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

Percentage Accurate: 100.0% → 100.0%

Time: 4.1s

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

\[\begin{array}{l} \\ \mathsf{fma}\left(-z, y, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. sub-neg N/A

      \[\leadsto \color{blue}{x + \left(\mathsf{neg}\left(y \cdot z\right)\right)} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(y \cdot z\right)\right) + x} \]

   3. *-commutative N/A

      \[\leadsto \left(\mathsf{neg}\left(\color{blue}{z \cdot y}\right)\right) + x \]

   4. distribute-lft-neg-in N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot y} + x \]

   5. accelerator-lowering-fma.f64 N/A

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

   6. neg-lowering-neg.f64 100.0

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

4. Applied egg-rr 100.0%

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

Alternative 2: 77.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-y\right)\\ \mathbf{if}\;z \cdot y \leq -40:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \cdot y \leq 5 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- y))))
   (if (<= (* z y) -40.0) t_0 (if (<= (* z y) 5e+108) x t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * -y;
	double tmp;
	if ((z * y) <= -40.0) {
		tmp = t_0;
	} else if ((z * y) <= 5e+108) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = z * -y
    if ((z * y) <= (-40.0d0)) then
        tmp = t_0
    else if ((z * y) <= 5d+108) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -y;
	double tmp;
	if ((z * y) <= -40.0) {
		tmp = t_0;
	} else if ((z * y) <= 5e+108) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -y
	tmp = 0
	if (z * y) <= -40.0:
		tmp = t_0
	elif (z * y) <= 5e+108:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-y))
	tmp = 0.0
	if (Float64(z * y) <= -40.0)
		tmp = t_0;
	elseif (Float64(z * y) <= 5e+108)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -y;
	tmp = 0.0;
	if ((z * y) <= -40.0)
		tmp = t_0;
	elseif ((z * y) <= 5e+108)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-y)), $MachinePrecision]}, If[LessEqual[N[(z * y), $MachinePrecision], -40.0], t$95$0, If[LessEqual[N[(z * y), $MachinePrecision], 5e+108], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -40 or 4.99999999999999991e108 < (*.f64 y z)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. neg-lowering-neg.f64 86.7

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

   5. Simplified 86.7%

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

   if -40 < (*.f64 y z) < 4.99999999999999991e108

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 78.2%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot y \leq -40:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;z \cdot y \leq 5 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - (z * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

   \[\leadsto x - z \cdot y \]
4. Add Preprocessing

Alternative 4: 50.5% accurate, 9.0× 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

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

5. Simplified 49.7%

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

Developer Target 1: 87.8% accurate, 0.2× 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 2024198 
(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)))