Rosa's TurbineBenchmark

Percentage Accurate: 85.0% → 98.4%

Time: 9.8s

Precision: binary64

Cost: 8580

• 53.2% of points produce a very large (infinite) output. You may want to add a precondition.

Math

\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]

↓

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;\left(3 + t_0\right) + \frac{\left(r \cdot \left(r \cdot \left(w \cdot w\right)\right)\right) \cdot \left(0.125 \cdot \left(2 \cdot v - 3\right)\right)}{1 - v} \leq 3:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot \frac{0.375 + v \cdot -0.25}{1 - v}\right)\\ \mathbf{else}:\\ \;\;\;\;-1.5 + 2 \cdot {r}^{-2}\\ \end{array} \]

FPCore

(FPCore (v w r)
 :precision binary64
 (-
  (-
   (+ 3.0 (/ 2.0 (* r r)))
   (/ (* (* 0.125 (- 3.0 (* 2.0 v))) (* (* (* w w) r) r)) (- 1.0 v)))
  4.5))

↓

(FPCore (v w r)
 :precision binary64
 (let* ((t_0 (/ 2.0 (* r r))))
   (if (<=
        (+
         (+ 3.0 t_0)
         (/ (* (* r (* r (* w w))) (* 0.125 (- (* 2.0 v) 3.0))) (- 1.0 v)))
        3.0)
     (+
      t_0
      (- -1.5 (* (* r (* w (* r w))) (/ (+ 0.375 (* v -0.25)) (- 1.0 v)))))
     (+ -1.5 (* 2.0 (pow r -2.0))))))

C

double code(double v, double w, double r) {
	return ((3.0 + (2.0 / (r * r))) - (((0.125 * (3.0 - (2.0 * v))) * (((w * w) * r) * r)) / (1.0 - v))) - 4.5;
}

↓

double code(double v, double w, double r) {
	double t_0 = 2.0 / (r * r);
	double tmp;
	if (((3.0 + t_0) + (((r * (r * (w * w))) * (0.125 * ((2.0 * v) - 3.0))) / (1.0 - v))) <= 3.0) {
		tmp = t_0 + (-1.5 - ((r * (w * (r * w))) * ((0.375 + (v * -0.25)) / (1.0 - v))));
	} else {
		tmp = -1.5 + (2.0 * pow(r, -2.0));
	}
	return tmp;
}

Fortran

real(8) function code(v, w, r)
    real(8), intent (in) :: v
    real(8), intent (in) :: w
    real(8), intent (in) :: r
    code = ((3.0d0 + (2.0d0 / (r * r))) - (((0.125d0 * (3.0d0 - (2.0d0 * v))) * (((w * w) * r) * r)) / (1.0d0 - v))) - 4.5d0
end function

↓

real(8) function code(v, w, r)
    real(8), intent (in) :: v
    real(8), intent (in) :: w
    real(8), intent (in) :: r
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 2.0d0 / (r * r)
    if (((3.0d0 + t_0) + (((r * (r * (w * w))) * (0.125d0 * ((2.0d0 * v) - 3.0d0))) / (1.0d0 - v))) <= 3.0d0) then
        tmp = t_0 + ((-1.5d0) - ((r * (w * (r * w))) * ((0.375d0 + (v * (-0.25d0))) / (1.0d0 - v))))
    else
        tmp = (-1.5d0) + (2.0d0 * (r ** (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double v, double w, double r) {
	return ((3.0 + (2.0 / (r * r))) - (((0.125 * (3.0 - (2.0 * v))) * (((w * w) * r) * r)) / (1.0 - v))) - 4.5;
}

↓

public static double code(double v, double w, double r) {
	double t_0 = 2.0 / (r * r);
	double tmp;
	if (((3.0 + t_0) + (((r * (r * (w * w))) * (0.125 * ((2.0 * v) - 3.0))) / (1.0 - v))) <= 3.0) {
		tmp = t_0 + (-1.5 - ((r * (w * (r * w))) * ((0.375 + (v * -0.25)) / (1.0 - v))));
	} else {
		tmp = -1.5 + (2.0 * Math.pow(r, -2.0));
	}
	return tmp;
}

Python

def code(v, w, r):
	return ((3.0 + (2.0 / (r * r))) - (((0.125 * (3.0 - (2.0 * v))) * (((w * w) * r) * r)) / (1.0 - v))) - 4.5

