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

Percentage Accurate: 95.7% → 99.7%

Time: 10.2s

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: 95.7% 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, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+248}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(z, -t, y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{z} \cdot x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) (- INFINITY))
   (* (/ -1.0 z) (/ x t))
   (if (<= (* z t) 2e+248) (/ x (fma z (- t) y)) (/ (* (/ -1.0 z) x) t))))

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+248) {
		tmp = x / fma(z, -t, y);
	} else {
		tmp = ((-1.0 / z) * x) / t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= Float64(-Inf))
		tmp = Float64(Float64(-1.0 / z) * Float64(x / t));
	elseif (Float64(z * t) <= 2e+248)
		tmp = Float64(x / fma(z, Float64(-t), y));
	else
		tmp = Float64(Float64(Float64(-1.0 / z) * x) / t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], (-Infinity)], N[(N[(-1.0 / z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e+248], N[(x / N[(z * (-t) + y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-1.0 / z), $MachinePrecision] * x), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 45.3%

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

   3. Taylor expanded in y around 0 45.3%

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

      1. associate-*r/ 45.3%

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

      2. neg-mul-1 45.3%

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

   5. Simplified 45.3%

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

      1. neg-mul-1 45.3%

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

      2. *-commutative 45.3%

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

      3. times-frac 99.7%

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

   7. Applied egg-rr 99.7%

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

   if -inf.0 < (*.f64 z t) < 2.00000000000000009e248

   1. Initial program 99.9%

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

      1. cancel-sign-sub-inv 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-lft-neg-out 99.9%

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

      4. distribute-rgt-neg-out 99.9%

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

      5. fma-def 99.9%

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

   3. Simplified 99.9%

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

   if 2.00000000000000009e248 < (*.f64 z t)

   1. Initial program 71.4%

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

   3. Taylor expanded in y around 0 71.4%

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

      1. associate-*r/ 71.4%

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

      2. neg-mul-1 71.4%

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

   5. Simplified 71.4%

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

      1. neg-mul-1 71.4%

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

      2. *-commutative 71.4%

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

      3. times-frac 99.5%

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

   7. Applied egg-rr 99.5%

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

      1. associate-*r/ 99.9%

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

   9. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{\frac{-1}{z} \cdot x}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+248}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(z, -t, y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{z} \cdot x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+117}:\\ \;\;\;\;\frac{-\frac{x}{t}}{z}\\ \mathbf{elif}\;z \cdot t \leq -20:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq -2 \cdot 10^{-95}:\\ \;\;\;\;-\frac{x}{z \cdot t}\\ \mathbf{elif}\;z \cdot t \leq 10^{-12}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{x}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) -5e+117)
   (/ (- (/ x t)) z)
   (if (<= (* z t) -20.0)
     (/ x y)
     (if (<= (* z t) -2e-95)
       (- (/ x (* z t)))
       (if (<= (* z t) 1e-12) (/ x y) (/ (- (/ x z)) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -5e+117) {
		tmp = -(x / t) / z;
	} else if ((z * t) <= -20.0) {
		tmp = x / y;
	} else if ((z * t) <= -2e-95) {
		tmp = -(x / (z * t));
	} else if ((z * t) <= 1e-12) {
		tmp = x / y;
	} else {
		tmp = -(x / z) / t;
	}
	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 ((z * t) <= (-5d+117)) then
        tmp = -(x / t) / z
    else if ((z * t) <= (-20.0d0)) then
        tmp = x / y
    else if ((z * t) <= (-2d-95)) then
        tmp = -(x / (z * t))
    else if ((z * t) <= 1d-12) then
        tmp = x / y
    else
        tmp = -(x / z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -5e+117) {
		tmp = -(x / t) / z;
	} else if ((z * t) <= -20.0) {
		tmp = x / y;
	} else if ((z * t) <= -2e-95) {
		tmp = -(x / (z * t));
	} else if ((z * t) <= 1e-12) {
		tmp = x / y;
	} else {
		tmp = -(x / z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -5e+117:
		tmp = -(x / t) / z
	elif (z * t) <= -20.0:
		tmp = x / y
	elif (z * t) <= -2e-95:
		tmp = -(x / (z * t))
	elif (z * t) <= 1e-12:
		tmp = x / y
	else:
		tmp = -(x / z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= -5e+117)
		tmp = Float64(Float64(-Float64(x / t)) / z);
	elseif (Float64(z * t) <= -20.0)
		tmp = Float64(x / y);
	elseif (Float64(z * t) <= -2e-95)
		tmp = Float64(-Float64(x / Float64(z * t)));
	elseif (Float64(z * t) <= 1e-12)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(-Float64(x / z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -5e+117)
		tmp = -(x / t) / z;
	elseif ((z * t) <= -20.0)
		tmp = x / y;
	elseif ((z * t) <= -2e-95)
		tmp = -(x / (z * t));
	elseif ((z * t) <= 1e-12)
		tmp = x / y;
	else
		tmp = -(x / z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], -5e+117], N[((-N[(x / t), $MachinePrecision]) / z), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], -20.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], -2e-95], (-N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), If[LessEqual[N[(z * t), $MachinePrecision], 1e-12], N[(x / y), $MachinePrecision], N[((-N[(x / z), $MachinePrecision]) / t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 z t) < -4.99999999999999983e117

