Rust f32::acosh

Percentage Accurate: 53.1% → 98.1%

Time: 6.3s

Alternatives: 6

Speedup: 1.2×

Specification

\[x \geq 1\]

Math

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

FPCore

(FPCore (x) :precision binary32 (acosh x))

C

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

Julia

function code(x)
	return acosh(x)
end

MATLAB

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

Initial Program: 53.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \log \left(x + \sqrt{x \cdot x - 1}\right) \end{array} \]

FPCore

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

C

float code(float x) {
	return logf((x + sqrtf(((x * x) - 1.0f))));
}

Fortran

real(4) function code(x)
    real(4), intent (in) :: x
    code = log((x + sqrt(((x * x) - 1.0e0))))
end function

Julia

function code(x)
	return log(Float32(x + sqrt(Float32(Float32(x * x) - Float32(1.0)))))
end

MATLAB

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

Alternative 1: 98.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \log \left(x + \left(x - \frac{0.5}{x}\right)\right) \end{array} \]

FPCore

(FPCore (x) :precision binary32 (log (+ x (- x (/ 0.5 x)))))

C

float code(float x) {
	return logf((x + (x - (0.5f / x))));
}

Fortran

real(4) function code(x)
    real(4), intent (in) :: x
    code = log((x + (x - (0.5e0 / x))))
end function

Julia

function code(x)
	return log(Float32(x + Float32(x - Float32(Float32(0.5) / x))))
end

MATLAB

function tmp = code(x)
	tmp = log((x + (x - (single(0.5) / x))));
end

Derivation

1. Initial program 55.0%

   \[\log \left(x + \sqrt{x \cdot x - 1}\right) \]
2. Add Preprocessing

3. Taylor expanded in x around inf

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

   1. sub-neg N/A

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

   2. distribute-lft-in N/A

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

   3. *-rgt-identity N/A

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

   4. distribute-rgt-neg-out N/A

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

   5. unsub-neg N/A

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

   6. remove-double-neg N/A

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

   7. distribute-rgt-neg-out N/A

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

   8. distribute-lft-neg-out N/A

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

   9. mul-1-neg N/A

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

   10. lower--.f32 N/A

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

   11. mul-1-neg N/A

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

   12. distribute-lft-neg-out N/A

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

   13. *-commutative N/A

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

   14. distribute-rgt-neg-in N/A

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

   15. metadata-eval N/A

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

   16. associate-*r* N/A

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

5. Applied rewrites 99.3%

   \[\leadsto \log \left(x + \color{blue}{\left(x - \frac{0.5}{x}\right)}\right) \]
6. Add Preprocessing

Alternative 2: 97.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ -\log \left(\frac{0.5}{x}\right) \end{array} \]

FPCore

(FPCore (x) :precision binary32 (- (log (/ 0.5 x))))

C

float code(float x) {
	return -logf((0.5f / x));
}

Fortran

real(4) function code(x)
    real(4), intent (in) :: x
    code = -log((0.5e0 / x))
end function

Julia

function code(x)
	return Float32(-log(Float32(Float32(0.5) / x)))
end

MATLAB

function tmp = code(x)
	tmp = -log((single(0.5) / x));
end

Derivation

1. Initial program 55.0%

   \[\log \left(x + \sqrt{x \cdot x - 1}\right) \]
2. Add Preprocessing

3. Taylor expanded in x around inf

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

   1. +-commutative N/A

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

   2. lower-+.f32 N/A

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

   3. mul-1-neg N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\log \left(\frac{1}{x}\right)\right)\right)} + \log 2 \]

   4. log-rec N/A

      \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(\log x\right)\right)}\right)\right) + \log 2 \]

   5. remove-double-neg N/A

      \[\leadsto \color{blue}{\log x} + \log 2 \]

   6. lower-log.f32 N/A

      \[\leadsto \color{blue}{\log x} + \log 2 \]

   7. lower-log.f32 97.6

      \[\leadsto \log x + \color{blue}{\log 2} \]

