0%

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

   7. Taylor expanded in a around 0 76.2%

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

      1. mul-1-neg 76.2%

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

      2. unsub-neg 76.2%

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

   9. Simplified 76.2%

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

   if -5e-31 < z < 5.8e7

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. neg-sub0 99.8%

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

      4. associate-+l- 99.8%

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

      5. sub0-neg 99.8%

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

      6. neg-mul-1 99.8%

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

      7. sub-neg 99.8%

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

      8. +-commutative 99.8%

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

      9. neg-sub0 99.8%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 99.8%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 99.8%

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

      12. neg-mul-1 99.8%

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

      13. times-frac 99.8%

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

      14. metadata-eval 99.8%

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

      15. *-lft-identity 99.8%

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

      16. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 77.4%

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

      1. associate-*r/ 77.4%

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

      2. neg-mul-1 77.4%

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

      3. neg-sub0 77.4%

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

      4. sub-neg 77.4%

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

      5. +-commutative 77.4%

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

      6. associate--r+ 77.4%

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

      7. neg-sub0 77.4%

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

      8. remove-double-neg 77.4%

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

      9. *-commutative 77.4%

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

   6. Simplified 77.4%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-31} \lor \neg \left(z \leq 58000000\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \end{array} \]

Alternative 11: 72.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-31}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-5}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.6e-31)
   (/ y (- a (/ t z)))
   (if (<= z 3e-5) (/ (- x (* z y)) t) (/ (- y (/ x z)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e-31) {
		tmp = y / (a - (t / z));
	} else if (z <= 3e-5) {
		tmp = (x - (z * y)) / t;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.6d-31)) then
        tmp = y / (a - (t / z))
    else if (z <= 3d-5) then
        tmp = (x - (z * y)) / t
    else
        tmp = (y - (x / z)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e-31) {
		tmp = y / (a - (t / z));
	} else if (z <= 3e-5) {
		tmp = (x - (z * y)) / t;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.6e-31:
		tmp = y / (a - (t / z))
	elif z <= 3e-5:
		tmp = (x - (z * y)) / t
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.6e-31)
		tmp = Float64(y / Float64(a - Float64(t / z)));
	elseif (z <= 3e-5)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.6e-31)
		tmp = y / (a - (t / z));
	elseif (z <= 3e-5)
		tmp = (x - (z * y)) / t;
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.6e-31], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-5], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.59999999999999995e-31

   1. Initial program 65.4%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 65.4%

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

      2. +-commutative 65.4%

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

      3. neg-sub0 65.4%

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

      4. associate-+l- 65.4%

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

      5. sub0-neg 65.4%

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

      6. neg-mul-1 65.4%

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

      7. sub-neg 65.4%

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

      8. +-commutative 65.4%

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

      9. neg-sub0 65.4%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 65.4%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 65.4%

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

      12. neg-mul-1 65.4%

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

      13. times-frac 65.4%

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

      14. metadata-eval 65.4%

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

      15. *-lft-identity 65.4%

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

      16. *-commutative 65.4%

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

   3. Simplified 65.4%

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

   4. Taylor expanded in y around inf 50.4%

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

      1. associate-/l* 60.0%

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

   6. Simplified 60.0%

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

   7. Taylor expanded in a around 0 81.0%

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

      1. mul-1-neg 81.0%

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

      2. unsub-neg 81.0%

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

   9. Simplified 81.0%

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

   if -2.59999999999999995e-31 < z < 3.00000000000000008e-5

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. neg-sub0 99.8%

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

      4. associate-+l- 99.8%

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

      5. sub0-neg 99.8%

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

      6. neg-mul-1 99.8%

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

      7. sub-neg 99.8%

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

      8. +-commutative 99.8%

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

      9. neg-sub0 99.8%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 99.8%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 99.8%

