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

Percentage Accurate: 85.3% → 90.9%

Time: 11.1s

Alternatives: 8

Speedup: 0.5×

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: 85.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+188} \lor \neg \left(z \leq 6 \cdot 10^{+129}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y - x}{z \cdot a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.6e+188) (not (<= z 6e+129)))
   (/ (- y (/ x z)) a)
   (/ (- (* z y) x) (- (* z a) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e+188) || !(z <= 6e+129)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = ((z * y) - x) / ((z * a) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.6d+188)) .or. (.not. (z <= 6d+129))) then
        tmp = (y - (x / z)) / a
    else
        tmp = ((z * y) - x) / ((z * a) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e+188) || !(z <= 6e+129)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = ((z * y) - x) / ((z * a) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.6e+188) or not (z <= 6e+129):
		tmp = (y - (x / z)) / a
	else:
		tmp = ((z * y) - x) / ((z * a) - t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.6e+188) || !(z <= 6e+129))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(Float64(z * y) - x) / Float64(Float64(z * a) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.6e+188) || ~((z <= 6e+129)))
		tmp = (y - (x / z)) / a;
	else
		tmp = ((z * y) - x) / ((z * a) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.6e+188], N[Not[LessEqual[z, 6e+129]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(N[(z * y), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.59999999999999987e188 or 6.0000000000000006e129 < z

   1. Initial program 52.8%

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

      1. *-commutative 52.8%

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

   3. Simplified 52.8%

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

   5. Taylor expanded in a around -inf 56.0%

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

      1. mul-1-neg 56.0%

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

      2. associate--l+ 56.0%

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

      3. associate-/l* 64.0%

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

   7. Simplified 64.0%

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

   8. Taylor expanded in t around 0 88.2%

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

   if -2.59999999999999987e188 < z < 6.0000000000000006e129

   1. Initial program 97.4%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+188} \lor \neg \left(z \leq 6 \cdot 10^{+129}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y - x}{z \cdot a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 52.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{-t}\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+15}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{-127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+111}:\\ \;\;\;\;\frac{\frac{x}{a}}{-z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- t)))))
   (if (<= z -1.3e+15)
     (/ y a)
     (if (<= z -1.62e-127)
       t_1
       (if (<= z 6.5e-35)
         (/ x t)
         (if (<= z 8e+44)
           t_1
           (if (<= z 3.3e+111)
             (/ (/ x a) (- z))
             (if (<= z 4.4e+124) t_1 (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / -t);
	double tmp;
	if (z <= -1.3e+15) {
		tmp = y / a;
	} else if (z <= -1.62e-127) {
		tmp = t_1;
	} else if (z <= 6.5e-35) {
		tmp = x / t;
	} else if (z <= 8e+44) {
		tmp = t_1;
	} else if (z <= 3.3e+111) {
		tmp = (x / a) / -z;
	} else if (z <= 4.4e+124) {
		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 = y * (z / -t)
    if (z <= (-1.3d+15)) then
        tmp = y / a
    else if (z <= (-1.62d-127)) then
        tmp = t_1
    else if (z <= 6.5d-35) then
        tmp = x / t
    else if (z <= 8d+44) then
        tmp = t_1
    else if (z <= 3.3d+111) then
        tmp = (x / a) / -z
    else if (z <= 4.4d+124) 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 = y * (z / -t);
	double tmp;
	if (z <= -1.3e+15) {
		tmp = y / a;
	} else if (z <= -1.62e-127) {
		tmp = t_1;
	} else if (z <= 6.5e-35) {
		tmp = x / t;
	} else if (z <= 8e+44) {
		tmp = t_1;
	} else if (z <= 3.3e+111) {
		tmp = (x / a) / -z;
	} else if (z <= 4.4e+124) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / -t)
	tmp = 0
	if z <= -1.3e+15:
		tmp = y / a
	elif z <= -1.62e-127:
		tmp = t_1
	elif z <= 6.5e-35:
		tmp = x / t
	elif z <= 8e+44:
		tmp = t_1
	elif z <= 3.3e+111:
		tmp = (x / a) / -z
	elif z <= 4.4e+124:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(-t)))
	tmp = 0.0
	if (z <= -1.3e+15)
		tmp = Float64(y / a);
	elseif (z <= -1.62e-127)
		tmp = t_1;
	elseif (z <= 6.5e-35)
		tmp = Float64(x / t);
	elseif (z <= 8e+44)
		tmp = t_1;
	elseif (z <= 3.3e+111)
		tmp = Float64(Float64(x / a) / Float64(-z));
	elseif (z <= 4.4e+124)
		tmp = t_1;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / -t);
	tmp = 0.0;
	if (z <= -1.3e+15)
		tmp = y / a;
	elseif (z <= -1.62e-127)
		tmp = t_1;
	elseif (z <= 6.5e-35)
		tmp = x / t;
	elseif (z <= 8e+44)
		tmp = t_1;
	elseif (z <= 3.3e+111)
		tmp = (x / a) / -z;
	elseif (z <= 4.4e+124)
		tmp = t_1;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+15], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.62e-127], t$95$1, If[LessEqual[z, 6.5e-35], N[(x / t), $MachinePrecision], If[LessEqual[z, 8e+44], t$95$1, If[LessEqual[z, 3.3e+111], N[(N[(x / a), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[z, 4.4e+124], t$95$1, N[(y / a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.3e15 or 4.4000000000000002e124 < z

