Rust f32::atanh

Percentage Accurate: 92.6% → 98.6%

Time: 5.3s

Alternatives: 3

Speedup: 11.4×

Specification

Math

\[\begin{array}{l} \\ \tanh^{-1} x \end{array} \]

FPCore

(FPCore (x) :precision binary32 (atanh x))

C

float code(float x) {
	return atanhf(x);
}

Julia

function code(x)
	return atanh(x)
end

MATLAB

function tmp = code(x)
	tmp = atanh(x);
end

Initial Program: 92.6% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x) :precision binary32 (* 0.5 (log1p (/ (* 2.0 x) (- 1.0 x)))))

C

float code(float x) {
	return 0.5f * log1pf(((2.0f * x) / (1.0f - x)));
}

Julia

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

Alternative 1: 98.6% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \left(\left(\left(x \cdot x\right) \cdot 0.6666666666666666\right) \cdot x + x \cdot 2\right) \end{array} \]

FPCore

(FPCore (x)
 :precision binary32
 (* 0.5 (+ (* (* (* x x) 0.6666666666666666) x) (* x 2.0))))

C

float code(float x) {
	return 0.5f * ((((x * x) * 0.6666666666666666f) * x) + (x * 2.0f));
}

Fortran

real(4) function code(x)
    real(4), intent (in) :: x
    code = 0.5e0 * ((((x * x) * 0.6666666666666666e0) * x) + (x * 2.0e0))
end function

Julia

function code(x)
	return Float32(Float32(0.5) * Float32(Float32(Float32(Float32(x * x) * Float32(0.6666666666666666)) * x) + Float32(x * Float32(2.0))))
end

MATLAB

function tmp = code(x)
	tmp = single(0.5) * ((((x * x) * single(0.6666666666666666)) * x) + (x * single(2.0)));
end

Derivation

1. Initial program 93.0%

   \[0.5 \cdot \mathsf{log1p}\left(\frac{2 \cdot x}{1 - x}\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-/.f32 N/A

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

   2. lift--.f32 N/A

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

   3. flip-- N/A

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

   4. associate-/r/ N/A

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

   5. +-commutative N/A

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

   6. distribute-lft-in N/A

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

   7. lower-fma.f32 N/A

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

   8. lift-*.f32 N/A

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

   9. associate-/l* N/A

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

   10. lower-*.f32 N/A

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

   11. lower-/.f32 N/A

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

   12. metadata-eval N/A

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

   13. lower--.f32 N/A

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

   14. lower-*.f32 N/A

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

   15. lower-*.f32 N/A

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

4. Applied rewrites 97.0%

   \[\leadsto 0.5 \cdot \mathsf{log1p}\left(\color{blue}{\mathsf{fma}\left(2 \cdot \frac{x}{1 - x \cdot x}, x, \left(2 \cdot \frac{x}{1 - x \cdot x}\right) \cdot 1\right)}\right) \]
5. Step-by-step derivation

   1. lift--.f32 N/A

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

   2. sub-neg N/A

      \[\leadsto \frac{1}{2} \cdot \mathsf{log1p}\left(\mathsf{fma}\left(2 \cdot \frac{x}{\color{blue}{1 + \left(\mathsf{neg}\left(x \cdot x\right)\right)}}, x, \left(2 \cdot \frac{x}{1 - x \cdot x}\right) \cdot 1\right)\right) \]

   3. +-commutative N/A

      \[\leadsto \frac{1}{2} \cdot \mathsf{log1p}\left(\mathsf{fma}\left(2 \cdot \frac{x}{\color{blue}{\left(\mathsf{neg}\left(x \cdot x\right)\right) + 1}}, x, \left(2 \cdot \frac{x}{1 - x \cdot x}\right) \cdot 1\right)\right) \]

   4. lift-*.f32 N/A

      \[\leadsto \frac{1}{2} \cdot \mathsf{log1p}\left(\mathsf{fma}\left(2 \cdot \frac{x}{\left(\mathsf{neg}\left(\color{blue}{x \cdot x}\right)\right) + 1}, x, \left(2 \cdot \frac{x}{1 - x \cdot x}\right) \cdot 1\right)\right) \]

   5. distribute-lft-neg-in N/A

      \[\leadsto \frac{1}{2} \cdot \mathsf{log1p}\left(\mathsf{fma}\left(2 \cdot \frac{x}{\color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot x} + 1}, x, \left(2 \cdot \frac{x}{1 - x \cdot x}\right) \cdot 1\right)\right) \]