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

      12. neg-mul-1 99.8%

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

      13. times-frac 99.8%

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

      14. metadata-eval 99.8%

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

      15. *-lft-identity 99.8%

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

      16. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 78.6%

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

      1. associate-*r/ 78.6%

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

      2. neg-mul-1 78.6%

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

      3. neg-sub0 78.6%

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

      4. sub-neg 78.6%

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

      5. +-commutative 78.6%

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

      6. associate--r+ 78.6%

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

      7. neg-sub0 78.6%

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

      8. remove-double-neg 78.6%

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

      9. *-commutative 78.6%

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

   6. Simplified 78.6%

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

   if 3.00000000000000008e-5 < z

   1. Initial program 61.2%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 61.2%

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

      2. +-commutative 61.2%

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

      3. neg-sub0 61.2%

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

      4. associate-+l- 61.2%

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

      5. sub0-neg 61.2%

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

      6. neg-mul-1 61.2%

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

      7. sub-neg 61.2%

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

      8. +-commutative 61.2%

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

      9. neg-sub0 61.2%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 61.2%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 61.2%

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

      12. neg-mul-1 61.2%

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

      13. times-frac 61.2%

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

      14. metadata-eval 61.2%

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

      15. *-lft-identity 61.2%

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

      16. *-commutative 61.2%

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

   3. Simplified 61.2%

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

   4. Taylor expanded in z around inf 57.2%

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

      1. mul-1-neg 57.2%

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

      2. +-commutative 57.2%

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

      3. associate--l+ 57.2%

         \[\leadsto \color{blue}{\frac{y}{a} + \left(\left(-\frac{x}{a \cdot z}\right) - -1 \cdot \frac{y \cdot t}{{a}^{2} \cdot z}\right)} \]

      4. associate-/r* 65.5%

         \[\leadsto \frac{y}{a} + \left(\left(-\color{blue}{\frac{\frac{x}{a}}{z}}\right) - -1 \cdot \frac{y \cdot t}{{a}^{2} \cdot z}\right) \]

      5. distribute-neg-frac 65.5%

         \[\leadsto \frac{y}{a} + \left(\color{blue}{\frac{-\frac{x}{a}}{z}} - -1 \cdot \frac{y \cdot t}{{a}^{2} \cdot z}\right) \]

      6. mul-1-neg 65.5%

         \[\leadsto \frac{y}{a} + \left(\frac{\color{blue}{-1 \cdot \frac{x}{a}}}{z} - -1 \cdot \frac{y \cdot t}{{a}^{2} \cdot z}\right) \]

      7. associate-/r* 65.6%

         \[\leadsto \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - -1 \cdot \color{blue}{\frac{\frac{y \cdot t}{{a}^{2}}}{z}}\right) \]

      8. associate-*r/ 65.6%

         \[\leadsto \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - \color{blue}{\frac{-1 \cdot \frac{y \cdot t}{{a}^{2}}}{z}}\right) \]

      9. div-sub 65.6%

         \[\leadsto \frac{y}{a} + \color{blue}{\frac{-1 \cdot \frac{x}{a} - -1 \cdot \frac{y \cdot t}{{a}^{2}}}{z}} \]

      10. distribute-lft-out-- 65.6%

          \[\leadsto \frac{y}{a} + \frac{\color{blue}{-1 \cdot \left(\frac{x}{a} - \frac{y \cdot t}{{a}^{2}}\right)}}{z} \]

      11. associate-*r/ 65.6%

          \[\leadsto \frac{y}{a} + \color{blue}{-1 \cdot \frac{\frac{x}{a} - \frac{y \cdot t}{{a}^{2}}}{z}} \]

   6. Simplified 70.0%

      \[\leadsto \color{blue}{\frac{y}{a} - \frac{\frac{x}{a} - \frac{y}{a} \cdot \frac{t}{a}}{z}} \]

