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

Percentage Accurate: 86.4% → 88.2%

Time: 11.9s

Alternatives: 11

Speedup: 0.8×

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: 86.4% 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: 88.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ \mathbf{if}\;z \leq 4.8 \cdot 10^{+92}:\\ \;\;\;\;\frac{x}{t_1} - \frac{z \cdot y}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* z a))))
   (if (<= z 4.8e+92) (- (/ x t_1) (/ (* z y) t_1)) (/ (- y (/ x z)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double tmp;
	if (z <= 4.8e+92) {
		tmp = (x / t_1) - ((z * y) / t_1);
	} 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) :: tmp
    t_1 = t - (z * a)
    if (z <= 4.8d+92) then
        tmp = (x / t_1) - ((z * y) / t_1)
    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 = t - (z * a);
	double tmp;
	if (z <= 4.8e+92) {
		tmp = (x / t_1) - ((z * y) / t_1);
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (z * a)
	tmp = 0
	if z <= 4.8e+92:
		tmp = (x / t_1) - ((z * y) / t_1)
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(z * a))
	tmp = 0.0
	if (z <= 4.8e+92)
		tmp = Float64(Float64(x / t_1) - Float64(Float64(z * y) / t_1));
	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 = t - (z * a);
	tmp = 0.0;
	if (z <= 4.8e+92)
		tmp = (x / t_1) - ((z * y) / t_1);
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 4.8e+92], N[(N[(x / t$95$1), $MachinePrecision] - N[(N[(z * y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 4.80000000000000009e92