   1. Initial program 69.8%

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

      1. *-commutative 69.8%

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

   3. Simplified 69.8%

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

   5. Taylor expanded in z around inf 61.7%

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

   if -1.3e15 < z < -1.61999999999999993e-127 or 6.4999999999999999e-35 < z < 8.0000000000000007e44 or 3.3000000000000001e111 < z < 4.4000000000000002e124

   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. Add Preprocessing

   5. Taylor expanded in t around inf 72.0%

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

   6. Taylor expanded in x around 0 48.5%

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

      1. associate-*r* 48.5%

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

      2. neg-mul-1 48.5%

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

   8. Simplified 48.5%

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

   9. Taylor expanded in y around 0 48.5%

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

       1. mul-1-neg 48.5%

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

       2. associate-*r/ 50.1%

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

       3. distribute-rgt-neg-in 50.1%

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

       4. distribute-frac-neg 50.1%

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

   11. Simplified 50.1%

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

   if -1.61999999999999993e-127 < z < 6.4999999999999999e-35

   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. Add Preprocessing

   5. Taylor expanded in z around 0 64.7%

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

   if 8.0000000000000007e44 < z < 3.3000000000000001e111

   1. Initial program 92.4%

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

      1. *-commutative 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in t around 0 63.5%

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

      1. associate-*r/ 63.5%

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

      2. neg-mul-1 63.5%

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

      3. neg-sub0 63.5%

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

      4. sub-neg 63.5%

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

      5. distribute-rgt-neg-out 63.5%

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

      6. +-commutative 63.5%

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

      7. associate--r+ 63.5%

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

      8. neg-sub0 63.5%

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

      9. distribute-rgt-neg-out 63.5%

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

      10. remove-double-neg 63.5%

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

      11. *-commutative 63.5%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in y around 0 55.0%

