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

Percentage Accurate: 95.8% → 99.7%

Time: 9.6s

Alternatives: 8

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{\frac{-1}{\frac{z}{x}}}{t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+242}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) (- INFINITY))
   (/ (/ -1.0 (/ z x)) t)
   (if (<= (* z t) 2e+242) (/ x (- y (* z t))) (/ (/ x (- t)) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -((double) INFINITY)) {
		tmp = (-1.0 / (z / x)) / t;
	} else if ((z * t) <= 2e+242) {
		tmp = x / (y - (z * t));
	} else {
		tmp = (x / -t) / z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -Double.POSITIVE_INFINITY) {
		tmp = (-1.0 / (z / x)) / t;
	} else if ((z * t) <= 2e+242) {
		tmp = x / (y - (z * t));
	} else {
		tmp = (x / -t) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -math.inf:
		tmp = (-1.0 / (z / x)) / t
	elif (z * t) <= 2e+242:
		tmp = x / (y - (z * t))
	else:
		tmp = (x / -t) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= Float64(-Inf))
		tmp = Float64(Float64(-1.0 / Float64(z / x)) / t);
	elseif (Float64(z * t) <= 2e+242)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = Float64(Float64(x / Float64(-t)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -Inf)
		tmp = (-1.0 / (z / x)) / t;
	elseif ((z * t) <= 2e+242)
		tmp = x / (y - (z * t));
	else
		tmp = (x / -t) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], (-Infinity)], N[(N[(-1.0 / N[(z / x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e+242], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / (-t)), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -inf.0

   1. Initial program 71.0%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 99.9%

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

   4. Taylor expanded in z around inf 99.9%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

   6. Applied egg-rr 100.0%

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

      1. unpow-1 100.0%

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

   8. Simplified 100.0%

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

   if -inf.0 < (*.f64 z t) < 2.0000000000000001e242

   1. Initial program 99.9%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   if 2.0000000000000001e242 < (*.f64 z t)

   1. Initial program 59.2%

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

      1. clear-num 59.3%

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

      2. inv-pow 59.3%

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

   4. Applied egg-rr 59.3%

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

   5. Taylor expanded in t around inf 94.7%

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

      1. +-commutative 94.7%

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

      2. mul-1-neg 94.7%

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

      3. unsub-neg 94.7%

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

      4. *-commutative 94.7%

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

   7. Simplified 94.7%

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

   8. Taylor expanded in t around inf 59.2%

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

      1. neg-mul-1 59.2%

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

      2. associate-/r* 99.9%

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

      3. distribute-frac-neg 99.9%

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

      4. distribute-neg-frac2 99.9%

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

   10. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{\frac{-1}{\frac{z}{x}}}{t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+242}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 66.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-203}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+160}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2e-203)
   (/ (/ x z) (- t))
   (if (<= t 2.9e+59)
     (/ x y)
     (if (<= t 2.6e+160) (/ x (* z (- t))) (/ (/ x (- t)) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2e-203) {
		tmp = (x / z) / -t;
	} else if (t <= 2.9e+59) {
		tmp = x / y;
	} else if (t <= 2.6e+160) {
		tmp = x / (z * -t);
	} else {
		tmp = (x / -t) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2d-203)) then
        tmp = (x / z) / -t
    else if (t <= 2.9d+59) then
        tmp = x / y
    else if (t <= 2.6d+160) then
        tmp = x / (z * -t)
    else
        tmp = (x / -t) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2e-203) {
		tmp = (x / z) / -t;
	} else if (t <= 2.9e+59) {
		tmp = x / y;
	} else if (t <= 2.6e+160) {
		tmp = x / (z * -t);
	} else {
		tmp = (x / -t) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2e-203:
		tmp = (x / z) / -t
	elif t <= 2.9e+59:
		tmp = x / y
	elif t <= 2.6e+160:
		tmp = x / (z * -t)
	else:
		tmp = (x / -t) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2e-203)
		tmp = Float64(Float64(x / z) / Float64(-t));
	elseif (t <= 2.9e+59)
		tmp = Float64(x / y);
	elseif (t <= 2.6e+160)
		tmp = Float64(x / Float64(z * Float64(-t)));
	else
		tmp = Float64(Float64(x / Float64(-t)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2e-203)
		tmp = (x / z) / -t;
	elseif (t <= 2.9e+59)
		tmp = x / y;
	elseif (t <= 2.6e+160)
		tmp = x / (z * -t);
	else
		tmp = (x / -t) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2e-203], N[(N[(x / z), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[t, 2.9e+59], N[(x / y), $MachinePrecision], If[LessEqual[t, 2.6e+160], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], N[(N[(x / (-t)), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.0000000000000001e-203