   6. lower-fma.f32 N/A

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

   7. lower-neg.f32 95.3

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

6. Applied rewrites 97.4%

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

7. Taylor expanded in x around 0

   \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(x \cdot \left(2 + \frac{2}{3} \cdot {x}^{2}\right)\right)} \]
8. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(\left(2 + \frac{2}{3} \cdot {x}^{2}\right) \cdot x\right)} \]

   2. lower-*.f32 N/A

      \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(\left(2 + \frac{2}{3} \cdot {x}^{2}\right) \cdot x\right)} \]

   3. +-commutative N/A

      \[\leadsto \frac{1}{2} \cdot \left(\color{blue}{\left(\frac{2}{3} \cdot {x}^{2} + 2\right)} \cdot x\right) \]

   4. lower-fma.f32 N/A

      \[\leadsto \frac{1}{2} \cdot \left(\color{blue}{\mathsf{fma}\left(\frac{2}{3}, {x}^{2}, 2\right)} \cdot x\right) \]

   5. unpow2 N/A

      \[\leadsto \frac{1}{2} \cdot \left(\mathsf{fma}\left(\frac{2}{3}, \color{blue}{x \cdot x}, 2\right) \cdot x\right) \]

   6. lower-*.f32 97.3

      \[\leadsto 0.5 \cdot \left(\mathsf{fma}\left(0.6666666666666666, \color{blue}{x \cdot x}, 2\right) \cdot x\right) \]

9. Applied rewrites 96.5%

   \[\leadsto 0.5 \cdot \color{blue}{\left(\mathsf{fma}\left(0.6666666666666666, x \cdot x, 2\right) \cdot x\right)} \]
10. Step-by-step derivation

11. Applied rewrites 98.7%

    \[\leadsto 0.5 \cdot \left(\left(\left(x \cdot x\right) \cdot 0.6666666666666666\right) \cdot x + \color{blue}{x \cdot 2}\right) \]

12. Final simplification 98.7%

    \[\leadsto 0.5 \cdot \left(\left(\left(x \cdot x\right) \cdot 0.6666666666666666\right) \cdot x + x \cdot 2\right) \]
13. Add Preprocessing

Alternative 2: 98.5% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \left(\left(\left(x \cdot x\right) \cdot 0.6666666666666666 + 2\right) \cdot x\right) \end{array} \]

FPCore

(FPCore (x)
 :precision binary32
 (* 0.5 (* (+ (* (* x x) 0.6666666666666666) 2.0) x)))

C

float code(float x) {
	return 0.5f * ((((x * x) * 0.6666666666666666f) + 2.0f) * x);
}

Fortran

real(4) function code(x)
    real(4), intent (in) :: x
    code = 0.5e0 * ((((x * x) * 0.6666666666666666e0) + 2.0e0) * x)
end function

Julia

function code(x)
	return Float32(Float32(0.5) * Float32(Float32(Float32(Float32(x * x) * Float32(0.6666666666666666)) + Float32(2.0)) * x))
end

MATLAB

function tmp = code(x)
	tmp = single(0.5) * ((((x * x) * single(0.6666666666666666)) + single(2.0)) * x);
end

Derivation

1. Initial program 88.7%

   \[0.5 \cdot \mathsf{log1p}\left(\frac{2 \cdot x}{1 - x}\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-/.f32 N/A

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

   2. lift--.f32 N/A

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

   3. flip-- N/A

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

   4. associate-/r/ N/A

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

   5. +-commutative N/A

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

   6. distribute-lft-in N/A

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

   7. lower-fma.f32 N/A

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

   8. lift-*.f32 N/A

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

   9. associate-/l* N/A

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

   10. lower-*.f32 N/A

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

   11. lower-/.f32 N/A

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

   12. metadata-eval N/A

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

   13. lower--.f32 N/A

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

   14. lower-*.f32 N/A

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

   15. lower-*.f32 N/A

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

4. Applied rewrites 97.0%

   \[\leadsto 0.5 \cdot \mathsf{log1p}\left(\color{blue}{\mathsf{fma}\left(2 \cdot \frac{x}{1 - x \cdot x}, x, \left(2 \cdot \frac{x}{1 - x \cdot x}\right) \cdot 1\right)}\right) \]
5. Step-by-step derivation

   1. lift--.f32 N/A

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

   2. sub-neg N/A

      \[\leadsto \frac{1}{2} \cdot \mathsf{log1p}\left(\mathsf{fma}\left(2 \cdot \frac{x}{\color{blue}{1 + \left(\mathsf{neg}\left(x \cdot x\right)\right)}}, x, \left(2 \cdot \frac{x}{1 - x \cdot x}\right) \cdot 1\right)\right) \]

