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

Percentage Accurate: 69.8% → 77.4%

Time: 13.0s

Alternatives: 12

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: 69.8% 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: 77.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sin \left(\frac{t \cdot z}{3}\right)\\ t_2 := \frac{a}{b \cdot 3}\\ \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 2:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(t\_1, \sin y, \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), -1, t\_1 \cdot \left(-\sin \mathsf{PI}\left(\right)\right)\right) \cdot \left(-\cos y\right)\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot e^{\log x \cdot 0.5}\right) \cdot \sin \left(\left(-y\right) + \frac{\mathsf{PI}\left(\right)}{2}\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (sin (/ (* t z) 3.0))) (t_2 (/ a (* b 3.0))))
   (if (<= (cos (- y (/ (* z t) 3.0))) 2.0)
     (-
      (*
       (* 2.0 (sqrt x))
       (fma
        t_1
        (sin y)
        (*
         (fma (cos (/ (* t z) -3.0)) -1.0 (* t_1 (- (sin (PI)))))
         (- (cos y)))))
      t_2)
     (- (* (* 2.0 (exp (* (log x) 0.5))) (sin (+ (- y) (/ (PI) 2.0)))) t_2))))

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))) < 2

   1. Initial program 82.9%

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

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

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

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

      4. lower-sin.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-PI.f64 66.7

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

   4. Applied rewrites 66.7%

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

      1. lift-sin.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-PI.f64 N/A

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

      5. sin-+PI/2 N/A

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

      6. lift-neg.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. cos-neg-rev N/A

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

      12. cos-diff N/A

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

   6. Applied rewrites 83.8%

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

   8. Applied rewrites 84.6%

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

   if 2 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))

   1. Initial program 0.0%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   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 70.6%

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

      1. lift-sqrt.f64 N/A

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

      2. pow1/2 N/A

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

      3. pow-to-exp N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-log.f64 70.6

         \[\leadsto \left(2 \cdot e^{\color{blue}{\log x} \cdot 0.5}\right) \cdot \cos y - \frac{a}{b \cdot 3} \]

   7. Applied rewrites 70.6%

      \[\leadsto \left(2 \cdot \color{blue}{e^{\log x \cdot 0.5}}\right) \cdot \cos y - \frac{a}{b \cdot 3} \]
   8. Step-by-step derivation

      1. lift-cos.f64 N/A

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

      2. cos-neg-rev N/A

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

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

         \[\leadsto \left(2 \cdot e^{\log x \cdot \frac{1}{2}}\right) \cdot \color{blue}{\sin \left(\left(\mathsf{neg}\left(y\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]

      4. lower-sin.f64 N/A

         \[\leadsto \left(2 \cdot e^{\log x \cdot \frac{1}{2}}\right) \cdot \color{blue}{\sin \left(\left(\mathsf{neg}\left(y\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]

      5. lower-+.f64 N/A

         \[\leadsto \left(2 \cdot e^{\log x \cdot \frac{1}{2}}\right) \cdot \sin \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]

      6. lower-neg.f64 N/A

         \[\leadsto \left(2 \cdot e^{\log x \cdot \frac{1}{2}}\right) \cdot \sin \left(\color{blue}{\left(-y\right)} + \frac{\mathsf{PI}\left(\right)}{2}\right) - \frac{a}{b \cdot 3} \]

      7. lift-PI.f64 N/A

         \[\leadsto \left(2 \cdot e^{\log x \cdot \frac{1}{2}}\right) \cdot \sin \left(\left(-y\right) + \frac{\color{blue}{\mathsf{PI}\left(\right)}}{2}\right) - \frac{a}{b \cdot 3} \]

      8. lower-/.f64 72.0

         \[\leadsto \left(2 \cdot e^{\log x \cdot 0.5}\right) \cdot \sin \left(\left(-y\right) + \color{blue}{\frac{\mathsf{PI}\left(\right)}{2}}\right) - \frac{a}{b \cdot 3} \]

