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

Percentage Accurate: 70.7% → 77.1%

Time: 13.0s

Alternatives: 8

Speedup: N/A×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 70.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 77.1% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right)\\ t_2 := \left(t \cdot z\right) \cdot -0.3333333333333333\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+37}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-0.3333333333333333, a, 2 \cdot \left(\left(b \cdot \left(\cos y \cdot \sin \left(\mathsf{fma}\left(-0.3333333333333333, t \cdot z, \frac{\pi}{2}\right)\right) - \sin y \cdot \sin \left(-0.3333333333333333 \cdot \left(t \cdot z\right)\right)\right)\right) \cdot {x}^{0.5}\right)\right)}{b}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+150}:\\ \;\;\;\;\mathsf{fma}\left(2 \cdot {\left({x}^{-1}\right)}^{0.5}, \cos t\_2 \cdot \cos y - \sin t\_2 \cdot \sin y, \frac{\frac{a}{b}}{x} \cdot -0.3333333333333333\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0)))))
        (t_2 (* (* t z) -0.3333333333333333)))
   (if (<= t_1 2e+37)
     (/
      (fma
       -0.3333333333333333
       a
       (*
        2.0
        (*
         (*
          b
          (-
           (* (cos y) (sin (fma -0.3333333333333333 (* t z) (/ PI 2.0))))
           (* (sin y) (sin (* -0.3333333333333333 (* t z))))))
         (pow x 0.5))))
      b)
     (if (<= t_1 4e+150)
       (*
        (fma
         (* 2.0 (pow (pow x -1.0) 0.5))
         (- (* (cos t_2) (cos y)) (* (sin t_2) (sin y)))
         (* (/ (/ a b) x) -0.3333333333333333))
        x)
       (* -0.3333333333333333 (/ a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (2.0 * sqrt(x)) * cos((y - ((z * t) / 3.0)));
	double t_2 = (t * z) * -0.3333333333333333;
	double tmp;
	if (t_1 <= 2e+37) {
		tmp = fma(-0.3333333333333333, a, (2.0 * ((b * ((cos(y) * sin(fma(-0.3333333333333333, (t * z), (((double) M_PI) / 2.0)))) - (sin(y) * sin((-0.3333333333333333 * (t * z)))))) * pow(x, 0.5)))) / b;
	} else if (t_1 <= 4e+150) {
		tmp = fma((2.0 * pow(pow(x, -1.0), 0.5)), ((cos(t_2) * cos(y)) - (sin(t_2) * sin(y))), (((a / b) / x) * -0.3333333333333333)) * x;
	} else {
		tmp = -0.3333333333333333 * (a / b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(2.0 * sqrt(x)) * cos(Float64(y - Float64(Float64(z * t) / 3.0))))
	t_2 = Float64(Float64(t * z) * -0.3333333333333333)
	tmp = 0.0
	if (t_1 <= 2e+37)
		tmp = Float64(fma(-0.3333333333333333, a, Float64(2.0 * Float64(Float64(b * Float64(Float64(cos(y) * sin(fma(-0.3333333333333333, Float64(t * z), Float64(pi / 2.0)))) - Float64(sin(y) * sin(Float64(-0.3333333333333333 * Float64(t * z)))))) * (x ^ 0.5)))) / b);
	elseif (t_1 <= 4e+150)
		tmp = Float64(fma(Float64(2.0 * ((x ^ -1.0) ^ 0.5)), Float64(Float64(cos(t_2) * cos(y)) - Float64(sin(t_2) * sin(y))), Float64(Float64(Float64(a / b) / x) * -0.3333333333333333)) * x);
	else
		tmp = Float64(-0.3333333333333333 * Float64(a / b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+37], N[(N[(-0.3333333333333333 * a + N[(2.0 * N[(N[(b * N[(N[(N[Cos[y], $MachinePrecision] * N[Sin[N[(-0.3333333333333333 * N[(t * z), $MachinePrecision] + N[(Pi / 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * N[Sin[N[(-0.3333333333333333 * N[(t * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Power[x, 0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$1, 4e+150], N[(N[(N[(2.0 * N[Power[N[Power[x, -1.0], $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision] * N[(N[(N[Cos[t$95$2], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[t$95$2], $MachinePrecision] * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(a / b), $MachinePrecision] / x), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(-0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) < 1.99999999999999991e37

   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. 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 83.0%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   8. Applied rewrites 74.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2 \cdot {\left({x}^{-1}\right)}^{0.5}, \cos \left(\mathsf{fma}\left(t \cdot z, -0.3333333333333333, y\right)\right), \frac{\frac{a}{b}}{x} \cdot -0.3333333333333333\right) \cdot x} \]

