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

Percentage Accurate: 70.2% → 77.5%

Time: 7.6s

Alternatives: 7

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 70.2% 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: 77.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt{x} \cdot 2\\ \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \leq 10^{+154}:\\ \;\;\;\;\mathsf{fma}\left(-0.3333333333333333, \frac{a}{b}, t\_1 \cdot \mathsf{fma}\left(\cos y, \cos \left(\left(t \cdot z\right) \cdot -0.3333333333333333\right), \sin y \cdot \sin \left(\left(t \cdot z\right) \cdot 0.3333333333333333\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \cos y - \frac{\frac{a}{b}}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (sqrt x) 2.0)))
   (if (<=
        (- (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0)))) (/ a (* b 3.0)))
        1e+154)
     (fma
      -0.3333333333333333
      (/ a b)
      (*
       t_1
       (fma
        (cos y)
        (cos (* (* t z) -0.3333333333333333))
        (* (sin y) (sin (* (* t z) 0.3333333333333333))))))
     (- (* t_1 (cos y)) (/ (/ a b) 3.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = sqrt(x) * 2.0;
	double tmp;
	if ((((2.0 * sqrt(x)) * cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0))) <= 1e+154) {
		tmp = fma(-0.3333333333333333, (a / b), (t_1 * fma(cos(y), cos(((t * z) * -0.3333333333333333)), (sin(y) * sin(((t * z) * 0.3333333333333333))))));
	} else {
		tmp = (t_1 * cos(y)) - ((a / b) / 3.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(sqrt(x) * 2.0)
	tmp = 0.0
	if (Float64(Float64(Float64(2.0 * sqrt(x)) * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - Float64(a / Float64(b * 3.0))) <= 1e+154)
		tmp = fma(-0.3333333333333333, Float64(a / b), Float64(t_1 * fma(cos(y), cos(Float64(Float64(t * z) * -0.3333333333333333)), Float64(sin(y) * sin(Float64(Float64(t * z) * 0.3333333333333333))))));
	else
		tmp = Float64(Float64(t_1 * cos(y)) - Float64(Float64(a / b) / 3.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Sqrt[x], $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[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], 1e+154], N[(-0.3333333333333333 * N[(a / b), $MachinePrecision] + N[(t$95$1 * N[(N[Cos[y], $MachinePrecision] * N[Cos[N[(N[(t * z), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]], $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * N[Sin[N[(N[(t * z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(N[(a / b), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) (/.f64 a (*.f64 b #s(literal 3 binary64)))) < 1.00000000000000004e154

   1. Initial program 75.0%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. associate-*r* N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lift-sqrt.f64 N/A

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

      11. lower-cos.f64 N/A

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

      12. metadata-eval N/A

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

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

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

      14. +-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. lower-*.f64 75.2

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

   5. Applied rewrites 75.2%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lower-cos.f64 N/A

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

      4. +-commutative N/A

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

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

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

      6. metadata-eval N/A

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

      7. cos-diff N/A

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

      8. cos-neg N/A

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

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

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

      10. metadata-eval N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-cos.f64 N/A

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

      13. lower-cos.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. lower-*.f64 N/A

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

      18. lower-sin.f64 N/A

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

      19. lower-sin.f64 N/A

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

   7. Applied rewrites 76.1%

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

   if 1.00000000000000004e154 < (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) (/.f64 a (*.f64 b #s(literal 3 binary64))))

   1. Initial program 54.3%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   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 87.0%

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

      1. lift-*.f64 N/A

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

      2. lift-sqrt.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-sqrt.f64 N/A

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

      5. lift-*.f64 87.0

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

      6. lift-*.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. associate-/r* N/A

