Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, K

Percentage Accurate: 70.7% → 77.3%

Time: 15.6s

Alternatives: 11

Speedup: 1.2×

Specification

Math

\[\begin{array}{l} \\ \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (- (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0)))) (/ a (* b 3.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * sqrt(x)) * cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0));
}

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, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((2.0d0 * sqrt(x)) * cos((y - ((z * t) / 3.0d0)))) - (a / (b * 3.0d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * Math.sqrt(x)) * Math.cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0));
}

Python

def code(x, y, z, t, a, b):
	return ((2.0 * math.sqrt(x)) * math.cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(2.0 * sqrt(x)) * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - Float64(a / Float64(b * 3.0)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 70.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (- (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0)))) (/ a (* b 3.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * sqrt(x)) * cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0));
}

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, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((2.0d0 * sqrt(x)) * cos((y - ((z * t) / 3.0d0)))) - (a / (b * 3.0d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * Math.sqrt(x)) * Math.cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0));
}

Python

def code(x, y, z, t, a, b):
	return ((2.0 * math.sqrt(x)) * math.cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(2.0 * sqrt(x)) * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - Float64(a / Float64(b * 3.0)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 77.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{b \cdot 3}\\ t_2 := 2 \cdot \sqrt{x}\\ t_3 := \frac{t \cdot z}{3}\\ \mathbf{if}\;t\_2 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - t\_1 \leq 4 \cdot 10^{+143}:\\ \;\;\;\;t\_2 \cdot \mathsf{fma}\left(\cos t\_3, \cos y, \sin t\_3 \cdot \sin y\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 \cdot \sin \left(\left(-y\right) + \frac{\mathsf{PI}\left(\right)}{2}\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* b 3.0))) (t_2 (* 2.0 (sqrt x))) (t_3 (/ (* t z) 3.0)))
   (if (<= (- (* t_2 (cos (- y (/ (* z t) 3.0)))) t_1) 4e+143)
     (- (* t_2 (fma (cos t_3) (cos y) (* (sin t_3) (sin y)))) t_1)
     (- (* t_2 (sin (+ (- y) (/ (PI) 2.0)))) t_1))))

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) (/.f64 a (*.f64 b #s(literal 3 binary64)))) < 4.0000000000000001e143

   1. Initial program 76.8%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-cos.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos \left(y - \frac{z \cdot t}{3}\right)} - \frac{a}{b \cdot 3} \]

      2. lift--.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{\left(y - \frac{z \cdot t}{3}\right)} - \frac{a}{b \cdot 3} \]

      3. cos-diff N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right) + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3} \]

      4. *-commutative N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\color{blue}{\cos \left(\frac{z \cdot t}{3}\right) \cdot \cos y} + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\mathsf{fma}\left(\cos \left(\frac{z \cdot t}{3}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3} \]

      6. lower-cos.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\color{blue}{\cos \left(\frac{z \cdot t}{3}\right)}, \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{\color{blue}{z \cdot t}}{3}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      8. *-commutative N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{\color{blue}{t \cdot z}}{3}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      9. lower-*.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{\color{blue}{t \cdot z}}{3}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      10. lower-cos.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{3}\right), \color{blue}{\cos y}, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      11. *-commutative N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{3}\right), \cos y, \color{blue}{\sin \left(\frac{z \cdot t}{3}\right) \cdot \sin y}\right) - \frac{a}{b \cdot 3} \]

      12. lower-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{3}\right), \cos y, \color{blue}{\sin \left(\frac{z \cdot t}{3}\right) \cdot \sin y}\right) - \frac{a}{b \cdot 3} \]

      13. lower-sin.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{3}\right), \cos y, \color{blue}{\sin \left(\frac{z \cdot t}{3}\right)} \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      14. lift-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{3}\right), \cos y, \sin \left(\frac{\color{blue}{z \cdot t}}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      15. *-commutative N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{3}\right), \cos y, \sin \left(\frac{\color{blue}{t \cdot z}}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      16. lower-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{3}\right), \cos y, \sin \left(\frac{\color{blue}{t \cdot z}}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      17. lower-sin.f64 78.7

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{3}\right), \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \color{blue}{\sin y}\right) - \frac{a}{b \cdot 3} \]

   4. Applied rewrites 78.7%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\mathsf{fma}\left(\cos \left(\frac{t \cdot z}{3}\right), \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right)} - \frac{a}{b \cdot 3} \]

   if 4.0000000000000001e143 < (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) (/.f64 a (*.f64 b #s(literal 3 binary64))))

   1. Initial program 51.5%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{y} - \frac{a}{b \cdot 3} \]
   4. Step-by-step derivation

   5. Applied rewrites 73.1%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{y} - \frac{a}{b \cdot 3} \]
   6. Step-by-step derivation

      1. lift-cos.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]

      2. cos-neg-rev N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos \left(\mathsf{neg}\left(y\right)\right)} - \frac{a}{b \cdot 3} \]

      3. sin-+PI/2-rev N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\sin \left(\left(\mathsf{neg}\left(y\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]

      4. lower-sin.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\sin \left(\left(\mathsf{neg}\left(y\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]

      5. lift-PI.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \left(\left(\mathsf{neg}\left(y\right)\right) + \frac{\color{blue}{\mathsf{PI}\left(\right)}}{2}\right) - \frac{a}{b \cdot 3} \]

      6. lift-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \left(\left(\mathsf{neg}\left(y\right)\right) + \color{blue}{\frac{\mathsf{PI}\left(\right)}{2}}\right) - \frac{a}{b \cdot 3} \]

      7. lower-+.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]

      8. lower-neg.f64 73.7

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \left(\color{blue}{\left(-y\right)} + \frac{\mathsf{PI}\left(\right)}{2}\right) - \frac{a}{b \cdot 3} \]

