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

Percentage Accurate: 70.7% → 77.9%

Time: 25.9s

Alternatives: 8

Speedup: 1.0×

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: 70.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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: 77.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := t \cdot \left(z \cdot 0.3333333333333333\right)\\ \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.82:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \left(\cos y \cdot \cos t_2 + \sin y \cdot \sin t_2\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot {\cos y}^{2}} - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b))) (t_2 (* t (* z 0.3333333333333333))))
   (if (<= (cos (- y (/ (* z t) 3.0))) 0.82)
     (-
      (* 2.0 (* (sqrt x) (+ (* (cos y) (cos t_2)) (* (sin y) (sin t_2)))))
      t_1)
     (- (* 2.0 (sqrt (* x (pow (cos y) 2.0)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = t * (z * 0.3333333333333333);
	double tmp;
	if (cos((y - ((z * t) / 3.0))) <= 0.82) {
		tmp = (2.0 * (sqrt(x) * ((cos(y) * cos(t_2)) + (sin(y) * sin(t_2))))) - t_1;
	} else {
		tmp = (2.0 * sqrt((x * pow(cos(y), 2.0)))) - t_1;
	}
	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) :: tmp
    t_1 = a / (3.0d0 * b)
    t_2 = t * (z * 0.3333333333333333d0)
    if (cos((y - ((z * t) / 3.0d0))) <= 0.82d0) then
        tmp = (2.0d0 * (sqrt(x) * ((cos(y) * cos(t_2)) + (sin(y) * sin(t_2))))) - t_1
    else
        tmp = (2.0d0 * sqrt((x * (cos(y) ** 2.0d0)))) - t_1
    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 = a / (3.0 * b);
	double t_2 = t * (z * 0.3333333333333333);
	double tmp;
	if (Math.cos((y - ((z * t) / 3.0))) <= 0.82) {
		tmp = (2.0 * (Math.sqrt(x) * ((Math.cos(y) * Math.cos(t_2)) + (Math.sin(y) * Math.sin(t_2))))) - t_1;
	} else {
		tmp = (2.0 * Math.sqrt((x * Math.pow(Math.cos(y), 2.0)))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	t_2 = t * (z * 0.3333333333333333)
	tmp = 0
	if math.cos((y - ((z * t) / 3.0))) <= 0.82:
		tmp = (2.0 * (math.sqrt(x) * ((math.cos(y) * math.cos(t_2)) + (math.sin(y) * math.sin(t_2))))) - t_1
	else:
		tmp = (2.0 * math.sqrt((x * math.pow(math.cos(y), 2.0)))) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	t_2 = Float64(t * Float64(z * 0.3333333333333333))
	tmp = 0.0
	if (cos(Float64(y - Float64(Float64(z * t) / 3.0))) <= 0.82)
		tmp = Float64(Float64(2.0 * Float64(sqrt(x) * Float64(Float64(cos(y) * cos(t_2)) + Float64(sin(y) * sin(t_2))))) - t_1);
	else
		tmp = Float64(Float64(2.0 * sqrt(Float64(x * (cos(y) ^ 2.0)))) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	t_2 = t * (z * 0.3333333333333333);
	tmp = 0.0;
	if (cos((y - ((z * t) / 3.0))) <= 0.82)
		tmp = (2.0 * (sqrt(x) * ((cos(y) * cos(t_2)) + (sin(y) * sin(t_2))))) - t_1;
	else
		tmp = (2.0 * sqrt((x * (cos(y) ^ 2.0)))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 0.82], N[(N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(N[(N[Cos[y], $MachinePrecision] * N[Cos[t$95$2], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * N[Sin[t$95$2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(2.0 * N[Sqrt[N[(x * N[Power[N[Cos[y], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))) < 0.819999999999999951

   1. Initial program 70.3%

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

      1. associate-*l* 70.3%

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

      2. fma-neg 70.3%

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

      3. remove-double-neg 70.3%

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

      4. fma-neg 70.3%

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

      5. remove-double-neg 70.3%

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

      6. associate-*l/ 70.3%

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

      7. *-commutative 70.3%

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

   3. Simplified 70.3%

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

      1. cos-diff 72.8%

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

      2. div-inv 73.4%

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

      3. metadata-eval 73.4%

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

      4. div-inv 73.2%

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

      5. metadata-eval 73.2%

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

   5. Applied egg-rr 73.2%

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

   if 0.819999999999999951 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))