   1. Initial program 83.1%

      \[\frac{x}{y - z \cdot t} \]
   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. mul-1-neg 73.3%

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

      2. associate-/r* 85.2%

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

      3. distribute-neg-frac 85.2%

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

   5. Simplified 85.2%

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

   if -4.99999999999999983e117 < (*.f64 z t) < -20 or -1.99999999999999998e-95 < (*.f64 z t) < 9.9999999999999998e-13

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 81.9%

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

   if -20 < (*.f64 z t) < -1.99999999999999998e-95

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 62.1%

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

      1. associate-*r/ 62.1%

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

      2. neg-mul-1 62.1%

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

   5. Simplified 62.1%

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

   if 9.9999999999999998e-13 < (*.f64 z t)

   1. Initial program 91.1%

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

   3. Taylor expanded in y around 0 68.1%

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

      1. associate-*r/ 68.1%

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

      2. neg-mul-1 68.1%

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

   5. Simplified 68.1%

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

      1. neg-mul-1 68.1%

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

      2. *-commutative 68.1%

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

      3. times-frac 74.0%

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

   7. Applied egg-rr 74.0%

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

      1. associate-*r/ 72.7%

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

   9. Applied egg-rr 72.7%

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

   10. Taylor expanded in z around 0 72.7%

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

       1. neg-mul-1 72.7%

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

       2. distribute-frac-neg 72.7%

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

   12. Simplified 72.7%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+117}:\\ \;\;\;\;\frac{-\frac{x}{t}}{z}\\ \mathbf{elif}\;z \cdot t \leq -20:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq -2 \cdot 10^{-95}:\\ \;\;\;\;-\frac{x}{z \cdot t}\\ \mathbf{elif}\;z \cdot t \leq 10^{-12}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{x}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+117}:\\ \;\;\;\;\frac{-1}{z \cdot \frac{t}{x}}\\ \mathbf{elif}\;z \cdot t \leq -20:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq -2 \cdot 10^{-95}:\\ \;\;\;\;-\frac{x}{z \cdot t}\\ \mathbf{elif}\;z \cdot t \leq 10^{-12}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{x}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) -5e+117)
   (/ -1.0 (* z (/ t x)))
   (if (<= (* z t) -20.0)
     (/ x y)
     (if (<= (* z t) -2e-95)
       (- (/ x (* z t)))
       (if (<= (* z t) 1e-12) (/ x y) (/ (- (/ x z)) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -5e+117) {
		tmp = -1.0 / (z * (t / x));
	} else if ((z * t) <= -20.0) {
		tmp = x / y;
	} else if ((z * t) <= -2e-95) {
		tmp = -(x / (z * t));
	} else if ((z * t) <= 1e-12) {
		tmp = x / y;
	} else {
		tmp = -(x / z) / t;