5. Applied rewrites 97.6%

   \[\leadsto \color{blue}{\log x + \log 2} \]
6. Step-by-step derivation

7. Applied rewrites 98.5%

   \[\leadsto -\log \left(\frac{0.5}{x}\right) \]
8. Add Preprocessing

Alternative 3: 96.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Julia

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

MATLAB

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

Derivation

1. Initial program 55.0%

   \[\log \left(x + \sqrt{x \cdot x - 1}\right) \]
2. Add Preprocessing

3. Taylor expanded in x around inf

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

   1. lower-*.f32 98.1

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

5. Applied rewrites 98.1%

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

Alternative 4: 5.3% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \frac{-1}{\frac{x}{\frac{0.25}{x}}} \end{array} \]

FPCore

(FPCore (x) :precision binary32 (/ -1.0 (/ x (/ 0.25 x))))

C

float code(float x) {
	return -1.0f / (x / (0.25f / x));
}

Fortran

real(4) function code(x)
    real(4), intent (in) :: x
    code = (-1.0e0) / (x / (0.25e0 / x))
end function

Julia

function code(x)
	return Float32(Float32(-1.0) / Float32(x / Float32(Float32(0.25) / x)))
end

MATLAB

function tmp = code(x)
	tmp = single(-1.0) / (x / (single(0.25) / x));
end

Derivation

1. Initial program 55.0%

   \[\log \left(x + \sqrt{x \cdot x - 1}\right) \]
2. Add Preprocessing

3. Taylor expanded in x around inf

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

   1. lower--.f32 N/A

      \[\leadsto \color{blue}{\left(\log 2 + -1 \cdot \log \left(\frac{1}{x}\right)\right) - \frac{1}{4} \cdot \frac{1}{{x}^{2}}} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \log 2\right)} - \frac{1}{4} \cdot \frac{1}{{x}^{2}} \]

   3. lower-+.f32 N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \log 2\right)} - \frac{1}{4} \cdot \frac{1}{{x}^{2}} \]

   4. mul-1-neg N/A

      \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\log \left(\frac{1}{x}\right)\right)\right)} + \log 2\right) - \frac{1}{4} \cdot \frac{1}{{x}^{2}} \]

   5. log-rec N/A

      \[\leadsto \left(\left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(\log x\right)\right)}\right)\right) + \log 2\right) - \frac{1}{4} \cdot \frac{1}{{x}^{2}} \]

   6. remove-double-neg N/A

      \[\leadsto \left(\color{blue}{\log x} + \log 2\right) - \frac{1}{4} \cdot \frac{1}{{x}^{2}} \]

   7. lower-log.f32 N/A

      \[\leadsto \left(\color{blue}{\log x} + \log 2\right) - \frac{1}{4} \cdot \frac{1}{{x}^{2}} \]

   8. lower-log.f32 N/A

      \[\leadsto \left(\log x + \color{blue}{\log 2}\right) - \frac{1}{4} \cdot \frac{1}{{x}^{2}} \]

   9. associate-*r/ N/A

      \[\leadsto \left(\log x + \log 2\right) - \color{blue}{\frac{\frac{1}{4} \cdot 1}{{x}^{2}}} \]

   10. metadata-eval N/A

       \[\leadsto \left(\log x + \log 2\right) - \frac{\color{blue}{\frac{1}{4}}}{{x}^{2}} \]

   11. lower-/.f32 N/A

       \[\leadsto \left(\log x + \log 2\right) - \color{blue}{\frac{\frac{1}{4}}{{x}^{2}}} \]

   12. unpow2 N/A

       \[\leadsto \left(\log x + \log 2\right) - \frac{\frac{1}{4}}{\color{blue}{x \cdot x}} \]

   13. lower-*.f32 98.8

       \[\leadsto \left(\log x + \log 2\right) - \frac{0.25}{\color{blue}{x \cdot x}} \]

5. Applied rewrites 98.8%

   \[\leadsto \color{blue}{\left(\log x + \log 2\right) - \frac{0.25}{x \cdot x}} \]

6. Taylor expanded in x around 0

   \[\leadsto \frac{\frac{-1}{4}}{\color{blue}{{x}^{2}}} \]
7. Step-by-step derivation

8. Applied rewrites 5.3%

   \[\leadsto \frac{-0.25}{\color{blue}{x \cdot x}} \]
9. Step-by-step derivation

10. Applied rewrites 5.3%

    \[\leadsto \frac{1}{\frac{-x}{\color{blue}{\frac{0.25}{x}}}} \]