   7. Taylor expanded in a around inf 78.2%

      \[\leadsto \color{blue}{\frac{y - \frac{x}{z}}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-31}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-5}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 12: 55.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-33} \lor \neg \left(z \leq 15500000000\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.15e-33) (not (<= z 15500000000.0))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.15e-33) || !(z <= 15500000000.0)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.15d-33)) .or. (.not. (z <= 15500000000.0d0))) then
        tmp = y / a
    else
        tmp = x / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.15e-33) || !(z <= 15500000000.0)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.15e-33) or not (z <= 15500000000.0):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.15e-33) || !(z <= 15500000000.0))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.15e-33) || ~((z <= 15500000000.0)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.15e-33], N[Not[LessEqual[z, 15500000000.0]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.15000000000000015e-33 or 1.55e10 < z

   1. Initial program 62.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 62.8%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{t + \left(-a \cdot z\right)}} \]

      2. +-commutative 62.8%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{\left(-a \cdot z\right) + t}} \]

      3. neg-sub0 62.8%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]

      4. associate-+l- 62.8%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]

      5. sub0-neg 62.8%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{-\left(a \cdot z - t\right)}} \]

      6. neg-mul-1 62.8%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{-1 \cdot \left(a \cdot z - t\right)}} \]

      7. sub-neg 62.8%

         \[\leadsto \frac{\color{blue}{x + \left(-y \cdot z\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      8. +-commutative 62.8%

         \[\leadsto \frac{\color{blue}{\left(-y \cdot z\right) + x}}{-1 \cdot \left(a \cdot z - t\right)} \]

      9. neg-sub0 62.8%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 62.8%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 62.8%

          \[\leadsto \frac{\color{blue}{-\left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      12. neg-mul-1 62.8%

          \[\leadsto \frac{\color{blue}{-1 \cdot \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      13. times-frac 62.8%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]

      14. metadata-eval 62.8%

          \[\leadsto \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]

      15. *-lft-identity 62.8%

          \[\leadsto \color{blue}{\frac{y \cdot z - x}{a \cdot z - t}} \]

      16. *-commutative 62.8%

          \[\leadsto \frac{y \cdot z - x}{\color{blue}{z \cdot a} - t} \]

   3. Simplified 62.8%

      \[\leadsto \color{blue}{\frac{y \cdot z - x}{z \cdot a - t}} \]

   4. Taylor expanded in z around inf 59.3%

      \[\leadsto \color{blue}{\frac{y}{a}} \]

   if -2.15000000000000015e-33 < z < 1.55e10

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{t + \left(-a \cdot z\right)}} \]

      2. +-commutative 99.8%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{\left(-a \cdot z\right) + t}} \]

      3. neg-sub0 99.8%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]

      4. associate-+l- 99.8%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]

      5. sub0-neg 99.8%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{-\left(a \cdot z - t\right)}} \]

      6. neg-mul-1 99.8%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{-1 \cdot \left(a \cdot z - t\right)}} \]

      7. sub-neg 99.8%

         \[\leadsto \frac{\color{blue}{x + \left(-y \cdot z\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      8. +-commutative 99.8%

         \[\leadsto \frac{\color{blue}{\left(-y \cdot z\right) + x}}{-1 \cdot \left(a \cdot z - t\right)} \]

      9. neg-sub0 99.8%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 99.8%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 99.8%

          \[\leadsto \frac{\color{blue}{-\left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      12. neg-mul-1 99.8%

          \[\leadsto \frac{\color{blue}{-1 \cdot \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      13. times-frac 99.8%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]

      14. metadata-eval 99.8%

          \[\leadsto \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]

      15. *-lft-identity 99.8%

          \[\leadsto \color{blue}{\frac{y \cdot z - x}{a \cdot z - t}} \]

      16. *-commutative 99.8%

          \[\leadsto \frac{y \cdot z - x}{\color{blue}{z \cdot a} - t} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{y \cdot z - x}{z \cdot a - t}} \]

   4. Taylor expanded in z around 0 58.0%

      \[\leadsto \color{blue}{\frac{x}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-33} \lor \neg \left(z \leq 15500000000\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]

Alternative 13: 35.4% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \frac{x}{t} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (/ x t))

C

double code(double x, double y, double z, double t, double a) {
	return x / 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 / t
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x / t;
}

