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

Percentage Accurate: 70.3% → 77.6%

Time: 21.2s

Alternatives: 13

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

real(8) function code(x, y, z, t, a, b)
    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: 70.3% 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

real(8) function code(x, y, z, t, a, b)
    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: 77.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := z \cdot \left(t \cdot 0.3333333333333333\right)\\ t_2 := \frac{\mathsf{fma}\left(z, t \cdot -0.3333333333333333, y\right)}{t\_1 - y}\\ t_3 := t\_1 \cdot t\_2\\ t_4 := 2 \cdot \sqrt{x}\\ t_5 := y \cdot t\_2\\ \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.9999999999999287:\\ \;\;\;\;t\_4 \cdot \mathsf{fma}\left(\cos t\_3, \cos t\_5, \sin t\_3 \cdot \sin t\_5\right) - \frac{\frac{a}{b}}{3}\\ \mathbf{else}:\\ \;\;\;\;t\_4 - \frac{a}{3 \cdot b}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (* t 0.3333333333333333)))
        (t_2 (/ (fma z (* t -0.3333333333333333) y) (- t_1 y)))
        (t_3 (* t_1 t_2))
        (t_4 (* 2.0 (sqrt x)))
        (t_5 (* y t_2)))
   (if (<= (cos (- y (/ (* z t) 3.0))) 0.9999999999999287)
     (-
      (* t_4 (fma (cos t_3) (cos t_5) (* (sin t_3) (sin t_5))))
      (/ (/ a b) 3.0))
     (- t_4 (/ a (* 3.0 b))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t * 0.3333333333333333);
	double t_2 = fma(z, (t * -0.3333333333333333), y) / (t_1 - y);
	double t_3 = t_1 * t_2;
	double t_4 = 2.0 * sqrt(x);
	double t_5 = y * t_2;
	double tmp;
	if (cos((y - ((z * t) / 3.0))) <= 0.9999999999999287) {
		tmp = (t_4 * fma(cos(t_3), cos(t_5), (sin(t_3) * sin(t_5)))) - ((a / b) / 3.0);
	} else {
		tmp = t_4 - (a / (3.0 * b));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t * 0.3333333333333333))
	t_2 = Float64(fma(z, Float64(t * -0.3333333333333333), y) / Float64(t_1 - y))
	t_3 = Float64(t_1 * t_2)
	t_4 = Float64(2.0 * sqrt(x))
	t_5 = Float64(y * t_2)
	tmp = 0.0
	if (cos(Float64(y - Float64(Float64(z * t) / 3.0))) <= 0.9999999999999287)
		tmp = Float64(Float64(t_4 * fma(cos(t_3), cos(t_5), Float64(sin(t_3) * sin(t_5)))) - Float64(Float64(a / b) / 3.0));
	else
		tmp = Float64(t_4 - Float64(a / Float64(3.0 * b)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * N[(t * -0.3333333333333333), $MachinePrecision] + y), $MachinePrecision] / N[(t$95$1 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 * t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y * t$95$2), $MachinePrecision]}, If[LessEqual[N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 0.9999999999999287], N[(N[(t$95$4 * N[(N[Cos[t$95$3], $MachinePrecision] * N[Cos[t$95$5], $MachinePrecision] + N[(N[Sin[t$95$3], $MachinePrecision] * N[Sin[t$95$5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a / b), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision], N[(t$95$4 - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))) < 0.99999999999992872

   1. Initial program 69.1%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

      3. /-lowering-/.f64 69.1

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

   4. Applied egg-rr 69.1%

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

   6. Applied egg-rr 26.8%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{\left(\frac{\mathsf{fma}\left(z, t \cdot 0.3333333333333333, y\right) \cdot \mathsf{fma}\left(z \cdot t, -0.3333333333333333, y\right)}{\left(z \cdot \left(z \cdot \left(t \cdot t\right)\right)\right) \cdot 0.1111111111111111 - y \cdot y} \cdot \left(z \cdot \left(t \cdot 0.3333333333333333\right) - y\right)\right)} - \frac{\frac{a}{b}}{3} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{\left(\left(z \cdot \left(t \cdot \frac{1}{3}\right) - y\right) \cdot \frac{\left(z \cdot \left(t \cdot \frac{1}{3}\right) + y\right) \cdot \left(\left(z \cdot t\right) \cdot \frac{-1}{3} + y\right)}{\left(z \cdot \left(z \cdot \left(t \cdot t\right)\right)\right) \cdot \frac{1}{9} - y \cdot y}\right)} - \frac{\frac{a}{b}}{3} \]

      2. clear-num N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\left(z \cdot \left(t \cdot \frac{1}{3}\right) - y\right) \cdot \color{blue}{\frac{1}{\frac{\left(z \cdot \left(z \cdot \left(t \cdot t\right)\right)\right) \cdot \frac{1}{9} - y \cdot y}{\left(z \cdot \left(t \cdot \frac{1}{3}\right) + y\right) \cdot \left(\left(z \cdot t\right) \cdot \frac{-1}{3} + y\right)}}}\right) - \frac{\frac{a}{b}}{3} \]