   7. Applied rewrites 73.7%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\sin \left(\left(-y\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 77.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{b \cdot 3}\\ t_2 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t\_2 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - t\_1 \leq 4 \cdot 10^{+143}:\\ \;\;\;\;t\_2 \cdot \mathsf{fma}\left(\cos \left(\frac{t}{-3} \cdot z\right), \cos y, \sin \left(\frac{t}{3} \cdot z\right) \cdot \sin y\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 \cdot \sin \left(\left(-y\right) + \frac{\mathsf{PI}\left(\right)}{2}\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* b 3.0))) (t_2 (* 2.0 (sqrt x))))
   (if (<= (- (* t_2 (cos (- y (/ (* z t) 3.0)))) t_1) 4e+143)
     (-
      (*
       t_2
       (fma (cos (* (/ t -3.0) z)) (cos y) (* (sin (* (/ t 3.0) z)) (sin y))))
      t_1)
     (- (* t_2 (sin (+ (- y) (/ (PI) 2.0)))) t_1))))

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) (/.f64 a (*.f64 b #s(literal 3 binary64)))) < 4.0000000000000001e143

   1. Initial program 76.8%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-cos.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos \left(y - \frac{z \cdot t}{3}\right)} - \frac{a}{b \cdot 3} \]

      2. sin-+PI/2-rev N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\sin \left(\left(y - \frac{z \cdot t}{3}\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]

      3. lower-sin.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\sin \left(\left(y - \frac{z \cdot t}{3}\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]

      4. +-commutative N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \color{blue}{\left(\frac{\mathsf{PI}\left(\right)}{2} + \left(y - \frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3} \]

      5. lower-+.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \color{blue}{\left(\frac{\mathsf{PI}\left(\right)}{2} + \left(y - \frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3} \]

      6. lower-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \left(\color{blue}{\frac{\mathsf{PI}\left(\right)}{2}} + \left(y - \frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      7. lower-PI.f64 57.6

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \left(\frac{\color{blue}{\mathsf{PI}\left(\right)}}{2} + \left(y - \frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      8. lift-*.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \left(\frac{\mathsf{PI}\left(\right)}{2} + \left(y - \frac{\color{blue}{z \cdot t}}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      9. *-commutative N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \left(\frac{\mathsf{PI}\left(\right)}{2} + \left(y - \frac{\color{blue}{t \cdot z}}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      10. lower-*.f64 57.6

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \left(\frac{\mathsf{PI}\left(\right)}{2} + \left(y - \frac{\color{blue}{t \cdot z}}{3}\right)\right) - \frac{a}{b \cdot 3} \]

   4. Applied rewrites 57.6%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\sin \left(\frac{\mathsf{PI}\left(\right)}{2} + \left(y - \frac{t \cdot z}{3}\right)\right)} - \frac{a}{b \cdot 3} \]
   5. Step-by-step derivation

      1. lift-sin.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\sin \left(\frac{\mathsf{PI}\left(\right)}{2} + \left(y - \frac{t \cdot z}{3}\right)\right)} - \frac{a}{b \cdot 3} \]

      2. lift-+.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \color{blue}{\left(\frac{\mathsf{PI}\left(\right)}{2} + \left(y - \frac{t \cdot z}{3}\right)\right)} - \frac{a}{b \cdot 3} \]

      3. +-commutative N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \color{blue}{\left(\left(y - \frac{t \cdot z}{3}\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]

      4. lift--.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \left(\color{blue}{\left(y - \frac{t \cdot z}{3}\right)} + \frac{\mathsf{PI}\left(\right)}{2}\right) - \frac{a}{b \cdot 3} \]

      5. lift-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \left(\left(y - \color{blue}{\frac{t \cdot z}{3}}\right) + \frac{\mathsf{PI}\left(\right)}{2}\right) - \frac{a}{b \cdot 3} \]

      6. lift-*.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \left(\left(y - \frac{\color{blue}{t \cdot z}}{3}\right) + \frac{\mathsf{PI}\left(\right)}{2}\right) - \frac{a}{b \cdot 3} \]

      7. *-commutative N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \left(\left(y - \frac{\color{blue}{z \cdot t}}{3}\right) + \frac{\mathsf{PI}\left(\right)}{2}\right) - \frac{a}{b \cdot 3} \]

      8. lift-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \left(\left(y - \frac{z \cdot t}{3}\right) + \color{blue}{\frac{\mathsf{PI}\left(\right)}{2}}\right) - \frac{a}{b \cdot 3} \]

      9. lift-PI.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \left(\left(y - \frac{z \cdot t}{3}\right) + \frac{\color{blue}{\mathsf{PI}\left(\right)}}{2}\right) - \frac{a}{b \cdot 3} \]

      10. sin-+PI/2-rev N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos \left(y - \frac{z \cdot t}{3}\right)} - \frac{a}{b \cdot 3} \]

      11. cos-diff N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right) + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3} \]

      12. associate-/l* N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \color{blue}{\left(z \cdot \frac{t}{3}\right)} + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      13. lift-/.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(z \cdot \color{blue}{\frac{t}{3}}\right) + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      14. *-commutative N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \color{blue}{\left(\frac{t}{3} \cdot z\right)} + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      15. lift-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \color{blue}{\left(\frac{t}{3} \cdot z\right)} + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      16. associate-/l* N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\frac{t}{3} \cdot z\right) + \sin y \cdot \sin \color{blue}{\left(z \cdot \frac{t}{3}\right)}\right) - \frac{a}{b \cdot 3} \]

      17. lift-/.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\frac{t}{3} \cdot z\right) + \sin y \cdot \sin \left(z \cdot \color{blue}{\frac{t}{3}}\right)\right) - \frac{a}{b \cdot 3} \]

      18. *-commutative N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\frac{t}{3} \cdot z\right) + \sin y \cdot \sin \color{blue}{\left(\frac{t}{3} \cdot z\right)}\right) - \frac{a}{b \cdot 3} \]

      19. lift-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\frac{t}{3} \cdot z\right) + \sin y \cdot \sin \color{blue}{\left(\frac{t}{3} \cdot z\right)}\right) - \frac{a}{b \cdot 3} \]