11. Final simplification 5.3%

    \[\leadsto \frac{-1}{\frac{x}{\frac{0.25}{x}}} \]
12. Add Preprocessing

Alternative 5: 5.3% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\left(x \cdot x\right) \cdot -4} \end{array} \]

FPCore

(FPCore (x) :precision binary32 (/ 1.0 (* (* x x) -4.0)))

C

float code(float x) {
	return 1.0f / ((x * x) * -4.0f);
}

Fortran

real(4) function code(x)
    real(4), intent (in) :: x
    code = 1.0e0 / ((x * x) * (-4.0e0))
end function

Julia

function code(x)
	return Float32(Float32(1.0) / Float32(Float32(x * x) * Float32(-4.0)))
end

MATLAB

function tmp = code(x)
	tmp = single(1.0) / ((x * x) * single(-4.0));
end

Derivation

1. Initial program 55.0%

   \[\log \left(x + \sqrt{x \cdot x - 1}\right) \]
2. Add Preprocessing

3. Taylor expanded in x around inf

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

   1. lower--.f32 N/A

      \[\leadsto \color{blue}{\left(\log 2 + -1 \cdot \log \left(\frac{1}{x}\right)\right) - \frac{1}{4} \cdot \frac{1}{{x}^{2}}} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \log 2\right)} - \frac{1}{4} \cdot \frac{1}{{x}^{2}} \]

   3. lower-+.f32 N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \log 2\right)} - \frac{1}{4} \cdot \frac{1}{{x}^{2}} \]

   4. mul-1-neg N/A

      \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\log \left(\frac{1}{x}\right)\right)\right)} + \log 2\right) - \frac{1}{4} \cdot \frac{1}{{x}^{2}} \]

   5. log-rec N/A

      \[\leadsto \left(\left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(\log x\right)\right)}\right)\right) + \log 2\right) - \frac{1}{4} \cdot \frac{1}{{x}^{2}} \]

   6. remove-double-neg N/A

      \[\leadsto \left(\color{blue}{\log x} + \log 2\right) - \frac{1}{4} \cdot \frac{1}{{x}^{2}} \]

   7. lower-log.f32 N/A

      \[\leadsto \left(\color{blue}{\log x} + \log 2\right) - \frac{1}{4} \cdot \frac{1}{{x}^{2}} \]

   8. lower-log.f32 N/A

      \[\leadsto \left(\log x + \color{blue}{\log 2}\right) - \frac{1}{4} \cdot \frac{1}{{x}^{2}} \]

   9. associate-*r/ N/A

      \[\leadsto \left(\log x + \log 2\right) - \color{blue}{\frac{\frac{1}{4} \cdot 1}{{x}^{2}}} \]

   10. metadata-eval N/A

       \[\leadsto \left(\log x + \log 2\right) - \frac{\color{blue}{\frac{1}{4}}}{{x}^{2}} \]

   11. lower-/.f32 N/A

       \[\leadsto \left(\log x + \log 2\right) - \color{blue}{\frac{\frac{1}{4}}{{x}^{2}}} \]

   12. unpow2 N/A

       \[\leadsto \left(\log x + \log 2\right) - \frac{\frac{1}{4}}{\color{blue}{x \cdot x}} \]

   13. lower-*.f32 98.8

       \[\leadsto \left(\log x + \log 2\right) - \frac{0.25}{\color{blue}{x \cdot x}} \]

5. Applied rewrites 98.8%

   \[\leadsto \color{blue}{\left(\log x + \log 2\right) - \frac{0.25}{x \cdot x}} \]

6. Taylor expanded in x around 0

   \[\leadsto \frac{\frac{-1}{4}}{\color{blue}{{x}^{2}}} \]
7. Step-by-step derivation

8. Applied rewrites 5.3%

   \[\leadsto \frac{-0.25}{\color{blue}{x \cdot x}} \]
9. Step-by-step derivation

10. Applied rewrites 5.3%

    \[\leadsto \frac{1}{\left(x \cdot x\right) \cdot \color{blue}{-4}} \]
11. Add Preprocessing

Alternative 6: 5.3% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \frac{-0.25}{x \cdot x} \end{array} \]

FPCore

(FPCore (x) :precision binary32 (/ -0.25 (* x x)))

C

float code(float x) {
	return -0.25f / (x * x);
}

Fortran

real(4) function code(x)
    real(4), intent (in) :: x
    code = (-0.25e0) / (x * x)
end function