   1. Initial program 95.5%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 38.1%

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

   4. Taylor expanded in z around inf 49.6%

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

      1. mul-1-neg 49.6%

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

      2. distribute-neg-frac2 49.6%

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

   6. Applied egg-rr 49.6%

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

   if -2.0000000000000001e-203 < t < 2.89999999999999991e59

   1. Initial program 99.0%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 71.1%

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

   if 2.89999999999999991e59 < t < 2.6e160

   1. Initial program 92.2%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 73.3%

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

      1. associate-*r/ 73.3%

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

      2. neg-mul-1 73.3%

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

   5. Simplified 73.3%

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

   if 2.6e160 < t

   1. Initial program 73.2%

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

      1. clear-num 73.0%

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

      2. inv-pow 73.0%

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

   4. Applied egg-rr 73.0%

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

   5. Taylor expanded in t around inf 88.5%

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

      1. +-commutative 88.5%

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

      2. mul-1-neg 88.5%

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

      3. unsub-neg 88.5%

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

      4. *-commutative 88.5%

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

   7. Simplified 88.5%

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

   8. Taylor expanded in t around inf 64.4%

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

      1. neg-mul-1 64.4%

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

      2. associate-/r* 89.7%

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

      3. distribute-frac-neg 89.7%

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

      4. distribute-neg-frac2 89.7%

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

   10. Simplified 89.7%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-203}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+160}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+242}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) (- INFINITY))
   (/ (/ x z) (- t))
   (if (<= (* z t) 2e+242) (/ x (- y (* z t))) (/ (/ x (- t)) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -((double) INFINITY)) {
		tmp = (x / z) / -t;
	} else if ((z * t) <= 2e+242) {
		tmp = x / (y - (z * t));
	} else {
		tmp = (x / -t) / z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -Double.POSITIVE_INFINITY) {
		tmp = (x / z) / -t;
	} else if ((z * t) <= 2e+242) {
		tmp = x / (y - (z * t));
	} else {
		tmp = (x / -t) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -math.inf:
		tmp = (x / z) / -t
	elif (z * t) <= 2e+242:
		tmp = x / (y - (z * t))
	else:
		tmp = (x / -t) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= Float64(-Inf))
		tmp = Float64(Float64(x / z) / Float64(-t));
	elseif (Float64(z * t) <= 2e+242)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = Float64(Float64(x / Float64(-t)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -Inf)
		tmp = (x / z) / -t;
	elseif ((z * t) <= 2e+242)
		tmp = x / (y - (z * t));
	else
		tmp = (x / -t) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], (-Infinity)], N[(N[(x / z), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e+242], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / (-t)), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -inf.0

   1. Initial program 71.0%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 99.9%

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

   4. Taylor expanded in z around inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-neg-frac2 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -inf.0 < (*.f64 z t) < 2.0000000000000001e242

   1. Initial program 99.9%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   if 2.0000000000000001e242 < (*.f64 z t)

   1. Initial program 59.2%

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

      1. clear-num 59.3%

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

      2. inv-pow 59.3%

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

   4. Applied egg-rr 59.3%

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

   5. Taylor expanded in t around inf 94.7%

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

      1. +-commutative 94.7%

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

      2. mul-1-neg 94.7%

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

      3. unsub-neg 94.7%

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

      4. *-commutative 94.7%

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

   7. Simplified 94.7%

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

   8. Taylor expanded in t around inf 59.2%

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

      1. neg-mul-1 59.2%

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

      2. associate-/r* 99.9%

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

      3. distribute-frac-neg 99.9%

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

      4. distribute-neg-frac2 99.9%

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

   10. Simplified 99.9%

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

Alternative 4: 66.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-203} \lor \neg \left(t \leq 8.8 \cdot 10^{+59}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2e-203) (not (<= t 8.8e+59))) (/ (/ x z) (- t)) (/ x y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2e-203) || !(t <= 8.8e+59)) {
		tmp = (x / z) / -t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2d-203)) .or. (.not. (t <= 8.8d+59))) then
        tmp = (x / z) / -t
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2e-203) || !(t <= 8.8e+59)) {
		tmp = (x / z) / -t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2e-203) or not (t <= 8.8e+59):
		tmp = (x / z) / -t
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2e-203) || !(t <= 8.8e+59))
		tmp = Float64(Float64(x / z) / Float64(-t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2e-203) || ~((t <= 8.8e+59)))
		tmp = (x / z) / -t;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2e-203], N[Not[LessEqual[t, 8.8e+59]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / (-t)), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.0000000000000001e-203 or 8.7999999999999998e59 < t

