Rosa's TurbineBenchmark

Average Error: 12.9 → 0.3

Time: 16.9s

Precision: binary64

Cost: 2116

Math

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

↓

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r} + 3\\ \mathbf{if}\;w \cdot w \leq 2 \cdot 10^{+56}:\\ \;\;\;\;-4.5 + \left(t_0 + \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot \frac{0.125 \cdot \left(2 \cdot v + -3\right)}{1 - v}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 + \left(t_0 - w \cdot \left(r \cdot \left(\left(r \cdot w\right) \cdot \frac{3 + v \cdot -2}{\left(1 - v\right) \cdot 8}\right)\right)\right)\\ \end{array} \]

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)) 3.0)))
   (if (<= (* w w) 2e+56)
     (+
      -4.5
      (+
       t_0
       (* (* r (* w (* r w))) (/ (* 0.125 (+ (* 2.0 v) -3.0)) (- 1.0 v)))))
     (+
      -4.5
      (-
       t_0
       (* w (* r (* (* r w) (/ (+ 3.0 (* v -2.0)) (* (- 1.0 v) 8.0))))))))))

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)) + 3.0;
	double tmp;
	if ((w * w) <= 2e+56) {
		tmp = -4.5 + (t_0 + ((r * (w * (r * w))) * ((0.125 * ((2.0 * v) + -3.0)) / (1.0 - v))));
	} else {
		tmp = -4.5 + (t_0 - (w * (r * ((r * w) * ((3.0 + (v * -2.0)) / ((1.0 - v) * 8.0))))));
	}
	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)) + 3.0d0
    if ((w * w) <= 2d+56) then
        tmp = (-4.5d0) + (t_0 + ((r * (w * (r * w))) * ((0.125d0 * ((2.0d0 * v) + (-3.0d0))) / (1.0d0 - v))))
    else
        tmp = (-4.5d0) + (t_0 - (w * (r * ((r * w) * ((3.0d0 + (v * (-2.0d0))) / ((1.0d0 - v) * 8.0d0))))))
    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)) + 3.0;
	double tmp;
	if ((w * w) <= 2e+56) {
		tmp = -4.5 + (t_0 + ((r * (w * (r * w))) * ((0.125 * ((2.0 * v) + -3.0)) / (1.0 - v))));
	} else {
		tmp = -4.5 + (t_0 - (w * (r * ((r * w) * ((3.0 + (v * -2.0)) / ((1.0 - v) * 8.0))))));
	}
	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)) + 3.0
	tmp = 0
	if (w * w) <= 2e+56:
		tmp = -4.5 + (t_0 + ((r * (w * (r * w))) * ((0.125 * ((2.0 * v) + -3.0)) / (1.0 - v))))
	else:
		tmp = -4.5 + (t_0 - (w * (r * ((r * w) * ((3.0 + (v * -2.0)) / ((1.0 - v) * 8.0))))))
	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(Float64(2.0 / Float64(r * r)) + 3.0)
	tmp = 0.0
	if (Float64(w * w) <= 2e+56)
		tmp = Float64(-4.5 + Float64(t_0 + Float64(Float64(r * Float64(w * Float64(r * w))) * Float64(Float64(0.125 * Float64(Float64(2.0 * v) + -3.0)) / Float64(1.0 - v)))));
	else
		tmp = Float64(-4.5 + Float64(t_0 - Float64(w * Float64(r * Float64(Float64(r * w) * Float64(Float64(3.0 + Float64(v * -2.0)) / Float64(Float64(1.0 - v) * 8.0)))))));
	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)) + 3.0;
	tmp = 0.0;
	if ((w * w) <= 2e+56)
		tmp = -4.5 + (t_0 + ((r * (w * (r * w))) * ((0.125 * ((2.0 * v) + -3.0)) / (1.0 - v))));
	else
		tmp = -4.5 + (t_0 - (w * (r * ((r * w) * ((3.0 + (v * -2.0)) / ((1.0 - v) * 8.0))))));
	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[(N[(2.0 / N[(r * r), $MachinePrecision]), $MachinePrecision] + 3.0), $MachinePrecision]}, If[LessEqual[N[(w * w), $MachinePrecision], 2e+56], N[(-4.5 + N[(t$95$0 + N[(N[(r * N[(w * N[(r * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(0.125 * N[(N[(2.0 * v), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision] / N[(1.0 - v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 + N[(t$95$0 - N[(w * N[(r * N[(N[(r * w), $MachinePrecision] * N[(N[(3.0 + N[(v * -2.0), $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 - v), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 w w) < 2.00000000000000018e56

