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

Percentage Accurate: 85.3% → 90.9%

Time: 8.7s

Alternatives: 8

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: 85.3% 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, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+137} \lor \neg \left(z \leq 5.1 \cdot 10^{+148}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.75e+137) (not (<= z 5.1e+148)))
   (/ (- y (/ x z)) a)
   (/ (- x (* z y)) (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.75e+137) || !(z <= 5.1e+148)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (z * y)) / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.75d+137)) .or. (.not. (z <= 5.1d+148))) then
        tmp = (y - (x / z)) / a
    else
        tmp = (x - (z * y)) / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.75e+137) || !(z <= 5.1e+148)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (z * y)) / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.75e+137) or not (z <= 5.1e+148):
		tmp = (y - (x / z)) / a
	else:
		tmp = (x - (z * y)) / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.75e+137) || !(z <= 5.1e+148))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x - Float64(z * y)) / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.75e+137) || ~((z <= 5.1e+148)))
		tmp = (y - (x / z)) / a;
	else
		tmp = (x - (z * y)) / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.75e+137], N[Not[LessEqual[z, 5.1e+148]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7500000000000001e137 or 5.09999999999999985e148 < z

   1. Initial program 44.8%

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

      1. *-commutative 44.8%

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

   3. Simplified 44.8%

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

   4. Taylor expanded in z around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. associate--l+ 61.4%

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

      3. associate-/r* 63.4%

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

      4. associate-*r/ 63.4%

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

      5. associate-/r* 63.5%

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

      6. associate-*r/ 63.5%

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

      7. div-sub 63.5%

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

      8. distribute-lft-out-- 63.5%

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

      9. associate-*r/ 63.5%

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

      10. mul-1-neg 63.5%

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

      11. unsub-neg 63.5%

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

   6. Simplified 70.4%

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

   7. Taylor expanded in a around inf 84.1%

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

   if -1.7500000000000001e137 < z < 5.09999999999999985e148

   1. Initial program 96.7%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+137} \lor \neg \left(z \leq 5.1 \cdot 10^{+148}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \end{array} \]

