Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.5% → 99.8%
Time: 3.3s
Alternatives: 5
Speedup: 1.0×

Specification

?
\[\begin{array}{l} \\ \frac{x \cdot 100}{x + y} \end{array} \]
(FPCore (x y) :precision binary64 (/ (* x 100.0) (+ x y)))
double code(double x, double y) {
	return (x * 100.0) / (x + y);
}
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * 100.0d0) / (x + y)
end function
public static double code(double x, double y) {
	return (x * 100.0) / (x + y);
}
def code(x, y):
	return (x * 100.0) / (x + y)
function code(x, y)
	return Float64(Float64(x * 100.0) / Float64(x + y))
end
function tmp = code(x, y)
	tmp = (x * 100.0) / (x + y);
end
code[x_, y_] := N[(N[(x * 100.0), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}

\\
\frac{x \cdot 100}{x + y}
\end{array}

Sampling outcomes in binary64 precision:

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Accuracy vs Speed?

Herbie found 5 alternatives:

AlternativeAccuracySpeedup
The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Initial Program: 99.5% accurate, 1.0× speedup?

\[\begin{array}{l} \\ \frac{x \cdot 100}{x + y} \end{array} \]
(FPCore (x y) :precision binary64 (/ (* x 100.0) (+ x y)))
double code(double x, double y) {
	return (x * 100.0) / (x + y);
}
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * 100.0d0) / (x + y)
end function
public static double code(double x, double y) {
	return (x * 100.0) / (x + y);
}
def code(x, y):
	return (x * 100.0) / (x + y)
function code(x, y)
	return Float64(Float64(x * 100.0) / Float64(x + y))
end
function tmp = code(x, y)
	tmp = (x * 100.0) / (x + y);
end
code[x_, y_] := N[(N[(x * 100.0), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}

\\
\frac{x \cdot 100}{x + y}
\end{array}

Alternative 1: 99.8% accurate, 1.0× speedup?

\[\begin{array}{l} \\ x \cdot \frac{100}{x + y} \end{array} \]
(FPCore (x y) :precision binary64 (* x (/ 100.0 (+ x y))))
double code(double x, double y) {
	return x * (100.0 / (x + y));
}
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (100.0d0 / (x + y))
end function
public static double code(double x, double y) {
	return x * (100.0 / (x + y));
}
def code(x, y):
	return x * (100.0 / (x + y))
function code(x, y)
	return Float64(x * Float64(100.0 / Float64(x + y)))
end
function tmp = code(x, y)
	tmp = x * (100.0 / (x + y));
end
code[x_, y_] := N[(x * N[(100.0 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}

\\
x \cdot \frac{100}{x + y}
\end{array}
Derivation
  1. Initial program 99.7%

    \[\frac{x \cdot 100}{x + y} \]
  2. Step-by-step derivation
    1. *-commutative99.7%

      \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]
    2. associate-/l*99.0%

      \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]
  3. Simplified99.0%

    \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]
  4. Step-by-step derivation
    1. associate-/r/99.7%

      \[\leadsto \color{blue}{\frac{100}{x + y} \cdot x} \]
  5. Applied egg-rr99.7%

    \[\leadsto \color{blue}{\frac{100}{x + y} \cdot x} \]
  6. Final simplification99.7%

    \[\leadsto x \cdot \frac{100}{x + y} \]