      3. un-div-inv N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{\left(\frac{z \cdot \left(t \cdot \frac{1}{3}\right) - y}{\frac{\left(z \cdot \left(z \cdot \left(t \cdot t\right)\right)\right) \cdot \frac{1}{9} - y \cdot y}{\left(z \cdot \left(t \cdot \frac{1}{3}\right) + y\right) \cdot \left(\left(z \cdot t\right) \cdot \frac{-1}{3} + y\right)}}\right)} - \frac{\frac{a}{b}}{3} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{\left(\frac{z \cdot \left(t \cdot \frac{1}{3}\right) - y}{\frac{\left(z \cdot \left(z \cdot \left(t \cdot t\right)\right)\right) \cdot \frac{1}{9} - y \cdot y}{\left(z \cdot \left(t \cdot \frac{1}{3}\right) + y\right) \cdot \left(\left(z \cdot t\right) \cdot \frac{-1}{3} + y\right)}}\right)} - \frac{\frac{a}{b}}{3} \]

      5. --lowering--.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\frac{\color{blue}{z \cdot \left(t \cdot \frac{1}{3}\right) - y}}{\frac{\left(z \cdot \left(z \cdot \left(t \cdot t\right)\right)\right) \cdot \frac{1}{9} - y \cdot y}{\left(z \cdot \left(t \cdot \frac{1}{3}\right) + y\right) \cdot \left(\left(z \cdot t\right) \cdot \frac{-1}{3} + y\right)}}\right) - \frac{\frac{a}{b}}{3} \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\frac{\color{blue}{z \cdot \left(t \cdot \frac{1}{3}\right)} - y}{\frac{\left(z \cdot \left(z \cdot \left(t \cdot t\right)\right)\right) \cdot \frac{1}{9} - y \cdot y}{\left(z \cdot \left(t \cdot \frac{1}{3}\right) + y\right) \cdot \left(\left(z \cdot t\right) \cdot \frac{-1}{3} + y\right)}}\right) - \frac{\frac{a}{b}}{3} \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\frac{z \cdot \color{blue}{\left(t \cdot \frac{1}{3}\right)} - y}{\frac{\left(z \cdot \left(z \cdot \left(t \cdot t\right)\right)\right) \cdot \frac{1}{9} - y \cdot y}{\left(z \cdot \left(t \cdot \frac{1}{3}\right) + y\right) \cdot \left(\left(z \cdot t\right) \cdot \frac{-1}{3} + y\right)}}\right) - \frac{\frac{a}{b}}{3} \]

      8. associate-/r* N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\frac{z \cdot \left(t \cdot \frac{1}{3}\right) - y}{\color{blue}{\frac{\frac{\left(z \cdot \left(z \cdot \left(t \cdot t\right)\right)\right) \cdot \frac{1}{9} - y \cdot y}{z \cdot \left(t \cdot \frac{1}{3}\right) + y}}{\left(z \cdot t\right) \cdot \frac{-1}{3} + y}}}\right) - \frac{\frac{a}{b}}{3} \]

   8. Applied egg-rr 68.6%

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

      1. div-sub N/A

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

      2. cos-diff N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

   10. Applied egg-rr 69.9%

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

   if 0.99999999999992872 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))

   1. Initial program 55.4%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   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. Simplified 81.4%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot \sqrt{x}} - \frac{a}{b \cdot 3} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{2 \cdot \sqrt{x}} - \frac{a}{b \cdot 3} \]

      2. sqrt-lowering-sqrt.f64 82.4

         \[\leadsto 2 \cdot \color{blue}{\sqrt{x}} - \frac{a}{b \cdot 3} \]

   8. Simplified 82.4%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x}} - \frac{a}{b \cdot 3} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.9999999999999287:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\left(z \cdot \left(t \cdot 0.3333333333333333\right)\right) \cdot \frac{\mathsf{fma}\left(z, t \cdot -0.3333333333333333, y\right)}{z \cdot \left(t \cdot 0.3333333333333333\right) - y}\right), \cos \left(y \cdot \frac{\mathsf{fma}\left(z, t \cdot -0.3333333333333333, y\right)}{z \cdot \left(t \cdot 0.3333333333333333\right) - y}\right), \sin \left(\left(z \cdot \left(t \cdot 0.3333333333333333\right)\right) \cdot \frac{\mathsf{fma}\left(z, t \cdot -0.3333333333333333, y\right)}{z \cdot \left(t \cdot 0.3333333333333333\right) - y}\right) \cdot \sin \left(y \cdot \frac{\mathsf{fma}\left(z, t \cdot -0.3333333333333333, y\right)}{z \cdot \left(t \cdot 0.3333333333333333\right) - y}\right)\right) - \frac{\frac{a}{b}}{3}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ t_2 := \frac{a}{3 \cdot b}\\ \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \cdot t\_1 - t\_2 \leq 5 \cdot 10^{+155}:\\ \;\;\;\;t\_1 \cdot \left(\cos y \cdot \cos \left(z \cdot \left(t \cdot 0.3333333333333333\right)\right) - \sin \left(\left(z \cdot t\right) \cdot -0.3333333333333333\right) \cdot \sin y\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, \sqrt{x}, \frac{-0.3333333333333333 \cdot a}{b}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x))) (t_2 (/ a (* 3.0 b))))
   (if (<= (- (* (cos (- y (/ (* z t) 3.0))) t_1) t_2) 5e+155)
     (-
      (*
       t_1
       (-
        (* (cos y) (cos (* z (* t 0.3333333333333333))))
        (* (sin (* (* z t) -0.3333333333333333)) (sin y))))
      t_2)
     (fma 2.0 (sqrt x) (/ (* -0.3333333333333333 a) b)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * sqrt(x);
	double t_2 = a / (3.0 * b);
	double tmp;
	if (((cos((y - ((z * t) / 3.0))) * t_1) - t_2) <= 5e+155) {
		tmp = (t_1 * ((cos(y) * cos((z * (t * 0.3333333333333333)))) - (sin(((z * t) * -0.3333333333333333)) * sin(y)))) - t_2;
	} else {
		tmp = fma(2.0, sqrt(x), ((-0.3333333333333333 * a) / b));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	t_2 = Float64(a / Float64(3.0 * b))
	tmp = 0.0
	if (Float64(Float64(cos(Float64(y - Float64(Float64(z * t) / 3.0))) * t_1) - t_2) <= 5e+155)
		tmp = Float64(Float64(t_1 * Float64(Float64(cos(y) * cos(Float64(z * Float64(t * 0.3333333333333333)))) - Float64(sin(Float64(Float64(z * t) * -0.3333333333333333)) * sin(y)))) - t_2);
	else
		tmp = fma(2.0, sqrt(x), Float64(Float64(-0.3333333333333333 * a) / b));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], 5e+155], N[(N[(t$95$1 * N[(N[(N[Cos[y], $MachinePrecision] * N[Cos[N[(z * N[(t * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[N[(N[(z * t), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]], $MachinePrecision] * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(2.0 * N[Sqrt[x], $MachinePrecision] + N[(N[(-0.3333333333333333 * a), $MachinePrecision] / b), $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)))) < 4.9999999999999999e155