Alternative 2: 65.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - z \cdot y}{t}\\ t_2 := \frac{x}{t - z \cdot a}\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+93}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-67}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* z y)) t)) (t_2 (/ x (- t (* z a)))))
   (if (<= z -8.2e+93)
     (/ y a)
     (if (<= z -5.6e+51)
       t_2
       (if (<= z -1.55e+33)
         (/ y a)
         (if (<= z -8.2e-7)
           t_1
           (if (<= z -1.18e-67) t_2 (if (<= z 5.2e+37) t_1 (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (z * y)) / t;
	double t_2 = x / (t - (z * a));
	double tmp;
	if (z <= -8.2e+93) {
		tmp = y / a;
	} else if (z <= -5.6e+51) {
		tmp = t_2;
	} else if (z <= -1.55e+33) {
		tmp = y / a;
	} else if (z <= -8.2e-7) {
		tmp = t_1;
	} else if (z <= -1.18e-67) {
		tmp = t_2;
	} else if (z <= 5.2e+37) {
		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) :: t_2
    real(8) :: tmp
    t_1 = (x - (z * y)) / t
    t_2 = x / (t - (z * a))
    if (z <= (-8.2d+93)) then
        tmp = y / a
    else if (z <= (-5.6d+51)) then
        tmp = t_2
    else if (z <= (-1.55d+33)) then
        tmp = y / a
    else if (z <= (-8.2d-7)) then
        tmp = t_1
    else if (z <= (-1.18d-67)) then
        tmp = t_2
    else if (z <= 5.2d+37) 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 - (z * y)) / t;
	double t_2 = x / (t - (z * a));
	double tmp;
	if (z <= -8.2e+93) {
		tmp = y / a;
	} else if (z <= -5.6e+51) {
		tmp = t_2;
	} else if (z <= -1.55e+33) {
		tmp = y / a;
	} else if (z <= -8.2e-7) {
		tmp = t_1;
	} else if (z <= -1.18e-67) {
		tmp = t_2;
	} else if (z <= 5.2e+37) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (z * y)) / t
	t_2 = x / (t - (z * a))
	tmp = 0
	if z <= -8.2e+93:
		tmp = y / a
	elif z <= -5.6e+51:
		tmp = t_2
	elif z <= -1.55e+33:
		tmp = y / a
	elif z <= -8.2e-7:
		tmp = t_1
	elif z <= -1.18e-67:
		tmp = t_2
	elif z <= 5.2e+37:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(z * y)) / t)
	t_2 = Float64(x / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (z <= -8.2e+93)
		tmp = Float64(y / a);
	elseif (z <= -5.6e+51)
		tmp = t_2;
	elseif (z <= -1.55e+33)
		tmp = Float64(y / a);
	elseif (z <= -8.2e-7)
		tmp = t_1;
	elseif (z <= -1.18e-67)
		tmp = t_2;
	elseif (z <= 5.2e+37)
		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 - (z * y)) / t;
	t_2 = x / (t - (z * a));
	tmp = 0.0;
	if (z <= -8.2e+93)
		tmp = y / a;
	elseif (z <= -5.6e+51)
		tmp = t_2;
	elseif (z <= -1.55e+33)
		tmp = y / a;
	elseif (z <= -8.2e-7)
		tmp = t_1;
	elseif (z <= -1.18e-67)
		tmp = t_2;
	elseif (z <= 5.2e+37)
		tmp = t_1;
	else
		tmp = y / a;
	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[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.2e+93], N[(y / a), $MachinePrecision], If[LessEqual[z, -5.6e+51], t$95$2, If[LessEqual[z, -1.55e+33], N[(y / a), $MachinePrecision], If[LessEqual[z, -8.2e-7], t$95$1, If[LessEqual[z, -1.18e-67], t$95$2, If[LessEqual[z, 5.2e+37], t$95$1, N[(y / a), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.2000000000000002e93 or -5.60000000000000009e51 < z < -1.55e33 or 5.1999999999999998e37 < z

   1. Initial program 59.4%

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

      1. *-commutative 59.4%

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

   3. Simplified 59.4%

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

   4. Taylor expanded in z around inf 67.4%

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

   if -8.2000000000000002e93 < z < -5.60000000000000009e51 or -8.1999999999999998e-7 < z < -1.18e-67

   1. Initial program 89.7%

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

      1. *-commutative 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in x around inf 84.6%

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

      1. *-commutative 84.6%

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

   6. Simplified 84.6%

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

   if -1.55e33 < z < -8.1999999999999998e-7 or -1.18e-67 < z < 5.1999999999999998e37