   1. Initial program 8.5

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

   2. Simplified 5.1

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

      [Start] 8.5	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]
      sub-neg [=>] 8.5	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(-4.5\right)} \]
      associate-*l/ [<=] 5.1	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}\right) + \left(-4.5\right) \]
      *-commutative [=>] 5.1	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \color{blue}{\left(r \cdot \left(\left(w \cdot w\right) \cdot r\right)\right)}\right) + \left(-4.5\right) \]
      *-commutative [=>] 5.1	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \color{blue}{\left(r \cdot \left(w \cdot w\right)\right)}\right)\right) + \left(-4.5\right) \]
      metadata-eval [=>] 5.1	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \left(r \cdot \left(w \cdot w\right)\right)\right)\right) + \color{blue}{-4.5} \]

   3. Taylor expanded in r around 0 5.1

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

   4. Simplified 0.3

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

      [Start] 5.1	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \left({w}^{2} \cdot r\right)\right)\right) + -4.5 \]
      unpow2 [=>] 5.1	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \left(\color{blue}{\left(w \cdot w\right)} \cdot r\right)\right)\right) + -4.5 \]
      associate-*l* [=>] 0.3	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \color{blue}{\left(w \cdot \left(w \cdot r\right)\right)}\right)\right) + -4.5 \]

   if 2.00000000000000018e56 < (*.f64 w w)

   1. Initial program 28.2

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

   2. Simplified 20.4

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

      [Start] 28.2	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]
      sub-neg [=>] 28.2	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(-4.5\right)} \]
      associate-*l/ [<=] 20.4	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}\right) + \left(-4.5\right) \]
      *-commutative [=>] 20.4	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \color{blue}{\left(r \cdot \left(\left(w \cdot w\right) \cdot r\right)\right)}\right) + \left(-4.5\right) \]
      *-commutative [=>] 20.4	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \color{blue}{\left(r \cdot \left(w \cdot w\right)\right)}\right)\right) + \left(-4.5\right) \]
      metadata-eval [=>] 20.4	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \left(r \cdot \left(w \cdot w\right)\right)\right)\right) + \color{blue}{-4.5} \]

   3. Applied egg-rr 0.4

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

   4. Applied egg-rr 0.4

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\left(\left(\left(r \cdot w\right) \cdot \frac{3 + v \cdot -2}{\left(1 - v\right) \cdot 8}\right) \cdot r\right) \cdot w}\right) + -4.5 \]
3. Recombined 2 regimes into one program.

4. Final simplification 0.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \cdot w \leq 2 \cdot 10^{+56}:\\ \;\;\;\;-4.5 + \left(\left(\frac{2}{r \cdot r} + 3\right) + \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot \frac{0.125 \cdot \left(2 \cdot v + -3\right)}{1 - v}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 + \left(\left(\frac{2}{r \cdot r} + 3\right) - w \cdot \left(r \cdot \left(\left(r \cdot w\right) \cdot \frac{3 + v \cdot -2}{\left(1 - v\right) \cdot 8}\right)\right)\right)\\ \end{array} \]

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	0.6
Cost	2376

\[\begin{array}{l} t_0 := 0.375 + v \cdot -0.25\\ t_1 := \frac{2}{r \cdot r}\\ \mathbf{if}\;w \cdot w \leq 10^{-295}:\\ \;\;\;\;t_1 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{\left(r \cdot w\right) \cdot t_0}{1 - v}\right)\\ \mathbf{elif}\;w \cdot w \leq 10^{+223}:\\ \;\;\;\;-4.5 + \left(3 + \left(t_1 - \frac{0.125 \cdot \left(3 + v \cdot -2\right)}{\frac{1 - v}{r \cdot \left(r \cdot \left(w \cdot w\right)\right)}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{1 - v}{r \cdot t_0}}\right)\\ \end{array} \]