↓

def code(v, w, r):
	t_0 = 2.0 / (r * r)
	tmp = 0
	if ((3.0 + t_0) + (((r * (r * (w * w))) * (0.125 * ((2.0 * v) - 3.0))) / (1.0 - v))) <= 3.0:
		tmp = t_0 + (-1.5 - ((r * (w * (r * w))) * ((0.375 + (v * -0.25)) / (1.0 - v))))
	else:
		tmp = -1.5 + (2.0 * math.pow(r, -2.0))
	return tmp

Julia

function code(v, w, r)
	return Float64(Float64(Float64(3.0 + Float64(2.0 / Float64(r * r))) - Float64(Float64(Float64(0.125 * Float64(3.0 - Float64(2.0 * v))) * Float64(Float64(Float64(w * w) * r) * r)) / Float64(1.0 - v))) - 4.5)
end

↓

function code(v, w, r)
	t_0 = Float64(2.0 / Float64(r * r))
	tmp = 0.0
	if (Float64(Float64(3.0 + t_0) + Float64(Float64(Float64(r * Float64(r * Float64(w * w))) * Float64(0.125 * Float64(Float64(2.0 * v) - 3.0))) / Float64(1.0 - v))) <= 3.0)
		tmp = Float64(t_0 + Float64(-1.5 - Float64(Float64(r * Float64(w * Float64(r * w))) * Float64(Float64(0.375 + Float64(v * -0.25)) / Float64(1.0 - v)))));
	else
		tmp = Float64(-1.5 + Float64(2.0 * (r ^ -2.0)));
	end
	return tmp
end

MATLAB

function tmp = code(v, w, r)
	tmp = ((3.0 + (2.0 / (r * r))) - (((0.125 * (3.0 - (2.0 * v))) * (((w * w) * r) * r)) / (1.0 - v))) - 4.5;
end

↓

function tmp_2 = code(v, w, r)
	t_0 = 2.0 / (r * r);
	tmp = 0.0;
	if (((3.0 + t_0) + (((r * (r * (w * w))) * (0.125 * ((2.0 * v) - 3.0))) / (1.0 - v))) <= 3.0)
		tmp = t_0 + (-1.5 - ((r * (w * (r * w))) * ((0.375 + (v * -0.25)) / (1.0 - v))));
	else
		tmp = -1.5 + (2.0 * (r ^ -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[v_, w_, r_] := N[(N[(N[(3.0 + N[(2.0 / N[(r * r), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(0.125 * N[(3.0 - N[(2.0 * v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(w * w), $MachinePrecision] * r), $MachinePrecision] * r), $MachinePrecision]), $MachinePrecision] / N[(1.0 - v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 4.5), $MachinePrecision]

↓

code[v_, w_, r_] := Block[{t$95$0 = N[(2.0 / N[(r * r), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(3.0 + t$95$0), $MachinePrecision] + N[(N[(N[(r * N[(r * N[(w * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.125 * N[(N[(2.0 * v), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 - v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 3.0], N[(t$95$0 + N[(-1.5 - N[(N[(r * N[(w * N[(r * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(0.375 + N[(v * -0.25), $MachinePrecision]), $MachinePrecision] / N[(1.0 - v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.5 + N[(2.0 * N[Power[r, -2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (/.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) (-.f64 1 v))) < 3

   1. Initial program 84.2%

      \[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]

   2. Simplified 91.1%

      \[\leadsto \color{blue}{\frac{2}{r \cdot r} + \left(-1.5 - \left(r \cdot \left(r \cdot \left(w \cdot w\right)\right)\right) \cdot \frac{0.375 + v \cdot -0.25}{1 - v}\right)} \]
      Step-by-step derivation

