SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 3.0s

Alternatives: 5

Speedup: 1.0×

• 20.9% 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, 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 2: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+140} \lor \neg \left(x \leq 7.5 \cdot 10^{-13}\right):\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.7e+140) (not (<= x 7.5e-13))) (- x (* x y)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.7e+140) || !(x <= 7.5e-13)) {
		tmp = x - (x * y);
	} 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 <= (-1.7d+140)) .or. (.not. (x <= 7.5d-13))) then
        tmp = x - (x * y)
    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 <= -1.7e+140) || !(x <= 7.5e-13)) {
		tmp = x - (x * y);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.7e+140) or not (x <= 7.5e-13):
		tmp = x - (x * y)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.7e+140) || !(x <= 7.5e-13))
		tmp = Float64(x - Float64(x * y));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.7e+140) || ~((x <= 7.5e-13)))
		tmp = x - (x * y);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.7e+140], N[Not[LessEqual[x, 7.5e-13]], $MachinePrecision]], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7e140 or 7.5000000000000004e-13 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 96.3%

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

      1. +-commutative 96.3%

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

      2. distribute-rgt1-in 96.3%

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

      3. mul-1-neg 96.3%

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

      4. cancel-sign-sub-inv 96.3%

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

   4. Simplified 96.3%

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

   if -1.7e140 < x < 7.5000000000000004e-13

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 89.9%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+140} \lor \neg \left(x \leq 7.5 \cdot 10^{-13}\right):\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 3: 62.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-69}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.25e-69) (* y z) (if (<= y 2.9e-6) x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.25e-69) {
		tmp = y * z;
	} else if (y <= 2.9e-6) {
		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 <= (-1.25d-69)) then
        tmp = y * z
    else if (y <= 2.9d-6) 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 <= -1.25e-69) {
		tmp = y * z;
	} else if (y <= 2.9e-6) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.25e-69:
		tmp = y * z
	elif y <= 2.9e-6:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.25e-69)
		tmp = Float64(y * z);
	elseif (y <= 2.9e-6)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.25e-69)
		tmp = y * z;
	elseif (y <= 2.9e-6)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.25e-69], N[(y * z), $MachinePrecision], If[LessEqual[y, 2.9e-6], x, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25000000000000008e-69 or 2.9000000000000002e-6 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 54.3%

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

   3. Taylor expanded in x around 0 51.9%

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

   if -1.25000000000000008e-69 < y < 2.9000000000000002e-6

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 73.3%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-69}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 4: 76.3% 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 76.7%

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

3. Final simplification 76.7%

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

Alternative 5: 37.2% 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 39.1%

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

3. Final simplification 39.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023268 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))