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

Percentage Accurate: 84.5% → 91.1%

Time: 9.6s

Alternatives: 12

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.5% 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: 91.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+142} \lor \neg \left(z \leq 2.3 \cdot 10^{+144}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{\mathsf{fma}\left(-z, a, t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.8e+142) (not (<= z 2.3e+144)))
   (/ (- y (/ x z)) a)
   (/ (- x (* z y)) (fma (- z) a t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.8e+142) || !(z <= 2.3e+144)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (z * y)) / fma(-z, a, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.8e+142) || !(z <= 2.3e+144))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x - Float64(z * y)) / fma(Float64(-z), a, t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.8e+142], N[Not[LessEqual[z, 2.3e+144]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[((-z) * a + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8e142 or 2.3000000000000001e144 < z

   1. Initial program 47.0%

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

      1. *-commutative 47.0%

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

   3. Simplified 47.0%

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

      1. sub-neg 47.0%

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

      2. +-commutative 47.0%

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

      3. distribute-lft-neg-in 47.0%

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

      4. fma-def 47.0%

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

   5. Applied egg-rr 47.0%

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

   6. Taylor expanded in x around 0 44.9%

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

      1. mul-1-neg 44.9%

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

      2. unsub-neg 44.9%

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

      3. mul-1-neg 44.9%

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

      4. sub-neg 44.9%

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

      5. *-commutative 44.9%

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

      6. associate-/l* 59.7%

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

      7. associate-/r/ 51.5%

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

      8. mul-1-neg 51.5%

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

      9. sub-neg 51.5%

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

      10. *-commutative 51.5%

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

   8. Simplified 51.5%

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

   9. Taylor expanded in t around 0 79.1%

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

       1. distribute-lft-out-- 79.1%

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

       2. *-commutative 79.1%

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

       3. associate-/r* 84.4%

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

       4. div-sub 86.5%

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

       5. mul-1-neg 86.5%

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

   11. Simplified 86.5%

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

   if -2.8e142 < z < 2.3000000000000001e144

   1. Initial program 95.3%

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

      1. *-commutative 95.3%

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

   3. Simplified 95.3%

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

      1. sub-neg 95.3%

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

      2. +-commutative 95.3%

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

      3. distribute-lft-neg-in 95.3%

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

      4. fma-def 95.3%

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

   5. Applied egg-rr 95.3%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+142} \lor \neg \left(z \leq 2.3 \cdot 10^{+144}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{\mathsf{fma}\left(-z, a, t\right)}\\ \end{array} \]

Alternative 2: 64.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{+142}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+85}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{a}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+68}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+51}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+20} \lor \neg \left(z \leq -55\right) \land z \leq 1.3 \cdot 10^{+73}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.08e+142)
   (/ y a)
   (if (<= z -8.5e+85)
     (* (/ x z) (/ -1.0 a))
     (if (<= z -1.1e+68)
       (/ y a)
       (if (<= z -5.8e+51)
         (/ (* z (- y)) t)
         (if (or (<= z -3.3e+20) (and (not (<= z -55.0)) (<= z 1.3e+73)))
           (/ x (- t (* z a)))
           (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.08e+142) {
		tmp = y / a;
	} else if (z <= -8.5e+85) {
		tmp = (x / z) * (-1.0 / a);
	} else if (z <= -1.1e+68) {
		tmp = y / a;
	} else if (z <= -5.8e+51) {
		tmp = (z * -y) / t;
	} else if ((z <= -3.3e+20) || (!(z <= -55.0) && (z <= 1.3e+73))) {
		tmp = x / (t - (z * a));
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.08d+142)) then
        tmp = y / a
    else if (z <= (-8.5d+85)) then
        tmp = (x / z) * ((-1.0d0) / a)
    else if (z <= (-1.1d+68)) then
        tmp = y / a
    else if (z <= (-5.8d+51)) then
        tmp = (z * -y) / t
    else if ((z <= (-3.3d+20)) .or. (.not. (z <= (-55.0d0))) .and. (z <= 1.3d+73)) then
        tmp = x / (t - (z * a))
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.08e+142) {
		tmp = y / a;
	} else if (z <= -8.5e+85) {
		tmp = (x / z) * (-1.0 / a);
	} else if (z <= -1.1e+68) {
		tmp = y / a;
	} else if (z <= -5.8e+51) {
		tmp = (z * -y) / t;
	} else if ((z <= -3.3e+20) || (!(z <= -55.0) && (z <= 1.3e+73))) {
		tmp = x / (t - (z * a));
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.08e+142:
		tmp = y / a
	elif z <= -8.5e+85:
		tmp = (x / z) * (-1.0 / a)
	elif z <= -1.1e+68:
		tmp = y / a
	elif z <= -5.8e+51:
		tmp = (z * -y) / t
	elif (z <= -3.3e+20) or (not (z <= -55.0) and (z <= 1.3e+73)):
		tmp = x / (t - (z * a))
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.08e+142)
		tmp = Float64(y / a);
	elseif (z <= -8.5e+85)
		tmp = Float64(Float64(x / z) * Float64(-1.0 / a));
	elseif (z <= -1.1e+68)
		tmp = Float64(y / a);
	elseif (z <= -5.8e+51)
		tmp = Float64(Float64(z * Float64(-y)) / t);
	elseif ((z <= -3.3e+20) || (!(z <= -55.0) && (z <= 1.3e+73)))
		tmp = Float64(x / Float64(t - Float64(z * a)));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.08e+142)
		tmp = y / a;
	elseif (z <= -8.5e+85)
		tmp = (x / z) * (-1.0 / a);
	elseif (z <= -1.1e+68)
		tmp = y / a;
	elseif (z <= -5.8e+51)
		tmp = (z * -y) / t;
	elseif ((z <= -3.3e+20) || (~((z <= -55.0)) && (z <= 1.3e+73)))
		tmp = x / (t - (z * a));
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.08e+142], N[(y / a), $MachinePrecision], If[LessEqual[z, -8.5e+85], N[(N[(x / z), $MachinePrecision] * N[(-1.0 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.1e+68], N[(y / a), $MachinePrecision], If[LessEqual[z, -5.8e+51], N[(N[(z * (-y)), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[z, -3.3e+20], And[N[Not[LessEqual[z, -55.0]], $MachinePrecision], LessEqual[z, 1.3e+73]]], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.08e142 or -8.4999999999999994e85 < z < -1.09999999999999994e68 or -3.3e20 < z < -55 or 1.3e73 < z

