Rust f32::asinh

Percentage Accurate: 38.0% → 99.6%

Time: 5.6s

Alternatives: 4

Speedup: 1.9×

Specification

Math

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

FPCore

(FPCore (x) :precision binary32 (asinh x))

C

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

Julia

function code(x)
	return asinh(x)
end

MATLAB

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

Initial Program: 38.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right) \end{array} \]

FPCore

(FPCore (x)
 :precision binary32
 (copysign (log (+ (fabs x) (sqrt (+ (* x x) 1.0)))) x))

C

float code(float x) {
	return copysignf(logf((fabsf(x) + sqrtf(((x * x) + 1.0f)))), x);
}

Julia

function code(x)
	return copysign(log(Float32(abs(x) + sqrt(Float32(Float32(x * x) + Float32(1.0))))), x)
end

MATLAB

function tmp = code(x)
	tmp = sign(x) * abs(log((abs(x) + sqrt(((x * x) + single(1.0))))));
end

Alternative 1: 99.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{copysign}\left(\sinh^{-1} x, x\right) \end{array} \]

FPCore

(FPCore (x) :precision binary32 (copysign (asinh x) x))

C

float code(float x) {
	return copysignf(asinhf(x), x);
}

Julia

function code(x)
	return copysign(asinh(x), x)
end

MATLAB

function tmp = code(x)
	tmp = sign(x) * abs(asinh(x));
end

Derivation

1. Initial program 35.8%

   \[\mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-log.f32 N/A

      \[\leadsto \mathsf{copysign}\left(\color{blue}{\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right)}, x\right) \]

   2. lift-+.f32 N/A

      \[\leadsto \mathsf{copysign}\left(\log \color{blue}{\left(\left|x\right| + \sqrt{x \cdot x + 1}\right)}, x\right) \]

   3. lift-sqrt.f32 N/A

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \color{blue}{\sqrt{x \cdot x + 1}}\right), x\right) \]

   4. lift-+.f32 N/A

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{x \cdot x + 1}}\right), x\right) \]

   5. lift-*.f32 N/A

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{x \cdot x} + 1}\right), x\right) \]

   6. sqr-abs-rev N/A

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{\left|x\right| \cdot \left|x\right|} + 1}\right), x\right) \]

   7. lift-fabs.f32 N/A

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{\left|x\right|} \cdot \left|x\right| + 1}\right), x\right) \]

   8. lift-fabs.f32 N/A

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\left|x\right| \cdot \color{blue}{\left|x\right|} + 1}\right), x\right) \]

   9. asinh-def-rev N/A

      \[\leadsto \mathsf{copysign}\left(\color{blue}{\sinh^{-1} \left(\left|x\right|\right)}, x\right) \]

   10. lower-asinh.f32 99.6

       \[\leadsto \mathsf{copysign}\left(\color{blue}{\sinh^{-1} \left(\left|x\right|\right)}, x\right) \]

   11. lift-fabs.f32 N/A

       \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \color{blue}{\left(\left|x\right|\right)}, x\right) \]

   12. rem-sqrt-square-rev N/A

       \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \color{blue}{\left(\sqrt{x \cdot x}\right)}, x\right) \]

   13. pow2 N/A

       \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \left(\sqrt{\color{blue}{{x}^{2}}}\right), x\right) \]

   14. sqrt-pow1 N/A

       \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \color{blue}{\left({x}^{\left(\frac{2}{2}\right)}\right)}, x\right) \]

   15. metadata-eval N/A

       \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \left({x}^{\color{blue}{1}}\right), x\right) \]

   16. unpow1 99.6

       \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \color{blue}{x}, x\right) \]

4. Applied rewrites 99.6%

   \[\leadsto \color{blue}{\mathsf{copysign}\left(\sinh^{-1} x, x\right)} \]
5. Add Preprocessing

Alternative 2: 53.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \mathsf{copysign}\left(\mathsf{fma}\left(x \cdot x, x \cdot -0.16666666666666666, x\right), x\right) \end{array} \]

FPCore

(FPCore (x)
 :precision binary32
 (copysign (fma (* x x) (* x -0.16666666666666666) x) x))