   6. Applied rewrites 78.6%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\mathsf{fma}\left(\cos \left(\frac{t}{-3} \cdot z\right), \cos y, \sin \left(\frac{t}{3} \cdot z\right) \cdot \sin y\right)} - \frac{a}{b \cdot 3} \]

   if 4.0000000000000001e143 < (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) (/.f64 a (*.f64 b #s(literal 3 binary64))))

   1. Initial program 51.5%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{y} - \frac{a}{b \cdot 3} \]
   4. Step-by-step derivation

   5. Applied rewrites 73.1%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{y} - \frac{a}{b \cdot 3} \]
   6. Step-by-step derivation

      1. lift-cos.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]

      2. cos-neg-rev N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos \left(\mathsf{neg}\left(y\right)\right)} - \frac{a}{b \cdot 3} \]

      3. sin-+PI/2-rev N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\sin \left(\left(\mathsf{neg}\left(y\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]

      4. lower-sin.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\sin \left(\left(\mathsf{neg}\left(y\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]

      5. lift-PI.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \left(\left(\mathsf{neg}\left(y\right)\right) + \frac{\color{blue}{\mathsf{PI}\left(\right)}}{2}\right) - \frac{a}{b \cdot 3} \]

      6. lift-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \left(\left(\mathsf{neg}\left(y\right)\right) + \color{blue}{\frac{\mathsf{PI}\left(\right)}{2}}\right) - \frac{a}{b \cdot 3} \]

      7. lower-+.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]

      8. lower-neg.f64 73.7

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \left(\color{blue}{\left(-y\right)} + \frac{\mathsf{PI}\left(\right)}{2}\right) - \frac{a}{b \cdot 3} \]

   7. Applied rewrites 73.7%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\sin \left(\left(-y\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 72.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{b \cdot 3}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-83} \lor \neg \left(t\_1 \leq 10^{-93}\right):\\ \;\;\;\;\mathsf{fma}\left(\sqrt{x}, 2, -0.3333333333333333 \cdot \frac{a}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(-0.3333333333333333, t \cdot z, y\right)\right) \cdot \left(\sqrt{x} \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* b 3.0))))
   (if (or (<= t_1 -1e-83) (not (<= t_1 1e-93)))
     (fma (sqrt x) 2.0 (* -0.3333333333333333 (/ a b)))
     (* (cos (fma -0.3333333333333333 (* t z) y)) (* (sqrt x) 2.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (b * 3.0);
	double tmp;
	if ((t_1 <= -1e-83) || !(t_1 <= 1e-93)) {
		tmp = fma(sqrt(x), 2.0, (-0.3333333333333333 * (a / b)));
	} else {
		tmp = cos(fma(-0.3333333333333333, (t * z), y)) * (sqrt(x) * 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(b * 3.0))
	tmp = 0.0
	if ((t_1 <= -1e-83) || !(t_1 <= 1e-93))
		tmp = fma(sqrt(x), 2.0, Float64(-0.3333333333333333 * Float64(a / b)));
	else
		tmp = Float64(cos(fma(-0.3333333333333333, Float64(t * z), y)) * Float64(sqrt(x) * 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-83], N[Not[LessEqual[t$95$1, 1e-93]], $MachinePrecision]], N[(N[Sqrt[x], $MachinePrecision] * 2.0 + N[(-0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[N[(-0.3333333333333333 * N[(t * z), $MachinePrecision] + y), $MachinePrecision]], $MachinePrecision] * N[(N[Sqrt[x], $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 a (*.f64 b #s(literal 3 binary64))) < -1e-83 or 9.999999999999999e-94 < (/.f64 a (*.f64 b #s(literal 3 binary64)))

   1. Initial program 78.1%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{y} - \frac{a}{b \cdot 3} \]
   4. Step-by-step derivation

   5. Applied rewrites 85.3%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{y} - \frac{a}{b \cdot 3} \]

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos y\right) - \frac{1}{3} \cdot \frac{a}{b}} \]
   7. Step-by-step derivation

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

         \[\leadsto 2 \cdot \left(\sqrt{x} \cdot \cos y\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot \frac{a}{b}} \]

      2. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot \cos y\right) \cdot 2 + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right)} \cdot \frac{a}{b} \]

      3. metadata-eval N/A

         \[\leadsto \left(\sqrt{x} \cdot \cos y\right) \cdot 2 + \frac{-1}{3} \cdot \frac{\color{blue}{a}}{b} \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\sqrt{x} \cdot \cos y, \color{blue}{2}, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

      7. lower-cos.f64 N/A

         \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

      8. lower-sqrt.f64 N/A

         \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

      10. lower-/.f64 85.1

          \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, -0.3333333333333333 \cdot \frac{a}{b}\right) \]

   8. Applied rewrites 85.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, -0.3333333333333333 \cdot \frac{a}{b}\right)} \]

   9. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]
   10. Step-by-step derivation

       1. lower-sqrt.f64 77.0

          \[\leadsto \mathsf{fma}\left(\sqrt{x}, 2, -0.3333333333333333 \cdot \frac{a}{b}\right) \]

   11. Applied rewrites 77.0%

       \[\leadsto \mathsf{fma}\left(\sqrt{x}, 2, -0.3333333333333333 \cdot \frac{a}{b}\right) \]

   if -1e-83 < (/.f64 a (*.f64 b #s(literal 3 binary64))) < 9.999999999999999e-94

   1. Initial program 57.5%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right) \cdot \color{blue}{\left(2 \cdot \sqrt{x}\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right) \cdot \color{blue}{\left(2 \cdot \sqrt{x}\right)} \]

      4. lower-cos.f64 N/A

         \[\leadsto \cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right) \cdot \left(\color{blue}{2} \cdot \sqrt{x}\right) \]

      5. cancel-sign-sub-inv N/A

         \[\leadsto \cos \left(y + \left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot \left(t \cdot z\right)\right) \cdot \left(2 \cdot \sqrt{x}\right) \]

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

         \[\leadsto \cos \left(y + \left(\mathsf{neg}\left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right) \cdot \left(2 \cdot \sqrt{x}\right) \]

      7. +-commutative N/A

         \[\leadsto \cos \left(\left(\mathsf{neg}\left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)\right) + y\right) \cdot \left(2 \cdot \sqrt{x}\right) \]