Alternative 2: 72.2% accurate, 0.5× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+58} \lor \neg \left(y \leq 0.0054 \lor \neg \left(y \leq 4.4 \cdot 10^{+207}\right) \land y \leq 2.55 \cdot 10^{+222}\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]
(FPCore (x y)
 :precision binary64
 (if (or (<= y -4.9e+58)
         (not (or (<= y 0.0054) (and (not (<= y 4.4e+207)) (<= y 2.55e+222)))))
   (* 100.0 (/ x y))
   100.0))
double code(double x, double y) {
	double tmp;
	if ((y <= -4.9e+58) || !((y <= 0.0054) || (!(y <= 4.4e+207) && (y <= 2.55e+222)))) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-4.9d+58)) .or. (.not. (y <= 0.0054d0) .or. (.not. (y <= 4.4d+207)) .and. (y <= 2.55d+222))) then
        tmp = 100.0d0 * (x / y)
    else
        tmp = 100.0d0
    end if
    code = tmp
end function
public static double code(double x, double y) {
	double tmp;
	if ((y <= -4.9e+58) || !((y <= 0.0054) || (!(y <= 4.4e+207) && (y <= 2.55e+222)))) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}
def code(x, y):
	tmp = 0
	if (y <= -4.9e+58) or not ((y <= 0.0054) or (not (y <= 4.4e+207) and (y <= 2.55e+222))):
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp
function code(x, y)
	tmp = 0.0
	if ((y <= -4.9e+58) || !((y <= 0.0054) || (!(y <= 4.4e+207) && (y <= 2.55e+222))))
		tmp = Float64(100.0 * Float64(x / y));
	else
		tmp = 100.0;
	end
	return tmp
end
function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -4.9e+58) || ~(((y <= 0.0054) || (~((y <= 4.4e+207)) && (y <= 2.55e+222)))))
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end
code[x_, y_] := If[Or[LessEqual[y, -4.9e+58], N[Not[Or[LessEqual[y, 0.0054], And[N[Not[LessEqual[y, 4.4e+207]], $MachinePrecision], LessEqual[y, 2.55e+222]]]], $MachinePrecision]], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]
\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;y \leq -4.9 \cdot 10^{+58} \lor \neg \left(y \leq 0.0054 \lor \neg \left(y \leq 4.4 \cdot 10^{+207}\right) \land y \leq 2.55 \cdot 10^{+222}\right):\\
\;\;\;\;100 \cdot \frac{x}{y}\\

\mathbf{else}:\\
\;\;\;\;100\\


\end{array}
\end{array}
Derivation
  1. Split input into 2 regimes
  2. if y < -4.90000000000000018e58 or 0.0054000000000000003 < y < 4.40000000000000017e207 or 2.55e222 < y

    1. Initial program 99.7%

      \[\frac{x \cdot 100}{x + y} \]
    2. Step-by-step derivation
      1. *-commutative99.7%

        \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]
      2. associate-/l*98.1%

        \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]
    3. Simplified98.1%

      \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]
    4. Taylor expanded in x around 0 78.6%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{y}} \]

    if -4.90000000000000018e58 < y < 0.0054000000000000003 or 4.40000000000000017e207 < y < 2.55e222

    1. Initial program 99.8%

      \[\frac{x \cdot 100}{x + y} \]
    2. Step-by-step derivation
      1. *-commutative99.8%

        \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]
      2. associate-/l*99.9%

        \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]
    3. Simplified99.9%

      \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]
    4. Taylor expanded in x around inf 79.8%

      \[\leadsto \color{blue}{100} \]
  3. Recombined 2 regimes into one program.
  4. Final simplification79.3%

