Rosa's TurbineBenchmark

Average Error: 12.9 → 0.8

Time: 17.7s

Precision: binary64

Cost: 1864

Math

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

↓

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -4 \cdot 10^{+185}:\\ \;\;\;\;-4.5 + \left(\left(t_0 + 3\right) - \frac{r \cdot \left(r \cdot w\right)}{\frac{4}{w}}\right)\\ \mathbf{elif}\;v \leq 225:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \frac{\left(r \cdot w\right) \cdot \left(-0.375 - v \cdot -0.25\right)}{1 - v}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r}}\right)\\ \end{array} \]

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 (<= v -4e+185)
     (+ -4.5 (- (+ t_0 3.0) (/ (* r (* r w)) (/ 4.0 w))))
     (if (<= v 225.0)
       (+
        t_0
        (+ -1.5 (* (* r w) (/ (* (* r w) (- -0.375 (* v -0.25))) (- 1.0 v)))))
       (+ t_0 (- -1.5 (* (* r w) (/ w (/ 4.0 r)))))))))

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 (v <= -4e+185) {
		tmp = -4.5 + ((t_0 + 3.0) - ((r * (r * w)) / (4.0 / w)));
	} else if (v <= 225.0) {
		tmp = t_0 + (-1.5 + ((r * w) * (((r * w) * (-0.375 - (v * -0.25))) / (1.0 - v))));
	} else {
		tmp = t_0 + (-1.5 - ((r * w) * (w / (4.0 / r))));
	}
	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 (v <= (-4d+185)) then
        tmp = (-4.5d0) + ((t_0 + 3.0d0) - ((r * (r * w)) / (4.0d0 / w)))
    else if (v <= 225.0d0) then
        tmp = t_0 + ((-1.5d0) + ((r * w) * (((r * w) * ((-0.375d0) - (v * (-0.25d0)))) / (1.0d0 - v))))
    else
        tmp = t_0 + ((-1.5d0) - ((r * w) * (w / (4.0d0 / r))))
    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 (v <= -4e+185) {
		tmp = -4.5 + ((t_0 + 3.0) - ((r * (r * w)) / (4.0 / w)));
	} else if (v <= 225.0) {
		tmp = t_0 + (-1.5 + ((r * w) * (((r * w) * (-0.375 - (v * -0.25))) / (1.0 - v))));
	} else {
		tmp = t_0 + (-1.5 - ((r * w) * (w / (4.0 / r))));
	}
	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 v <= -4e+185:
		tmp = -4.5 + ((t_0 + 3.0) - ((r * (r * w)) / (4.0 / w)))
	elif v <= 225.0:
		tmp = t_0 + (-1.5 + ((r * w) * (((r * w) * (-0.375 - (v * -0.25))) / (1.0 - v))))
	else:
		tmp = t_0 + (-1.5 - ((r * w) * (w / (4.0 / r))))
	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 (v <= -4e+185)
		tmp = Float64(-4.5 + Float64(Float64(t_0 + 3.0) - Float64(Float64(r * Float64(r * w)) / Float64(4.0 / w))));
	elseif (v <= 225.0)
		tmp = Float64(t_0 + Float64(-1.5 + Float64(Float64(r * w) * Float64(Float64(Float64(r * w) * Float64(-0.375 - Float64(v * -0.25))) / Float64(1.0 - v)))));
	else
		tmp = Float64(t_0 + Float64(-1.5 - Float64(Float64(r * w) * Float64(w / Float64(4.0 / r)))));
	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 (v <= -4e+185)
		tmp = -4.5 + ((t_0 + 3.0) - ((r * (r * w)) / (4.0 / w)));
	elseif (v <= 225.0)
		tmp = t_0 + (-1.5 + ((r * w) * (((r * w) * (-0.375 - (v * -0.25))) / (1.0 - v))));
	else
		tmp = t_0 + (-1.5 - ((r * w) * (w / (4.0 / r))));
	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[v, -4e+185], N[(-4.5 + N[(N[(t$95$0 + 3.0), $MachinePrecision] - N[(N[(r * N[(r * w), $MachinePrecision]), $MachinePrecision] / N[(4.0 / w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[v, 225.0], N[(t$95$0 + N[(-1.5 + N[(N[(r * w), $MachinePrecision] * N[(N[(N[(r * w), $MachinePrecision] * N[(-0.375 - N[(v * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 - v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(-1.5 - N[(N[(r * w), $MachinePrecision] * N[(w / N[(4.0 / r), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if v < -3.9999999999999999e185

   1. Initial program 22.8

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

   2. Simplified 9.5

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

      [Start] 22.8	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]
      sub-neg [=>] 22.8	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(-4.5\right)} \]
      associate-*l/ [<=] 9.5	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}\right) + \left(-4.5\right) \]
      *-commutative [=>] 9.5	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \color{blue}{\left(r \cdot \left(\left(w \cdot w\right) \cdot r\right)\right)}\right) + \left(-4.5\right) \]
      *-commutative [=>] 9.5	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \color{blue}{\left(r \cdot \left(w \cdot w\right)\right)}\right)\right) + \left(-4.5\right) \]
      metadata-eval [=>] 9.5	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \left(r \cdot \left(w \cdot w\right)\right)\right)\right) + \color{blue}{-4.5} \]

