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

Percentage Accurate: 70.6% → 77.2%

Time: 18.0s

Alternatives: 12

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: 70.6% 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: 77.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 2:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y + \frac{-1}{\frac{3}{z \cdot t}}\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot e^{\log x \cdot 0.5}\right) \cdot \cos y - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b))))
   (if (<= (cos (- y (/ (* z t) 3.0))) 2.0)
     (- (* (* 2.0 (sqrt x)) (cos (+ y (/ -1.0 (/ 3.0 (* z t)))))) t_1)
     (- (* (* 2.0 (exp (* (log x) 0.5))) (cos y)) 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 tmp;
	if (cos((y - ((z * t) / 3.0))) <= 2.0) {
		tmp = ((2.0 * sqrt(x)) * cos((y + (-1.0 / (3.0 / (z * t)))))) - t_1;
	} else {
		tmp = ((2.0 * exp((log(x) * 0.5))) * cos(y)) - 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) :: tmp
    t_1 = a / (3.0d0 * b)
    if (cos((y - ((z * t) / 3.0d0))) <= 2.0d0) then
        tmp = ((2.0d0 * sqrt(x)) * cos((y + ((-1.0d0) / (3.0d0 / (z * t)))))) - t_1
    else
        tmp = ((2.0d0 * exp((log(x) * 0.5d0))) * cos(y)) - 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 tmp;
	if (Math.cos((y - ((z * t) / 3.0))) <= 2.0) {
		tmp = ((2.0 * Math.sqrt(x)) * Math.cos((y + (-1.0 / (3.0 / (z * t)))))) - t_1;
	} else {
		tmp = ((2.0 * Math.exp((Math.log(x) * 0.5))) * Math.cos(y)) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	tmp = 0
	if math.cos((y - ((z * t) / 3.0))) <= 2.0:
		tmp = ((2.0 * math.sqrt(x)) * math.cos((y + (-1.0 / (3.0 / (z * t)))))) - t_1
	else:
		tmp = ((2.0 * math.exp((math.log(x) * 0.5))) * math.cos(y)) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	tmp = 0.0
	if (cos(Float64(y - Float64(Float64(z * t) / 3.0))) <= 2.0)
		tmp = Float64(Float64(Float64(2.0 * sqrt(x)) * cos(Float64(y + Float64(-1.0 / Float64(3.0 / Float64(z * t)))))) - t_1);
	else
		tmp = Float64(Float64(Float64(2.0 * exp(Float64(log(x) * 0.5))) * cos(y)) - t_1);
	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 (cos((y - ((z * t) / 3.0))) <= 2.0)
		tmp = ((2.0 * sqrt(x)) * cos((y + (-1.0 / (3.0 / (z * t)))))) - t_1;
	else
		tmp = ((2.0 * exp((log(x) * 0.5))) * cos(y)) - 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]}, If[LessEqual[N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 2.0], N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(y + N[(-1.0 / N[(3.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(2.0 * N[Exp[N[(N[Log[x], $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 79.9%

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

      1. clear-num N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{1}{\frac{3}{z \cdot t}}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(1, \left(\frac{3}{z \cdot t}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(3, \left(z \cdot t\right)\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      4. *-lowering-*.f64 79.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(3, \mathsf{*.f64}\left(z, t\right)\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   4. Applied egg-rr 79.9%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   4. Step-by-step derivation

      1. cos-lowering-cos.f64 53.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   5. Simplified 53.2%

