Ian Simplification

Percentage Accurate: 6.7% → 8.1%

Time: 9.8s

Alternatives: 4

Speedup: 1.1×

Specification

Math

\[\begin{array}{l} \\ \frac{\mathsf{PI}\left(\right)}{2} - 2 \cdot \sin^{-1} \left(\sqrt{\frac{1 - x}{2}}\right) \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (- (/ (PI) 2.0) (* 2.0 (asin (sqrt (/ (- 1.0 x) 2.0))))))

Initial Program: 6.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\mathsf{PI}\left(\right)}{2} - 2 \cdot \sin^{-1} \left(\sqrt{\frac{1 - x}{2}}\right) \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (- (/ (PI) 2.0) (* 2.0 (asin (sqrt (/ (- 1.0 x) 2.0))))))

Alternative 1: 8.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot \mathsf{PI}\left(\right)\\ t_1 := t\_0 - \cos^{-1} \left(\sqrt{\left(1 - x\right) \cdot 0.5}\right)\\ t_2 := t\_1 \cdot -2\\ t_3 := \mathsf{fma}\left(t\_0, t\_0 - t\_2, {t\_2}^{2}\right)\\ \frac{{t\_1}^{3} \cdot -8}{t\_3} + \frac{{t\_0}^{3}}{t\_3} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (* 0.5 (PI)))
        (t_1 (- t_0 (acos (sqrt (* (- 1.0 x) 0.5)))))
        (t_2 (* t_1 -2.0))
        (t_3 (fma t_0 (- t_0 t_2) (pow t_2 2.0))))
   (+ (/ (* (pow t_1 3.0) -8.0) t_3) (/ (pow t_0 3.0) t_3))))

Derivation

1. Initial program 6.5%

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

   1. lift-asin.f64 N/A

      \[\leadsto \frac{\mathsf{PI}\left(\right)}{2} - 2 \cdot \color{blue}{\sin^{-1} \left(\sqrt{\frac{1 - x}{2}}\right)} \]

   2. asin-acos N/A

      \[\leadsto \frac{\mathsf{PI}\left(\right)}{2} - 2 \cdot \color{blue}{\left(\frac{\mathsf{PI}\left(\right)}{2} - \cos^{-1} \left(\sqrt{\frac{1 - x}{2}}\right)\right)} \]

   3. lift-PI.f64 N/A

      \[\leadsto \frac{\mathsf{PI}\left(\right)}{2} - 2 \cdot \left(\frac{\color{blue}{\mathsf{PI}\left(\right)}}{2} - \cos^{-1} \left(\sqrt{\frac{1 - x}{2}}\right)\right) \]

   4. lift-/.f64 N/A

      \[\leadsto \frac{\mathsf{PI}\left(\right)}{2} - 2 \cdot \left(\color{blue}{\frac{\mathsf{PI}\left(\right)}{2}} - \cos^{-1} \left(\sqrt{\frac{1 - x}{2}}\right)\right) \]

   5. lower--.f64 N/A

      \[\leadsto \frac{\mathsf{PI}\left(\right)}{2} - 2 \cdot \color{blue}{\left(\frac{\mathsf{PI}\left(\right)}{2} - \cos^{-1} \left(\sqrt{\frac{1 - x}{2}}\right)\right)} \]

   6. lower-acos.f64 8.1

      \[\leadsto \frac{\mathsf{PI}\left(\right)}{2} - 2 \cdot \left(\frac{\mathsf{PI}\left(\right)}{2} - \color{blue}{\cos^{-1} \left(\sqrt{\frac{1 - x}{2}}\right)}\right) \]

4. Applied rewrites 8.1%

   \[\leadsto \frac{\mathsf{PI}\left(\right)}{2} - 2 \cdot \color{blue}{\left(\frac{\mathsf{PI}\left(\right)}{2} - \cos^{-1} \left(\sqrt{\frac{1 - x}{2}}\right)\right)} \]

5. Taylor expanded in x around 0

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

   1. fp-cancel-sub-sign-inv N/A

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

   2. +-commutative N/A

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

   3. *-commutative N/A

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

   4. *-lft-identity N/A

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

   5. metadata-eval N/A

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

   6. cancel-sign-sub N/A

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

   7. *-commutative N/A

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

7. Applied rewrites 8.1%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-2, \mathsf{PI}\left(\right) \cdot 0.5 - \cos^{-1} \left(\sqrt{1 - x} \cdot \sqrt{0.5}\right), \mathsf{PI}\left(\right) \cdot 0.5\right)} \]
8. Step-by-step derivation

