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

Percentage Accurate: 85.2% → 89.5%

Time: 12.7s

Alternatives: 10

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.2% 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: 89.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+38} \lor \neg \left(z \leq 2.45 \cdot 10^{+222}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.8e+38) (not (<= z 2.45e+222)))
   (/ (- 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 <= -4.8e+38) || !(z <= 2.45e+222)) {
		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 <= (-4.8d+38)) .or. (.not. (z <= 2.45d+222))) 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 <= -4.8e+38) || !(z <= 2.45e+222)) {
		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 <= -4.8e+38) or not (z <= 2.45e+222):
		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 <= -4.8e+38) || !(z <= 2.45e+222))
		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 <= -4.8e+38) || ~((z <= 2.45e+222)))
		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, -4.8e+38], N[Not[LessEqual[z, 2.45e+222]], $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 < -4.80000000000000035e38 or 2.44999999999999995e222 < z

   1. Initial program 56.3%

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

      1. *-commutative 56.3%

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

   3. Simplified 56.3%

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

      1. div-sub 56.3%

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

      2. sub-neg 56.3%

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

      3. +-commutative 56.3%

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

      4. *-commutative 56.3%

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

      5. distribute-rgt-neg-in 56.3%

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

      6. fma-def 56.3%

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

      7. associate-/l* 70.8%

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

      8. sub-neg 70.8%

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

      9. +-commutative 70.8%

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

      10. *-commutative 70.8%

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

      11. distribute-rgt-neg-in 70.8%

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

      12. fma-def 70.9%

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

   5. Applied egg-rr 70.9%

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

   6. Taylor expanded in a around inf 86.7%

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

      1. distribute-lft-out-- 86.7%

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

      2. associate-*r/ 86.7%

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

      3. mul-1-neg 86.7%

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

   8. Simplified 86.7%

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

   if -4.80000000000000035e38 < z < 2.44999999999999995e222

   1. Initial program 97.3%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+38} \lor \neg \left(z \leq 2.45 \cdot 10^{+222}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \end{array} \]

Alternative 2: 70.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - z \cdot y}{t}\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-135}:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+68}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* z y)) t)) (t_2 (/ (- y (/ x z)) a)))
   (if (<= z -1.15e+34)
     t_2
     (if (<= z -2.5e-77)
       t_1
       (if (<= z -3.2e-135)
         (- (/ y a) (/ (/ x a) z))
         (if (<= z -1.36e-195)
           t_1
           (if (<= z 3.5e+68) (/ x (- t (* z a))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (z * y)) / t;
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.15e+34) {
		tmp = t_2;
	} else if (z <= -2.5e-77) {
		tmp = t_1;
	} else if (z <= -3.2e-135) {
		tmp = (y / a) - ((x / a) / z);
	} else if (z <= -1.36e-195) {
		tmp = t_1;
	} else if (z <= 3.5e+68) {
		tmp = x / (t - (z * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - (z * y)) / t
    t_2 = (y - (x / z)) / a
    if (z <= (-1.15d+34)) then
        tmp = t_2
    else if (z <= (-2.5d-77)) then
        tmp = t_1
    else if (z <= (-3.2d-135)) then
        tmp = (y / a) - ((x / a) / z)
    else if (z <= (-1.36d-195)) then
        tmp = t_1
    else if (z <= 3.5d+68) then
        tmp = x / (t - (z * a))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (z * y)) / t;
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.15e+34) {
		tmp = t_2;
	} else if (z <= -2.5e-77) {
		tmp = t_1;
	} else if (z <= -3.2e-135) {
		tmp = (y / a) - ((x / a) / z);
	} else if (z <= -1.36e-195) {
		tmp = t_1;
	} else if (z <= 3.5e+68) {
		tmp = x / (t - (z * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (z * y)) / t
	t_2 = (y - (x / z)) / a
	tmp = 0
	if z <= -1.15e+34:
		tmp = t_2
	elif z <= -2.5e-77:
		tmp = t_1
	elif z <= -3.2e-135:
		tmp = (y / a) - ((x / a) / z)
	elif z <= -1.36e-195:
		tmp = t_1
	elif z <= 3.5e+68:
		tmp = x / (t - (z * a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(z * y)) / t)
	t_2 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -1.15e+34)
		tmp = t_2;
	elseif (z <= -2.5e-77)
		tmp = t_1;
	elseif (z <= -3.2e-135)
		tmp = Float64(Float64(y / a) - Float64(Float64(x / a) / z));
	elseif (z <= -1.36e-195)
		tmp = t_1;
	elseif (z <= 3.5e+68)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (z * y)) / t;
	t_2 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -1.15e+34)
		tmp = t_2;
	elseif (z <= -2.5e-77)
		tmp = t_1;
	elseif (z <= -3.2e-135)
		tmp = (y / a) - ((x / a) / z);
	elseif (z <= -1.36e-195)
		tmp = t_1;
	elseif (z <= 3.5e+68)
		tmp = x / (t - (z * a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -1.15e+34], t$95$2, If[LessEqual[z, -2.5e-77], t$95$1, If[LessEqual[z, -3.2e-135], N[(N[(y / a), $MachinePrecision] - N[(N[(x / a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.36e-195], t$95$1, If[LessEqual[z, 3.5e+68], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1499999999999999e34 or 3.49999999999999977e68 < z