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

   3. Simplified 93.9%

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

      1. clear-num 92.8%

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

      2. associate-/r/ 93.5%

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

      3. sub-neg 93.5%

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

      4. +-commutative 93.5%

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

      5. *-commutative 93.5%

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

      6. distribute-rgt-neg-in 93.5%

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

      7. fma-def 93.5%

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

   5. Applied egg-rr 93.5%

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

   6. Taylor expanded in x around 0 93.9%

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

      1. +-commutative 93.9%

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

      2. mul-1-neg 93.9%

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

      3. sub-neg 93.9%

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

      4. mul-1-neg 93.9%

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

      5. associate-/l* 93.3%

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

      6. mul-1-neg 93.3%

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

      7. sub-neg 93.3%

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

      8. associate-/l* 93.9%

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

      9. unsub-neg 93.9%

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

      10. *-commutative 93.9%

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

      11. *-commutative 93.9%

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

   8. Simplified 93.9%

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

   if 4.80000000000000009e92 < z

   1. Initial program 53.2%

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

      1. *-commutative 53.2%

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

   3. Simplified 53.2%

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

      1. clear-num 53.2%

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

      2. associate-/r/ 53.1%

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

      3. sub-neg 53.1%

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

      4. +-commutative 53.1%

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

      5. *-commutative 53.1%

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

      6. distribute-rgt-neg-in 53.1%

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

      7. fma-def 53.1%

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

   5. Applied egg-rr 53.1%

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

   6. Taylor expanded in x around 0 51.4%

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

      1. +-commutative 51.4%

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

      2. mul-1-neg 51.4%

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

      3. sub-neg 51.4%

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

      4. mul-1-neg 51.4%

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

      5. associate-/l* 70.3%

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

      6. mul-1-neg 70.3%

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

      7. sub-neg 70.3%

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

      8. associate-/l* 51.4%

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

      9. unsub-neg 51.4%

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

      10. *-commutative 51.4%

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

      11. *-commutative 51.4%

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

   8. Simplified 51.4%

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

   9. Taylor expanded in t around 0 84.5%

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

       1. distribute-lft-out-- 84.5%

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

       2. *-commutative 84.5%

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

       3. associate-/r* 85.5%

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

       4. div-sub 87.3%

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

       5. sub-neg 87.3%

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

       6. mul-1-neg 87.3%

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

       7. +-commutative 87.3%

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

       8. associate-*r/ 87.3%

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

       9. distribute-lft-in 87.3%

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

       10. neg-mul-1 87.3%

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

       11. mul-1-neg 87.3%

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

       12. remove-double-neg 87.3%

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

       13. mul-1-neg 87.3%

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

       14. unsub-neg 87.3%

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

   11. Simplified 87.3%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4.8 \cdot 10^{+92}:\\ \;\;\;\;\frac{x}{t - z \cdot a} - \frac{z \cdot y}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 2: 71.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ t_2 := t - z \cdot a\\ \mathbf{if}\;z \leq -8.4 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{t} - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.6:\\ \;\;\;\;\frac{x}{t_2}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \frac{-z}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)) (t_2 (- t (* z a))))
   (if (<= z -8.4e+21)
     t_1
     (if (<= z -7.4e-53)
       (- (/ x t) (/ y (/ t z)))
       (if (<= z -2.3e-70)
         t_1
         (if (<= z 3.6)
           (/ x t_2)
           (if (<= z 3.8e+82) (* y (/ (- z) t_2)) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double t_2 = t - (z * a);
	double tmp;
	if (z <= -8.4e+21) {
		tmp = t_1;
	} else if (z <= -7.4e-53) {
		tmp = (x / t) - (y / (t / z));
	} else if (z <= -2.3e-70) {
		tmp = t_1;
	} else if (z <= 3.6) {
		tmp = x / t_2;
	} else if (z <= 3.8e+82) {
		tmp = y * (-z / t_2);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - (x / z)) / a
    t_2 = t - (z * a)
    if (z <= (-8.4d+21)) then
        tmp = t_1
    else if (z <= (-7.4d-53)) then
        tmp = (x / t) - (y / (t / z))
    else if (z <= (-2.3d-70)) then
        tmp = t_1
    else if (z <= 3.6d0) then
        tmp = x / t_2
    else if (z <= 3.8d+82) then
        tmp = y * (-z / t_2)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double t_2 = t - (z * a);
	double tmp;
	if (z <= -8.4e+21) {
		tmp = t_1;
	} else if (z <= -7.4e-53) {
		tmp = (x / t) - (y / (t / z));
	} else if (z <= -2.3e-70) {
		tmp = t_1;
	} else if (z <= 3.6) {
		tmp = x / t_2;
	} else if (z <= 3.8e+82) {
		tmp = y * (-z / t_2);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	t_2 = t - (z * a)
	tmp = 0
	if z <= -8.4e+21:
		tmp = t_1
	elif z <= -7.4e-53:
		tmp = (x / t) - (y / (t / z))
	elif z <= -2.3e-70:
		tmp = t_1
	elif z <= 3.6:
		tmp = x / t_2
	elif z <= 3.8e+82:
		tmp = y * (-z / t_2)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	t_2 = Float64(t - Float64(z * a))
	tmp = 0.0
	if (z <= -8.4e+21)
		tmp = t_1;
	elseif (z <= -7.4e-53)
		tmp = Float64(Float64(x / t) - Float64(y / Float64(t / z)));
	elseif (z <= -2.3e-70)
		tmp = t_1;
	elseif (z <= 3.6)
		tmp = Float64(x / t_2);
	elseif (z <= 3.8e+82)
		tmp = Float64(y * Float64(Float64(-z) / t_2));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	t_2 = t - (z * a);
	tmp = 0.0;
	if (z <= -8.4e+21)
		tmp = t_1;
	elseif (z <= -7.4e-53)
		tmp = (x / t) - (y / (t / z));
	elseif (z <= -2.3e-70)
		tmp = t_1;
	elseif (z <= 3.6)
		tmp = x / t_2;
	elseif (z <= 3.8e+82)
		tmp = y * (-z / t_2);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.4e+21], t$95$1, If[LessEqual[z, -7.4e-53], N[(N[(x / t), $MachinePrecision] - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.3e-70], t$95$1, If[LessEqual[z, 3.6], N[(x / t$95$2), $MachinePrecision], If[LessEqual[z, 3.8e+82], N[(y * N[((-z) / t$95$2), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.4e21 or -7.39999999999999965e-53 < z < -2.30000000000000001e-70 or 3.80000000000000033e82 < z