C

float code(float x) {
	return copysignf(fmaf((x * x), (x * -0.16666666666666666f), x), x);
}

Julia

function code(x)
	return copysign(fma(Float32(x * x), Float32(x * Float32(-0.16666666666666666)), x), x)
end

Derivation

1. Initial program 35.8%

   \[\mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-log.f32 N/A

      \[\leadsto \mathsf{copysign}\left(\color{blue}{\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right)}, x\right) \]

   2. lift-+.f32 N/A

      \[\leadsto \mathsf{copysign}\left(\log \color{blue}{\left(\left|x\right| + \sqrt{x \cdot x + 1}\right)}, x\right) \]

   3. lift-sqrt.f32 N/A

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \color{blue}{\sqrt{x \cdot x + 1}}\right), x\right) \]

   4. lift-+.f32 N/A

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{x \cdot x + 1}}\right), x\right) \]

   5. lift-*.f32 N/A

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{x \cdot x} + 1}\right), x\right) \]

   6. sqr-abs-rev N/A

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{\left|x\right| \cdot \left|x\right|} + 1}\right), x\right) \]

   7. lift-fabs.f32 N/A

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{\left|x\right|} \cdot \left|x\right| + 1}\right), x\right) \]

   8. lift-fabs.f32 N/A

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\left|x\right| \cdot \color{blue}{\left|x\right|} + 1}\right), x\right) \]

   9. asinh-def-rev N/A

      \[\leadsto \mathsf{copysign}\left(\color{blue}{\sinh^{-1} \left(\left|x\right|\right)}, x\right) \]

   10. lower-asinh.f32 99.6

       \[\leadsto \mathsf{copysign}\left(\color{blue}{\sinh^{-1} \left(\left|x\right|\right)}, x\right) \]

   11. lift-fabs.f32 N/A

       \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \color{blue}{\left(\left|x\right|\right)}, x\right) \]

   12. rem-sqrt-square-rev N/A

       \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \color{blue}{\left(\sqrt{x \cdot x}\right)}, x\right) \]

   13. pow2 N/A

       \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \left(\sqrt{\color{blue}{{x}^{2}}}\right), x\right) \]

   14. sqrt-pow1 N/A

       \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \color{blue}{\left({x}^{\left(\frac{2}{2}\right)}\right)}, x\right) \]

   15. metadata-eval N/A

       \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \left({x}^{\color{blue}{1}}\right), x\right) \]

   16. unpow1 99.6

       \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \color{blue}{x}, x\right) \]

4. Applied rewrites 99.6%

   \[\leadsto \color{blue}{\mathsf{copysign}\left(\sinh^{-1} x, x\right)} \]

5. Taylor expanded in x around 0

   \[\leadsto \mathsf{copysign}\left(\color{blue}{x \cdot \left(1 + \frac{-1}{6} \cdot {x}^{2}\right)}, x\right) \]
6. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \mathsf{copysign}\left(x \cdot \color{blue}{\left(\frac{-1}{6} \cdot {x}^{2} + 1\right)}, x\right) \]

   2. distribute-lft-in N/A

      \[\leadsto \mathsf{copysign}\left(\color{blue}{x \cdot \left(\frac{-1}{6} \cdot {x}^{2}\right) + x \cdot 1}, x\right) \]

   3. *-commutative N/A

      \[\leadsto \mathsf{copysign}\left(x \cdot \color{blue}{\left({x}^{2} \cdot \frac{-1}{6}\right)} + x \cdot 1, x\right) \]

   4. associate-*r* N/A

      \[\leadsto \mathsf{copysign}\left(\color{blue}{\left(x \cdot {x}^{2}\right) \cdot \frac{-1}{6}} + x \cdot 1, x\right) \]

   5. unpow2 N/A

      \[\leadsto \mathsf{copysign}\left(\left(x \cdot \color{blue}{\left(x \cdot x\right)}\right) \cdot \frac{-1}{6} + x \cdot 1, x\right) \]

   6. cube-mult N/A

      \[\leadsto \mathsf{copysign}\left(\color{blue}{{x}^{3}} \cdot \frac{-1}{6} + x \cdot 1, x\right) \]