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

      1. pow1/2 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left({x}^{\frac{1}{2}}\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      2. pow-to-exp N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left(e^{\log x \cdot \frac{1}{2}}\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{exp.f64}\left(\left(\log x \cdot \frac{1}{2}\right)\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(\log x, \frac{1}{2}\right)\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      5. log-lowering-log.f64 53.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(x\right), \frac{1}{2}\right)\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   7. Applied egg-rr 53.2%

      \[\leadsto \left(2 \cdot \color{blue}{e^{\log x \cdot 0.5}}\right) \cdot \cos y - \frac{a}{b \cdot 3} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 2:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y + \frac{-1}{\frac{3}{z \cdot t}}\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot e^{\log x \cdot 0.5}\right) \cdot \cos y - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ t_2 := \frac{a}{3 \cdot b}\\ t_3 := \cos \left(y - \frac{z \cdot t}{3}\right) \cdot t\_1 - t\_2\\ \mathbf{if}\;t\_3 \leq 2 \cdot 10^{+144}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \cos y - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x)))
        (t_2 (/ a (* 3.0 b)))
        (t_3 (- (* (cos (- y (/ (* z t) 3.0))) t_1) t_2)))
   (if (<= t_3 2e+144) t_3 (- (* t_1 (cos y)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * sqrt(x);
	double t_2 = a / (3.0 * b);
	double t_3 = (cos((y - ((z * t) / 3.0))) * t_1) - t_2;
	double tmp;
	if (t_3 <= 2e+144) {
		tmp = t_3;
	} else {
		tmp = (t_1 * cos(y)) - t_2;
	}
	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 = 2.0d0 * sqrt(x)
    t_2 = a / (3.0d0 * b)
    t_3 = (cos((y - ((z * t) / 3.0d0))) * t_1) - t_2
    if (t_3 <= 2d+144) then
        tmp = t_3
    else
        tmp = (t_1 * cos(y)) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * Math.sqrt(x);
	double t_2 = a / (3.0 * b);
	double t_3 = (Math.cos((y - ((z * t) / 3.0))) * t_1) - t_2;
	double tmp;
	if (t_3 <= 2e+144) {
		tmp = t_3;
	} else {
		tmp = (t_1 * Math.cos(y)) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 2.0 * math.sqrt(x)
	t_2 = a / (3.0 * b)
	t_3 = (math.cos((y - ((z * t) / 3.0))) * t_1) - t_2
	tmp = 0
	if t_3 <= 2e+144:
		tmp = t_3
	else:
		tmp = (t_1 * math.cos(y)) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	t_2 = Float64(a / Float64(3.0 * b))
	t_3 = Float64(Float64(cos(Float64(y - Float64(Float64(z * t) / 3.0))) * t_1) - t_2)
	tmp = 0.0
	if (t_3 <= 2e+144)
		tmp = t_3;
	else
		tmp = Float64(Float64(t_1 * cos(y)) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 2.0 * sqrt(x);
	t_2 = a / (3.0 * b);
	t_3 = (cos((y - ((z * t) / 3.0))) * t_1) - t_2;
	tmp = 0.0;
	if (t_3 <= 2e+144)
		tmp = t_3;
	else
		tmp = (t_1 * cos(y)) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

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]}, Block[{t$95$3 = N[(N[(N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]}, If[LessEqual[t$95$3, 2e+144], t$95$3, N[(N[(t$95$1 * N[Cos[y], $MachinePrecision]), $MachinePrecision] - t$95$2), $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)))) < 2.00000000000000005e144

   1. Initial program 77.2%

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

   if 2.00000000000000005e144 < (-.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 48.6%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   4. Step-by-step derivation

      1. cos-lowering-cos.f64 75.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   5. Simplified 75.3%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \cdot \left(2 \cdot \sqrt{x}\right) - \frac{a}{3 \cdot b} \leq 2 \cdot 10^{+144}:\\ \;\;\;\;\cos \left(y - \frac{z \cdot t}{3}\right) \cdot \left(2 \cdot \sqrt{x}\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.2% accurate, 0.7× speedup

