SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 3.4s

Alternatives: 7

Speedup: 1.0×

• 21.3% 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. Add Preprocessing

5. Final simplification 100.0%

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

Alternative 2: 72.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-10} \lor \neg \left(x \leq -6.5 \cdot 10^{-46}\right) \land \left(x \leq -4.1 \cdot 10^{-106} \lor \neg \left(x \leq 3.5 \cdot 10^{-159}\right) \land \left(x \leq 1.65 \cdot 10^{-91} \lor \neg \left(x \leq 4.3 \cdot 10^{+43}\right)\right)\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1e-10)
         (and (not (<= x -6.5e-46))
              (or (<= x -4.1e-106)
                  (and (not (<= x 3.5e-159))
                       (or (<= x 1.65e-91) (not (<= x 4.3e+43)))))))
   (* x (- 1.0 y))
   (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1e-10) || (!(x <= -6.5e-46) && ((x <= -4.1e-106) || (!(x <= 3.5e-159) && ((x <= 1.65e-91) || !(x <= 4.3e+43)))))) {
		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 <= (-1d-10)) .or. (.not. (x <= (-6.5d-46))) .and. (x <= (-4.1d-106)) .or. (.not. (x <= 3.5d-159)) .and. (x <= 1.65d-91) .or. (.not. (x <= 4.3d+43))) 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 <= -1e-10) || (!(x <= -6.5e-46) && ((x <= -4.1e-106) || (!(x <= 3.5e-159) && ((x <= 1.65e-91) || !(x <= 4.3e+43)))))) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1e-10) or (not (x <= -6.5e-46) and ((x <= -4.1e-106) or (not (x <= 3.5e-159) and ((x <= 1.65e-91) or not (x <= 4.3e+43))))):
		tmp = x * (1.0 - y)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1e-10) || (!(x <= -6.5e-46) && ((x <= -4.1e-106) || (!(x <= 3.5e-159) && ((x <= 1.65e-91) || !(x <= 4.3e+43))))))
		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 <= -1e-10) || (~((x <= -6.5e-46)) && ((x <= -4.1e-106) || (~((x <= 3.5e-159)) && ((x <= 1.65e-91) || ~((x <= 4.3e+43)))))))
		tmp = x * (1.0 - y);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1e-10], And[N[Not[LessEqual[x, -6.5e-46]], $MachinePrecision], Or[LessEqual[x, -4.1e-106], And[N[Not[LessEqual[x, 3.5e-159]], $MachinePrecision], Or[LessEqual[x, 1.65e-91], N[Not[LessEqual[x, 4.3e+43]], $MachinePrecision]]]]]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.00000000000000004e-10 or -6.49999999999999966e-46 < x < -4.0999999999999999e-106 or 3.50000000000000002e-159 < x < 1.65000000000000006e-91 or 4.3e43 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 87.1%

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

      1. mul-1-neg 87.1%

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

      2. unsub-neg 87.1%

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

   5. Simplified 87.1%

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

   if -1.00000000000000004e-10 < x < -6.49999999999999966e-46 or -4.0999999999999999e-106 < x < 3.50000000000000002e-159 or 1.65000000000000006e-91 < x < 4.3e43

