SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 3.4s

Alternatives: 7

Speedup: 1.0×

• 20.9% 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: 61.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+21}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-50}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 16200000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= y -2.4e+21)
     t_0
     (if (<= y -4.6e-50) (* y z) (if (<= y 16200000.0) x t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -2.4e+21) {
		tmp = t_0;
	} else if (y <= -4.6e-50) {
		tmp = y * z;
	} else if (y <= 16200000.0) {
		tmp = x;
	} 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 <= (-2.4d+21)) then
        tmp = t_0
    else if (y <= (-4.6d-50)) then
        tmp = y * z
    else if (y <= 16200000.0d0) then
        tmp = x
    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 <= -2.4e+21) {
		tmp = t_0;
	} else if (y <= -4.6e-50) {
		tmp = y * z;
	} else if (y <= 16200000.0) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if y <= -2.4e+21:
		tmp = t_0
	elif y <= -4.6e-50:
		tmp = y * z
	elif y <= 16200000.0:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-x))
	tmp = 0.0
	if (y <= -2.4e+21)
		tmp = t_0;
	elseif (y <= -4.6e-50)
		tmp = Float64(y * z);
	elseif (y <= 16200000.0)
		tmp = x;
	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 <= -2.4e+21)
		tmp = t_0;
	elseif (y <= -4.6e-50)
		tmp = y * z;
	elseif (y <= 16200000.0)
		tmp = x;
	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, -2.4e+21], t$95$0, If[LessEqual[y, -4.6e-50], N[(y * z), $MachinePrecision], If[LessEqual[y, 16200000.0], x, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4e21 or 1.62e7 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 57.6%

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

      1. mul-1-neg 57.6%

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

      2. unsub-neg 57.6%

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

      3. distribute-rgt-out-- 57.6%

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

      4. *-lft-identity 57.6%

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

   4. Simplified 57.6%

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

   5. Taylor expanded in y around inf 57.4%

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

      1. associate-*r* 57.4%

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

      2. neg-mul-1 57.4%

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

   7. Simplified 57.4%

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

   if -2.4e21 < y < -4.60000000000000039e-50

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 68.3%

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

   if -4.60000000000000039e-50 < y < 1.62e7

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.0%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-50}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 16200000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 3: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-50} \lor \neg \left(y \leq 0.054\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.4e-50) (not (<= y 0.054))) (* y (- z x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.4e-50) || !(y <= 0.054)) {
		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 <= (-5.4d-50)) .or. (.not. (y <= 0.054d0))) 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 <= -5.4e-50) || !(y <= 0.054)) {
		tmp = y * (z - x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.4e-50) or not (y <= 0.054):
		tmp = y * (z - x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.4e-50) || !(y <= 0.054))
		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 <= -5.4e-50) || ~((y <= 0.054)))
		tmp = y * (z - x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.4e-50], N[Not[LessEqual[y, 0.054]], $MachinePrecision]], N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.3999999999999999e-50 or 0.0539999999999999994 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 96.9%

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

   if -5.3999999999999999e-50 < y < 0.0539999999999999994

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 80.0%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-50} \lor \neg \left(y \leq 0.054\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-45} \lor \neg \left(y \leq 27\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.5e-45) (not (<= y 27.0))) (* y (- z x)) (- x (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.5e-45) || !(y <= 27.0)) {
		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 ((y <= (-1.5d-45)) .or. (.not. (y <= 27.0d0))) 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 ((y <= -1.5e-45) || !(y <= 27.0)) {
		tmp = y * (z - x);
	} else {
		tmp = x - (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.5e-45) or not (y <= 27.0):
		tmp = y * (z - x)
	else:
		tmp = x - (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.5e-45) || !(y <= 27.0))
		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 ((y <= -1.5e-45) || ~((y <= 27.0)))
		tmp = y * (z - x);
	else
		tmp = x - (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.5e-45], N[Not[LessEqual[y, 27.0]], $MachinePrecision]], N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.50000000000000005e-45 or 27 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 96.9%

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

   if -1.50000000000000005e-45 < y < 27

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 81.3%

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

      1. mul-1-neg 81.3%

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

      2. unsub-neg 81.3%

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

      3. distribute-rgt-out-- 81.3%

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

      4. *-lft-identity 81.3%

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

   4. Simplified 81.3%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-45} \lor \neg \left(y \leq 27\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot x\\ \end{array} \]

Alternative 5: 61.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-47}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 0.00052:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.9e-47) (* y z) (if (<= y 0.00052) x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.9e-47) {
		tmp = y * z;
	} else if (y <= 0.00052) {
		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 <= (-2.9d-47)) then
        tmp = y * z
    else if (y <= 0.00052d0) 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 <= -2.9e-47) {
		tmp = y * z;
	} else if (y <= 0.00052) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.9e-47:
		tmp = y * z
	elif y <= 0.00052:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.9e-47)
		tmp = Float64(y * z);
	elseif (y <= 0.00052)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.9e-47)
		tmp = y * z;
	elseif (y <= 0.00052)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.9e-47], N[(y * z), $MachinePrecision], If[LessEqual[y, 0.00052], x, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9e-47 or 5.19999999999999954e-4 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 50.5%

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

   if -2.9e-47 < y < 5.19999999999999954e-4

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 80.0%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-47}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 0.00052:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

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: 37.2% 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 44.1%

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

3. Final simplification 44.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023293 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))