   7. *-rgt-identity N/A

      \[\leadsto \mathsf{copysign}\left({x}^{3} \cdot \frac{-1}{6} + \color{blue}{x}, x\right) \]

   8. lower-fma.f32 N/A

      \[\leadsto \mathsf{copysign}\left(\color{blue}{\mathsf{fma}\left({x}^{3}, \frac{-1}{6}, x\right)}, x\right) \]

   9. lower-pow.f32 58.6

      \[\leadsto \mathsf{copysign}\left(\mathsf{fma}\left(\color{blue}{{x}^{3}}, -0.16666666666666666, x\right), x\right) \]

7. Applied rewrites 58.6%

   \[\leadsto \mathsf{copysign}\left(\color{blue}{\mathsf{fma}\left({x}^{3}, -0.16666666666666666, x\right)}, x\right) \]
8. Step-by-step derivation

9. Applied rewrites 58.6%

   \[\leadsto \mathsf{copysign}\left(\mathsf{fma}\left(x \cdot x, \color{blue}{x \cdot -0.16666666666666666}, x\right), x\right) \]
10. Add Preprocessing

Alternative 3: 53.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \mathsf{copysign}\left(\mathsf{fma}\left(-0.16666666666666666 \cdot \left(x \cdot x\right), x, x\right), x\right) \end{array} \]

FPCore

(FPCore (x)
 :precision binary32
 (copysign (fma (* -0.16666666666666666 (* x x)) x x) x))

C

float code(float x) {
	return copysignf(fmaf((-0.16666666666666666f * (x * x)), x, x), x);
}

Julia

function code(x)
	return copysign(fma(Float32(Float32(-0.16666666666666666) * Float32(x * x)), x, x), x)
end

Derivation

1. Initial program 35.8%

   \[\mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-log.f32 N/A

      \[\leadsto \mathsf{copysign}\left(\color{blue}{\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right)}, x\right) \]

   2. lift-+.f32 N/A

      \[\leadsto \mathsf{copysign}\left(\log \color{blue}{\left(\left|x\right| + \sqrt{x \cdot x + 1}\right)}, x\right) \]

   3. lift-sqrt.f32 N/A

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \color{blue}{\sqrt{x \cdot x + 1}}\right), x\right) \]

   4. lift-+.f32 N/A

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{x \cdot x + 1}}\right), x\right) \]

   5. lift-*.f32 N/A

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{x \cdot x} + 1}\right), x\right) \]

   6. sqr-abs-rev N/A

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{\left|x\right| \cdot \left|x\right|} + 1}\right), x\right) \]

   7. lift-fabs.f32 N/A

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{\left|x\right|} \cdot \left|x\right| + 1}\right), x\right) \]

   8. lift-fabs.f32 N/A

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\left|x\right| \cdot \color{blue}{\left|x\right|} + 1}\right), x\right) \]

   9. asinh-def-rev N/A

      \[\leadsto \mathsf{copysign}\left(\color{blue}{\sinh^{-1} \left(\left|x\right|\right)}, x\right) \]

   10. lower-asinh.f32 99.6

       \[\leadsto \mathsf{copysign}\left(\color{blue}{\sinh^{-1} \left(\left|x\right|\right)}, x\right) \]

   11. lift-fabs.f32 N/A

       \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \color{blue}{\left(\left|x\right|\right)}, x\right) \]

   12. rem-sqrt-square-rev N/A

       \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \color{blue}{\left(\sqrt{x \cdot x}\right)}, x\right) \]

   13. pow2 N/A

       \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \left(\sqrt{\color{blue}{{x}^{2}}}\right), x\right) \]

   14. sqrt-pow1 N/A

       \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \color{blue}{\left({x}^{\left(\frac{2}{2}\right)}\right)}, x\right) \]

   15. metadata-eval N/A

       \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \left({x}^{\color{blue}{1}}\right), x\right) \]

   16. unpow1 99.6

       \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \color{blue}{x}, x\right) \]

4. Applied rewrites 99.6%

   \[\leadsto \color{blue}{\mathsf{copysign}\left(\sinh^{-1} x, x\right)} \]

