SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 4.3s

Alternatives: 6

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, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, z - x, x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma y (- z x) x))

C

double code(double x, double y, double z) {
	return fma(y, (z - x), x);
}

Julia

function code(x, y, z)
	return fma(y, Float64(z - x), x)
end

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + y \cdot \left(z - x\right) \]
2. Step-by-step derivation

   1. +-commutative 100.0%

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

   2. fma-def 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z - x, x\right)} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, z - x, x\right)} \]

4. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(y, z - x, x\right) \]

Alternative 2: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-141} \lor \neg \left(z \leq 1.8 \cdot 10^{-80}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.2e-141) (not (<= z 1.8e-80))) (+ x (* y z)) (* x (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.2e-141) || !(z <= 1.8e-80)) {
		tmp = x + (y * z);
	} else {
		tmp = x * (1.0 - 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 <= (-2.2d-141)) .or. (.not. (z <= 1.8d-80))) then
        tmp = x + (y * z)
    else
        tmp = x * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.2e-141) || !(z <= 1.8e-80)) {
		tmp = x + (y * z);
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.2e-141) or not (z <= 1.8e-80):
		tmp = x + (y * z)
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.2e-141) || !(z <= 1.8e-80))
		tmp = Float64(x + Float64(y * z));
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.2e-141) || ~((z <= 1.8e-80)))
		tmp = x + (y * z);
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.2e-141], N[Not[LessEqual[z, 1.8e-80]], $MachinePrecision]], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.20000000000000009e-141 or 1.8e-80 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 90.4%

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

   if -2.20000000000000009e-141 < z < 1.8e-80

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. distribute-rgt-in 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around inf 86.5%

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

      1. mul-1-neg 86.5%

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

      2. sub-neg 86.5%

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

   6. Simplified 86.5%

      \[\leadsto \color{blue}{x \cdot \left(1 - y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-141} \lor \neg \left(z \leq 1.8 \cdot 10^{-80}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 3: 60.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+29} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.2e+29) (not (<= y 1.0))) (* y (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.2e+29) || !(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 <= (-2.2d+29)) .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 <= -2.2e+29) || !(y <= 1.0)) {
		tmp = y * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.2e+29) or not (y <= 1.0):
		tmp = y * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.2e+29) || !(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 <= -2.2e+29) || ~((y <= 1.0)))
		tmp = y * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.2e+29], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.2000000000000001e29 or 1 < y

   1. Initial program 100.0%

      \[x + y \cdot \left(z - x\right) \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. distribute-rgt-in 95.4%

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

   3. Applied egg-rr 95.4%

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

   4. Taylor expanded in x around inf 51.5%

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

      1. mul-1-neg 51.5%

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

      2. sub-neg 51.5%

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

   6. Simplified 51.5%

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

   7. Taylor expanded in y around inf 50.1%

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

      1. associate-*r* 50.1%

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

      2. neg-mul-1 50.1%

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

      3. *-commutative 50.1%

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

   9. Simplified 50.1%

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

   if -2.2000000000000001e29 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 68.8%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+29} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 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 5: 62.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 y)))

C

double code(double x, double y, double z) {
	return x * (1.0 - y);
}

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 * (1.0d0 - y)
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - y);
}

Python

def code(x, y, z):
	return x * (1.0 - y)

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - y);
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x + y \cdot \left(z - x\right) \]
2. Step-by-step derivation

   1. sub-neg 100.0%

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

   2. distribute-rgt-in 98.0%

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

3. Applied egg-rr 98.0%

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

4. Taylor expanded in x around inf 62.3%

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

   1. mul-1-neg 62.3%

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

   2. sub-neg 62.3%

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

6. Simplified 62.3%

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

7. Final simplification 62.3%

   \[\leadsto x \cdot \left(1 - y\right) \]

Alternative 6: 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 y around 0 40.8%

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

3. Final simplification 40.8%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023271 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))