      8. remove-double-neg N/A

         \[\leadsto \cos \left(\left(\mathsf{neg}\left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \cdot \left(2 \cdot \sqrt{x}\right) \]

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

         \[\leadsto \cos \left(\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot \left(t \cdot z\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \cdot \left(2 \cdot \sqrt{x}\right) \]

      10. metadata-eval N/A

          \[\leadsto \cos \left(\frac{-1}{3} \cdot \left(t \cdot z\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \cdot \left(2 \cdot \sqrt{x}\right) \]

      11. remove-double-neg N/A

          \[\leadsto \cos \left(\frac{-1}{3} \cdot \left(t \cdot z\right) + y\right) \cdot \left(2 \cdot \sqrt{x}\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \cos \left(\mathsf{fma}\left(\frac{-1}{3}, t \cdot z, y\right)\right) \cdot \left(2 \cdot \sqrt{x}\right) \]

      13. lower-*.f64 N/A

          \[\leadsto \cos \left(\mathsf{fma}\left(\frac{-1}{3}, t \cdot z, y\right)\right) \cdot \left(2 \cdot \sqrt{x}\right) \]

      14. *-commutative N/A

          \[\leadsto \cos \left(\mathsf{fma}\left(\frac{-1}{3}, t \cdot z, y\right)\right) \cdot \left(\sqrt{x} \cdot \color{blue}{2}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \cos \left(\mathsf{fma}\left(\frac{-1}{3}, t \cdot z, y\right)\right) \cdot \left(\sqrt{x} \cdot \color{blue}{2}\right) \]

      16. lower-sqrt.f64 58.0

          \[\leadsto \cos \left(\mathsf{fma}\left(-0.3333333333333333, t \cdot z, y\right)\right) \cdot \left(\sqrt{x} \cdot 2\right) \]

   5. Applied rewrites 58.0%

      \[\leadsto \color{blue}{\cos \left(\mathsf{fma}\left(-0.3333333333333333, t \cdot z, y\right)\right) \cdot \left(\sqrt{x} \cdot 2\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{b \cdot 3} \leq -1 \cdot 10^{-83} \lor \neg \left(\frac{a}{b \cdot 3} \leq 10^{-93}\right):\\ \;\;\;\;\mathsf{fma}\left(\sqrt{x}, 2, -0.3333333333333333 \cdot \frac{a}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(-0.3333333333333333, t \cdot z, y\right)\right) \cdot \left(\sqrt{x} \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{b \cdot 3}\\ \mathbf{if}\;t\_1 \leq -1.5 \cdot 10^{-30} \lor \neg \left(t\_1 \leq 5 \cdot 10^{-58}\right):\\ \;\;\;\;\mathsf{fma}\left(\sqrt{x}, 2, -0.3333333333333333 \cdot \frac{a}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot \left(\sqrt{x} \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* b 3.0))))
   (if (or (<= t_1 -1.5e-30) (not (<= t_1 5e-58)))
     (fma (sqrt x) 2.0 (* -0.3333333333333333 (/ a b)))
     (* (cos y) (* (sqrt x) 2.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (b * 3.0);
	double tmp;
	if ((t_1 <= -1.5e-30) || !(t_1 <= 5e-58)) {
		tmp = fma(sqrt(x), 2.0, (-0.3333333333333333 * (a / b)));
	} else {
		tmp = cos(y) * (sqrt(x) * 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(b * 3.0))
	tmp = 0.0
	if ((t_1 <= -1.5e-30) || !(t_1 <= 5e-58))
		tmp = fma(sqrt(x), 2.0, Float64(-0.3333333333333333 * Float64(a / b)));
	else
		tmp = Float64(cos(y) * Float64(sqrt(x) * 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1.5e-30], N[Not[LessEqual[t$95$1, 5e-58]], $MachinePrecision]], N[(N[Sqrt[x], $MachinePrecision] * 2.0 + N[(-0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] * N[(N[Sqrt[x], $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 a (*.f64 b #s(literal 3 binary64))) < -1.49999999999999995e-30 or 4.99999999999999977e-58 < (/.f64 a (*.f64 b #s(literal 3 binary64)))

   1. Initial program 83.0%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{y} - \frac{a}{b \cdot 3} \]
   4. Step-by-step derivation

   5. Applied rewrites 90.3%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{y} - \frac{a}{b \cdot 3} \]

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos y\right) - \frac{1}{3} \cdot \frac{a}{b}} \]
   7. Step-by-step derivation

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

         \[\leadsto 2 \cdot \left(\sqrt{x} \cdot \cos y\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot \frac{a}{b}} \]

      2. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot \cos y\right) \cdot 2 + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right)} \cdot \frac{a}{b} \]

      3. metadata-eval N/A

         \[\leadsto \left(\sqrt{x} \cdot \cos y\right) \cdot 2 + \frac{-1}{3} \cdot \frac{\color{blue}{a}}{b} \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\sqrt{x} \cdot \cos y, \color{blue}{2}, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

      7. lower-cos.f64 N/A

         \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

      8. lower-sqrt.f64 N/A

         \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

      10. lower-/.f64 90.1

          \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, -0.3333333333333333 \cdot \frac{a}{b}\right) \]

   8. Applied rewrites 90.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, -0.3333333333333333 \cdot \frac{a}{b}\right)} \]

   9. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]
   10. Step-by-step derivation

       1. lower-sqrt.f64 84.2

          \[\leadsto \mathsf{fma}\left(\sqrt{x}, 2, -0.3333333333333333 \cdot \frac{a}{b}\right) \]

   11. Applied rewrites 84.2%

       \[\leadsto \mathsf{fma}\left(\sqrt{x}, 2, -0.3333333333333333 \cdot \frac{a}{b}\right) \]

   if -1.49999999999999995e-30 < (/.f64 a (*.f64 b #s(literal 3 binary64))) < 4.99999999999999977e-58

   1. Initial program 56.2%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{y} - \frac{a}{b \cdot 3} \]
   4. Step-by-step derivation