   1. Initial program 66.2%

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

      1. *-commutative 66.2%

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

   3. Simplified 66.2%

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

      1. clear-num 66.2%

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

      2. associate-/r/ 66.1%

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

      3. sub-neg 66.1%

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

      4. +-commutative 66.1%

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

      5. *-commutative 66.1%

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

      6. distribute-rgt-neg-in 66.1%

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

      7. fma-def 66.1%

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

   5. Applied egg-rr 66.1%

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

   6. Taylor expanded in x around 0 65.3%

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

      1. +-commutative 65.3%

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

      2. mul-1-neg 65.3%

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

      3. sub-neg 65.3%

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

      4. mul-1-neg 65.3%

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

      5. associate-/l* 77.9%

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

      6. mul-1-neg 77.9%

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

      7. sub-neg 77.9%

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

      8. associate-/l* 65.3%

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

      9. unsub-neg 65.3%

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

      10. *-commutative 65.3%

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

      11. *-commutative 65.3%

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

   8. Simplified 65.3%

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

   9. Taylor expanded in t around 0 78.6%

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

       1. distribute-lft-out-- 78.6%

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

       2. *-commutative 78.6%

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

       3. associate-/r* 80.9%

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

       4. div-sub 81.8%

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

       5. sub-neg 81.8%

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

       6. mul-1-neg 81.8%

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

       7. +-commutative 81.8%

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

       8. associate-*r/ 81.8%

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

       9. distribute-lft-in 81.8%

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

       10. neg-mul-1 81.8%

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

       11. mul-1-neg 81.8%

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

       12. remove-double-neg 81.8%

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

       13. mul-1-neg 81.8%

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

       14. unsub-neg 81.8%

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

   11. Simplified 81.8%

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

   if -8.4e21 < z < -7.39999999999999965e-53

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 69.7%

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

      1. div-sub 69.7%

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

      2. associate-/l* 69.7%

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

   6. Applied egg-rr 69.7%

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

   if -2.30000000000000001e-70 < z < 3.60000000000000009

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 78.3%

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

      1. *-commutative 78.3%

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

   6. Simplified 78.3%

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

   if 3.60000000000000009 < z < 3.80000000000000033e82

   1. Initial program 86.4%

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

      1. *-commutative 86.4%

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

   3. Simplified 86.4%

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

      1. clear-num 85.9%

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

      2. associate-/r/ 85.7%

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

      3. sub-neg 85.7%

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

      4. +-commutative 85.7%

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

      5. *-commutative 85.7%

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

      6. distribute-rgt-neg-in 85.7%

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

      7. fma-def 85.7%

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

   5. Applied egg-rr 85.7%

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

   6. Taylor expanded in x around 0 86.4%

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

      1. +-commutative 86.4%

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

      2. mul-1-neg 86.4%

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

      3. sub-neg 86.4%

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

      4. mul-1-neg 86.4%

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

      5. associate-/l* 99.8%

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

      6. mul-1-neg 99.8%

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

      7. sub-neg 99.8%

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

      8. associate-/l* 86.4%

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

      9. unsub-neg 86.4%

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

      10. *-commutative 86.4%

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

      11. *-commutative 86.4%

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

   8. Simplified 86.4%

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

   9. Taylor expanded in x around 0 65.7%

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

       1. mul-1-neg 65.7%

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

       2. *-commutative 65.7%

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

       3. associate-*r/ 79.3%

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

       4. distribute-lft-neg-in 79.3%

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

   11. Simplified 79.3%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{+21}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{t} - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-70}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 3.6:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \frac{-z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 3: 71.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-53}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+82}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= z -7.2e+21)
     t_1
     (if (<= z -7.4e-53)
       (/ (- x (* z y)) t)
       (if (<= z -3.3e-70)
         t_1
         (if (<= z 2.0)
           (/ x (- t (* z a)))
           (if (<= z 2.95e+82) (* z (/ y (- (* z a) t))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -7.2e+21) {
		tmp = t_1;
	} else if (z <= -7.4e-53) {
		tmp = (x - (z * y)) / t;
	} else if (z <= -3.3e-70) {
		tmp = t_1;
	} else if (z <= 2.0) {
		tmp = x / (t - (z * a));
	} else if (z <= 2.95e+82) {
		tmp = z * (y / ((z * a) - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - (x / z)) / a
    if (z <= (-7.2d+21)) then
        tmp = t_1
    else if (z <= (-7.4d-53)) then
        tmp = (x - (z * y)) / t
    else if (z <= (-3.3d-70)) then
        tmp = t_1
    else if (z <= 2.0d0) then
        tmp = x / (t - (z * a))
    else if (z <= 2.95d+82) then
        tmp = z * (y / ((z * a) - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -7.2e+21) {
		tmp = t_1;
	} else if (z <= -7.4e-53) {
		tmp = (x - (z * y)) / t;
	} else if (z <= -3.3e-70) {
		tmp = t_1;
	} else if (z <= 2.0) {
		tmp = x / (t - (z * a));
	} else if (z <= 2.95e+82) {
		tmp = z * (y / ((z * a) - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if z <= -7.2e+21:
		tmp = t_1
	elif z <= -7.4e-53:
		tmp = (x - (z * y)) / t
	elif z <= -3.3e-70:
		tmp = t_1
	elif z <= 2.0:
		tmp = x / (t - (z * a))
	elif z <= 2.95e+82:
		tmp = z * (y / ((z * a) - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -7.2e+21)
		tmp = t_1;
	elseif (z <= -7.4e-53)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	elseif (z <= -3.3e-70)
		tmp = t_1;
	elseif (z <= 2.0)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 2.95e+82)
		tmp = Float64(z * Float64(y / Float64(Float64(z * a) - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -7.2e+21)
		tmp = t_1;
	elseif (z <= -7.4e-53)
		tmp = (x - (z * y)) / t;
	elseif (z <= -3.3e-70)
		tmp = t_1;
	elseif (z <= 2.0)
		tmp = x / (t - (z * a));
	elseif (z <= 2.95e+82)
		tmp = z * (y / ((z * a) - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -7.2e+21], t$95$1, If[LessEqual[z, -7.4e-53], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, -3.3e-70], t$95$1, If[LessEqual[z, 2.0], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.95e+82], N[(z * N[(y / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.2e21 or -7.39999999999999965e-53 < z < -3.30000000000000016e-70 or 2.9499999999999998e82 < z