   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 82.5%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+93}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{+51}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-7}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+37}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 3: 55.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+98}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+50}:\\ \;\;\;\;\frac{\frac{-x}{z}}{a}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-86}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{y}{t} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.2e+98)
   (/ y a)
   (if (<= z -4.6e+50)
     (/ (/ (- x) z) a)
     (if (<= z -1.2e+33)
       (/ y a)
       (if (<= z 6.1e-86)
         (/ x t)
         (if (<= z 5.5e-11) (* (/ y t) (- z)) (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e+98) {
		tmp = y / a;
	} else if (z <= -4.6e+50) {
		tmp = (-x / z) / a;
	} else if (z <= -1.2e+33) {
		tmp = y / a;
	} else if (z <= 6.1e-86) {
		tmp = x / t;
	} else if (z <= 5.5e-11) {
		tmp = (y / t) * -z;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.2d+98)) then
        tmp = y / a
    else if (z <= (-4.6d+50)) then
        tmp = (-x / z) / a
    else if (z <= (-1.2d+33)) then
        tmp = y / a
    else if (z <= 6.1d-86) then
        tmp = x / t
    else if (z <= 5.5d-11) then
        tmp = (y / t) * -z
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e+98) {
		tmp = y / a;
	} else if (z <= -4.6e+50) {
		tmp = (-x / z) / a;
	} else if (z <= -1.2e+33) {
		tmp = y / a;
	} else if (z <= 6.1e-86) {
		tmp = x / t;
	} else if (z <= 5.5e-11) {
		tmp = (y / t) * -z;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.2e+98:
		tmp = y / a
	elif z <= -4.6e+50:
		tmp = (-x / z) / a
	elif z <= -1.2e+33:
		tmp = y / a
	elif z <= 6.1e-86:
		tmp = x / t
	elif z <= 5.5e-11:
		tmp = (y / t) * -z
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.2e+98)
		tmp = Float64(y / a);
	elseif (z <= -4.6e+50)
		tmp = Float64(Float64(Float64(-x) / z) / a);
	elseif (z <= -1.2e+33)
		tmp = Float64(y / a);
	elseif (z <= 6.1e-86)
		tmp = Float64(x / t);
	elseif (z <= 5.5e-11)
		tmp = Float64(Float64(y / t) * Float64(-z));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.2e+98)
		tmp = y / a;
	elseif (z <= -4.6e+50)
		tmp = (-x / z) / a;
	elseif (z <= -1.2e+33)
		tmp = y / a;
	elseif (z <= 6.1e-86)
		tmp = x / t;
	elseif (z <= 5.5e-11)
		tmp = (y / t) * -z;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.2e+98], N[(y / a), $MachinePrecision], If[LessEqual[z, -4.6e+50], N[(N[((-x) / z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, -1.2e+33], N[(y / a), $MachinePrecision], If[LessEqual[z, 6.1e-86], N[(x / t), $MachinePrecision], If[LessEqual[z, 5.5e-11], N[(N[(y / t), $MachinePrecision] * (-z)), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1999999999999999e98 or -4.59999999999999994e50 < z < -1.2e33 or 5.49999999999999975e-11 < z

   1. Initial program 61.2%

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

      1. *-commutative 61.2%

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

   3. Simplified 61.2%

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

   4. Taylor expanded in z around inf 65.5%

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

   if -1.1999999999999999e98 < z < -4.59999999999999994e50

   1. Initial program 83.9%

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

      1. *-commutative 83.9%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in z around inf 51.1%