   1. Initial program 61.1%

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

      1. *-commutative 61.1%

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

   3. Simplified 61.1%

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

   4. Taylor expanded in z around inf 70.5%

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

   if -1.08e142 < z < -8.4999999999999994e85

   1. Initial program 89.1%

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

      1. *-commutative 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in t around 0 67.1%

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

      1. associate-*r/ 67.1%

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

      2. neg-mul-1 67.1%

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

      3. neg-sub0 67.1%

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

      4. sub-neg 67.1%

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

      5. distribute-rgt-neg-out 67.1%

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

      6. +-commutative 67.1%

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

      7. associate--r+ 67.1%

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

      8. neg-sub0 67.1%

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

      9. distribute-rgt-neg-out 67.1%

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

      10. remove-double-neg 67.1%

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

      11. *-commutative 67.1%

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

   6. Simplified 67.1%

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

   7. Taylor expanded in y around 0 68.0%

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

      1. neg-mul-1 68.0%

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

   9. Simplified 68.0%

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

       1. neg-mul-1 68.0%

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

       2. *-commutative 68.0%

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

       3. times-frac 78.0%

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

   11. Applied egg-rr 78.0%

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

   if -1.09999999999999994e68 < z < -5.7999999999999997e51

   1. Initial program 76.0%

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

      1. *-commutative 76.0%

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

   3. Simplified 76.0%

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

   4. Taylor expanded in t around inf 63.6%

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

   5. Taylor expanded in x around 0 63.7%

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

      1. mul-1-neg 63.7%

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

      2. distribute-rgt-neg-out 63.7%

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

   7. Simplified 63.7%

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

   if -5.7999999999999997e51 < z < -3.3e20 or -55 < z < 1.3e73

   1. Initial program 98.1%

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

      1. *-commutative 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in x around inf 77.3%

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

      1. *-commutative 77.3%

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

   6. Simplified 77.3%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{+142}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+85}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{a}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+68}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+51}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+20} \lor \neg \left(z \leq -55\right) \land z \leq 1.3 \cdot 10^{+73}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 3: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-5}:\\ \;\;\;\;z \cdot \frac{-y}{t_1}\\ \mathbf{elif}\;z \leq 10^{+51}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+144}:\\ \;\;\;\;\frac{y}{\frac{t_1}{-z}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* z a))) (t_2 (/ (- y (/ x z)) a)))
   (if (<= z -1.5e+68)
     t_2
     (if (<= z -9.8e-5)
       (* z (/ (- y) t_1))
       (if (<= z 1e+51)
         (/ x t_1)
         (if (<= z 2.35e+144) (/ y (/ t_1 (- z))) t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.5e+68) {
		tmp = t_2;
	} else if (z <= -9.8e-5) {
		tmp = z * (-y / t_1);
	} else if (z <= 1e+51) {
		tmp = x / t_1;
	} else if (z <= 2.35e+144) {
		tmp = y / (t_1 / -z);
	} 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 - (z * a)
    t_2 = (y - (x / z)) / a
    if (z <= (-1.5d+68)) then
        tmp = t_2
    else if (z <= (-9.8d-5)) then
        tmp = z * (-y / t_1)
    else if (z <= 1d+51) then
        tmp = x / t_1
    else if (z <= 2.35d+144) then
        tmp = y / (t_1 / -z)
    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 - (z * a);
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.5e+68) {
		tmp = t_2;
	} else if (z <= -9.8e-5) {
		tmp = z * (-y / t_1);
	} else if (z <= 1e+51) {
		tmp = x / t_1;
	} else if (z <= 2.35e+144) {
		tmp = y / (t_1 / -z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (z * a)
	t_2 = (y - (x / z)) / a
	tmp = 0
	if z <= -1.5e+68:
		tmp = t_2
	elif z <= -9.8e-5:
		tmp = z * (-y / t_1)
	elif z <= 1e+51:
		tmp = x / t_1
	elif z <= 2.35e+144:
		tmp = y / (t_1 / -z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(z * a))
	t_2 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -1.5e+68)
		tmp = t_2;
	elseif (z <= -9.8e-5)
		tmp = Float64(z * Float64(Float64(-y) / t_1));
	elseif (z <= 1e+51)
		tmp = Float64(x / t_1);
	elseif (z <= 2.35e+144)
		tmp = Float64(y / Float64(t_1 / Float64(-z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (z * a);
	t_2 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -1.5e+68)
		tmp = t_2;
	elseif (z <= -9.8e-5)
		tmp = z * (-y / t_1);
	elseif (z <= 1e+51)
		tmp = x / t_1;
	elseif (z <= 2.35e+144)
		tmp = y / (t_1 / -z);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -1.5e+68], t$95$2, If[LessEqual[z, -9.8e-5], N[(z * N[((-y) / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+51], N[(x / t$95$1), $MachinePrecision], If[LessEqual[z, 2.35e+144], N[(y / N[(t$95$1 / (-z)), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.5000000000000001e68 or 2.3500000000000001e144 < z

