Rosa's TurbineBenchmark

Average Error: 12.9 → 0.2

Time: 20.0s

Precision: binary64

Cost: 7689

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;v \leq -4.2 \cdot 10^{+43} \lor \neg \left(v \leq 100000000000\right):\\ \;\;\;\;2 \cdot {r}^{-2} + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{2}{r \cdot r} + 3\right) + \frac{\left(r \cdot w\right) \cdot \left(\left(3 - 2 \cdot v\right) \cdot -0.125\right)}{\frac{1 - v}{r \cdot w}}\right) + -4.5\\ \end{array} \]

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
 (if (or (<= v -4.2e+43) (not (<= v 100000000000.0)))
   (+ (* 2.0 (pow r -2.0)) (- -1.5 (* (* r w) (/ w (/ 4.0 r)))))
   (+
    (+
     (+ (/ 2.0 (* r r)) 3.0)
     (/ (* (* r w) (* (- 3.0 (* 2.0 v)) -0.125)) (/ (- 1.0 v) (* r w))))
    -4.5)))

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 tmp;
	if ((v <= -4.2e+43) || !(v <= 100000000000.0)) {
		tmp = (2.0 * pow(r, -2.0)) + (-1.5 - ((r * w) * (w / (4.0 / r))));
	} else {
		tmp = (((2.0 / (r * r)) + 3.0) + (((r * w) * ((3.0 - (2.0 * v)) * -0.125)) / ((1.0 - v) / (r * w)))) + -4.5;
	}
	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) :: tmp
    if ((v <= (-4.2d+43)) .or. (.not. (v <= 100000000000.0d0))) then
        tmp = (2.0d0 * (r ** (-2.0d0))) + ((-1.5d0) - ((r * w) * (w / (4.0d0 / r))))
    else
        tmp = (((2.0d0 / (r * r)) + 3.0d0) + (((r * w) * ((3.0d0 - (2.0d0 * v)) * (-0.125d0))) / ((1.0d0 - v) / (r * w)))) + (-4.5d0)
    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 tmp;
	if ((v <= -4.2e+43) || !(v <= 100000000000.0)) {
		tmp = (2.0 * Math.pow(r, -2.0)) + (-1.5 - ((r * w) * (w / (4.0 / r))));
	} else {
		tmp = (((2.0 / (r * r)) + 3.0) + (((r * w) * ((3.0 - (2.0 * v)) * -0.125)) / ((1.0 - v) / (r * w)))) + -4.5;
	}
	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):
	tmp = 0
	if (v <= -4.2e+43) or not (v <= 100000000000.0):
		tmp = (2.0 * math.pow(r, -2.0)) + (-1.5 - ((r * w) * (w / (4.0 / r))))
	else:
		tmp = (((2.0 / (r * r)) + 3.0) + (((r * w) * ((3.0 - (2.0 * v)) * -0.125)) / ((1.0 - v) / (r * w)))) + -4.5
	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)
	tmp = 0.0
	if ((v <= -4.2e+43) || !(v <= 100000000000.0))
		tmp = Float64(Float64(2.0 * (r ^ -2.0)) + Float64(-1.5 - Float64(Float64(r * w) * Float64(w / Float64(4.0 / r)))));
	else
		tmp = Float64(Float64(Float64(Float64(2.0 / Float64(r * r)) + 3.0) + Float64(Float64(Float64(r * w) * Float64(Float64(3.0 - Float64(2.0 * v)) * -0.125)) / Float64(Float64(1.0 - v) / Float64(r * w)))) + -4.5);
	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)
	tmp = 0.0;
	if ((v <= -4.2e+43) || ~((v <= 100000000000.0)))
		tmp = (2.0 * (r ^ -2.0)) + (-1.5 - ((r * w) * (w / (4.0 / r))));
	else
		tmp = (((2.0 / (r * r)) + 3.0) + (((r * w) * ((3.0 - (2.0 * v)) * -0.125)) / ((1.0 - v) / (r * w)))) + -4.5;
	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_] := If[Or[LessEqual[v, -4.2e+43], N[Not[LessEqual[v, 100000000000.0]], $MachinePrecision]], N[(N[(2.0 * N[Power[r, -2.0], $MachinePrecision]), $MachinePrecision] + N[(-1.5 - N[(N[(r * w), $MachinePrecision] * N[(w / N[(4.0 / r), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(2.0 / N[(r * r), $MachinePrecision]), $MachinePrecision] + 3.0), $MachinePrecision] + N[(N[(N[(r * w), $MachinePrecision] * N[(N[(3.0 - N[(2.0 * v), $MachinePrecision]), $MachinePrecision] * -0.125), $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 - v), $MachinePrecision] / N[(r * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -4.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if v < -4.20000000000000003e43 or 1e11 < v

