Rosa's TurbineBenchmark

Average Error: 20.27% → 1%

Time: 16.9s

Precision: binary64

Cost: 2121

Math

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

↓

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r} + 3\\ \mathbf{if}\;w \leq -5 \cdot 10^{+97} \lor \neg \left(w \leq 10^{-87}\right):\\ \;\;\;\;\left(t_0 - \frac{r \cdot \left(r \cdot w\right)}{\frac{\frac{1 - v}{0.375 + 0.125 \cdot \left(v \cdot -2\right)}}{w}}\right) + -4.5\\ \mathbf{else}:\\ \;\;\;\;-4.5 + \left(t_0 + \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot \frac{0.125 \cdot \left(-3 - v \cdot -2\right)}{1 - v}\right)\\ \end{array} \]

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 (or (<= w -5e+97) (not (<= w 1e-87)))
     (+
      (-
       t_0
       (/ (* r (* r w)) (/ (/ (- 1.0 v) (+ 0.375 (* 0.125 (* v -2.0)))) w)))
      -4.5)
     (+
      -4.5
      (+
       t_0
       (* (* r (* w (* r w))) (/ (* 0.125 (- -3.0 (* v -2.0))) (- 1.0 v))))))))

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 <= -5e+97) || !(w <= 1e-87)) {
		tmp = (t_0 - ((r * (r * w)) / (((1.0 - v) / (0.375 + (0.125 * (v * -2.0)))) / w))) + -4.5;
	} else {
		tmp = -4.5 + (t_0 + ((r * (w * (r * w))) * ((0.125 * (-3.0 - (v * -2.0))) / (1.0 - v))));
	}
	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 <= (-5d+97)) .or. (.not. (w <= 1d-87))) then
        tmp = (t_0 - ((r * (r * w)) / (((1.0d0 - v) / (0.375d0 + (0.125d0 * (v * (-2.0d0))))) / w))) + (-4.5d0)
    else
        tmp = (-4.5d0) + (t_0 + ((r * (w * (r * w))) * ((0.125d0 * ((-3.0d0) - (v * (-2.0d0)))) / (1.0d0 - v))))
    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 <= -5e+97) || !(w <= 1e-87)) {
		tmp = (t_0 - ((r * (r * w)) / (((1.0 - v) / (0.375 + (0.125 * (v * -2.0)))) / w))) + -4.5;
	} else {
		tmp = -4.5 + (t_0 + ((r * (w * (r * w))) * ((0.125 * (-3.0 - (v * -2.0))) / (1.0 - v))));
	}
	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 <= -5e+97) or not (w <= 1e-87):
		tmp = (t_0 - ((r * (r * w)) / (((1.0 - v) / (0.375 + (0.125 * (v * -2.0)))) / w))) + -4.5
	else:
		tmp = -4.5 + (t_0 + ((r * (w * (r * w))) * ((0.125 * (-3.0 - (v * -2.0))) / (1.0 - v))))
	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 ((w <= -5e+97) || !(w <= 1e-87))
		tmp = Float64(Float64(t_0 - Float64(Float64(r * Float64(r * w)) / Float64(Float64(Float64(1.0 - v) / Float64(0.375 + Float64(0.125 * Float64(v * -2.0)))) / w))) + -4.5);
	else
		tmp = Float64(-4.5 + Float64(t_0 + Float64(Float64(r * Float64(w * Float64(r * w))) * Float64(Float64(0.125 * Float64(-3.0 - Float64(v * -2.0))) / Float64(1.0 - v)))));
	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 <= -5e+97) || ~((w <= 1e-87)))
		tmp = (t_0 - ((r * (r * w)) / (((1.0 - v) / (0.375 + (0.125 * (v * -2.0)))) / w))) + -4.5;
	else
		tmp = -4.5 + (t_0 + ((r * (w * (r * w))) * ((0.125 * (-3.0 - (v * -2.0))) / (1.0 - v))));
	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[Or[LessEqual[w, -5e+97], N[Not[LessEqual[w, 1e-87]], $MachinePrecision]], N[(N[(t$95$0 - N[(N[(r * N[(r * w), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(1.0 - v), $MachinePrecision] / N[(0.375 + N[(0.125 * N[(v * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -4.5), $MachinePrecision], N[(-4.5 + N[(t$95$0 + N[(N[(r * N[(w * N[(r * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(0.125 * N[(-3.0 - N[(v * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 - v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if w < -4.99999999999999999e97 or 1.00000000000000002e-87 < w

