SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 6.2s

Alternatives: 8

Speedup: 1.0×

• 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, 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-define 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. Add Preprocessing

5. Final simplification 100.0%

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

Alternative 2: 61.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -3 \cdot 10^{+242}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+113}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -32:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-104}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 380000000000 \lor \neg \left(y \leq 4.1 \cdot 10^{+37} \lor \neg \left(y \leq 1.6 \cdot 10^{+127}\right) \land y \leq 3.5 \cdot 10^{+262}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= y -3e+242)
     t_0
     (if (<= y -8.5e+113)
       (* y z)
       (if (<= y -32.0)
         t_0
         (if (<= y -3e-93)
           x
           (if (<= y -9.2e-104)
             (* y z)
             (if (<= y 5.5e-20)
               x
               (if (or (<= y 380000000000.0)
                       (not
                        (or (<= y 4.1e+37)
                            (and (not (<= y 1.6e+127)) (<= y 3.5e+262)))))
                 (* y z)
                 t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -3e+242) {
		tmp = t_0;
	} else if (y <= -8.5e+113) {
		tmp = y * z;
	} else if (y <= -32.0) {
		tmp = t_0;
	} else if (y <= -3e-93) {
		tmp = x;
	} else if (y <= -9.2e-104) {
		tmp = y * z;
	} else if (y <= 5.5e-20) {
		tmp = x;
	} else if ((y <= 380000000000.0) || !((y <= 4.1e+37) || (!(y <= 1.6e+127) && (y <= 3.5e+262)))) {
		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 <= (-3d+242)) then
        tmp = t_0
    else if (y <= (-8.5d+113)) then
        tmp = y * z
    else if (y <= (-32.0d0)) then
        tmp = t_0
    else if (y <= (-3d-93)) then
        tmp = x
    else if (y <= (-9.2d-104)) then
        tmp = y * z
    else if (y <= 5.5d-20) then
        tmp = x
    else if ((y <= 380000000000.0d0) .or. (.not. (y <= 4.1d+37) .or. (.not. (y <= 1.6d+127)) .and. (y <= 3.5d+262))) 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 <= -3e+242) {
		tmp = t_0;
	} else if (y <= -8.5e+113) {
		tmp = y * z;
	} else if (y <= -32.0) {
		tmp = t_0;
	} else if (y <= -3e-93) {
		tmp = x;
	} else if (y <= -9.2e-104) {
		tmp = y * z;
	} else if (y <= 5.5e-20) {
		tmp = x;
	} else if ((y <= 380000000000.0) || !((y <= 4.1e+37) || (!(y <= 1.6e+127) && (y <= 3.5e+262)))) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -x
	tmp = 0
	if y <= -3e+242:
		tmp = t_0
	elif y <= -8.5e+113:
		tmp = y * z
	elif y <= -32.0:
		tmp = t_0
	elif y <= -3e-93:
		tmp = x
	elif y <= -9.2e-104:
		tmp = y * z
	elif y <= 5.5e-20:
		tmp = x
	elif (y <= 380000000000.0) or not ((y <= 4.1e+37) or (not (y <= 1.6e+127) and (y <= 3.5e+262))):
		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 <= -3e+242)
		tmp = t_0;
	elseif (y <= -8.5e+113)
		tmp = Float64(y * z);
	elseif (y <= -32.0)
		tmp = t_0;
	elseif (y <= -3e-93)
		tmp = x;
	elseif (y <= -9.2e-104)
		tmp = Float64(y * z);
	elseif (y <= 5.5e-20)
		tmp = x;
	elseif ((y <= 380000000000.0) || !((y <= 4.1e+37) || (!(y <= 1.6e+127) && (y <= 3.5e+262))))
		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 <= -3e+242)
		tmp = t_0;
	elseif (y <= -8.5e+113)
		tmp = y * z;
	elseif (y <= -32.0)
		tmp = t_0;
	elseif (y <= -3e-93)
		tmp = x;
	elseif (y <= -9.2e-104)
		tmp = y * z;
	elseif (y <= 5.5e-20)
		tmp = x;
	elseif ((y <= 380000000000.0) || ~(((y <= 4.1e+37) || (~((y <= 1.6e+127)) && (y <= 3.5e+262)))))
		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, -3e+242], t$95$0, If[LessEqual[y, -8.5e+113], N[(y * z), $MachinePrecision], If[LessEqual[y, -32.0], t$95$0, If[LessEqual[y, -3e-93], x, If[LessEqual[y, -9.2e-104], N[(y * z), $MachinePrecision], If[LessEqual[y, 5.5e-20], x, If[Or[LessEqual[y, 380000000000.0], N[Not[Or[LessEqual[y, 4.1e+37], And[N[Not[LessEqual[y, 1.6e+127]], $MachinePrecision], LessEqual[y, 3.5e+262]]]], $MachinePrecision]], N[(y * z), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3e242 or -8.5000000000000001e113 < y < -32 or 3.8e11 < y < 4.0999999999999998e37 or 1.59999999999999988e127 < y < 3.4999999999999997e262