Alternative 3
Error	2.3
Cost	2120

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;r \leq -5 \cdot 10^{+173}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{\left(r \cdot w\right) \cdot \left(0.375 + v \cdot -0.25\right)}{1 - v}\right)\\ \mathbf{elif}\;r \leq 2.2 \cdot 10^{+194}:\\ \;\;\;\;-4.5 + \left(\left(t_0 + 3\right) - w \cdot \left(r \cdot \left(\left(r \cdot w\right) \cdot \frac{3 + v \cdot -2}{\left(1 - v\right) \cdot 8}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot -0.375\right)\\ \end{array} \]

Alternative 4
Error	0.3
Cost	1864

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -6.4 \cdot 10^{+42}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r}}\right)\\ \mathbf{elif}\;v \leq 21000000000:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{1 - v}{r \cdot \left(0.375 + v \cdot -0.25\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 + \left(\left(t_0 + 3\right) - \frac{r \cdot w}{\frac{\frac{4}{w}}{r}}\right)\\ \end{array} \]

Alternative 5
Error	0.3
Cost	1864

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -1 \cdot 10^{+20}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r}}\right)\\ \mathbf{elif}\;v \leq 21000000000:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w \cdot \left(r \cdot \left(0.375 + v \cdot -0.25\right)\right)}{1 - v}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 + \left(\left(t_0 + 3\right) - \frac{r \cdot w}{\frac{\frac{4}{w}}{r}}\right)\\ \end{array} \]

Alternative 6
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 7
Error	0.8
Cost	1736

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -6.5 \cdot 10^{+15}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r}}\right)\\ \mathbf{elif}\;v \leq 1:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{2.6666666666666665}{r} + -0.8888888888888888 \cdot \frac{v}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 + \left(\left(t_0 + 3\right) - \frac{r \cdot w}{\frac{\frac{4}{w}}{r}}\right)\\ \end{array} \]

Alternative 8
Error	0.7
Cost	1736

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -6.5 \cdot 10^{+15}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r}}\right)\\ \mathbf{elif}\;v \leq 1:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{2.6666666666666665}{r} + -0.8888888888888888 \cdot \frac{v}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r} + \frac{2}{r \cdot v}}\right)\\ \end{array} \]

Alternative 9
Error	1.9
Cost	1732

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq 21000000000:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{\left(r \cdot w\right) \cdot \left(0.375 + v \cdot -0.25\right)}{1 - v}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 + \left(\left(t_0 + 3\right) - \frac{r \cdot w}{\frac{\frac{4}{w}}{r}}\right)\\ \end{array} \]

Alternative 10
Error	0.9
Cost	1480

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -6.5 \cdot 10^{+15}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r}}\right)\\ \mathbf{elif}\;v \leq 1:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{2.6666666666666665}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 + \left(\left(t_0 + 3\right) - \frac{r \cdot w}{\frac{\frac{4}{w}}{r}}\right)\\ \end{array} \]

Alternative 11
Error	0.9
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -6.5 \cdot 10^{+15} \lor \neg \left(v \leq 1\right):\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot -0.25\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(\left(r \cdot w\right) \cdot -0.375\right)\right)\\ \end{array} \]

Alternative 12
Error	0.9
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -6.5 \cdot 10^{+15} \lor \neg \left(v \leq 1\right):\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot -0.25\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{2.6666666666666665}{r}}\right)\\ \end{array} \]

Alternative 13
Error	0.9
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -6.5 \cdot 10^{+15} \lor \neg \left(v \leq 1\right):\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{2.6666666666666665}{r}}\right)\\ \end{array} \]

Alternative 14
Error	12.5
Cost	1348

\[\begin{array}{l} \mathbf{if}\;w \cdot w \leq 3.3 \cdot 10^{+307}:\\ \;\;\;\;\frac{2}{r \cdot r} + \left(-1.5 + \left(r \cdot \left(r \cdot \left(w \cdot w\right)\right)\right) \cdot -0.375\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{r}}{r}\\ \end{array} \]

Alternative 15
Error	10.8
Cost	1088

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

Alternative 16
Error	9.3
Cost	1088

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

Alternative 17
Error	9.3
Cost	1088

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

Alternative 18
Error	21.0
Cost	448

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

Alternative 19
Error	38.3
Cost	320

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

Alternative 20
Error	38.3
Cost	320

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

Reproduce

herbie shell --seed 2023027 
(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))