   1. Initial program 36.78

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

   2. Simplified 25.28

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

      [Start] 36.78	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]
      sub-neg [=>] 36.78	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(-4.5\right)} \]
      associate-*l/ [<=] 25.28	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}\right) + \left(-4.5\right) \]
      *-commutative [=>] 25.28	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \color{blue}{\left(r \cdot \left(\left(w \cdot w\right) \cdot r\right)\right)}\right) + \left(-4.5\right) \]
      *-commutative [=>] 25.28	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \color{blue}{\left(r \cdot \left(w \cdot w\right)\right)}\right)\right) + \left(-4.5\right) \]
      metadata-eval [=>] 25.28	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \left(r \cdot \left(w \cdot w\right)\right)\right)\right) + \color{blue}{-4.5} \]

   3. Taylor expanded in r around 0 25.28

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

   4. Simplified 13.09

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

      [Start] 25.28	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \left({w}^{2} \cdot r\right)\right)\right) + -4.5 \]
      unpow2 [=>] 25.28	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \left(\color{blue}{\left(w \cdot w\right)} \cdot r\right)\right)\right) + -4.5 \]
      *-commutative [<=] 25.28	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \color{blue}{\left(r \cdot \left(w \cdot w\right)\right)}\right)\right) + -4.5 \]
      associate-*r* [=>] 13.09	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \color{blue}{\left(\left(r \cdot w\right) \cdot w\right)}\right)\right) + -4.5 \]
      *-commutative [=>] 13.09	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \left(\color{blue}{\left(w \cdot r\right)} \cdot w\right)\right)\right) + -4.5 \]

   5. Applied egg-rr 2.33

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\frac{r \cdot \left(r \cdot w\right)}{\frac{\frac{1 - v}{0.375 + 0.125 \cdot \left(v \cdot -2\right)}}{w}}}\right) + -4.5 \]

   if -4.99999999999999999e97 < w < 1.00000000000000002e-87

   1. Initial program 13.6

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

   2. Simplified 8.52

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

      [Start] 13.6	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]
      sub-neg [=>] 13.6	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(-4.5\right)} \]
      associate-*l/ [<=] 8.52	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}\right) + \left(-4.5\right) \]
      *-commutative [=>] 8.52	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \color{blue}{\left(r \cdot \left(\left(w \cdot w\right) \cdot r\right)\right)}\right) + \left(-4.5\right) \]
      *-commutative [=>] 8.52	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \color{blue}{\left(r \cdot \left(w \cdot w\right)\right)}\right)\right) + \left(-4.5\right) \]
      metadata-eval [=>] 8.52	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \left(r \cdot \left(w \cdot w\right)\right)\right)\right) + \color{blue}{-4.5} \]

   3. Taylor expanded in r around 0 8.52

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

   4. Simplified 0.47

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

      [Start] 8.52	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \left({w}^{2} \cdot r\right)\right)\right) + -4.5 \]
      unpow2 [=>] 8.52	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \left(\color{blue}{\left(w \cdot w\right)} \cdot r\right)\right)\right) + -4.5 \]
      *-commutative [<=] 8.52	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \color{blue}{\left(r \cdot \left(w \cdot w\right)\right)}\right)\right) + -4.5 \]
      associate-*r* [=>] 0.47	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \color{blue}{\left(\left(r \cdot w\right) \cdot w\right)}\right)\right) + -4.5 \]
      *-commutative [=>] 0.47	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \left(\color{blue}{\left(w \cdot r\right)} \cdot w\right)\right)\right) + -4.5 \]

