SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 3.8s

Alternatives: 5

Speedup: 1.0×

• 21.5% 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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 75.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+258} \lor \neg \left(y \leq -5.2 \cdot 10^{+223}\right) \land y \leq -4.8 \cdot 10^{+137}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.5e+258) (and (not (<= y -5.2e+223)) (<= y -4.8e+137)))
   (* x (- y))
   (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.5e+258) || (!(y <= -5.2e+223) && (y <= -4.8e+137))) {
		tmp = 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 ((y <= (-7.5d+258)) .or. (.not. (y <= (-5.2d+223))) .and. (y <= (-4.8d+137))) then
        tmp = 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 ((y <= -7.5e+258) || (!(y <= -5.2e+223) && (y <= -4.8e+137))) {
		tmp = x * -y;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.5e+258) or (not (y <= -5.2e+223) and (y <= -4.8e+137)):
		tmp = x * -y
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.5e+258) || (!(y <= -5.2e+223) && (y <= -4.8e+137)))
		tmp = Float64(x * Float64(-y));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7.5e+258) || (~((y <= -5.2e+223)) && (y <= -4.8e+137)))
		tmp = x * -y;
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.5e+258], And[N[Not[LessEqual[y, -5.2e+223]], $MachinePrecision], LessEqual[y, -4.8e+137]]], N[(x * (-y)), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.50000000000000032e258 or -5.2000000000000005e223 < y < -4.79999999999999966e137

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 83.8%

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

      1. mul-1-neg 83.8%

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

      2. distribute-rgt-neg-in 83.8%

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

   5. Simplified 83.8%

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

   6. Taylor expanded in y around inf 83.8%

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

      1. mul-1-neg 83.8%

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

   8. Simplified 83.8%

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

   if -7.50000000000000032e258 < y < -5.2000000000000005e223 or -4.79999999999999966e137 < y

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 81.8%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+258} \lor \neg \left(y \leq -5.2 \cdot 10^{+223}\right) \land y \leq -4.8 \cdot 10^{+137}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-38} \lor \neg \left(z \leq 2.1 \cdot 10^{-90}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.9e-38) (not (<= z 2.1e-90))) (+ x (* y z)) (- x (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.9e-38) || !(z <= 2.1e-90)) {
		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 <= (-1.9d-38)) .or. (.not. (z <= 2.1d-90))) 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 <= -1.9e-38) || !(z <= 2.1e-90)) {
		tmp = x + (y * z);
	} else {
		tmp = x - (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.9e-38) or not (z <= 2.1e-90):
		tmp = x + (y * z)
	else:
		tmp = x - (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.9e-38) || !(z <= 2.1e-90))
		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 <= -1.9e-38) || ~((z <= 2.1e-90)))
		tmp = x + (y * z);
	else
		tmp = x - (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.9e-38], N[Not[LessEqual[z, 2.1e-90]], $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 < -1.9e-38 or 2.0999999999999999e-90 < z

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 91.1%

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

   if -1.9e-38 < z < 2.0999999999999999e-90

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 91.3%

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

      1. mul-1-neg 91.3%

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

      2. distribute-rgt-neg-in 91.3%

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

   5. Simplified 91.3%

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

      1. distribute-rgt-neg-out 91.3%

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

      2. unsub-neg 91.3%

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

   7. Applied egg-rr 91.3%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-38} \lor \neg \left(z \leq 2.1 \cdot 10^{-90}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-33} \lor \neg \left(y \leq 0.0072\right):\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.7e-33) (not (<= y 0.0072))) (* x (- y)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.7e-33) || !(y <= 0.0072)) {
		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 <= (-1.7d-33)) .or. (.not. (y <= 0.0072d0))) 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 <= -1.7e-33) || !(y <= 0.0072)) {
		tmp = x * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.7e-33) or not (y <= 0.0072):
		tmp = x * -y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.7e-33) || !(y <= 0.0072))
		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 <= -1.7e-33) || ~((y <= 0.0072)))
		tmp = x * -y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.7e-33], N[Not[LessEqual[y, 0.0072]], $MachinePrecision]], N[(x * (-y)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.7e-33 or 0.0071999999999999998 < y

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 50.0%

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

      1. mul-1-neg 50.0%

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

      2. distribute-rgt-neg-in 50.0%

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

   5. Simplified 50.0%

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

   6. Taylor expanded in y around inf 49.7%

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

      1. mul-1-neg 49.7%

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

   8. Simplified 49.7%

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

   if -1.7e-33 < y < 0.0071999999999999998

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 69.1%

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

      1. mul-1-neg 69.1%

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

      2. distribute-rgt-neg-in 69.1%

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

   5. Simplified 69.1%

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

   6. Taylor expanded in y around 0 68.8%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-33} \lor \neg \left(y \leq 0.0072\right):\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

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. Add Preprocessing

3. Taylor expanded in z around 0 59.1%

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

   1. mul-1-neg 59.1%

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

   2. distribute-rgt-neg-in 59.1%

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

5. Simplified 59.1%

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

6. Taylor expanded in y around 0 34.4%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))