	}
	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 ((z * t) <= (-5d+117)) then
        tmp = (-1.0d0) / (z * (t / x))
    else if ((z * t) <= (-20.0d0)) then
        tmp = x / y
    else if ((z * t) <= (-2d-95)) then
        tmp = -(x / (z * t))
    else if ((z * t) <= 1d-12) then
        tmp = x / y
    else
        tmp = -(x / z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -5e+117) {
		tmp = -1.0 / (z * (t / x));
	} else if ((z * t) <= -20.0) {
		tmp = x / y;
	} else if ((z * t) <= -2e-95) {
		tmp = -(x / (z * t));
	} else if ((z * t) <= 1e-12) {
		tmp = x / y;
	} else {
		tmp = -(x / z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -5e+117:
		tmp = -1.0 / (z * (t / x))
	elif (z * t) <= -20.0:
		tmp = x / y
	elif (z * t) <= -2e-95:
		tmp = -(x / (z * t))
	elif (z * t) <= 1e-12:
		tmp = x / y
	else:
		tmp = -(x / z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= -5e+117)
		tmp = Float64(-1.0 / Float64(z * Float64(t / x)));
	elseif (Float64(z * t) <= -20.0)
		tmp = Float64(x / y);
	elseif (Float64(z * t) <= -2e-95)
		tmp = Float64(-Float64(x / Float64(z * t)));
	elseif (Float64(z * t) <= 1e-12)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(-Float64(x / z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -5e+117)
		tmp = -1.0 / (z * (t / x));
	elseif ((z * t) <= -20.0)
		tmp = x / y;
	elseif ((z * t) <= -2e-95)
		tmp = -(x / (z * t));
	elseif ((z * t) <= 1e-12)
		tmp = x / y;
	else
		tmp = -(x / z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], -5e+117], N[(-1.0 / N[(z * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], -20.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], -2e-95], (-N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), If[LessEqual[N[(z * t), $MachinePrecision], 1e-12], N[(x / y), $MachinePrecision], N[((-N[(x / z), $MachinePrecision]) / t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 z t) < -4.99999999999999983e117

   1. Initial program 83.1%

      \[\frac{x}{y - z \cdot t} \]
   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%

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

      1. neg-mul-1 73.3%

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

      2. *-commutative 73.3%

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

      3. times-frac 85.3%

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

   7. Applied egg-rr 85.3%

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

      1. *-commutative 85.3%

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

      2. clear-num 85.1%

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

      3. frac-times 85.2%

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

      4. metadata-eval 85.2%

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

   9. Applied egg-rr 85.2%

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

   if -4.99999999999999983e117 < (*.f64 z t) < -20 or -1.99999999999999998e-95 < (*.f64 z t) < 9.9999999999999998e-13

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 81.9%

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

   if -20 < (*.f64 z t) < -1.99999999999999998e-95

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 62.1%

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

      1. associate-*r/ 62.1%

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

      2. neg-mul-1 62.1%

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

   5. Simplified 62.1%

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

   if 9.9999999999999998e-13 < (*.f64 z t)