Math

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

FPCore

(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))) 1.0)
     (- (* t_1 (cos (+ y (/ -1.0 (/ 3.0 (* z t)))))) t_2)
     (- (* t_1 (cos y)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * sqrt(x);
	double t_2 = a / (3.0 * b);
	double tmp;
	if (cos((y - ((z * t) / 3.0))) <= 1.0) {
		tmp = (t_1 * cos((y + (-1.0 / (3.0 / (z * t)))))) - t_2;
	} else {
		tmp = (t_1 * cos(y)) - t_2;
	}
	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 = 2.0d0 * sqrt(x)
    t_2 = a / (3.0d0 * b)
    if (cos((y - ((z * t) / 3.0d0))) <= 1.0d0) then
        tmp = (t_1 * cos((y + ((-1.0d0) / (3.0d0 / (z * t)))))) - t_2
    else
        tmp = (t_1 * cos(y)) - t_2
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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 (cos(Float64(y - Float64(Float64(z * t) / 3.0))) <= 1.0)
		tmp = Float64(Float64(t_1 * cos(Float64(y + Float64(-1.0 / Float64(3.0 / Float64(z * t)))))) - t_2);
	else
		tmp = Float64(Float64(t_1 * cos(y)) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 2.0 * sqrt(x);
	t_2 = a / (3.0 * b);
	tmp = 0.0;
	if (cos((y - ((z * t) / 3.0))) <= 1.0)
		tmp = (t_1 * cos((y + (-1.0 / (3.0 / (z * t)))))) - t_2;
	else
		tmp = (t_1 * cos(y)) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

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[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 1.0], N[(N[(t$95$1 * N[Cos[N[(y + N[(-1.0 / N[(3.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(t$95$1 * N[Cos[y], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))) < 1

   1. Initial program 79.9%

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

      1. clear-num N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{1}{\frac{3}{z \cdot t}}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(1, \left(\frac{3}{z \cdot t}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(3, \left(z \cdot t\right)\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      4. *-lowering-*.f64 79.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(3, \mathsf{*.f64}\left(z, t\right)\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   4. Applied egg-rr 79.9%

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

   if 1 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))

   1. Initial program 0.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   4. Step-by-step derivation

      1. cos-lowering-cos.f64 53.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   5. Simplified 53.2%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 1:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y + \frac{-1}{\frac{3}{z \cdot t}}\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := 2 \cdot \sqrt{x} - t\_1\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-107}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-142}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos \left(t \cdot \left(z \cdot 0.3333333333333333\right) - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b))) (t_2 (- (* 2.0 (sqrt x)) t_1)))
   (if (<= t_1 -2e-107)
     t_2
     (if (<= t_1 2e-142)
       (* 2.0 (* (sqrt x) (cos (- (* t (* z 0.3333333333333333)) y))))
       t_2))))

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 = (2.0 * sqrt(x)) - t_1;
	double tmp;
	if (t_1 <= -2e-107) {
		tmp = t_2;
	} else if (t_1 <= 2e-142) {
		tmp = 2.0 * (sqrt(x) * cos(((t * (z * 0.3333333333333333)) - y)));
	} else {
		tmp = t_2;
	}
	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 = (2.0d0 * sqrt(x)) - t_1
    if (t_1 <= (-2d-107)) then
        tmp = t_2
    else if (t_1 <= 2d-142) then
        tmp = 2.0d0 * (sqrt(x) * cos(((t * (z * 0.3333333333333333d0)) - y)))
    else
        tmp = t_2
    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 = (2.0 * Math.sqrt(x)) - t_1;
	double tmp;
	if (t_1 <= -2e-107) {
		tmp = t_2;
	} else if (t_1 <= 2e-142) {
		tmp = 2.0 * (Math.sqrt(x) * Math.cos(((t * (z * 0.3333333333333333)) - y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	t_2 = (2.0 * math.sqrt(x)) - t_1
	tmp = 0
	if t_1 <= -2e-107:
		tmp = t_2
	elif t_1 <= 2e-142:
		tmp = 2.0 * (math.sqrt(x) * math.cos(((t * (z * 0.3333333333333333)) - y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	t_2 = Float64(Float64(2.0 * sqrt(x)) - t_1)
	tmp = 0.0
	if (t_1 <= -2e-107)
		tmp = t_2;
	elseif (t_1 <= 2e-142)
		tmp = Float64(2.0 * Float64(sqrt(x) * cos(Float64(Float64(t * Float64(z * 0.3333333333333333)) - y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	t_2 = (2.0 * sqrt(x)) - t_1;
	tmp = 0.0;
	if (t_1 <= -2e-107)
		tmp = t_2;
	elseif (t_1 <= 2e-142)
		tmp = 2.0 * (sqrt(x) * cos(((t * (z * 0.3333333333333333)) - y)));
	else
		tmp = t_2;
	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[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-107], t$95$2, If[LessEqual[t$95$1, 2e-142], N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[Cos[N[(N[(t * N[(z * 0.3333333333333333), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 a (*.f64 b #s(literal 3 binary64))) < -2e-107 or 2.0000000000000001e-142 < (/.f64 a (*.f64 b #s(literal 3 binary64)))