   9. Applied rewrites 72.0%

      \[\leadsto \left(2 \cdot e^{\log x \cdot 0.5}\right) \cdot \color{blue}{\sin \left(\left(-y\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 2:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\sin \left(\frac{t \cdot z}{3}\right), \sin y, \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), -1, \sin \left(\frac{t \cdot z}{3}\right) \cdot \left(-\sin \mathsf{PI}\left(\right)\right)\right) \cdot \left(-\cos y\right)\right) - \frac{a}{b \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot e^{\log x \cdot 0.5}\right) \cdot \sin \left(\left(-y\right) + \frac{\mathsf{PI}\left(\right)}{2}\right) - \frac{a}{b \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{b \cdot 3}\\ t_2 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t\_2 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - t\_1 \leq 4 \cdot 10^{+147}:\\ \;\;\;\;t\_2 \cdot \left(\cos y \cdot \cos \left(\frac{t \cdot z}{-3}\right) - \sin \left(-0.3333333333333333 \cdot \left(t \cdot z\right)\right) \cdot \sin y\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot e^{\log x \cdot 0.5}\right) \cdot \sin \left(\left(-y\right) + \frac{\mathsf{PI}\left(\right)}{2}\right) - t\_1\\ \end{array} \end{array} \]

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+147)
     (-
      (*
       t_2
       (-
        (* (cos y) (cos (/ (* t z) -3.0)))
        (* (sin (* -0.3333333333333333 (* t z))) (sin y))))
      t_1)
     (- (* (* 2.0 (exp (* (log x) 0.5))) (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)))) < 3.9999999999999999e147

   1. Initial program 80.0%

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

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

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

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

      4. lower-sin.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-PI.f64 61.1

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

   4. Applied rewrites 61.1%

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

      1. lift--.f64 N/A

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

      2. flip-- N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. pow2 N/A

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

      7. lower-pow.f64 N/A

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

      8. +-commutative N/A

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

      9. lift-/.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. associate-/l* N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-/.f64 38.7

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

   6. Applied rewrites 38.7%

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

   8. Applied rewrites 81.9%

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

   9. Taylor expanded in z around inf

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\frac{t \cdot z}{-3}\right) - \color{blue}{\sin \left(\mathsf{PI}\left(\right) + \frac{1}{3} \cdot \left(t \cdot z\right)\right)} \cdot \sin y\right) - \frac{a}{b \cdot 3} \]
   10. Step-by-step derivation

   11. Applied rewrites 81.9%

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\frac{t \cdot z}{-3}\right) - \color{blue}{\sin \left(-0.3333333333333333 \cdot \left(t \cdot z\right)\right)} \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

   if 3.9999999999999999e147 < (-.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 53.0%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   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 86.1%

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

      1. lift-sqrt.f64 N/A

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

      2. pow1/2 N/A

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

      3. pow-to-exp N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-log.f64 86.1

         \[\leadsto \left(2 \cdot e^{\color{blue}{\log x} \cdot 0.5}\right) \cdot \cos y - \frac{a}{b \cdot 3} \]

   7. Applied rewrites 86.1%

      \[\leadsto \left(2 \cdot \color{blue}{e^{\log x \cdot 0.5}}\right) \cdot \cos y - \frac{a}{b \cdot 3} \]
   8. Step-by-step derivation

      1. lift-cos.f64 N/A

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

      2. cos-neg-rev N/A

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

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

         \[\leadsto \left(2 \cdot e^{\log x \cdot \frac{1}{2}}\right) \cdot \color{blue}{\sin \left(\left(\mathsf{neg}\left(y\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]

      4. lower-sin.f64 N/A

         \[\leadsto \left(2 \cdot e^{\log x \cdot \frac{1}{2}}\right) \cdot \color{blue}{\sin \left(\left(\mathsf{neg}\left(y\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]