   1. Initial program 90.9%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 46.8%

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

   4. Taylor expanded in z around inf 59.8%

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

      1. mul-1-neg 59.8%

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

      2. distribute-neg-frac2 59.8%

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

   6. Applied egg-rr 59.8%

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

   if -2.0000000000000001e-203 < t < 8.7999999999999998e59

   1. Initial program 99.0%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 71.1%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-203} \lor \neg \left(t \leq 8.8 \cdot 10^{+59}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-11}:\\ \;\;\;\;\frac{1}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-34}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.9e-11)
   (/ 1.0 (/ y x))
   (if (<= y 4.4e-34) (/ x (* z (- t))) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.9e-11) {
		tmp = 1.0 / (y / x);
	} else if (y <= 4.4e-34) {
		tmp = x / (z * -t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.9d-11)) then
        tmp = 1.0d0 / (y / x)
    else if (y <= 4.4d-34) then
        tmp = x / (z * -t)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.9e-11) {
		tmp = 1.0 / (y / x);
	} else if (y <= 4.4e-34) {
		tmp = x / (z * -t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.9e-11:
		tmp = 1.0 / (y / x)
	elif y <= 4.4e-34:
		tmp = x / (z * -t)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.9e-11)
		tmp = Float64(1.0 / Float64(y / x));
	elseif (y <= 4.4e-34)
		tmp = Float64(x / Float64(z * Float64(-t)));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.9e-11)
		tmp = 1.0 / (y / x);
	elseif (y <= 4.4e-34)
		tmp = x / (z * -t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.9e-11], N[(1.0 / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.4e-34], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9000000000000001e-11

   1. Initial program 93.7%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 75.7%

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

      1. clear-num 76.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}}} \]

      2. inv-pow 76.9%

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

   5. Applied egg-rr 76.9%

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

      1. unpow-1 76.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}}} \]

   7. Simplified 76.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}}} \]

   if -3.9000000000000001e-11 < y < 4.3999999999999998e-34

   1. Initial program 94.3%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 69.9%

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

      1. associate-*r/ 69.9%

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

      2. neg-mul-1 69.9%

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

   5. Simplified 69.9%

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

   if 4.3999999999999998e-34 < y

   1. Initial program 93.7%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 79.2%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-11}:\\ \;\;\;\;\frac{1}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-34}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2300000000000 \lor \neg \left(t \leq 2.4 \cdot 10^{+240}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2300000000000.0) (not (<= t 2.4e+240))) (/ x (* z t)) (/ x y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2300000000000.0) || !(t <= 2.4e+240)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2300000000000.0d0)) .or. (.not. (t <= 2.4d+240))) then
        tmp = x / (z * t)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2300000000000.0) || !(t <= 2.4e+240)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2300000000000.0) or not (t <= 2.4e+240):
		tmp = x / (z * t)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2300000000000.0) || !(t <= 2.4e+240))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2300000000000.0) || ~((t <= 2.4e+240)))
		tmp = x / (z * t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2300000000000.0], N[Not[LessEqual[t, 2.4e+240]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.3e12 or 2.3999999999999999e240 < t

   1. Initial program 90.3%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 59.4%

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

      1. associate-*r/ 59.4%

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

      2. neg-mul-1 59.4%

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

   5. Simplified 59.4%

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

      1. neg-sub0 59.4%

         \[\leadsto \frac{\color{blue}{0 - x}}{t \cdot z} \]

      2. sub-neg 59.4%

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

      3. add-sqr-sqrt 33.3%

         \[\leadsto \frac{0 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{t \cdot z} \]

      4. sqrt-unprod 44.8%

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

      5. sqr-neg 44.8%

         \[\leadsto \frac{0 + \sqrt{\color{blue}{x \cdot x}}}{t \cdot z} \]

      6. sqrt-unprod 14.2%

         \[\leadsto \frac{0 + \color{blue}{\sqrt{x} \cdot \sqrt{x}}}{t \cdot z} \]

      7. add-sqr-sqrt 38.7%

         \[\leadsto \frac{0 + \color{blue}{x}}{t \cdot z} \]

   7. Applied egg-rr 38.7%

      \[\leadsto \frac{\color{blue}{0 + x}}{t \cdot z} \]
   8. Step-by-step derivation

      1. +-lft-identity 38.7%

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

   9. Simplified 38.7%

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

   if -2.3e12 < t < 2.3999999999999999e240

   1. Initial program 95.5%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 60.8%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2300000000000 \lor \neg \left(t \leq 2.4 \cdot 10^{+240}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2300000000000:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{elif}\;t \leq 10^{+108}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2300000000000.0)
   (/ x (* z t))
   (if (<= t 1e+108) (/ x y) (/ (/ x t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2300000000000.0) {
		tmp = x / (z * t);
	} else if (t <= 1e+108) {
		tmp = x / y;
	} else {
		tmp = (x / t) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2300000000000.0d0)) then
        tmp = x / (z * t)
    else if (t <= 1d+108) then
        tmp = x / y
    else
        tmp = (x / t) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2300000000000.0) {
		tmp = x / (z * t);
	} else if (t <= 1e+108) {
		tmp = x / y;
	} else {
		tmp = (x / t) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2300000000000.0:
		tmp = x / (z * t)
	elif t <= 1e+108:
		tmp = x / y
	else:
		tmp = (x / t) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2300000000000.0)
		tmp = Float64(x / Float64(z * t));
	elseif (t <= 1e+108)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(x / t) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2300000000000.0)
		tmp = x / (z * t);
	elseif (t <= 1e+108)
		tmp = x / y;
	else
		tmp = (x / t) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2300000000000.0], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+108], N[(x / y), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.3e12

