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

Percentage Accurate: 70.7% → 77.3%

Time: 20.4s

Alternatives: 8

Speedup: 1.1×

Specification

Math

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

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (- (* (* 2 (sqrt x)) (cos (- y (/ (* z t) 3)))) (/ a (* b 3))))

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 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(a / N[(b * 3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 70.7% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (- (* (* 2 (sqrt x)) (cos (- y (/ (* z t) 3)))) (/ a (* b 3))))

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 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(a / N[(b * 3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 77.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ t_2 := \left(-\frac{-1}{3} \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq \frac{5764607523034235}{1152921504606846976}:\\ \;\;\;\;t\_1 \cdot \left(\cos y \cdot \cos t\_2 + \sin y \cdot \sin t\_2\right) - \frac{a}{b \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \cos y - \frac{\frac{a}{3}}{b}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (* 2 (sqrt x))) (t_2 (* (- (* -1/3 z)) t)))
  (if (<=
       (* t_1 (cos (- y (/ (* z t) 3))))
       5764607523034235/1152921504606846976)
    (-
     (* t_1 (+ (* (cos y) (cos t_2)) (* (sin y) (sin t_2))))
     (/ a (* b 3)))
    (- (* t_1 (cos y)) (/ (/ a 3) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * sqrt(x);
	double t_2 = -(-0.3333333333333333 * z) * t;
	double tmp;
	if ((t_1 * cos((y - ((z * t) / 3.0)))) <= 0.005) {
		tmp = (t_1 * ((cos(y) * cos(t_2)) + (sin(y) * sin(t_2)))) - (a / (b * 3.0));
	} else {
		tmp = (t_1 * cos(y)) - ((a / 3.0) / b);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * sqrt(x)
    t_2 = -((-0.3333333333333333d0) * z) * t
    if ((t_1 * cos((y - ((z * t) / 3.0d0)))) <= 0.005d0) then
        tmp = (t_1 * ((cos(y) * cos(t_2)) + (sin(y) * sin(t_2)))) - (a / (b * 3.0d0))
    else
        tmp = (t_1 * cos(y)) - ((a / 3.0d0) / b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * Math.sqrt(x);
	double t_2 = -(-0.3333333333333333 * z) * t;
	double tmp;
	if ((t_1 * Math.cos((y - ((z * t) / 3.0)))) <= 0.005) {
		tmp = (t_1 * ((Math.cos(y) * Math.cos(t_2)) + (Math.sin(y) * Math.sin(t_2)))) - (a / (b * 3.0));
	} else {
		tmp = (t_1 * Math.cos(y)) - ((a / 3.0) / b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 2.0 * math.sqrt(x)
	t_2 = -(-0.3333333333333333 * z) * t
	tmp = 0
	if (t_1 * math.cos((y - ((z * t) / 3.0)))) <= 0.005:
		tmp = (t_1 * ((math.cos(y) * math.cos(t_2)) + (math.sin(y) * math.sin(t_2)))) - (a / (b * 3.0))
	else:
		tmp = (t_1 * math.cos(y)) - ((a / 3.0) / b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	t_2 = Float64(Float64(-Float64(-0.3333333333333333 * z)) * t)
	tmp = 0.0
	if (Float64(t_1 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) <= 0.005)
		tmp = Float64(Float64(t_1 * Float64(Float64(cos(y) * cos(t_2)) + Float64(sin(y) * sin(t_2)))) - Float64(a / Float64(b * 3.0)));
	else
		tmp = Float64(Float64(t_1 * cos(y)) - Float64(Float64(a / 3.0) / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 2.0 * sqrt(x);
	t_2 = -(-0.3333333333333333 * z) * t;
	tmp = 0.0;
	if ((t_1 * cos((y - ((z * t) / 3.0)))) <= 0.005)
		tmp = (t_1 * ((cos(y) * cos(t_2)) + (sin(y) * sin(t_2)))) - (a / (b * 3.0));
	else
		tmp = (t_1 * cos(y)) - ((a / 3.0) / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(2 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-N[(-1/3 * z), $MachinePrecision]) * t), $MachinePrecision]}, If[LessEqual[N[(t$95$1 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 5764607523034235/1152921504606846976], N[(N[(t$95$1 * N[(N[(N[Cos[y], $MachinePrecision] * N[Cos[t$95$2], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * N[Sin[t$95$2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b * 3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(N[(a / 3), $MachinePrecision] / 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))))) < 0.0050000000000000001

   1. Initial program 70.7%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. metadata-eval 70.8%

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

   3. Applied rewrites 70.8%

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

      1. lift-cos.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

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

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

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

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

      6. cos-diff N/A

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

      7. lower-+.f64 N/A

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

   5. Applied rewrites 71.2%

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

   if 0.0050000000000000001 < (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))))

