SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 5.4s

Alternatives: 6

Speedup: 1.2×

• 21.1% 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: 76.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -x \cdot y\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+135}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+41}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1450000:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* x y))))
   (if (<= y -3.5e+135)
     (fma z y x)
     (if (<= y -7e+41) t_0 (if (<= y 1450000.0) (fma z y x) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -(x * y);
	double tmp;
	if (y <= -3.5e+135) {
		tmp = fma(z, y, x);
	} else if (y <= -7e+41) {
		tmp = t_0;
	} else if (y <= 1450000.0) {
		tmp = fma(z, y, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(-Float64(x * y))
	tmp = 0.0
	if (y <= -3.5e+135)
		tmp = fma(z, y, x);
	elseif (y <= -7e+41)
		tmp = t_0;
	elseif (y <= 1450000.0)
		tmp = fma(z, y, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = (-N[(x * y), $MachinePrecision])}, If[LessEqual[y, -3.5e+135], N[(z * y + x), $MachinePrecision], If[LessEqual[y, -7e+41], t$95$0, If[LessEqual[y, 1450000.0], N[(z * y + x), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5000000000000003e135 or -6.9999999999999998e41 < y < 1.45e6

   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 93.5

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

   5. Simplified 93.5%

      \[\leadsto x + \color{blue}{y \cdot z} \]
   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 93.5

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

   7. Applied egg-rr 93.5%

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

   if -3.5000000000000003e135 < y < -6.9999999999999998e41 or 1.45e6 < 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 100.0

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 66.7

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

   8. Simplified 66.7%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+135}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+41}:\\ \;\;\;\;-x \cdot y\\ \mathbf{elif}\;y \leq 1450000:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;-x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z - x\right) \cdot y\\ \mathbf{if}\;y \leq -76000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- z x) y)))
   (if (<= y -76000.0) t_0 (if (<= y 8.6e-10) (fma z y x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (z - x) * y;
	double tmp;
	if (y <= -76000.0) {
		tmp = t_0;
	} else if (y <= 8.6e-10) {
		tmp = fma(z, y, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z - x) * y)
	tmp = 0.0
	if (y <= -76000.0)
		tmp = t_0;
	elseif (y <= 8.6e-10)
		tmp = fma(z, y, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z - x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -76000.0], t$95$0, If[LessEqual[y, 8.6e-10], N[(z * y + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -76000 or 8.60000000000000029e-10 < 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 98.6

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

   5. Simplified 98.6%

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

   if -76000 < y < 8.60000000000000029e-10

   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 99.6

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

   5. Simplified 99.6%

      \[\leadsto x + \color{blue}{y \cdot z} \]
   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 99.6

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

   7. Applied egg-rr 99.6%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -76000:\\ \;\;\;\;\left(z - x\right) \cdot y\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z - x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-83}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.5e-83) (* z y) (if (<= y 5.5e-53) x (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.5e-83) {
		tmp = z * y;
	} else if (y <= 5.5e-53) {
		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 <= (-2.5d-83)) then
        tmp = z * y
    else if (y <= 5.5d-53) 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 <= -2.5e-83) {
		tmp = z * y;
	} else if (y <= 5.5e-53) {
		tmp = x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.5e-83:
		tmp = z * y
	elif y <= 5.5e-53:
		tmp = x
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.5e-83)
		tmp = Float64(z * y);
	elseif (y <= 5.5e-53)
		tmp = x;
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.5e-83)
		tmp = z * y;
	elseif (y <= 5.5e-53)
		tmp = x;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.5e-83], N[(z * y), $MachinePrecision], If[LessEqual[y, 5.5e-53], x, N[(z * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.5e-83 or 5.50000000000000023e-53 < 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 52.6

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

   5. Simplified 52.6%

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

   if -2.5e-83 < y < 5.50000000000000023e-53

   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 76.1%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-83}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.1% 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: 36.9% 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 35.9%

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

Reproduce

herbie shell --seed 2024199 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))