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

      1. mul-1-neg 55.0%

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

      2. associate-/r* 55.0%

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

      3. distribute-neg-frac2 55.0%

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

   10. Simplified 55.0%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+15}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{-127}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+111}:\\ \;\;\;\;\frac{\frac{x}{a}}{-z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+124}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{-t}\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+14}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{-127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+114}:\\ \;\;\;\;\frac{\frac{x}{z}}{-a}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- t)))))
   (if (<= z -4.4e+14)
     (/ y a)
     (if (<= z -1.62e-127)
       t_1
       (if (<= z 1.55e-39)
         (/ x t)
         (if (<= z 1.66e+47)
           t_1
           (if (<= z 1.16e+114)
             (/ (/ x z) (- a))
             (if (<= z 1.45e+125) t_1 (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / -t);
	double tmp;
	if (z <= -4.4e+14) {
		tmp = y / a;
	} else if (z <= -1.62e-127) {
		tmp = t_1;
	} else if (z <= 1.55e-39) {
		tmp = x / t;
	} else if (z <= 1.66e+47) {
		tmp = t_1;
	} else if (z <= 1.16e+114) {
		tmp = (x / z) / -a;
	} else if (z <= 1.45e+125) {
		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 = y * (z / -t)
    if (z <= (-4.4d+14)) then
        tmp = y / a
    else if (z <= (-1.62d-127)) then
        tmp = t_1
    else if (z <= 1.55d-39) then
        tmp = x / t
    else if (z <= 1.66d+47) then
        tmp = t_1
    else if (z <= 1.16d+114) then
        tmp = (x / z) / -a
    else if (z <= 1.45d+125) 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 = y * (z / -t);
	double tmp;
	if (z <= -4.4e+14) {
		tmp = y / a;
	} else if (z <= -1.62e-127) {
		tmp = t_1;
	} else if (z <= 1.55e-39) {
		tmp = x / t;
	} else if (z <= 1.66e+47) {
		tmp = t_1;
	} else if (z <= 1.16e+114) {
		tmp = (x / z) / -a;
	} else if (z <= 1.45e+125) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / -t)
	tmp = 0
	if z <= -4.4e+14:
		tmp = y / a
	elif z <= -1.62e-127:
		tmp = t_1
	elif z <= 1.55e-39:
		tmp = x / t
	elif z <= 1.66e+47:
		tmp = t_1
	elif z <= 1.16e+114:
		tmp = (x / z) / -a
	elif z <= 1.45e+125:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(-t)))
	tmp = 0.0
	if (z <= -4.4e+14)
		tmp = Float64(y / a);
	elseif (z <= -1.62e-127)
		tmp = t_1;
	elseif (z <= 1.55e-39)
		tmp = Float64(x / t);
	elseif (z <= 1.66e+47)
		tmp = t_1;
	elseif (z <= 1.16e+114)
		tmp = Float64(Float64(x / z) / Float64(-a));
	elseif (z <= 1.45e+125)
		tmp = t_1;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / -t);
	tmp = 0.0;
	if (z <= -4.4e+14)
		tmp = y / a;
	elseif (z <= -1.62e-127)
		tmp = t_1;
	elseif (z <= 1.55e-39)
		tmp = x / t;
	elseif (z <= 1.66e+47)
		tmp = t_1;
	elseif (z <= 1.16e+114)
		tmp = (x / z) / -a;
	elseif (z <= 1.45e+125)
		tmp = t_1;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.4e+14], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.62e-127], t$95$1, If[LessEqual[z, 1.55e-39], N[(x / t), $MachinePrecision], If[LessEqual[z, 1.66e+47], t$95$1, If[LessEqual[z, 1.16e+114], N[(N[(x / z), $MachinePrecision] / (-a)), $MachinePrecision], If[LessEqual[z, 1.45e+125], t$95$1, N[(y / a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.4e14 or 1.44999999999999997e125 < z

   1. Initial program 69.8%

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

      1. *-commutative 69.8%

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

   3. Simplified 69.8%

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

   5. Taylor expanded in z around inf 61.7%

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

   if -4.4e14 < z < -1.61999999999999993e-127 or 1.54999999999999985e-39 < z < 1.6599999999999999e47 or 1.15999999999999994e114 < z < 1.44999999999999997e125

   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. Add Preprocessing

   5. Taylor expanded in t around inf 72.0%

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

   6. Taylor expanded in x around 0 48.5%

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

      1. associate-*r* 48.5%

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

      2. neg-mul-1 48.5%

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

   8. Simplified 48.5%

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

   9. Taylor expanded in y around 0 48.5%

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

       1. mul-1-neg 48.5%

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

       2. associate-*r/ 50.1%

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

       3. distribute-rgt-neg-in 50.1%

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

       4. distribute-frac-neg 50.1%

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

   11. Simplified 50.1%

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

   if -1.61999999999999993e-127 < z < 1.54999999999999985e-39

   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. Add Preprocessing

   5. Taylor expanded in z around 0 64.7%

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

   if 1.6599999999999999e47 < z < 1.15999999999999994e114

   1. Initial program 92.4%

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

      1. *-commutative 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in a around -inf 61.7%