   1. Initial program 65.4%

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

      1. *-commutative 65.4%

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

   3. Simplified 65.4%

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

      1. div-sub 65.4%

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

      2. sub-neg 65.4%

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

      3. +-commutative 65.4%

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

      4. *-commutative 65.4%

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

      5. distribute-rgt-neg-in 65.4%

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

      6. fma-def 65.4%

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

      7. associate-/l* 76.6%

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

      8. sub-neg 76.6%

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

      9. +-commutative 76.6%

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

      10. *-commutative 76.6%

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

      11. distribute-rgt-neg-in 76.6%

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

      12. fma-def 76.6%

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

   5. Applied egg-rr 76.6%

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

   6. Taylor expanded in a around inf 80.6%

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

      1. distribute-lft-out-- 80.6%

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

      2. associate-*r/ 80.6%

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

      3. mul-1-neg 80.6%

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

   8. Simplified 80.6%

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

   if -1.1499999999999999e34 < z < -2.49999999999999982e-77 or -3.2e-135 < z < -1.36e-195

   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 t around inf 81.6%

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

   if -2.49999999999999982e-77 < z < -3.2e-135

   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. Step-by-step derivation

      1. div-sub 99.8%

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

      2. sub-neg 99.8%

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

      3. +-commutative 99.8%

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

      4. *-commutative 99.8%

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

      5. distribute-rgt-neg-in 99.8%

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

      6. fma-def 99.8%

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

      7. associate-/l* 95.9%

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

      8. sub-neg 95.9%

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

      9. +-commutative 95.9%

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

      10. *-commutative 95.9%

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

      11. distribute-rgt-neg-in 95.9%

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

      12. fma-def 95.9%

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

   5. Applied egg-rr 95.9%

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

   6. Taylor expanded in t around 0 72.7%

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

      1. cancel-sign-sub-inv 72.7%

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

      2. metadata-eval 72.7%

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

      3. *-lft-identity 72.7%

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

      4. +-commutative 72.7%

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

      5. neg-mul-1 72.7%

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

      6. unsub-neg 72.7%

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

      7. associate-/r* 72.8%

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

   8. Simplified 72.8%

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

   if -1.36e-195 < z < 3.49999999999999977e68

   1. Initial program 98.9%

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

      1. *-commutative 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in x around inf 78.0%