   1. Initial program 73.6%

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

   4. Applied egg-rr 16.6%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{\left(\frac{\left(\mathsf{fma}\left(y, y \cdot y, \left(\left(z \cdot t\right) \cdot \left(z \cdot \left(t \cdot \left(z \cdot t\right)\right)\right)\right) \cdot 0.037037037037037035\right) \cdot \mathsf{fma}\left(y, y \cdot y, \left(\left(z \cdot t\right) \cdot \left(z \cdot \left(t \cdot \left(z \cdot t\right)\right)\right)\right) \cdot -0.037037037037037035\right)\right) \cdot \frac{1}{\mathsf{fma}\left(z \cdot \left(t \cdot 0.3333333333333333\right), \mathsf{fma}\left(z, t \cdot 0.3333333333333333, y\right), y \cdot y\right)}}{\mathsf{fma}\left(y, y \cdot y, \left(\left(z \cdot t\right) \cdot \left(z \cdot \left(t \cdot \left(z \cdot t\right)\right)\right)\right) \cdot 0.037037037037037035\right)}\right)} - \frac{a}{b \cdot 3} \]

   6. Applied egg-rr 74.3%

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

   if 4.9999999999999999e155 < (-.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 35.8%

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

   3. Taylor expanded in 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. Simplified 73.1%

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

   6. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

         \[\leadsto 2 \cdot \sqrt{x} + \color{blue}{\frac{-1}{3}} \cdot \frac{a}{b} \]

      3. accelerator-lowering-fma.f64 N/A

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

      4. sqrt-lowering-sqrt.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. /-lowering-/.f64 N/A

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

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

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

      9. *-commutative N/A

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

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

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

      11. metadata-eval N/A

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

      12. *-lowering-*.f64 74.6

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

   8. Simplified 74.6%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \cdot \left(2 \cdot \sqrt{x}\right) - \frac{a}{3 \cdot b} \leq 5 \cdot 10^{+155}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(z \cdot \left(t \cdot 0.3333333333333333\right)\right) - \sin \left(\left(z \cdot t\right) \cdot -0.3333333333333333\right) \cdot \sin y\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, \sqrt{x}, \frac{-0.3333333333333333 \cdot a}{b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := 2 \cdot \sqrt{x}\\ t_3 := t\_2 - t\_1\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-103}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-131}:\\ \;\;\;\;t\_2 \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b))) (t_2 (* 2.0 (sqrt x))) (t_3 (- t_2 t_1)))
   (if (<= t_1 -2e-103) t_3 (if (<= t_1 2e-131) (* t_2 (cos y)) t_3))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = 2.0 * sqrt(x);
	double t_3 = t_2 - t_1;
	double tmp;
	if (t_1 <= -2e-103) {
		tmp = t_3;
	} else if (t_1 <= 2e-131) {
		tmp = t_2 * cos(y);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a / (3.0d0 * b)
    t_2 = 2.0d0 * sqrt(x)
    t_3 = t_2 - t_1
    if (t_1 <= (-2d-103)) then
        tmp = t_3
    else if (t_1 <= 2d-131) then
        tmp = t_2 * cos(y)
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = 2.0 * Math.sqrt(x);
	double t_3 = t_2 - t_1;
	double tmp;
	if (t_1 <= -2e-103) {
		tmp = t_3;
	} else if (t_1 <= 2e-131) {
		tmp = t_2 * Math.cos(y);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	t_2 = 2.0 * math.sqrt(x)
	t_3 = t_2 - t_1
	tmp = 0
	if t_1 <= -2e-103:
		tmp = t_3
	elif t_1 <= 2e-131:
		tmp = t_2 * math.cos(y)
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	t_2 = Float64(2.0 * sqrt(x))
	t_3 = Float64(t_2 - t_1)
	tmp = 0.0
	if (t_1 <= -2e-103)
		tmp = t_3;
	elseif (t_1 <= 2e-131)
		tmp = Float64(t_2 * cos(y));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	t_2 = 2.0 * sqrt(x);
	t_3 = t_2 - t_1;
	tmp = 0.0;
	if (t_1 <= -2e-103)
		tmp = t_3;
	elseif (t_1 <= 2e-131)
		tmp = t_2 * cos(y);
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-103], t$95$3, If[LessEqual[t$95$1, 2e-131], N[(t$95$2 * N[Cos[y], $MachinePrecision]), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 a (*.f64 b #s(literal 3 binary64))) < -1.99999999999999992e-103 or 2e-131 < (/.f64 a (*.f64 b #s(literal 3 binary64)))

