SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 3.3s

Alternatives: 5

Speedup: 1.0×

• 21.9% 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: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-31} \lor \neg \left(z \leq 3.2 \cdot 10^{-25}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.35e-31) (not (<= z 3.2e-25))) (+ x (* y z)) (- x (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.35e-31) || !(z <= 3.2e-25)) {
		tmp = x + (y * z);
	} else {
		tmp = x - (x * y);
	}
	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 <= (-1.35d-31)) .or. (.not. (z <= 3.2d-25))) then
        tmp = x + (y * z)
    else
        tmp = x - (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.35e-31) || !(z <= 3.2e-25)) {
		tmp = x + (y * z);
	} else {
		tmp = x - (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.35e-31) or not (z <= 3.2e-25):
		tmp = x + (y * z)
	else:
		tmp = x - (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.35e-31) || !(z <= 3.2e-25))
		tmp = Float64(x + Float64(y * z));
	else
		tmp = Float64(x - Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.35e-31) || ~((z <= 3.2e-25)))
		tmp = x + (y * z);
	else
		tmp = x - (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.35e-31], N[Not[LessEqual[z, 3.2e-25]], $MachinePrecision]], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35000000000000007e-31 or 3.2000000000000001e-25 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 94.6%

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

   if -1.35000000000000007e-31 < z < 3.2000000000000001e-25

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 86.7%

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

      1. mul-1-neg 86.7%

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

      2. distribute-rgt-neg-out 86.7%

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

   4. Simplified 86.7%

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

   5. Taylor expanded in x around 0 86.6%

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

      1. neg-mul-1 86.6%

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

      2. +-commutative 86.6%

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

      3. distribute-rgt1-in 86.7%

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

      4. cancel-sign-sub-inv 86.7%

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

   7. Simplified 86.7%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-31} \lor \neg \left(z \leq 3.2 \cdot 10^{-25}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot y\\ \end{array} \]

Alternative 3: 60.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -16000000000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -16000000000.0) (not (<= y 1.0))) (* y (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -16000000000.0) || !(y <= 1.0)) {
		tmp = y * -x;
	} 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 ((y <= (-16000000000.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = y * -x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -16000000000.0) || !(y <= 1.0)) {
		tmp = y * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -16000000000.0) or not (y <= 1.0):
		tmp = y * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -16000000000.0) || !(y <= 1.0))
		tmp = Float64(y * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -16000000000.0) || ~((y <= 1.0)))
		tmp = y * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -16000000000.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.6e10 or 1 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 44.3%

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

      1. mul-1-neg 44.3%

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

      2. distribute-rgt-neg-out 44.3%

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

   4. Simplified 44.3%

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

   5. Taylor expanded in y around inf 44.0%

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

      1. associate-*r* 44.0%

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

      2. neg-mul-1 44.0%

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

   7. Simplified 44.0%

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

   if -1.6e10 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 68.1%

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

      1. mul-1-neg 68.1%

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

      2. distribute-rgt-neg-out 68.1%

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

   4. Simplified 68.1%

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

   5. Taylor expanded in y around 0 67.5%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -16000000000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 75.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+151}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.08e+151) (* y (- x)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.08e+151) {
		tmp = 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 (y <= (-1.08d+151)) then
        tmp = 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 (y <= -1.08e+151) {
		tmp = y * -x;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.08e+151:
		tmp = y * -x
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.08e+151)
		tmp = Float64(y * Float64(-x));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.08e+151)
		tmp = y * -x;
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.08e+151], N[(y * (-x)), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.08000000000000003e151

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 62.7%

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

      1. mul-1-neg 62.7%

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

      2. distribute-rgt-neg-out 62.7%

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

   4. Simplified 62.7%

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

   5. Taylor expanded in y around inf 62.7%

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

      1. associate-*r* 62.7%

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

      2. neg-mul-1 62.7%

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

   7. Simplified 62.7%

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

   if -1.08000000000000003e151 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 85.4%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+151}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 5: 36.2% 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 z around 0 56.8%

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

   1. mul-1-neg 56.8%

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

   2. distribute-rgt-neg-out 56.8%

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

4. Simplified 56.8%

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

5. Taylor expanded in y around 0 36.7%

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

6. Final simplification 36.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023195 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))