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

Percentage Accurate: 95.8% → 96.4%

Time: 8.2s

Alternatives: 7

Speedup: 1.0×

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: 96.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+134}:\\ \;\;\;\;\frac{\frac{x}{1 - \frac{t}{\frac{y}{z}}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2e+134) (/ (/ x (- 1.0 (/ t (/ y z)))) y) (/ x (- y (* t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2e+134) {
		tmp = (x / (1.0 - (t / (y / z)))) / y;
	} else {
		tmp = x / (y - (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 (y <= (-2d+134)) then
        tmp = (x / (1.0d0 - (t / (y / z)))) / y
    else
        tmp = x / (y - (t * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2e+134) {
		tmp = (x / (1.0 - (t / (y / z)))) / y;
	} else {
		tmp = x / (y - (t * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2e+134:
		tmp = (x / (1.0 - (t / (y / z)))) / y
	else:
		tmp = x / (y - (t * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2e+134)
		tmp = Float64(Float64(x / Float64(1.0 - Float64(t / Float64(y / z)))) / y);
	else
		tmp = Float64(x / Float64(y - Float64(t * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2e+134)
		tmp = (x / (1.0 - (t / (y / z)))) / y;
	else
		tmp = x / (y - (t * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2e+134], N[(N[(x / N[(1.0 - N[(t / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.99999999999999984e134

   1. Initial program 87.5%

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

   3. Taylor expanded in y around inf 87.5%

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

      1. mul-1-neg 87.5%

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

      2. unsub-neg 87.5%

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

      3. associate-/l* 87.5%

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

   5. Simplified 87.5%

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

      1. *-un-lft-identity 87.5%

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

      2. times-frac 99.6%

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

      3. clear-num 99.6%

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

      4. un-div-inv 99.6%

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

   7. Applied egg-rr 99.6%

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

      1. associate-*l/ 99.9%

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

      2. *-lft-identity 99.9%

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

   9. Simplified 99.9%

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

   if -1.99999999999999984e134 < y

   1. Initial program 98.6%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+134}:\\ \;\;\;\;\frac{\frac{x}{1 - \frac{t}{\frac{y}{z}}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \cdot z \leq -5 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{elif}\;t \cdot z \leq 5 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* t z) -5e+18)
   (/ x (* t (- z)))
   (if (<= (* t z) 5e+55) (/ x y) (/ (/ x z) (- t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t * z) <= -5e+18) {
		tmp = x / (t * -z);
	} else if ((t * z) <= 5e+55) {
		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 ((t * z) <= (-5d+18)) then
        tmp = x / (t * -z)
    else if ((t * z) <= 5d+55) 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 ((t * z) <= -5e+18) {
		tmp = x / (t * -z);
	} else if ((t * z) <= 5e+55) {
		tmp = x / y;
	} else {
		tmp = (x / z) / -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t * z) <= -5e+18:
		tmp = x / (t * -z)
	elif (t * z) <= 5e+55:
		tmp = x / y
	else:
		tmp = (x / z) / -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(t * z) <= -5e+18)
		tmp = Float64(x / Float64(t * Float64(-z)));
	elseif (Float64(t * z) <= 5e+55)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(x / z) / Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t * z) <= -5e+18)
		tmp = x / (t * -z);
	elseif ((t * z) <= 5e+55)
		tmp = x / y;
	else
		tmp = (x / z) / -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(t * z), $MachinePrecision], -5e+18], N[(x / N[(t * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(t * z), $MachinePrecision], 5e+55], N[(x / y), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / (-t)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -5e18

   1. Initial program 91.7%

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

   3. Taylor expanded in y around 0 80.9%

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

      1. associate-*r/ 80.9%

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

      2. neg-mul-1 80.9%

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

   5. Simplified 80.9%

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

   if -5e18 < (*.f64 z t) < 5.00000000000000046e55

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 78.7%

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

   if 5.00000000000000046e55 < (*.f64 z t)

   1. Initial program 93.5%

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

      1. clear-num 93.4%

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

      2. associate-/r/ 93.3%

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

   4. Applied egg-rr 93.3%

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

   5. Taylor expanded in t around inf 61.7%

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

      1. distribute-lft-out 61.7%

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

      2. mul-1-neg 61.7%

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

      3. +-commutative 61.7%

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

      4. associate-/l* 72.1%

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

      5. fma-define 72.1%

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

      6. associate-/r* 72.1%

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

   7. Simplified 72.1%

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

   8. Taylor expanded in y around 0 77.3%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot z \leq -5 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{elif}\;t \cdot z \leq 5 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \cdot z \leq -5 \cdot 10^{+18}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;t \cdot z \leq 5 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* t z) -5e+18)
   (/ (/ x t) (- z))
   (if (<= (* t z) 5e+55) (/ x y) (/ (/ x z) (- t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t * z) <= -5e+18) {
		tmp = (x / t) / -z;
	} else if ((t * z) <= 5e+55) {
		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 ((t * z) <= (-5d+18)) then
        tmp = (x / t) / -z
    else if ((t * z) <= 5d+55) 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 ((t * z) <= -5e+18) {
		tmp = (x / t) / -z;
	} else if ((t * z) <= 5e+55) {
		tmp = x / y;
	} else {
		tmp = (x / z) / -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t * z) <= -5e+18:
		tmp = (x / t) / -z
	elif (t * z) <= 5e+55:
		tmp = x / y
	else:
		tmp = (x / z) / -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(t * z) <= -5e+18)
		tmp = Float64(Float64(x / t) / Float64(-z));
	elseif (Float64(t * z) <= 5e+55)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(x / z) / Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t * z) <= -5e+18)
		tmp = (x / t) / -z;
	elseif ((t * z) <= 5e+55)
		tmp = x / y;
	else
		tmp = (x / z) / -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(t * z), $MachinePrecision], -5e+18], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[N[(t * z), $MachinePrecision], 5e+55], N[(x / y), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / (-t)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -5e18