   1. Initial program 77.1%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   4. Step-by-step derivation

      1. cos-lowering-cos.f64 85.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   5. Simplified 85.3%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(2 \cdot \sqrt{x}\right)}, \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \left(\sqrt{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      2. sqrt-lowering-sqrt.f64 81.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   8. Simplified 81.4%

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

   if -2e-107 < (/.f64 a (*.f64 b #s(literal 3 binary64))) < 2.0000000000000001e-142

   1. Initial program 57.6%

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

   3. Taylor expanded in x around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{x} \cdot \cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \cos \color{blue}{\left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)}\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \cos \left(y + \left(\mathsf{neg}\left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right)\right)\right) \]

      5. remove-double-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \cos \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \left(\mathsf{neg}\left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \cos \left(\left(\mathsf{neg}\left(-1 \cdot y\right)\right) + \left(\mathsf{neg}\left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right)\right)\right) \]

      7. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \cos \left(\mathsf{neg}\left(\left(-1 \cdot y + \frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right)\right)\right) \]

      8. cos-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \cos \left(-1 \cdot y + \frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\left(-1 \cdot y + \frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\left(\frac{1}{3} \cdot \left(t \cdot z\right) + -1 \cdot y\right)\right)\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\left(\frac{1}{3} \cdot \left(t \cdot z\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\left(\frac{1}{3} \cdot \left(t \cdot z\right) - y\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\left(\frac{1}{3} \cdot \left(t \cdot z\right)\right), y\right)\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\left(\left(t \cdot z\right) \cdot \frac{1}{3}\right), y\right)\right)\right)\right) \]

      15. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\left(t \cdot \left(z \cdot \frac{1}{3}\right)\right), y\right)\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\left(t \cdot \left(z \cdot \left(\mathsf{neg}\left(\frac{-1}{3}\right)\right)\right)\right), y\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\left(t \cdot \left(\mathsf{neg}\left(z \cdot \frac{-1}{3}\right)\right)\right), y\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\left(t \cdot \left(\mathsf{neg}\left(\frac{-1}{3} \cdot z\right)\right)\right), y\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\left(t \cdot \left(\left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot z\right)\right), y\right)\right)\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\left(t \cdot \left(\frac{1}{3} \cdot z\right)\right), y\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{1}{3} \cdot z\right)\right), y\right)\right)\right)\right) \]

      22. *-lowering-*.f64 57.5%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{3}, z\right)\right), y\right)\right)\right)\right) \]