   1. Initial program 91.1%

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

   3. Taylor expanded in y around 0 68.1%

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

      1. associate-*r/ 68.1%

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

      2. neg-mul-1 68.1%

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

   5. Simplified 68.1%

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

      1. neg-mul-1 68.1%

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

      2. *-commutative 68.1%

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

      3. times-frac 74.0%

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

   7. Applied egg-rr 74.0%

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

      1. associate-*r/ 72.7%

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

   9. Applied egg-rr 72.7%

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

   10. Taylor expanded in z around 0 72.7%

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

       1. neg-mul-1 72.7%

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

       2. distribute-frac-neg 72.7%

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

   12. Simplified 72.7%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+117}:\\ \;\;\;\;\frac{-1}{z \cdot \frac{t}{x}}\\ \mathbf{elif}\;z \cdot t \leq -20:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq -2 \cdot 10^{-95}:\\ \;\;\;\;-\frac{x}{z \cdot t}\\ \mathbf{elif}\;z \cdot t \leq 10^{-12}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{x}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+293}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) (- INFINITY))
   (* (/ -1.0 z) (/ x t))
   (if (<= (* z t) 5e+293) (/ 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) <= 5e+293) {
		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) <= 5e+293) {
		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) <= 5e+293:
		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 / z) * Float64(x / t));
	elseif (Float64(z * t) <= 5e+293)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = Float64(Float64(-Float64(x / 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) <= 5e+293)
		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 / z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+293], 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 45.3%

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

   3. Taylor expanded in y around 0 45.3%

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

      1. associate-*r/ 45.3%

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

      2. neg-mul-1 45.3%

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

   5. Simplified 45.3%

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

      1. neg-mul-1 45.3%

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

      2. *-commutative 45.3%

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

      3. times-frac 99.7%

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

   7. Applied egg-rr 99.7%

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

   if -inf.0 < (*.f64 z t) < 5.00000000000000033e293

   1. Initial program 99.9%

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

   if 5.00000000000000033e293 < (*.f64 z t)

   1. Initial program 68.4%

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

   3. Taylor expanded in y around 0 68.4%

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

      1. mul-1-neg 68.4%

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

      2. associate-/r* 99.7%

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

      3. distribute-neg-frac 99.7%

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

   5. Simplified 99.7%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+293}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{x}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+248}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{z} \cdot x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) (- INFINITY))
   (* (/ -1.0 z) (/ x t))
   (if (<= (* z t) 2e+248) (/ x (- y (* z t))) (/ (* (/ -1.0 z) x) t))))

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+248) {
		tmp = x / (y - (z * t));
	} else {
		tmp = ((-1.0 / z) * x) / t;
	}
	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+248) {
		tmp = x / (y - (z * t));
	} else {
		tmp = ((-1.0 / z) * x) / t;
	}
	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+248:
		tmp = x / (y - (z * t))
	else:
		tmp = ((-1.0 / z) * x) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= Float64(-Inf))
		tmp = Float64(Float64(-1.0 / z) * Float64(x / t));
	elseif (Float64(z * t) <= 2e+248)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = Float64(Float64(Float64(-1.0 / z) * x) / t);
	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+248)
		tmp = x / (y - (z * t));
	else
		tmp = ((-1.0 / z) * x) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], (-Infinity)], N[(N[(-1.0 / z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e+248], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-1.0 / z), $MachinePrecision] * x), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 45.3%

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

   3. Taylor expanded in y around 0 45.3%

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

      1. associate-*r/ 45.3%

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

      2. neg-mul-1 45.3%

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

   5. Simplified 45.3%

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

      1. neg-mul-1 45.3%

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

      2. *-commutative 45.3%

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

      3. times-frac 99.7%

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

   7. Applied egg-rr 99.7%

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

   if -inf.0 < (*.f64 z t) < 2.00000000000000009e248

   1. Initial program 99.9%

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

   if 2.00000000000000009e248 < (*.f64 z t)