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

      1. *-commutative 78.0%

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

   6. Simplified 78.0%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+34}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-77}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-135}:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-195}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+68}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 3: 65.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+43}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-196}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a)))))
   (if (<= z -3.2e+43)
     (/ y a)
     (if (<= z -3.5e-136)
       t_1
       (if (<= z -9e-196)
         (/ (- x (* z y)) t)
         (if (<= z 2.5e+111) t_1 (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double tmp;
	if (z <= -3.2e+43) {
		tmp = y / a;
	} else if (z <= -3.5e-136) {
		tmp = t_1;
	} else if (z <= -9e-196) {
		tmp = (x - (z * y)) / t;
	} else if (z <= 2.5e+111) {
		tmp = t_1;
	} 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 / (t - (z * a))
    if (z <= (-3.2d+43)) then
        tmp = y / a
    else if (z <= (-3.5d-136)) then
        tmp = t_1
    else if (z <= (-9d-196)) then
        tmp = (x - (z * y)) / t
    else if (z <= 2.5d+111) then
        tmp = t_1
    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 / (t - (z * a));
	double tmp;
	if (z <= -3.2e+43) {
		tmp = y / a;
	} else if (z <= -3.5e-136) {
		tmp = t_1;
	} else if (z <= -9e-196) {
		tmp = (x - (z * y)) / t;
	} else if (z <= 2.5e+111) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t - (z * a))
	tmp = 0
	if z <= -3.2e+43:
		tmp = y / a
	elif z <= -3.5e-136:
		tmp = t_1
	elif z <= -9e-196:
		tmp = (x - (z * y)) / t
	elif z <= 2.5e+111:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (z <= -3.2e+43)
		tmp = Float64(y / a);
	elseif (z <= -3.5e-136)
		tmp = t_1;
	elseif (z <= -9e-196)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	elseif (z <= 2.5e+111)
		tmp = t_1;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t - (z * a));
	tmp = 0.0;
	if (z <= -3.2e+43)
		tmp = y / a;
	elseif (z <= -3.5e-136)
		tmp = t_1;
	elseif (z <= -9e-196)
		tmp = (x - (z * y)) / t;
	elseif (z <= 2.5e+111)
		tmp = t_1;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+43], N[(y / a), $MachinePrecision], If[LessEqual[z, -3.5e-136], t$95$1, If[LessEqual[z, -9e-196], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 2.5e+111], t$95$1, N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.20000000000000014e43 or 2.4999999999999998e111 < z

   1. Initial program 62.9%

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

      1. *-commutative 62.9%

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

   3. Simplified 62.9%

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

   4. Taylor expanded in z around inf 71.0%

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

   if -3.20000000000000014e43 < z < -3.50000000000000029e-136 or -9e-196 < z < 2.4999999999999998e111

   1. Initial program 98.6%

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

      1. *-commutative 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in x around inf 71.1%

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

      1. *-commutative 71.1%

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

   6. Simplified 71.1%

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

   if -3.50000000000000029e-136 < z < -9e-196

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 99.9%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+43}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-136}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-196}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+111}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 4: 72.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-195}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a)))) (t_2 (/ (- y (/ x z)) a)))
   (if (<= z -2.6e+38)
     t_2
     (if (<= z -1.9e-135)
       t_1
       (if (<= z -1.4e-195)
         (/ (- x (* z y)) t)
         (if (<= z 3.5e+68) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -2.6e+38) {
		tmp = t_2;
	} else if (z <= -1.9e-135) {
		tmp = t_1;
	} else if (z <= -1.4e-195) {
		tmp = (x - (z * y)) / t;
	} else if (z <= 3.5e+68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (t - (z * a))
    t_2 = (y - (x / z)) / a
    if (z <= (-2.6d+38)) then
        tmp = t_2
    else if (z <= (-1.9d-135)) then
        tmp = t_1
    else if (z <= (-1.4d-195)) then
        tmp = (x - (z * y)) / t
    else if (z <= 3.5d+68) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -2.6e+38) {
		tmp = t_2;
	} else if (z <= -1.9e-135) {
		tmp = t_1;
	} else if (z <= -1.4e-195) {
		tmp = (x - (z * y)) / t;
	} else if (z <= 3.5e+68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t - (z * a))
	t_2 = (y - (x / z)) / a
	tmp = 0
	if z <= -2.6e+38:
		tmp = t_2
	elif z <= -1.9e-135:
		tmp = t_1
	elif z <= -1.4e-195:
		tmp = (x - (z * y)) / t
	elif z <= 3.5e+68:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t - Float64(z * a)))
	t_2 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -2.6e+38)
		tmp = t_2;
	elseif (z <= -1.9e-135)
		tmp = t_1;
	elseif (z <= -1.4e-195)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	elseif (z <= 3.5e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t - (z * a));
	t_2 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -2.6e+38)
		tmp = t_2;
	elseif (z <= -1.9e-135)
		tmp = t_1;
	elseif (z <= -1.4e-195)
		tmp = (x - (z * y)) / t;
	elseif (z <= 3.5e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -2.6e+38], t$95$2, If[LessEqual[z, -1.9e-135], t$95$1, If[LessEqual[z, -1.4e-195], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 3.5e+68], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5999999999999999e38 or 3.49999999999999977e68 < z