   1. Initial program 66.2%

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

      1. *-commutative 66.2%

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

   3. Simplified 66.2%

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

      1. clear-num 66.2%

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

      2. associate-/r/ 66.1%

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

      3. sub-neg 66.1%

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

      4. +-commutative 66.1%

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

      5. *-commutative 66.1%

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

      6. distribute-rgt-neg-in 66.1%

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

      7. fma-def 66.1%

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

   5. Applied egg-rr 66.1%

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

   6. Taylor expanded in x around 0 65.3%

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

      1. +-commutative 65.3%

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

      2. mul-1-neg 65.3%

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

      3. sub-neg 65.3%

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

      4. mul-1-neg 65.3%

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

      5. associate-/l* 77.9%

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

      6. mul-1-neg 77.9%

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

      7. sub-neg 77.9%

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

      8. associate-/l* 65.3%

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

      9. unsub-neg 65.3%

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

      10. *-commutative 65.3%

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

      11. *-commutative 65.3%

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

   8. Simplified 65.3%

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

   9. Taylor expanded in t around 0 78.6%

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

       1. distribute-lft-out-- 78.6%

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

       2. *-commutative 78.6%

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

       3. associate-/r* 80.9%

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

       4. div-sub 81.8%

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

       5. sub-neg 81.8%

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

       6. mul-1-neg 81.8%

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

       7. +-commutative 81.8%

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

       8. associate-*r/ 81.8%

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

       9. distribute-lft-in 81.8%

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

       10. neg-mul-1 81.8%

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

       11. mul-1-neg 81.8%

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

       12. remove-double-neg 81.8%

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

       13. mul-1-neg 81.8%

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

       14. unsub-neg 81.8%

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

   11. Simplified 81.8%

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

   if -7.2e21 < z < -7.39999999999999965e-53

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 69.7%

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

   if -3.30000000000000016e-70 < z < 2

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 78.3%

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

      1. *-commutative 78.3%

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

   6. Simplified 78.3%

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

   if 2 < z < 2.9499999999999998e82

   1. Initial program 86.4%

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

      1. *-commutative 86.4%

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

   3. Simplified 86.4%

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

      1. clear-num 85.9%

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

      2. associate-/r/ 85.7%

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

      3. sub-neg 85.7%

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

      4. +-commutative 85.7%

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

      5. *-commutative 85.7%

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

      6. distribute-rgt-neg-in 85.7%

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

      7. fma-def 85.7%

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

   5. Applied egg-rr 85.7%

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

   6. Taylor expanded in x around 0 86.4%

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

      1. +-commutative 86.4%

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

      2. mul-1-neg 86.4%

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

      3. sub-neg 86.4%

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

      4. mul-1-neg 86.4%

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

      5. associate-/l* 99.8%

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

      6. mul-1-neg 99.8%

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

      7. sub-neg 99.8%

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

      8. associate-/l* 86.4%

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

      9. unsub-neg 86.4%

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

      10. *-commutative 86.4%

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

      11. *-commutative 86.4%

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

   8. Simplified 86.4%

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

   9. Taylor expanded in x around 0 65.7%

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

       1. mul-1-neg 65.7%

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

       2. *-commutative 65.7%

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

       3. associate-*l/ 79.1%

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

       4. distribute-rgt-neg-in 79.1%

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

   11. Simplified 79.1%

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

       1. frac-2neg 79.1%

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

       2. associate-*l/ 65.7%

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

       3. add-sqr-sqrt 0.0%

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

       4. sqrt-unprod 1.6%

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

       5. sqr-neg 1.6%

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

       6. sqrt-unprod 1.6%

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

       7. add-sqr-sqrt 1.6%

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

       8. distribute-lft-neg-in 1.6%

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

       9. distribute-rgt-neg-in 1.6%

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

       10. add-sqr-sqrt 0.0%

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

       11. sqrt-unprod 65.7%

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

       12. sqr-neg 65.7%

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

       13. sqrt-unprod 65.2%

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

       14. add-sqr-sqrt 65.7%

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

       15. sub-neg 65.7%

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

       16. distribute-neg-in 65.7%

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

       17. distribute-lft-neg-in 65.7%

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

       18. add-sqr-sqrt 0.0%

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

       19. sqrt-unprod 28.4%

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

       20. sqr-neg 28.4%

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

       21. sqrt-unprod 28.4%

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

       22. add-sqr-sqrt 28.4%

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

   13. Applied egg-rr 65.7%

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

       1. associate-/l* 79.1%

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

       2. associate-/r/ 79.1%

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

       3. +-commutative 79.1%

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

       4. unsub-neg 79.1%

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

   15. Simplified 79.1%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+21}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-53}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-70}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 2:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+82}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 4: 71.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{t} - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.49:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+82}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= z -3.3e+22)
     t_1
     (if (<= z -7.4e-53)
       (- (/ x t) (/ y (/ t z)))
       (if (<= z -1.35e-71)
         t_1
         (if (<= z 0.49)
           (/ x (- t (* z a)))
           (if (<= z 1.7e+82) (* z (/ y (- (* z a) t))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -3.3e+22) {
		tmp = t_1;
	} else if (z <= -7.4e-53) {
		tmp = (x / t) - (y / (t / z));
	} else if (z <= -1.35e-71) {
		tmp = t_1;
	} else if (z <= 0.49) {
		tmp = x / (t - (z * a));
	} else if (z <= 1.7e+82) {
		tmp = z * (y / ((z * a) - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - (x / z)) / a
    if (z <= (-3.3d+22)) then
        tmp = t_1
    else if (z <= (-7.4d-53)) then
        tmp = (x / t) - (y / (t / z))
    else if (z <= (-1.35d-71)) then
        tmp = t_1
    else if (z <= 0.49d0) then
        tmp = x / (t - (z * a))
    else if (z <= 1.7d+82) then
        tmp = z * (y / ((z * a) - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -3.3e+22) {
		tmp = t_1;
	} else if (z <= -7.4e-53) {
		tmp = (x / t) - (y / (t / z));
	} else if (z <= -1.35e-71) {
		tmp = t_1;
	} else if (z <= 0.49) {
		tmp = x / (t - (z * a));
	} else if (z <= 1.7e+82) {
		tmp = z * (y / ((z * a) - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if z <= -3.3e+22:
		tmp = t_1
	elif z <= -7.4e-53:
		tmp = (x / t) - (y / (t / z))
	elif z <= -1.35e-71:
		tmp = t_1
	elif z <= 0.49:
		tmp = x / (t - (z * a))
	elif z <= 1.7e+82:
		tmp = z * (y / ((z * a) - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -3.3e+22)
		tmp = t_1;
	elseif (z <= -7.4e-53)
		tmp = Float64(Float64(x / t) - Float64(y / Float64(t / z)));
	elseif (z <= -1.35e-71)
		tmp = t_1;
	elseif (z <= 0.49)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 1.7e+82)
		tmp = Float64(z * Float64(y / Float64(Float64(z * a) - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -3.3e+22)
		tmp = t_1;
	elseif (z <= -7.4e-53)
		tmp = (x / t) - (y / (t / z));
	elseif (z <= -1.35e-71)
		tmp = t_1;
	elseif (z <= 0.49)
		tmp = x / (t - (z * a));
	elseif (z <= 1.7e+82)
		tmp = z * (y / ((z * a) - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -3.3e+22], t$95$1, If[LessEqual[z, -7.4e-53], N[(N[(x / t), $MachinePrecision] - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.35e-71], t$95$1, If[LessEqual[z, 0.49], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+82], N[(z * N[(y / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.2999999999999998e22 or -7.39999999999999965e-53 < z < -1.3500000000000001e-71 or 1.69999999999999997e82 < z