5. Taylor expanded in x around 0

   \[\leadsto \mathsf{copysign}\left(\color{blue}{x \cdot \left(1 + \frac{-1}{6} \cdot {x}^{2}\right)}, x\right) \]
6. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \mathsf{copysign}\left(x \cdot \color{blue}{\left(\frac{-1}{6} \cdot {x}^{2} + 1\right)}, x\right) \]

   2. distribute-lft-in N/A

      \[\leadsto \mathsf{copysign}\left(\color{blue}{x \cdot \left(\frac{-1}{6} \cdot {x}^{2}\right) + x \cdot 1}, x\right) \]

   3. *-commutative N/A

      \[\leadsto \mathsf{copysign}\left(x \cdot \color{blue}{\left({x}^{2} \cdot \frac{-1}{6}\right)} + x \cdot 1, x\right) \]

   4. associate-*r* N/A

      \[\leadsto \mathsf{copysign}\left(\color{blue}{\left(x \cdot {x}^{2}\right) \cdot \frac{-1}{6}} + x \cdot 1, x\right) \]

   5. unpow2 N/A

      \[\leadsto \mathsf{copysign}\left(\left(x \cdot \color{blue}{\left(x \cdot x\right)}\right) \cdot \frac{-1}{6} + x \cdot 1, x\right) \]

   6. cube-mult N/A

      \[\leadsto \mathsf{copysign}\left(\color{blue}{{x}^{3}} \cdot \frac{-1}{6} + x \cdot 1, x\right) \]

   7. *-rgt-identity N/A

      \[\leadsto \mathsf{copysign}\left({x}^{3} \cdot \frac{-1}{6} + \color{blue}{x}, x\right) \]

   8. lower-fma.f32 N/A

      \[\leadsto \mathsf{copysign}\left(\color{blue}{\mathsf{fma}\left({x}^{3}, \frac{-1}{6}, x\right)}, x\right) \]

   9. lower-pow.f32 58.6

      \[\leadsto \mathsf{copysign}\left(\mathsf{fma}\left(\color{blue}{{x}^{3}}, -0.16666666666666666, x\right), x\right) \]

7. Applied rewrites 58.6%

   \[\leadsto \mathsf{copysign}\left(\color{blue}{\mathsf{fma}\left({x}^{3}, -0.16666666666666666, x\right)}, x\right) \]
8. Step-by-step derivation

9. Applied rewrites 58.6%

   \[\leadsto \mathsf{copysign}\left(\mathsf{fma}\left(-0.16666666666666666 \cdot \left(x \cdot x\right), \color{blue}{x}, x\right), x\right) \]
10. Add Preprocessing

Alternative 4: 19.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{copysign}\left(-0.5 \cdot x, x\right) \end{array} \]

FPCore

(FPCore (x) :precision binary32 (copysign (* -0.5 x) x))

C

float code(float x) {
	return copysignf((-0.5f * x), x);
}

Julia

function code(x)
	return copysign(Float32(Float32(-0.5) * x), x)
end

MATLAB

function tmp = code(x)
	tmp = sign(x) * abs((single(-0.5) * x));
end

Derivation

1. Initial program 35.8%

   \[\mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \mathsf{copysign}\left(\color{blue}{\log \left(1 + \left|x\right|\right) + \frac{1}{2} \cdot \frac{{x}^{2}}{1 + \left|x\right|}}, x\right) \]
4. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \mathsf{copysign}\left(\color{blue}{\frac{1}{2} \cdot \frac{{x}^{2}}{1 + \left|x\right|} + \log \left(1 + \left|x\right|\right)}, x\right) \]

   2. *-lft-identity N/A

      \[\leadsto \mathsf{copysign}\left(\frac{1}{2} \cdot \frac{\color{blue}{1 \cdot {x}^{2}}}{1 + \left|x\right|} + \log \left(1 + \left|x\right|\right), x\right) \]

   3. associate-*l/ N/A

      \[\leadsto \mathsf{copysign}\left(\frac{1}{2} \cdot \color{blue}{\left(\frac{1}{1 + \left|x\right|} \cdot {x}^{2}\right)} + \log \left(1 + \left|x\right|\right), x\right) \]

