Rosa's TurbineBenchmark

Average Error: 79.9% → 98.7%

Time: 33.6s

Precision: binary64

Cost: 1737.00

Math

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

↓

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -25000000000 \lor \neg \left(v \leq 1.7 \cdot 10^{-19}\right):\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4 + \frac{2}{v}}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{2.6666666666666665}{r} + \frac{v \cdot -0.8888888888888888}{r}}\right)\\ \end{array} \]

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 (or (<= v -25000000000.0) (not (<= v 1.7e-19)))
     (+ t_0 (- -1.5 (* (* r w) (/ w (/ (+ 4.0 (/ 2.0 v)) r)))))
     (+
      t_0
      (-
       -1.5
       (*
        (* r w)
        (/
         w
         (+ (/ 2.6666666666666665 r) (/ (* v -0.8888888888888888) 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 <= -25000000000.0) || !(v <= 1.7e-19)) {
		tmp = t_0 + (-1.5 - ((r * w) * (w / ((4.0 + (2.0 / v)) / r))));
	} else {
		tmp = t_0 + (-1.5 - ((r * w) * (w / ((2.6666666666666665 / r) + ((v * -0.8888888888888888) / 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 <= (-25000000000.0d0)) .or. (.not. (v <= 1.7d-19))) then
        tmp = t_0 + ((-1.5d0) - ((r * w) * (w / ((4.0d0 + (2.0d0 / v)) / r))))
    else
        tmp = t_0 + ((-1.5d0) - ((r * w) * (w / ((2.6666666666666665d0 / r) + ((v * (-0.8888888888888888d0)) / 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 <= -25000000000.0) || !(v <= 1.7e-19)) {
		tmp = t_0 + (-1.5 - ((r * w) * (w / ((4.0 + (2.0 / v)) / r))));
	} else {
		tmp = t_0 + (-1.5 - ((r * w) * (w / ((2.6666666666666665 / r) + ((v * -0.8888888888888888) / 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 <= -25000000000.0) or not (v <= 1.7e-19):
		tmp = t_0 + (-1.5 - ((r * w) * (w / ((4.0 + (2.0 / v)) / r))))
	else:
		tmp = t_0 + (-1.5 - ((r * w) * (w / ((2.6666666666666665 / r) + ((v * -0.8888888888888888) / 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 <= -25000000000.0) || !(v <= 1.7e-19))
		tmp = Float64(t_0 + Float64(-1.5 - Float64(Float64(r * w) * Float64(w / Float64(Float64(4.0 + Float64(2.0 / v)) / r)))));
	else
		tmp = Float64(t_0 + Float64(-1.5 - Float64(Float64(r * w) * Float64(w / Float64(Float64(2.6666666666666665 / r) + Float64(Float64(v * -0.8888888888888888) / 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 <= -25000000000.0) || ~((v <= 1.7e-19)))
		tmp = t_0 + (-1.5 - ((r * w) * (w / ((4.0 + (2.0 / v)) / r))));
	else
		tmp = t_0 + (-1.5 - ((r * w) * (w / ((2.6666666666666665 / r) + ((v * -0.8888888888888888) / 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[Or[LessEqual[v, -25000000000.0], N[Not[LessEqual[v, 1.7e-19]], $MachinePrecision]], N[(t$95$0 + N[(-1.5 - N[(N[(r * w), $MachinePrecision] * N[(w / N[(N[(4.0 + N[(2.0 / v), $MachinePrecision]), $MachinePrecision] / r), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(-1.5 - N[(N[(r * w), $MachinePrecision] * N[(w / N[(N[(2.6666666666666665 / r), $MachinePrecision] + N[(N[(v * -0.8888888888888888), $MachinePrecision] / r), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if v < -2.5e10 or 1.7000000000000001e-19 < v