   9. Taylor expanded in b around 0

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

       1. lower-/.f64 N/A

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

   11. Applied rewrites 82.0%

       \[\leadsto \frac{\mathsf{fma}\left(-0.3333333333333333, a, 2 \cdot \left(\left(b \cdot \cos \left(y + -0.3333333333333333 \cdot \left(t \cdot z\right)\right)\right) \cdot {x}^{0.5}\right)\right)}{\color{blue}{b}} \]
   12. Step-by-step derivation

       1. lift-cos.f64 N/A

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

       2. lift-+.f64 N/A

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

       3. lift-*.f64 N/A

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

       4. lift-*.f64 N/A

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

       5. cos-sum N/A

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

       6. lower--.f64 N/A

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

       7. lower-*.f64 N/A

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

       8. lift-cos.f64 N/A

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

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

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

       10. lower-sin.f64 N/A

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

       11. lift-/.f64 N/A

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

       12. lift-PI.f64 N/A

           \[\leadsto \frac{\mathsf{fma}\left(\frac{-1}{3}, a, 2 \cdot \left(\left(b \cdot \left(\cos y \cdot \sin \left(\frac{-1}{3} \cdot \left(t \cdot z\right) + \frac{\pi}{2}\right) - \sin y \cdot \sin \left(\frac{-1}{3} \cdot \left(t \cdot z\right)\right)\right)\right) \cdot {x}^{\frac{1}{2}}\right)\right)}{b} \]

       13. lower-fma.f64 N/A

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

       14. lift-*.f64 N/A

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

       15. lower-*.f64 N/A

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

       16. lift-sin.f64 N/A

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

       17. lower-sin.f64 N/A

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

       18. lift-*.f64 N/A

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

       19. lift-*.f64 83.3

           \[\leadsto \frac{\mathsf{fma}\left(-0.3333333333333333, a, 2 \cdot \left(\left(b \cdot \left(\cos y \cdot \sin \left(\mathsf{fma}\left(-0.3333333333333333, t \cdot z, \frac{\pi}{2}\right)\right) - \sin y \cdot \sin \left(-0.3333333333333333 \cdot \left(t \cdot z\right)\right)\right)\right) \cdot {x}^{0.5}\right)\right)}{b} \]

   13. Applied rewrites 83.3%

       \[\leadsto \frac{\mathsf{fma}\left(-0.3333333333333333, a, 2 \cdot \left(\left(b \cdot \left(\cos y \cdot \sin \left(\mathsf{fma}\left(-0.3333333333333333, t \cdot z, \frac{\pi}{2}\right)\right) - \sin y \cdot \sin \left(-0.3333333333333333 \cdot \left(t \cdot z\right)\right)\right)\right) \cdot {x}^{0.5}\right)\right)}{b} \]

   if 1.99999999999999991e37 < (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) < 3.99999999999999992e150

   1. Initial program 73.2%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 73.4%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   8. Applied rewrites 73.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2 \cdot {\left({x}^{-1}\right)}^{0.5}, \cos \left(\mathsf{fma}\left(t \cdot z, -0.3333333333333333, y\right)\right), \frac{\frac{a}{b}}{x} \cdot -0.3333333333333333\right) \cdot x} \]
   9. Step-by-step derivation

      1. lift-cos.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. cos-sum N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-cos.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lift-sin.f64 N/A

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

      15. lift-sin.f64 75.0

          \[\leadsto \mathsf{fma}\left(2 \cdot {\left({x}^{-1}\right)}^{0.5}, \cos \left(\left(t \cdot z\right) \cdot -0.3333333333333333\right) \cdot \cos y - \sin \left(\left(t \cdot z\right) \cdot -0.3333333333333333\right) \cdot \sin y, \frac{\frac{a}{b}}{x} \cdot -0.3333333333333333\right) \cdot x \]

   10. Applied rewrites 75.0%

       \[\leadsto \mathsf{fma}\left(2 \cdot {\left({x}^{-1}\right)}^{0.5}, \cos \left(\left(t \cdot z\right) \cdot -0.3333333333333333\right) \cdot \cos y - \sin \left(\left(t \cdot z\right) \cdot -0.3333333333333333\right) \cdot \sin y, \frac{\frac{a}{b}}{x} \cdot -0.3333333333333333\right) \cdot x \]

   if 3.99999999999999992e150 < (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (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 a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 57.0