   1. Initial program 66.2%

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

      1. *-commutative 66.2%

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

   3. Simplified 66.2%

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

      1. clear-num 66.2%

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

      2. associate-/r/ 66.1%

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

      3. sub-neg 66.1%

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

      4. +-commutative 66.1%

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

      5. *-commutative 66.1%

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

      6. distribute-rgt-neg-in 66.1%

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

      7. fma-def 66.1%

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

   5. Applied egg-rr 66.1%

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

   6. Taylor expanded in x around 0 65.3%

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

      1. +-commutative 65.3%

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

      2. mul-1-neg 65.3%

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

      3. sub-neg 65.3%

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

      4. mul-1-neg 65.3%

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

      5. associate-/l* 77.9%

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

      6. mul-1-neg 77.9%

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

      7. sub-neg 77.9%

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

      8. associate-/l* 65.3%

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

      9. unsub-neg 65.3%

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

      10. *-commutative 65.3%

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

      11. *-commutative 65.3%

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

   8. Simplified 65.3%

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

   9. Taylor expanded in t around 0 78.6%

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

       1. distribute-lft-out-- 78.6%

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

       2. *-commutative 78.6%

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

       3. associate-/r* 80.9%

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

       4. div-sub 81.8%

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

       5. sub-neg 81.8%

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

       6. mul-1-neg 81.8%

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

       7. +-commutative 81.8%

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

       8. associate-*r/ 81.8%

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

       9. distribute-lft-in 81.8%

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

       10. neg-mul-1 81.8%

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

       11. mul-1-neg 81.8%

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

       12. remove-double-neg 81.8%

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

       13. mul-1-neg 81.8%

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

       14. unsub-neg 81.8%

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

   11. Simplified 81.8%

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

   if -3.2999999999999998e22 < z < -7.39999999999999965e-53

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 69.7%

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

      1. div-sub 69.7%

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

      2. associate-/l* 69.7%

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

   6. Applied egg-rr 69.7%

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

   if -1.3500000000000001e-71 < z < 0.48999999999999999

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 78.3%

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

      1. *-commutative 78.3%

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

   6. Simplified 78.3%

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

   if 0.48999999999999999 < z < 1.69999999999999997e82

   1. Initial program 86.4%

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

      1. *-commutative 86.4%

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

   3. Simplified 86.4%

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

      1. clear-num 85.9%

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

      2. associate-/r/ 85.7%

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

      3. sub-neg 85.7%

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

      4. +-commutative 85.7%

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

      5. *-commutative 85.7%

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

      6. distribute-rgt-neg-in 85.7%

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

      7. fma-def 85.7%

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

   5. Applied egg-rr 85.7%

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

   6. Taylor expanded in x around 0 86.4%

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

      1. +-commutative 86.4%

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

      2. mul-1-neg 86.4%

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

      3. sub-neg 86.4%

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

      4. mul-1-neg 86.4%

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

      5. associate-/l* 99.8%

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

      6. mul-1-neg 99.8%

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

      7. sub-neg 99.8%

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

      8. associate-/l* 86.4%

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

      9. unsub-neg 86.4%

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

      10. *-commutative 86.4%

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

      11. *-commutative 86.4%

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

   8. Simplified 86.4%

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

   9. Taylor expanded in x around 0 65.7%

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

       1. mul-1-neg 65.7%

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

       2. *-commutative 65.7%

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

       3. associate-*l/ 79.1%

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

       4. distribute-rgt-neg-in 79.1%

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

   11. Simplified 79.1%

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

       1. frac-2neg 79.1%

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

       2. associate-*l/ 65.7%

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

       3. add-sqr-sqrt 0.0%

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

       4. sqrt-unprod 1.6%

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

       5. sqr-neg 1.6%

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

       6. sqrt-unprod 1.6%

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

       7. add-sqr-sqrt 1.6%

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

       8. distribute-lft-neg-in 1.6%

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

       9. distribute-rgt-neg-in 1.6%

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

       10. add-sqr-sqrt 0.0%

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

       11. sqrt-unprod 65.7%

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

       12. sqr-neg 65.7%

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

       13. sqrt-unprod 65.2%

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

       14. add-sqr-sqrt 65.7%

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

       15. sub-neg 65.7%

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

       16. distribute-neg-in 65.7%

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