   1. Initial program 53.7%

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

      1. *-commutative 53.7%

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

   3. Simplified 53.7%

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

      1. sub-neg 53.7%

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

      2. +-commutative 53.7%

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

      3. distribute-lft-neg-in 53.7%

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

      4. fma-def 53.8%

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

   5. Applied egg-rr 53.8%

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

   6. Taylor expanded in x around 0 52.0%

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

      1. mul-1-neg 52.0%

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

      2. unsub-neg 52.0%

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

      3. mul-1-neg 52.0%

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

      4. sub-neg 52.0%

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

      5. *-commutative 52.0%

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

      6. associate-/l* 63.9%

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

      7. associate-/r/ 55.7%

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

      8. mul-1-neg 55.7%

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

      9. sub-neg 55.7%

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

      10. *-commutative 55.7%

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

   8. Simplified 55.7%

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

   9. Taylor expanded in t around 0 77.9%

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

       1. distribute-lft-out-- 77.9%

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

       2. *-commutative 77.9%

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

       3. associate-/r* 83.8%

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

       4. div-sub 85.6%

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

       5. mul-1-neg 85.6%

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

   11. Simplified 85.6%

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

   if -1.5000000000000001e68 < z < -9.8e-5

   1. Initial program 81.6%

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

      1. *-commutative 81.6%

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

   3. Simplified 81.6%

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

      1. sub-neg 81.6%

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

      2. +-commutative 81.6%

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

      3. distribute-lft-neg-in 81.6%

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

      4. fma-def 81.6%

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

   5. Applied egg-rr 81.6%

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

   6. Taylor expanded in x around 0 81.6%

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

      1. mul-1-neg 81.6%

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

      2. unsub-neg 81.6%

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

      3. mul-1-neg 81.6%

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

      4. sub-neg 81.6%

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

      5. *-commutative 81.6%

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

      6. associate-/l* 95.1%

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

      7. associate-/r/ 95.3%

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

      8. mul-1-neg 95.3%

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

      9. sub-neg 95.3%

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

      10. *-commutative 95.3%

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

   8. Simplified 95.3%

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

   9. Taylor expanded in x around 0 66.8%

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

       1. mul-1-neg 66.8%

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

       2. *-commutative 66.8%

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

       3. *-commutative 66.8%

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

       4. associate-*r/ 80.4%

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

       5. distribute-rgt-neg-in 80.4%

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

       6. distribute-neg-frac 80.4%

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

   11. Simplified 80.4%

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

   if -9.8e-5 < z < 1e51

   1. Initial program 99.2%

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

      1. *-commutative 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in x around inf 79.3%

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

      1. *-commutative 79.3%

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

   6. Simplified 79.3%

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

   if 1e51 < z < 2.3500000000000001e144

   1. Initial program 87.2%

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

      1. *-commutative 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in x around 0 69.3%