   5. Applied rewrites 57.4%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{y} - \frac{a}{b \cdot 3} \]

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos y\right) - \frac{1}{3} \cdot \frac{a}{b}} \]
   7. Step-by-step derivation

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

         \[\leadsto 2 \cdot \left(\sqrt{x} \cdot \cos y\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot \frac{a}{b}} \]

      2. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot \cos y\right) \cdot 2 + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right)} \cdot \frac{a}{b} \]

      3. metadata-eval N/A

         \[\leadsto \left(\sqrt{x} \cdot \cos y\right) \cdot 2 + \frac{-1}{3} \cdot \frac{\color{blue}{a}}{b} \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\sqrt{x} \cdot \cos y, \color{blue}{2}, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

      7. lower-cos.f64 N/A

         \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

      8. lower-sqrt.f64 N/A

         \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

      10. lower-/.f64 57.4

          \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, -0.3333333333333333 \cdot \frac{a}{b}\right) \]

   8. Applied rewrites 57.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, -0.3333333333333333 \cdot \frac{a}{b}\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto 2 \cdot \color{blue}{\left(\sqrt{x} \cdot \cos y\right)} \]
   10. Step-by-step derivation

       1. count-2-rev N/A

          \[\leadsto \sqrt{x} \cdot \cos y + \sqrt{x} \cdot \color{blue}{\cos y} \]

       2. distribute-rgt-in N/A

          \[\leadsto \cos y \cdot \left(\sqrt{x} + \color{blue}{\sqrt{x}}\right) \]

       3. count-2-rev N/A

          \[\leadsto \cos y \cdot \left(2 \cdot \sqrt{x}\right) \]

       4. lower-*.f64 N/A

          \[\leadsto \cos y \cdot \left(2 \cdot \color{blue}{\sqrt{x}}\right) \]

       5. lower-cos.f64 N/A

          \[\leadsto \cos y \cdot \left(2 \cdot \sqrt{\color{blue}{x}}\right) \]

       6. *-commutative N/A

          \[\leadsto \cos y \cdot \left(\sqrt{x} \cdot 2\right) \]

       7. lower-*.f64 N/A

          \[\leadsto \cos y \cdot \left(\sqrt{x} \cdot 2\right) \]

       8. lower-sqrt.f64 53.4

          \[\leadsto \cos y \cdot \left(\sqrt{x} \cdot 2\right) \]

   11. Applied rewrites 53.4%

       \[\leadsto \cos y \cdot \color{blue}{\left(\sqrt{x} \cdot 2\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{b \cdot 3} \leq -1.5 \cdot 10^{-30} \lor \neg \left(\frac{a}{b \cdot 3} \leq 5 \cdot 10^{-58}\right):\\ \;\;\;\;\mathsf{fma}\left(\sqrt{x}, 2, -0.3333333333333333 \cdot \frac{a}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot \left(\sqrt{x} \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{b \cdot 3} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (- (* (* 2.0 (sqrt x)) (cos y)) (/ a (* b 3.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * sqrt(x)) * cos(y)) - (a / (b * 3.0));
}

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, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((2.0d0 * sqrt(x)) * cos(y)) - (a / (b * 3.0d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * Math.sqrt(x)) * Math.cos(y)) - (a / (b * 3.0));
}

Python

def code(x, y, z, t, a, b):
	return ((2.0 * math.sqrt(x)) * math.cos(y)) - (a / (b * 3.0))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(2.0 * sqrt(x)) * cos(y)) - Float64(a / Float64(b * 3.0)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * cos(y)) - (a / (b * 3.0));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.9%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in y around inf

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{y} - \frac{a}{b \cdot 3} \]
4. Step-by-step derivation

5. Applied rewrites 75.4%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{y} - \frac{a}{b \cdot 3} \]
6. Add Preprocessing

Alternative 6: 76.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, -0.3333333333333333 \cdot \frac{a}{b}\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (fma (* (cos y) (sqrt x)) 2.0 (* -0.3333333333333333 (/ a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return fma((cos(y) * sqrt(x)), 2.0, (-0.3333333333333333 * (a / b)));
}

Julia

function code(x, y, z, t, a, b)
	return fma(Float64(cos(y) * sqrt(x)), 2.0, Float64(-0.3333333333333333 * Float64(a / b)))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[Cos[y], $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * 2.0 + N[(-0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.9%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in y around inf

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{y} - \frac{a}{b \cdot 3} \]
4. Step-by-step derivation

5. Applied rewrites 75.4%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{y} - \frac{a}{b \cdot 3} \]

6. Taylor expanded in z around 0

   \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos y\right) - \frac{1}{3} \cdot \frac{a}{b}} \]
7. Step-by-step derivation

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

      \[\leadsto 2 \cdot \left(\sqrt{x} \cdot \cos y\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot \frac{a}{b}} \]

   2. *-commutative N/A

      \[\leadsto \left(\sqrt{x} \cdot \cos y\right) \cdot 2 + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right)} \cdot \frac{a}{b} \]

   3. metadata-eval N/A

      \[\leadsto \left(\sqrt{x} \cdot \cos y\right) \cdot 2 + \frac{-1}{3} \cdot \frac{\color{blue}{a}}{b} \]

   4. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(\sqrt{x} \cdot \cos y, \color{blue}{2}, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

   5. *-commutative N/A

      \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

   6. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

   7. lower-cos.f64 N/A

      \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

   8. lower-sqrt.f64 N/A

      \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

   9. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

   10. lower-/.f64 75.3

       \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, -0.3333333333333333 \cdot \frac{a}{b}\right) \]

8. Applied rewrites 75.3%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, -0.3333333333333333 \cdot \frac{a}{b}\right)} \]
9. Add Preprocessing

Alternative 7: 76.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(2 \cdot \cos y, \sqrt{x}, -0.3333333333333333 \cdot \frac{a}{b}\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (fma (* 2.0 (cos y)) (sqrt x) (* -0.3333333333333333 (/ a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return fma((2.0 * cos(y)), sqrt(x), (-0.3333333333333333 * (a / b)));
}

