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

Percentage Accurate: 100.0% → 100.0%

Time: 6.3s

Alternatives: 4

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x - y \cdot z \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 69.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-138} \lor \neg \left(z \leq 1.1 \cdot 10^{+37}\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.65e-138) (not (<= z 1.1e+37))) (* z (- y)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.65e-138) || !(z <= 1.1e+37)) {
		tmp = z * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.65d-138)) .or. (.not. (z <= 1.1d+37))) then
        tmp = z * -y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.65e-138) || !(z <= 1.1e+37)) {
		tmp = z * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.65e-138) or not (z <= 1.1e+37):
		tmp = z * -y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.65e-138) || !(z <= 1.1e+37))
		tmp = Float64(z * Float64(-y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.65e-138) || ~((z <= 1.1e+37)))
		tmp = z * -y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.65e-138], N[Not[LessEqual[z, 1.1e+37]], $MachinePrecision]], N[(z * (-y)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.64999999999999991e-138 or 1.1e37 < z

   1. Initial program 100.0%

      \[x - y \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 71.1%

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

      1. associate-*r* 71.1%

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

      2. neg-mul-1 71.1%

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

   5. Simplified 71.1%

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

   if -1.64999999999999991e-138 < z < 1.1e37

   1. Initial program 100.0%

      \[x - y \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 75.1%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-138} \lor \neg \left(z \leq 1.1 \cdot 10^{+37}\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.7% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

   \[x - y \cdot z \]
2. Add Preprocessing

3. Taylor expanded in x around inf 49.4%

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

Alternative 4: 2.7% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 0.0)

C

double code(double x, double y, double z) {
	return 0.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 0.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 0.0;
}

Python

def code(x, y, z):
	return 0.0

Julia

function code(x, y, z)
	return 0.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_] := 0.0

Derivation

1. Initial program 100.0%

   \[x - y \cdot z \]
2. Add Preprocessing

3. Taylor expanded in x around 0 52.3%

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

   1. associate-*r* 52.3%

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

   2. neg-mul-1 52.3%

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

5. Simplified 52.3%

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

   1. add-log-exp 18.3%

      \[\leadsto \color{blue}{\log \left(e^{\left(-y\right) \cdot z}\right)} \]

   2. add-sqr-sqrt 18.2%

      \[\leadsto \log \color{blue}{\left(\sqrt{e^{\left(-y\right) \cdot z}} \cdot \sqrt{e^{\left(-y\right) \cdot z}}\right)} \]

   3. sqrt-unprod 18.3%

      \[\leadsto \log \color{blue}{\left(\sqrt{e^{\left(-y\right) \cdot z} \cdot e^{\left(-y\right) \cdot z}}\right)} \]

   4. distribute-lft-neg-out 18.3%

      \[\leadsto \log \left(\sqrt{e^{\left(-y\right) \cdot z} \cdot e^{\color{blue}{-y \cdot z}}}\right) \]

   5. distribute-rgt-neg-in 18.3%

      \[\leadsto \log \left(\sqrt{e^{\left(-y\right) \cdot z} \cdot e^{\color{blue}{y \cdot \left(-z\right)}}}\right) \]

   6. add-sqr-sqrt 8.2%

      \[\leadsto \log \left(\sqrt{e^{\left(-y\right) \cdot z} \cdot e^{\color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)} \cdot \left(-z\right)}}\right) \]

   7. sqrt-unprod 9.2%

      \[\leadsto \log \left(\sqrt{e^{\left(-y\right) \cdot z} \cdot e^{\color{blue}{\sqrt{y \cdot y}} \cdot \left(-z\right)}}\right) \]

   8. sqr-neg 9.2%

      \[\leadsto \log \left(\sqrt{e^{\left(-y\right) \cdot z} \cdot e^{\sqrt{\color{blue}{\left(-y\right) \cdot \left(-y\right)}} \cdot \left(-z\right)}}\right) \]

   9. sqrt-unprod 0.9%

      \[\leadsto \log \left(\sqrt{e^{\left(-y\right) \cdot z} \cdot e^{\color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)} \cdot \left(-z\right)}}\right) \]

   10. add-sqr-sqrt 1.8%

       \[\leadsto \log \left(\sqrt{e^{\left(-y\right) \cdot z} \cdot e^{\color{blue}{\left(-y\right)} \cdot \left(-z\right)}}\right) \]

   11. exp-prod 2.2%

       \[\leadsto \log \left(\sqrt{e^{\left(-y\right) \cdot z} \cdot \color{blue}{{\left(e^{-y}\right)}^{\left(-z\right)}}}\right) \]

   12. pow-flip 2.2%

       \[\leadsto \log \left(\sqrt{e^{\left(-y\right) \cdot z} \cdot \color{blue}{\frac{1}{{\left(e^{-y}\right)}^{z}}}}\right) \]

   13. exp-prod 1.8%

       \[\leadsto \log \left(\sqrt{e^{\left(-y\right) \cdot z} \cdot \frac{1}{\color{blue}{e^{\left(-y\right) \cdot z}}}}\right) \]

   14. rgt-mult-inverse 2.6%

       \[\leadsto \log \left(\sqrt{\color{blue}{1}}\right) \]

   15. metadata-eval 2.6%

       \[\leadsto \log \color{blue}{1} \]

   16. metadata-eval 2.6%

       \[\leadsto \color{blue}{0} \]

7. Applied egg-rr 2.6%

   \[\leadsto \color{blue}{0} \]
8. Add Preprocessing

Developer Target 1: 86.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot z\\ \frac{t\_0}{\frac{t\_0}{x - y \cdot z}} \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y z)))) (/ t_0 (/ t_0 (- x (* y z))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * z);
	return t_0 / (t_0 / (x - (y * z)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    t_0 = x + (y * z)
    code = t_0 / (t_0 / (x - (y * z)))
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y * z);
	return t_0 / (t_0 / (x - (y * z)));
}

Python

def code(x, y, z):
	t_0 = x + (y * z)
	return t_0 / (t_0 / (x - (y * z)))

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * z))
	return Float64(t_0 / Float64(t_0 / Float64(x - Float64(y * z))))
end

MATLAB

function tmp = code(x, y, z)
	t_0 = x + (y * z);
	tmp = t_0 / (t_0 / (x - (y * z)));
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]}, N[(t$95$0 / N[(t$95$0 / N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2024150 
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, C"
  :precision binary64

  :alt
  (! :herbie-platform default (/ (+ x (* y z)) (/ (+ x (* y z)) (- x (* y z)))))

  (- x (* y z)))