   1. Initial program 91.7%

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

      1. clear-num 90.8%

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

      2. associate-/r/ 91.9%

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

   4. Applied egg-rr 91.9%

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

   5. Taylor expanded in y around 0 80.9%

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

      1. mul-1-neg 80.9%

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

      2. associate-/r* 84.1%

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

      3. distribute-neg-frac2 84.1%

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

   7. Simplified 84.1%

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

   if -5e18 < (*.f64 z t) < 5.00000000000000046e55

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 78.7%

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

   if 5.00000000000000046e55 < (*.f64 z t)

   1. Initial program 93.5%

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

      1. clear-num 93.4%

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

      2. associate-/r/ 93.3%

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

   4. Applied egg-rr 93.3%

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

   5. Taylor expanded in t around inf 61.7%

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

      1. distribute-lft-out 61.7%

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

      2. mul-1-neg 61.7%

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

      3. +-commutative 61.7%

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

      4. associate-/l* 72.1%

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

      5. fma-define 72.1%

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

      6. associate-/r* 72.1%

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

   7. Simplified 72.1%

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

   8. Taylor expanded in y around 0 77.3%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot z \leq -5 \cdot 10^{+18}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;t \cdot z \leq 5 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \cdot z \leq -2 \cdot 10^{+133} \lor \neg \left(t \cdot z \leq 5 \cdot 10^{+150}\right):\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* t z) -2e+133) (not (<= (* t z) 5e+150)))
   (/ x (* t z))
   (/ x y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((t * z) <= -2e+133) || !((t * z) <= 5e+150)) {
		tmp = x / (t * z);
	} 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 * z) <= (-2d+133)) .or. (.not. ((t * z) <= 5d+150))) then
        tmp = x / (t * z)
    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 * z) <= -2e+133) || !((t * z) <= 5e+150)) {
		tmp = x / (t * z);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((t * z) <= -2e+133) or not ((t * z) <= 5e+150):
		tmp = x / (t * z)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(t * z) <= -2e+133) || !(Float64(t * z) <= 5e+150))
		tmp = Float64(x / Float64(t * z));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((t * z) <= -2e+133) || ~(((t * z) <= 5e+150)))
		tmp = x / (t * z);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(t * z), $MachinePrecision], -2e+133], N[Not[LessEqual[N[(t * z), $MachinePrecision], 5e+150]], $MachinePrecision]], N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -2e133 or 5.00000000000000009e150 < (*.f64 z t)

   1. Initial program 89.0%

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

      1. clear-num 88.3%

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

      2. associate-/r/ 89.0%

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

   4. Applied egg-rr 89.0%

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

   5. Taylor expanded in y around 0 87.0%

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

      1. associate-/r* 89.1%

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

   7. Simplified 89.1%

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

      1. *-commutative 89.1%

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

      2. associate-*r/ 95.7%

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

      3. div-inv 95.7%

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

      4. mul-1-neg 95.7%

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

      5. distribute-rgt-neg-in 95.7%

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

      6. div-inv 95.8%

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

      7. distribute-frac-neg 95.8%

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

      8. distribute-frac-neg2 95.8%

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

      9. associate-/l/ 86.9%

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

      10. add-sqr-sqrt 38.8%

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

      11. sqrt-unprod 67.9%

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

      12. sqr-neg 67.9%

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

      13. sqrt-prod 35.6%

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

      14. add-sqr-sqrt 59.5%

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

   9. Applied egg-rr 59.5%

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

   if -2e133 < (*.f64 z t) < 5.00000000000000009e150

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 70.5%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot z \leq -2 \cdot 10^{+133} \lor \neg \left(t \cdot z \leq 5 \cdot 10^{+150}\right):\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-48} \lor \neg \left(y \leq 5.5 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.2e-48) (not (<= y 5.5e+22))) (/ x y) (/ x (* t (- z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.2e-48) || !(y <= 5.5e+22)) {
		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 ((y <= (-2.2d-48)) .or. (.not. (y <= 5.5d+22))) 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 ((y <= -2.2e-48) || !(y <= 5.5e+22)) {
		tmp = x / y;
	} else {
		tmp = x / (t * -z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.2e-48) or not (y <= 5.5e+22):
		tmp = x / y
	else:
		tmp = x / (t * -z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.2e-48) || !(y <= 5.5e+22))
		tmp = Float64(x / y);
	else
		tmp = Float64(x / Float64(t * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.2e-48) || ~((y <= 5.5e+22)))
		tmp = x / y;
	else
		tmp = x / (t * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.2e-48], N[Not[LessEqual[y, 5.5e+22]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(x / N[(t * (-z)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.20000000000000013e-48 or 5.50000000000000021e22 < y

   1. Initial program 95.2%

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

   3. Taylor expanded in y around inf 78.2%

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

   if -2.20000000000000013e-48 < y < 5.50000000000000021e22

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 81.3%

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

      1. associate-*r/ 81.3%

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

      2. neg-mul-1 81.3%

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

   5. Simplified 81.3%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-48} \lor \neg \left(y \leq 5.5 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - (t * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

3. Final simplification 96.9%

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

Alternative 7: 54.1% 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 96.9%

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

3. Taylor expanded in y around inf 55.3%

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

4. Final simplification 55.3%

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

Developer target: 96.2% 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 2024077 
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (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))))