   1. Initial program 65.0%

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

      1. *-commutative 65.0%

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

   3. Simplified 65.0%

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

      1. div-sub 65.0%

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

      2. sub-neg 65.0%

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

      3. +-commutative 65.0%

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

      4. *-commutative 65.0%

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

      5. distribute-rgt-neg-in 65.0%

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

      6. fma-def 65.0%

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

      7. associate-/l* 76.4%

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

      8. sub-neg 76.4%

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

      9. +-commutative 76.4%

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

      10. *-commutative 76.4%

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

      11. distribute-rgt-neg-in 76.4%

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

      12. fma-def 76.4%

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

   5. Applied egg-rr 76.4%

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

   6. Taylor expanded in a around inf 80.4%

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

      1. distribute-lft-out-- 80.4%

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

      2. associate-*r/ 80.4%

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

      3. mul-1-neg 80.4%

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

   8. Simplified 80.4%

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

   if -2.5999999999999999e38 < z < -1.9000000000000001e-135 or -1.40000000000000002e-195 < z < 3.49999999999999977e68

   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 72.3%

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

      1. *-commutative 72.3%

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

   6. Simplified 72.3%

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

   if -1.9000000000000001e-135 < z < -1.40000000000000002e-195

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 99.9%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+38}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-135}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-195}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+68}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 5: 53.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -0.0025:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(-\frac{z}{t}\right)\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-137}:\\ \;\;\;\;\frac{\frac{-x}{a}}{z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.1e+33)
   (/ y a)
   (if (<= z -0.0025)
     (/ x t)
     (if (<= z -2.9e-40)
       (* y (- (/ z t)))
       (if (<= z -1.85e-137)
         (/ (/ (- x) a) z)
         (if (<= z 3e+52) (/ x t) (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.1e+33) {
		tmp = y / a;
	} else if (z <= -0.0025) {
		tmp = x / t;
	} else if (z <= -2.9e-40) {
		tmp = y * -(z / t);
	} else if (z <= -1.85e-137) {
		tmp = (-x / a) / z;
	} else if (z <= 3e+52) {
		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 <= (-5.1d+33)) then
        tmp = y / a
    else if (z <= (-0.0025d0)) then
        tmp = x / t
    else if (z <= (-2.9d-40)) then
        tmp = y * -(z / t)
    else if (z <= (-1.85d-137)) then
        tmp = (-x / a) / z
    else if (z <= 3d+52) 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 <= -5.1e+33) {
		tmp = y / a;
	} else if (z <= -0.0025) {
		tmp = x / t;
	} else if (z <= -2.9e-40) {
		tmp = y * -(z / t);
	} else if (z <= -1.85e-137) {
		tmp = (-x / a) / z;
	} else if (z <= 3e+52) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.1e+33:
		tmp = y / a
	elif z <= -0.0025:
		tmp = x / t
	elif z <= -2.9e-40:
		tmp = y * -(z / t)
	elif z <= -1.85e-137:
		tmp = (-x / a) / z
	elif z <= 3e+52:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.1e+33)
		tmp = Float64(y / a);
	elseif (z <= -0.0025)
		tmp = Float64(x / t);
	elseif (z <= -2.9e-40)
		tmp = Float64(y * Float64(-Float64(z / t)));
	elseif (z <= -1.85e-137)
		tmp = Float64(Float64(Float64(-x) / a) / z);
	elseif (z <= 3e+52)
		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 <= -5.1e+33)
		tmp = y / a;
	elseif (z <= -0.0025)
		tmp = x / t;
	elseif (z <= -2.9e-40)
		tmp = y * -(z / t);
	elseif (z <= -1.85e-137)
		tmp = (-x / a) / z;
	elseif (z <= 3e+52)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.1e+33], N[(y / a), $MachinePrecision], If[LessEqual[z, -0.0025], N[(x / t), $MachinePrecision], If[LessEqual[z, -2.9e-40], N[(y * (-N[(z / t), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, -1.85e-137], N[(N[((-x) / a), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 3e+52], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.0999999999999999e33 or 3e52 < 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. Taylor expanded in z around inf 65.8%