   4. associate-*l* N/A

      \[\leadsto \mathsf{copysign}\left(\color{blue}{\left(\frac{1}{2} \cdot \frac{1}{1 + \left|x\right|}\right) \cdot {x}^{2}} + \log \left(1 + \left|x\right|\right), x\right) \]

   5. *-commutative N/A

      \[\leadsto \mathsf{copysign}\left(\color{blue}{{x}^{2} \cdot \left(\frac{1}{2} \cdot \frac{1}{1 + \left|x\right|}\right)} + \log \left(1 + \left|x\right|\right), x\right) \]

   6. unpow2 N/A

      \[\leadsto \mathsf{copysign}\left(\color{blue}{\left(x \cdot x\right)} \cdot \left(\frac{1}{2} \cdot \frac{1}{1 + \left|x\right|}\right) + \log \left(1 + \left|x\right|\right), x\right) \]

   7. associate-*l* N/A

      \[\leadsto \mathsf{copysign}\left(\color{blue}{x \cdot \left(x \cdot \left(\frac{1}{2} \cdot \frac{1}{1 + \left|x\right|}\right)\right)} + \log \left(1 + \left|x\right|\right), x\right) \]

   8. *-commutative N/A

      \[\leadsto \mathsf{copysign}\left(\color{blue}{\left(x \cdot \left(\frac{1}{2} \cdot \frac{1}{1 + \left|x\right|}\right)\right) \cdot x} + \log \left(1 + \left|x\right|\right), x\right) \]

   9. lower-fma.f32 N/A

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

5. Applied rewrites 60.0%

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

6. Taylor expanded in x around inf

   \[\leadsto \mathsf{copysign}\left(\frac{1}{2} \cdot \color{blue}{\frac{{x}^{2}}{1 + \left|x\right|}}, x\right) \]
7. Step-by-step derivation

8. Applied rewrites 12.7%

   \[\leadsto \mathsf{copysign}\left(\left(\frac{0.5}{1 + \left|x\right|} \cdot x\right) \cdot \color{blue}{x}, x\right) \]
9. Step-by-step derivation

10. Applied rewrites 12.7%

    \[\leadsto \mathsf{copysign}\left(\frac{x \cdot -0.5}{-1 + x} \cdot x, x\right) \]

11. Taylor expanded in x around inf

    \[\leadsto \mathsf{copysign}\left(\frac{-1}{2} \cdot x, x\right) \]
12. Step-by-step derivation

13. Applied rewrites 20.8%

    \[\leadsto \mathsf{copysign}\left(-0.5 \cdot x, x\right) \]
14. Add Preprocessing

Developer Target 1: 99.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{\left|x\right|}\\ \mathsf{copysign}\left(\mathsf{log1p}\left(\left|x\right| + \frac{\left|x\right|}{\mathsf{hypot}\left(1, t\_0\right) + t\_0}\right), x\right) \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary32
 (let* ((t_0 (/ 1.0 (fabs x))))
   (copysign (log1p (+ (fabs x) (/ (fabs x) (+ (hypot 1.0 t_0) t_0)))) x)))

C

float code(float x) {
	float t_0 = 1.0f / fabsf(x);
	return copysignf(log1pf((fabsf(x) + (fabsf(x) / (hypotf(1.0f, t_0) + t_0)))), x);
}

Julia

function code(x)
	t_0 = Float32(Float32(1.0) / abs(x))
	return copysign(log1p(Float32(abs(x) + Float32(abs(x) / Float32(hypot(Float32(1.0), t_0) + t_0)))), x)
end

Reproduce

herbie shell --seed 2024363 
(FPCore (x)
  :name "Rust f32::asinh"
  :precision binary32

  :alt
  (! :herbie-platform default (let* ((ax (fabs x)) (ix (/ 1 ax))) (copysign (log1p (+ ax (/ ax (+ (hypot 1 ix) ix)))) x)))

  (copysign (log (+ (fabs x) (sqrt (+ (* x x) 1.0)))) x))