?

Average Error: 0.1 → 0.1
Time: 7.0s
Precision: binary32
Cost: 3488

?

\[0.5 \cdot \mathsf{log1p}\left(\frac{2 \cdot x}{1 - x}\right) \]
↓
\[0.5 \cdot \mathsf{log1p}\left(\frac{2 \cdot x}{1 - x}\right) \]
(FPCore (x) :precision binary32 (* 0.5 (log1p (/ (* 2.0 x) (- 1.0 x)))))
↓
(FPCore (x) :precision binary32 (* 0.5 (log1p (/ (* 2.0 x) (- 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(((2.0f * x) / (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(Float32(Float32(2.0) * x) / 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(\frac{2 \cdot x}{1 - x}\right)

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 0.1

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

  2. Final simplification0.1

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

Alternatives

Alternative 1
Error0.1
Cost3488
\[0.5 \cdot \mathsf{log1p}\left(x \cdot \frac{2}{1 - x}\right) \]
Alternative 2
Error1.0
Cost160
\[0.5 \cdot \left(2 \cdot x\right) \]

Error

Reproduce?

herbie shell --seed 2023187 
(FPCore (x)
  :name "Rust f32::atanh"
  :precision binary32
  (* 0.5 (log1p (/ (* 2.0 x) (- 1.0 x)))))