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

   5. Applied rewrites 57.0%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 77.1% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right)\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+35}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-0.3333333333333333, a, 2 \cdot \left(\left(b \cdot \left(\cos y \cdot \sin \left(\mathsf{fma}\left(-0.3333333333333333, t \cdot z, \frac{\pi}{2}\right)\right) - \sin y \cdot \sin \left(-0.3333333333333333 \cdot \left(t \cdot z\right)\right)\right)\right) \cdot {x}^{0.5}\right)\right)}{b}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+142}:\\ \;\;\;\;\mathsf{fma}\left(2 \cdot \frac{1}{{x}^{0.5}}, \cos \left(\mathsf{fma}\left(t \cdot z, -0.3333333333333333, y\right)\right), \frac{\frac{a}{b}}{x} \cdot -0.3333333333333333\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))))
   (if (<= t_1 5e+35)
     (/
      (fma
       -0.3333333333333333
       a
       (*
        2.0
        (*
         (*
          b
          (-
           (* (cos y) (sin (fma -0.3333333333333333 (* t z) (/ PI 2.0))))
           (* (sin y) (sin (* -0.3333333333333333 (* t z))))))
         (pow x 0.5))))
      b)
     (if (<= t_1 5e+142)
       (*
        (fma
         (* 2.0 (/ 1.0 (pow x 0.5)))
         (cos (fma (* t z) -0.3333333333333333 y))
         (* (/ (/ a b) x) -0.3333333333333333))
        x)
       (* -0.3333333333333333 (/ a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (2.0 * sqrt(x)) * cos((y - ((z * t) / 3.0)));
	double tmp;
	if (t_1 <= 5e+35) {
		tmp = fma(-0.3333333333333333, a, (2.0 * ((b * ((cos(y) * sin(fma(-0.3333333333333333, (t * z), (((double) M_PI) / 2.0)))) - (sin(y) * sin((-0.3333333333333333 * (t * z)))))) * pow(x, 0.5)))) / b;
	} else if (t_1 <= 5e+142) {
		tmp = fma((2.0 * (1.0 / pow(x, 0.5))), cos(fma((t * z), -0.3333333333333333, y)), (((a / b) / x) * -0.3333333333333333)) * x;
	} else {
		tmp = -0.3333333333333333 * (a / b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(2.0 * sqrt(x)) * cos(Float64(y - Float64(Float64(z * t) / 3.0))))
	tmp = 0.0
	if (t_1 <= 5e+35)
		tmp = Float64(fma(-0.3333333333333333, a, Float64(2.0 * Float64(Float64(b * Float64(Float64(cos(y) * sin(fma(-0.3333333333333333, Float64(t * z), Float64(pi / 2.0)))) - Float64(sin(y) * sin(Float64(-0.3333333333333333 * Float64(t * z)))))) * (x ^ 0.5)))) / b);
	elseif (t_1 <= 5e+142)
		tmp = Float64(fma(Float64(2.0 * Float64(1.0 / (x ^ 0.5))), cos(fma(Float64(t * z), -0.3333333333333333, y)), Float64(Float64(Float64(a / b) / x) * -0.3333333333333333)) * x);
	else
		tmp = Float64(-0.3333333333333333 * Float64(a / b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+35], N[(N[(-0.3333333333333333 * a + N[(2.0 * N[(N[(b * N[(N[(N[Cos[y], $MachinePrecision] * N[Sin[N[(-0.3333333333333333 * N[(t * z), $MachinePrecision] + N[(Pi / 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * N[Sin[N[(-0.3333333333333333 * N[(t * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Power[x, 0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$1, 5e+142], N[(N[(N[(2.0 * N[(1.0 / N[Power[x, 0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(t * z), $MachinePrecision] * -0.3333333333333333 + y), $MachinePrecision]], $MachinePrecision] + N[(N[(N[(a / b), $MachinePrecision] / x), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(-0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) < 5.00000000000000021e35

   1. Initial program 83.3%

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

   3. Taylor expanded in 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 83.4%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   8. Applied rewrites 74.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2 \cdot {\left({x}^{-1}\right)}^{0.5}, \cos \left(\mathsf{fma}\left(t \cdot z, -0.3333333333333333, y\right)\right), \frac{\frac{a}{b}}{x} \cdot -0.3333333333333333\right) \cdot x} \]

   9. Taylor expanded in b around 0

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

       1. lower-/.f64 N/A

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

   11. Applied rewrites 82.4%

       \[\leadsto \frac{\mathsf{fma}\left(-0.3333333333333333, a, 2 \cdot \left(\left(b \cdot \cos \left(y + -0.3333333333333333 \cdot \left(t \cdot z\right)\right)\right) \cdot {x}^{0.5}\right)\right)}{\color{blue}{b}} \]
   12. Step-by-step derivation