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

   if -5.0999999999999999e33 < z < -0.00250000000000000005 or -1.85e-137 < z < 3e52

   1. Initial program 99.1%

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

      1. *-commutative 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around 0 57.2%

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

   if -0.00250000000000000005 < z < -2.8999999999999999e-40

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

   3. Simplified 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-lft-neg-in 100.0%

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

      4. fma-def 100.0%

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

   5. Applied egg-rr 100.0%

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

      1. div-sub 88.9%

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

      2. fma-udef 88.9%

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

      3. distribute-lft-neg-in 88.9%

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

      4. *-commutative 88.9%

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

      5. distribute-rgt-neg-in 88.9%

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

      6. fma-udef 88.9%

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

      7. add-sqr-sqrt 88.9%

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

      8. sqrt-unprod 88.9%

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

      9. sqr-neg 88.9%

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

      10. sqrt-unprod 0.0%

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

      11. add-sqr-sqrt 88.9%

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

      12. associate-/l* 88.5%

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

      13. fma-udef 88.5%

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

      14. distribute-lft-neg-in 88.5%

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

      15. *-commutative 88.5%

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

      16. distribute-rgt-neg-in 88.5%

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

      17. fma-udef 88.5%

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

      18. div-inv 88.5%

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

      19. clear-num 88.7%

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

   7. Applied egg-rr 56.1%

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

   8. Taylor expanded in x around 0 56.8%

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

      1. mul-1-neg 56.8%

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

      2. associate-*r/ 56.6%

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

      3. +-commutative 56.6%

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

      4. fma-udef 56.6%

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

      5. distribute-lft-neg-in 56.6%

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

      6. fma-udef 56.6%

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

      7. *-commutative 56.6%

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

      8. fma-def 56.6%

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

   10. Simplified 56.6%

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

   11. Taylor expanded in z around 0 56.4%

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

   if -2.8999999999999999e-40 < z < -1.85e-137

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

      1. div-sub 99.7%

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

      2. sub-neg 99.7%

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

      3. +-commutative 99.7%

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

      4. *-commutative 99.7%

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

      5. distribute-rgt-neg-in 99.7%

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

      6. fma-def 99.7%

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

      7. associate-/l* 96.9%

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

      8. sub-neg 96.9%

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

      9. +-commutative 96.9%

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

      10. *-commutative 96.9%

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

      11. distribute-rgt-neg-in 96.9%

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

      12. fma-def 96.9%

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

   5. Applied egg-rr 96.9%

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

   6. Taylor expanded in a around inf 55.8%

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

      1. distribute-lft-out-- 55.8%

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

      2. associate-*r/ 55.8%

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

      3. mul-1-neg 55.8%

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

   8. Simplified 55.8%

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

   9. Taylor expanded in x around inf 43.7%

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

       1. associate-/r* 43.8%

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

   11. Simplified 43.8%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -0.0025:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(-\frac{z}{t}\right)\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-137}:\\ \;\;\;\;\frac{\frac{-x}{a}}{z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 6: 53.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -0.00022:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-37}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-135}:\\ \;\;\;\;\frac{\frac{-x}{a}}{z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.3e+33)
   (/ y a)
   (if (<= z -0.00022)
     (/ x t)
     (if (<= z -9e-37)
       (/ (* z (- y)) t)
       (if (<= z -3e-135)
         (/ (/ (- x) a) z)
         (if (<= z 3e+52) (/ x t) (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.3e+33) {
		tmp = y / a;
	} else if (z <= -0.00022) {
		tmp = x / t;
	} else if (z <= -9e-37) {
		tmp = (z * -y) / t;
	} else if (z <= -3e-135) {
		tmp = (-x / a) / z;
	} else if (z <= 3e+52) {
		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 <= (-2.3d+33)) then
        tmp = y / a
    else if (z <= (-0.00022d0)) then
        tmp = x / t
    else if (z <= (-9d-37)) then
        tmp = (z * -y) / t
    else if (z <= (-3d-135)) then
        tmp = (-x / a) / z
    else if (z <= 3d+52) 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 <= -2.3e+33) {
		tmp = y / a;
	} else if (z <= -0.00022) {
		tmp = x / t;
	} else if (z <= -9e-37) {
		tmp = (z * -y) / t;
	} else if (z <= -3e-135) {
		tmp = (-x / a) / z;
	} else if (z <= 3e+52) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.3e+33:
		tmp = y / a
	elif z <= -0.00022:
		tmp = x / t
	elif z <= -9e-37:
		tmp = (z * -y) / t
	elif z <= -3e-135:
		tmp = (-x / a) / z
	elif z <= 3e+52:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.3e+33)
		tmp = Float64(y / a);
	elseif (z <= -0.00022)
		tmp = Float64(x / t);
	elseif (z <= -9e-37)
		tmp = Float64(Float64(z * Float64(-y)) / t);
	elseif (z <= -3e-135)
		tmp = Float64(Float64(Float64(-x) / a) / z);
	elseif (z <= 3e+52)
		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 <= -2.3e+33)
		tmp = y / a;
	elseif (z <= -0.00022)
		tmp = x / t;
	elseif (z <= -9e-37)
		tmp = (z * -y) / t;
	elseif (z <= -3e-135)
		tmp = (-x / a) / z;
	elseif (z <= 3e+52)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.3e+33], N[(y / a), $MachinePrecision], If[LessEqual[z, -0.00022], N[(x / t), $MachinePrecision], If[LessEqual[z, -9e-37], N[(N[(z * (-y)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, -3e-135], N[(N[((-x) / a), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 3e+52], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.30000000000000011e33 or 3e52 < 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. Taylor expanded in z around inf 65.8%