9. Applied rewrites 8.1%

   \[\leadsto \frac{{\left(0.5 \cdot \mathsf{PI}\left(\right) - \cos^{-1} \left(\sqrt{\left(1 - x\right) \cdot 0.5}\right)\right)}^{3} \cdot -8}{\mathsf{fma}\left(0.5 \cdot \mathsf{PI}\left(\right), 0.5 \cdot \mathsf{PI}\left(\right) - \left(0.5 \cdot \mathsf{PI}\left(\right) - \cos^{-1} \left(\sqrt{\left(1 - x\right) \cdot 0.5}\right)\right) \cdot -2, {\left(\left(0.5 \cdot \mathsf{PI}\left(\right) - \cos^{-1} \left(\sqrt{\left(1 - x\right) \cdot 0.5}\right)\right) \cdot -2\right)}^{2}\right)} + \color{blue}{\frac{{\left(0.5 \cdot \mathsf{PI}\left(\right)\right)}^{3}}{\mathsf{fma}\left(0.5 \cdot \mathsf{PI}\left(\right), 0.5 \cdot \mathsf{PI}\left(\right) - \left(0.5 \cdot \mathsf{PI}\left(\right) - \cos^{-1} \left(\sqrt{\left(1 - x\right) \cdot 0.5}\right)\right) \cdot -2, {\left(\left(0.5 \cdot \mathsf{PI}\left(\right) - \cos^{-1} \left(\sqrt{\left(1 - x\right) \cdot 0.5}\right)\right) \cdot -2\right)}^{2}\right)}} \]
10. Add Preprocessing

Alternative 2: 8.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot \mathsf{PI}\left(\right)\\ \mathsf{fma}\left(t\_0 - \cos^{-1} \left(\sqrt{\left(1 - x\right) \cdot 0.5}\right), -2, t\_0\right) \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (* 0.5 (PI))))
   (fma (- t_0 (acos (sqrt (* (- 1.0 x) 0.5)))) -2.0 t_0)))

Derivation

1. Initial program 6.5%

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

   1. lift-asin.f64 N/A

      \[\leadsto \frac{\mathsf{PI}\left(\right)}{2} - 2 \cdot \color{blue}{\sin^{-1} \left(\sqrt{\frac{1 - x}{2}}\right)} \]

   2. asin-acos N/A

      \[\leadsto \frac{\mathsf{PI}\left(\right)}{2} - 2 \cdot \color{blue}{\left(\frac{\mathsf{PI}\left(\right)}{2} - \cos^{-1} \left(\sqrt{\frac{1 - x}{2}}\right)\right)} \]

   3. lift-PI.f64 N/A

      \[\leadsto \frac{\mathsf{PI}\left(\right)}{2} - 2 \cdot \left(\frac{\color{blue}{\mathsf{PI}\left(\right)}}{2} - \cos^{-1} \left(\sqrt{\frac{1 - x}{2}}\right)\right) \]

   4. lift-/.f64 N/A

      \[\leadsto \frac{\mathsf{PI}\left(\right)}{2} - 2 \cdot \left(\color{blue}{\frac{\mathsf{PI}\left(\right)}{2}} - \cos^{-1} \left(\sqrt{\frac{1 - x}{2}}\right)\right) \]

   5. lower--.f64 N/A

      \[\leadsto \frac{\mathsf{PI}\left(\right)}{2} - 2 \cdot \color{blue}{\left(\frac{\mathsf{PI}\left(\right)}{2} - \cos^{-1} \left(\sqrt{\frac{1 - x}{2}}\right)\right)} \]

   6. lower-acos.f64 8.1

      \[\leadsto \frac{\mathsf{PI}\left(\right)}{2} - 2 \cdot \left(\frac{\mathsf{PI}\left(\right)}{2} - \color{blue}{\cos^{-1} \left(\sqrt{\frac{1 - x}{2}}\right)}\right) \]

4. Applied rewrites 8.1%

   \[\leadsto \frac{\mathsf{PI}\left(\right)}{2} - 2 \cdot \color{blue}{\left(\frac{\mathsf{PI}\left(\right)}{2} - \cos^{-1} \left(\sqrt{\frac{1 - x}{2}}\right)\right)} \]

5. Taylor expanded in x around 0

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

   1. fp-cancel-sub-sign-inv N/A

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

   2. +-commutative N/A

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

   3. *-commutative N/A

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

   4. *-lft-identity N/A

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

   5. metadata-eval N/A

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

   6. cancel-sign-sub N/A

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

   7. *-commutative N/A

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

7. Applied rewrites 8.1%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-2, \mathsf{PI}\left(\right) \cdot 0.5 - \cos^{-1} \left(\sqrt{1 - x} \cdot \sqrt{0.5}\right), \mathsf{PI}\left(\right) \cdot 0.5\right)} \]
8. Step-by-step derivation

9. Applied rewrites 8.1%

   \[\leadsto \color{blue}{\mathsf{fma}\left(0.5 \cdot \mathsf{PI}\left(\right) - \cos^{-1} \left(\sqrt{\left(1 - x\right) \cdot 0.5}\right), -2, 0.5 \cdot \mathsf{PI}\left(\right)\right)} \]
10. Add Preprocessing

Alternative 3: 6.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\sin^{-1} \left(\sqrt{\mathsf{fma}\left(-0.5, x, 0.5\right)}\right), -2, \frac{\mathsf{PI}\left(\right)}{2}\right) \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (fma (asin (sqrt (fma -0.5 x 0.5))) -2.0 (/ (PI) 2.0)))

