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

Percentage Accurate: 96.0% → 99.6%

Time: 10.0s

Alternatives: 7

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: 96.0% 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: 99.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+226}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(z, -t, y\right)}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) (- INFINITY))
   (/ (/ x z) (- t))
   (if (<= (* z t) 2e+226) (/ x (fma z (- t) y)) (- (/ (/ x t) z)))))

C

assert(x < y && y < z && z < t);
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+226) {
		tmp = x / fma(z, -t, y);
	} else {
		tmp = -((x / t) / z);
	}
	return tmp;
}

Julia

x, y, z, t = sort([x, y, z, t])
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+226)
		tmp = Float64(x / fma(z, Float64(-t), y));
	else
		tmp = Float64(-Float64(Float64(x / t) / z));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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+226], N[(x / N[(z * (-t) + y), $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 50.5%

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

   3. Taylor expanded in t around inf 99.9%

      \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x}{z} + -1 \cdot \frac{x \cdot y}{t \cdot {z}^{2}}}{t}} \]
   4. Step-by-step derivation

      1. distribute-lft-out 99.9%

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

      2. associate-*r/ 99.9%

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

      3. mul-1-neg 99.9%

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

      4. associate-/l* 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around inf 99.9%

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

   if -inf.0 < (*.f64 z t) < 1.99999999999999992e226

   1. Initial program 99.8%

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

      1. cancel-sign-sub-inv 99.8%

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

      2. +-commutative 99.8%

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

      3. distribute-lft-neg-out 99.8%

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

      4. distribute-rgt-neg-out 99.8%

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

      5. fma-define 99.8%

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

   3. Simplified 99.8%

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

   if 1.99999999999999992e226 < (*.f64 z t)

   1. Initial program 63.2%

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

      1. cancel-sign-sub-inv 63.2%

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

      2. +-commutative 63.2%

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

      3. distribute-lft-neg-out 63.2%

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

      4. distribute-rgt-neg-out 63.2%

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

      5. fma-define 63.2%

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

   3. Simplified 63.2%

      \[\leadsto \color{blue}{\frac{x}{\mathsf{fma}\left(z, -t, y\right)}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-cube-cbrt 62.8%

         \[\leadsto \frac{x}{\mathsf{fma}\left(z, -\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}, y\right)} \]

      2. distribute-rgt-neg-in 62.8%

         \[\leadsto \frac{x}{\mathsf{fma}\left(z, \color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(-\sqrt[3]{t}\right)}, y\right)} \]

      3. pow2 62.8%

         \[\leadsto \frac{x}{\mathsf{fma}\left(z, \color{blue}{{\left(\sqrt[3]{t}\right)}^{2}} \cdot \left(-\sqrt[3]{t}\right), y\right)} \]

   6. Applied egg-rr 62.8%

      \[\leadsto \frac{x}{\mathsf{fma}\left(z, \color{blue}{{\left(\sqrt[3]{t}\right)}^{2} \cdot \left(-\sqrt[3]{t}\right)}, y\right)} \]

   7. Taylor expanded in z around inf 83.0%

      \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x}{t} + -1 \cdot \frac{x \cdot y}{{t}^{2} \cdot z}}{z}} \]
   8. Step-by-step derivation

      1. +-commutative 83.0%

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

      2. mul-1-neg 83.0%

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

      3. sub-neg 83.0%

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

      4. associate-*r/ 83.0%

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

      5. neg-mul-1 83.0%

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

      6. distribute-rgt-neg-in 83.0%

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

      7. *-commutative 83.0%

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

   9. Simplified 83.0%

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

   10. Taylor expanded in y around 0 99.7%

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

       1. neg-mul-1 99.7%

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

       2. distribute-neg-frac 99.7%

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

   12. Simplified 99.7%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+226}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(z, -t, y\right)}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\frac{x}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+226}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) (- INFINITY))
   (/ (/ x z) (- t))
   (if (<= (* z t) 2e+226) (/ x (- y (* z t))) (- (/ (/ x t) z)))))