   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. Simplified 82.4%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot \sqrt{x}} - \frac{a}{b \cdot 3} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{2 \cdot \sqrt{x}} - \frac{a}{b \cdot 3} \]

      2. sqrt-lowering-sqrt.f64 81.0

         \[\leadsto 2 \cdot \color{blue}{\sqrt{x}} - \frac{a}{b \cdot 3} \]

   8. Simplified 81.0%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x}} - \frac{a}{b \cdot 3} \]

   if -1.99999999999999992e-103 < (/.f64 a (*.f64 b #s(literal 3 binary64))) < 2e-131

   1. Initial program 52.3%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   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. Simplified 52.0%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. sqrt-lowering-sqrt.f64 N/A

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

      5. cos-lowering-cos.f64 51.8

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

   8. Simplified 51.8%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{3 \cdot b} \leq -2 \cdot 10^{-103}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \mathbf{elif}\;\frac{a}{3 \cdot b} \leq 2 \cdot 10^{-131}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.4% accurate, 1.2× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (fma (* 2.0 (cos y)) (sqrt x) (/ a (* b -3.0))))

C

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

Julia

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

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(2.0 * N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[Sqrt[x], $MachinePrecision] + N[(a / N[(b * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 64.2%

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

3. Taylor expanded in y around inf

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

5. Simplified 72.9%

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

   1. sub-neg N/A

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

   2. *-commutative N/A

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

   3. associate-*r* N/A

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

   4. accelerator-lowering-fma.f64 N/A

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

   5. *-lowering-*.f64 N/A

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

   6. cos-lowering-cos.f64 N/A

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

   7. sqrt-lowering-sqrt.f64 N/A

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

   8. distribute-neg-frac2 N/A

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

   9. /-lowering-/.f64 N/A

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

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

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

   11. *-lowering-*.f64 N/A

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

   12. metadata-eval 72.9

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

7. Applied egg-rr 72.9%

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

8. Final simplification 72.9%

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

Alternative 5: 76.3% accurate, 1.2× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (fma 2.0 (* (sqrt x) (cos y)) (* -0.3333333333333333 (/ a b))))

C

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

Julia

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

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] + N[(-0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 64.2%

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

3. Taylor expanded in z around 0

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

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

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

   2. metadata-eval N/A

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

   3. accelerator-lowering-fma.f64 N/A

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

   4. *-lowering-*.f64 N/A

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

   5. sqrt-lowering-sqrt.f64 N/A

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

   6. cos-lowering-cos.f64 N/A

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

   7. *-commutative N/A

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

   8. *-lowering-*.f64 N/A

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

   9. /-lowering-/.f64 72.8

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

5. Simplified 72.8%

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

6. Final simplification 72.8%

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

Alternative 6: 59.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := \frac{\frac{a}{-3}}{b}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-53}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-94}:\\ \;\;\;\;2 \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b))) (t_2 (/ (/ a -3.0) b)))
   (if (<= t_1 -2e-53) t_2 (if (<= t_1 1e-94) (* 2.0 (sqrt x)) t_2))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = (a / -3.0) / b;
	double tmp;
	if (t_1 <= -2e-53) {
		tmp = t_2;
	} else if (t_1 <= 1e-94) {
		tmp = 2.0 * sqrt(x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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 = a / (3.0d0 * b)
    t_2 = (a / (-3.0d0)) / b
    if (t_1 <= (-2d-53)) then
        tmp = t_2
    else if (t_1 <= 1d-94) then
        tmp = 2.0d0 * sqrt(x)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = (a / -3.0) / b;
	double tmp;
	if (t_1 <= -2e-53) {
		tmp = t_2;
	} else if (t_1 <= 1e-94) {
		tmp = 2.0 * Math.sqrt(x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	t_2 = (a / -3.0) / b
	tmp = 0
	if t_1 <= -2e-53:
		tmp = t_2
	elif t_1 <= 1e-94:
		tmp = 2.0 * math.sqrt(x)
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	t_2 = Float64(Float64(a / -3.0) / b)
	tmp = 0.0
	if (t_1 <= -2e-53)
		tmp = t_2;
	elseif (t_1 <= 1e-94)
		tmp = Float64(2.0 * sqrt(x));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	t_2 = (a / -3.0) / b;
	tmp = 0.0;
	if (t_1 <= -2e-53)
		tmp = t_2;
	elseif (t_1 <= 1e-94)
		tmp = 2.0 * sqrt(x);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a / -3.0), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-53], t$95$2, If[LessEqual[t$95$1, 1e-94], N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 a (*.f64 b #s(literal 3 binary64))) < -2.00000000000000006e-53 or 9.9999999999999996e-95 < (/.f64 a (*.f64 b #s(literal 3 binary64)))