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

      1. +-commutative 51.1%

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

      2. associate--l+ 51.1%

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

      3. associate-/r* 59.0%

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

      4. associate-*r/ 59.0%

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

      5. associate-/r* 59.0%

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

      6. associate-*r/ 59.0%

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

      7. div-sub 59.0%

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

      8. distribute-lft-out-- 59.0%

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

      9. associate-*r/ 59.0%

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

      10. mul-1-neg 59.0%

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

      11. unsub-neg 59.0%

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

   6. Simplified 67.3%

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

   7. Taylor expanded in a around inf 67.4%

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

   8. Taylor expanded in y around 0 67.3%

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

      1. associate-*r/ 67.3%

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

      2. neg-mul-1 67.3%

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

   10. Simplified 67.3%

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

   if -1.2e33 < z < 6.10000000000000032e-86

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 64.9%

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

   if 6.10000000000000032e-86 < z < 5.49999999999999975e-11

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 67.3%

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

   5. Taylor expanded in x around 0 55.4%

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

      1. mul-1-neg 55.4%

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

      2. associate-/l* 55.2%

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

   7. Simplified 55.2%

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

      1. associate-/r/ 55.4%

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

   9. Applied egg-rr 55.4%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+98}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+50}:\\ \;\;\;\;\frac{\frac{-x}{z}}{a}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-86}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{y}{t} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 4: 72.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - z \cdot y}{t}\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-68}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* z y)) t)) (t_2 (/ (- y (/ x z)) a)))
   (if (<= z -1.4e+33)
     t_2
     (if (<= z -7.2e-7)
       t_1
       (if (<= z -5e-68) (/ x (- t (* z a))) (if (<= z 9.8e-20) t_1 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 <= -1.4e+33) {
		tmp = t_2;
	} else if (z <= -7.2e-7) {
		tmp = t_1;
	} else if (z <= -5e-68) {
		tmp = x / (t - (z * a));
	} else if (z <= 9.8e-20) {
		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 - (z * y)) / t
    t_2 = (y - (x / z)) / a
    if (z <= (-1.4d+33)) then
        tmp = t_2
    else if (z <= (-7.2d-7)) then
        tmp = t_1
    else if (z <= (-5d-68)) then
        tmp = x / (t - (z * a))
    else if (z <= 9.8d-20) 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 - (z * y)) / t;
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.4e+33) {
		tmp = t_2;
	} else if (z <= -7.2e-7) {
		tmp = t_1;
	} else if (z <= -5e-68) {
		tmp = x / (t - (z * a));
	} else if (z <= 9.8e-20) {
		tmp = t_1;
	} 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 <= -1.4e+33:
		tmp = t_2
	elif z <= -7.2e-7:
		tmp = t_1
	elif z <= -5e-68:
		tmp = x / (t - (z * a))
	elif z <= 9.8e-20:
		tmp = t_1
	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 <= -1.4e+33)
		tmp = t_2;
	elseif (z <= -7.2e-7)
		tmp = t_1;
	elseif (z <= -5e-68)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 9.8e-20)
		tmp = t_1;
	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 <= -1.4e+33)
		tmp = t_2;
	elseif (z <= -7.2e-7)
		tmp = t_1;
	elseif (z <= -5e-68)
		tmp = x / (t - (z * a));
	elseif (z <= 9.8e-20)
		tmp = t_1;
	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, -1.4e+33], t$95$2, If[LessEqual[z, -7.2e-7], t$95$1, If[LessEqual[z, -5e-68], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.8e-20], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4e33 or 9.8000000000000003e-20 < z

   1. Initial program 63.9%

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

      1. *-commutative 63.9%

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

   3. Simplified 63.9%

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

   4. Taylor expanded in z around inf 62.8%

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

      1. +-commutative 62.8%

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

      2. associate--l+ 62.8%

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

      3. associate-/r* 63.9%

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

      4. associate-*r/ 63.9%

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

      5. associate-/r* 64.0%

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

      6. associate-*r/ 64.0%

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

      7. div-sub 64.0%

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

      8. distribute-lft-out-- 64.0%

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

      9. associate-*r/ 64.0%

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

      10. mul-1-neg 64.0%

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

      11. unsub-neg 64.0%

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

   6. Simplified 70.2%

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

   7. Taylor expanded in a around inf 78.2%

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

   if -1.4e33 < z < -7.19999999999999989e-7 or -4.99999999999999971e-68 < z < 9.8000000000000003e-20

   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 84.7%

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

   if -7.19999999999999989e-7 < z < -4.99999999999999971e-68

   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 x around inf 99.8%

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

      1. *-commutative 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+33}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-7}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-68}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-20}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 5: 55.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-86}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-11}:\\ \;\;\;\;\frac{y}{t} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.05e+33)
   (/ y a)
   (if (<= z 3.8e-86) (/ x t) (if (<= z 2.65e-11) (* (/ y t) (- z)) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+33) {
		tmp = y / a;
	} else if (z <= 3.8e-86) {
		tmp = x / t;
	} else if (z <= 2.65e-11) {
		tmp = (y / t) * -z;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.05d+33)) then
        tmp = y / a
    else if (z <= 3.8d-86) then
        tmp = x / t
    else if (z <= 2.65d-11) then
        tmp = (y / t) * -z
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+33) {
		tmp = y / a;
	} else if (z <= 3.8e-86) {
		tmp = x / t;
	} else if (z <= 2.65e-11) {
		tmp = (y / t) * -z;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.05e+33:
		tmp = y / a
	elif z <= 3.8e-86:
		tmp = x / t
	elif z <= 2.65e-11:
		tmp = (y / t) * -z
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.05e+33)
		tmp = Float64(y / a);
	elseif (z <= 3.8e-86)
		tmp = Float64(x / t);
	elseif (z <= 2.65e-11)
		tmp = Float64(Float64(y / t) * Float64(-z));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.05e+33)
		tmp = y / a;
	elseif (z <= 3.8e-86)
		tmp = x / t;
	elseif (z <= 2.65e-11)
		tmp = (y / t) * -z;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.05e+33], N[(y / a), $MachinePrecision], If[LessEqual[z, 3.8e-86], N[(x / t), $MachinePrecision], If[LessEqual[z, 2.65e-11], N[(N[(y / t), $MachinePrecision] * (-z)), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05e33 or 2.6499999999999999e-11 < z