      [Start] 84.2%	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]
      associate--l- [=>] 84.2%	\[ \color{blue}{\left(3 + \frac{2}{r \cdot r}\right) - \left(\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v} + 4.5\right)} \]
      +-commutative [=>] 84.2%	\[ \color{blue}{\left(\frac{2}{r \cdot r} + 3\right)} - \left(\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v} + 4.5\right) \]
      associate--l+ [=>] 84.2%	\[ \color{blue}{\frac{2}{r \cdot r} + \left(3 - \left(\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v} + 4.5\right)\right)} \]
      +-commutative [=>] 84.2%	\[ \frac{2}{r \cdot r} + \left(3 - \color{blue}{\left(4.5 + \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)}\right) \]
      associate--r+ [=>] 84.2%	\[ \frac{2}{r \cdot r} + \color{blue}{\left(\left(3 - 4.5\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)} \]
      metadata-eval [=>] 84.2%	\[ \frac{2}{r \cdot r} + \left(\color{blue}{-1.5} - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      associate-*l/ [<=] 91.1%	\[ \frac{2}{r \cdot r} + \left(-1.5 - \color{blue}{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}\right) \]
      *-commutative [=>] 91.1%	\[ \frac{2}{r \cdot r} + \left(-1.5 - \color{blue}{\left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right) \cdot \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v}}\right) \]
      *-commutative [=>] 91.1%	\[ \frac{2}{r \cdot r} + \left(-1.5 - \color{blue}{\left(r \cdot \left(\left(w \cdot w\right) \cdot r\right)\right)} \cdot \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v}\right) \]
      *-commutative [=>] 91.1%	\[ \frac{2}{r \cdot r} + \left(-1.5 - \left(r \cdot \color{blue}{\left(r \cdot \left(w \cdot w\right)\right)}\right) \cdot \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v}\right) \]

   3. Taylor expanded in r around 0 91.1%

      \[\leadsto \frac{2}{r \cdot r} + \left(-1.5 - \left(r \cdot \color{blue}{\left({w}^{2} \cdot r\right)}\right) \cdot \frac{0.375 + v \cdot -0.25}{1 - v}\right) \]

   4. Simplified 99.8%

      \[\leadsto \frac{2}{r \cdot r} + \left(-1.5 - \left(r \cdot \color{blue}{\left(w \cdot \left(w \cdot r\right)\right)}\right) \cdot \frac{0.375 + v \cdot -0.25}{1 - v}\right) \]
      Step-by-step derivation

      [Start] 91.1%	\[ \frac{2}{r \cdot r} + \left(-1.5 - \left(r \cdot \left({w}^{2} \cdot r\right)\right) \cdot \frac{0.375 + v \cdot -0.25}{1 - v}\right) \]
      unpow2 [=>] 91.1%	\[ \frac{2}{r \cdot r} + \left(-1.5 - \left(r \cdot \left(\color{blue}{\left(w \cdot w\right)} \cdot r\right)\right) \cdot \frac{0.375 + v \cdot -0.25}{1 - v}\right) \]
      associate-*l* [=>] 99.8%	\[ \frac{2}{r \cdot r} + \left(-1.5 - \left(r \cdot \color{blue}{\left(w \cdot \left(w \cdot r\right)\right)}\right) \cdot \frac{0.375 + v \cdot -0.25}{1 - v}\right) \]

   if 3 < (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (/.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) (-.f64 1 v)))

   1. Initial program 87.7%

      \[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]

   2. Simplified 87.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(v, 0.25, -0.375\right)}{1 - v}, \left(r \cdot r\right) \cdot \left(w \cdot w\right), \frac{2}{r \cdot r} + -1.5\right)} \]
      Step-by-step derivation

      [Start] 87.7%	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]
      sub-neg [=>] 87.7%	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)\right)} - 4.5 \]
      +-commutative [=>] 87.7%	\[ \color{blue}{\left(\left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(3 + \frac{2}{r \cdot r}\right)\right)} - 4.5 \]
      associate--l+ [=>] 87.7%	\[ \color{blue}{\left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right)} \]
      associate-/l* [=>] 87.7%	\[ \left(-\color{blue}{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{1 - v}{\left(\left(w \cdot w\right) \cdot r\right) \cdot r}}}\right) + \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) \]
      distribute-neg-frac [=>] 87.7%	\[ \color{blue}{\frac{-0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{1 - v}{\left(\left(w \cdot w\right) \cdot r\right) \cdot r}}} + \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) \]
      associate-/r/ [=>] 87.7%	\[ \color{blue}{\frac{-0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)} + \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) \]
      fma-def [=>] 87.7%	\[ \color{blue}{\mathsf{fma}\left(\frac{-0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v}, \left(\left(w \cdot w\right) \cdot r\right) \cdot r, \left(3 + \frac{2}{r \cdot r}\right) - 4.5\right)} \]
      sub-neg [=>] 87.7%	\[ \mathsf{fma}\left(\frac{-0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v}, \left(\left(w \cdot w\right) \cdot r\right) \cdot r, \color{blue}{\left(3 + \frac{2}{r \cdot r}\right) + \left(-4.5\right)}\right) \]