   3. Applied egg-rr 4.1

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

   4. Taylor expanded in v around inf 4.1

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{r \cdot \left(r \cdot w\right)}{\color{blue}{\frac{4}{w}}}\right) + -4.5 \]

   if -3.9999999999999999e185 < v < 225

   1. Initial program 9.6

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

   2. Simplified 0.3

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

      [Start] 9.6	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]
      sub-neg [=>] 9.6	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)\right)} - 4.5 \]
      +-commutative [=>] 9.6	\[ \color{blue}{\left(\left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(3 + \frac{2}{r \cdot r}\right)\right)} - 4.5 \]
      associate--l+ [=>] 9.6	\[ \color{blue}{\left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right)} \]
      +-commutative [=>] 9.6	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)} \]
      sub-neg [=>] 9.6	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) + \left(-4.5\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      +-commutative [=>] 9.6	\[ \color{blue}{\left(\left(-4.5\right) + \left(3 + \frac{2}{r \cdot r}\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      associate-+r+ [=>] 9.6	\[ \color{blue}{\left(\left(\left(-4.5\right) + 3\right) + \frac{2}{r \cdot r}\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      +-commutative [<=] 9.6	\[ \color{blue}{\left(\frac{2}{r \cdot r} + \left(\left(-4.5\right) + 3\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      associate-+r+ [<=] 9.6	\[ \color{blue}{\frac{2}{r \cdot r} + \left(\left(\left(-4.5\right) + 3\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)\right)} \]

   3. Taylor expanded in w around inf 0.4

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

   if 225 < v

   1. Initial program 17.4

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

   2. Simplified 0.3

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

      [Start] 17.4	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]
      sub-neg [=>] 17.4	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)\right)} - 4.5 \]
      +-commutative [=>] 17.4	\[ \color{blue}{\left(\left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(3 + \frac{2}{r \cdot r}\right)\right)} - 4.5 \]
      associate--l+ [=>] 17.4	\[ \color{blue}{\left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right)} \]
      +-commutative [=>] 17.4	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)} \]
      sub-neg [=>] 17.4	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) + \left(-4.5\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      +-commutative [=>] 17.4	\[ \color{blue}{\left(\left(-4.5\right) + \left(3 + \frac{2}{r \cdot r}\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      associate-+r+ [=>] 17.4	\[ \color{blue}{\left(\left(\left(-4.5\right) + 3\right) + \frac{2}{r \cdot r}\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      +-commutative [<=] 17.4	\[ \color{blue}{\left(\frac{2}{r \cdot r} + \left(\left(-4.5\right) + 3\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      associate-+r+ [<=] 17.4	\[ \color{blue}{\frac{2}{r \cdot r} + \left(\left(\left(-4.5\right) + 3\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)\right)} \]

   3. Taylor expanded in v around inf 0.5

      \[\leadsto \frac{2}{r \cdot r} + \left(-1.5 - \frac{w}{\color{blue}{\frac{4}{r}}} \cdot \left(r \cdot w\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 0.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;v \leq -4 \cdot 10^{+185}:\\ \;\;\;\;-4.5 + \left(\left(\frac{2}{r \cdot r} + 3\right) - \frac{r \cdot \left(r \cdot w\right)}{\frac{4}{w}}\right)\\ \mathbf{elif}\;v \leq 225:\\ \;\;\;\;\frac{2}{r \cdot r} + \left(-1.5 + \left(r \cdot w\right) \cdot \frac{\left(r \cdot w\right) \cdot \left(-0.375 - v \cdot -0.25\right)}{1 - v}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{r \cdot r} + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r}}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	0.3
Cost	7872

\[\frac{2}{r \cdot r} + \left(-1.5 - \frac{w}{\frac{\frac{1 - v}{\mathsf{fma}\left(v, -0.25, 0.375\right)}}{r}} \cdot \left(r \cdot w\right)\right) \]

Alternative 2
Error	23.1
Cost	2265

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r} + -1.5\\ \mathbf{if}\;w \cdot w \leq 10^{-147}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;w \cdot w \leq 5 \cdot 10^{-99}:\\ \;\;\;\;\left(r \cdot \left(r \cdot \left(3 \cdot \left(w \cdot w\right)\right)\right)\right) \cdot -0.125\\ \mathbf{elif}\;w \cdot w \leq 1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;w \cdot w \leq 10^{+24}:\\ \;\;\;\;\left(\left(r \cdot r\right) \cdot \left(w \cdot w\right)\right) \cdot -0.375\\ \mathbf{elif}\;w \cdot w \leq 5 \cdot 10^{+136} \lor \neg \left(w \cdot w \leq 10^{+176}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-0.125 \cdot \left(r \cdot \left(2 \cdot \left(r \cdot \left(w \cdot w\right)\right)\right)\right)\\ \end{array} \]