   1. Initial program 92.3%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 55.8%

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

      1. associate-*r/ 55.8%

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

      2. neg-mul-1 55.8%

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

   5. Simplified 55.8%

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

      1. neg-sub0 55.8%

         \[\leadsto \frac{\color{blue}{0 - x}}{t \cdot z} \]

      2. sub-neg 55.8%

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

      3. add-sqr-sqrt 32.8%

         \[\leadsto \frac{0 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{t \cdot z} \]

      4. sqrt-unprod 41.7%

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

      5. sqr-neg 41.7%

         \[\leadsto \frac{0 + \sqrt{\color{blue}{x \cdot x}}}{t \cdot z} \]

      6. sqrt-unprod 9.7%

         \[\leadsto \frac{0 + \color{blue}{\sqrt{x} \cdot \sqrt{x}}}{t \cdot z} \]

      7. add-sqr-sqrt 34.6%

         \[\leadsto \frac{0 + \color{blue}{x}}{t \cdot z} \]

   7. Applied egg-rr 34.6%

      \[\leadsto \frac{\color{blue}{0 + x}}{t \cdot z} \]
   8. Step-by-step derivation

      1. +-lft-identity 34.6%

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

   9. Simplified 34.6%

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

   if -2.3e12 < t < 1e108

   1. Initial program 99.3%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 68.1%

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

   if 1e108 < t

   1. Initial program 76.4%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 66.0%

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

   4. Taylor expanded in z around inf 84.3%

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

      1. mul-1-neg 84.3%

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

      2. associate-/l/ 67.9%

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

      3. distribute-frac-neg 67.9%

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

      4. associate-/r* 85.7%

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

      5. add-sqr-sqrt 41.3%

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

      6. sqrt-unprod 47.7%

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

      7. sqr-neg 47.7%

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

      8. sqrt-unprod 20.6%

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

      9. add-sqr-sqrt 36.4%

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

   6. Applied egg-rr 36.4%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2300000000000:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{elif}\;t \leq 10^{+108}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ x y))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(x / y), $MachinePrecision]

Derivation

1. Initial program 94.0%

   \[\frac{x}{y - z \cdot t} \]
2. Add Preprocessing

3. Taylor expanded in y around inf 54.2%

   \[\leadsto \color{blue}{\frac{x}{y}} \]
4. Add Preprocessing

Developer Target 1: 96.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{if}\;x < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x < 2.1378306434876444 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 1.0 (- (/ y x) (* (/ z x) t)))))
   (if (< x -1.618195973607049e+50)
     t_1
     (if (< x 2.1378306434876444e+131) (/ x (- y (* z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / ((y / x) - ((z / x) * t));
	double tmp;
	if (x < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (x < 2.1378306434876444e+131) {
		tmp = x / (y - (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 / ((y / x) - ((z / x) * t))
    if (x < (-1.618195973607049d+50)) then
        tmp = t_1
    else if (x < 2.1378306434876444d+131) then
        tmp = x / (y - (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / ((y / x) - ((z / x) * t));
	double tmp;
	if (x < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (x < 2.1378306434876444e+131) {
		tmp = x / (y - (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 / ((y / x) - ((z / x) * t))
	tmp = 0
	if x < -1.618195973607049e+50:
		tmp = t_1
	elif x < 2.1378306434876444e+131:
		tmp = x / (y - (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 / Float64(Float64(y / x) - Float64(Float64(z / x) * t)))
	tmp = 0.0
	if (x < -1.618195973607049e+50)
		tmp = t_1;
	elseif (x < 2.1378306434876444e+131)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 / ((y / x) - ((z / x) * t));
	tmp = 0.0;
	if (x < -1.618195973607049e+50)
		tmp = t_1;
	elseif (x < 2.1378306434876444e+131)
		tmp = x / (y - (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 / N[(N[(y / x), $MachinePrecision] - N[(N[(z / x), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[x, -1.618195973607049e+50], t$95$1, If[Less[x, 2.1378306434876444e+131], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024133 
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -161819597360704900000000000000000000000000000000000) (/ 1 (- (/ y x) (* (/ z x) t))) (if (< x 213783064348764440000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ x (- y (* z t))) (/ 1 (- (/ y x) (* (/ z x) t))))))

  (/ x (- y (* z t))))