   5. Simplified 57.5%

      \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos \left(t \cdot \left(0.3333333333333333 \cdot z\right) - y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{3 \cdot b} \leq -2 \cdot 10^{-107}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \mathbf{elif}\;\frac{a}{3 \cdot b} \leq 2 \cdot 10^{-142}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos \left(t \cdot \left(z \cdot 0.3333333333333333\right) - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := 2 \cdot \sqrt{x} - t\_1\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-107}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-142}:\\ \;\;\;\;\sqrt{x} \cdot \left(2 \cdot \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b))) (t_2 (- (* 2.0 (sqrt x)) t_1)))
   (if (<= t_1 -2e-107)
     t_2
     (if (<= t_1 2e-142) (* (sqrt x) (* 2.0 (cos y))) t_2))))

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 = (2.0 * sqrt(x)) - t_1;
	double tmp;
	if (t_1 <= -2e-107) {
		tmp = t_2;
	} else if (t_1 <= 2e-142) {
		tmp = sqrt(x) * (2.0 * cos(y));
	} else {
		tmp = t_2;
	}
	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 = (2.0d0 * sqrt(x)) - t_1
    if (t_1 <= (-2d-107)) then
        tmp = t_2
    else if (t_1 <= 2d-142) then
        tmp = sqrt(x) * (2.0d0 * cos(y))
    else
        tmp = t_2
    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 = (2.0 * Math.sqrt(x)) - t_1;
	double tmp;
	if (t_1 <= -2e-107) {
		tmp = t_2;
	} else if (t_1 <= 2e-142) {
		tmp = Math.sqrt(x) * (2.0 * Math.cos(y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	t_2 = (2.0 * math.sqrt(x)) - t_1
	tmp = 0
	if t_1 <= -2e-107:
		tmp = t_2
	elif t_1 <= 2e-142:
		tmp = math.sqrt(x) * (2.0 * math.cos(y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	t_2 = Float64(Float64(2.0 * sqrt(x)) - t_1)
	tmp = 0.0
	if (t_1 <= -2e-107)
		tmp = t_2;
	elseif (t_1 <= 2e-142)
		tmp = Float64(sqrt(x) * Float64(2.0 * cos(y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	t_2 = (2.0 * sqrt(x)) - t_1;
	tmp = 0.0;
	if (t_1 <= -2e-107)
		tmp = t_2;
	elseif (t_1 <= 2e-142)
		tmp = sqrt(x) * (2.0 * cos(y));
	else
		tmp = t_2;
	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[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-107], t$95$2, If[LessEqual[t$95$1, 2e-142], N[(N[Sqrt[x], $MachinePrecision] * N[(2.0 * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 a (*.f64 b #s(literal 3 binary64))) < -2e-107 or 2.0000000000000001e-142 < (/.f64 a (*.f64 b #s(literal 3 binary64)))

   1. Initial program 77.1%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   4. Step-by-step derivation

      1. cos-lowering-cos.f64 85.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   5. Simplified 85.3%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(2 \cdot \sqrt{x}\right)}, \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \left(\sqrt{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      2. sqrt-lowering-sqrt.f64 81.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   8. Simplified 81.4%

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

   if -2e-107 < (/.f64 a (*.f64 b #s(literal 3 binary64))) < 2.0000000000000001e-142

   1. Initial program 57.6%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   4. Step-by-step derivation

      1. cos-lowering-cos.f64 54.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   5. Simplified 54.6%

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

   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

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(2 \cdot \cos y\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{2} \cdot \cos y\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{*.f64}\left(2, \color{blue}{\cos y}\right)\right) \]

      7. cos-lowering-cos.f64 54.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{*.f64}\left(2, \mathsf{cos.f64}\left(y\right)\right)\right) \]

   8. Simplified 54.6%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{3 \cdot b} \leq -2 \cdot 10^{-107}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \mathbf{elif}\;\frac{a}{3 \cdot b} \leq 2 \cdot 10^{-142}:\\ \;\;\;\;\sqrt{x} \cdot \left(2 \cdot \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 70.5%

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

3. Taylor expanded in z around 0

   \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
4. Step-by-step derivation

   1. cos-lowering-cos.f64 74.9%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