      5. lower-+.f64 N/A

         \[\leadsto \left(2 \cdot e^{\log x \cdot \frac{1}{2}}\right) \cdot \sin \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]

      6. lower-neg.f64 N/A

         \[\leadsto \left(2 \cdot e^{\log x \cdot \frac{1}{2}}\right) \cdot \sin \left(\color{blue}{\left(-y\right)} + \frac{\mathsf{PI}\left(\right)}{2}\right) - \frac{a}{b \cdot 3} \]

      7. lift-PI.f64 N/A

         \[\leadsto \left(2 \cdot e^{\log x \cdot \frac{1}{2}}\right) \cdot \sin \left(\left(-y\right) + \frac{\color{blue}{\mathsf{PI}\left(\right)}}{2}\right) - \frac{a}{b \cdot 3} \]

      8. lower-/.f64 86.7

         \[\leadsto \left(2 \cdot e^{\log x \cdot 0.5}\right) \cdot \sin \left(\left(-y\right) + \color{blue}{\frac{\mathsf{PI}\left(\right)}{2}}\right) - \frac{a}{b \cdot 3} \]

   9. Applied rewrites 86.7%

      \[\leadsto \left(2 \cdot e^{\log x \cdot 0.5}\right) \cdot \color{blue}{\sin \left(\left(-y\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 77.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{b \cdot 3}\\ t_2 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t\_2 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - t\_1 \leq 4 \cdot 10^{+147}:\\ \;\;\;\;t\_2 \cdot \mathsf{fma}\left(\sin \left(\left(t \cdot z\right) \cdot 0.3333333333333333\right), \sin y, \cos \left(\frac{t \cdot z}{3}\right) \cdot \cos y\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot e^{\log x \cdot 0.5}\right) \cdot \sin \left(\left(-y\right) + \frac{\mathsf{PI}\left(\right)}{2}\right) - t\_1\\ \end{array} \end{array} \]

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+147)
     (-
      (*
       t_2
       (fma
        (sin (* (* t z) 0.3333333333333333))
        (sin y)
        (* (cos (/ (* t z) 3.0)) (cos y))))
      t_1)
     (- (* (* 2.0 (exp (* (log x) 0.5))) (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)))) < 3.9999999999999999e147

   1. Initial program 80.0%

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

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-sin.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-cos.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

      18. lower-cos.f64 82.0

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

   4. Applied rewrites 82.0%

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

   5. Taylor expanded in z around 0

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\sin \color{blue}{\left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)}, \sin y, \cos \left(\frac{t \cdot z}{3}\right) \cdot \cos y\right) - \frac{a}{b \cdot 3} \]
   6. Step-by-step derivation

   7. Applied rewrites 81.9%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\sin \color{blue}{\left(\left(t \cdot z\right) \cdot 0.3333333333333333\right)}, \sin y, \cos \left(\frac{t \cdot z}{3}\right) \cdot \cos y\right) - \frac{a}{b \cdot 3} \]

   if 3.9999999999999999e147 < (-.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 53.0%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   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 86.1%

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

      1. lift-sqrt.f64 N/A

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

      2. pow1/2 N/A

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

      3. pow-to-exp N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-log.f64 86.1

         \[\leadsto \left(2 \cdot e^{\color{blue}{\log x} \cdot 0.5}\right) \cdot \cos y - \frac{a}{b \cdot 3} \]

   7. Applied rewrites 86.1%

      \[\leadsto \left(2 \cdot \color{blue}{e^{\log x \cdot 0.5}}\right) \cdot \cos y - \frac{a}{b \cdot 3} \]
   8. Step-by-step derivation

      1. lift-cos.f64 N/A

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

      2. cos-neg-rev N/A

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

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

         \[\leadsto \left(2 \cdot e^{\log x \cdot \frac{1}{2}}\right) \cdot \color{blue}{\sin \left(\left(\mathsf{neg}\left(y\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]