       1. lift-cos.f64 N/A

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

       2. lift-+.f64 N/A

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

       3. lift-*.f64 N/A

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

       4. lift-*.f64 N/A

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

       5. cos-sum N/A

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

       6. lower--.f64 N/A

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

       7. lower-*.f64 N/A

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

       8. lift-cos.f64 N/A

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

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

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

       10. lower-sin.f64 N/A

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

       11. lift-/.f64 N/A

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

       12. lift-PI.f64 N/A

           \[\leadsto \frac{\mathsf{fma}\left(\frac{-1}{3}, a, 2 \cdot \left(\left(b \cdot \left(\cos y \cdot \sin \left(\frac{-1}{3} \cdot \left(t \cdot z\right) + \frac{\pi}{2}\right) - \sin y \cdot \sin \left(\frac{-1}{3} \cdot \left(t \cdot z\right)\right)\right)\right) \cdot {x}^{\frac{1}{2}}\right)\right)}{b} \]

       13. lower-fma.f64 N/A

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

       14. lift-*.f64 N/A

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

       15. lower-*.f64 N/A

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

       16. lift-sin.f64 N/A

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

       17. lower-sin.f64 N/A

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

       18. lift-*.f64 N/A

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

       19. lift-*.f64 83.7

           \[\leadsto \frac{\mathsf{fma}\left(-0.3333333333333333, a, 2 \cdot \left(\left(b \cdot \left(\cos y \cdot \sin \left(\mathsf{fma}\left(-0.3333333333333333, t \cdot z, \frac{\pi}{2}\right)\right) - \sin y \cdot \sin \left(-0.3333333333333333 \cdot \left(t \cdot z\right)\right)\right)\right) \cdot {x}^{0.5}\right)\right)}{b} \]

   13. Applied rewrites 83.7%

       \[\leadsto \frac{\mathsf{fma}\left(-0.3333333333333333, a, 2 \cdot \left(\left(b \cdot \left(\cos y \cdot \sin \left(\mathsf{fma}\left(-0.3333333333333333, t \cdot z, \frac{\pi}{2}\right)\right) - \sin y \cdot \sin \left(-0.3333333333333333 \cdot \left(t \cdot z\right)\right)\right)\right) \cdot {x}^{0.5}\right)\right)}{b} \]

   if 5.00000000000000021e35 < (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) < 5.0000000000000001e142

   1. Initial program 76.0%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   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 75.8%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   8. Applied rewrites 76.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2 \cdot {\left({x}^{-1}\right)}^{0.5}, \cos \left(\mathsf{fma}\left(t \cdot z, -0.3333333333333333, y\right)\right), \frac{\frac{a}{b}}{x} \cdot -0.3333333333333333\right) \cdot x} \]
   9. Step-by-step derivation

      1. lift-pow.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. pow1/2 N/A

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

      4. inv-pow N/A

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

      5. sqrt-div N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. pow1/2 N/A

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

      9. lower-pow.f64 76.3

         \[\leadsto \mathsf{fma}\left(2 \cdot \frac{1}{{x}^{0.5}}, \cos \left(\mathsf{fma}\left(t \cdot z, -0.3333333333333333, y\right)\right), \frac{\frac{a}{b}}{x} \cdot -0.3333333333333333\right) \cdot x \]

   10. Applied rewrites 76.3%

       \[\leadsto \mathsf{fma}\left(2 \cdot \frac{1}{{x}^{0.5}}, \cos \left(\mathsf{fma}\left(t \cdot z, -0.3333333333333333, y\right)\right), \frac{\frac{a}{b}}{x} \cdot -0.3333333333333333\right) \cdot x \]

   if 5.0000000000000001e142 < (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))))

   1. Initial program 0.1%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 53.2

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

   5. Applied rewrites 53.2%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 77.1% accurate, N/A× speedup

Math

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

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(Float64(a / 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[(N[(a / b), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 68.3%

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

3. Taylor expanded in 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 77.0%

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

   1. lift-*.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. associate-/r* N/A

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

   4. lower-/.f64 N/A

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

   5. lift-/.f64 77.1

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

7. Applied rewrites 77.1%

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

Alternative 4: 76.0% accurate, N/A× 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 68.3%