   1. Initial program 18.0

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

   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] 18.0	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]
      sub-neg [=>] 18.0	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)\right)} - 4.5 \]
      +-commutative [=>] 18.0	\[ \color{blue}{\left(\left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(3 + \frac{2}{r \cdot r}\right)\right)} - 4.5 \]
      associate--l+ [=>] 18.0	\[ \color{blue}{\left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right)} \]
      +-commutative [=>] 18.0	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)} \]
      sub-neg [=>] 18.0	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) + \left(-4.5\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      +-commutative [=>] 18.0	\[ \color{blue}{\left(\left(-4.5\right) + \left(3 + \frac{2}{r \cdot r}\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      associate-+r+ [=>] 18.0	\[ \color{blue}{\left(\left(\left(-4.5\right) + 3\right) + \frac{2}{r \cdot r}\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      +-commutative [<=] 18.0	\[ \color{blue}{\left(\frac{2}{r \cdot r} + \left(\left(-4.5\right) + 3\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      associate-+r+ [<=] 18.0	\[ \color{blue}{\frac{2}{r \cdot r} + \left(\left(\left(-4.5\right) + 3\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)\right)} \]

   3. Taylor expanded in v around inf 0.3

      \[\leadsto \frac{2}{r \cdot r} + \left(-1.5 - \frac{w}{\color{blue}{\frac{4}{r}}} \cdot \left(r \cdot w\right)\right) \]

   4. Applied egg-rr 0.2

      \[\leadsto \color{blue}{{r}^{-2} \cdot 2} + \left(-1.5 - \frac{w}{\frac{4}{r}} \cdot \left(r \cdot w\right)\right) \]

   if -4.20000000000000003e43 < v < 1e11

   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 8.4

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

      [Start] 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/ [<=] 8.4	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}\right) + \left(-4.5\right) \]
      *-commutative [=>] 8.4	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \color{blue}{\left(r \cdot \left(\left(w \cdot w\right) \cdot r\right)\right)}\right) + \left(-4.5\right) \]
      *-commutative [=>] 8.4	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \color{blue}{\left(r \cdot \left(w \cdot w\right)\right)}\right)\right) + \left(-4.5\right) \]
      metadata-eval [=>] 8.4	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \left(r \cdot \left(w \cdot w\right)\right)\right)\right) + \color{blue}{-4.5} \]

   3. Applied egg-rr 0.3

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

4. Final simplification 0.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;v \leq -4.2 \cdot 10^{+43} \lor \neg \left(v \leq 100000000000\right):\\ \;\;\;\;2 \cdot {r}^{-2} + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{2}{r \cdot r} + 3\right) + \frac{\left(r \cdot w\right) \cdot \left(\left(3 - 2 \cdot v\right) \cdot -0.125\right)}{\frac{1 - v}{r \cdot w}}\right) + -4.5\\ \end{array} \]

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	0.8
Cost	2120

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -3 \cdot 10^{+44}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{r}{\frac{4 + \frac{2}{v}}{w}}\right)\\ \mathbf{elif}\;v \leq 3 \cdot 10^{+146}:\\ \;\;\;\;\left(\left(t_0 + 3\right) + \frac{\left(r \cdot w\right) \cdot \left(\left(3 - 2 \cdot v\right) \cdot -0.125\right)}{\frac{1 - v}{r \cdot w}}\right) + -4.5\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \frac{w}{\frac{\frac{\frac{4}{r} + \frac{2}{r \cdot v}}{w}}{r}}\right)\\ \end{array} \]