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

      1. associate-*r/ 69.3%

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

      2. *-commutative 69.3%

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

      3. mul-1-neg 69.3%

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

      4. distribute-rgt-neg-out 69.3%

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

      5. associate-/l* 77.5%

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

   6. Simplified 77.5%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+68}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-5}:\\ \;\;\;\;z \cdot \frac{-y}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 10^{+51}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+144}:\\ \;\;\;\;\frac{y}{\frac{t - z \cdot a}{-z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 4: 54.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{-1}{a}\\ \mathbf{if}\;z \leq -1.08 \cdot 10^{+142}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{+68}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.48 \cdot 10^{+51}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.075:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ x z) (/ -1.0 a))))
   (if (<= z -1.08e+142)
     (/ y a)
     (if (<= z -8.6e+85)
       t_1
       (if (<= z -1.02e+68)
         (/ y a)
         (if (<= z -1.48e+51)
           (/ (* z (- y)) t)
           (if (<= z -3.7e+20)
             t_1
             (if (<= z -0.075)
               (/ y a)
               (if (<= z 8.6e+22) (/ x t) (/ y a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / z) * (-1.0 / a);
	double tmp;
	if (z <= -1.08e+142) {
		tmp = y / a;
	} else if (z <= -8.6e+85) {
		tmp = t_1;
	} else if (z <= -1.02e+68) {
		tmp = y / a;
	} else if (z <= -1.48e+51) {
		tmp = (z * -y) / t;
	} else if (z <= -3.7e+20) {
		tmp = t_1;
	} else if (z <= -0.075) {
		tmp = y / a;
	} else if (z <= 8.6e+22) {
		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) :: t_1
    real(8) :: tmp
    t_1 = (x / z) * ((-1.0d0) / a)
    if (z <= (-1.08d+142)) then
        tmp = y / a
    else if (z <= (-8.6d+85)) then
        tmp = t_1
    else if (z <= (-1.02d+68)) then
        tmp = y / a
    else if (z <= (-1.48d+51)) then
        tmp = (z * -y) / t
    else if (z <= (-3.7d+20)) then
        tmp = t_1
    else if (z <= (-0.075d0)) then
        tmp = y / a
    else if (z <= 8.6d+22) 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 t_1 = (x / z) * (-1.0 / a);
	double tmp;
	if (z <= -1.08e+142) {
		tmp = y / a;
	} else if (z <= -8.6e+85) {
		tmp = t_1;
	} else if (z <= -1.02e+68) {
		tmp = y / a;
	} else if (z <= -1.48e+51) {
		tmp = (z * -y) / t;
	} else if (z <= -3.7e+20) {
		tmp = t_1;
	} else if (z <= -0.075) {
		tmp = y / a;
	} else if (z <= 8.6e+22) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x / z) * (-1.0 / a)
	tmp = 0
	if z <= -1.08e+142:
		tmp = y / a
	elif z <= -8.6e+85:
		tmp = t_1
	elif z <= -1.02e+68:
		tmp = y / a
	elif z <= -1.48e+51:
		tmp = (z * -y) / t
	elif z <= -3.7e+20:
		tmp = t_1
	elif z <= -0.075:
		tmp = y / a
	elif z <= 8.6e+22:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x / z) * Float64(-1.0 / a))
	tmp = 0.0
	if (z <= -1.08e+142)
		tmp = Float64(y / a);
	elseif (z <= -8.6e+85)
		tmp = t_1;
	elseif (z <= -1.02e+68)
		tmp = Float64(y / a);
	elseif (z <= -1.48e+51)
		tmp = Float64(Float64(z * Float64(-y)) / t);
	elseif (z <= -3.7e+20)
		tmp = t_1;
	elseif (z <= -0.075)
		tmp = Float64(y / a);
	elseif (z <= 8.6e+22)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x / z) * (-1.0 / a);
	tmp = 0.0;
	if (z <= -1.08e+142)
		tmp = y / a;
	elseif (z <= -8.6e+85)
		tmp = t_1;
	elseif (z <= -1.02e+68)
		tmp = y / a;
	elseif (z <= -1.48e+51)
		tmp = (z * -y) / t;
	elseif (z <= -3.7e+20)
		tmp = t_1;
	elseif (z <= -0.075)
		tmp = y / a;
	elseif (z <= 8.6e+22)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.08e+142], N[(y / a), $MachinePrecision], If[LessEqual[z, -8.6e+85], t$95$1, If[LessEqual[z, -1.02e+68], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.48e+51], N[(N[(z * (-y)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, -3.7e+20], t$95$1, If[LessEqual[z, -0.075], N[(y / a), $MachinePrecision], If[LessEqual[z, 8.6e+22], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.08e142 or -8.5999999999999998e85 < z < -1.02e68 or -3.7e20 < z < -0.0749999999999999972 or 8.6000000000000004e22 < z