   1. Initial program 70.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

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

      3. /-lowering-/.f64 78.4

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

   5. Simplified 78.4%

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

      1. associate-*l/ N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 78.4

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

   7. Applied egg-rr 78.4%

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

      1. metadata-eval N/A

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

      2. associate-/r* N/A

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

      3. *-commutative N/A

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

      4. div-inv N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. /-lowering-/.f64 N/A

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

      8. /-lowering-/.f64 78.6

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

   9. Applied egg-rr 78.6%

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

   if -2.00000000000000006e-53 < (/.f64 a (*.f64 b #s(literal 3 binary64))) < 9.9999999999999996e-95

   1. Initial program 53.1%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 53.3%

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

   6. Taylor expanded in b around 0

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

      1. /-lowering-/.f64 N/A

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

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

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

      3. associate-*r* N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. cos-lowering-cos.f64 N/A

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

      9. sqrt-lowering-sqrt.f64 N/A

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

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

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

      11. *-commutative N/A

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

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

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

      13. metadata-eval N/A

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

      14. *-lowering-*.f64 48.6

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

   8. Simplified 48.6%

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

   9. Taylor expanded in b around inf

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

       1. *-lowering-*.f64 N/A

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

       2. *-commutative N/A

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

       3. *-lowering-*.f64 N/A

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

       4. sqrt-lowering-sqrt.f64 N/A

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

       5. *-lowering-*.f64 N/A

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

       6. cos-lowering-cos.f64 45.5

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

   11. Simplified 45.5%

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

   12. Taylor expanded in y around 0

       \[\leadsto \color{blue}{2 \cdot \sqrt{x}} \]
   13. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \color{blue}{\sqrt{x} \cdot 2} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{\sqrt{x} \cdot 2} \]

       3. sqrt-lowering-sqrt.f64 31.8

          \[\leadsto \color{blue}{\sqrt{x}} \cdot 2 \]

   14. Simplified 31.8%

       \[\leadsto \color{blue}{\sqrt{x} \cdot 2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{3 \cdot b} \leq -2 \cdot 10^{-53}:\\ \;\;\;\;\frac{\frac{a}{-3}}{b}\\ \mathbf{elif}\;\frac{a}{3 \cdot b} \leq 10^{-94}:\\ \;\;\;\;2 \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a}{-3}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := \frac{a}{b \cdot -3}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-53}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-94}:\\ \;\;\;\;2 \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b))) (t_2 (/ a (* b -3.0))))
   (if (<= t_1 -2e-53) t_2 (if (<= t_1 1e-94) (* 2.0 (sqrt x)) t_2))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = a / (b * -3.0);
	double tmp;
	if (t_1 <= -2e-53) {
		tmp = t_2;
	} else if (t_1 <= 1e-94) {
		tmp = 2.0 * sqrt(x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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 = a / (3.0d0 * b)
    t_2 = a / (b * (-3.0d0))
    if (t_1 <= (-2d-53)) then
        tmp = t_2
    else if (t_1 <= 1d-94) then
        tmp = 2.0d0 * sqrt(x)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = a / (b * -3.0);
	double tmp;
	if (t_1 <= -2e-53) {
		tmp = t_2;
	} else if (t_1 <= 1e-94) {
		tmp = 2.0 * Math.sqrt(x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	t_2 = a / (b * -3.0)
	tmp = 0
	if t_1 <= -2e-53:
		tmp = t_2
	elif t_1 <= 1e-94:
		tmp = 2.0 * math.sqrt(x)
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	t_2 = Float64(a / Float64(b * -3.0))
	tmp = 0.0
	if (t_1 <= -2e-53)
		tmp = t_2;
	elseif (t_1 <= 1e-94)
		tmp = Float64(2.0 * sqrt(x));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	t_2 = a / (b * -3.0);
	tmp = 0.0;
	if (t_1 <= -2e-53)
		tmp = t_2;
	elseif (t_1 <= 1e-94)
		tmp = 2.0 * sqrt(x);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(b * -3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-53], t$95$2, If[LessEqual[t$95$1, 1e-94], N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 a (*.f64 b #s(literal 3 binary64))) < -2.00000000000000006e-53 or 9.9999999999999996e-95 < (/.f64 a (*.f64 b #s(literal 3 binary64)))

   1. Initial program 70.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

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

      3. /-lowering-/.f64 78.4

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

   5. Simplified 78.4%

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

      1. metadata-eval N/A

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

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

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

      3. metadata-eval N/A

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

      4. div-inv N/A

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

      5. associate-/r* N/A

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

      6. distribute-neg-frac2 N/A

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

      7. /-lowering-/.f64 N/A

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

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

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

      9. *-lowering-*.f64 N/A

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

      10. metadata-eval 78.6

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

   7. Applied egg-rr 78.6%

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

   if -2.00000000000000006e-53 < (/.f64 a (*.f64 b #s(literal 3 binary64))) < 9.9999999999999996e-95

   1. Initial program 53.1%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 53.3%

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

   6. Taylor expanded in b around 0

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

      1. /-lowering-/.f64 N/A

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

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

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

      3. associate-*r* N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. cos-lowering-cos.f64 N/A

