SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.0s

Alternatives: 6

Speedup: 1.2×

• 20.6% 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. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 100.0

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

4. Applied rewrites 100.0%

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

Alternative 2: 86.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - x \cdot y\\ \mathbf{if}\;x \leq -1.85 \cdot 10^{+47}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.42:\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- x (* x y))))
   (if (<= x -1.85e+47) t_0 (if (<= x 0.42) (+ x (* z y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x - (x * y);
	double tmp;
	if (x <= -1.85e+47) {
		tmp = t_0;
	} else if (x <= 0.42) {
		tmp = x + (z * y);
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = x - (x * y)
    if (x <= (-1.85d+47)) then
        tmp = t_0
    else if (x <= 0.42d0) then
        tmp = x + (z * y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x - (x * y);
	double tmp;
	if (x <= -1.85e+47) {
		tmp = t_0;
	} else if (x <= 0.42) {
		tmp = x + (z * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x - (x * y)
	tmp = 0
	if x <= -1.85e+47:
		tmp = t_0
	elif x <= 0.42:
		tmp = x + (z * y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x - Float64(x * y))
	tmp = 0.0
	if (x <= -1.85e+47)
		tmp = t_0;
	elseif (x <= 0.42)
		tmp = Float64(x + Float64(z * y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x - (x * y);
	tmp = 0.0;
	if (x <= -1.85e+47)
		tmp = t_0;
	elseif (x <= 0.42)
		tmp = x + (z * y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.85e+47], t$95$0, If[LessEqual[x, 0.42], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8500000000000002e47 or 0.419999999999999984 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{x \cdot 1 - x \cdot y} \]

      4. *-rgt-identity N/A

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

      5. lower--.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 93.7

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

   5. Applied rewrites 93.7%

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

   if -1.8500000000000002e47 < x < 0.419999999999999984

   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. lower-*.f64 92.5

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

   5. Applied rewrites 92.5%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+47}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;x \leq 0.42:\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - x \cdot y\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{-67}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-139}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- x (* x y))))
   (if (<= x -2.8e-67) t_0 (if (<= x 5.6e-139) (* z y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x - (x * y);
	double tmp;
	if (x <= -2.8e-67) {
		tmp = t_0;
	} else if (x <= 5.6e-139) {
		tmp = z * y;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = x - (x * y)
    if (x <= (-2.8d-67)) then
        tmp = t_0
    else if (x <= 5.6d-139) then
        tmp = z * y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x - (x * y);
	double tmp;
	if (x <= -2.8e-67) {
		tmp = t_0;
	} else if (x <= 5.6e-139) {
		tmp = z * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x - (x * y)
	tmp = 0
	if x <= -2.8e-67:
		tmp = t_0
	elif x <= 5.6e-139:
		tmp = z * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x - Float64(x * y))
	tmp = 0.0
	if (x <= -2.8e-67)
		tmp = t_0;
	elseif (x <= 5.6e-139)
		tmp = Float64(z * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x - (x * y);
	tmp = 0.0;
	if (x <= -2.8e-67)
		tmp = t_0;
	elseif (x <= 5.6e-139)
		tmp = z * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.8e-67], t$95$0, If[LessEqual[x, 5.6e-139], N[(z * y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8000000000000001e-67 or 5.5999999999999997e-139 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{x \cdot 1 - x \cdot y} \]

      4. *-rgt-identity N/A

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

      5. lower--.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 84.9

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

   5. Applied rewrites 84.9%

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

   if -2.8000000000000001e-67 < x < 5.5999999999999997e-139

   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. lower-*.f64 82.4

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

   5. Applied rewrites 82.4%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-67}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-139}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;x \leq -1.85 \cdot 10^{+47}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.39:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- y))))
   (if (<= x -1.85e+47) t_0 (if (<= x 0.39) (* z y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * -y;
	double tmp;
	if (x <= -1.85e+47) {
		tmp = t_0;
	} else if (x <= 0.39) {
		tmp = z * y;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = x * -y
    if (x <= (-1.85d+47)) then
        tmp = t_0
    else if (x <= 0.39d0) then
        tmp = z * y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -y;
	double tmp;
	if (x <= -1.85e+47) {
		tmp = t_0;
	} else if (x <= 0.39) {
		tmp = z * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -y
	tmp = 0
	if x <= -1.85e+47:
		tmp = t_0
	elif x <= 0.39:
		tmp = z * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-y))
	tmp = 0.0
	if (x <= -1.85e+47)
		tmp = t_0;
	elseif (x <= 0.39)
		tmp = Float64(z * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -y;
	tmp = 0.0;
	if (x <= -1.85e+47)
		tmp = t_0;
	elseif (x <= 0.39)
		tmp = z * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[x, -1.85e+47], t$95$0, If[LessEqual[x, 0.39], N[(z * y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8500000000000002e47 or 0.39000000000000001 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{x \cdot 1 - x \cdot y} \]

      4. *-rgt-identity N/A

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

      5. lower--.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 93.7

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

   5. Applied rewrites 93.7%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 45.2%

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

   if -1.8500000000000002e47 < x < 0.39000000000000001

   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. lower-*.f64 68.6

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

   5. Applied rewrites 68.6%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq 0.39:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 41.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ z \cdot y \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return z * 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 = z * y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. lower-*.f64 42.3

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

5. Applied rewrites 42.3%

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

6. Final simplification 42.3%

   \[\leadsto z \cdot y \]
7. Add Preprocessing

Alternative 6: 3.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ x \cdot y \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return x * 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 * y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around inf

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

   1. mul-1-neg N/A

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

   2. unsub-neg N/A

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

   3. distribute-lft-out-- N/A

      \[\leadsto \color{blue}{x \cdot 1 - x \cdot y} \]

   4. *-rgt-identity N/A

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

   5. lower--.f64 N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 63.2

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

5. Applied rewrites 63.2%

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

6. Taylor expanded in y around inf

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

8. Applied rewrites 28.0%

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

10. Applied rewrites 4.0%

    \[\leadsto y \cdot x \]

11. Final simplification 4.0%

    \[\leadsto x \cdot y \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024219 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))