5. Simplified 74.9%

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

6. Final simplification 74.9%

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

Alternative 7: 60.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := \frac{a}{b \cdot \left(0 - 3\right)}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-124}:\\ \;\;\;\;2 \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b))) (t_2 (/ a (* b (- 0.0 3.0)))))
   (if (<= t_1 -2e-49) t_2 (if (<= t_1 1e-124) (* 2.0 (sqrt x)) t_2))))

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 = a / (b * (0.0 - 3.0));
	double tmp;
	if (t_1 <= -2e-49) {
		tmp = t_2;
	} else if (t_1 <= 1e-124) {
		tmp = 2.0 * sqrt(x);
	} else {
		tmp = t_2;
	}
	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 = a / (b * (0.0d0 - 3.0d0))
    if (t_1 <= (-2d-49)) then
        tmp = t_2
    else if (t_1 <= 1d-124) then
        tmp = 2.0d0 * sqrt(x)
    else
        tmp = t_2
    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 = a / (b * (0.0 - 3.0));
	double tmp;
	if (t_1 <= -2e-49) {
		tmp = t_2;
	} else if (t_1 <= 1e-124) {
		tmp = 2.0 * Math.sqrt(x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	t_2 = a / (b * (0.0 - 3.0))
	tmp = 0
	if t_1 <= -2e-49:
		tmp = t_2
	elif t_1 <= 1e-124:
		tmp = 2.0 * math.sqrt(x)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	t_2 = Float64(a / Float64(b * Float64(0.0 - 3.0)))
	tmp = 0.0
	if (t_1 <= -2e-49)
		tmp = t_2;
	elseif (t_1 <= 1e-124)
		tmp = Float64(2.0 * sqrt(x));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	t_2 = a / (b * (0.0 - 3.0));
	tmp = 0.0;
	if (t_1 <= -2e-49)
		tmp = t_2;
	elseif (t_1 <= 1e-124)
		tmp = 2.0 * sqrt(x);
	else
		tmp = t_2;
	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[(a / N[(b * N[(0.0 - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-49], t$95$2, If[LessEqual[t$95$1, 1e-124], 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))) < -1.99999999999999987e-49 or 9.99999999999999933e-125 < (/.f64 a (*.f64 b #s(literal 3 binary64)))

   1. Initial program 79.2%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{a}{b}\right), \color{blue}{\frac{-1}{3}}\right) \]

      3. /-lowering-/.f64 80.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, b\right), \frac{-1}{3}\right) \]

   5. Simplified 80.3%

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

      1. associate-*l/ N/A

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

      2. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{\frac{-1}{3}}{b}\right)}\right) \]

      4. /-lowering-/.f64 80.3%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(\frac{-1}{3}, \color{blue}{b}\right)\right) \]

   7. Applied egg-rr 80.3%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

      3. div-inv N/A

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

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

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

      7. distribute-neg-frac2 N/A

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

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

         \[\leadsto \mathsf{neg.f64}\left(\left(\frac{a}{b \cdot 3}\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{/.f64}\left(a, \left(b \cdot 3\right)\right)\right) \]

      10. *-lowering-*.f64 80.4%

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   9. Applied egg-rr 80.4%

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

   if -1.99999999999999987e-49 < (/.f64 a (*.f64 b #s(literal 3 binary64))) < 9.99999999999999933e-125