   3. Taylor expanded in r around 0 99.9%

      \[\leadsto \color{blue}{2 \cdot \frac{1}{{r}^{2}} - 1.5} \]

   4. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{2}{r \cdot r} + -1.5} \]
      Step-by-step derivation

      [Start] 99.9%	\[ 2 \cdot \frac{1}{{r}^{2}} - 1.5 \]
      sub-neg [=>] 99.9%	\[ \color{blue}{2 \cdot \frac{1}{{r}^{2}} + \left(-1.5\right)} \]
      associate-*r/ [=>] 99.9%	\[ \color{blue}{\frac{2 \cdot 1}{{r}^{2}}} + \left(-1.5\right) \]
      metadata-eval [=>] 99.9%	\[ \frac{\color{blue}{2}}{{r}^{2}} + \left(-1.5\right) \]
      unpow2 [=>] 99.9%	\[ \frac{2}{\color{blue}{r \cdot r}} + \left(-1.5\right) \]
      metadata-eval [=>] 99.9%	\[ \frac{2}{r \cdot r} + \color{blue}{-1.5} \]

   5. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\sqrt{\frac{2}{r \cdot r}} \cdot \sqrt{\frac{2}{r \cdot r}}} + -1.5 \]
      Step-by-step derivation

      [Start] 99.9%	\[ \frac{2}{r \cdot r} + -1.5 \]
      add-sqr-sqrt [=>] 99.6%	\[ \color{blue}{\sqrt{\frac{2}{r \cdot r}} \cdot \sqrt{\frac{2}{r \cdot r}}} + -1.5 \]

   6. Applied egg-rr 96.3%

      \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(2 \cdot {r}^{-2}\right)} - 1\right)} + -1.5 \]
      Step-by-step derivation

      [Start] 99.6%	\[ \sqrt{\frac{2}{r \cdot r}} \cdot \sqrt{\frac{2}{r \cdot r}} + -1.5 \]
      expm1-log1p-u [=>] 96.3%	\[ \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt{\frac{2}{r \cdot r}} \cdot \sqrt{\frac{2}{r \cdot r}}\right)\right)} + -1.5 \]
      expm1-udef [=>] 96.3%	\[ \color{blue}{\left(e^{\mathsf{log1p}\left(\sqrt{\frac{2}{r \cdot r}} \cdot \sqrt{\frac{2}{r \cdot r}}\right)} - 1\right)} + -1.5 \]
      add-sqr-sqrt [<=] 96.3%	\[ \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{2}{r \cdot r}}\right)} - 1\right) + -1.5 \]
      div-inv [=>] 96.3%	\[ \left(e^{\mathsf{log1p}\left(\color{blue}{2 \cdot \frac{1}{r \cdot r}}\right)} - 1\right) + -1.5 \]
      pow2 [=>] 96.3%	\[ \left(e^{\mathsf{log1p}\left(2 \cdot \frac{1}{\color{blue}{{r}^{2}}}\right)} - 1\right) + -1.5 \]
      pow-flip [=>] 96.3%	\[ \left(e^{\mathsf{log1p}\left(2 \cdot \color{blue}{{r}^{\left(-2\right)}}\right)} - 1\right) + -1.5 \]
      metadata-eval [=>] 96.3%	\[ \left(e^{\mathsf{log1p}\left(2 \cdot {r}^{\color{blue}{-2}}\right)} - 1\right) + -1.5 \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{2 \cdot {r}^{-2}} + -1.5 \]
      Step-by-step derivation

      [Start] 96.3%	\[ \left(e^{\mathsf{log1p}\left(2 \cdot {r}^{-2}\right)} - 1\right) + -1.5 \]
      expm1-def [=>] 96.3%	\[ \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(2 \cdot {r}^{-2}\right)\right)} + -1.5 \]
      expm1-log1p [=>] 100.0%	\[ \color{blue}{2 \cdot {r}^{-2}} + -1.5 \]