Derivation

1. Initial program 6.5%

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

   1. lift--.f64 N/A

      \[\leadsto \color{blue}{\frac{\mathsf{PI}\left(\right)}{2} - 2 \cdot \sin^{-1} \left(\sqrt{\frac{1 - x}{2}}\right)} \]

   2. lift-*.f64 N/A

      \[\leadsto \frac{\mathsf{PI}\left(\right)}{2} - \color{blue}{2 \cdot \sin^{-1} \left(\sqrt{\frac{1 - x}{2}}\right)} \]

   3. fp-cancel-sub-sign-inv N/A

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

   4. +-commutative N/A

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

   5. *-commutative N/A

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

   6. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sin^{-1} \left(\sqrt{\frac{1 - x}{2}}\right), \mathsf{neg}\left(2\right), \frac{\mathsf{PI}\left(\right)}{2}\right)} \]

   7. metadata-eval 6.5

      \[\leadsto \mathsf{fma}\left(\sin^{-1} \left(\sqrt{\frac{1 - x}{2}}\right), \color{blue}{-2}, \frac{\mathsf{PI}\left(\right)}{2}\right) \]

4. Applied rewrites 6.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\sin^{-1} \left(\sqrt{\frac{1 - x}{2}}\right), -2, \frac{\mathsf{PI}\left(\right)}{2}\right)} \]

5. Taylor expanded in x around 0

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

   1. +-commutative N/A

      \[\leadsto \mathsf{fma}\left(\sin^{-1} \left(\sqrt{\color{blue}{\frac{-1}{2} \cdot x + \frac{1}{2}}}\right), -2, \frac{\mathsf{PI}\left(\right)}{2}\right) \]

   2. lower-fma.f64 6.5

      \[\leadsto \mathsf{fma}\left(\sin^{-1} \left(\sqrt{\color{blue}{\mathsf{fma}\left(-0.5, x, 0.5\right)}}\right), -2, \frac{\mathsf{PI}\left(\right)}{2}\right) \]

7. Applied rewrites 6.5%

   \[\leadsto \mathsf{fma}\left(\sin^{-1} \left(\sqrt{\color{blue}{\mathsf{fma}\left(-0.5, x, 0.5\right)}}\right), -2, \frac{\mathsf{PI}\left(\right)}{2}\right) \]
8. Add Preprocessing

Alternative 4: 4.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\sin^{-1} \left(\sqrt{0.5}\right), -2, \frac{\mathsf{PI}\left(\right)}{2}\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (fma (asin (sqrt 0.5)) -2.0 (/ (PI) 2.0)))

Derivation

1. Initial program 6.5%

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

   1. lift--.f64 N/A

      \[\leadsto \color{blue}{\frac{\mathsf{PI}\left(\right)}{2} - 2 \cdot \sin^{-1} \left(\sqrt{\frac{1 - x}{2}}\right)} \]

   2. lift-*.f64 N/A

      \[\leadsto \frac{\mathsf{PI}\left(\right)}{2} - \color{blue}{2 \cdot \sin^{-1} \left(\sqrt{\frac{1 - x}{2}}\right)} \]

   3. fp-cancel-sub-sign-inv N/A

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

   4. +-commutative N/A

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

   5. *-commutative N/A

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

   6. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sin^{-1} \left(\sqrt{\frac{1 - x}{2}}\right), \mathsf{neg}\left(2\right), \frac{\mathsf{PI}\left(\right)}{2}\right)} \]

   7. metadata-eval 6.5

      \[\leadsto \mathsf{fma}\left(\sin^{-1} \left(\sqrt{\frac{1 - x}{2}}\right), \color{blue}{-2}, \frac{\mathsf{PI}\left(\right)}{2}\right) \]

4. Applied rewrites 6.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\sin^{-1} \left(\sqrt{\frac{1 - x}{2}}\right), -2, \frac{\mathsf{PI}\left(\right)}{2}\right)} \]

5. Taylor expanded in x around 0

   \[\leadsto \mathsf{fma}\left(\sin^{-1} \left(\sqrt{\color{blue}{\frac{1}{2}}}\right), -2, \frac{\mathsf{PI}\left(\right)}{2}\right) \]
6. Step-by-step derivation

7. Applied rewrites 4.0%

   \[\leadsto \mathsf{fma}\left(\sin^{-1} \left(\sqrt{\color{blue}{0.5}}\right), -2, \frac{\mathsf{PI}\left(\right)}{2}\right) \]
8. Add Preprocessing

Developer Target 1: 100.0% accurate, 1.4× speedup

Math

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

FPCore

(FPCore (x) :precision binary64 (asin x))

C

double code(double x) {
	return asin(x);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    code = asin(x)
end function

Java

public static double code(double x) {
	return Math.asin(x);
}

Python

def code(x):
	return math.asin(x)

Julia

function code(x)
	return asin(x)
end

MATLAB

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

Wolfram

code[x_] := N[ArcSin[x], $MachinePrecision]

Reproduce

herbie shell --seed 2025015 
(FPCore (x)
  :name "Ian Simplification"
  :precision binary64

  :alt
  (! :herbie-platform default (asin x))

  (- (/ (PI) 2.0) (* 2.0 (asin (sqrt (/ (- 1.0 x) 2.0))))))