Python

def code(x, y, z, t, a):
	return x / t

Julia

function code(x, y, z, t, a)
	return Float64(x / t)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x / t;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x / t), $MachinePrecision]

Derivation

1. Initial program 79.6%

   \[\frac{x - y \cdot z}{t - a \cdot z} \]
2. Step-by-step derivation

   1. sub-neg 79.6%

      \[\leadsto \frac{x - y \cdot z}{\color{blue}{t + \left(-a \cdot z\right)}} \]

   2. +-commutative 79.6%

      \[\leadsto \frac{x - y \cdot z}{\color{blue}{\left(-a \cdot z\right) + t}} \]

   3. neg-sub0 79.6%

      \[\leadsto \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]

   4. associate-+l- 79.6%

      \[\leadsto \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]

   5. sub0-neg 79.6%

      \[\leadsto \frac{x - y \cdot z}{\color{blue}{-\left(a \cdot z - t\right)}} \]

   6. neg-mul-1 79.6%

      \[\leadsto \frac{x - y \cdot z}{\color{blue}{-1 \cdot \left(a \cdot z - t\right)}} \]

   7. sub-neg 79.6%

      \[\leadsto \frac{\color{blue}{x + \left(-y \cdot z\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

   8. +-commutative 79.6%

      \[\leadsto \frac{\color{blue}{\left(-y \cdot z\right) + x}}{-1 \cdot \left(a \cdot z - t\right)} \]

   9. neg-sub0 79.6%

      \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

   10. associate-+l- 79.6%

       \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

   11. sub0-neg 79.6%

       \[\leadsto \frac{\color{blue}{-\left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

   12. neg-mul-1 79.6%

       \[\leadsto \frac{\color{blue}{-1 \cdot \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

   13. times-frac 79.6%

       \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]

   14. metadata-eval 79.6%

       \[\leadsto \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]

   15. *-lft-identity 79.6%

       \[\leadsto \color{blue}{\frac{y \cdot z - x}{a \cdot z - t}} \]

   16. *-commutative 79.6%

       \[\leadsto \frac{y \cdot z - x}{\color{blue}{z \cdot a} - t} \]

3. Simplified 79.6%

   \[\leadsto \color{blue}{\frac{y \cdot z - x}{z \cdot a - t}} \]

4. Taylor expanded in z around 0 32.0%

   \[\leadsto \color{blue}{\frac{x}{t}} \]

5. Final simplification 32.0%

   \[\leadsto \frac{x}{t} \]

Developer target: 97.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot z\\ t_2 := \frac{x}{t_1} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{if}\;z < -32113435955957344:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z < 3.5139522372978296 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a z))) (t_2 (- (/ x t_1) (/ y (- (/ t z) a)))))
   (if (< z -32113435955957344.0)
     t_2
     (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 t_1)) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / 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 = t - (a * z)
    t_2 = (x / t_1) - (y / ((t / z) - a))
    if (z < (-32113435955957344.0d0)) then
        tmp = t_2
    else if (z < 3.5139522372978296d-86) then
        tmp = (x - (y * z)) * (1.0d0 / 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 = t - (a * z);
	double t_2 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a * z)
	t_2 = (x / t_1) - (y / ((t / z) - a))
	tmp = 0
	if z < -32113435955957344.0:
		tmp = t_2
	elif z < 3.5139522372978296e-86:
		tmp = (x - (y * z)) * (1.0 / t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a * z))
	t_2 = Float64(Float64(x / t_1) - Float64(y / Float64(Float64(t / z) - a)))
	tmp = 0.0
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = Float64(Float64(x - Float64(y * z)) * Float64(1.0 / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a * z);
	t_2 = (x / t_1) - (y / ((t / z) - a));
	tmp = 0.0;
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = (x - (y * z)) * (1.0 / t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / t$95$1), $MachinePrecision] - N[(y / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -32113435955957344.0], t$95$2, If[Less[z, 3.5139522372978296e-86], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023207 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< z -32113435955957344.0) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))) (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

  (/ (- x (* y z)) (- t (* a z))))