       17. distribute-lft-neg-in 65.7%

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

       18. add-sqr-sqrt 0.0%

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

       19. sqrt-unprod 28.4%

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

       20. sqr-neg 28.4%

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

       21. sqrt-unprod 28.4%

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

       22. add-sqr-sqrt 28.4%

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

   13. Applied egg-rr 65.7%

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

       1. associate-/l* 79.1%

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

       2. associate-/r/ 79.1%

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

       3. +-commutative 79.1%

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

       4. unsub-neg 79.1%

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

   15. Simplified 79.1%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+22}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{t} - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-71}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 0.49:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+82}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 5: 71.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -5.9 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-53}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-75} \lor \neg \left(z \leq 350\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= z -5.9e+23)
     t_1
     (if (<= z -7.4e-53)
       (/ (- x (* z y)) t)
       (if (or (<= z -1.8e-75) (not (<= z 350.0))) t_1 (/ x (- t (* z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -5.9e+23) {
		tmp = t_1;
	} else if (z <= -7.4e-53) {
		tmp = (x - (z * y)) / t;
	} else if ((z <= -1.8e-75) || !(z <= 350.0)) {
		tmp = t_1;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - (x / z)) / a
    if (z <= (-5.9d+23)) then
        tmp = t_1
    else if (z <= (-7.4d-53)) then
        tmp = (x - (z * y)) / t
    else if ((z <= (-1.8d-75)) .or. (.not. (z <= 350.0d0))) then
        tmp = t_1
    else
        tmp = x / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -5.9e+23) {
		tmp = t_1;
	} else if (z <= -7.4e-53) {
		tmp = (x - (z * y)) / t;
	} else if ((z <= -1.8e-75) || !(z <= 350.0)) {
		tmp = t_1;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if z <= -5.9e+23:
		tmp = t_1
	elif z <= -7.4e-53:
		tmp = (x - (z * y)) / t
	elif (z <= -1.8e-75) or not (z <= 350.0):
		tmp = t_1
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -5.9e+23)
		tmp = t_1;
	elseif (z <= -7.4e-53)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	elseif ((z <= -1.8e-75) || !(z <= 350.0))
		tmp = t_1;
	else
		tmp = Float64(x / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -5.9e+23)
		tmp = t_1;
	elseif (z <= -7.4e-53)
		tmp = (x - (z * y)) / t;
	elseif ((z <= -1.8e-75) || ~((z <= 350.0)))
		tmp = t_1;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -5.9e+23], t$95$1, If[LessEqual[z, -7.4e-53], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[z, -1.8e-75], N[Not[LessEqual[z, 350.0]], $MachinePrecision]], t$95$1, N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.89999999999999987e23 or -7.39999999999999965e-53 < z < -1.8e-75 or 350 < z

   1. Initial program 68.3%

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

      1. *-commutative 68.3%

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

   3. Simplified 68.3%

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

      1. clear-num 68.2%

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

      2. associate-/r/ 68.1%

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

      3. sub-neg 68.1%

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

      4. +-commutative 68.1%

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

      5. *-commutative 68.1%

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

      6. distribute-rgt-neg-in 68.1%

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

      7. fma-def 68.1%

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

   5. Applied egg-rr 68.1%

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

   6. Taylor expanded in x around 0 67.4%

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

      1. +-commutative 67.4%

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

      2. mul-1-neg 67.4%

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

      3. sub-neg 67.4%

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

      4. mul-1-neg 67.4%

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

      5. associate-/l* 80.2%

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

      6. mul-1-neg 80.2%

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

      7. sub-neg 80.2%

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

      8. associate-/l* 67.4%

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

      9. unsub-neg 67.4%

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

      10. *-commutative 67.4%

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

      11. *-commutative 67.4%

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

   8. Simplified 67.4%

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

   9. Taylor expanded in t around 0 75.7%

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

       1. distribute-lft-out-- 75.7%

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

       2. *-commutative 75.7%

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

       3. associate-/r* 77.7%

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

       4. div-sub 78.5%

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

       5. sub-neg 78.5%

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

       6. mul-1-neg 78.5%

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

       7. +-commutative 78.5%

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

       8. associate-*r/ 78.5%

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

       9. distribute-lft-in 78.5%

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

       10. neg-mul-1 78.5%

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

       11. mul-1-neg 78.5%

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

       12. remove-double-neg 78.5%

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

       13. mul-1-neg 78.5%

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

       14. unsub-neg 78.5%

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

   11. Simplified 78.5%

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

   if -5.89999999999999987e23 < z < -7.39999999999999965e-53

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 69.7%

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

   if -1.8e-75 < z < 350

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 77.7%

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

      1. *-commutative 77.7%

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

   6. Simplified 77.7%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+23}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-53}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-75} \lor \neg \left(z \leq 350\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]

Alternative 6: 88.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.6 \cdot 10^{+92}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z 1.6e+92) (/ (- 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 <= 1.6e+92) {
		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 <= 1.6d+92) 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 <= 1.6e+92) {
		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 <= 1.6e+92:
		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 <= 1.6e+92)
		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 <= 1.6e+92)
		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, 1.6e+92], 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 2 regimes