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

3. Taylor expanded in 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 77.0%

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

Alternative 5: 75.2% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{b \cdot 3}\\ \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.9999999999998:\\ \;\;\;\;\left(2 \cdot e^{\log x \cdot 0.5}\right) \cdot \left(\cos y \cdot \cos \left(z \cdot \frac{t}{3}\right) + \sin y \cdot \sin \left(\frac{t \cdot z}{3}\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \sin \left(\pi \cdot 0.5\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* b 3.0))))
   (if (<= (cos (- y (/ (* z t) 3.0))) 0.9999999999998)
     (-
      (*
       (* 2.0 (exp (* (log x) 0.5)))
       (+ (* (cos y) (cos (* z (/ t 3.0)))) (* (sin y) (sin (/ (* t z) 3.0)))))
      t_1)
     (- (* (* 2.0 (sqrt x)) (sin (* PI 0.5))) t_1))))

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 (cos((y - ((z * t) / 3.0))) <= 0.9999999999998) {
		tmp = ((2.0 * exp((log(x) * 0.5))) * ((cos(y) * cos((z * (t / 3.0)))) + (sin(y) * sin(((t * z) / 3.0))))) - t_1;
	} else {
		tmp = ((2.0 * sqrt(x)) * sin((((double) M_PI) * 0.5))) - t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (b * 3.0);
	double tmp;
	if (Math.cos((y - ((z * t) / 3.0))) <= 0.9999999999998) {
		tmp = ((2.0 * Math.exp((Math.log(x) * 0.5))) * ((Math.cos(y) * Math.cos((z * (t / 3.0)))) + (Math.sin(y) * Math.sin(((t * z) / 3.0))))) - t_1;
	} else {
		tmp = ((2.0 * Math.sqrt(x)) * Math.sin((Math.PI * 0.5))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / (b * 3.0)
	tmp = 0
	if math.cos((y - ((z * t) / 3.0))) <= 0.9999999999998:
		tmp = ((2.0 * math.exp((math.log(x) * 0.5))) * ((math.cos(y) * math.cos((z * (t / 3.0)))) + (math.sin(y) * math.sin(((t * z) / 3.0))))) - t_1
	else:
		tmp = ((2.0 * math.sqrt(x)) * math.sin((math.pi * 0.5))) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(b * 3.0))
	tmp = 0.0
	if (cos(Float64(y - Float64(Float64(z * t) / 3.0))) <= 0.9999999999998)
		tmp = Float64(Float64(Float64(2.0 * exp(Float64(log(x) * 0.5))) * Float64(Float64(cos(y) * cos(Float64(z * Float64(t / 3.0)))) + Float64(sin(y) * sin(Float64(Float64(t * z) / 3.0))))) - t_1);
	else
		tmp = Float64(Float64(Float64(2.0 * sqrt(x)) * sin(Float64(pi * 0.5))) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (b * 3.0);
	tmp = 0.0;
	if (cos((y - ((z * t) / 3.0))) <= 0.9999999999998)
		tmp = ((2.0 * exp((log(x) * 0.5))) * ((cos(y) * cos((z * (t / 3.0)))) + (sin(y) * sin(((t * z) / 3.0))))) - t_1;
	else
		tmp = ((2.0 * sqrt(x)) * sin((pi * 0.5))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 0.9999999999998], N[(N[(N[(2.0 * N[Exp[N[(N[Log[x], $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(N[Cos[y], $MachinePrecision] * N[Cos[N[(z * N[(t / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * N[Sin[N[(N[(t * z), $MachinePrecision] / 3.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Sin[N[(Pi * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))) < 0.999999999999800049

   1. Initial program 72.1%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing
   3. 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. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. 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. lower-+.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-cos.f64 N/A

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

      9. lower-cos.f64 N/A

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

      10. associate-/l* N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-sin.f64 N/A

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

      15. lower-sin.f64 N/A

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

      16. associate-/l* N/A

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

      17. lower-*.f64 N/A

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

      18. lower-/.f64 73.2

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

   4. Applied rewrites 73.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 73.6

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

   6. Applied rewrites 73.6%

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

      1. lift-sqrt.f64 N/A

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

      2. pow1/2 N/A

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

      3. pow-to-exp N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-log.f64 72.0

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

   8. Applied rewrites 72.0%

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

   if 0.999999999999800049 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))

   1. Initial program 62.1%

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

   3. Taylor expanded in y around 0

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

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

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \left(\left(\mathsf{neg}\left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right) - \frac{a}{b \cdot 3} \]

      2. lower-sin.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \left(\left(\mathsf{neg}\left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right) - \frac{a}{b \cdot 3} \]