   1. Initial program 70.7%

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

   2. Taylor expanded in z around 0

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

      1. lower-cos.f64 76.7%

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

   4. Applied rewrites 76.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 76.7%

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

   6. Applied rewrites 76.7%

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

Alternative 2: 77.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{a}{b \cdot 3}\\ t_2 := 2 \cdot \sqrt{x}\\ t_3 := \frac{-1}{3} \cdot \left(t \cdot z\right)\\ \mathbf{if}\;t\_2 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 499999999999999988998191202828830087182411944733900540386126622484631969614553746213463024711630256984884134207768538734419216153365573197681917952:\\ \;\;\;\;t\_2 \cdot \left(\cos t\_3 \cdot \cos y - \sin t\_3 \cdot \sin y\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \frac{1}{{x}^{\frac{-1}{2}}}\right) \cdot \sin \left(\left(-y\right) + \frac{1}{2} \cdot \pi\right) - t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (/ a (* b 3)))
       (t_2 (* 2 (sqrt x)))
       (t_3 (* -1/3 (* t z))))
  (if (<=
       (* t_2 (cos (- y (/ (* z t) 3))))
       499999999999999988998191202828830087182411944733900540386126622484631969614553746213463024711630256984884134207768538734419216153365573197681917952)
    (- (* t_2 (- (* (cos t_3) (cos y)) (* (sin t_3) (sin y)))) t_1)
    (- (* (* 2 (/ 1 (pow x -1/2))) (sin (+ (- y) (* 1/2 PI)))) 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 t_2 = 2.0 * sqrt(x);
	double t_3 = -0.3333333333333333 * (t * z);
	double tmp;
	if ((t_2 * cos((y - ((z * t) / 3.0)))) <= 5e+146) {
		tmp = (t_2 * ((cos(t_3) * cos(y)) - (sin(t_3) * sin(y)))) - t_1;
	} else {
		tmp = ((2.0 * (1.0 / pow(x, -0.5))) * sin((-y + (0.5 * ((double) M_PI))))) - 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 t_2 = 2.0 * Math.sqrt(x);
	double t_3 = -0.3333333333333333 * (t * z);
	double tmp;
	if ((t_2 * Math.cos((y - ((z * t) / 3.0)))) <= 5e+146) {
		tmp = (t_2 * ((Math.cos(t_3) * Math.cos(y)) - (Math.sin(t_3) * Math.sin(y)))) - t_1;
	} else {
		tmp = ((2.0 * (1.0 / Math.pow(x, -0.5))) * Math.sin((-y + (0.5 * Math.PI)))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / (b * 3.0)
	t_2 = 2.0 * math.sqrt(x)
	t_3 = -0.3333333333333333 * (t * z)
	tmp = 0
	if (t_2 * math.cos((y - ((z * t) / 3.0)))) <= 5e+146:
		tmp = (t_2 * ((math.cos(t_3) * math.cos(y)) - (math.sin(t_3) * math.sin(y)))) - t_1
	else:
		tmp = ((2.0 * (1.0 / math.pow(x, -0.5))) * math.sin((-y + (0.5 * math.pi)))) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(b * 3.0))
	t_2 = Float64(2.0 * sqrt(x))
	t_3 = Float64(-0.3333333333333333 * Float64(t * z))
	tmp = 0.0
	if (Float64(t_2 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) <= 5e+146)
		tmp = Float64(Float64(t_2 * Float64(Float64(cos(t_3) * cos(y)) - Float64(sin(t_3) * sin(y)))) - t_1);
	else
		tmp = Float64(Float64(Float64(2.0 * Float64(1.0 / (x ^ -0.5))) * sin(Float64(Float64(-y) + Float64(0.5 * pi)))) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (b * 3.0);
	t_2 = 2.0 * sqrt(x);
	t_3 = -0.3333333333333333 * (t * z);
	tmp = 0.0;
	if ((t_2 * cos((y - ((z * t) / 3.0)))) <= 5e+146)
		tmp = (t_2 * ((cos(t_3) * cos(y)) - (sin(t_3) * sin(y)))) - t_1;
	else
		tmp = ((2.0 * (1.0 / (x ^ -0.5))) * sin((-y + (0.5 * pi)))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(b * 3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-1/3 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 499999999999999988998191202828830087182411944733900540386126622484631969614553746213463024711630256984884134207768538734419216153365573197681917952], N[(N[(t$95$2 * N[(N[(N[Cos[t$95$3], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[t$95$3], $MachinePrecision] * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(2 * N[(1 / N[Power[x, -1/2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sin[N[((-y) + N[(1/2 * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$1), $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))))) < 4.9999999999999999e146