Alternative 3
Error	0.8
Cost	1864

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -64000000000000:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{r}{\frac{4 + \frac{2}{v}}{w}}\right)\\ \mathbf{elif}\;v \leq 2 \cdot 10^{+146}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{\left(r \cdot w\right) \cdot \left(0.375 + v \cdot -0.25\right)}{1 - v}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \frac{w}{\frac{\frac{\frac{4}{r} + \frac{2}{r \cdot v}}{w}}{r}}\right)\\ \end{array} \]

Alternative 4
Error	0.6
Cost	1737

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -2500000000000 \lor \neg \left(v \leq 1\right):\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{r}{\frac{4 + \frac{2}{v}}{w}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{2.6666666666666665}{r} + -0.8888888888888888 \cdot \frac{v}{r}}\right)\\ \end{array} \]

Alternative 5
Error	0.6
Cost	1736

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -2500000000000:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{r}{\frac{4 + \frac{2}{v}}{w}}\right)\\ \mathbf{elif}\;v \leq 1:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{2.6666666666666665}{r} + -0.8888888888888888 \cdot \frac{v}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r} + \frac{2}{r \cdot v}}\right)\\ \end{array} \]

Alternative 6
Error	0.7
Cost	1609

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -2500000000000 \lor \neg \left(v \leq 1\right):\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \left(r \cdot \frac{w}{4 + \frac{2}{v}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot -0.375\right)\right)\right)\\ \end{array} \]

Alternative 7
Error	0.7
Cost	1609

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -2500000000000 \lor \neg \left(v \leq 1\right):\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{r}{\frac{4 + \frac{2}{v}}{w}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot -0.375\right)\right)\right)\\ \end{array} \]

Alternative 8
Error	14.0
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;r \leq -1.34 \cdot 10^{+154} \lor \neg \left(r \leq 1.4 \cdot 10^{+154}\right):\\ \;\;\;\;t_0 + -1.5\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 + -0.25 \cdot \left(w \cdot \left(\left(r \cdot r\right) \cdot w\right)\right)\right)\\ \end{array} \]

Alternative 9
Error	8.1
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -15500000000000 \lor \neg \left(v \leq 1900000000000\right):\\ \;\;\;\;t_0 + \left(-1.5 + -0.25 \cdot \left(w \cdot \left(\left(r \cdot r\right) \cdot w\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot -0.375\right)\\ \end{array} \]

Alternative 10
Error	7.6
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -5800000000000 \lor \neg \left(v \leq 5 \cdot 10^{+162}\right):\\ \;\;\;\;t_0 + \left(-1.5 + -0.25 \cdot \left(w \cdot \left(\left(r \cdot r\right) \cdot w\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - 0.375 \cdot \left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right)\right)\\ \end{array} \]

Alternative 11
Error	7.6
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -2500000000000 \lor \neg \left(v \leq 1.15 \cdot 10^{+164}\right):\\ \;\;\;\;t_0 + \left(-1.5 + -0.25 \cdot \left(w \cdot \left(\left(r \cdot r\right) \cdot w\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(\left(r \cdot w\right) \cdot -0.375\right)\right)\\ \end{array} \]

Alternative 12
Error	0.8
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -2500000000000 \lor \neg \left(v \leq 1\right):\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot 0.25\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(\left(r \cdot w\right) \cdot -0.375\right)\right)\\ \end{array} \]

Alternative 13
Error	0.8
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -2500000000000 \lor \neg \left(v \leq 1\right):\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot 0.25\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot -0.375\right)\right)\right)\\ \end{array} \]

Alternative 14
Error	0.8
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -2500000000000 \lor \neg \left(v \leq 1\right):\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot -0.375\right)\right)\right)\\ \end{array} \]

Alternative 15
Error	21.4
Cost	448

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

Alternative 16
Error	38.4
Cost	320

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

Reproduce

herbie shell --seed 2023060 
(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))