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

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \left(\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot \left(t \cdot z\right) + \frac{\mathsf{PI}\left(\right)}{2}\right) - \frac{a}{b \cdot 3} \]

      4. metadata-eval N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \left(\frac{-1}{3} \cdot \left(t \cdot z\right) + \frac{\mathsf{PI}\left(\right)}{2}\right) - \frac{a}{b \cdot 3} \]

      5. associate-*r* N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \left(\left(\frac{-1}{3} \cdot t\right) \cdot z + \frac{\mathsf{PI}\left(\right)}{2}\right) - \frac{a}{b \cdot 3} \]

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-PI.f64 62.1

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

   5. Applied rewrites 62.1%

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

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-PI.f64 85.2

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \left(\pi \cdot 0.5\right) - \frac{a}{b \cdot 3} \]

   8. Applied rewrites 85.2%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \left(\pi \cdot 0.5\right) - \frac{a}{b \cdot 3} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 73.9% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 4 \cdot 10^{+150}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-0.3333333333333333, a, 2 \cdot \left(\left(b \cdot \left(\cos y \cdot \sin \left(\mathsf{fma}\left(-0.3333333333333333, t \cdot z, \frac{\pi}{2}\right)\right) - \sin y \cdot \sin \left(-0.3333333333333333 \cdot \left(t \cdot z\right)\right)\right)\right) \cdot {x}^{0.5}\right)\right)}{b}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0)))) 4e+150)
   (/
    (fma
     -0.3333333333333333
     a
     (*
      2.0
      (*
       (*
        b
        (-
         (* (cos y) (sin (fma -0.3333333333333333 (* t z) (/ PI 2.0))))
         (* (sin y) (sin (* -0.3333333333333333 (* t z))))))
       (pow x 0.5))))
    b)
   (* -0.3333333333333333 (/ a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((2.0 * sqrt(x)) * cos((y - ((z * t) / 3.0)))) <= 4e+150) {
		tmp = fma(-0.3333333333333333, a, (2.0 * ((b * ((cos(y) * sin(fma(-0.3333333333333333, (t * z), (((double) M_PI) / 2.0)))) - (sin(y) * sin((-0.3333333333333333 * (t * z)))))) * pow(x, 0.5)))) / b;
	} else {
		tmp = -0.3333333333333333 * (a / b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(2.0 * sqrt(x)) * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) <= 4e+150)
		tmp = Float64(fma(-0.3333333333333333, a, Float64(2.0 * Float64(Float64(b * Float64(Float64(cos(y) * sin(fma(-0.3333333333333333, Float64(t * z), Float64(pi / 2.0)))) - Float64(sin(y) * sin(Float64(-0.3333333333333333 * Float64(t * z)))))) * (x ^ 0.5)))) / b);
	else
		tmp = Float64(-0.3333333333333333 * Float64(a / b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 4e+150], N[(N[(-0.3333333333333333 * a + N[(2.0 * N[(N[(b * N[(N[(N[Cos[y], $MachinePrecision] * N[Sin[N[(-0.3333333333333333 * N[(t * z), $MachinePrecision] + N[(Pi / 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * N[Sin[N[(-0.3333333333333333 * N[(t * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Power[x, 0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(-0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) < 3.99999999999999992e150

   1. Initial program 80.2%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 80.3%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   8. Applied rewrites 73.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2 \cdot {\left({x}^{-1}\right)}^{0.5}, \cos \left(\mathsf{fma}\left(t \cdot z, -0.3333333333333333, y\right)\right), \frac{\frac{a}{b}}{x} \cdot -0.3333333333333333\right) \cdot x} \]

   9. Taylor expanded in b around 0

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

       1. lower-/.f64 N/A

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

   11. Applied rewrites 76.7%

       \[\leadsto \frac{\mathsf{fma}\left(-0.3333333333333333, a, 2 \cdot \left(\left(b \cdot \cos \left(y + -0.3333333333333333 \cdot \left(t \cdot z\right)\right)\right) \cdot {x}^{0.5}\right)\right)}{\color{blue}{b}} \]
   12. Step-by-step derivation

       1. lift-cos.f64 N/A

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

       2. lift-+.f64 N/A

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

       3. lift-*.f64 N/A

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

       4. lift-*.f64 N/A

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

       5. cos-sum N/A

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

       6. lower--.f64 N/A

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

       7. lower-*.f64 N/A

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

       8. lift-cos.f64 N/A

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

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

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

       10. lower-sin.f64 N/A

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

       11. lift-/.f64 N/A

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

       12. lift-PI.f64 N/A

           \[\leadsto \frac{\mathsf{fma}\left(\frac{-1}{3}, a, 2 \cdot \left(\left(b \cdot \left(\cos y \cdot \sin \left(\frac{-1}{3} \cdot \left(t \cdot z\right) + \frac{\pi}{2}\right) - \sin y \cdot \sin \left(\frac{-1}{3} \cdot \left(t \cdot z\right)\right)\right)\right) \cdot {x}^{\frac{1}{2}}\right)\right)}{b} \]