   1. Initial program 70.7%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. sub-to-fraction N/A

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

      4. mult-flip N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lower-134-z0z1z2z3z4 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{3}\right), y, 3, z, t\right)} - \frac{a}{b \cdot 3} \]

      8. metadata-eval 70.7%

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\frac{1}{3}}, y, 3, z, t\right) - \frac{a}{b \cdot 3} \]

   3. Applied rewrites 70.7%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\frac{1}{3}, y, 3, z, t\right)} - \frac{a}{b \cdot 3} \]

   5. Applied rewrites 71.1%

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

   if 4.9999999999999999e146 < (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))))

   1. Initial program 70.7%

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

   2. Taylor expanded in z around 0

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

      1. lower-cos.f64 76.7%

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

   4. Applied rewrites 76.7%

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

      1. lift-sqrt.f64 N/A

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

      2. pow1/2 N/A

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

      3. metadata-eval N/A

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

      4. metadata-eval N/A

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

      5. pow-neg N/A

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

      6. lower-unsound-/.f64 N/A

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

      7. lower-unsound-pow.f64 N/A

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

      8. metadata-eval 76.7%

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

   6. Applied rewrites 76.7%

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

      1. lift-cos.f64 N/A

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

      2. cos-neg-rev N/A

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

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

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

      4. lower-sin.f64 N/A

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

      5. lift-PI.f64 N/A

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

      6. mult-flip N/A

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

      7. metadata-eval N/A

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

      8. lift-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. lower-neg.f64 65.6%

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 65.6%

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

   8. Applied rewrites 65.6%

      \[\leadsto \left(2 \cdot \frac{1}{{x}^{\frac{-1}{2}}}\right) \cdot \sin \left(\left(-y\right) + \frac{1}{2} \cdot \pi\right) - \frac{a}{b \cdot 3} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 76.7% accurate, 1.1× speedup

Math

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

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (- (* (* 2 (sqrt x)) (cos y)) (/ (/ a 3) b)))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(N[(a / 3), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.7%

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

2. Taylor expanded in z around 0

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

   1. lower-cos.f64 76.7%

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

4. Applied rewrites 76.7%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. associate-/r* N/A

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

   5. lower-/.f64 N/A

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

   6. lower-/.f64 76.7%

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

6. Applied rewrites 76.7%

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

Alternative 4: 76.6% accurate, 1.1× speedup

Math

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

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (- (* (* 2 (sqrt x)) (cos y)) (* (/ 1/3 b) a)))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((2.0d0 * sqrt(x)) * cos(y)) - ((0.3333333333333333d0 / b) * a)
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)) - ((0.3333333333333333 / b) * a);
}

Python

def code(x, y, z, t, a, b):
	return ((2.0 * math.sqrt(x)) * math.cos(y)) - ((0.3333333333333333 / b) * a)

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * cos(y)) - ((0.3333333333333333 / b) * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(N[(1/3 / b), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.7%

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

2. Taylor expanded in z around 0

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

   1. lower-cos.f64 76.7%

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

4. Applied rewrites 76.7%

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

   1. lift-/.f64 N/A

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

   2. mult-flip N/A

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

   3. *-commutative N/A

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

   4. lower-*.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. *-commutative N/A

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

   7. associate-/r* N/A

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

   8. metadata-eval N/A

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

   9. lower-/.f64 76.6%

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

6. Applied rewrites 76.6%

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

Alternative 5: 65.4% accurate, 4.0× speedup

Math

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

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (- (* (* 2 (sqrt x)) 1) (/ a (* b 3))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * sqrt(x)) * 1.0) - (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)) * 1.0d0) - (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)) * 1.0) - (a / (b * 3.0));
}

Python

def code(x, y, z, t, a, b):
	return ((2.0 * math.sqrt(x)) * 1.0) - (a / (b * 3.0))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(2.0 * sqrt(x)) * 1.0) - Float64(a / Float64(b * 3.0)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * 1.0) - (a / (b * 3.0));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * 1), $MachinePrecision] - N[(a / N[(b * 3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.7%

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

2. Taylor expanded in z around 0

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

   1. lower-cos.f64 76.7%

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

4. Applied rewrites 76.7%

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

5. Taylor expanded in y around 0

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

7. Applied rewrites 65.4%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot 1 - \frac{a}{b \cdot 3} \]
8. Add Preprocessing

Alternative 6: 50.4% accurate, 6.9× speedup

Math

\[\frac{\frac{a}{-3}}{b} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (/ (/ a -3) b))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (a / -3.0) / b;
}