   1. Initial program 64.6%

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

      1. *-commutative 64.6%

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

   3. Simplified 64.6%

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

   4. Taylor expanded in z around inf 65.9%

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

   if -1.08e142 < z < -8.5999999999999998e85 or -1.48e51 < z < -3.7e20

   1. Initial program 80.7%

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

      1. *-commutative 80.7%

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

   3. Simplified 80.7%

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

   4. Taylor expanded in t around 0 58.7%

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

      1. associate-*r/ 58.7%

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

      2. neg-mul-1 58.7%

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

      3. neg-sub0 58.7%

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

      4. sub-neg 58.7%

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

      5. distribute-rgt-neg-out 58.7%

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

      6. +-commutative 58.7%

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

      7. associate--r+ 58.7%

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

      8. neg-sub0 58.7%

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

      9. distribute-rgt-neg-out 58.7%

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

      10. remove-double-neg 58.7%

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

      11. *-commutative 58.7%

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

   6. Simplified 58.7%

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

   7. Taylor expanded in y around 0 61.2%

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

      1. neg-mul-1 61.2%

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

   9. Simplified 61.2%

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

       1. neg-mul-1 61.2%

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

       2. *-commutative 61.2%

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

       3. times-frac 73.4%

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

   11. Applied egg-rr 73.4%

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

   if -1.02e68 < z < -1.48e51

   1. Initial program 76.0%

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

      1. *-commutative 76.0%

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

   3. Simplified 76.0%

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

   4. Taylor expanded in t around inf 63.6%

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

   5. Taylor expanded in x around 0 63.7%

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

      1. mul-1-neg 63.7%

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

      2. distribute-rgt-neg-out 63.7%

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

   7. Simplified 63.7%

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

   if -0.0749999999999999972 < z < 8.6000000000000004e22

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 57.8%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{+142}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{+85}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{a}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{+68}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.48 \cdot 10^{+51}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{a}\\ \mathbf{elif}\;z \leq -0.075:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 5: 54.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+142}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+84}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+68}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{+51}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;z \leq -7.2:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.75e+142)
   (/ y a)
   (if (<= z -1.7e+84)
     (/ (- x) (* z a))
     (if (<= z -1.6e+68)
       (/ y a)
       (if (<= z -3.9e+51)
         (/ (* z (- y)) t)
         (if (<= z -7.2) (/ y a) (if (<= z 7.5e+22) (/ x t) (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.75e+142) {
		tmp = y / a;
	} else if (z <= -1.7e+84) {
		tmp = -x / (z * a);
	} else if (z <= -1.6e+68) {
		tmp = y / a;
	} else if (z <= -3.9e+51) {
		tmp = (z * -y) / t;
	} else if (z <= -7.2) {
		tmp = y / a;
	} else if (z <= 7.5e+22) {
		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 <= (-1.75d+142)) then
        tmp = y / a
    else if (z <= (-1.7d+84)) then
        tmp = -x / (z * a)
    else if (z <= (-1.6d+68)) then
        tmp = y / a
    else if (z <= (-3.9d+51)) then
        tmp = (z * -y) / t
    else if (z <= (-7.2d0)) then
        tmp = y / a
    else if (z <= 7.5d+22) 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 <= -1.75e+142) {
		tmp = y / a;
	} else if (z <= -1.7e+84) {
		tmp = -x / (z * a);
	} else if (z <= -1.6e+68) {
		tmp = y / a;
	} else if (z <= -3.9e+51) {
		tmp = (z * -y) / t;
	} else if (z <= -7.2) {
		tmp = y / a;
	} else if (z <= 7.5e+22) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.75e+142:
		tmp = y / a
	elif z <= -1.7e+84:
		tmp = -x / (z * a)
	elif z <= -1.6e+68:
		tmp = y / a
	elif z <= -3.9e+51:
		tmp = (z * -y) / t
	elif z <= -7.2:
		tmp = y / a
	elif z <= 7.5e+22:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.75e+142)
		tmp = Float64(y / a);
	elseif (z <= -1.7e+84)
		tmp = Float64(Float64(-x) / Float64(z * a));
	elseif (z <= -1.6e+68)
		tmp = Float64(y / a);
	elseif (z <= -3.9e+51)
		tmp = Float64(Float64(z * Float64(-y)) / t);
	elseif (z <= -7.2)
		tmp = Float64(y / a);
	elseif (z <= 7.5e+22)
		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 <= -1.75e+142)
		tmp = y / a;
	elseif (z <= -1.7e+84)
		tmp = -x / (z * a);
	elseif (z <= -1.6e+68)
		tmp = y / a;
	elseif (z <= -3.9e+51)
		tmp = (z * -y) / t;
	elseif (z <= -7.2)
		tmp = y / a;
	elseif (z <= 7.5e+22)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.75e+142], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.7e+84], N[((-x) / N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.6e+68], N[(y / a), $MachinePrecision], If[LessEqual[z, -3.9e+51], N[(N[(z * (-y)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, -7.2], N[(y / a), $MachinePrecision], If[LessEqual[z, 7.5e+22], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.74999999999999999e142 or -1.6999999999999999e84 < z < -1.59999999999999997e68 or -3.89999999999999984e51 < z < -7.20000000000000018 or 7.5000000000000002e22 < z

   1. Initial program 64.8%

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

      1. *-commutative 64.8%

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

   3. Simplified 64.8%

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

   4. Taylor expanded in z around inf 63.6%

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

   if -1.74999999999999999e142 < z < -1.6999999999999999e84

   1. Initial program 89.1%

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

      1. *-commutative 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in t around 0 67.1%