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

      9. sqrt-lowering-sqrt.f64 N/A

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

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

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

      11. *-commutative N/A

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

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

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

      13. metadata-eval N/A

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

      14. *-lowering-*.f64 48.6

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

   8. Simplified 48.6%

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

   9. Taylor expanded in b around inf

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

       1. *-lowering-*.f64 N/A

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

       2. *-commutative N/A

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

       3. *-lowering-*.f64 N/A

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

       4. sqrt-lowering-sqrt.f64 N/A

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

       5. *-lowering-*.f64 N/A

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

       6. cos-lowering-cos.f64 45.5

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

   11. Simplified 45.5%

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

   12. Taylor expanded in y around 0

       \[\leadsto \color{blue}{2 \cdot \sqrt{x}} \]
   13. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \color{blue}{\sqrt{x} \cdot 2} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{\sqrt{x} \cdot 2} \]

       3. sqrt-lowering-sqrt.f64 31.8

          \[\leadsto \color{blue}{\sqrt{x}} \cdot 2 \]

   14. Simplified 31.8%

       \[\leadsto \color{blue}{\sqrt{x} \cdot 2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{3 \cdot b} \leq -2 \cdot 10^{-53}:\\ \;\;\;\;\frac{a}{b \cdot -3}\\ \mathbf{elif}\;\frac{a}{3 \cdot b} \leq 10^{-94}:\\ \;\;\;\;2 \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{b \cdot -3}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-53}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{a}{b}\\ \mathbf{elif}\;t\_1 \leq 10^{-94}:\\ \;\;\;\;2 \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-0.3333333333333333}{b}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b))))
   (if (<= t_1 -2e-53)
     (* -0.3333333333333333 (/ a b))
     (if (<= t_1 1e-94) (* 2.0 (sqrt x)) (* a (/ -0.3333333333333333 b))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double tmp;
	if (t_1 <= -2e-53) {
		tmp = -0.3333333333333333 * (a / b);
	} else if (t_1 <= 1e-94) {
		tmp = 2.0 * sqrt(x);
	} else {
		tmp = a * (-0.3333333333333333 / b);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    t_1 = a / (3.0d0 * b)
    if (t_1 <= (-2d-53)) then
        tmp = (-0.3333333333333333d0) * (a / b)
    else if (t_1 <= 1d-94) then
        tmp = 2.0d0 * sqrt(x)
    else
        tmp = a * ((-0.3333333333333333d0) / b)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double tmp;
	if (t_1 <= -2e-53) {
		tmp = -0.3333333333333333 * (a / b);
	} else if (t_1 <= 1e-94) {
		tmp = 2.0 * Math.sqrt(x);
	} else {
		tmp = a * (-0.3333333333333333 / b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	tmp = 0
	if t_1 <= -2e-53:
		tmp = -0.3333333333333333 * (a / b)
	elif t_1 <= 1e-94:
		tmp = 2.0 * math.sqrt(x)
	else:
		tmp = a * (-0.3333333333333333 / b)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	tmp = 0.0
	if (t_1 <= -2e-53)
		tmp = Float64(-0.3333333333333333 * Float64(a / b));
	elseif (t_1 <= 1e-94)
		tmp = Float64(2.0 * sqrt(x));
	else
		tmp = Float64(a * Float64(-0.3333333333333333 / b));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	tmp = 0.0;
	if (t_1 <= -2e-53)
		tmp = -0.3333333333333333 * (a / b);
	elseif (t_1 <= 1e-94)
		tmp = 2.0 * sqrt(x);
	else
		tmp = a * (-0.3333333333333333 / b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-53], N[(-0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-94], N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision], N[(a * N[(-0.3333333333333333 / b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 a (*.f64 b #s(literal 3 binary64))) < -2.00000000000000006e-53

   1. Initial program 66.3%

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

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

      2. *-lowering-*.f64 N/A

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

      3. /-lowering-/.f64 82.6

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

   5. Simplified 82.6%

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

   if -2.00000000000000006e-53 < (/.f64 a (*.f64 b #s(literal 3 binary64))) < 9.9999999999999996e-95

   1. Initial program 53.1%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 53.3%

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

   6. Taylor expanded in b around 0

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

      1. /-lowering-/.f64 N/A

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

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

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

      3. associate-*r* N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. cos-lowering-cos.f64 N/A

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

      9. sqrt-lowering-sqrt.f64 N/A

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

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

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

      11. *-commutative N/A

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

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

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

      13. metadata-eval N/A

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

      14. *-lowering-*.f64 48.6

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

   8. Simplified 48.6%

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

   9. Taylor expanded in b around inf

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

       1. *-lowering-*.f64 N/A

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

       2. *-commutative N/A

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

       3. *-lowering-*.f64 N/A

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

       4. sqrt-lowering-sqrt.f64 N/A

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

       5. *-lowering-*.f64 N/A

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

       6. cos-lowering-cos.f64 45.5

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

   11. Simplified 45.5%

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

   12. Taylor expanded in y around 0

       \[\leadsto \color{blue}{2 \cdot \sqrt{x}} \]
   13. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \color{blue}{\sqrt{x} \cdot 2} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{\sqrt{x} \cdot 2} \]

       3. sqrt-lowering-sqrt.f64 31.8

          \[\leadsto \color{blue}{\sqrt{x}} \cdot 2 \]

