SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 3.6s

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: 74.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-295} \lor \neg \left(z \leq 9.8 \cdot 10^{-167}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.1e-295) (not (<= z 9.8e-167))) (+ x (* y z)) (* x (- y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.1e-295) || !(z <= 9.8e-167)) {
		tmp = x + (y * z);
	} else {
		tmp = 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 <= (-4.1d-295)) .or. (.not. (z <= 9.8d-167))) then
        tmp = x + (y * z)
    else
        tmp = x * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.1e-295) || !(z <= 9.8e-167)) {
		tmp = x + (y * z);
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.1e-295) or not (z <= 9.8e-167):
		tmp = x + (y * z)
	else:
		tmp = x * -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.1e-295) || !(z <= 9.8e-167))
		tmp = Float64(x + Float64(y * z));
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.1e-295) || ~((z <= 9.8e-167)))
		tmp = x + (y * z);
	else
		tmp = x * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.1e-295], N[Not[LessEqual[z, 9.8e-167]], $MachinePrecision]], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.10000000000000005e-295 or 9.80000000000000006e-167 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 82.8%

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

   if -4.10000000000000005e-295 < z < 9.80000000000000006e-167

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 97.2%

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

      1. mul-1-neg 97.2%

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

      2. distribute-rgt-neg-out 97.2%

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

   4. Simplified 97.2%

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

   5. Taylor expanded in y around inf 61.9%

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

      1. associate-*r* 61.9%

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

      2. neg-mul-1 61.9%

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

   7. Simplified 61.9%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-295} \lor \neg \left(z \leq 9.8 \cdot 10^{-167}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]

Alternative 3: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+28} \lor \neg \left(z \leq 6 \cdot 10^{-143}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6.4e+28) (not (<= z 6e-143))) (+ x (* y z)) (- x (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.4e+28) || !(z <= 6e-143)) {
		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 <= (-6.4d+28)) .or. (.not. (z <= 6d-143))) 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 <= -6.4e+28) || !(z <= 6e-143)) {
		tmp = x + (y * z);
	} else {
		tmp = x - (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6.4e+28) or not (z <= 6e-143):
		tmp = x + (y * z)
	else:
		tmp = x - (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6.4e+28) || !(z <= 6e-143))
		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 <= -6.4e+28) || ~((z <= 6e-143)))
		tmp = x + (y * z);
	else
		tmp = x - (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6.4e+28], N[Not[LessEqual[z, 6e-143]], $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 < -6.4000000000000001e28 or 5.9999999999999997e-143 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 91.1%

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

   if -6.4000000000000001e28 < z < 5.9999999999999997e-143

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 92.5%

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

      1. mul-1-neg 92.5%

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

      2. distribute-rgt-neg-out 92.5%

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

   4. Simplified 92.5%

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

   5. Taylor expanded in x around 0 92.4%

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

      1. neg-mul-1 92.4%

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

      2. +-commutative 92.4%

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

      3. distribute-rgt1-in 92.5%

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

      4. cancel-sign-sub-inv 92.5%

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

   7. Simplified 92.5%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+28} \lor \neg \left(z \leq 6 \cdot 10^{-143}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot y\\ \end{array} \]

Alternative 4: 60.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-5} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3e-5) (not (<= y 1.0))) (* x (- y)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3e-5) || !(y <= 1.0)) {
		tmp = x * -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 ((y <= (-3d-5)) .or. (.not. (y <= 1.0d0))) then
        tmp = x * -y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3e-5) || !(y <= 1.0)) {
		tmp = x * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3e-5) or not (y <= 1.0):
		tmp = x * -y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3e-5) || !(y <= 1.0))
		tmp = Float64(x * Float64(-y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3e-5) || ~((y <= 1.0)))
		tmp = x * -y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3e-5], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(x * (-y)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.00000000000000008e-5 or 1 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 51.3%

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

      1. mul-1-neg 51.3%

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

      2. distribute-rgt-neg-out 51.3%

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

   4. Simplified 51.3%

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

   5. Taylor expanded in y around inf 50.3%

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

      1. associate-*r* 50.3%

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

      2. neg-mul-1 50.3%

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

   7. Simplified 50.3%

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

   if -3.00000000000000008e-5 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 79.9%

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

      1. mul-1-neg 79.9%

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

      2. distribute-rgt-neg-out 79.9%

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

   4. Simplified 79.9%

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

   5. Taylor expanded in y around 0 79.2%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-5} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 36.1% 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 64.7%

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

   1. mul-1-neg 64.7%

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

   2. distribute-rgt-neg-out 64.7%

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

4. Simplified 64.7%

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

5. Taylor expanded in y around 0 38.7%

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

6. Final simplification 38.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023242 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))