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

   if -2.30000000000000011e33 < z < -2.20000000000000008e-4 or -3.00000000000000012e-135 < z < 3e52

   1. Initial program 99.1%

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

      1. *-commutative 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around 0 57.2%

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

   if -2.20000000000000008e-4 < z < -9.00000000000000081e-37

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 89.4%

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

      1. associate-*r/ 89.4%

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

      2. associate-*r* 89.4%

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

      3. neg-mul-1 89.4%

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

      4. *-commutative 89.4%

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

   6. Simplified 89.4%

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

   7. Taylor expanded in z around 0 56.6%

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

      1. associate-*r/ 56.6%

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

      2. associate-*r* 56.6%

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

      3. mul-1-neg 56.6%

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

   9. Simplified 56.6%

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

   if -9.00000000000000081e-37 < z < -3.00000000000000012e-135

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

      1. div-sub 99.7%

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

      2. sub-neg 99.7%

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

      3. +-commutative 99.7%

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

      4. *-commutative 99.7%

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

      5. distribute-rgt-neg-in 99.7%

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

      6. fma-def 99.7%

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

      7. associate-/l* 96.9%

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

      8. sub-neg 96.9%

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

      9. +-commutative 96.9%

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

      10. *-commutative 96.9%

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

      11. distribute-rgt-neg-in 96.9%

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

      12. fma-def 96.9%

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

   5. Applied egg-rr 96.9%

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

   6. Taylor expanded in a around inf 55.8%

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

      1. distribute-lft-out-- 55.8%

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

      2. associate-*r/ 55.8%

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

      3. mul-1-neg 55.8%

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

   8. Simplified 55.8%

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

   9. Taylor expanded in x around inf 43.7%

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

       1. associate-/r* 43.8%

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

   11. Simplified 43.8%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -0.00022:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-37}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-135}:\\ \;\;\;\;\frac{\frac{-x}{a}}{z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 7: 65.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+47} \lor \neg \left(z \leq 1.76 \cdot 10^{+115}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.3e+47) (not (<= z 1.76e+115))) (/ y a) (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.3e+47) || !(z <= 1.76e+115)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5.3d+47)) .or. (.not. (z <= 1.76d+115))) then
        tmp = y / a
    else
        tmp = x / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.3e+47) || !(z <= 1.76e+115)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.3e+47) or not (z <= 1.76e+115):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.3e+47) || !(z <= 1.76e+115))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.3e+47) || ~((z <= 1.76e+115)))
		tmp = y / a;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.3e+47], N[Not[LessEqual[z, 1.76e+115]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.3e47 or 1.76e115 < z

   1. Initial program 62.9%

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

      1. *-commutative 62.9%

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

   3. Simplified 62.9%

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

   4. Taylor expanded in z around inf 71.0%

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

   if -5.3e47 < z < 1.76e115

   1. Initial program 98.7%

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

      1. *-commutative 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in x around inf 70.4%