   14. Simplified 31.8%

       \[\leadsto \color{blue}{\sqrt{x} \cdot 2} \]

   if 9.9999999999999996e-95 < (/.f64 a (*.f64 b #s(literal 3 binary64)))

   1. Initial program 74.1%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

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

      3. /-lowering-/.f64 75.5

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

   5. Simplified 75.5%

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

      1. associate-*l/ N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 75.5

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

   7. Applied egg-rr 75.5%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{3 \cdot b} \leq -2 \cdot 10^{-53}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{a}{b}\\ \mathbf{elif}\;\frac{a}{3 \cdot b} \leq 10^{-94}:\\ \;\;\;\;2 \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-0.3333333333333333}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := a \cdot \frac{-0.3333333333333333}{b}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-53}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-94}:\\ \;\;\;\;2 \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b))) (t_2 (* a (/ -0.3333333333333333 b))))
   (if (<= t_1 -2e-53) t_2 (if (<= t_1 1e-94) (* 2.0 (sqrt x)) t_2))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = a * (-0.3333333333333333 / b);
	double tmp;
	if (t_1 <= -2e-53) {
		tmp = t_2;
	} else if (t_1 <= 1e-94) {
		tmp = 2.0 * sqrt(x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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 = a / (3.0d0 * b)
    t_2 = a * ((-0.3333333333333333d0) / b)
    if (t_1 <= (-2d-53)) then
        tmp = t_2
    else if (t_1 <= 1d-94) then
        tmp = 2.0d0 * sqrt(x)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = a * (-0.3333333333333333 / b);
	double tmp;
	if (t_1 <= -2e-53) {
		tmp = t_2;
	} else if (t_1 <= 1e-94) {
		tmp = 2.0 * Math.sqrt(x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	t_2 = a * (-0.3333333333333333 / b)
	tmp = 0
	if t_1 <= -2e-53:
		tmp = t_2
	elif t_1 <= 1e-94:
		tmp = 2.0 * math.sqrt(x)
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	t_2 = Float64(a * Float64(-0.3333333333333333 / b))
	tmp = 0.0
	if (t_1 <= -2e-53)
		tmp = t_2;
	elseif (t_1 <= 1e-94)
		tmp = Float64(2.0 * sqrt(x));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	t_2 = a * (-0.3333333333333333 / b);
	tmp = 0.0;
	if (t_1 <= -2e-53)
		tmp = t_2;
	elseif (t_1 <= 1e-94)
		tmp = 2.0 * sqrt(x);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(-0.3333333333333333 / b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-53], t$95$2, If[LessEqual[t$95$1, 1e-94], N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 a (*.f64 b #s(literal 3 binary64))) < -2.00000000000000006e-53 or 9.9999999999999996e-95 < (/.f64 a (*.f64 b #s(literal 3 binary64)))

   1. Initial program 70.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

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

      3. /-lowering-/.f64 78.4

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

   5. Simplified 78.4%

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

      1. associate-*l/ N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 78.4

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

   7. Applied egg-rr 78.4%

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

   if -2.00000000000000006e-53 < (/.f64 a (*.f64 b #s(literal 3 binary64))) < 9.9999999999999996e-95

   1. Initial program 53.1%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 53.3%

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

   6. Taylor expanded in b around 0

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

      1. /-lowering-/.f64 N/A

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

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

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

      3. associate-*r* N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. cos-lowering-cos.f64 N/A

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

      9. sqrt-lowering-sqrt.f64 N/A

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

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

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

      11. *-commutative N/A

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

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

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

      13. metadata-eval N/A

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

      14. *-lowering-*.f64 48.6

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

   8. Simplified 48.6%

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

   9. Taylor expanded in b around inf

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

       1. *-lowering-*.f64 N/A

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

       2. *-commutative N/A

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

       3. *-lowering-*.f64 N/A

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

       4. sqrt-lowering-sqrt.f64 N/A

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

       5. *-lowering-*.f64 N/A

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

       6. cos-lowering-cos.f64 45.5

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

   11. Simplified 45.5%

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

   12. Taylor expanded in y around 0

       \[\leadsto \color{blue}{2 \cdot \sqrt{x}} \]
   13. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \color{blue}{\sqrt{x} \cdot 2} \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{\sqrt{x} \cdot 2} \]

       3. sqrt-lowering-sqrt.f64 31.8

          \[\leadsto \color{blue}{\sqrt{x}} \cdot 2 \]

   14. Simplified 31.8%

       \[\leadsto \color{blue}{\sqrt{x} \cdot 2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{3 \cdot b} \leq -2 \cdot 10^{-53}:\\ \;\;\;\;a \cdot \frac{-0.3333333333333333}{b}\\ \mathbf{elif}\;\frac{a}{3 \cdot b} \leq 10^{-94}:\\ \;\;\;\;2 \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-0.3333333333333333}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.9% accurate, 4.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ 2 \cdot \sqrt{x} - \frac{a}{3 \cdot b} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (- (* 2.0 (sqrt x)) (/ a (* 3.0 b))))

C

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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)) - (a / (3.0d0 * b))
end function

Java

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

Python

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

Julia

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

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = (2.0 * sqrt(x)) - (a / (3.0 * b));
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 64.2%

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

3. Taylor expanded in y around inf

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

5. Simplified 72.9%

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

6. Taylor expanded in y around 0

   \[\leadsto \color{blue}{2 \cdot \sqrt{x}} - \frac{a}{b \cdot 3} \]
7. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \color{blue}{2 \cdot \sqrt{x}} - \frac{a}{b \cdot 3} \]