      4. lower-sin.f64 N/A

         \[\leadsto \left(2 \cdot e^{\log x \cdot \frac{1}{2}}\right) \cdot \color{blue}{\sin \left(\left(\mathsf{neg}\left(y\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]

      5. lower-+.f64 N/A

         \[\leadsto \left(2 \cdot e^{\log x \cdot \frac{1}{2}}\right) \cdot \sin \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]

      6. lower-neg.f64 N/A

         \[\leadsto \left(2 \cdot e^{\log x \cdot \frac{1}{2}}\right) \cdot \sin \left(\color{blue}{\left(-y\right)} + \frac{\mathsf{PI}\left(\right)}{2}\right) - \frac{a}{b \cdot 3} \]

      7. lift-PI.f64 N/A

         \[\leadsto \left(2 \cdot e^{\log x \cdot \frac{1}{2}}\right) \cdot \sin \left(\left(-y\right) + \frac{\color{blue}{\mathsf{PI}\left(\right)}}{2}\right) - \frac{a}{b \cdot 3} \]

      8. lower-/.f64 86.7

         \[\leadsto \left(2 \cdot e^{\log x \cdot 0.5}\right) \cdot \sin \left(\left(-y\right) + \color{blue}{\frac{\mathsf{PI}\left(\right)}{2}}\right) - \frac{a}{b \cdot 3} \]

   9. Applied rewrites 86.7%

      \[\leadsto \left(2 \cdot e^{\log x \cdot 0.5}\right) \cdot \color{blue}{\sin \left(\left(-y\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 77.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot z}{3}\\ t_2 := \frac{a}{b \cdot 3}\\ \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 2:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\sin t\_1, \sin y, \cos t\_1 \cdot \cos y\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot e^{\log x \cdot 0.5}\right) \cdot \sin \left(\left(-y\right) + \frac{\mathsf{PI}\left(\right)}{2}\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* t z) 3.0)) (t_2 (/ a (* b 3.0))))
   (if (<= (cos (- y (/ (* z t) 3.0))) 2.0)
     (- (* (* 2.0 (sqrt x)) (fma (sin t_1) (sin y) (* (cos t_1) (cos y)))) t_2)
     (- (* (* 2.0 (exp (* (log x) 0.5))) (sin (+ (- y) (/ (PI) 2.0)))) t_2))))

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))) < 2

   1. Initial program 82.9%

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

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-sin.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-cos.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

      18. lower-cos.f64 84.6

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

   4. Applied rewrites 84.6%

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

   if 2 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))

   1. Initial program 0.0%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   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 70.6%

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

      1. lift-sqrt.f64 N/A

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

      2. pow1/2 N/A

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

      3. pow-to-exp N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-log.f64 70.6

         \[\leadsto \left(2 \cdot e^{\color{blue}{\log x} \cdot 0.5}\right) \cdot \cos y - \frac{a}{b \cdot 3} \]

   7. Applied rewrites 70.6%

      \[\leadsto \left(2 \cdot \color{blue}{e^{\log x \cdot 0.5}}\right) \cdot \cos y - \frac{a}{b \cdot 3} \]
   8. Step-by-step derivation

      1. lift-cos.f64 N/A

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

      2. cos-neg-rev N/A

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

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

         \[\leadsto \left(2 \cdot e^{\log x \cdot \frac{1}{2}}\right) \cdot \color{blue}{\sin \left(\left(\mathsf{neg}\left(y\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]

      4. lower-sin.f64 N/A

         \[\leadsto \left(2 \cdot e^{\log x \cdot \frac{1}{2}}\right) \cdot \color{blue}{\sin \left(\left(\mathsf{neg}\left(y\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]

      5. lower-+.f64 N/A

         \[\leadsto \left(2 \cdot e^{\log x \cdot \frac{1}{2}}\right) \cdot \sin \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]