2. if z < 1.60000000000000013e92

   1. Initial program 93.9%

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

   if 1.60000000000000013e92 < z

   1. Initial program 53.2%

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

      1. *-commutative 53.2%

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

   3. Simplified 53.2%

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

      1. clear-num 53.2%

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

      2. associate-/r/ 53.1%

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

      3. sub-neg 53.1%

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

      4. +-commutative 53.1%

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

      5. *-commutative 53.1%

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

      6. distribute-rgt-neg-in 53.1%

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

      7. fma-def 53.1%

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

   5. Applied egg-rr 53.1%

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

   6. Taylor expanded in x around 0 51.4%

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

      1. +-commutative 51.4%

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

      2. mul-1-neg 51.4%

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

      3. sub-neg 51.4%

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

      4. mul-1-neg 51.4%

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

      5. associate-/l* 70.3%

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

      6. mul-1-neg 70.3%

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

      7. sub-neg 70.3%

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

      8. associate-/l* 51.4%

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

      9. unsub-neg 51.4%

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

      10. *-commutative 51.4%

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

      11. *-commutative 51.4%

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

   8. Simplified 51.4%

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

   9. Taylor expanded in t around 0 84.5%

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

       1. distribute-lft-out-- 84.5%

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

       2. *-commutative 84.5%

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

       3. associate-/r* 85.5%

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

       4. div-sub 87.3%

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

       5. sub-neg 87.3%

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

       6. mul-1-neg 87.3%

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

       7. +-commutative 87.3%

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

       8. associate-*r/ 87.3%

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

       9. distribute-lft-in 87.3%

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

       10. neg-mul-1 87.3%

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

       11. mul-1-neg 87.3%

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

       12. remove-double-neg 87.3%

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

       13. mul-1-neg 87.3%

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

       14. unsub-neg 87.3%

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

   11. Simplified 87.3%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.6 \cdot 10^{+92}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 7: 54.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+23}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-51}:\\ \;\;\;\;\frac{-z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-86}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 195:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.8e+23)
   (/ y a)
   (if (<= z -1.75e-51)
     (/ (- z) (/ t y))
     (if (<= z -3.2e-86)
       (/ (- x) (* z a))
       (if (<= z 195.0) (/ x t) (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+23) {
		tmp = y / a;
	} else if (z <= -1.75e-51) {
		tmp = -z / (t / y);
	} else if (z <= -3.2e-86) {
		tmp = -x / (z * a);
	} else if (z <= 195.0) {
		tmp = x / 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 <= (-4.8d+23)) then
        tmp = y / a
    else if (z <= (-1.75d-51)) then
        tmp = -z / (t / y)
    else if (z <= (-3.2d-86)) then
        tmp = -x / (z * a)
    else if (z <= 195.0d0) then
        tmp = x / 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 <= -4.8e+23) {
		tmp = y / a;
	} else if (z <= -1.75e-51) {
		tmp = -z / (t / y);
	} else if (z <= -3.2e-86) {
		tmp = -x / (z * a);
	} else if (z <= 195.0) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.8e+23:
		tmp = y / a
	elif z <= -1.75e-51:
		tmp = -z / (t / y)
	elif z <= -3.2e-86:
		tmp = -x / (z * a)
	elif z <= 195.0:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.8e+23)
		tmp = Float64(y / a);
	elseif (z <= -1.75e-51)
		tmp = Float64(Float64(-z) / Float64(t / y));
	elseif (z <= -3.2e-86)
		tmp = Float64(Float64(-x) / Float64(z * a));
	elseif (z <= 195.0)
		tmp = Float64(x / 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 <= -4.8e+23)
		tmp = y / a;
	elseif (z <= -1.75e-51)
		tmp = -z / (t / y);
	elseif (z <= -3.2e-86)
		tmp = -x / (z * a);
	elseif (z <= 195.0)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.8e+23], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.75e-51], N[((-z) / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.2e-86], N[((-x) / N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 195.0], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.8e23 or 195 < z

