SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 3.9s

Alternatives: 6

Speedup: 1.0×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + y \cdot \left(z - x\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return x + (y * (z - 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 + (y * (z - x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \left(z - x\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return x + (y * (z - 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 + (y * (z - x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + y \cdot \left(z - x\right) \]
2. Step-by-step derivation

   1. +-commutative 100.0%

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

   2. fma-def 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-17} \lor \neg \left(x \leq 2.35 \cdot 10^{+126}\right):\\ \;\;\;\;x - y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.3e-17) (not (<= x 2.35e+126))) (- x (* y x)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.3e-17) || !(x <= 2.35e+126)) {
		tmp = x - (y * x);
	} else {
		tmp = x + (y * z);
	}
	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 ((x <= (-3.3d-17)) .or. (.not. (x <= 2.35d+126))) then
        tmp = x - (y * x)
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.3e-17) || !(x <= 2.35e+126)) {
		tmp = x - (y * x);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.3e-17) or not (x <= 2.35e+126):
		tmp = x - (y * x)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.3e-17) || !(x <= 2.35e+126))
		tmp = Float64(x - Float64(y * x));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.3e-17) || ~((x <= 2.35e+126)))
		tmp = x - (y * x);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.3e-17], N[Not[LessEqual[x, 2.35e+126]], $MachinePrecision]], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.3e-17 or 2.3499999999999999e126 < x

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]

   2. Taylor expanded in x around inf 90.4%

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

      1. +-commutative 90.4%

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

      2. distribute-rgt1-in 90.4%

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

      3. mul-1-neg 90.4%

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

      4. cancel-sign-sub-inv 90.4%

         \[\leadsto \color{blue}{x - y \cdot x} \]

   4. Simplified 90.4%

      \[\leadsto \color{blue}{x - y \cdot x} \]

   if -3.3e-17 < x < 2.3499999999999999e126

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]

   2. Taylor expanded in z around inf 86.7%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-17} \lor \neg \left(x \leq 2.35 \cdot 10^{+126}\right):\\ \;\;\;\;x - y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 3: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-57}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.8e-57) (* y z) (if (<= y 9.8e-67) x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.8e-57) {
		tmp = y * z;
	} else if (y <= 9.8e-67) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	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 (y <= (-9.8d-57)) then
        tmp = y * z
    else if (y <= 9.8d-67) then
        tmp = x
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.8e-57) {
		tmp = y * z;
	} else if (y <= 9.8e-67) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.8e-57:
		tmp = y * z
	elif y <= 9.8e-67:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.8e-57)
		tmp = Float64(y * z);
	elseif (y <= 9.8e-67)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9.8e-57)
		tmp = y * z;
	elseif (y <= 9.8e-67)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.8e-57], N[(y * z), $MachinePrecision], If[LessEqual[y, 9.8e-67], x, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.79999999999999976e-57 or 9.79999999999999987e-67 < y

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]

   2. Taylor expanded in z around inf 64.1%

      \[\leadsto x + \color{blue}{y \cdot z} \]

   3. Taylor expanded in x around 0 56.2%

      \[\leadsto \color{blue}{y \cdot z} \]

   if -9.79999999999999976e-57 < y < 9.79999999999999987e-67

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]

   2. Taylor expanded in y around 0 78.9%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-57}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 4: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \left(z - x\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return x + (y * (z - 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 + (y * (z - x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + y \cdot \left(z - x\right) \]

2. Final simplification 100.0%

   \[\leadsto x + y \cdot \left(z - x\right) \]

Alternative 5: 76.1% accurate, 1.4× 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%

   \[x + y \cdot \left(z - x\right) \]

2. Taylor expanded in z around inf 79.2%

   \[\leadsto x + \color{blue}{y \cdot z} \]

3. Final simplification 79.2%

   \[\leadsto x + y \cdot z \]

Alternative 6: 36.6% accurate, 7.0× 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%

   \[x + y \cdot \left(z - x\right) \]

2. Taylor expanded in y around 0 39.3%

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

3. Final simplification 39.3%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023175 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))