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 74.8%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-10} \lor \neg \left(x \leq -6.5 \cdot 10^{-46}\right) \land \left(x \leq -4.1 \cdot 10^{-106} \lor \neg \left(x \leq 3.5 \cdot 10^{-159}\right) \land \left(x \leq 1.65 \cdot 10^{-91} \lor \neg \left(x \leq 4.3 \cdot 10^{+43}\right)\right)\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -y \cdot x\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{+83}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{+21}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-112}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-78}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+131} \lor \neg \left(y \leq 4 \cdot 10^{+218}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* y x))))
   (if (<= y -4.3e+83)
     (* y z)
     (if (<= y -8.8e+21)
       t_0
       (if (<= y -4.8e-112)
         (* y z)
         (if (<= y 1.95e-78)
           x
           (if (or (<= y 5.4e+131) (not (<= y 4e+218))) (* y z) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = -(y * x);
	double tmp;
	if (y <= -4.3e+83) {
		tmp = y * z;
	} else if (y <= -8.8e+21) {
		tmp = t_0;
	} else if (y <= -4.8e-112) {
		tmp = y * z;
	} else if (y <= 1.95e-78) {
		tmp = x;
	} else if ((y <= 5.4e+131) || !(y <= 4e+218)) {
		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 <= (-4.3d+83)) then
        tmp = y * z
    else if (y <= (-8.8d+21)) then
        tmp = t_0
    else if (y <= (-4.8d-112)) then
        tmp = y * z
    else if (y <= 1.95d-78) then
        tmp = x
    else if ((y <= 5.4d+131) .or. (.not. (y <= 4d+218))) 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 <= -4.3e+83) {
		tmp = y * z;
	} else if (y <= -8.8e+21) {
		tmp = t_0;
	} else if (y <= -4.8e-112) {
		tmp = y * z;
	} else if (y <= 1.95e-78) {
		tmp = x;
	} else if ((y <= 5.4e+131) || !(y <= 4e+218)) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -(y * x)
	tmp = 0
	if y <= -4.3e+83:
		tmp = y * z
	elif y <= -8.8e+21:
		tmp = t_0
	elif y <= -4.8e-112:
		tmp = y * z
	elif y <= 1.95e-78:
		tmp = x
	elif (y <= 5.4e+131) or not (y <= 4e+218):
		tmp = y * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-Float64(y * x))
	tmp = 0.0
	if (y <= -4.3e+83)
		tmp = Float64(y * z);
	elseif (y <= -8.8e+21)
		tmp = t_0;
	elseif (y <= -4.8e-112)
		tmp = Float64(y * z);
	elseif (y <= 1.95e-78)
		tmp = x;
	elseif ((y <= 5.4e+131) || !(y <= 4e+218))
		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 <= -4.3e+83)
		tmp = y * z;
	elseif (y <= -8.8e+21)
		tmp = t_0;
	elseif (y <= -4.8e-112)
		tmp = y * z;
	elseif (y <= 1.95e-78)
		tmp = x;
	elseif ((y <= 5.4e+131) || ~((y <= 4e+218)))
		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, -4.3e+83], N[(y * z), $MachinePrecision], If[LessEqual[y, -8.8e+21], t$95$0, If[LessEqual[y, -4.8e-112], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.95e-78], x, If[Or[LessEqual[y, 5.4e+131], N[Not[LessEqual[y, 4e+218]], $MachinePrecision]], N[(y * z), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.3e83 or -8.8e21 < y < -4.8000000000000001e-112 or 1.9500000000000001e-78 < y < 5.40000000000000008e131 or 4.00000000000000033e218 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 63.8%

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

   if -4.3e83 < y < -8.8e21 or 5.40000000000000008e131 < y < 4.00000000000000033e218

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in z around 0 71.4%

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

      1. mul-1-neg 71.4%

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

      2. distribute-lft-neg-out 71.4%

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

      3. *-commutative 71.4%

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

   6. Simplified 71.4%

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

   if -4.8000000000000001e-112 < y < 1.9500000000000001e-78

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 89.8%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+83}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{+21}:\\ \;\;\;\;-y \cdot x\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-112}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-78}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+131} \lor \neg \left(y \leq 4 \cdot 10^{+218}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;-y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-112} \lor \neg \left(y \leq 0.92\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.2e-112) (not (<= y 0.92))) (* y (- z x)) (* x (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.2e-112) || !(y <= 0.92)) {
		tmp = y * (z - x);
	} else {
		tmp = x * (1.0 - 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 <= (-5.2d-112)) .or. (.not. (y <= 0.92d0))) then
        tmp = y * (z - x)
    else
        tmp = x * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.2e-112) || !(y <= 0.92)) {
		tmp = y * (z - x);
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.2e-112) or not (y <= 0.92):
		tmp = y * (z - x)
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.2e-112) || !(y <= 0.92))
		tmp = Float64(y * Float64(z - x));
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.2e-112) || ~((y <= 0.92)))
		tmp = y * (z - x);
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.2e-112], N[Not[LessEqual[y, 0.92]], $MachinePrecision]], N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.19999999999999983e-112 or 0.92000000000000004 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 93.3%

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

   if -5.19999999999999983e-112 < y < 0.92000000000000004

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 84.6%

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

      1. mul-1-neg 84.6%

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

      2. unsub-neg 84.6%

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

   5. Simplified 84.6%

      \[\leadsto \color{blue}{x \cdot \left(1 - y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-112} \lor \neg \left(y \leq 0.92\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-113} \lor \neg \left(y \leq 8.6 \cdot 10^{-75}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.5e-113) (not (<= y 8.6e-75))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.5e-113) || !(y <= 8.6e-75)) {
		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 <= (-2.5d-113)) .or. (.not. (y <= 8.6d-75))) 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 <= -2.5e-113) || !(y <= 8.6e-75)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.5e-113) or not (y <= 8.6e-75):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.5e-113) || !(y <= 8.6e-75))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.5e-113) || ~((y <= 8.6e-75)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.5e-113], N[Not[LessEqual[y, 8.6e-75]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.4999999999999999e-113 or 8.5999999999999998e-75 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 57.4%

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

   if -2.4999999999999999e-113 < y < 8.5999999999999998e-75

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 89.8%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-113} \lor \neg \left(y \leq 8.6 \cdot 10^{-75}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

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. Add Preprocessing

3. Final simplification 100.0%

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

Alternative 7: 36.4% 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 38.2%

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

4. Final simplification 38.2%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024020 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))