       13. lower-fma.f64 N/A

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

       14. lift-*.f64 N/A

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

       15. lower-*.f64 N/A

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

       16. lift-sin.f64 N/A

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

       17. lower-sin.f64 N/A

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

       18. lift-*.f64 N/A

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

       19. lift-*.f64 77.9

           \[\leadsto \frac{\mathsf{fma}\left(-0.3333333333333333, a, 2 \cdot \left(\left(b \cdot \left(\cos y \cdot \sin \left(\mathsf{fma}\left(-0.3333333333333333, t \cdot z, \frac{\pi}{2}\right)\right) - \sin y \cdot \sin \left(-0.3333333333333333 \cdot \left(t \cdot z\right)\right)\right)\right) \cdot {x}^{0.5}\right)\right)}{b} \]

   13. Applied rewrites 77.9%

       \[\leadsto \frac{\mathsf{fma}\left(-0.3333333333333333, a, 2 \cdot \left(\left(b \cdot \left(\cos y \cdot \sin \left(\mathsf{fma}\left(-0.3333333333333333, t \cdot z, \frac{\pi}{2}\right)\right) - \sin y \cdot \sin \left(-0.3333333333333333 \cdot \left(t \cdot z\right)\right)\right)\right) \cdot {x}^{0.5}\right)\right)}{b} \]

   if 3.99999999999999992e150 < (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (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 a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 57.0

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

   5. Applied rewrites 57.0%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 67.7% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \frac{\mathsf{fma}\left(-0.3333333333333333, a, 2 \cdot \left(\left(b \cdot \left(\cos y \cdot \sin \left(\mathsf{fma}\left(-0.3333333333333333, t \cdot z, \frac{\pi}{2}\right)\right) - \sin y \cdot \sin \left(-0.3333333333333333 \cdot \left(t \cdot z\right)\right)\right)\right) \cdot {x}^{0.5}\right)\right)}{b} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/
  (fma
   -0.3333333333333333
   a
   (*
    2.0
    (*
     (*
      b
      (-
       (* (cos y) (sin (fma -0.3333333333333333 (* t z) (/ PI 2.0))))
       (* (sin y) (sin (* -0.3333333333333333 (* t z))))))
     (pow x 0.5))))
  b))

C

double code(double x, double y, double z, double t, double a, double b) {
	return fma(-0.3333333333333333, a, (2.0 * ((b * ((cos(y) * sin(fma(-0.3333333333333333, (t * z), (((double) M_PI) / 2.0)))) - (sin(y) * sin((-0.3333333333333333 * (t * z)))))) * pow(x, 0.5)))) / b;
}

Julia

function code(x, y, z, t, a, b)
	return Float64(fma(-0.3333333333333333, a, Float64(2.0 * Float64(Float64(b * Float64(Float64(cos(y) * sin(fma(-0.3333333333333333, Float64(t * z), Float64(pi / 2.0)))) - Float64(sin(y) * sin(Float64(-0.3333333333333333 * Float64(t * z)))))) * (x ^ 0.5)))) / b)
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(-0.3333333333333333 * a + N[(2.0 * N[(N[(b * N[(N[(N[Cos[y], $MachinePrecision] * N[Sin[N[(-0.3333333333333333 * N[(t * z), $MachinePrecision] + N[(Pi / 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * N[Sin[N[(-0.3333333333333333 * N[(t * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Power[x, 0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]

Derivation

1. Initial program 68.3%

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

3. Taylor expanded in 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 77.0%

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

6. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

8. Applied rewrites 62.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(2 \cdot {\left({x}^{-1}\right)}^{0.5}, \cos \left(\mathsf{fma}\left(t \cdot z, -0.3333333333333333, y\right)\right), \frac{\frac{a}{b}}{x} \cdot -0.3333333333333333\right) \cdot x} \]

9. Taylor expanded in b around 0

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

    1. lower-/.f64 N/A

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

11. Applied rewrites 65.3%

    \[\leadsto \frac{\mathsf{fma}\left(-0.3333333333333333, a, 2 \cdot \left(\left(b \cdot \cos \left(y + -0.3333333333333333 \cdot \left(t \cdot z\right)\right)\right) \cdot {x}^{0.5}\right)\right)}{\color{blue}{b}} \]
12. Step-by-step derivation

