SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 3.2s

Alternatives: 5

Speedup: 1.0×

• 20.0% 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, 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: 77.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.6 \cdot 10^{+46} \lor \neg \left(y \leq 6.5 \cdot 10^{+86}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y 4.6e+46) (not (<= y 6.5e+86))) (+ x (* y z)) (* x (- y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= 4.6e+46) || !(y <= 6.5e+86)) {
		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 ((y <= 4.6d+46) .or. (.not. (y <= 6.5d+86))) 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 ((y <= 4.6e+46) || !(y <= 6.5e+86)) {
		tmp = x + (y * z);
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= 4.6e+46) or not (y <= 6.5e+86):
		tmp = x + (y * z)
	else:
		tmp = x * -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= 4.6e+46) || !(y <= 6.5e+86))
		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 ((y <= 4.6e+46) || ~((y <= 6.5e+86)))
		tmp = x + (y * z);
	else
		tmp = x * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, 4.6e+46], N[Not[LessEqual[y, 6.5e+86]], $MachinePrecision]], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.6000000000000001e46 or 6.49999999999999996e86 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 86.5%

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

   if 4.6000000000000001e46 < y < 6.49999999999999996e86

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 80.0%

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

      1. mul-1-neg 80.0%

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

      2. distribute-rgt-neg-out 80.0%

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

   4. Simplified 80.0%

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

   5. Taylor expanded in y around inf 80.0%

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

      1. associate-*r* 80.0%

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

      2. neg-mul-1 80.0%

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

   7. Simplified 80.0%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.6 \cdot 10^{+46} \lor \neg \left(y \leq 6.5 \cdot 10^{+86}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]

Alternative 3: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+223} \lor \neg \left(x \leq 5.2 \cdot 10^{-31}\right):\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.8e+223) (not (<= x 5.2e-31))) (- x (* x y)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.8e+223) || !(x <= 5.2e-31)) {
		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 <= (-5.8d+223)) .or. (.not. (x <= 5.2d-31))) 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 <= -5.8e+223) || !(x <= 5.2e-31)) {
		tmp = x - (x * y);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.8e+223) or not (x <= 5.2e-31):
		tmp = x - (x * y)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.8e+223) || !(x <= 5.2e-31))
		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 <= -5.8e+223) || ~((x <= 5.2e-31)))
		tmp = x - (x * y);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.8e+223], N[Not[LessEqual[x, 5.2e-31]], $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 < -5.8000000000000004e223 or 5.19999999999999991e-31 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 92.3%

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

      1. mul-1-neg 92.3%

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

      2. distribute-rgt-neg-out 92.3%

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

   4. Simplified 92.3%

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

   5. Taylor expanded in x around 0 92.3%

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

      1. neg-mul-1 92.3%

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

      2. +-commutative 92.3%

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

      3. distribute-rgt1-in 92.3%

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

      4. cancel-sign-sub-inv 92.3%

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

   7. Simplified 92.3%

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

   if -5.8000000000000004e223 < x < 5.19999999999999991e-31

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 86.6%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+223} \lor \neg \left(x \leq 5.2 \cdot 10^{-31}\right):\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 4: 60.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-6} \lor \neg \left(y \leq 48\right):\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.2e-6) (not (<= y 48.0))) (* x (- y)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.2e-6) || !(y <= 48.0)) {
		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 <= (-6.2d-6)) .or. (.not. (y <= 48.0d0))) 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 <= -6.2e-6) || !(y <= 48.0)) {
		tmp = x * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.2e-6) or not (y <= 48.0):
		tmp = x * -y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.2e-6) || !(y <= 48.0))
		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 <= -6.2e-6) || ~((y <= 48.0)))
		tmp = x * -y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.2e-6], N[Not[LessEqual[y, 48.0]], $MachinePrecision]], N[(x * (-y)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -6.1999999999999999e-6 or 48 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 49.2%

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

      1. mul-1-neg 49.2%

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

      2. distribute-rgt-neg-out 49.2%

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

   4. Simplified 49.2%

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

   5. Taylor expanded in y around inf 49.0%

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

      1. associate-*r* 49.0%

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

      2. neg-mul-1 49.0%

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

   7. Simplified 49.0%

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

   if -6.1999999999999999e-6 < y < 48

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 71.9%

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

      1. mul-1-neg 71.9%

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

      2. distribute-rgt-neg-out 71.9%

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

   4. Simplified 71.9%

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

   5. Taylor expanded in y around 0 71.3%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-6} \lor \neg \left(y \leq 48\right):\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 36.8% 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 61.3%

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

   1. mul-1-neg 61.3%

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

   2. distribute-rgt-neg-out 61.3%

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

4. Simplified 61.3%

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

5. Taylor expanded in y around 0 39.1%

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

6. Final simplification 39.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023185 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))