?

Average Accuracy: 99.8% → 99.7%
Time: 4.9s
Precision: binary32
Cost: 3488

?

\[0.5 \cdot \mathsf{log1p}\left(\frac{2 \cdot x}{1 - x}\right) \]
↓
\[0.5 \cdot \mathsf{log1p}\left(x \cdot \frac{2}{1 - x}\right) \]
(FPCore (x) :precision binary32 (* 0.5 (log1p (/ (* 2.0 x) (- 1.0 x)))))
↓
(FPCore (x) :precision binary32 (* 0.5 (log1p (* x (/ 2.0 (- 1.0 x))))))
float code(float x) {
	return 0.5f * log1pf(((2.0f * x) / (1.0f - x)));
}
↓
float code(float x) {
	return 0.5f * log1pf((x * (2.0f / (1.0f - x))));
}

function code(x)
	return Float32(Float32(0.5) * log1p(Float32(Float32(Float32(2.0) * x) / Float32(Float32(1.0) - x))))
end
↓
function code(x)
	return Float32(Float32(0.5) * log1p(Float32(x * Float32(Float32(2.0) / Float32(Float32(1.0) - x)))))
end

0.5 \cdot \mathsf{log1p}\left(\frac{2 \cdot x}{1 - x}\right)
↓
0.5 \cdot \mathsf{log1p}\left(x \cdot \frac{2}{1 - x}\right)

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 99.8%

    \[0.5 \cdot \mathsf{log1p}\left(\frac{2 \cdot x}{1 - x}\right) \]

  2. Simplified99.7%

    \[\leadsto \color{blue}{0.5 \cdot \mathsf{log1p}\left(\frac{2}{1 - x} \cdot x\right)} \]
    Proof

    [Start]99.8

    \[ 0.5 \cdot \mathsf{log1p}\left(\frac{2 \cdot x}{1 - x}\right) \]

    associate-*l/ [<=]99.7

    \[ 0.5 \cdot \mathsf{log1p}\left(\color{blue}{\frac{2}{1 - x} \cdot x}\right) \]

  3. Final simplification99.7%

    \[\leadsto 0.5 \cdot \mathsf{log1p}\left(x \cdot \frac{2}{1 - x}\right) \]

Alternatives

Alternative 1
Accuracy97.1%
Cost160
\[0.5 \cdot \left(2 \cdot x\right) \]

Error

Reproduce?

herbie shell --seed 2023126 
(FPCore (x)
  :name "Rust f32::atanh"
  :precision binary32
  (* 0.5 (log1p (/ (* 2.0 x) (- 1.0 x)))))