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

      1. associate-*r/ 67.1%

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

      2. neg-mul-1 67.1%

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

      3. neg-sub0 67.1%

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

      4. sub-neg 67.1%

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

      5. distribute-rgt-neg-out 67.1%

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

      6. +-commutative 67.1%

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

      7. associate--r+ 67.1%

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

      8. neg-sub0 67.1%

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

      9. distribute-rgt-neg-out 67.1%

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

      10. remove-double-neg 67.1%

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

      11. *-commutative 67.1%

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

   6. Simplified 67.1%

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

   7. Taylor expanded in y around 0 68.0%

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

      1. neg-mul-1 68.0%

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

   9. Simplified 68.0%

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

   if -1.59999999999999997e68 < z < -3.89999999999999984e51

   1. Initial program 76.0%

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

      1. *-commutative 76.0%

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

   3. Simplified 76.0%

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

   4. Taylor expanded in t around inf 63.6%

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

   5. Taylor expanded in x around 0 63.7%

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

      1. mul-1-neg 63.7%

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

      2. distribute-rgt-neg-out 63.7%

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

   7. Simplified 63.7%

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

   if -7.20000000000000018 < z < 7.5000000000000002e22

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 57.8%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+142}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+84}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+68}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{+51}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;z \leq -7.2:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 6: 91.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+142} \lor \neg \left(z \leq 4.6 \cdot 10^{+144}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.95e+142) (not (<= z 4.6e+144)))
   (/ (- y (/ x z)) a)
   (/ (- x (* z y)) (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.95e+142) || !(z <= 4.6e+144)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (z * y)) / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.95d+142)) .or. (.not. (z <= 4.6d+144))) then
        tmp = (y - (x / z)) / a
    else
        tmp = (x - (z * y)) / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.95e+142) || !(z <= 4.6e+144)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (z * y)) / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.95e+142) or not (z <= 4.6e+144):
		tmp = (y - (x / z)) / a
	else:
		tmp = (x - (z * y)) / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.95e+142) || !(z <= 4.6e+144))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x - Float64(z * y)) / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.95e+142) || ~((z <= 4.6e+144)))
		tmp = (y - (x / z)) / a;
	else
		tmp = (x - (z * y)) / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.95e+142], N[Not[LessEqual[z, 4.6e+144]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e142 or 4.6000000000000003e144 < z

   1. Initial program 47.0%

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

      1. *-commutative 47.0%

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

   3. Simplified 47.0%

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

      1. sub-neg 47.0%

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

      2. +-commutative 47.0%

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

      3. distribute-lft-neg-in 47.0%

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

      4. fma-def 47.0%

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

   5. Applied egg-rr 47.0%

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

   6. Taylor expanded in x around 0 44.9%

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

      1. mul-1-neg 44.9%

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

      2. unsub-neg 44.9%

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

      3. mul-1-neg 44.9%

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

      4. sub-neg 44.9%

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

      5. *-commutative 44.9%

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

      6. associate-/l* 59.7%

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

      7. associate-/r/ 51.5%

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

      8. mul-1-neg 51.5%

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

      9. sub-neg 51.5%

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

      10. *-commutative 51.5%

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

   8. Simplified 51.5%

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

   9. Taylor expanded in t around 0 79.1%

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

       1. distribute-lft-out-- 79.1%

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

       2. *-commutative 79.1%

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

       3. associate-/r* 84.4%

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

       4. div-sub 86.5%

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

       5. mul-1-neg 86.5%

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

   11. Simplified 86.5%

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

   if -1.95e142 < z < 4.6000000000000003e144

   1. Initial program 95.3%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+142} \lor \neg \left(z \leq 4.6 \cdot 10^{+144}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \end{array} \]

Alternative 7: 72.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -4 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-5}:\\ \;\;\;\;z \cdot \frac{-y}{t_1}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* z a))) (t_2 (/ (- y (/ x z)) a)))
   (if (<= z -4e+69)
     t_2
     (if (<= z -7e-5) (* z (/ (- y) t_1)) (if (<= z 7.8e+55) (/ x t_1) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -4e+69) {
		tmp = t_2;
	} else if (z <= -7e-5) {
		tmp = z * (-y / t_1);
	} else if (z <= 7.8e+55) {
		tmp = x / 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 - (z * a)
    t_2 = (y - (x / z)) / a
    if (z <= (-4d+69)) then
        tmp = t_2
    else if (z <= (-7d-5)) then
        tmp = z * (-y / t_1)
    else if (z <= 7.8d+55) then
        tmp = x / 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 - (z * a);
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -4e+69) {
		tmp = t_2;
	} else if (z <= -7e-5) {
		tmp = z * (-y / t_1);
	} else if (z <= 7.8e+55) {
		tmp = x / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (z * a)
	t_2 = (y - (x / z)) / a
	tmp = 0
	if z <= -4e+69:
		tmp = t_2
	elif z <= -7e-5:
		tmp = z * (-y / t_1)
	elif z <= 7.8e+55:
		tmp = x / t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(z * a))
	t_2 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -4e+69)
		tmp = t_2;
	elseif (z <= -7e-5)
		tmp = Float64(z * Float64(Float64(-y) / t_1));
	elseif (z <= 7.8e+55)
		tmp = Float64(x / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (z * a);
	t_2 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -4e+69)
		tmp = t_2;
	elseif (z <= -7e-5)
		tmp = z * (-y / t_1);
	elseif (z <= 7.8e+55)
		tmp = x / 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[(z * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -4e+69], t$95$2, If[LessEqual[z, -7e-5], N[(z * N[((-y) / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e+55], N[(x / t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.0000000000000003e69 or 7.80000000000000054e55 < z