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 70.6%

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

      1. mul-1-neg 70.6%

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

      2. unsub-neg 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in y around inf 69.0%

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

      1. associate-*r* 69.0%

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

      2. mul-1-neg 69.0%

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

   8. Simplified 69.0%

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

   if -3e242 < y < -8.5000000000000001e113 or -3.0000000000000001e-93 < y < -9.1999999999999998e-104 or 5.4999999999999996e-20 < y < 3.8e11 or 4.0999999999999998e37 < y < 1.59999999999999988e127 or 3.4999999999999997e262 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 97.3%

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

      1. fma-define 100.0%

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

      2. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 74.1%

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

   if -32 < y < -3.0000000000000001e-93 or -9.1999999999999998e-104 < y < 5.4999999999999996e-20

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 73.0%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+242}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+113}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -32:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-104}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 380000000000 \lor \neg \left(y \leq 4.1 \cdot 10^{+37} \lor \neg \left(y \leq 1.6 \cdot 10^{+127}\right) \land y \leq 3.5 \cdot 10^{+262}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-31} \lor \neg \left(x \leq 7 \cdot 10^{-94} \lor \neg \left(x \leq 1.7 \cdot 10^{-73}\right) \land x \leq 1.4 \cdot 10^{-21}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9.5e-31)
         (not (or (<= x 7e-94) (and (not (<= x 1.7e-73)) (<= x 1.4e-21)))))
   (* x (- 1.0 y))
   (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.5e-31) || !((x <= 7e-94) || (!(x <= 1.7e-73) && (x <= 1.4e-21)))) {
		tmp = x * (1.0 - y);
	} 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 ((x <= (-9.5d-31)) .or. (.not. (x <= 7d-94) .or. (.not. (x <= 1.7d-73)) .and. (x <= 1.4d-21))) then
        tmp = x * (1.0d0 - y)
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.5e-31) || !((x <= 7e-94) || (!(x <= 1.7e-73) && (x <= 1.4e-21)))) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9.5e-31) or not ((x <= 7e-94) or (not (x <= 1.7e-73) and (x <= 1.4e-21))):
		tmp = x * (1.0 - y)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9.5e-31) || !((x <= 7e-94) || (!(x <= 1.7e-73) && (x <= 1.4e-21))))
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -9.5e-31) || ~(((x <= 7e-94) || (~((x <= 1.7e-73)) && (x <= 1.4e-21)))))
		tmp = x * (1.0 - y);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9.5e-31], N[Not[Or[LessEqual[x, 7e-94], And[N[Not[LessEqual[x, 1.7e-73]], $MachinePrecision], LessEqual[x, 1.4e-21]]]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5000000000000008e-31 or 6.99999999999999996e-94 < x < 1.7000000000000001e-73 or 1.40000000000000002e-21 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 85.8%

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

      1. mul-1-neg 85.8%

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

      2. unsub-neg 85.8%

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

   5. Simplified 85.8%

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

   if -9.5000000000000008e-31 < x < 6.99999999999999996e-94 or 1.7000000000000001e-73 < x < 1.40000000000000002e-21