   1. Initial program 67.2%

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

      1. *-commutative 67.2%

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

   3. Simplified 67.2%

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

   4. Taylor expanded in z around inf 64.7%

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

   if -4.8e23 < z < -1.7499999999999999e-51

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 67.8%

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

   5. Taylor expanded in x around 0 56.0%

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

      1. mul-1-neg 56.0%

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

      2. associate-/l* 56.0%

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

      3. associate-/r/ 55.9%

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

      4. distribute-rgt-neg-in 55.9%

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

   7. Simplified 55.9%

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

      1. distribute-rgt-neg-out 55.9%

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

      2. associate-/r/ 56.0%

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

      3. associate-/r/ 55.9%

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

      4. clear-num 55.8%

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

      5. associate-*l/ 56.0%

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

      6. *-un-lft-identity 56.0%

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

   9. Applied egg-rr 56.0%

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

   if -1.7499999999999999e-51 < z < -3.20000000000000006e-86

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around 0 83.7%

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

      1. associate-*r/ 83.7%

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

      2. neg-mul-1 83.7%

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

      3. neg-sub0 83.7%

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

      4. sub-neg 83.7%

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

      5. distribute-rgt-neg-out 83.7%

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

      6. +-commutative 83.7%

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

      7. associate--r+ 83.7%

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

      8. neg-sub0 83.7%

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

      9. distribute-rgt-neg-out 83.7%

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

      10. remove-double-neg 83.7%

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

      11. *-commutative 83.7%

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

   6. Simplified 83.7%

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

   7. Taylor expanded in y around 0 51.5%

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

      1. neg-mul-1 51.5%

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

      2. distribute-neg-frac 51.5%

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

      3. *-commutative 51.5%

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

   9. Simplified 51.5%

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

   if -3.20000000000000006e-86 < z < 195

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 59.4%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+23}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-51}:\\ \;\;\;\;\frac{-z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-86}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 195:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 8: 54.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+21}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-50}:\\ \;\;\;\;\frac{-y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-84}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 122:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6e+21)
   (/ y a)
   (if (<= z -7e-50)
     (/ (- y) (/ t z))
     (if (<= z -1.25e-84)
       (/ (- x) (* z a))
       (if (<= z 122.0) (/ x t) (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6e+21) {
		tmp = y / a;
	} else if (z <= -7e-50) {
		tmp = -y / (t / z);
	} else if (z <= -1.25e-84) {
		tmp = -x / (z * a);
	} else if (z <= 122.0) {
		tmp = x / 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 <= (-6d+21)) then
        tmp = y / a
    else if (z <= (-7d-50)) then
        tmp = -y / (t / z)
    else if (z <= (-1.25d-84)) then
        tmp = -x / (z * a)
    else if (z <= 122.0d0) then
        tmp = x / 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 <= -6e+21) {
		tmp = y / a;
	} else if (z <= -7e-50) {
		tmp = -y / (t / z);
	} else if (z <= -1.25e-84) {
		tmp = -x / (z * a);
	} else if (z <= 122.0) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6e+21:
		tmp = y / a
	elif z <= -7e-50:
		tmp = -y / (t / z)
	elif z <= -1.25e-84:
		tmp = -x / (z * a)
	elif z <= 122.0:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6e+21)
		tmp = Float64(y / a);
	elseif (z <= -7e-50)
		tmp = Float64(Float64(-y) / Float64(t / z));
	elseif (z <= -1.25e-84)
		tmp = Float64(Float64(-x) / Float64(z * a));
	elseif (z <= 122.0)
		tmp = Float64(x / 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 <= -6e+21)
		tmp = y / a;
	elseif (z <= -7e-50)
		tmp = -y / (t / z);
	elseif (z <= -1.25e-84)
		tmp = -x / (z * a);
	elseif (z <= 122.0)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6e+21], N[(y / a), $MachinePrecision], If[LessEqual[z, -7e-50], N[((-y) / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.25e-84], N[((-x) / N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 122.0], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6e21 or 122 < z

   1. Initial program 67.2%

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

      1. *-commutative 67.2%

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

   3. Simplified 67.2%

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

   4. Taylor expanded in z around inf 64.7%

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

   if -6e21 < z < -6.99999999999999993e-50

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 67.8%

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

   5. Taylor expanded in x around 0 56.0%

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

      1. mul-1-neg 56.0%

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

      2. associate-/l* 56.0%

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

      3. associate-/r/ 55.9%

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

      4. distribute-rgt-neg-in 55.9%

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

   7. Simplified 55.9%

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

      1. distribute-rgt-neg-out 55.9%

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

      2. associate-/r/ 56.0%

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

      3. distribute-neg-frac 56.0%

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

   9. Applied egg-rr 56.0%

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

   if -6.99999999999999993e-50 < z < -1.25e-84

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around 0 83.7%

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

      1. associate-*r/ 83.7%

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

      2. neg-mul-1 83.7%

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

      3. neg-sub0 83.7%

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

      4. sub-neg 83.7%

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

      5. distribute-rgt-neg-out 83.7%

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

      6. +-commutative 83.7%

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

      7. associate--r+ 83.7%

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

      8. neg-sub0 83.7%

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

      9. distribute-rgt-neg-out 83.7%

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

      10. remove-double-neg 83.7%

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

      11. *-commutative 83.7%

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

   6. Simplified 83.7%

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

   7. Taylor expanded in y around 0 51.5%

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

      1. neg-mul-1 51.5%

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

      2. distribute-neg-frac 51.5%

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

      3. *-commutative 51.5%

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

   9. Simplified 51.5%

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

   if -1.25e-84 < z < 122

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 59.4%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+21}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-50}:\\ \;\;\;\;\frac{-y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-84}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 122:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 9: 65.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+109} \lor \neg \left(z \leq 620\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.5e+109) (not (<= z 620.0))) (/ y a) (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.5e+109) || !(z <= 620.0)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-6.5d+109)) .or. (.not. (z <= 620.0d0))) then
        tmp = y / a
    else
        tmp = x / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.5e+109) || !(z <= 620.0)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.5e+109) or not (z <= 620.0):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.5e+109) || !(z <= 620.0))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.5e+109) || ~((z <= 620.0)))
		tmp = y / a;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.5e+109], N[Not[LessEqual[z, 620.0]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5e109 or 620 < z

   1. Initial program 65.2%

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

      1. *-commutative 65.2%

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

   3. Simplified 65.2%

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

   4. Taylor expanded in z around inf 68.2%

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

   if -6.5e109 < z < 620

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 73.6%

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

      1. *-commutative 73.6%

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

   6. Simplified 73.6%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+109} \lor \neg \left(z \leq 620\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]

Alternative 10: 53.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+109} \lor \neg \left(z \leq 51\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.2e+109) (not (<= z 51.0))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.2e+109) || !(z <= 51.0)) {
		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 <= (-5.2d+109)) .or. (.not. (z <= 51.0d0))) 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 <= -5.2e+109) || !(z <= 51.0)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.2e+109) or not (z <= 51.0):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.2e+109) || !(z <= 51.0))
		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 <= -5.2e+109) || ~((z <= 51.0)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.2e+109], N[Not[LessEqual[z, 51.0]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.1999999999999997e109 or 51 < z

   1. Initial program 65.2%

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

      1. *-commutative 65.2%

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

   3. Simplified 65.2%

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

   4. Taylor expanded in z around inf 68.2%

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

   if -5.1999999999999997e109 < z < 51

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 53.0%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+109} \lor \neg \left(z \leq 51\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]

Alternative 11: 36.4% 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 84.8%

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

   1. *-commutative 84.8%

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

3. Simplified 84.8%

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

4. Taylor expanded in z around 0 35.6%

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

5. Final simplification 35.6%

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

Developer target: 97.6% 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 2023306 
(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))))