   1. Initial program 56.8%

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

      1. clear-num N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{1}{\frac{3}{z \cdot t}}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(1, \left(\frac{3}{z \cdot t}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(3, \left(z \cdot t\right)\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      4. *-lowering-*.f64 56.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(3, \mathsf{*.f64}\left(z, t\right)\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   4. Applied egg-rr 56.6%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\left(\cos y + \frac{1}{3} \cdot \left(t \cdot \left(z \cdot \sin y\right)\right)\right)}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\cos y + \frac{1}{3} \cdot \left(\left(z \cdot \sin y\right) \cdot t\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\cos y + \left(\frac{1}{3} \cdot \left(z \cdot \sin y\right)\right) \cdot t\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\cos y, \left(\left(\frac{1}{3} \cdot \left(z \cdot \sin y\right)\right) \cdot t\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \left(\left(\frac{1}{3} \cdot \left(z \cdot \sin y\right)\right) \cdot t\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \left(\frac{1}{3} \cdot \left(\left(z \cdot \sin y\right) \cdot t\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \left(\frac{1}{3} \cdot \left(t \cdot \left(z \cdot \sin y\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{*.f64}\left(\frac{1}{3}, \left(t \cdot \left(z \cdot \sin y\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{*.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(t, \left(z \cdot \sin y\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{*.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \sin y\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      10. sin-lowering-sin.f64 49.5%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{*.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \mathsf{sin.f64}\left(y\right)\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   7. Simplified 49.5%

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

   8. Taylor expanded in x around inf

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

      1. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(2 \cdot \sqrt{x}\right), \color{blue}{\left(\cos y + \frac{1}{3} \cdot \left(t \cdot \left(z \cdot \sin y\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left(\sqrt{x}\right)\right), \left(\color{blue}{\cos y} + \frac{1}{3} \cdot \left(t \cdot \left(z \cdot \sin y\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\cos y + \frac{1}{3} \cdot \left(t \cdot \left(z \cdot \sin y\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\cos y, \color{blue}{\left(\frac{1}{3} \cdot \left(t \cdot \left(z \cdot \sin y\right)\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \left(\color{blue}{\frac{1}{3}} \cdot \left(t \cdot \left(z \cdot \sin y\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{*.f64}\left(\frac{1}{3}, \color{blue}{\left(t \cdot \left(z \cdot \sin y\right)\right)}\right)\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{*.f64}\left(\frac{1}{3}, \left(\left(t \cdot z\right) \cdot \color{blue}{\sin y}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{*.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(\left(t \cdot z\right), \color{blue}{\sin y}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{*.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), \sin \color{blue}{y}\right)\right)\right)\right) \]

      11. sin-lowering-sin.f64 48.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{*.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{sin.f64}\left(y\right)\right)\right)\right)\right) \]

   10. Simplified 48.5%

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

   11. Taylor expanded in y around 0

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

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

          \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{x}\right)}\right) \]

       2. sqrt-lowering-sqrt.f64 27.4%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right) \]

   13. Simplified 27.4%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{3 \cdot b} \leq -2 \cdot 10^{-49}:\\ \;\;\;\;\frac{a}{b \cdot \left(0 - 3\right)}\\ \mathbf{elif}\;\frac{a}{3 \cdot b} \leq 10^{-124}:\\ \;\;\;\;2 \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{b \cdot \left(0 - 3\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.6% 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 70.5%

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

3. Taylor expanded in z around 0

   \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
4. Step-by-step derivation

   1. cos-lowering-cos.f64 74.9%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

5. Simplified 74.9%

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

6. Taylor expanded in y around 0

   \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(2 \cdot \sqrt{x}\right)}, \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
7. Step-by-step derivation

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \left(\sqrt{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   2. sqrt-lowering-sqrt.f64 63.2%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

8. Simplified 63.2%

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

9. Final simplification 63.2%

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

Alternative 9: 50.9% accurate, 31.0× speedup

Math

\[\begin{array}{l} \\ \frac{a}{b \cdot \left(0 - 3\right)} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ a (* b (- 0.0 3.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return a / (b * (0.0 - 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 * (0.0d0 - 3.0d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return a / (b * (0.0 - 3.0));
}

Python

def code(x, y, z, t, a, b):
	return a / (b * (0.0 - 3.0))

Julia

function code(x, y, z, t, a, b)
	return Float64(a / Float64(b * Float64(0.0 - 3.0)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = a / (b * (0.0 - 3.0));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(a / N[(b * N[(0.0 - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.5%