    1. lift-cos.f64 N/A

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

    2. lift-+.f64 N/A

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

    3. lift-*.f64 N/A

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

    4. lift-*.f64 N/A

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

    5. cos-sum N/A

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

    6. lower--.f64 N/A

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

    7. lower-*.f64 N/A

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

    8. lift-cos.f64 N/A

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

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

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

    10. lower-sin.f64 N/A

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

    11. lift-/.f64 N/A

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

    12. lift-PI.f64 N/A

        \[\leadsto \frac{\mathsf{fma}\left(\frac{-1}{3}, a, 2 \cdot \left(\left(b \cdot \left(\cos y \cdot \sin \left(\frac{-1}{3} \cdot \left(t \cdot z\right) + \frac{\pi}{2}\right) - \sin y \cdot \sin \left(\frac{-1}{3} \cdot \left(t \cdot z\right)\right)\right)\right) \cdot {x}^{\frac{1}{2}}\right)\right)}{b} \]

    13. lower-fma.f64 N/A

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

    14. lift-*.f64 N/A

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

    15. lower-*.f64 N/A

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

    16. lift-sin.f64 N/A

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

    17. lower-sin.f64 N/A

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

    18. lift-*.f64 N/A

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

    19. lift-*.f64 66.4

        \[\leadsto \frac{\mathsf{fma}\left(-0.3333333333333333, a, 2 \cdot \left(\left(b \cdot \left(\cos y \cdot \sin \left(\mathsf{fma}\left(-0.3333333333333333, t \cdot z, \frac{\pi}{2}\right)\right) - \sin y \cdot \sin \left(-0.3333333333333333 \cdot \left(t \cdot z\right)\right)\right)\right) \cdot {x}^{0.5}\right)\right)}{b} \]

13. Applied rewrites 66.4%

    \[\leadsto \frac{\mathsf{fma}\left(-0.3333333333333333, a, 2 \cdot \left(\left(b \cdot \left(\cos y \cdot \sin \left(\mathsf{fma}\left(-0.3333333333333333, t \cdot z, \frac{\pi}{2}\right)\right) - \sin y \cdot \sin \left(-0.3333333333333333 \cdot \left(t \cdot z\right)\right)\right)\right) \cdot {x}^{0.5}\right)\right)}{b} \]
14. Add Preprocessing

Alternative 8: 67.3% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \frac{\mathsf{fma}\left(-0.3333333333333333, a, 2 \cdot \left(\left(b \cdot \cos \left(y + -0.3333333333333333 \cdot \left(t \cdot z\right)\right)\right) \cdot {x}^{0.5}\right)\right)}{b} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/
  (fma
   -0.3333333333333333
   a
   (* 2.0 (* (* b (cos (+ y (* -0.3333333333333333 (* t z))))) (pow x 0.5))))
  b))

C

double code(double x, double y, double z, double t, double a, double b) {
	return fma(-0.3333333333333333, a, (2.0 * ((b * cos((y + (-0.3333333333333333 * (t * z))))) * pow(x, 0.5)))) / b;
}

Julia

function code(x, y, z, t, a, b)
	return Float64(fma(-0.3333333333333333, a, Float64(2.0 * Float64(Float64(b * cos(Float64(y + Float64(-0.3333333333333333 * Float64(t * z))))) * (x ^ 0.5)))) / b)
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(-0.3333333333333333 * a + N[(2.0 * N[(N[(b * N[Cos[N[(y + N[(-0.3333333333333333 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Power[x, 0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]

Derivation

1. Initial program 68.3%

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

3. Taylor expanded in 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 77.0%

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

6. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

8. Applied rewrites 62.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(2 \cdot {\left({x}^{-1}\right)}^{0.5}, \cos \left(\mathsf{fma}\left(t \cdot z, -0.3333333333333333, y\right)\right), \frac{\frac{a}{b}}{x} \cdot -0.3333333333333333\right) \cdot x} \]

9. Taylor expanded in b around 0

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

    1. lower-/.f64 N/A

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

11. Applied rewrites 65.3%

    \[\leadsto \frac{\mathsf{fma}\left(-0.3333333333333333, a, 2 \cdot \left(\left(b \cdot \cos \left(y + -0.3333333333333333 \cdot \left(t \cdot z\right)\right)\right) \cdot {x}^{0.5}\right)\right)}{\color{blue}{b}} \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2025065 
(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))))