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+58} \lor \neg \left(y \leq 0.0054 \lor \neg \left(y \leq 4.4 \cdot 10^{+207}\right) \land y \leq 2.55 \cdot 10^{+222}\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 3: 72.3% accurate, 0.5× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+58} \lor \neg \left(y \leq 0.017\right) \land \left(y \leq 4.4 \cdot 10^{+207} \lor \neg \left(y \leq 2.55 \cdot 10^{+222}\right)\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]
(FPCore (x y)
 :precision binary64
 (if (or (<= y -3.5e+58)
         (and (not (<= y 0.017)) (or (<= y 4.4e+207) (not (<= y 2.55e+222)))))
   (* x (/ 100.0 y))
   100.0))
double code(double x, double y) {
	double tmp;
	if ((y <= -3.5e+58) || (!(y <= 0.017) && ((y <= 4.4e+207) || !(y <= 2.55e+222)))) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-3.5d+58)) .or. (.not. (y <= 0.017d0)) .and. (y <= 4.4d+207) .or. (.not. (y <= 2.55d+222))) then
        tmp = x * (100.0d0 / y)
    else
        tmp = 100.0d0
    end if
    code = tmp
end function
public static double code(double x, double y) {
	double tmp;
	if ((y <= -3.5e+58) || (!(y <= 0.017) && ((y <= 4.4e+207) || !(y <= 2.55e+222)))) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}
def code(x, y):
	tmp = 0
	if (y <= -3.5e+58) or (not (y <= 0.017) and ((y <= 4.4e+207) or not (y <= 2.55e+222))):
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp
function code(x, y)
	tmp = 0.0
	if ((y <= -3.5e+58) || (!(y <= 0.017) && ((y <= 4.4e+207) || !(y <= 2.55e+222))))
		tmp = Float64(x * Float64(100.0 / y));
	else
		tmp = 100.0;
	end
	return tmp
end
function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -3.5e+58) || (~((y <= 0.017)) && ((y <= 4.4e+207) || ~((y <= 2.55e+222)))))
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end
code[x_, y_] := If[Or[LessEqual[y, -3.5e+58], And[N[Not[LessEqual[y, 0.017]], $MachinePrecision], Or[LessEqual[y, 4.4e+207], N[Not[LessEqual[y, 2.55e+222]], $MachinePrecision]]]], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]
\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;y \leq -3.5 \cdot 10^{+58} \lor \neg \left(y \leq 0.017\right) \land \left(y \leq 4.4 \cdot 10^{+207} \lor \neg \left(y \leq 2.55 \cdot 10^{+222}\right)\right):\\
\;\;\;\;x \cdot \frac{100}{y}\\

\mathbf{else}:\\
\;\;\;\;100\\


\end{array}
\end{array}
Derivation
  1. Split input into 2 regimes
  2. if y < -3.4999999999999997e58 or 0.017000000000000001 < y < 4.40000000000000017e207 or 2.55e222 < y

    1. Initial program 99.7%

      \[\frac{x \cdot 100}{x + y} \]
    2. Step-by-step derivation
      1. *-commutative99.7%

        \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]
      2. associate-/l*98.1%

        \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]
    3. Simplified98.1%

      \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]
    4. Step-by-step derivation
      1. associate-/r/99.7%

        \[\leadsto \color{blue}{\frac{100}{x + y} \cdot x} \]
    5. Applied egg-rr99.7%

      \[\leadsto \color{blue}{\frac{100}{x + y} \cdot x} \]
    6. Taylor expanded in x around 0 78.8%

      \[\leadsto \color{blue}{\frac{100}{y}} \cdot x \]

    if -3.4999999999999997e58 < y < 0.017000000000000001 or 4.40000000000000017e207 < y < 2.55e222

    1. Initial program 99.8%

      \[\frac{x \cdot 100}{x + y} \]
    2. Step-by-step derivation
      1. *-commutative99.8%

        \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]
      2. associate-/l*99.9%

        \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]
    3. Simplified99.9%

      \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]
    4. Taylor expanded in x around inf 79.8%

      \[\leadsto \color{blue}{100} \]
  3. Recombined 2 regimes into one program.
  4. Final simplification79.3%

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+58} \lor \neg \left(y \leq 0.017\right) \land \left(y \leq 4.4 \cdot 10^{+207} \lor \neg \left(y \leq 2.55 \cdot 10^{+222}\right)\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 4: 72.3% accurate, 0.5× speedup?

