?

Average Accuracy: 99.8% → 99.8%

Time: 10.2s

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)

Try it out?

In
Out

Enter valid numbers for all inputs

Initial program 99.8%
\[0.5 \cdot \mathsf{log1p}\left(\frac{2 \cdot x}{1 - x}\right) \]
Final simplification99.8%
\[\leadsto 0.5 \cdot \mathsf{log1p}\left(\frac{2 \cdot x}{1 - x}\right) \]

Alternative 1
Accuracy	99.7%
Cost	3488

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

Alternative 2
Accuracy	98.0%
Cost	416

\[0.5 \cdot \frac{1}{x \cdot -0.16666666666666666 + 0.5 \cdot \frac{1}{x}} \]

Alternative 3
Accuracy	96.7%
Cost	160

\[0.5 \cdot \left(2 \cdot x\right) \]

herbie shell --seed 2023137 
(FPCore (x)
  :name "Rust f32::atanh"
  :precision binary32
  (* 0.5 (log1p (/ (* 2.0 x) (- 1.0 x)))))