Python

def code(x, y, z, t, a, b):
	return (a / -3.0) / b

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(a / -3), $MachinePrecision] / b), $MachinePrecision]

Derivation

1. Initial program 70.7%

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

2. Taylor expanded in a around inf

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

   1. lower-*.f64 N/A

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

   2. lower-/.f64 50.3%

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

4. Applied rewrites 50.3%

   \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
5. 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 50.4%

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

6. Applied rewrites 50.4%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. metadata-eval N/A

      \[\leadsto \frac{a \cdot \left(\mathsf{neg}\left(\frac{1}{3}\right)\right)}{b} \]

   4. distribute-rgt-neg-in N/A

      \[\leadsto \frac{\mathsf{neg}\left(a \cdot \frac{1}{3}\right)}{b} \]

   5. metadata-eval N/A

      \[\leadsto \frac{\mathsf{neg}\left(a \cdot \frac{1}{3}\right)}{b} \]

   6. mult-flip N/A

      \[\leadsto \frac{\mathsf{neg}\left(\frac{a}{3}\right)}{b} \]

   7. lift-/.f64 N/A

      \[\leadsto \frac{\mathsf{neg}\left(\frac{a}{3}\right)}{b} \]

   8. lift-/.f64 N/A

      \[\leadsto \frac{\mathsf{neg}\left(\frac{a}{3}\right)}{b} \]

   9. distribute-neg-frac2 N/A

      \[\leadsto \frac{\frac{a}{\mathsf{neg}\left(3\right)}}{b} \]

   10. lower-/.f64 N/A

       \[\leadsto \frac{\frac{a}{\mathsf{neg}\left(3\right)}}{b} \]

   11. metadata-eval 50.4%

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

8. Applied rewrites 50.4%

   \[\leadsto \frac{\frac{a}{-3}}{b} \]
9. Add Preprocessing

Alternative 7: 50.3% accurate, 9.4× speedup

Math

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

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (* a (/ -1/3 b)))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(a * N[(-1/3 / b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.7%

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

2. Taylor expanded in a around inf

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

   1. lower-*.f64 N/A

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

   2. lower-/.f64 50.3%

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

4. Applied rewrites 50.3%

   \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
5. 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 50.4%

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

6. Applied rewrites 50.4%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. metadata-eval N/A

      \[\leadsto \frac{a \cdot \left(\mathsf{neg}\left(\frac{1}{3}\right)\right)}{b} \]

   4. distribute-rgt-neg-in N/A

      \[\leadsto \frac{\mathsf{neg}\left(a \cdot \frac{1}{3}\right)}{b} \]

   5. metadata-eval N/A

      \[\leadsto \frac{\mathsf{neg}\left(a \cdot \frac{1}{3}\right)}{b} \]

   6. mult-flip N/A

      \[\leadsto \frac{\mathsf{neg}\left(\frac{a}{3}\right)}{b} \]

   7. lift-/.f64 N/A

      \[\leadsto \frac{\mathsf{neg}\left(\frac{a}{3}\right)}{b} \]

   8. lower-/.f64 N/A

      \[\leadsto \frac{\mathsf{neg}\left(\frac{a}{3}\right)}{\color{blue}{b}} \]

   9. lift-/.f64 N/A

      \[\leadsto \frac{\mathsf{neg}\left(\frac{a}{3}\right)}{b} \]

   10. mult-flip N/A

       \[\leadsto \frac{\mathsf{neg}\left(a \cdot \frac{1}{3}\right)}{b} \]

   11. metadata-eval N/A

       \[\leadsto \frac{\mathsf{neg}\left(a \cdot \frac{1}{3}\right)}{b} \]

   12. distribute-rgt-neg-in N/A

       \[\leadsto \frac{a \cdot \left(\mathsf{neg}\left(\frac{1}{3}\right)\right)}{b} \]

   13. metadata-eval N/A

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

   14. associate-/l* N/A

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

   15. lower-*.f64 N/A

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

   16. lower-/.f64 50.3%

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

8. Applied rewrites 50.3%

   \[\leadsto a \cdot \color{blue}{\frac{\frac{-1}{3}}{b}} \]
9. Add Preprocessing

Alternative 8: 50.3% accurate, 9.4× speedup

Math

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

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (* -1/3 (/ 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[(-1/3 * N[(a / b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.7%

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

2. Taylor expanded in a around inf

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

   1. lower-*.f64 N/A

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

   2. lower-/.f64 50.3%

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

4. Applied rewrites 50.3%

   \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64
  (- (* (* 2 (sqrt x)) (cos (- y (/ (* z t) 3)))) (/ a (* b 3))))