SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 2.6s

Alternatives: 7

Speedup: 1.0×

• 20.4% 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: 60.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -450000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+52} \lor \neg \left(y \leq 3.1 \cdot 10^{+91}\right) \land y \leq 5 \cdot 10^{+207}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= y -450000000.0)
     t_0
     (if (<= y 5.8e-104)
       x
       (if (or (<= y 3e+52) (and (not (<= y 3.1e+91)) (<= y 5e+207)))
         (* y z)
         t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -450000000.0) {
		tmp = t_0;
	} else if (y <= 5.8e-104) {
		tmp = x;
	} else if ((y <= 3e+52) || (!(y <= 3.1e+91) && (y <= 5e+207))) {
		tmp = y * z;
	} 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 = y * -x
    if (y <= (-450000000.0d0)) then
        tmp = t_0
    else if (y <= 5.8d-104) then
        tmp = x
    else if ((y <= 3d+52) .or. (.not. (y <= 3.1d+91)) .and. (y <= 5d+207)) then
        tmp = y * z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -450000000.0) {
		tmp = t_0;
	} else if (y <= 5.8e-104) {
		tmp = x;
	} else if ((y <= 3e+52) || (!(y <= 3.1e+91) && (y <= 5e+207))) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if y <= -450000000.0:
		tmp = t_0
	elif y <= 5.8e-104:
		tmp = x
	elif (y <= 3e+52) or (not (y <= 3.1e+91) and (y <= 5e+207)):
		tmp = y * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-x))
	tmp = 0.0
	if (y <= -450000000.0)
		tmp = t_0;
	elseif (y <= 5.8e-104)
		tmp = x;
	elseif ((y <= 3e+52) || (!(y <= 3.1e+91) && (y <= 5e+207)))
		tmp = Float64(y * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -x;
	tmp = 0.0;
	if (y <= -450000000.0)
		tmp = t_0;
	elseif (y <= 5.8e-104)
		tmp = x;
	elseif ((y <= 3e+52) || (~((y <= 3.1e+91)) && (y <= 5e+207)))
		tmp = y * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[y, -450000000.0], t$95$0, If[LessEqual[y, 5.8e-104], x, If[Or[LessEqual[y, 3e+52], And[N[Not[LessEqual[y, 3.1e+91]], $MachinePrecision], LessEqual[y, 5e+207]]], N[(y * z), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5e8 or 3e52 < y < 3.09999999999999998e91 or 4.9999999999999999e207 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 59.1%

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

      1. +-commutative 59.1%

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

      2. distribute-rgt1-in 59.1%

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

      3. mul-1-neg 59.1%

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

      4. cancel-sign-sub-inv 59.1%

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

   4. Simplified 59.1%

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

   5. Taylor expanded in y around inf 59.1%

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

      1. mul-1-neg 59.1%

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

      2. distribute-rgt-neg-in 59.1%

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

   7. Simplified 59.1%

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

   if -4.5e8 < y < 5.8000000000000002e-104

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 72.3%

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

   if 5.8000000000000002e-104 < y < 3e52 or 3.09999999999999998e91 < y < 4.9999999999999999e207

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 59.4%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -450000000:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+52} \lor \neg \left(y \leq 3.1 \cdot 10^{+91}\right) \land y \leq 5 \cdot 10^{+207}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 3: 84.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.054 \lor \neg \left(y \leq 6.5 \cdot 10^{-96}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.054) (not (<= y 6.5e-96))) (* y (- z x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.054) || !(y <= 6.5e-96)) {
		tmp = y * (z - 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 <= (-0.054d0)) .or. (.not. (y <= 6.5d-96))) then
        tmp = y * (z - 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 <= -0.054) || !(y <= 6.5e-96)) {
		tmp = y * (z - x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.054) or not (y <= 6.5e-96):
		tmp = y * (z - x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.054) || !(y <= 6.5e-96))
		tmp = Float64(y * Float64(z - x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.054) || ~((y <= 6.5e-96)))
		tmp = y * (z - x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.054], N[Not[LessEqual[y, 6.5e-96]], $MachinePrecision]], N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -0.0539999999999999994 or 6.50000000000000001e-96 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 92.5%

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

   if -0.0539999999999999994 < y < 6.50000000000000001e-96

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 72.9%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.054 \lor \neg \left(y \leq 6.5 \cdot 10^{-96}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 78.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+71} \lor \neg \left(z \leq 3.1 \cdot 10^{-23}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.5e+71) (not (<= z 3.1e-23))) (* y (- z x)) (- x (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.5e+71) || !(z <= 3.1e-23)) {
		tmp = y * (z - x);
	} else {
		tmp = x - (y * 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 ((z <= (-1.5d+71)) .or. (.not. (z <= 3.1d-23))) then
        tmp = y * (z - x)
    else
        tmp = x - (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.5e+71) || !(z <= 3.1e-23)) {
		tmp = y * (z - x);
	} else {
		tmp = x - (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.5e+71) or not (z <= 3.1e-23):
		tmp = y * (z - x)
	else:
		tmp = x - (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.5e+71) || !(z <= 3.1e-23))
		tmp = Float64(y * Float64(z - x));
	else
		tmp = Float64(x - Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.5e+71) || ~((z <= 3.1e-23)))
		tmp = y * (z - x);
	else
		tmp = x - (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.5e+71], N[Not[LessEqual[z, 3.1e-23]], $MachinePrecision]], N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.50000000000000006e71 or 3.0999999999999999e-23 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 85.6%

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

   if -1.50000000000000006e71 < z < 3.0999999999999999e-23

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 86.3%

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

      1. +-commutative 86.3%

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

      2. distribute-rgt1-in 86.3%

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

      3. mul-1-neg 86.3%

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

      4. cancel-sign-sub-inv 86.3%

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

   4. Simplified 86.3%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+71} \lor \neg \left(z \leq 3.1 \cdot 10^{-23}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot x\\ \end{array} \]

Alternative 5: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.054:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.054) (* y z) (if (<= y 6.5e-96) x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.054) {
		tmp = y * z;
	} else if (y <= 6.5e-96) {
		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 <= (-0.054d0)) then
        tmp = y * z
    else if (y <= 6.5d-96) 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 <= -0.054) {
		tmp = y * z;
	} else if (y <= 6.5e-96) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.054:
		tmp = y * z
	elif y <= 6.5e-96:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.054)
		tmp = Float64(y * z);
	elseif (y <= 6.5e-96)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -0.054)
		tmp = y * z;
	elseif (y <= 6.5e-96)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.054], N[(y * z), $MachinePrecision], If[LessEqual[y, 6.5e-96], x, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0539999999999999994 or 6.50000000000000001e-96 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 51.6%

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

   if -0.0539999999999999994 < y < 6.50000000000000001e-96

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 72.9%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.054:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 6: 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 7: 37.1% 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 36.3%

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

3. Final simplification 36.3%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023257 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))