C

assert(x < y && y < z && z < t);
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+226) {
		tmp = x / (y - (z * t));
	} else {
		tmp = -((x / t) / z);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t;
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+226) {
		tmp = x / (y - (z * t));
	} else {
		tmp = -((x / t) / z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -math.inf:
		tmp = (x / z) / -t
	elif (z * t) <= 2e+226:
		tmp = x / (y - (z * t))
	else:
		tmp = -((x / t) / z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
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+226)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = Float64(-Float64(Float64(x / t) / z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -Inf)
		tmp = (x / z) / -t;
	elseif ((z * t) <= 2e+226)
		tmp = x / (y - (z * t));
	else
		tmp = -((x / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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+226], 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 50.5%

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

   3. Taylor expanded in t around inf 99.9%

      \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x}{z} + -1 \cdot \frac{x \cdot y}{t \cdot {z}^{2}}}{t}} \]
   4. Step-by-step derivation

      1. distribute-lft-out 99.9%

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

      2. associate-*r/ 99.9%

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

      3. mul-1-neg 99.9%

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

      4. associate-/l* 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around inf 99.9%

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

   if -inf.0 < (*.f64 z t) < 1.99999999999999992e226

   1. Initial program 99.8%

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

   if 1.99999999999999992e226 < (*.f64 z t)

   1. Initial program 63.2%

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

      1. cancel-sign-sub-inv 63.2%

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

      2. +-commutative 63.2%

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

      3. distribute-lft-neg-out 63.2%

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

      4. distribute-rgt-neg-out 63.2%

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

      5. fma-define 63.2%

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

   3. Simplified 63.2%

      \[\leadsto \color{blue}{\frac{x}{\mathsf{fma}\left(z, -t, y\right)}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-cube-cbrt 62.8%

         \[\leadsto \frac{x}{\mathsf{fma}\left(z, -\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}, y\right)} \]

      2. distribute-rgt-neg-in 62.8%

         \[\leadsto \frac{x}{\mathsf{fma}\left(z, \color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(-\sqrt[3]{t}\right)}, y\right)} \]

      3. pow2 62.8%

         \[\leadsto \frac{x}{\mathsf{fma}\left(z, \color{blue}{{\left(\sqrt[3]{t}\right)}^{2}} \cdot \left(-\sqrt[3]{t}\right), y\right)} \]

   6. Applied egg-rr 62.8%

      \[\leadsto \frac{x}{\mathsf{fma}\left(z, \color{blue}{{\left(\sqrt[3]{t}\right)}^{2} \cdot \left(-\sqrt[3]{t}\right)}, y\right)} \]

   7. Taylor expanded in z around inf 83.0%

      \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x}{t} + -1 \cdot \frac{x \cdot y}{{t}^{2} \cdot z}}{z}} \]
   8. Step-by-step derivation

      1. +-commutative 83.0%

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

      2. mul-1-neg 83.0%

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

      3. sub-neg 83.0%

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

      4. associate-*r/ 83.0%

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

      5. neg-mul-1 83.0%

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

      6. distribute-rgt-neg-in 83.0%

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

      7. *-commutative 83.0%

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

   9. Simplified 83.0%

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

   10. Taylor expanded in y around 0 99.7%

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

       1. neg-mul-1 99.7%

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

       2. distribute-neg-frac 99.7%

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

   12. Simplified 99.7%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+226}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\frac{x}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{-57} \lor \neg \left(t \leq 3800\right):\\ \;\;\;\;-\frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.22e-57) (not (<= t 3800.0))) (- (/ (/ x t) z)) (/ x y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.22e-57) || !(t <= 3800.0)) {
		tmp = -((x / t) / z);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-1.22d-57)) .or. (.not. (t <= 3800.0d0))) then
        tmp = -((x / t) / z)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.22e-57) || !(t <= 3800.0)) {
		tmp = -((x / t) / z);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (t <= -1.22e-57) or not (t <= 3800.0):
		tmp = -((x / t) / z)
	else:
		tmp = x / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.22e-57) || !(t <= 3800.0))
		tmp = Float64(-Float64(Float64(x / t) / z));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.22e-57) || ~((t <= 3800.0)))
		tmp = -((x / t) / z);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.22e-57], N[Not[LessEqual[t, 3800.0]], $MachinePrecision]], (-N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2200000000000001e-57 or 3800 < t

