Average Error: 0.3 → 0.2
Time: 1.3s
Precision: binary64
\[\frac{x \cdot 100}{x + y} \]
↓
\[\frac{x}{\left(x + y\right) \cdot 0.01} \]
(FPCore (x y) :precision binary64 (/ (* x 100.0) (+ x y)))
↓
(FPCore (x y) :precision binary64 (/ x (* (+ x y) 0.01)))
double code(double x, double y) {
	return (x * 100.0) / (x + y);
}
↓
double code(double x, double y) {
	return x / ((x + y) * 0.01);
}

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * 100.0d0) / (x + y)
end function
↓
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x / ((x + y) * 0.01d0)
end function

public static double code(double x, double y) {
	return (x * 100.0) / (x + y);
}
↓
public static double code(double x, double y) {
	return x / ((x + y) * 0.01);
}

def code(x, y):
	return (x * 100.0) / (x + y)
↓
def code(x, y):
	return x / ((x + y) * 0.01)

function code(x, y)
	return Float64(Float64(x * 100.0) / Float64(x + y))
end
↓
function code(x, y)
	return Float64(x / Float64(Float64(x + y) * 0.01))
end

function tmp = code(x, y)
	tmp = (x * 100.0) / (x + y);
end
↓
function tmp = code(x, y)
	tmp = x / ((x + y) * 0.01);
end

code[x_, y_] := N[(N[(x * 100.0), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[(x / N[(N[(x + y), $MachinePrecision] * 0.01), $MachinePrecision]), $MachinePrecision]

\frac{x \cdot 100}{x + y}
↓
\frac{x}{\left(x + y\right) \cdot 0.01}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.2
Herbie0.2
\[\frac{x}{1} \cdot \frac{100}{x + y} \]

Derivation

  1. Initial program 0.3

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

  2. Simplified0.2

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

  3. Applied egg-rr0.2

    \[\leadsto \color{blue}{\frac{x}{\left(x + y\right) \cdot 0.01}} \]

  4. Final simplification0.2

    \[\leadsto \frac{x}{\left(x + y\right) \cdot 0.01} \]

Reproduce

herbie shell --seed 2022150 
(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)))