      6. lower-neg.f64 N/A

         \[\leadsto \left(2 \cdot e^{\log x \cdot \frac{1}{2}}\right) \cdot \sin \left(\color{blue}{\left(-y\right)} + \frac{\mathsf{PI}\left(\right)}{2}\right) - \frac{a}{b \cdot 3} \]

      7. lift-PI.f64 N/A

         \[\leadsto \left(2 \cdot e^{\log x \cdot \frac{1}{2}}\right) \cdot \sin \left(\left(-y\right) + \frac{\color{blue}{\mathsf{PI}\left(\right)}}{2}\right) - \frac{a}{b \cdot 3} \]

      8. lower-/.f64 72.0

         \[\leadsto \left(2 \cdot e^{\log x \cdot 0.5}\right) \cdot \sin \left(\left(-y\right) + \color{blue}{\frac{\mathsf{PI}\left(\right)}{2}}\right) - \frac{a}{b \cdot 3} \]

   9. Applied rewrites 72.0%

      \[\leadsto \left(2 \cdot e^{\log x \cdot 0.5}\right) \cdot \color{blue}{\sin \left(\left(-y\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 77.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot z}{3}\\ t_2 := \frac{a}{b \cdot 3}\\ \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 2:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos t\_1, \cos y, \sin t\_1 \cdot \sin y\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot e^{\log x \cdot 0.5}\right) \cdot \sin \left(\left(-y\right) + \frac{\mathsf{PI}\left(\right)}{2}\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* t z) 3.0)) (t_2 (/ a (* b 3.0))))
   (if (<= (cos (- y (/ (* z t) 3.0))) 2.0)
     (- (* (* 2.0 (sqrt x)) (fma (cos t_1) (cos y) (* (sin t_1) (sin y)))) t_2)
     (- (* (* 2.0 (exp (* (log x) 0.5))) (sin (+ (- y) (/ (PI) 2.0)))) t_2))))

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))) < 2

   1. Initial program 82.9%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing
   3. 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 84.6

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

   4. Applied rewrites 84.6%

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

   if 2 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))

   1. Initial program 0.0%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   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 70.6%

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

      1. lift-sqrt.f64 N/A

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

      2. pow1/2 N/A

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

      3. pow-to-exp N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-log.f64 70.6

         \[\leadsto \left(2 \cdot e^{\color{blue}{\log x} \cdot 0.5}\right) \cdot \cos y - \frac{a}{b \cdot 3} \]

   7. Applied rewrites 70.6%

      \[\leadsto \left(2 \cdot \color{blue}{e^{\log x \cdot 0.5}}\right) \cdot \cos y - \frac{a}{b \cdot 3} \]
   8. Step-by-step derivation

      1. lift-cos.f64 N/A

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

      2. cos-neg-rev N/A

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

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

         \[\leadsto \left(2 \cdot e^{\log x \cdot \frac{1}{2}}\right) \cdot \color{blue}{\sin \left(\left(\mathsf{neg}\left(y\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]

      4. lower-sin.f64 N/A

         \[\leadsto \left(2 \cdot e^{\log x \cdot \frac{1}{2}}\right) \cdot \color{blue}{\sin \left(\left(\mathsf{neg}\left(y\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]

      5. lower-+.f64 N/A

         \[\leadsto \left(2 \cdot e^{\log x \cdot \frac{1}{2}}\right) \cdot \sin \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]

      6. lower-neg.f64 N/A

         \[\leadsto \left(2 \cdot e^{\log x \cdot \frac{1}{2}}\right) \cdot \sin \left(\color{blue}{\left(-y\right)} + \frac{\mathsf{PI}\left(\right)}{2}\right) - \frac{a}{b \cdot 3} \]

      7. lift-PI.f64 N/A

         \[\leadsto \left(2 \cdot e^{\log x \cdot \frac{1}{2}}\right) \cdot \sin \left(\left(-y\right) + \frac{\color{blue}{\mathsf{PI}\left(\right)}}{2}\right) - \frac{a}{b \cdot 3} \]