Julia

function code(x)
	return Float32(Float32(-0.25) / Float32(x * x))
end

MATLAB

function tmp = code(x)
	tmp = single(-0.25) / (x * x);
end

Derivation

1. Initial program 55.0%

   \[\log \left(x + \sqrt{x \cdot x - 1}\right) \]
2. Add Preprocessing

3. Taylor expanded in x around inf

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

   1. lower--.f32 N/A

      \[\leadsto \color{blue}{\left(\log 2 + -1 \cdot \log \left(\frac{1}{x}\right)\right) - \frac{1}{4} \cdot \frac{1}{{x}^{2}}} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \log 2\right)} - \frac{1}{4} \cdot \frac{1}{{x}^{2}} \]

   3. lower-+.f32 N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) + \log 2\right)} - \frac{1}{4} \cdot \frac{1}{{x}^{2}} \]

   4. mul-1-neg N/A

      \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\log \left(\frac{1}{x}\right)\right)\right)} + \log 2\right) - \frac{1}{4} \cdot \frac{1}{{x}^{2}} \]

   5. log-rec N/A

      \[\leadsto \left(\left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(\log x\right)\right)}\right)\right) + \log 2\right) - \frac{1}{4} \cdot \frac{1}{{x}^{2}} \]

   6. remove-double-neg N/A

      \[\leadsto \left(\color{blue}{\log x} + \log 2\right) - \frac{1}{4} \cdot \frac{1}{{x}^{2}} \]

   7. lower-log.f32 N/A

      \[\leadsto \left(\color{blue}{\log x} + \log 2\right) - \frac{1}{4} \cdot \frac{1}{{x}^{2}} \]

   8. lower-log.f32 N/A

      \[\leadsto \left(\log x + \color{blue}{\log 2}\right) - \frac{1}{4} \cdot \frac{1}{{x}^{2}} \]

   9. associate-*r/ N/A

      \[\leadsto \left(\log x + \log 2\right) - \color{blue}{\frac{\frac{1}{4} \cdot 1}{{x}^{2}}} \]

   10. metadata-eval N/A

       \[\leadsto \left(\log x + \log 2\right) - \frac{\color{blue}{\frac{1}{4}}}{{x}^{2}} \]

   11. lower-/.f32 N/A

       \[\leadsto \left(\log x + \log 2\right) - \color{blue}{\frac{\frac{1}{4}}{{x}^{2}}} \]

   12. unpow2 N/A

       \[\leadsto \left(\log x + \log 2\right) - \frac{\frac{1}{4}}{\color{blue}{x \cdot x}} \]

   13. lower-*.f32 98.8

       \[\leadsto \left(\log x + \log 2\right) - \frac{0.25}{\color{blue}{x \cdot x}} \]

5. Applied rewrites 98.8%

   \[\leadsto \color{blue}{\left(\log x + \log 2\right) - \frac{0.25}{x \cdot x}} \]

6. Taylor expanded in x around 0

   \[\leadsto \frac{\frac{-1}{4}}{\color{blue}{{x}^{2}}} \]
7. Step-by-step derivation

8. Applied rewrites 5.3%

   \[\leadsto \frac{-0.25}{\color{blue}{x \cdot x}} \]
9. Add Preprocessing

Developer Target 1: 99.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \log \left(x + \sqrt{x - 1} \cdot \sqrt{x + 1}\right) \end{array} \]

FPCore

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

C

float code(float x) {
	return logf((x + (sqrtf((x - 1.0f)) * sqrtf((x + 1.0f)))));
}

Fortran

real(4) function code(x)
    real(4), intent (in) :: x
    code = log((x + (sqrt((x - 1.0e0)) * sqrt((x + 1.0e0)))))
end function

Julia

function code(x)
	return log(Float32(x + Float32(sqrt(Float32(x - Float32(1.0))) * sqrt(Float32(x + Float32(1.0))))))
end

MATLAB

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

Reproduce

herbie shell --seed 2024313 
(FPCore (x)
  :name "Rust f32::acosh"
  :precision binary32
  :pre (>= x 1.0)

  :alt
  (! :herbie-platform default (log (+ x (* (sqrt (- x 1)) (sqrt (+ x 1))))))

  (log (+ x (sqrt (- (* x x) 1.0)))))