SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 6.8s

Alternatives: 5

Speedup: 1.2×

• 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, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. accelerator-lowering-fma.f64 N/A

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

   4. --lowering--.f64 100.0

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

4. Applied egg-rr 100.0%

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

Alternative 2: 81.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(0 - y, x, x\right)\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{+113}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-152}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (- 0.0 y) x x)))
   (if (<= x -5.8e+113) t_0 (if (<= x 3.2e-152) (fma z y x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma((0.0 - y), x, x);
	double tmp;
	if (x <= -5.8e+113) {
		tmp = t_0;
	} else if (x <= 3.2e-152) {
		tmp = fma(z, y, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(0.0 - y), x, x)
	tmp = 0.0
	if (x <= -5.8e+113)
		tmp = t_0;
	elseif (x <= 3.2e-152)
		tmp = fma(z, y, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(0.0 - y), $MachinePrecision] * x + x), $MachinePrecision]}, If[LessEqual[x, -5.8e+113], t$95$0, If[LessEqual[x, 3.2e-152], N[(z * y + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.79999999999999968e113 or 3.20000000000000013e-152 < x

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. --lowering--.f64 100.0

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

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - x, y, x\right)} \]
   5. Step-by-step derivation

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. distribute-lft-in N/A

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

      4. *-commutative N/A

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

      5. sub0-neg N/A

         \[\leadsto \left(y \cdot z + \color{blue}{\left(0 - x\right)} \cdot y\right) + x \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(0 - x\right) \cdot y + y \cdot z\right)} + x \]

      7. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(0 - x\right) \cdot y + \left(y \cdot z + x\right)} \]

      8. sub0-neg N/A

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

      9. +-commutative N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. sub0-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{0 - x}, y, x + y \cdot z\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{0 - x}, y, x + y \cdot z\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(0 - x, y, \color{blue}{y \cdot z + x}\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(0 - x, y, \color{blue}{z \cdot y} + x\right) \]

      15. accelerator-lowering-fma.f64 97.2

          \[\leadsto \mathsf{fma}\left(0 - x, y, \color{blue}{\mathsf{fma}\left(z, y, x\right)}\right) \]

   6. Applied egg-rr 97.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0 - x, y, \mathsf{fma}\left(z, y, x\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{y \cdot \left(0 - x\right)} + \left(z \cdot y + x\right) \]

      2. sub0-neg N/A

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

      3. distribute-rgt-neg-out N/A

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

      4. distribute-lft-neg-in N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. neg-lowering-neg.f64 N/A

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

      7. accelerator-lowering-fma.f64 97.2

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

   8. Applied egg-rr 97.2%

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

   9. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(y\right), x, \color{blue}{x}\right) \]
   10. Step-by-step derivation

   11. Simplified 86.9%

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

   if -5.79999999999999968e113 < x < 3.20000000000000013e-152

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 88.3%

      \[\leadsto x + y \cdot \color{blue}{z} \]
   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 88.3

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

   7. Applied egg-rr 88.3%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+113}:\\ \;\;\;\;\mathsf{fma}\left(0 - y, x, x\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-152}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0 - y, x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-28}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.3e-28) (* z y) (if (<= y 2e-42) x (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.3e-28) {
		tmp = z * y;
	} else if (y <= 2e-42) {
		tmp = x;
	} else {
		tmp = z * 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 <= (-2.3d-28)) then
        tmp = z * y
    else if (y <= 2d-42) then
        tmp = x
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.3e-28) {
		tmp = z * y;
	} else if (y <= 2e-42) {
		tmp = x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.3e-28:
		tmp = z * y
	elif y <= 2e-42:
		tmp = x
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.3e-28)
		tmp = Float64(z * y);
	elseif (y <= 2e-42)
		tmp = x;
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.3e-28)
		tmp = z * y;
	elseif (y <= 2e-42)
		tmp = x;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.3e-28], N[(z * y), $MachinePrecision], If[LessEqual[y, 2e-42], x, N[(z * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.29999999999999986e-28 or 2.00000000000000008e-42 < 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. +-rgt-identity N/A

         \[\leadsto \color{blue}{y \cdot z + 0} \]

      2. accelerator-lowering-fma.f64 52.5

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, z, 0\right)} \]

   5. Simplified 52.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 52.5

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

   7. Applied egg-rr 52.5%

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

   if -2.29999999999999986e-28 < y < 2.00000000000000008e-42

   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 77.8%

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

Alternative 4: 75.8% 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

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

5. Simplified 74.0%

   \[\leadsto x + y \cdot \color{blue}{z} \]
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 74.0

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

7. Applied egg-rr 74.0%

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

Alternative 5: 36.4% 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 36.1%

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

Reproduce

herbie shell --seed 2024198 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))