      8. lower-/.f64 72.0

         \[\leadsto \left(2 \cdot e^{\log x \cdot 0.5}\right) \cdot \sin \left(\left(-y\right) + \color{blue}{\frac{\mathsf{PI}\left(\right)}{2}}\right) - \frac{a}{b \cdot 3} \]

   9. Applied rewrites 72.0%

      \[\leadsto \left(2 \cdot e^{\log x \cdot 0.5}\right) \cdot \color{blue}{\sin \left(\left(-y\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - \frac{a}{b \cdot 3} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 67.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{b \cdot 3}\\ \mathbf{if}\;t\_1 \leq -0.2 \lor \neg \left(t\_1 \leq 2 \cdot 10^{-104}\right):\\ \;\;\;\;\frac{-0.3333333333333333 \cdot a}{b}\\ \mathbf{else}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(-0.3333333333333333, t \cdot z, y\right)\right) \cdot \left(\sqrt{x} \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* b 3.0))))
   (if (or (<= t_1 -0.2) (not (<= t_1 2e-104)))
     (/ (* -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 <= -0.2) || !(t_1 <= 2e-104)) {
		tmp = (-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 <= -0.2) || !(t_1 <= 2e-104))
		tmp = Float64(Float64(-0.3333333333333333 * 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, -0.2], N[Not[LessEqual[t$95$1, 2e-104]], $MachinePrecision]], N[(N[(-0.3333333333333333 * a), $MachinePrecision] / b), $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))) < -0.20000000000000001 or 1.99999999999999985e-104 < (/.f64 a (*.f64 b #s(literal 3 binary64)))

   1. Initial program 79.3%

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

   5. Applied rewrites 86.6%

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

   7. Applied rewrites 86.7%

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

   if -0.20000000000000001 < (/.f64 a (*.f64 b #s(literal 3 binary64))) < 1.99999999999999985e-104

   1. Initial program 66.0%

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

   3. Taylor expanded in 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

   5. Applied rewrites 62.2%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{b \cdot 3} \leq -0.2 \lor \neg \left(\frac{a}{b \cdot 3} \leq 2 \cdot 10^{-104}\right):\\ \;\;\;\;\frac{-0.3333333333333333 \cdot a}{b}\\ \mathbf{else}:\\ \;\;\;\;\cos \left(\mathsf{fma}\left(-0.3333333333333333, t \cdot z, y\right)\right) \cdot \left(\sqrt{x} \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.5% accurate, 1.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * sqrt(x)) * cos(y)) - ((a / 3.0) / 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 = ((2.0d0 * sqrt(x)) * cos(y)) - ((a / 3.0d0) / b)
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 / 3.0) / b);
}

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * cos(y)) - ((a / 3.0) / b);
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[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 73.5%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
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 81.1%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. associate-/r* N/A

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

   5. lower-/.f64 N/A

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

   6. lower-/.f64 81.2

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

7. Applied rewrites 81.2%

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

Alternative 8: 76.4% 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 73.5%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
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 81.1%

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

Alternative 9: 76.3% 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 73.5%

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

3. Taylor expanded in 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

5. Applied rewrites 81.1%

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

Alternative 10: 50.6% 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 73.5%

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

3. Taylor expanded in a around inf

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

5. Applied rewrites 51.4%

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

7. Applied rewrites 51.5%

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

Alternative 11: 50.6% accurate, 9.4× speedup

Math

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

FPCore

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

C

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

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) / b) * a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.5%

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

3. Taylor expanded in a around inf

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

5. Applied rewrites 68.7%

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

6. Taylor expanded in a around inf

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

8. Applied rewrites 51.4%

   \[\leadsto \frac{-0.3333333333333333}{b} \cdot a \]
9. Add Preprocessing

Alternative 12: 50.5% 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 73.5%

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

3. Taylor expanded in a around inf

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

5. Applied rewrites 51.4%

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

Developer Target 1: 73.8% 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 2025021 
(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))))