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

3. Taylor expanded in a around inf

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

   1. *-commutative N/A

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

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

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{a}{b}\right), \color{blue}{\frac{-1}{3}}\right) \]

   3. /-lowering-/.f64 51.3%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, b\right), \frac{-1}{3}\right) \]

5. Simplified 51.3%

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

   1. associate-*l/ N/A

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

   2. associate-/l* N/A

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

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

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{\frac{-1}{3}}{b}\right)}\right) \]

   4. /-lowering-/.f64 51.3%

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(\frac{-1}{3}, \color{blue}{b}\right)\right) \]

7. Applied egg-rr 51.3%

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

   1. clear-num N/A

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

   2. un-div-inv N/A

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

   3. div-inv N/A

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

   4. metadata-eval N/A

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

   5. metadata-eval N/A

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

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

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

   7. distribute-neg-frac2 N/A

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

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

      \[\leadsto \mathsf{neg.f64}\left(\left(\frac{a}{b \cdot 3}\right)\right) \]

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

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{/.f64}\left(a, \left(b \cdot 3\right)\right)\right) \]

   10. *-lowering-*.f64 51.4%

       \[\leadsto \mathsf{neg.f64}\left(\mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

9. Applied egg-rr 51.4%

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

10. Final simplification 51.4%

    \[\leadsto \frac{a}{b \cdot \left(0 - 3\right)} \]
11. Add Preprocessing

Alternative 10: 50.8% accurate, 43.4× speedup

Math

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

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

Derivation

1. Initial program 70.5%

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

3. Taylor expanded in a around inf

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

   1. *-commutative N/A

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

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

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{a}{b}\right), \color{blue}{\frac{-1}{3}}\right) \]

   3. /-lowering-/.f64 51.3%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, b\right), \frac{-1}{3}\right) \]

5. Simplified 51.3%

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

   1. associate-*l/ N/A

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

   2. associate-/l* N/A

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

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

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{\frac{-1}{3}}{b}\right)}\right) \]

   4. /-lowering-/.f64 51.3%

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(\frac{-1}{3}, \color{blue}{b}\right)\right) \]

7. Applied egg-rr 51.3%

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

   1. clear-num N/A

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

   2. un-div-inv N/A

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

   3. div-inv N/A

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

   4. metadata-eval N/A

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

   5. metadata-eval N/A

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

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

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

   7. distribute-neg-frac2 N/A

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

   8. associate-/r* N/A

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

   9. distribute-neg-frac2 N/A

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

   10. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\left(\frac{a}{b}\right), \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right) \]

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

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), \left(\mathsf{neg}\left(\color{blue}{3}\right)\right)\right) \]

   12. metadata-eval 51.4%

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), -3\right) \]

9. Applied egg-rr 51.4%

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

Alternative 11: 50.8% 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 70.5%

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

3. Taylor expanded in a around inf

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

   1. *-commutative N/A

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

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

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{a}{b}\right), \color{blue}{\frac{-1}{3}}\right) \]

   3. /-lowering-/.f64 51.3%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, b\right), \frac{-1}{3}\right) \]

5. Simplified 51.3%

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

Alternative 12: 50.8% 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 70.5%

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

3. Taylor expanded in a around inf

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

   1. *-commutative N/A

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

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

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{a}{b}\right), \color{blue}{\frac{-1}{3}}\right) \]

   3. /-lowering-/.f64 51.3%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, b\right), \frac{-1}{3}\right) \]

5. Simplified 51.3%

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

   1. associate-*l/ N/A

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

   2. associate-/l* N/A

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

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

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{\frac{-1}{3}}{b}\right)}\right) \]

   4. /-lowering-/.f64 51.3%

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(\frac{-1}{3}, \color{blue}{b}\right)\right) \]

7. Applied egg-rr 51.3%

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

Developer Target 1: 74.3% 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 2024152 
(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))))