SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 3.6s

Alternatives: 5

Speedup: 1.0×

• 22.2% 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: 75.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+38} \lor \neg \left(y \leq 7.8 \cdot 10^{+28}\right) \land y \leq 10^{+252}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.2e+38) (and (not (<= y 7.8e+28)) (<= y 1e+252)))
   (* x (- y))
   (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.2e+38) || (!(y <= 7.8e+28) && (y <= 1e+252))) {
		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 <= (-4.2d+38)) .or. (.not. (y <= 7.8d+28)) .and. (y <= 1d+252)) 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 <= -4.2e+38) || (!(y <= 7.8e+28) && (y <= 1e+252))) {
		tmp = x * -y;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.2e+38) or (not (y <= 7.8e+28) and (y <= 1e+252)):
		tmp = x * -y
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.2e+38) || (!(y <= 7.8e+28) && (y <= 1e+252)))
		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 <= -4.2e+38) || (~((y <= 7.8e+28)) && (y <= 1e+252)))
		tmp = x * -y;
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.2e+38], And[N[Not[LessEqual[y, 7.8e+28]], $MachinePrecision], LessEqual[y, 1e+252]]], N[(x * (-y)), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2e38 or 7.7999999999999997e28 < y < 1.0000000000000001e252

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 60.2%

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

      1. mul-1-neg 60.2%

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

      2. distribute-lft-neg-out 60.2%

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

      3. *-commutative 60.2%

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

   4. Simplified 60.2%

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

   5. Taylor expanded in y around inf 60.2%

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

      1. associate-*r* 60.2%

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

      2. mul-1-neg 60.2%

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

   7. Simplified 60.2%

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

   if -4.2e38 < y < 7.7999999999999997e28 or 1.0000000000000001e252 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 91.5%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+38} \lor \neg \left(y \leq 7.8 \cdot 10^{+28}\right) \land y \leq 10^{+252}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 3: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-18} \lor \neg \left(z \leq 7.5 \cdot 10^{-84}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.4e-18) (not (<= z 7.5e-84))) (+ x (* y z)) (- x (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.4e-18) || !(z <= 7.5e-84)) {
		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 <= (-4.4d-18)) .or. (.not. (z <= 7.5d-84))) 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 <= -4.4e-18) || !(z <= 7.5e-84)) {
		tmp = x + (y * z);
	} else {
		tmp = x - (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.4e-18) or not (z <= 7.5e-84):
		tmp = x + (y * z)
	else:
		tmp = x - (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.4e-18) || !(z <= 7.5e-84))
		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 <= -4.4e-18) || ~((z <= 7.5e-84)))
		tmp = x + (y * z);
	else
		tmp = x - (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.4e-18], N[Not[LessEqual[z, 7.5e-84]], $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 < -4.3999999999999997e-18 or 7.50000000000000026e-84 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 85.5%

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

   if -4.3999999999999997e-18 < z < 7.50000000000000026e-84

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 86.2%

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

      1. mul-1-neg 86.2%

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

      2. distribute-lft-neg-out 86.2%

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

      3. *-commutative 86.2%

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

   4. Simplified 86.2%

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

      1. *-commutative 86.2%

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

      2. distribute-lft-neg-out 86.2%

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

      3. unsub-neg 86.2%

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

   6. Applied egg-rr 86.2%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-18} \lor \neg \left(z \leq 7.5 \cdot 10^{-84}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot y\\ \end{array} \]

Alternative 4: 61.4% accurate, 0.9× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(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 <= (-1.0d0)) .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 <= -1.0) || !(y <= 1.0)) {
		tmp = x * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 55.5%

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

      1. mul-1-neg 55.5%

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

      2. distribute-lft-neg-out 55.5%

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

      3. *-commutative 55.5%

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

   4. Simplified 55.5%

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

   5. Taylor expanded in y around inf 54.0%

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

      1. associate-*r* 54.0%

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

      2. mul-1-neg 54.0%

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

   7. Simplified 54.0%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 68.3%

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

      1. mul-1-neg 68.3%

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

      2. distribute-lft-neg-out 68.3%

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

      3. *-commutative 68.3%

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

   4. Simplified 68.3%

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

   5. Taylor expanded in y around 0 65.7%

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

4. Final simplification 59.3%

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

Alternative 5: 36.3% 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%

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

   1. mul-1-neg 61.3%

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

   2. distribute-lft-neg-out 61.3%

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

   3. *-commutative 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 31.4%

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

6. Final simplification 31.4%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023310 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))