Average Error: 7.5 → 0.0
Time: 1.5s
Precision: binary64
\[\frac{x \cdot y}{y + 1} \]
↓
\[x \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{y + 1}\right)\right) \]
(FPCore (x y) :precision binary64 (/ (* x y) (+ y 1.0)))
↓
(FPCore (x y) :precision binary64 (* x (expm1 (log1p (/ y (+ y 1.0))))))
double code(double x, double y) {
	return (x * y) / (y + 1.0);
}
↓
double code(double x, double y) {
	return x * expm1(log1p((y / (y + 1.0))));
}

public static double code(double x, double y) {
	return (x * y) / (y + 1.0);
}
↓
public static double code(double x, double y) {
	return x * Math.expm1(Math.log1p((y / (y + 1.0))));
}

def code(x, y):
	return (x * y) / (y + 1.0)
↓
def code(x, y):
	return x * math.expm1(math.log1p((y / (y + 1.0))))

function code(x, y)
	return Float64(Float64(x * y) / Float64(y + 1.0))
end
↓
function code(x, y)
	return Float64(x * expm1(log1p(Float64(y / Float64(y + 1.0)))))
end

code[x_, y_] := N[(N[(x * y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[(x * N[(Exp[N[Log[1 + N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision]

\frac{x \cdot y}{y + 1}
↓
x \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{y + 1}\right)\right)

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.5
Target0.0
Herbie0.0
\[\begin{array}{l} \mathbf{if}\;y < -3693.8482788297247:\\ \;\;\;\;\frac{x}{y \cdot y} - \left(\frac{x}{y} - x\right)\\ \mathbf{elif}\;y < 6799310503.41891:\\ \;\;\;\;\frac{x \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot y} - \left(\frac{x}{y} - x\right)\\ \end{array} \]

Derivation

  1. Initial program 7.5

    \[\frac{x \cdot y}{y + 1} \]

  2. Simplified0.0

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

  3. Applied egg-rr0.0

    \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{y + 1}\right)\right)} \]

  4. Final simplification0.0

    \[\leadsto x \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{y + 1}\right)\right) \]

Reproduce

herbie shell --seed 2022166 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, B"
  :precision binary64

  :herbie-target
  (if (< y -3693.8482788297247) (- (/ x (* y y)) (- (/ x y) x)) (if (< y 6799310503.41891) (/ (* x y) (+ y 1.0)) (- (/ x (* y y)) (- (/ x y) x))))

  (/ (* x y) (+ y 1.0)))