   3. +-commutative N/A

      \[\leadsto \frac{1}{2} \cdot \mathsf{log1p}\left(\mathsf{fma}\left(2 \cdot \frac{x}{\color{blue}{\left(\mathsf{neg}\left(x \cdot x\right)\right) + 1}}, x, \left(2 \cdot \frac{x}{1 - x \cdot x}\right) \cdot 1\right)\right) \]

   4. lift-*.f32 N/A

      \[\leadsto \frac{1}{2} \cdot \mathsf{log1p}\left(\mathsf{fma}\left(2 \cdot \frac{x}{\left(\mathsf{neg}\left(\color{blue}{x \cdot x}\right)\right) + 1}, x, \left(2 \cdot \frac{x}{1 - x \cdot x}\right) \cdot 1\right)\right) \]

   5. distribute-lft-neg-in N/A

      \[\leadsto \frac{1}{2} \cdot \mathsf{log1p}\left(\mathsf{fma}\left(2 \cdot \frac{x}{\color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot x} + 1}, x, \left(2 \cdot \frac{x}{1 - x \cdot x}\right) \cdot 1\right)\right) \]

   6. lower-fma.f32 N/A

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

   7. lower-neg.f32 95.3

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

6. Applied rewrites 97.4%

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

7. Taylor expanded in x around 0

   \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(x \cdot \left(2 + \frac{2}{3} \cdot {x}^{2}\right)\right)} \]
8. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(\left(2 + \frac{2}{3} \cdot {x}^{2}\right) \cdot x\right)} \]

   2. lower-*.f32 N/A

      \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(\left(2 + \frac{2}{3} \cdot {x}^{2}\right) \cdot x\right)} \]

   3. +-commutative N/A

      \[\leadsto \frac{1}{2} \cdot \left(\color{blue}{\left(\frac{2}{3} \cdot {x}^{2} + 2\right)} \cdot x\right) \]

   4. lower-fma.f32 N/A

      \[\leadsto \frac{1}{2} \cdot \left(\color{blue}{\mathsf{fma}\left(\frac{2}{3}, {x}^{2}, 2\right)} \cdot x\right) \]

   5. unpow2 N/A

      \[\leadsto \frac{1}{2} \cdot \left(\mathsf{fma}\left(\frac{2}{3}, \color{blue}{x \cdot x}, 2\right) \cdot x\right) \]

   6. lower-*.f32 97.3

      \[\leadsto 0.5 \cdot \left(\mathsf{fma}\left(0.6666666666666666, \color{blue}{x \cdot x}, 2\right) \cdot x\right) \]

9. Applied rewrites 97.6%

   \[\leadsto 0.5 \cdot \color{blue}{\left(\mathsf{fma}\left(0.6666666666666666, x \cdot x, 2\right) \cdot x\right)} \]
10. Step-by-step derivation

11. Applied rewrites 98.7%

    \[\leadsto 0.5 \cdot \left(\left(\left(x \cdot x\right) \cdot 0.6666666666666666 + 2\right) \cdot x\right) \]

12. Final simplification 98.7%

    \[\leadsto 0.5 \cdot \left(\left(\left(x \cdot x\right) \cdot 0.6666666666666666 + 2\right) \cdot x\right) \]
13. Add Preprocessing

Alternative 3: 96.9% accurate, 11.4× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \left(2 \cdot x\right) \end{array} \]

FPCore

(FPCore (x) :precision binary32 (* 0.5 (* 2.0 x)))

C

float code(float x) {
	return 0.5f * (2.0f * x);
}

Fortran

real(4) function code(x)
    real(4), intent (in) :: x
    code = 0.5e0 * (2.0e0 * x)
end function

Julia

function code(x)
	return Float32(Float32(0.5) * Float32(Float32(2.0) * x))
end

MATLAB

function tmp = code(x)
	tmp = single(0.5) * (single(2.0) * x);
end

Derivation

1. Initial program 94.7%

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

3. Taylor expanded in x around 0

   \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(2 \cdot x\right)} \]
4. Step-by-step derivation

   1. lower-*.f32 97.6

      \[\leadsto 0.5 \cdot \color{blue}{\left(2 \cdot x\right)} \]

5. Applied rewrites 97.6%

   \[\leadsto 0.5 \cdot \color{blue}{\left(2 \cdot x\right)} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024308 
(FPCore (x)
  :name "Rust f32::atanh"
  :precision binary32
  (* 0.5 (log1p (/ (* 2.0 x) (- 1.0 x)))))