   1. Initial program 62.8%

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

      1. *-commutative 62.8%

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

   3. Simplified 62.8%

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

      1. sub-neg 62.8%

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

      2. +-commutative 62.8%

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

      3. distribute-lft-neg-in 62.8%

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

      4. fma-def 62.8%

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

   5. Applied egg-rr 62.8%

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

   6. Taylor expanded in x around 0 61.6%

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

      1. mul-1-neg 61.6%

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

      2. unsub-neg 61.6%

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

      3. mul-1-neg 61.6%

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

      4. sub-neg 61.6%

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

      5. *-commutative 61.6%

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

      6. associate-/l* 72.5%

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

      7. associate-/r/ 66.6%

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

      8. mul-1-neg 66.6%

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

      9. sub-neg 66.6%

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

      10. *-commutative 66.6%

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

   8. Simplified 66.6%

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

   9. Taylor expanded in t around 0 73.0%

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

       1. distribute-lft-out-- 73.0%

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

       2. *-commutative 73.0%

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

       3. associate-/r* 77.3%

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

       4. div-sub 78.6%

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

       5. mul-1-neg 78.6%

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

   11. Simplified 78.6%

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

   if -4.0000000000000003e69 < z < -6.9999999999999994e-5

   1. Initial program 81.6%

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

      1. *-commutative 81.6%

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

   3. Simplified 81.6%

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

      1. sub-neg 81.6%

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

      2. +-commutative 81.6%

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

      3. distribute-lft-neg-in 81.6%

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

      4. fma-def 81.6%

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

   5. Applied egg-rr 81.6%

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

   6. Taylor expanded in x around 0 81.6%

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

      1. mul-1-neg 81.6%

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

      2. unsub-neg 81.6%

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

      3. mul-1-neg 81.6%

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

      4. sub-neg 81.6%

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

      5. *-commutative 81.6%

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

      6. associate-/l* 95.1%

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

      7. associate-/r/ 95.3%

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

      8. mul-1-neg 95.3%

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

      9. sub-neg 95.3%

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

      10. *-commutative 95.3%

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

   8. Simplified 95.3%

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

   9. Taylor expanded in x around 0 66.8%

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

       1. mul-1-neg 66.8%

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

       2. *-commutative 66.8%

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

       3. *-commutative 66.8%

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

       4. associate-*r/ 80.4%

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

       5. distribute-rgt-neg-in 80.4%

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

       6. distribute-neg-frac 80.4%

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

   11. Simplified 80.4%

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

   if -6.9999999999999994e-5 < z < 7.80000000000000054e55

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around inf 78.9%

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

      1. *-commutative 78.9%

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

   6. Simplified 78.9%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+69}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-5}:\\ \;\;\;\;z \cdot \frac{-y}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 8: 53.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{+142}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+20}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq -18:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.08e+142)
   (/ y a)
   (if (<= z -4e+20)
     (/ (- x) (* z a))
     (if (<= z -18.0) (/ y a) (if (<= z 7.5e+22) (/ x t) (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.08e+142) {
		tmp = y / a;
	} else if (z <= -4e+20) {
		tmp = -x / (z * a);
	} else if (z <= -18.0) {
		tmp = y / a;
	} else if (z <= 7.5e+22) {
		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 <= (-1.08d+142)) then
        tmp = y / a
    else if (z <= (-4d+20)) then
        tmp = -x / (z * a)
    else if (z <= (-18.0d0)) then
        tmp = y / a
    else if (z <= 7.5d+22) 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 <= -1.08e+142) {
		tmp = y / a;
	} else if (z <= -4e+20) {
		tmp = -x / (z * a);
	} else if (z <= -18.0) {
		tmp = y / a;
	} else if (z <= 7.5e+22) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.08e+142:
		tmp = y / a
	elif z <= -4e+20:
		tmp = -x / (z * a)
	elif z <= -18.0:
		tmp = y / a
	elif z <= 7.5e+22:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.08e+142)
		tmp = Float64(y / a);
	elseif (z <= -4e+20)
		tmp = Float64(Float64(-x) / Float64(z * a));
	elseif (z <= -18.0)
		tmp = Float64(y / a);
	elseif (z <= 7.5e+22)
		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 <= -1.08e+142)
		tmp = y / a;
	elseif (z <= -4e+20)
		tmp = -x / (z * a);
	elseif (z <= -18.0)
		tmp = y / a;
	elseif (z <= 7.5e+22)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.08e+142], N[(y / a), $MachinePrecision], If[LessEqual[z, -4e+20], N[((-x) / N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -18.0], N[(y / a), $MachinePrecision], If[LessEqual[z, 7.5e+22], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.08e142 or -4e20 < z < -18 or 7.5000000000000002e22 < z