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{100}{y}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+58}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.00165:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+207}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+222}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]
(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (/ 100.0 y))))
   (if (<= y -3.1e+58)
     t_0
     (if (<= y 0.00165)
       100.0
       (if (<= y 4.4e+207)
         (/ x (* y 0.01))
         (if (<= y 2.55e+222) 100.0 t_0))))))
double code(double x, double y) {
	double t_0 = x * (100.0 / y);
	double tmp;
	if (y <= -3.1e+58) {
		tmp = t_0;
	} else if (y <= 0.00165) {
		tmp = 100.0;
	} else if (y <= 4.4e+207) {
		tmp = x / (y * 0.01);
	} else if (y <= 2.55e+222) {
		tmp = 100.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (100.0d0 / y)
    if (y <= (-3.1d+58)) then
        tmp = t_0
    else if (y <= 0.00165d0) then
        tmp = 100.0d0
    else if (y <= 4.4d+207) then
        tmp = x / (y * 0.01d0)
    else if (y <= 2.55d+222) then
        tmp = 100.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function
public static double code(double x, double y) {
	double t_0 = x * (100.0 / y);
	double tmp;
	if (y <= -3.1e+58) {
		tmp = t_0;
	} else if (y <= 0.00165) {
		tmp = 100.0;
	} else if (y <= 4.4e+207) {
		tmp = x / (y * 0.01);
	} else if (y <= 2.55e+222) {
		tmp = 100.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}
def code(x, y):
	t_0 = x * (100.0 / y)
	tmp = 0
	if y <= -3.1e+58:
		tmp = t_0
	elif y <= 0.00165:
		tmp = 100.0
	elif y <= 4.4e+207:
		tmp = x / (y * 0.01)
	elif y <= 2.55e+222:
		tmp = 100.0
	else:
		tmp = t_0
	return tmp
function code(x, y)
	t_0 = Float64(x * Float64(100.0 / y))
	tmp = 0.0
	if (y <= -3.1e+58)
		tmp = t_0;
	elseif (y <= 0.00165)
		tmp = 100.0;
	elseif (y <= 4.4e+207)
		tmp = Float64(x / Float64(y * 0.01));
	elseif (y <= 2.55e+222)
		tmp = 100.0;
	else
		tmp = t_0;
	end
	return tmp
end
function tmp_2 = code(x, y)
	t_0 = x * (100.0 / y);
	tmp = 0.0;
	if (y <= -3.1e+58)
		tmp = t_0;
	elseif (y <= 0.00165)
		tmp = 100.0;
	elseif (y <= 4.4e+207)
		tmp = x / (y * 0.01);
	elseif (y <= 2.55e+222)
		tmp = 100.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end
code[x_, y_] := Block[{t$95$0 = N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.1e+58], t$95$0, If[LessEqual[y, 0.00165], 100.0, If[LessEqual[y, 4.4e+207], N[(x / N[(y * 0.01), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.55e+222], 100.0, t$95$0]]]]]
\begin{array}{l}

\\
\begin{array}{l}
t_0 := x \cdot \frac{100}{y}\\
\mathbf{if}\;y \leq -3.1 \cdot 10^{+58}:\\
\;\;\;\;t_0\\

\mathbf{elif}\;y \leq 0.00165:\\
\;\;\;\;100\\

\mathbf{elif}\;y \leq 4.4 \cdot 10^{+207}:\\
\;\;\;\;\frac{x}{y \cdot 0.01}\\

\mathbf{elif}\;y \leq 2.55 \cdot 10^{+222}:\\
\;\;\;\;100\\

\mathbf{else}:\\
\;\;\;\;t_0\\


\end{array}
\end{array}
Derivation
  1. Split input into 3 regimes
  2. if y < -3.0999999999999999e58 or 2.55e222 < y

    1. Initial program 99.7%

      \[\frac{x \cdot 100}{x + y} \]
    2. Step-by-step derivation
      1. *-commutative99.7%

        \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]
      2. associate-/l*97.9%