Julia

function code(x, y, z, t, a, b)
	return fma(Float64(2.0 * cos(y)), sqrt(x), Float64(-0.3333333333333333 * Float64(a / b)))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(2.0 * N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[Sqrt[x], $MachinePrecision] + N[(-0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.9%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in z around 0

   \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos y\right) - \frac{1}{3} \cdot \frac{a}{b}} \]
4. Step-by-step derivation

   1. associate-*r/ N/A

      \[\leadsto 2 \cdot \left(\sqrt{x} \cdot \cos y\right) - \frac{\frac{1}{3} \cdot a}{\color{blue}{b}} \]

   2. *-commutative N/A

      \[\leadsto 2 \cdot \left(\sqrt{x} \cdot \cos y\right) - \frac{a \cdot \frac{1}{3}}{b} \]

   3. associate-*r/ N/A

      \[\leadsto 2 \cdot \left(\sqrt{x} \cdot \cos y\right) - a \cdot \color{blue}{\frac{\frac{1}{3}}{b}} \]

   4. metadata-eval N/A

      \[\leadsto 2 \cdot \left(\sqrt{x} \cdot \cos y\right) - a \cdot \frac{\frac{1}{3} \cdot 1}{b} \]

   5. associate-*r/ N/A

      \[\leadsto 2 \cdot \left(\sqrt{x} \cdot \cos y\right) - a \cdot \left(\frac{1}{3} \cdot \color{blue}{\frac{1}{b}}\right) \]

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

      \[\leadsto 2 \cdot \left(\sqrt{x} \cdot \cos y\right) + \color{blue}{\left(\mathsf{neg}\left(a\right)\right) \cdot \left(\frac{1}{3} \cdot \frac{1}{b}\right)} \]

   7. *-commutative N/A

      \[\leadsto 2 \cdot \left(\cos y \cdot \sqrt{x}\right) + \left(\mathsf{neg}\left(a\right)\right) \cdot \left(\frac{1}{3} \cdot \frac{1}{b}\right) \]

   8. associate-*r* N/A

      \[\leadsto \left(2 \cdot \cos y\right) \cdot \sqrt{x} + \color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot \left(\frac{1}{3} \cdot \frac{1}{b}\right) \]

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

      \[\leadsto \left(2 \cdot \cos y\right) \cdot \sqrt{x} + \left(\mathsf{neg}\left(a \cdot \left(\frac{1}{3} \cdot \frac{1}{b}\right)\right)\right) \]

   10. associate-*r/ N/A

       \[\leadsto \left(2 \cdot \cos y\right) \cdot \sqrt{x} + \left(\mathsf{neg}\left(a \cdot \frac{\frac{1}{3} \cdot 1}{b}\right)\right) \]

   11. metadata-eval N/A

       \[\leadsto \left(2 \cdot \cos y\right) \cdot \sqrt{x} + \left(\mathsf{neg}\left(a \cdot \frac{\frac{1}{3}}{b}\right)\right) \]

   12. associate-*r/ N/A

       \[\leadsto \left(2 \cdot \cos y\right) \cdot \sqrt{x} + \left(\mathsf{neg}\left(\frac{a \cdot \frac{1}{3}}{b}\right)\right) \]

   13. *-commutative N/A

       \[\leadsto \left(2 \cdot \cos y\right) \cdot \sqrt{x} + \left(\mathsf{neg}\left(\frac{\frac{1}{3} \cdot a}{b}\right)\right) \]

   14. associate-*r/ N/A

       \[\leadsto \left(2 \cdot \cos y\right) \cdot \sqrt{x} + \left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{a}{b}\right)\right) \]

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

       \[\leadsto \left(2 \cdot \cos y\right) \cdot \sqrt{x} + \left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot \color{blue}{\frac{a}{b}} \]

   16. metadata-eval N/A

       \[\leadsto \left(2 \cdot \cos y\right) \cdot \sqrt{x} + \frac{-1}{3} \cdot \frac{\color{blue}{a}}{b} \]

   17. lower-fma.f64 N/A

       \[\leadsto \mathsf{fma}\left(2 \cdot \cos y, \color{blue}{\sqrt{x}}, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

5. Applied rewrites 75.3%

   \[\leadsto \color{blue}{\mathsf{fma}\left(2 \cdot \cos y, \sqrt{x}, -0.3333333333333333 \cdot \frac{a}{b}\right)} \]
6. Add Preprocessing

Alternative 8: 65.1% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\sqrt{x}, 2, -0.3333333333333333 \cdot \frac{a}{b}\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (fma (sqrt x) 2.0 (* -0.3333333333333333 (/ a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return fma(sqrt(x), 2.0, (-0.3333333333333333 * (a / b)));
}

Julia

function code(x, y, z, t, a, b)
	return fma(sqrt(x), 2.0, Float64(-0.3333333333333333 * Float64(a / b)))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[Sqrt[x], $MachinePrecision] * 2.0 + N[(-0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.9%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in y around inf

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{y} - \frac{a}{b \cdot 3} \]
4. Step-by-step derivation

5. Applied rewrites 75.4%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{y} - \frac{a}{b \cdot 3} \]

6. Taylor expanded in z around 0

   \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos y\right) - \frac{1}{3} \cdot \frac{a}{b}} \]
7. Step-by-step derivation

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

      \[\leadsto 2 \cdot \left(\sqrt{x} \cdot \cos y\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot \frac{a}{b}} \]

   2. *-commutative N/A

      \[\leadsto \left(\sqrt{x} \cdot \cos y\right) \cdot 2 + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right)} \cdot \frac{a}{b} \]

   3. metadata-eval N/A

      \[\leadsto \left(\sqrt{x} \cdot \cos y\right) \cdot 2 + \frac{-1}{3} \cdot \frac{\color{blue}{a}}{b} \]

   4. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(\sqrt{x} \cdot \cos y, \color{blue}{2}, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

   5. *-commutative N/A

      \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

   6. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

   7. lower-cos.f64 N/A

      \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

   8. lower-sqrt.f64 N/A

      \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

   9. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

   10. lower-/.f64 75.3

       \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, -0.3333333333333333 \cdot \frac{a}{b}\right) \]