   1. Initial program 71.4%

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

   3. Taylor expanded in y around 0 71.4%

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

      1. associate-*r/ 71.4%

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

      2. neg-mul-1 71.4%

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

   5. Simplified 71.4%

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

      1. neg-mul-1 71.4%

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

      2. *-commutative 71.4%

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

      3. times-frac 99.5%

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

   7. Applied egg-rr 99.5%

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

      1. associate-*r/ 99.9%

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

   9. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{\frac{-1}{z} \cdot x}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+248}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{z} \cdot x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+163} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{+175}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z t) -5e+163) (not (<= (* z t) 5e+175)))
   (/ x (* z t))
   (/ x y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -5e+163) || !((z * t) <= 5e+175)) {
		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 (((z * t) <= (-5d+163)) .or. (.not. ((z * t) <= 5d+175))) 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 (((z * t) <= -5e+163) || !((z * t) <= 5e+175)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * t) <= -5e+163) or not ((z * t) <= 5e+175):
		tmp = x / (z * t)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * t) <= -5e+163) || !(Float64(z * t) <= 5e+175))
		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 (((z * t) <= -5e+163) || ~(((z * t) <= 5e+175)))
		tmp = x / (z * t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -5e+163], N[Not[LessEqual[N[(z * t), $MachinePrecision], 5e+175]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -5e163 or 5e175 < (*.f64 z t)

   1. Initial program 79.7%

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

   3. Taylor expanded in y around 0 76.6%

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

      1. associate-*r/ 76.6%

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

      2. neg-mul-1 76.6%

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

   5. Simplified 76.6%

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

      1. neg-mul-1 76.6%

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

      2. *-commutative 76.6%

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

      3. times-frac 95.1%

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

   7. Applied egg-rr 95.1%

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

      1. frac-times 76.6%

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

      2. neg-mul-1 76.6%

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

      3. add-sqr-sqrt 28.3%

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

      4. sqrt-unprod 50.5%

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

      5. sqr-neg 50.5%

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

      6. sqrt-unprod 28.0%

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

      7. add-sqr-sqrt 44.1%

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

   9. Applied egg-rr 44.1%

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

   if -5e163 < (*.f64 z t) < 5e175

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 69.8%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+163} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{+175}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-113} \lor \neg \left(y \leq 1.5 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-\frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8.5e-113) (not (<= y 1.5e+57))) (/ x y) (- (/ x (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8.5e-113) || !(y <= 1.5e+57)) {
		tmp = x / y;
	} else {
		tmp = -(x / (z * t));
	}
	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 <= (-8.5d-113)) .or. (.not. (y <= 1.5d+57))) then
        tmp = x / y
    else
        tmp = -(x / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8.5e-113) || !(y <= 1.5e+57)) {
		tmp = x / y;
	} else {
		tmp = -(x / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -8.5e-113) or not (y <= 1.5e+57):
		tmp = x / y
	else:
		tmp = -(x / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -8.5e-113) || !(y <= 1.5e+57))
		tmp = Float64(x / y);
	else
		tmp = Float64(-Float64(x / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -8.5e-113) || ~((y <= 1.5e+57)))
		tmp = x / y;
	else
		tmp = -(x / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -8.5e-113], N[Not[LessEqual[y, 1.5e+57]], $MachinePrecision]], N[(x / y), $MachinePrecision], (-N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if y < -8.4999999999999995e-113 or 1.5e57 < y

   1. Initial program 94.0%

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

   3. Taylor expanded in y around inf 77.3%

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

   if -8.4999999999999995e-113 < y < 1.5e57

   1. Initial program 96.3%

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

   3. Taylor expanded in y around 0 75.4%

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

      1. associate-*r/ 75.4%

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

      2. neg-mul-1 75.4%

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

   5. Simplified 75.4%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-113} \lor \neg \left(y \leq 1.5 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-\frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.6% 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 95.0%

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

3. Taylor expanded in y around inf 57.0%

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

4. Final simplification 57.0%

   \[\leadsto \frac{x}{y} \]
5. Add Preprocessing

Developer target: 96.8% 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 2024024 
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (if (< x -1.618195973607049e+50) (/ 1.0 (- (/ y x) (* (/ z x) t))) (if (< x 2.1378306434876444e+131) (/ x (- y (* z t))) (/ 1.0 (- (/ y x) (* (/ z x) t)))))

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