   1. Initial program 67.9%

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

      1. associate-*l* 67.9%

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

      2. fma-neg 67.9%

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

      3. remove-double-neg 67.9%

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

      4. fma-neg 67.9%

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

      5. remove-double-neg 67.9%

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

      6. associate-*l/ 68.6%

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

      7. *-commutative 68.6%

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

   3. Simplified 68.6%

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

      1. add-log-exp 68.7%

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

      2. div-inv 68.7%

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

      3. metadata-eval 68.7%

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

   5. Applied egg-rr 68.7%

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

   6. Taylor expanded in z around 0 83.1%

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

      1. add-sqr-sqrt 79.5%

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

      2. sqrt-unprod 83.7%

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

      3. swap-sqr 83.7%

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

      4. add-sqr-sqrt 83.7%

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

      5. pow2 83.7%

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

      6. add-log-exp 83.7%

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

   8. Applied egg-rr 83.7%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.82:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \left(\cos y \cdot \cos \left(t \cdot \left(z \cdot 0.3333333333333333\right)\right) + \sin y \cdot \sin \left(t \cdot \left(z \cdot 0.3333333333333333\right)\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot {\cos y}^{2}} - \frac{a}{3 \cdot b}\\ \end{array} \]

Alternative 2: 73.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-93} \lor \neg \left(t_1 \leq 5 \cdot 10^{-117}\right):\\ \;\;\;\;2 \cdot \sqrt{x} - t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b))))
   (if (or (<= t_1 -5e-93) (not (<= t_1 5e-117)))
     (- (* 2.0 (sqrt x)) t_1)
     (* 2.0 (* (sqrt x) (cos y))))))

C

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 <= -5e-93) || !(t_1 <= 5e-117)) {
		tmp = (2.0 * sqrt(x)) - t_1;
	} else {
		tmp = 2.0 * (sqrt(x) * cos(y));
	}
	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) :: tmp
    t_1 = a / (3.0d0 * b)
    if ((t_1 <= (-5d-93)) .or. (.not. (t_1 <= 5d-117))) then
        tmp = (2.0d0 * sqrt(x)) - t_1
    else
        tmp = 2.0d0 * (sqrt(x) * cos(y))
    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 = a / (3.0 * b);
	double tmp;
	if ((t_1 <= -5e-93) || !(t_1 <= 5e-117)) {
		tmp = (2.0 * Math.sqrt(x)) - t_1;
	} else {
		tmp = 2.0 * (Math.sqrt(x) * Math.cos(y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	tmp = 0
	if (t_1 <= -5e-93) or not (t_1 <= 5e-117):
		tmp = (2.0 * math.sqrt(x)) - t_1
	else:
		tmp = 2.0 * (math.sqrt(x) * math.cos(y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	tmp = 0.0
	if ((t_1 <= -5e-93) || !(t_1 <= 5e-117))
		tmp = Float64(Float64(2.0 * sqrt(x)) - t_1);
	else
		tmp = Float64(2.0 * Float64(sqrt(x) * cos(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	tmp = 0.0;
	if ((t_1 <= -5e-93) || ~((t_1 <= 5e-117)))
		tmp = (2.0 * sqrt(x)) - t_1;
	else
		tmp = 2.0 * (sqrt(x) * cos(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-93], N[Not[LessEqual[t$95$1, 5e-117]], $MachinePrecision]], N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 a (*.f64 b 3)) < -4.99999999999999994e-93 or 5e-117 < (/.f64 a (*.f64 b 3))

   1. Initial program 75.1%

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

   2. Taylor expanded in z around 0 87.1%

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

      1. *-commutative 87.1%

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

      2. associate-*l* 87.1%

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

      3. *-commutative 87.1%

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

   4. Simplified 87.1%

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

   5. Taylor expanded in y around 0 83.4%

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

   if -4.99999999999999994e-93 < (/.f64 a (*.f64 b 3)) < 5e-117

   1. Initial program 58.9%

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

   2. Taylor expanded in z around 0 58.5%

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

      1. *-commutative 58.5%

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

      2. associate-*l* 58.5%

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

      3. *-commutative 58.5%

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

   4. Simplified 58.5%

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

      1. associate-*r* 58.5%

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

      2. fma-neg 58.5%

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

   6. Applied egg-rr 58.5%

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

   7. Taylor expanded in a around 0 57.6%

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

      1. *-commutative 57.6%

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

   9. Simplified 57.6%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{3 \cdot b} \leq -5 \cdot 10^{-93} \lor \neg \left(\frac{a}{3 \cdot b} \leq 5 \cdot 10^{-117}\right):\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \end{array} \]

Alternative 3: 77.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = (cos(y) * (2.0d0 * sqrt(x))) - (a / (3.0d0 * b))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Taylor expanded in z around 0 76.4%

