SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 4.9s

Alternatives: 6

Speedup: 1.0×

• 20.5% 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: 99.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z - x\right)\\ \mathbf{if}\;y \leq -2100:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z x))))
   (if (<= y -2100.0) t_0 (if (<= y 1.0) (fma z y x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z - x);
	double tmp;
	if (y <= -2100.0) {
		tmp = t_0;
	} else if (y <= 1.0) {
		tmp = fma(z, y, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(z - x))
	tmp = 0.0
	if (y <= -2100.0)
		tmp = t_0;
	elseif (y <= 1.0)
		tmp = fma(z, y, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2100.0], t$95$0, If[LessEqual[y, 1.0], N[(z * y + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -2100 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 99.3

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

   5. Simplified 99.3%

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

   if -2100 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{y \cdot z} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 98.9

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

   5. Simplified 98.9%

      \[\leadsto x + \color{blue}{y \cdot z} \]
   6. Step-by-step derivation

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 98.9

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

   7. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, y, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 72.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-108}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-215}:\\ \;\;\;\;-x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6e-108) (fma z y x) (if (<= z 5.8e-215) (- (* x y)) (fma z y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6e-108) {
		tmp = fma(z, y, x);
	} else if (z <= 5.8e-215) {
		tmp = -(x * y);
	} else {
		tmp = fma(z, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6e-108)
		tmp = fma(z, y, x);
	elseif (z <= 5.8e-215)
		tmp = Float64(-Float64(x * y));
	else
		tmp = fma(z, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6e-108], N[(z * y + x), $MachinePrecision], If[LessEqual[z, 5.8e-215], (-N[(x * y), $MachinePrecision]), N[(z * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.99999999999999986e-108 or 5.8000000000000001e-215 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{y \cdot z} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 85.8

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

   5. Simplified 85.8%

      \[\leadsto x + \color{blue}{y \cdot z} \]
   6. Step-by-step derivation

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 85.8

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

   7. Applied egg-rr 85.8%

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

   if -5.99999999999999986e-108 < z < 5.8000000000000001e-215

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 68.9

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

   5. Simplified 68.9%

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

   6. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. neg-lowering-neg.f64 65.5

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

   8. Simplified 65.5%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-108}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-215}:\\ \;\;\;\;-x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-37}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.5e-37) (* y z) (if (<= y 2.15e-26) x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.5e-37) {
		tmp = y * z;
	} else if (y <= 2.15e-26) {
		tmp = x;
	} else {
		tmp = 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 <= (-9.5d-37)) then
        tmp = y * z
    else if (y <= 2.15d-26) then
        tmp = x
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.5e-37) {
		tmp = y * z;
	} else if (y <= 2.15e-26) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.5e-37:
		tmp = y * z
	elif y <= 2.15e-26:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.5e-37)
		tmp = Float64(y * z);
	elseif (y <= 2.15e-26)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9.5e-37)
		tmp = y * z;
	elseif (y <= 2.15e-26)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.5e-37], N[(y * z), $MachinePrecision], If[LessEqual[y, 2.15e-26], x, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.49999999999999927e-37 or 2.14999999999999994e-26 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{y \cdot z} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 56.9

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

   5. Simplified 56.9%

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

   if -9.49999999999999927e-37 < y < 2.14999999999999994e-26

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 69.4%

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

Alternative 5: 76.3% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in z around inf

   \[\leadsto x + \color{blue}{y \cdot z} \]
4. Step-by-step derivation

   1. *-lowering-*.f64 75.3

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

5. Simplified 75.3%

   \[\leadsto x + \color{blue}{y \cdot z} \]
6. Step-by-step derivation

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. accelerator-lowering-fma.f64 75.3

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

7. Applied egg-rr 75.3%

   \[\leadsto \color{blue}{\mathsf{fma}\left(z, y, x\right)} \]
8. Add Preprocessing

Alternative 6: 36.6% accurate, 12.0× 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 y around 0

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 30.5%

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

Reproduce

herbie shell --seed 2024205 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))