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

      1. mul-1-neg 61.7%

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

      2. associate--l+ 61.7%

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

      3. associate-/l* 61.7%

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

   7. Simplified 61.7%

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

   8. Taylor expanded in t around 0 63.5%

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

   9. Taylor expanded in x around inf 55.0%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+14}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{-127}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+114}:\\ \;\;\;\;\frac{\frac{x}{z}}{-a}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+125}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{+57}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-17}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+142} \lor \neg \left(a \leq 9.4 \cdot 10^{+194}\right):\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.6e+57)
   (/ y a)
   (if (<= a 1.4e-17)
     (/ (- x (* z y)) t)
     (if (or (<= a 2.8e+142) (not (<= a 9.4e+194)))
       (/ x (- t (* z a)))
       (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.6e+57) {
		tmp = y / a;
	} else if (a <= 1.4e-17) {
		tmp = (x - (z * y)) / t;
	} else if ((a <= 2.8e+142) || !(a <= 9.4e+194)) {
		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 (a <= (-4.6d+57)) then
        tmp = y / a
    else if (a <= 1.4d-17) then
        tmp = (x - (z * y)) / t
    else if ((a <= 2.8d+142) .or. (.not. (a <= 9.4d+194))) 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 (a <= -4.6e+57) {
		tmp = y / a;
	} else if (a <= 1.4e-17) {
		tmp = (x - (z * y)) / t;
	} else if ((a <= 2.8e+142) || !(a <= 9.4e+194)) {
		tmp = x / (t - (z * a));
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.6e+57:
		tmp = y / a
	elif a <= 1.4e-17:
		tmp = (x - (z * y)) / t
	elif (a <= 2.8e+142) or not (a <= 9.4e+194):
		tmp = x / (t - (z * a))
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.6e+57)
		tmp = Float64(y / a);
	elseif (a <= 1.4e-17)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	elseif ((a <= 2.8e+142) || !(a <= 9.4e+194))
		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 (a <= -4.6e+57)
		tmp = y / a;
	elseif (a <= 1.4e-17)
		tmp = (x - (z * y)) / t;
	elseif ((a <= 2.8e+142) || ~((a <= 9.4e+194)))
		tmp = x / (t - (z * a));
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.6e+57], N[(y / a), $MachinePrecision], If[LessEqual[a, 1.4e-17], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[a, 2.8e+142], N[Not[LessEqual[a, 9.4e+194]], $MachinePrecision]], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.5999999999999998e57 or 2.8e142 < a < 9.39999999999999945e194

   1. Initial program 72.9%

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

      1. *-commutative 72.9%

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

   3. Simplified 72.9%

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

   5. Taylor expanded in z around inf 66.1%

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

   if -4.5999999999999998e57 < a < 1.3999999999999999e-17

   1. Initial program 96.4%

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

      1. *-commutative 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in t around inf 73.3%

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

   if 1.3999999999999999e-17 < a < 2.8e142 or 9.39999999999999945e194 < a

   1. Initial program 85.2%

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

      1. *-commutative 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in x around inf 65.6%

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

      1. *-commutative 65.6%

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

   7. Simplified 65.6%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{+57}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-17}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+142} \lor \neg \left(a \leq 9.4 \cdot 10^{+194}\right):\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+97}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a)))))
   (if (<= z -1.7e+97)
     (/ y a)
     (if (<= z 2.15e-33)
       t_1
       (if (<= z 2e+41) (* y (/ z (- t))) (if (<= z 7.8e+127) 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 <= -1.7e+97) {
		tmp = y / a;
	} else if (z <= 2.15e-33) {
		tmp = t_1;
	} else if (z <= 2e+41) {
		tmp = y * (z / -t);
	} else if (z <= 7.8e+127) {
		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 <= (-1.7d+97)) then
        tmp = y / a
    else if (z <= 2.15d-33) then
        tmp = t_1
    else if (z <= 2d+41) then
        tmp = y * (z / -t)
    else if (z <= 7.8d+127) 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 <= -1.7e+97) {
		tmp = y / a;
	} else if (z <= 2.15e-33) {
		tmp = t_1;
	} else if (z <= 2e+41) {
		tmp = y * (z / -t);
	} else if (z <= 7.8e+127) {
		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 <= -1.7e+97:
		tmp = y / a
	elif z <= 2.15e-33:
		tmp = t_1
	elif z <= 2e+41:
		tmp = y * (z / -t)
	elif z <= 7.8e+127:
		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 <= -1.7e+97)
		tmp = Float64(y / a);
	elseif (z <= 2.15e-33)
		tmp = t_1;
	elseif (z <= 2e+41)
		tmp = Float64(y * Float64(z / Float64(-t)));
	elseif (z <= 7.8e+127)
		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 <= -1.7e+97)
		tmp = y / a;
	elseif (z <= 2.15e-33)
		tmp = t_1;
	elseif (z <= 2e+41)
		tmp = y * (z / -t);
	elseif (z <= 7.8e+127)
		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, -1.7e+97], N[(y / a), $MachinePrecision], If[LessEqual[z, 2.15e-33], t$95$1, If[LessEqual[z, 2e+41], N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e+127], t$95$1, N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.70000000000000005e97 or 7.79999999999999962e127 < z