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

      1. *-commutative 70.4%

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

   6. Simplified 70.4%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+47} \lor \neg \left(z \leq 1.76 \cdot 10^{+115}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]

Alternative 8: 53.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+39}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-138}:\\ \;\;\;\;\frac{\frac{-x}{a}}{z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.8e+39)
   (/ y a)
   (if (<= z -2.1e-138) (/ (/ (- x) a) z) (if (<= z 3e+52) (/ x t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e+39) {
		tmp = y / a;
	} else if (z <= -2.1e-138) {
		tmp = (-x / a) / z;
	} else if (z <= 3e+52) {
		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 <= (-6.8d+39)) then
        tmp = y / a
    else if (z <= (-2.1d-138)) then
        tmp = (-x / a) / z
    else if (z <= 3d+52) 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 <= -6.8e+39) {
		tmp = y / a;
	} else if (z <= -2.1e-138) {
		tmp = (-x / a) / z;
	} else if (z <= 3e+52) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.8e+39:
		tmp = y / a
	elif z <= -2.1e-138:
		tmp = (-x / a) / z
	elif z <= 3e+52:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.8e+39)
		tmp = Float64(y / a);
	elseif (z <= -2.1e-138)
		tmp = Float64(Float64(Float64(-x) / a) / z);
	elseif (z <= 3e+52)
		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 <= -6.8e+39)
		tmp = y / a;
	elseif (z <= -2.1e-138)
		tmp = (-x / a) / z;
	elseif (z <= 3e+52)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.8e+39], N[(y / a), $MachinePrecision], If[LessEqual[z, -2.1e-138], N[(N[((-x) / a), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 3e+52], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.7999999999999998e39 or 3e52 < z

   1. Initial program 65.8%

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

      1. *-commutative 65.8%

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

   3. Simplified 65.8%

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

   4. Taylor expanded in z around inf 67.0%

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

   if -6.7999999999999998e39 < z < -2.09999999999999986e-138

   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. Step-by-step derivation

      1. div-sub 97.8%

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

      2. sub-neg 97.8%

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

      3. +-commutative 97.8%

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

      4. *-commutative 97.8%

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

      5. distribute-rgt-neg-in 97.8%

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

      6. fma-def 97.8%

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

      7. associate-/l* 95.9%

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

      8. sub-neg 95.9%

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

      9. +-commutative 95.9%

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

      10. *-commutative 95.9%

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

      11. distribute-rgt-neg-in 95.9%

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

      12. fma-def 95.9%

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

   5. Applied egg-rr 95.9%

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

   6. Taylor expanded in a around inf 52.4%

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

      1. distribute-lft-out-- 52.4%

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

      2. associate-*r/ 52.4%

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

      3. mul-1-neg 52.4%

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

   8. Simplified 52.4%

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

   9. Taylor expanded in x around inf 39.0%

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

       1. associate-/r* 39.1%

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

   11. Simplified 39.1%

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

   if -2.09999999999999986e-138 < z < 3e52

   1. Initial program 99.0%

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

      1. *-commutative 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in z around 0 56.4%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+39}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-138}:\\ \;\;\;\;\frac{\frac{-x}{a}}{z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 9: 54.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+32} \lor \neg \left(z \leq 3 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.7e+32) (not (<= z 3e+52))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.7e+32) || !(z <= 3e+52)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4.7d+32)) .or. (.not. (z <= 3d+52))) then
        tmp = y / a
    else
        tmp = x / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.7e+32) || !(z <= 3e+52)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.7e+32) or not (z <= 3e+52):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.7e+32) || !(z <= 3e+52))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.7e+32) || ~((z <= 3e+52)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.7e+32], N[Not[LessEqual[z, 3e+52]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.70000000000000023e32 or 3e52 < 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. Taylor expanded in z around inf 65.8%

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

   if -4.70000000000000023e32 < z < 3e52

   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 z around 0 48.6%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+32} \lor \neg \left(z \leq 3 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]

Alternative 10: 34.7% 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 86.6%

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

   1. *-commutative 86.6%

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

3. Simplified 86.6%

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

4. Taylor expanded in z around 0 33.7%

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

5. Final simplification 33.7%

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

Developer target: 97.4% 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 2023318 
(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))))