   1. Initial program 88.1%

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

      1. cancel-sign-sub-inv 88.1%

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

      2. +-commutative 88.1%

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

      3. distribute-lft-neg-out 88.1%

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

      4. distribute-rgt-neg-out 88.1%

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

      5. fma-define 88.1%

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

   3. Simplified 88.1%

      \[\leadsto \color{blue}{\frac{x}{\mathsf{fma}\left(z, -t, y\right)}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-cube-cbrt 87.5%

         \[\leadsto \frac{x}{\mathsf{fma}\left(z, -\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}, y\right)} \]

      2. distribute-rgt-neg-in 87.5%

         \[\leadsto \frac{x}{\mathsf{fma}\left(z, \color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(-\sqrt[3]{t}\right)}, y\right)} \]

      3. pow2 87.5%

         \[\leadsto \frac{x}{\mathsf{fma}\left(z, \color{blue}{{\left(\sqrt[3]{t}\right)}^{2}} \cdot \left(-\sqrt[3]{t}\right), y\right)} \]

   6. Applied egg-rr 87.5%

      \[\leadsto \frac{x}{\mathsf{fma}\left(z, \color{blue}{{\left(\sqrt[3]{t}\right)}^{2} \cdot \left(-\sqrt[3]{t}\right)}, y\right)} \]

   7. Taylor expanded in z around inf 62.4%

      \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x}{t} + -1 \cdot \frac{x \cdot y}{{t}^{2} \cdot z}}{z}} \]
   8. Step-by-step derivation

      1. +-commutative 62.4%

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

      2. mul-1-neg 62.4%

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

      3. sub-neg 62.4%

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

      4. associate-*r/ 62.4%

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

      5. neg-mul-1 62.4%

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

      6. distribute-rgt-neg-in 62.4%

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

      7. *-commutative 62.4%

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

   9. Simplified 62.4%

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

   10. Taylor expanded in y around 0 66.3%

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

       1. neg-mul-1 66.3%

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

       2. distribute-neg-frac 66.3%

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

   12. Simplified 66.3%

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

   if -1.2200000000000001e-57 < t < 3800

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 74.5%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{-57} \lor \neg \left(t \leq 3800\right):\\ \;\;\;\;-\frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{-55} \lor \neg \left(t \leq 1150\right):\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.75e-55) (not (<= t 1150.0))) (/ (/ x z) (- t)) (/ x y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.75e-55) || !(t <= 1150.0)) {
		tmp = (x / z) / -t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-2.75d-55)) .or. (.not. (t <= 1150.0d0))) then
        tmp = (x / z) / -t
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.75e-55) || !(t <= 1150.0)) {
		tmp = (x / z) / -t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (t <= -2.75e-55) or not (t <= 1150.0):
		tmp = (x / z) / -t
	else:
		tmp = x / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.75e-55) || !(t <= 1150.0))
		tmp = Float64(Float64(x / z) / Float64(-t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.75e-55) || ~((t <= 1150.0)))
		tmp = (x / z) / -t;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.75e-55], N[Not[LessEqual[t, 1150.0]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / (-t)), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.7499999999999999e-55 or 1150 < t

   1. Initial program 88.0%

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

   3. Taylor expanded in t around inf 48.1%

      \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x}{z} + -1 \cdot \frac{x \cdot y}{t \cdot {z}^{2}}}{t}} \]
   4. Step-by-step derivation