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

   1. *-commutative 76.4%

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

   2. associate-*l* 76.4%

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

   3. *-commutative 76.4%

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

4. Simplified 76.4%

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

5. Final simplification 76.4%

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

Alternative 4: 77.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = (cos(y) * (2.0d0 * sqrt(x))) - ((a / 3.0d0) / b)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Taylor expanded in z around 0 76.4%

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

   1. *-commutative 76.4%

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

   2. associate-*l* 76.4%

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

   3. *-commutative 76.4%

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

4. Simplified 76.4%

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

   1. add-sqr-sqrt 42.5%

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

6. Applied egg-rr 42.5%

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

   1. add-sqr-sqrt 76.4%

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

   2. *-commutative 76.4%

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

   3. associate-/r* 76.4%

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

8. Applied egg-rr 76.4%

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

9. Final simplification 76.4%

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

Alternative 5: 66.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \sqrt{x} - \frac{a}{3 \cdot b} \end{array} \]

FPCore

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

C

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

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)) - (a / (3.0d0 * b))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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 69.1%

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

2. Taylor expanded in z around 0 76.4%

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

   1. *-commutative 76.4%

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

   2. associate-*l* 76.4%

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

   3. *-commutative 76.4%

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

4. Simplified 76.4%

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

5. Taylor expanded in y around 0 65.7%

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

6. Final simplification 65.7%

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

Alternative 6: 51.1% accurate, 43.4× speedup

Math

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

FPCore

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

C

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

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 = a * ((-0.3333333333333333d0) / b)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Taylor expanded in z around 0 76.4%

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

   1. *-commutative 76.4%

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

   2. associate-*l* 76.4%

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

   3. *-commutative 76.4%

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

4. Simplified 76.4%

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

5. Taylor expanded in x around 0 49.1%

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

   1. metadata-eval 49.1%

      \[\leadsto \color{blue}{\left(-0.3333333333333333\right)} \cdot \frac{a}{b} \]

   2. distribute-lft-neg-in 49.1%

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

   3. metadata-eval 49.1%

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

   4. times-frac 49.2%

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

   5. *-commutative 49.2%

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

   6. *-lft-identity 49.2%

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

   7. *-rgt-identity 49.2%

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

   8. associate-*r/ 49.1%

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

   9. distribute-rgt-neg-in 49.1%

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

   10. distribute-neg-frac 49.1%

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

   11. metadata-eval 49.1%

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

   12. *-commutative 49.1%

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

   13. associate-/r* 49.1%

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

   14. metadata-eval 49.1%

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

7. Simplified 49.1%

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

8. Final simplification 49.1%

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

Alternative 7: 51.1% accurate, 43.4× speedup

Math

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

FPCore

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

C

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

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 = (a / b) * (-0.3333333333333333d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Taylor expanded in z around 0 76.4%

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

   1. *-commutative 76.4%

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

   2. associate-*l* 76.4%

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

   3. *-commutative 76.4%

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

4. Simplified 76.4%

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

5. Taylor expanded in x around 0 49.1%

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

   1. *-commutative 49.1%

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

7. Simplified 49.1%

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

8. Final simplification 49.1%

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

Alternative 8: 51.2% accurate, 43.4× speedup

Math

\[\begin{array}{l} \\ \frac{a}{b \cdot -3} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return 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 = a / (b * (-3.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Taylor expanded in z around 0 76.4%

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

   1. *-commutative 76.4%

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

   2. associate-*l* 76.4%

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

   3. *-commutative 76.4%

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

4. Simplified 76.4%

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

5. Taylor expanded in x around 0 49.1%

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

   1. *-commutative 49.1%

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

7. Simplified 49.1%

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

8. Taylor expanded in a around 0 49.1%

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

   1. *-commutative 49.1%

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

   2. associate-/r/ 49.2%

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

   3. metadata-eval 49.2%

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

   4. associate-/l* 49.2%

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

   5. /-rgt-identity 49.2%

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

10. Simplified 49.2%

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

11. Final simplification 49.2%

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

Developer target: 74.6% accurate, 1.0× 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 2023207 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

  :herbie-target
  (if (< z -1.3793337487235141e+129) (- (* (* 2.0 (sqrt x)) (cos (- (/ 1.0 y) (/ (/ 0.3333333333333333 z) t)))) (/ (/ a 3.0) b)) (if (< z 3.516290613555987e+106) (- (* (* (sqrt x) 2.0) (cos (- y (* (/ t 3.0) z)))) (/ (/ a 3.0) b)) (- (* (cos (- y (/ (/ 0.3333333333333333 z) t))) (* 2.0 (sqrt x))) (/ (/ a b) 3.0))))

  (- (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0)))) (/ a (* b 3.0))))