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. fma-define 100.0%

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

      2. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 75.6%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-31} \lor \neg \left(x \leq 7 \cdot 10^{-94} \lor \neg \left(x \leq 1.7 \cdot 10^{-73}\right) \land x \leq 1.4 \cdot 10^{-21}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-5} \lor \neg \left(y \leq -9.5 \cdot 10^{-91} \lor \neg \left(y \leq -4.8 \cdot 10^{-103}\right) \land y \leq 2.3 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.2e-5)
         (not
          (or (<= y -9.5e-91) (and (not (<= y -4.8e-103)) (<= y 2.3e-18)))))
   (* y z)
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.2e-5) || !((y <= -9.5e-91) || (!(y <= -4.8e-103) && (y <= 2.3e-18)))) {
		tmp = y * z;
	} 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 <= (-6.2d-5)) .or. (.not. (y <= (-9.5d-91)) .or. (.not. (y <= (-4.8d-103))) .and. (y <= 2.3d-18))) then
        tmp = y * z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.2e-5) || !((y <= -9.5e-91) || (!(y <= -4.8e-103) && (y <= 2.3e-18)))) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.2e-5) or not ((y <= -9.5e-91) or (not (y <= -4.8e-103) and (y <= 2.3e-18))):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.2e-5) || !((y <= -9.5e-91) || (!(y <= -4.8e-103) && (y <= 2.3e-18))))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.2e-5) || ~(((y <= -9.5e-91) || (~((y <= -4.8e-103)) && (y <= 2.3e-18)))))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.2e-5], N[Not[Or[LessEqual[y, -9.5e-91], And[N[Not[LessEqual[y, -4.8e-103]], $MachinePrecision], LessEqual[y, 2.3e-18]]]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -6.20000000000000027e-5 or -9.5e-91 < y < -4.8000000000000004e-103 or 2.3000000000000001e-18 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 97.9%

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

      1. fma-define 99.3%

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

      2. mul-1-neg 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x around 0 54.7%

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

   if -6.20000000000000027e-5 < y < -9.5e-91 or -4.8000000000000004e-103 < y < 2.3000000000000001e-18

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 73.6%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-5} \lor \neg \left(y \leq -9.5 \cdot 10^{-91} \lor \neg \left(y \leq -4.8 \cdot 10^{-103}\right) \land y \leq 2.3 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -620000000 \lor \neg \left(x \leq 2.6 \cdot 10^{+94}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -620000000.0) (not (<= x 2.6e+94)))
   (* x (- 1.0 y))
   (* y (- z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -620000000.0) || !(x <= 2.6e+94)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * (z - 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 ((x <= (-620000000.0d0)) .or. (.not. (x <= 2.6d+94))) then
        tmp = x * (1.0d0 - y)
    else
        tmp = y * (z - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -620000000.0) || !(x <= 2.6e+94)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * (z - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -620000000.0) or not (x <= 2.6e+94):
		tmp = x * (1.0 - y)
	else:
		tmp = y * (z - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -620000000.0) || !(x <= 2.6e+94))
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(y * Float64(z - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -620000000.0) || ~((x <= 2.6e+94)))
		tmp = x * (1.0 - y);
	else
		tmp = y * (z - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -620000000.0], N[Not[LessEqual[x, 2.6e+94]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.2e8 or 2.5999999999999999e94 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 88.9%

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

      1. mul-1-neg 88.9%

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

      2. unsub-neg 88.9%

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

   5. Simplified 88.9%

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

   if -6.2e8 < x < 2.5999999999999999e94

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 99.3%

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

      1. fma-define 99.3%

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

      2. mul-1-neg 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in y around inf 82.3%

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

      1. mul-1-neg 82.3%

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

      2. unsub-neg 82.3%

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

   8. Simplified 82.3%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -620000000 \lor \neg \left(x \leq 2.6 \cdot 10^{+94}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -32 \lor \neg \left(y \leq 0.045\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -32.0) (not (<= y 0.045))) (* y (- z x)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -32.0) || !(y <= 0.045)) {
		tmp = y * (z - x);
	} else {
		tmp = x + (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 <= (-32.0d0)) .or. (.not. (y <= 0.045d0))) then
        tmp = y * (z - x)
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -32.0) || !(y <= 0.045)) {
		tmp = y * (z - x);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -32.0) or not (y <= 0.045):
		tmp = y * (z - x)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -32.0) || !(y <= 0.045))
		tmp = Float64(y * Float64(z - x));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -32.0) || ~((y <= 0.045)))
		tmp = y * (z - x);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -32.0], N[Not[LessEqual[y, 0.045]], $MachinePrecision]], N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -32 or 0.044999999999999998 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 97.7%

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

      1. fma-define 99.2%

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

      2. mul-1-neg 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in y around inf 99.1%

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

      1. mul-1-neg 99.1%

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

      2. unsub-neg 99.1%

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

   8. Simplified 99.1%

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

   if -32 < y < 0.044999999999999998

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 98.2%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -32 \lor \neg \left(y \leq 0.045\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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. Add Preprocessing

3. Final simplification 100.0%

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

Alternative 8: 37.0% 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. Add Preprocessing

3. Taylor expanded in y around 0 34.4%

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

4. Final simplification 34.4%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024044 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))