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

      9. lift-/.f64 N/A

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

      10. lower-/.f64 87.0

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

   7. Applied rewrites 87.0%

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

Alternative 2: 66.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{b \cdot 3}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-14}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{a}{b}\\ \mathbf{elif}\;t\_1 \leq 10^{+23}:\\ \;\;\;\;\left(\sqrt{x} \cdot 2\right) \cdot \cos \left(\mathsf{fma}\left(-0.3333333333333333, t \cdot z, y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333 \cdot a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* b 3.0))))
   (if (<= t_1 -5e-14)
     (* -0.3333333333333333 (/ a b))
     (if (<= t_1 1e+23)
       (* (* (sqrt x) 2.0) (cos (fma -0.3333333333333333 (* t z) y)))
       (/ (* -0.3333333333333333 a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (b * 3.0);
	double tmp;
	if (t_1 <= -5e-14) {
		tmp = -0.3333333333333333 * (a / b);
	} else if (t_1 <= 1e+23) {
		tmp = (sqrt(x) * 2.0) * cos(fma(-0.3333333333333333, (t * z), y));
	} else {
		tmp = (-0.3333333333333333 * a) / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(b * 3.0))
	tmp = 0.0
	if (t_1 <= -5e-14)
		tmp = Float64(-0.3333333333333333 * Float64(a / b));
	elseif (t_1 <= 1e+23)
		tmp = Float64(Float64(sqrt(x) * 2.0) * cos(fma(-0.3333333333333333, Float64(t * z), y)));
	else
		tmp = Float64(Float64(-0.3333333333333333 * a) / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-14], N[(-0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+23], N[(N[(N[Sqrt[x], $MachinePrecision] * 2.0), $MachinePrecision] * N[Cos[N[(-0.3333333333333333 * N[(t * z), $MachinePrecision] + y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(-0.3333333333333333 * a), $MachinePrecision] / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 a (*.f64 b #s(literal 3 binary64))) < -5.0000000000000002e-14

   1. Initial program 79.3%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 87.6

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

   5. Applied rewrites 87.6%

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

   if -5.0000000000000002e-14 < (/.f64 a (*.f64 b #s(literal 3 binary64))) < 9.9999999999999992e22

   1. Initial program 55.8%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift-sqrt.f64 N/A

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

      6. lower-cos.f64 N/A

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

      7. metadata-eval N/A

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

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

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

      9. +-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 50.6

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

   5. Applied rewrites 50.6%

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

   if 9.9999999999999992e22 < (/.f64 a (*.f64 b #s(literal 3 binary64)))

   1. Initial program 84.9%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 90.0

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

   5. Applied rewrites 90.0%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 90.1

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

   7. Applied rewrites 90.1%

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

Alternative 3: 76.5% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.5%

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

3. Taylor expanded in y around inf

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

5. Applied rewrites 77.3%

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

   1. lift-*.f64 N/A

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

   2. lift-sqrt.f64 N/A

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

   3. *-commutative N/A

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

   4. lift-sqrt.f64 N/A

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

   5. lift-*.f64 77.3

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

   6. lift-*.f64 N/A

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

   7. lift-/.f64 N/A

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

   8. associate-/r* N/A

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

   9. lift-/.f64 N/A

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

   10. lower-/.f64 77.3

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

7. Applied rewrites 77.3%

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

Alternative 4: 76.6% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.5%

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

3. Taylor expanded in y around inf

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

5. Applied rewrites 77.3%

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

Alternative 5: 76.4% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 69.5%

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

3. Taylor expanded in x around 0

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

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

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

   2. metadata-eval N/A

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

   3. +-commutative N/A

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

   4. lower-fma.f64 N/A

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

   5. lower-/.f64 N/A

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

   6. associate-*r* N/A

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

   7. lower-*.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 N/A

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

   10. lift-sqrt.f64 N/A

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

   11. lower-cos.f64 N/A

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

   12. metadata-eval N/A

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

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

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

   14. +-commutative N/A

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

   15. lower-fma.f64 N/A

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

   16. lower-*.f64 69.6

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

5. Applied rewrites 69.6%

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

6. Taylor expanded in y around inf

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

8. Applied rewrites 77.3%

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

Alternative 6: 51.3% accurate, 9.4× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.5%

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

3. Taylor expanded in a around inf

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

   1. lower-*.f64 N/A

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

   2. lower-/.f64 51.6

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

5. Applied rewrites 51.6%

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

   1. lift-*.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. associate-*r/ N/A

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

   4. lower-/.f64 N/A

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

   5. lower-*.f64 51.6

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

7. Applied rewrites 51.6%

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

Alternative 7: 51.2% accurate, 9.4× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.5%

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

3. Taylor expanded in a around inf

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

   1. lower-*.f64 N/A

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

   2. lower-/.f64 51.6

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

5. Applied rewrites 51.6%

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

Reproduce

herbie shell --seed 2025084 
(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))))