   1. Initial program 63.3%

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

      1. *-commutative 63.3%

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

   3. Simplified 63.3%

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

   4. Taylor expanded in z around inf 62.0%

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

   if -1.05e33 < z < 3.8e-86

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 64.9%

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

   if 3.8e-86 < z < 2.6499999999999999e-11

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 67.3%

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

   5. Taylor expanded in x around 0 55.4%

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

      1. mul-1-neg 55.4%

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

      2. associate-/l* 55.2%

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

   7. Simplified 55.2%

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

      1. associate-/r/ 55.4%

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

   9. Applied egg-rr 55.4%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-86}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-11}:\\ \;\;\;\;\frac{y}{t} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 6: 66.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+98} \lor \neg \left(z \leq 4.8 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.4e+98) (not (<= z 4.8e+34))) (/ y a) (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.4e+98) || !(z <= 4.8e+34)) {
		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 <= (-3.4d+98)) .or. (.not. (z <= 4.8d+34))) 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 <= -3.4e+98) || !(z <= 4.8e+34)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.4e+98) or not (z <= 4.8e+34):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.4e+98) || !(z <= 4.8e+34))
		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 <= -3.4e+98) || ~((z <= 4.8e+34)))
		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, -3.4e+98], N[Not[LessEqual[z, 4.8e+34]], $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 < -3.39999999999999972e98 or 4.79999999999999974e34 < z

   1. Initial program 58.0%

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

      1. *-commutative 58.0%

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

   3. Simplified 58.0%

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

   4. Taylor expanded in z around inf 66.6%

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

   if -3.39999999999999972e98 < z < 4.79999999999999974e34

   1. Initial program 98.0%

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

      1. *-commutative 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in x around inf 74.7%

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

      1. *-commutative 74.7%

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

   6. Simplified 74.7%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+98} \lor \neg \left(z \leq 4.8 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]

Alternative 7: 55.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.35e+33) (/ y a) (if (<= z 1.5e+26) (/ x t) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e+33) {
		tmp = y / a;
	} else if (z <= 1.5e+26) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.35d+33)) then
        tmp = y / a
    else if (z <= 1.5d+26) then
        tmp = x / t
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e+33) {
		tmp = y / a;
	} else if (z <= 1.5e+26) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.35e+33:
		tmp = y / a
	elif z <= 1.5e+26:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.35e+33)
		tmp = Float64(y / a);
	elseif (z <= 1.5e+26)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.35e+33)
		tmp = y / a;
	elseif (z <= 1.5e+26)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.35e+33], N[(y / a), $MachinePrecision], If[LessEqual[z, 1.5e+26], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.34999999999999996e33 or 1.49999999999999999e26 < z

   1. Initial program 61.8%

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

      1. *-commutative 61.8%

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

   3. Simplified 61.8%

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

   4. Taylor expanded in z around inf 63.5%

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

   if -1.34999999999999996e33 < z < 1.49999999999999999e26

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 59.2%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 8: 36.5% 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 81.9%

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

   1. *-commutative 81.9%

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

3. Simplified 81.9%

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

4. Taylor expanded in z around 0 35.2%

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

5. Final simplification 35.2%

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

Developer target: 97.7% 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 2023290 
(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))))