8. Applied rewrites 75.3%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, -0.3333333333333333 \cdot \frac{a}{b}\right)} \]

9. Taylor expanded in y around 0

   \[\leadsto \mathsf{fma}\left(\sqrt{x}, 2, \frac{-1}{3} \cdot \frac{a}{b}\right) \]
10. Step-by-step derivation

    1. lower-sqrt.f64 60.7

       \[\leadsto \mathsf{fma}\left(\sqrt{x}, 2, -0.3333333333333333 \cdot \frac{a}{b}\right) \]

11. Applied rewrites 60.7%

    \[\leadsto \mathsf{fma}\left(\sqrt{x}, 2, -0.3333333333333333 \cdot \frac{a}{b}\right) \]
12. Add Preprocessing

Alternative 9: 50.3% accurate, 9.4× speedup

Math

\[\begin{array}{l} \\ \frac{-0.3333333333333333 \cdot a}{b} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ (* -0.3333333333333333 a) b))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (-0.3333333333333333 * a) / b;
}

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, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((-0.3333333333333333d0) * a) / b
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (-0.3333333333333333 * a) / b;
}

Python

def code(x, y, z, t, a, b):
	return (-0.3333333333333333 * a) / b

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(-0.3333333333333333 * a) / b)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (-0.3333333333333333 * a) / b;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(-0.3333333333333333 * a), $MachinePrecision] / b), $MachinePrecision]

Derivation

1. Initial program 70.9%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
4. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \frac{-1}{3} \cdot \color{blue}{\frac{a}{b}} \]

   2. lower-/.f64 45.5

      \[\leadsto -0.3333333333333333 \cdot \frac{a}{\color{blue}{b}} \]

5. Applied rewrites 45.5%

   \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b}} \]
6. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \frac{-1}{3} \cdot \color{blue}{\frac{a}{b}} \]

   2. lift-/.f64 N/A

      \[\leadsto \frac{-1}{3} \cdot \frac{a}{\color{blue}{b}} \]

   3. associate-*r/ N/A

      \[\leadsto \frac{\frac{-1}{3} \cdot a}{\color{blue}{b}} \]

   4. lower-/.f64 N/A

      \[\leadsto \frac{\frac{-1}{3} \cdot a}{\color{blue}{b}} \]

   5. lower-*.f64 45.5

      \[\leadsto \frac{-0.3333333333333333 \cdot a}{b} \]

7. Applied rewrites 45.5%

   \[\leadsto \frac{-0.3333333333333333 \cdot a}{\color{blue}{b}} \]
8. Add Preprocessing

Alternative 10: 50.3% accurate, 9.4× speedup

Math

\[\begin{array}{l} \\ a \cdot \frac{-0.3333333333333333}{b} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (* a (/ -0.3333333333333333 b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return a * (-0.3333333333333333 / b);
}

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, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = a * ((-0.3333333333333333d0) / b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return a * (-0.3333333333333333 / b);
}

Python

def code(x, y, z, t, a, b):
	return a * (-0.3333333333333333 / b)

Julia

function code(x, y, z, t, a, b)
	return Float64(a * Float64(-0.3333333333333333 / b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = a * (-0.3333333333333333 / b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(a * N[(-0.3333333333333333 / b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.9%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
4. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \frac{-1}{3} \cdot \color{blue}{\frac{a}{b}} \]

   2. lower-/.f64 45.5

      \[\leadsto -0.3333333333333333 \cdot \frac{a}{\color{blue}{b}} \]

5. Applied rewrites 45.5%

   \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b}} \]
6. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \frac{-1}{3} \cdot \color{blue}{\frac{a}{b}} \]

   2. lift-/.f64 N/A

      \[\leadsto \frac{-1}{3} \cdot \frac{a}{\color{blue}{b}} \]

   3. associate-*r/ N/A

      \[\leadsto \frac{\frac{-1}{3} \cdot a}{\color{blue}{b}} \]

   4. lower-/.f64 N/A

      \[\leadsto \frac{\frac{-1}{3} \cdot a}{\color{blue}{b}} \]

   5. lower-*.f64 45.5

      \[\leadsto \frac{-0.3333333333333333 \cdot a}{b} \]

7. Applied rewrites 45.5%

   \[\leadsto \frac{-0.3333333333333333 \cdot a}{\color{blue}{b}} \]
8. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \frac{\frac{-1}{3} \cdot a}{\color{blue}{b}} \]

   2. lift-*.f64 N/A

      \[\leadsto \frac{\frac{-1}{3} \cdot a}{b} \]

   3. *-commutative N/A

      \[\leadsto \frac{a \cdot \frac{-1}{3}}{b} \]

   4. associate-/l* N/A

      \[\leadsto a \cdot \color{blue}{\frac{\frac{-1}{3}}{b}} \]

   5. lower-*.f64 N/A

      \[\leadsto a \cdot \color{blue}{\frac{\frac{-1}{3}}{b}} \]

   6. lower-/.f64 45.5

      \[\leadsto a \cdot \frac{-0.3333333333333333}{\color{blue}{b}} \]

9. Applied rewrites 45.5%

   \[\leadsto a \cdot \color{blue}{\frac{-0.3333333333333333}{b}} \]
10. Add Preprocessing

Alternative 11: 50.3% accurate, 9.4× speedup

Math

\[\begin{array}{l} \\ -0.3333333333333333 \cdot \frac{a}{b} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (* -0.3333333333333333 (/ a b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return -0.3333333333333333 * (a / b);
}

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, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (-0.3333333333333333d0) * (a / b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return -0.3333333333333333 * (a / b);
}

Python

def code(x, y, z, t, a, b):
	return -0.3333333333333333 * (a / b)

Julia

function code(x, y, z, t, a, b)
	return Float64(-0.3333333333333333 * Float64(a / b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = -0.3333333333333333 * (a / b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(-0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.9%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
4. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \frac{-1}{3} \cdot \color{blue}{\frac{a}{b}} \]