   2. sqrt-lowering-sqrt.f64 64.8

      \[\leadsto 2 \cdot \color{blue}{\sqrt{x}} - \frac{a}{b \cdot 3} \]

8. Simplified 64.8%

   \[\leadsto \color{blue}{2 \cdot \sqrt{x}} - \frac{a}{b \cdot 3} \]

9. Final simplification 64.8%

   \[\leadsto 2 \cdot \sqrt{x} - \frac{a}{3 \cdot b} \]
10. Add Preprocessing

Alternative 11: 64.8% accurate, 4.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (fma 2.0 (sqrt x) (/ (* -0.3333333333333333 a) b)))

C

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

Julia

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

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(2.0 * N[Sqrt[x], $MachinePrecision] + N[(N[(-0.3333333333333333 * a), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 64.2%

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

3. Taylor expanded in y around inf

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

5. Simplified 72.9%

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

6. Taylor expanded in y around 0

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

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

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

   2. metadata-eval N/A

      \[\leadsto 2 \cdot \sqrt{x} + \color{blue}{\frac{-1}{3}} \cdot \frac{a}{b} \]

   3. accelerator-lowering-fma.f64 N/A

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

   4. sqrt-lowering-sqrt.f64 N/A

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

   5. associate-*r/ N/A

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

   6. metadata-eval N/A

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

   7. /-lowering-/.f64 N/A

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

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

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

   9. *-commutative N/A

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

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

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

   11. metadata-eval N/A

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

   12. *-lowering-*.f64 64.8

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

8. Simplified 64.8%

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

9. Final simplification 64.8%

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

Alternative 12: 64.7% accurate, 4.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (fma -0.3333333333333333 (/ a b) (* 2.0 (sqrt x))))

C

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

Julia

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

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(-0.3333333333333333 * N[(a / b), $MachinePrecision] + N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 64.2%

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

3. Taylor expanded in y around inf

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

5. Simplified 72.9%

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

   1. sub-neg N/A

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

   2. *-commutative N/A

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

   3. associate-*r* N/A

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

   4. accelerator-lowering-fma.f64 N/A

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

   5. *-lowering-*.f64 N/A

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

   6. cos-lowering-cos.f64 N/A

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

   7. sqrt-lowering-sqrt.f64 N/A

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

   8. distribute-neg-frac2 N/A

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

   9. /-lowering-/.f64 N/A

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

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

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

   11. *-lowering-*.f64 N/A

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

   12. metadata-eval 72.9

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

7. Applied egg-rr 72.9%

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

8. Taylor expanded in y around 0

   \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b} + 2 \cdot \sqrt{x}} \]
9. Step-by-step derivation

   1. accelerator-lowering-fma.f64 N/A

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

   2. /-lowering-/.f64 N/A

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

   3. *-lowering-*.f64 N/A

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

   4. sqrt-lowering-sqrt.f64 64.8

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

10. Simplified 64.8%

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

Alternative 13: 17.3% accurate, 9.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ 2 \cdot \sqrt{x} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (* 2.0 (sqrt x)))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return 2.0 * sqrt(x);
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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)
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return 2.0 * Math.sqrt(x);
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return 2.0 * math.sqrt(x)

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(2.0 * sqrt(x))
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = 2.0 * sqrt(x);
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 64.2%

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

3. Taylor expanded in y around inf

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

5. Simplified 72.9%

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

6. Taylor expanded in b around 0

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

   1. /-lowering-/.f64 N/A

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

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

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

   3. associate-*r* N/A

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

   4. accelerator-lowering-fma.f64 N/A

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

   5. *-lowering-*.f64 N/A

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

   6. *-commutative N/A

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

   7. *-lowering-*.f64 N/A

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

   8. cos-lowering-cos.f64 N/A

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

   9. sqrt-lowering-sqrt.f64 N/A

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

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

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

   11. *-commutative N/A

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

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

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

   13. metadata-eval N/A

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

   14. *-lowering-*.f64 70.6

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

8. Simplified 70.6%

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

9. Taylor expanded in b around inf

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

    1. *-lowering-*.f64 N/A

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

    2. *-commutative N/A

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

    3. *-lowering-*.f64 N/A

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

    4. sqrt-lowering-sqrt.f64 N/A

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

    5. *-lowering-*.f64 N/A

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

    6. cos-lowering-cos.f64 21.8

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

11. Simplified 21.8%

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

12. Taylor expanded in y around 0

    \[\leadsto \color{blue}{2 \cdot \sqrt{x}} \]
13. Step-by-step derivation

    1. *-commutative N/A

       \[\leadsto \color{blue}{\sqrt{x} \cdot 2} \]

    2. *-lowering-*.f64 N/A

       \[\leadsto \color{blue}{\sqrt{x} \cdot 2} \]

    3. sqrt-lowering-sqrt.f64 16.4

       \[\leadsto \color{blue}{\sqrt{x}} \cdot 2 \]

14. Simplified 16.4%

    \[\leadsto \color{blue}{\sqrt{x} \cdot 2} \]

15. Final simplification 16.4%

    \[\leadsto 2 \cdot \sqrt{x} \]
16. Add Preprocessing

Developer Target 1: 74.2% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024205 
(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))))