Alternative 3
Error	23.1
Cost	2137

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r} + -1.5\\ t_1 := \left(r \cdot r\right) \cdot \left(w \cdot w\right)\\ \mathbf{if}\;w \cdot w \leq 7 \cdot 10^{-146}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;w \cdot w \leq 3.3 \cdot 10^{-99}:\\ \;\;\;\;\left(r \cdot \left(r \cdot \left(3 \cdot \left(w \cdot w\right)\right)\right)\right) \cdot -0.125\\ \mathbf{elif}\;w \cdot w \leq 44:\\ \;\;\;\;t_0\\ \mathbf{elif}\;w \cdot w \leq 1.45 \cdot 10^{+25}:\\ \;\;\;\;t_1 \cdot -0.375\\ \mathbf{elif}\;w \cdot w \leq 1.5 \cdot 10^{+140} \lor \neg \left(w \cdot w \leq 7.4 \cdot 10^{+175}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-0.25 \cdot t_1\\ \end{array} \]

Alternative 4
Error	0.3
Cost	1856

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

Alternative 5
Error	0.6
Cost	1736

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -1.5:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot -0.25\right)\right)\right)\\ \mathbf{elif}\;v \leq 1.55 \cdot 10^{-8}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{2.6666666666666665}{r} + \frac{v \cdot -0.8888888888888888}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r}}\right)\\ \end{array} \]

Alternative 6
Error	0.6
Cost	1736

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -1.5:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot -0.25\right)\right)\right)\\ \mathbf{elif}\;v \leq 1.55 \cdot 10^{-8}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{2.6666666666666665}{r} + \frac{v \cdot -0.8888888888888888}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r} + \frac{2}{r \cdot v}}\right)\\ \end{array} \]

Alternative 7
Error	22.0
Cost	1617

\[\begin{array}{l} t_0 := \left(r \cdot r\right) \cdot \left(w \cdot w\right)\\ t_1 := \frac{2}{r \cdot r} + -1.5\\ \mathbf{if}\;w \cdot w \leq 44:\\ \;\;\;\;t_1\\ \mathbf{elif}\;w \cdot w \leq 3.8 \cdot 10^{+24}:\\ \;\;\;\;t_0 \cdot -0.375\\ \mathbf{elif}\;w \cdot w \leq 2.4 \cdot 10^{+144} \lor \neg \left(w \cdot w \leq 8.5 \cdot 10^{+175}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-0.25 \cdot t_0\\ \end{array} \]

Alternative 8
Error	0.6
Cost	1608

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -1.5:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot -0.25\right)\right)\right)\\ \mathbf{elif}\;v \leq 1.55 \cdot 10^{-8}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{r \cdot w}{2.6666666666666665 + v \cdot -0.8888888888888888}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r}}\right)\\ \end{array} \]

Alternative 9
Error	10.6
Cost	1353

\[\begin{array}{l} \mathbf{if}\;r \leq -2 \cdot 10^{-72} \lor \neg \left(r \leq 1.5 \cdot 10^{-70}\right):\\ \;\;\;\;\frac{2}{r \cdot r} + \left(-1.5 + \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot -0.375\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{r}}{r}\\ \end{array} \]

Alternative 10
Error	0.8
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -1.2 \lor \neg \left(v \leq 1.55 \cdot 10^{-8}\right):\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot -0.25\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \left(0.375 \cdot \left(r \cdot w\right)\right)\right)\\ \end{array} \]

Alternative 11
Error	0.7
Cost	1352

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -1.3:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot -0.25\right)\right)\right)\\ \mathbf{elif}\;v \leq 1.55 \cdot 10^{-8}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \left(0.375 \cdot \left(r \cdot w\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r}}\right)\\ \end{array} \]

Alternative 12
Error	9.6
Cost	1088

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

Alternative 13
Error	22.1
Cost	841

\[\begin{array}{l} \mathbf{if}\;w \leq 2.3 \cdot 10^{-25} \lor \neg \left(w \leq 2.5 \cdot 10^{+37}\right):\\ \;\;\;\;\frac{2}{r \cdot r} + -1.5\\ \mathbf{else}:\\ \;\;\;\;\left(r \cdot r\right) \cdot \left(\left(w \cdot w\right) \cdot -0.375\right)\\ \end{array} \]

Alternative 14
Error	21.3
Cost	448

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

Alternative 15
Error	38.1
Cost	320

\[\frac{2}{r \cdot r} \]

Alternative 16
Error	38.1
Cost	320

\[\frac{\frac{2}{r}}{r} \]

Reproduce

herbie shell --seed 2023045 
(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))