3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(3 + \frac{2}{r \cdot r}\right) + \frac{\left(r \cdot \left(r \cdot \left(w \cdot w\right)\right)\right) \cdot \left(0.125 \cdot \left(2 \cdot v - 3\right)\right)}{1 - v} \leq 3:\\ \;\;\;\;\frac{2}{r \cdot r} + \left(-1.5 - \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot \frac{0.375 + v \cdot -0.25}{1 - v}\right)\\ \mathbf{else}:\\ \;\;\;\;-1.5 + 2 \cdot {r}^{-2}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	98.4%
Cost	8580

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;\left(3 + t_0\right) + \frac{\left(r \cdot \left(r \cdot \left(w \cdot w\right)\right)\right) \cdot \left(0.125 \cdot \left(2 \cdot v - 3\right)\right)}{1 - v} \leq 3:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot \frac{0.375 + v \cdot -0.25}{1 - v}\right)\\ \mathbf{else}:\\ \;\;\;\;-1.5 + 2 \cdot {r}^{-2}\\ \end{array} \]

Alternative 2
Accuracy	99.7%
Cost	20800

\[\left(\left(3 + \frac{2}{r \cdot r}\right) - {\left(\frac{\frac{1 - v}{{\left(r \cdot w\right)}^{2}}}{0.125 \cdot \mathsf{fma}\left(-2, v, 3\right)}\right)}^{-1}\right) + -4.5 \]

Alternative 3
Accuracy	98.3%
Cost	3396

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;\left(3 + t_0\right) + \frac{\left(r \cdot \left(r \cdot \left(w \cdot w\right)\right)\right) \cdot \left(0.125 \cdot \left(2 \cdot v - 3\right)\right)}{1 - v} \leq 3:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot \frac{0.375 + v \cdot -0.25}{1 - v}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + -1.5\\ \end{array} \]

Alternative 4
Accuracy	95.3%
Cost	2121

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;w \cdot w \leq 0 \lor \neg \left(w \cdot w \leq 2 \cdot 10^{+295}\right):\\ \;\;\;\;t_0 + \left(-1.5 - r \cdot \left(\left(w \cdot \left(r \cdot w\right)\right) \cdot 0.375\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \frac{0.375 + v \cdot -0.25}{1 - v} \cdot \left(r \cdot \left(r \cdot \left(w \cdot w\right)\right)\right)\right)\\ \end{array} \]

Alternative 5
Accuracy	72.4%
Cost	1106

\[\begin{array}{l} \mathbf{if}\;r \leq -4.8 \cdot 10^{+94} \lor \neg \left(r \leq -125 \lor \neg \left(r \leq -1.05 \cdot 10^{-21}\right) \land r \leq 2.8 \cdot 10^{+51}\right):\\ \;\;\;\;\left(w \cdot w\right) \cdot \left(\left(r \cdot r\right) \cdot -0.375\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{r \cdot r} + -1.5\\ \end{array} \]

Alternative 6
Accuracy	90.9%
Cost	1088

\[\frac{2}{r \cdot r} + \left(-1.5 - r \cdot \left(\left(w \cdot \left(r \cdot w\right)\right) \cdot 0.375\right)\right) \]

Alternative 7
Accuracy	90.9%
Cost	1088

\[\frac{2}{r \cdot r} + \left(-1.5 - r \cdot \left(w \cdot \left(r \cdot \left(w \cdot 0.375\right)\right)\right)\right) \]

Alternative 8
Accuracy	56.1%
Cost	584

\[\begin{array}{l} \mathbf{if}\;r \leq -1.45 \cdot 10^{-8}:\\ \;\;\;\;-1.5\\ \mathbf{elif}\;r \leq 4.6 \cdot 10^{-8}:\\ \;\;\;\;\frac{2}{r \cdot r}\\ \mathbf{else}:\\ \;\;\;\;-1.5\\ \end{array} \]

Alternative 9
Accuracy	57.0%
Cost	448

\[\frac{2}{r \cdot r} + -1.5 \]

Alternative 10
Accuracy	13.9%
Cost	64

\[-1.5 \]

Reproduce

herbie shell --seed 2023178 
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  :precision binary64
  (- (- (+ 3.0 (/ 2.0 (* r r))) (/ (* (* 0.125 (- 3.0 (* 2.0 v))) (* (* (* w w) r) r)) (- 1.0 v))) 4.5))