   1. Initial program 64.9%

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

      1. *-commutative 64.9%

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

   3. Simplified 64.9%

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

   4. Taylor expanded in z around inf 65.1%

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

   if -1.08e142 < z < -4e20

   1. Initial program 76.8%

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

      1. *-commutative 76.8%

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

   3. Simplified 76.8%

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

   4. Taylor expanded in t around 0 44.3%

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

      1. associate-*r/ 44.3%

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

      2. neg-mul-1 44.3%

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

      3. neg-sub0 44.3%

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

      4. sub-neg 44.3%

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

      5. distribute-rgt-neg-out 44.3%

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

      6. +-commutative 44.3%

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

      7. associate--r+ 44.3%

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

      8. neg-sub0 44.3%

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

      9. distribute-rgt-neg-out 44.3%

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

      10. remove-double-neg 44.3%

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

      11. *-commutative 44.3%

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

   6. Simplified 44.3%

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

   7. Taylor expanded in y around 0 41.9%

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

      1. neg-mul-1 41.9%

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

   9. Simplified 41.9%

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

   if -18 < z < 7.5000000000000002e22

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 57.8%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{+142}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+20}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq -18:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 9: 72.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \lor \neg \left(z \leq 3.6 \cdot 10^{+64}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.8) (not (<= z 3.6e+64)))
   (/ (- y (/ x z)) a)
   (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.8) || !(z <= 3.6e+64)) {
		tmp = (y - (x / z)) / 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 <= (-7.8d0)) .or. (.not. (z <= 3.6d+64))) then
        tmp = (y - (x / z)) / 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 <= -7.8) || !(z <= 3.6e+64)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.8) or not (z <= 3.6e+64):
		tmp = (y - (x / z)) / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.8) || !(z <= 3.6e+64))
		tmp = Float64(Float64(y - Float64(x / z)) / 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 <= -7.8) || ~((z <= 3.6e+64)))
		tmp = (y - (x / z)) / a;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.8], N[Not[LessEqual[z, 3.6e+64]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.79999999999999982 or 3.60000000000000014e64 < z

   1. Initial program 66.4%

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

      1. *-commutative 66.4%

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

   3. Simplified 66.4%

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

      1. sub-neg 66.4%

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

      2. +-commutative 66.4%

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

      3. distribute-lft-neg-in 66.4%

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

      4. fma-def 66.4%

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

   5. Applied egg-rr 66.4%

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

   6. Taylor expanded in x around 0 65.4%

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

      1. mul-1-neg 65.4%

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

      2. unsub-neg 65.4%

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

      3. mul-1-neg 65.4%

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

      4. sub-neg 65.4%

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

      5. *-commutative 65.4%

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

      6. associate-/l* 77.0%

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

      7. associate-/r/ 72.3%

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

      8. mul-1-neg 72.3%

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

      9. sub-neg 72.3%

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

      10. *-commutative 72.3%

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

   8. Simplified 72.3%

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

   9. Taylor expanded in t around 0 67.6%

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

       1. distribute-lft-out-- 67.6%

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

       2. *-commutative 67.6%

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

       3. associate-/r* 72.0%

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

       4. div-sub 73.0%

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

       5. mul-1-neg 73.0%

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

   11. Simplified 73.0%

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

   if -7.79999999999999982 < z < 3.60000000000000014e64

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around inf 78.5%

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

      1. *-commutative 78.5%

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

   6. Simplified 78.5%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \lor \neg \left(z \leq 3.6 \cdot 10^{+64}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]

Alternative 10: 60.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+39}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -6e+39)
   (/ (- x (* z y)) t)
   (if (<= y 3.3e+106) (/ x (- t (* z a))) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6e+39) {
		tmp = (x - (z * y)) / t;
	} else if (y <= 3.3e+106) {
		tmp = x / (t - (z * a));
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-6d+39)) then
        tmp = (x - (z * y)) / t
    else if (y <= 3.3d+106) then
        tmp = x / (t - (z * a))
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6e+39) {
		tmp = (x - (z * y)) / t;
	} else if (y <= 3.3e+106) {
		tmp = x / (t - (z * a));
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -6e+39:
		tmp = (x - (z * y)) / t
	elif y <= 3.3e+106:
		tmp = x / (t - (z * a))
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -6e+39)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	elseif (y <= 3.3e+106)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -6e+39)
		tmp = (x - (z * y)) / t;
	elseif (y <= 3.3e+106)
		tmp = x / (t - (z * a));
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -6e+39], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 3.3e+106], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.9999999999999999e39

   1. Initial program 82.8%

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

      1. *-commutative 82.8%

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

   3. Simplified 82.8%

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

   4. Taylor expanded in t around inf 55.9%

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

   if -5.9999999999999999e39 < y < 3.30000000000000008e106

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in x around inf 81.7%

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

      1. *-commutative 81.7%

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

   6. Simplified 81.7%

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

   if 3.30000000000000008e106 < y

   1. Initial program 67.5%

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

      1. *-commutative 67.5%

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

   3. Simplified 67.5%

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

   4. Taylor expanded in z around inf 52.2%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+39}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 11: 55.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00066:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -0.00066) (/ y a) (if (<= z 1.6e+22) (/ x t) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.00066) {
		tmp = y / a;
	} else if (z <= 1.6e+22) {
		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 <= (-0.00066d0)) then
        tmp = y / a
    else if (z <= 1.6d+22) 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 <= -0.00066) {
		tmp = y / a;
	} else if (z <= 1.6e+22) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -0.00066:
		tmp = y / a
	elif z <= 1.6e+22:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -0.00066)
		tmp = Float64(y / a);
	elseif (z <= 1.6e+22)
		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 <= -0.00066)
		tmp = y / a;
	elseif (z <= 1.6e+22)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -0.00066], N[(y / a), $MachinePrecision], If[LessEqual[z, 1.6e+22], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.6e-4 or 1.6e22 < z

   1. Initial program 67.7%

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

      1. *-commutative 67.7%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in z around inf 54.9%

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

   if -6.6e-4 < z < 1.6e22

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 57.8%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00066:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 12: 34.9% 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 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. Taylor expanded in z around 0 39.5%

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

5. Final simplification 39.5%

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

Developer target: 97.5% 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 2023268 
(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))))