   1. Initial program 63.1%

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

      1. *-commutative 63.1%

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

   3. Simplified 63.1%

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

   5. Taylor expanded in z around inf 67.9%

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

   if -1.70000000000000005e97 < z < 2.15000000000000015e-33 or 2.00000000000000001e41 < z < 7.79999999999999962e127

   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. Add Preprocessing

   5. Taylor expanded in x around inf 67.0%

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

      1. *-commutative 67.0%

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

   7. Simplified 67.0%

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

   if 2.15000000000000015e-33 < z < 2.00000000000000001e41

   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. Add Preprocessing

   5. Taylor expanded in t around inf 62.0%

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

   6. Taylor expanded in x around 0 57.2%

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

      1. associate-*r* 57.2%

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

      2. neg-mul-1 57.2%

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

   8. Simplified 57.2%

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

   9. Taylor expanded in y around 0 57.2%

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

       1. mul-1-neg 57.2%

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

       2. associate-*r/ 57.4%

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

       3. distribute-rgt-neg-in 57.4%

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

       4. distribute-frac-neg 57.4%

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

   11. Simplified 57.4%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+97}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+127}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+49} \lor \neg \left(a \leq 8000000\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7.5e+49) (not (<= a 8000000.0)))
   (/ (- y (/ x z)) a)
   (/ (- x (* z y)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.5e+49) || !(a <= 8000000.0)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (z * y)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-7.5d+49)) .or. (.not. (a <= 8000000.0d0))) then
        tmp = (y - (x / z)) / a
    else
        tmp = (x - (z * y)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.5e+49) || !(a <= 8000000.0)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (z * y)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7.5e+49) or not (a <= 8000000.0):
		tmp = (y - (x / z)) / a
	else:
		tmp = (x - (z * y)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7.5e+49) || !(a <= 8000000.0))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -7.5e+49) || ~((a <= 8000000.0)))
		tmp = (y - (x / z)) / a;
	else
		tmp = (x - (z * y)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7.5e+49], N[Not[LessEqual[a, 8000000.0]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.4999999999999995e49 or 8e6 < a

   1. Initial program 78.5%

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

      1. *-commutative 78.5%

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

   3. Simplified 78.5%

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

   5. Taylor expanded in a around -inf 46.6%

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

      1. mul-1-neg 46.6%

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

      2. associate--l+ 46.6%

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

      3. associate-/l* 53.8%

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

   7. Simplified 53.8%

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

   8. Taylor expanded in t around 0 72.9%

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

   if -7.4999999999999995e49 < a < 8e6

   1. Initial program 96.5%

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

      1. *-commutative 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in t around inf 73.5%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+49} \lor \neg \left(a \leq 8000000\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -62000000000000 \lor \neg \left(z \leq 1.45 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -62000000000000.0) (not (<= z 1.45e-6))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -62000000000000.0) || !(z <= 1.45e-6)) {
		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 <= (-62000000000000.0d0)) .or. (.not. (z <= 1.45d-6))) 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 <= -62000000000000.0) || !(z <= 1.45e-6)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -62000000000000.0) or not (z <= 1.45e-6):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -62000000000000.0) || !(z <= 1.45e-6))
		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 <= -62000000000000.0) || ~((z <= 1.45e-6)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -62000000000000.0], N[Not[LessEqual[z, 1.45e-6]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.2e13 or 1.4500000000000001e-6 < z

   1. Initial program 75.7%

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

      1. *-commutative 75.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in z around inf 52.8%

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

   if -6.2e13 < z < 1.4500000000000001e-6

   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. Add Preprocessing

   5. Taylor expanded in z around 0 53.6%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -62000000000000 \lor \neg \left(z \leq 1.45 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 35.6% 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 88.7%

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

   1. *-commutative 88.7%

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

3. Simplified 88.7%

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

5. Taylor expanded in z around 0 36.5%

   \[\leadsto \color{blue}{\frac{x}{t}} \]
6. Add Preprocessing

Developer target: 97.4% accurate, 0.4× 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 2024089 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :alt
  (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))))