        \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]
    3. Simplified97.9%

      \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]
    4. Step-by-step derivation
      1. associate-/r/99.8%

        \[\leadsto \color{blue}{\frac{100}{x + y} \cdot x} \]
    5. Applied egg-rr99.8%

      \[\leadsto \color{blue}{\frac{100}{x + y} \cdot x} \]
    6. Taylor expanded in x around 0 82.4%

      \[\leadsto \color{blue}{\frac{100}{y}} \cdot x \]

    if -3.0999999999999999e58 < y < 0.00165 or 4.40000000000000017e207 < y < 2.55e222

    1. Initial program 99.8%

      \[\frac{x \cdot 100}{x + y} \]
    2. Step-by-step derivation
      1. *-commutative99.8%

        \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]
      2. associate-/l*99.9%

        \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]
    3. Simplified99.9%

      \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]
    4. Taylor expanded in x around inf 79.8%

      \[\leadsto \color{blue}{100} \]

    if 0.00165 < y < 4.40000000000000017e207

    1. Initial program 99.6%

      \[\frac{x \cdot 100}{x + y} \]
    2. Step-by-step derivation
      1. associate-/l*99.7%

        \[\leadsto \color{blue}{\frac{x}{\frac{x + y}{100}}} \]
    3. Simplified99.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{x + y}{100}}} \]
    4. Taylor expanded in x around 0 74.1%

      \[\leadsto \frac{x}{\color{blue}{0.01 \cdot y}} \]
    5. Step-by-step derivation
      1. *-commutative74.1%

        \[\leadsto \frac{x}{\color{blue}{y \cdot 0.01}} \]
    6. Simplified74.1%

      \[\leadsto \frac{x}{\color{blue}{y \cdot 0.01}} \]
  3. Recombined 3 regimes into one program.
  4. Final simplification79.3%

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;y \leq 0.00165:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+207}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+222}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \end{array} \]

Alternative 5: 50.8% accurate, 7.0× speedup?

\[\begin{array}{l} \\ 100 \end{array} \]
(FPCore (x y) :precision binary64 100.0)
double code(double x, double y) {
	return 100.0;
}
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 100.0d0
end function
public static double code(double x, double y) {
	return 100.0;
}
def code(x, y):
	return 100.0
function code(x, y)
	return 100.0
end
function tmp = code(x, y)
	tmp = 100.0;
end
code[x_, y_] := 100.0
\begin{array}{l}

\\
100
\end{array}
Derivation
  1. Initial program 99.7%

    \[\frac{x \cdot 100}{x + y} \]
  2. Step-by-step derivation
    1. *-commutative99.7%

      \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]
    2. associate-/l*99.0%

      \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]
  3. Simplified99.0%

    \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]
  4. Taylor expanded in x around inf 53.2%

    \[\leadsto \color{blue}{100} \]
  5. Final simplification53.2%

    \[\leadsto 100 \]

Developer target: 99.8% accurate, 0.8× speedup?

\[\begin{array}{l} \\ \frac{x}{1} \cdot \frac{100}{x + y} \end{array} \]
(FPCore (x y) :precision binary64 (* (/ x 1.0) (/ 100.0 (+ x y))))
double code(double x, double y) {
	return (x / 1.0) * (100.0 / (x + y));
}
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x / 1.0d0) * (100.0d0 / (x + y))
end function
public static double code(double x, double y) {
	return (x / 1.0) * (100.0 / (x + y));
}
def code(x, y):
	return (x / 1.0) * (100.0 / (x + y))
function code(x, y)
	return Float64(Float64(x / 1.0) * Float64(100.0 / Float64(x + y)))
end
function tmp = code(x, y)
	tmp = (x / 1.0) * (100.0 / (x + y));
end
code[x_, y_] := N[(N[(x / 1.0), $MachinePrecision] * N[(100.0 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}

\\
\frac{x}{1} \cdot \frac{100}{x + y}
\end{array}

Reproduce

?
herbie shell --seed 2023200 
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"
  :precision binary64

  :herbie-target
  (* (/ x 1.0) (/ 100.0 (+ x y)))

  (/ (* x 100.0) (+ x y)))