   2. lower-/.f64 45.5

      \[\leadsto -0.3333333333333333 \cdot \frac{a}{\color{blue}{b}} \]

5. Applied rewrites 45.5%

   \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b}} \]
6. Add Preprocessing

Developer Target 1: 74.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{0.3333333333333333}{z}}{t}\\ t_2 := \frac{\frac{a}{3}}{b}\\ t_3 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;z < -1.3793337487235141 \cdot 10^{+129}:\\ \;\;\;\;t\_3 \cdot \cos \left(\frac{1}{y} - t\_1\right) - t\_2\\ \mathbf{elif}\;z < 3.516290613555987 \cdot 10^{+106}:\\ \;\;\;\;\left(\sqrt{x} \cdot 2\right) \cdot \cos \left(y - \frac{t}{3} \cdot z\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;\cos \left(y - t\_1\right) \cdot t\_3 - \frac{\frac{a}{b}}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ 0.3333333333333333 z) t))
        (t_2 (/ (/ a 3.0) b))
        (t_3 (* 2.0 (sqrt x))))
   (if (< z -1.3793337487235141e+129)
     (- (* t_3 (cos (- (/ 1.0 y) t_1))) t_2)
     (if (< z 3.516290613555987e+106)
       (- (* (* (sqrt x) 2.0) (cos (- y (* (/ t 3.0) z)))) t_2)
       (- (* (cos (- y t_1)) t_3) (/ (/ a b) 3.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (0.3333333333333333 / z) / t;
	double t_2 = (a / 3.0) / b;
	double t_3 = 2.0 * sqrt(x);
	double tmp;
	if (z < -1.3793337487235141e+129) {
		tmp = (t_3 * cos(((1.0 / y) - t_1))) - t_2;
	} else if (z < 3.516290613555987e+106) {
		tmp = ((sqrt(x) * 2.0) * cos((y - ((t / 3.0) * z)))) - t_2;
	} else {
		tmp = (cos((y - t_1)) * t_3) - ((a / b) / 3.0);
	}
	return tmp;
}

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, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (0.3333333333333333d0 / z) / t
    t_2 = (a / 3.0d0) / b
    t_3 = 2.0d0 * sqrt(x)
    if (z < (-1.3793337487235141d+129)) then
        tmp = (t_3 * cos(((1.0d0 / y) - t_1))) - t_2
    else if (z < 3.516290613555987d+106) then
        tmp = ((sqrt(x) * 2.0d0) * cos((y - ((t / 3.0d0) * z)))) - t_2
    else
        tmp = (cos((y - t_1)) * t_3) - ((a / b) / 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (0.3333333333333333 / z) / t;
	double t_2 = (a / 3.0) / b;
	double t_3 = 2.0 * Math.sqrt(x);
	double tmp;
	if (z < -1.3793337487235141e+129) {
		tmp = (t_3 * Math.cos(((1.0 / y) - t_1))) - t_2;
	} else if (z < 3.516290613555987e+106) {
		tmp = ((Math.sqrt(x) * 2.0) * Math.cos((y - ((t / 3.0) * z)))) - t_2;
	} else {
		tmp = (Math.cos((y - t_1)) * t_3) - ((a / b) / 3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (0.3333333333333333 / z) / t
	t_2 = (a / 3.0) / b
	t_3 = 2.0 * math.sqrt(x)
	tmp = 0
	if z < -1.3793337487235141e+129:
		tmp = (t_3 * math.cos(((1.0 / y) - t_1))) - t_2
	elif z < 3.516290613555987e+106:
		tmp = ((math.sqrt(x) * 2.0) * math.cos((y - ((t / 3.0) * z)))) - t_2
	else:
		tmp = (math.cos((y - t_1)) * t_3) - ((a / b) / 3.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(0.3333333333333333 / z) / t)
	t_2 = Float64(Float64(a / 3.0) / b)
	t_3 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (z < -1.3793337487235141e+129)
		tmp = Float64(Float64(t_3 * cos(Float64(Float64(1.0 / y) - t_1))) - t_2);
	elseif (z < 3.516290613555987e+106)
		tmp = Float64(Float64(Float64(sqrt(x) * 2.0) * cos(Float64(y - Float64(Float64(t / 3.0) * z)))) - t_2);
	else
		tmp = Float64(Float64(cos(Float64(y - t_1)) * t_3) - Float64(Float64(a / b) / 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (0.3333333333333333 / z) / t;
	t_2 = (a / 3.0) / b;
	t_3 = 2.0 * sqrt(x);
	tmp = 0.0;
	if (z < -1.3793337487235141e+129)
		tmp = (t_3 * cos(((1.0 / y) - t_1))) - t_2;
	elseif (z < 3.516290613555987e+106)
		tmp = ((sqrt(x) * 2.0) * cos((y - ((t / 3.0) * z)))) - t_2;
	else
		tmp = (cos((y - t_1)) * t_3) - ((a / b) / 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(0.3333333333333333 / z), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.3793337487235141e+129], N[(N[(t$95$3 * N[Cos[N[(N[(1.0 / y), $MachinePrecision] - t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[z, 3.516290613555987e+106], N[(N[(N[(N[Sqrt[x], $MachinePrecision] * 2.0), $MachinePrecision] * N[Cos[N[(y - N[(N[(t / 3.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(N[Cos[N[(y - t$95$1), $MachinePrecision]], $MachinePrecision] * t$95$3), $MachinePrecision] - N[(N[(a / b), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]]]]]

Reproduce

herbie shell --seed 2025026 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -1379333748723514100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (* 2 (sqrt x)) (cos (- (/ 1 y) (/ (/ 3333333333333333/10000000000000000 z) t)))) (/ (/ a 3) b)) (if (< z 35162906135559870000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (* (sqrt x) 2) (cos (- y (* (/ t 3) z)))) (/ (/ a 3) b)) (- (* (cos (- y (/ (/ 3333333333333333/10000000000000000 z) t))) (* 2 (sqrt x))) (/ (/ a b) 3)))))

  (- (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0)))) (/ a (* b 3.0))))