      1. distribute-lft-out 48.1%

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

      2. associate-*r/ 48.1%

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

      3. mul-1-neg 48.1%

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

      4. associate-/l* 50.9%

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

   5. Simplified 50.9%

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

   6. Taylor expanded in z around inf 61.2%

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

   if -2.7499999999999999e-55 < t < 1150

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 73.9%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{-55} \lor \neg \left(t \leq 1150\right):\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-54}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;t \leq 9500:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.4e-54)
   (/ x (* z (- t)))
   (if (<= t 9500.0) (/ x y) (/ (/ x z) (- t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.4e-54) {
		tmp = x / (z * -t);
	} else if (t <= 9500.0) {
		tmp = x / y;
	} else {
		tmp = (x / z) / -t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-1.4d-54)) then
        tmp = x / (z * -t)
    else if (t <= 9500.0d0) then
        tmp = x / y
    else
        tmp = (x / z) / -t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.4e-54) {
		tmp = x / (z * -t);
	} else if (t <= 9500.0) {
		tmp = x / y;
	} else {
		tmp = (x / z) / -t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -1.4e-54:
		tmp = x / (z * -t)
	elif t <= 9500.0:
		tmp = x / y
	else:
		tmp = (x / z) / -t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.4e-54)
		tmp = Float64(x / Float64(z * Float64(-t)));
	elseif (t <= 9500.0)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(x / z) / Float64(-t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.4e-54)
		tmp = x / (z * -t);
	elseif (t <= 9500.0)
		tmp = x / y;
	else
		tmp = (x / z) / -t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -1.4e-54], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9500.0], N[(x / y), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / (-t)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.4000000000000001e-54

   1. Initial program 92.6%

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

   3. Taylor expanded in y around 0 56.4%

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

      1. associate-*r/ 56.4%

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

      2. neg-mul-1 56.4%

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

   5. Simplified 56.4%

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

   if -1.4000000000000001e-54 < t < 9500

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 73.9%

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

   if 9500 < t

   1. Initial program 82.5%

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

   3. Taylor expanded in t around inf 50.8%

      \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x}{z} + -1 \cdot \frac{x \cdot y}{t \cdot {z}^{2}}}{t}} \]
   4. Step-by-step derivation

      1. distribute-lft-out 50.8%

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

      2. associate-*r/ 50.8%

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

      3. mul-1-neg 50.8%

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

      4. associate-/l* 55.4%

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

   5. Simplified 55.4%

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

   6. Taylor expanded in z around inf 66.5%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-54}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;t \leq 9500:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+37} \lor \neg \left(t \leq 4 \cdot 10^{+240}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.3e+37) (not (<= t 4e+240))) (/ x (* z t)) (/ x y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.3e+37) || !(t <= 4e+240)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-3.3d+37)) .or. (.not. (t <= 4d+240))) then
        tmp = x / (z * t)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.3e+37) || !(t <= 4e+240)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (t <= -3.3e+37) or not (t <= 4e+240):
		tmp = x / (z * t)
	else:
		tmp = x / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.3e+37) || !(t <= 4e+240))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.3e+37) || ~((t <= 4e+240)))
		tmp = x / (z * t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.3e+37], N[Not[LessEqual[t, 4e+240]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.3000000000000001e37 or 4.00000000000000006e240 < t

   1. Initial program 85.8%

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

   3. Taylor expanded in y around 0 60.5%

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

      1. associate-*r/ 60.5%

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

      2. neg-mul-1 60.5%

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

   5. Simplified 60.5%

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

      1. add-sqr-sqrt 38.6%

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

      2. sqrt-unprod 47.0%

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

      3. sqr-neg 47.0%

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

      4. sqrt-unprod 13.7%

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

      5. add-sqr-sqrt 35.3%

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

      6. *-un-lft-identity 35.3%

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

   7. Applied egg-rr 35.3%

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

      1. *-lft-identity 35.3%

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

   9. Simplified 35.3%

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

   if -3.3000000000000001e37 < t < 4.00000000000000006e240

   1. Initial program 96.6%

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

   3. Taylor expanded in y around inf 64.4%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+37} \lor \neg \left(t \leq 4 \cdot 10^{+240}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \frac{x}{y} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ x y))

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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

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

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return x / y

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(x / y)
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = x / y;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(x / y), $MachinePrecision]

Derivation

1. Initial program 93.2%

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

3. Taylor expanded in y around inf 55.9%

   \[\leadsto \color{blue}{\frac{x}{y}} \]
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 2024165 
(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))))