3. Recombined 2 regimes into one program.

4. Final simplification 1

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq -5 \cdot 10^{+97} \lor \neg \left(w \leq 10^{-87}\right):\\ \;\;\;\;\left(\left(\frac{2}{r \cdot r} + 3\right) - \frac{r \cdot \left(r \cdot w\right)}{\frac{\frac{1 - v}{0.375 + 0.125 \cdot \left(v \cdot -2\right)}}{w}}\right) + -4.5\\ \mathbf{else}:\\ \;\;\;\;-4.5 + \left(\left(\frac{2}{r \cdot r} + 3\right) + \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot \frac{0.125 \cdot \left(-3 - v \cdot -2\right)}{1 - v}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	0.4%
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	1.1%
Cost	1992

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -5.2 \cdot 10^{+147}:\\ \;\;\;\;t_0 + \left(-1.5 - \frac{r}{\frac{\frac{\frac{4}{r} + \frac{2}{r \cdot v}}{w}}{w}}\right)\\ \mathbf{elif}\;v \leq 7200000000:\\ \;\;\;\;-4.5 + \left(\left(t_0 + 3\right) + \left(r \cdot w\right) \cdot \left(\frac{r}{\frac{1 - v}{w}} \cdot \left(-0.375 - v \cdot -0.25\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r}}\right)\\ \end{array} \]

Alternative 3
Error	1.14%
Cost	1608

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -3.5 \cdot 10^{+16}:\\ \;\;\;\;\left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r}}\right) + \frac{\frac{2}{r}}{r}\\ \mathbf{elif}\;v \leq 0.88:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot -0.375\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4 + \frac{2}{v}}{r}}\right)\\ \end{array} \]

Alternative 4
Error	6.49%
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -4.5 \cdot 10^{-18} \lor \neg \left(v \leq 500000\right):\\ \;\;\;\;t_0 + \left(-1.5 - 0.25 \cdot \left(w \cdot \left(r \cdot \left(r \cdot w\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot -0.375\right)\\ \end{array} \]

Alternative 5
Error	4.82%
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -3.5 \cdot 10^{+16} \lor \neg \left(v \leq 500000\right):\\ \;\;\;\;t_0 + \left(-1.5 - 0.25 \cdot \left(w \cdot \left(r \cdot \left(r \cdot w\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 + \left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) \cdot -0.375\right)\\ \end{array} \]

Alternative 6
Error	4.72%
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -3.5 \cdot 10^{+16} \lor \neg \left(v \leq 500000\right):\\ \;\;\;\;t_0 + \left(-1.5 - 0.25 \cdot \left(w \cdot \left(r \cdot \left(r \cdot w\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot 0.375\right)\right)\right)\\ \end{array} \]

Alternative 7
Error	1.29%
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -3.5 \cdot 10^{+16} \lor \neg \left(v \leq 0.88\right):\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot -0.25\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot -0.375\right)\right)\right)\\ \end{array} \]

Alternative 8
Error	1.28%
Cost	1352

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -3.5 \cdot 10^{+16}:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot -0.25\right)\right)\right)\\ \mathbf{elif}\;v \leq 0.88:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot -0.375\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r}}\right)\\ \end{array} \]

Alternative 9
Error	1.27%
Cost	1352

\[\begin{array}{l} t_0 := -1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r}}\\ t_1 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -3.5 \cdot 10^{+16}:\\ \;\;\;\;t_0 + \frac{\frac{2}{r}}{r}\\ \mathbf{elif}\;v \leq 0.88:\\ \;\;\;\;t_1 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot -0.375\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + t_0\\ \end{array} \]

Alternative 10
Error	17.91%
Cost	1088

\[\frac{2}{r \cdot r} + \left(-1.5 - 0.25 \cdot \left(w \cdot \left(r \cdot \left(r \cdot w\right)\right)\right)\right) \]

Alternative 11
Error	32.18%
Cost	708

\[\begin{array}{l} \mathbf{if}\;r \leq 9.5 \cdot 10^{+162}:\\ \;\;\;\;\frac{2}{r \cdot r} + -1.5\\ \mathbf{else}:\\ \;\;\;\;r \cdot \left(-0.25 \cdot \left(w \cdot \left(r \cdot w\right)\right)\right)\\ \end{array} \]

Alternative 12
Error	32.88%
Cost	448

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

Alternative 13
Error	59.43%
Cost	320

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

Alternative 14
Error	59.43%
Cost	320

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

Reproduce

herbie shell --seed 2023125 
(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))