   1. Initial program 73.5

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

   2. Simplified 99.6

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

      [Start] 73.5	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]
      sub-neg [=>] 73.5	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)\right)} - 4.5 \]
      +-commutative [=>] 73.5	\[ \color{blue}{\left(\left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(3 + \frac{2}{r \cdot r}\right)\right)} - 4.5 \]
      associate--l+ [=>] 73.5	\[ \color{blue}{\left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right)} \]
      +-commutative [=>] 73.5	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)} \]
      sub-neg [=>] 73.5	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) + \left(-4.5\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      +-commutative [=>] 73.5	\[ \color{blue}{\left(\left(-4.5\right) + \left(3 + \frac{2}{r \cdot r}\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      associate-+r+ [=>] 73.5	\[ \color{blue}{\left(\left(\left(-4.5\right) + 3\right) + \frac{2}{r \cdot r}\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      +-commutative [<=] 73.5	\[ \color{blue}{\left(\frac{2}{r \cdot r} + \left(\left(-4.5\right) + 3\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      associate-+r+ [<=] 73.5	\[ \color{blue}{\frac{2}{r \cdot r} + \left(\left(\left(-4.5\right) + 3\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)\right)} \]

   3. Taylor expanded in v around inf 98.4

      \[\leadsto \frac{2}{r \cdot r} + \left(-1.5 - \frac{w}{\color{blue}{4 \cdot \frac{1}{r} + 2 \cdot \frac{1}{v \cdot r}}} \cdot \left(r \cdot w\right)\right) \]

   4. Simplified 98.4

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

      [Start] 98.4	\[ \frac{2}{r \cdot r} + \left(-1.5 - \frac{w}{4 \cdot \frac{1}{r} + 2 \cdot \frac{1}{v \cdot r}} \cdot \left(r \cdot w\right)\right) \]
      associate-*r/ [=>] 98.4	\[ \frac{2}{r \cdot r} + \left(-1.5 - \frac{w}{\color{blue}{\frac{4 \cdot 1}{r}} + 2 \cdot \frac{1}{v \cdot r}} \cdot \left(r \cdot w\right)\right) \]
      metadata-eval [=>] 98.4	\[ \frac{2}{r \cdot r} + \left(-1.5 - \frac{w}{\frac{\color{blue}{4}}{r} + 2 \cdot \frac{1}{v \cdot r}} \cdot \left(r \cdot w\right)\right) \]
      associate-*r/ [=>] 98.4	\[ \frac{2}{r \cdot r} + \left(-1.5 - \frac{w}{\frac{4}{r} + \color{blue}{\frac{2 \cdot 1}{v \cdot r}}} \cdot \left(r \cdot w\right)\right) \]
      metadata-eval [=>] 98.4	\[ \frac{2}{r \cdot r} + \left(-1.5 - \frac{w}{\frac{4}{r} + \frac{\color{blue}{2}}{v \cdot r}} \cdot \left(r \cdot w\right)\right) \]

   5. Taylor expanded in r around 0 98.4

      \[\leadsto \frac{2}{r \cdot r} + \left(-1.5 - \color{blue}{\frac{w \cdot r}{4 + 2 \cdot \frac{1}{v}}} \cdot \left(r \cdot w\right)\right) \]

   6. Simplified 98.4

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

      [Start] 98.4	\[ \frac{2}{r \cdot r} + \left(-1.5 - \frac{w \cdot r}{4 + 2 \cdot \frac{1}{v}} \cdot \left(r \cdot w\right)\right) \]
      associate-/l* [=>] 98.4	\[ \frac{2}{r \cdot r} + \left(-1.5 - \color{blue}{\frac{w}{\frac{4 + 2 \cdot \frac{1}{v}}{r}}} \cdot \left(r \cdot w\right)\right) \]
      associate-*r/ [=>] 98.4	\[ \frac{2}{r \cdot r} + \left(-1.5 - \frac{w}{\frac{4 + \color{blue}{\frac{2 \cdot 1}{v}}}{r}} \cdot \left(r \cdot w\right)\right) \]
      metadata-eval [=>] 98.4	\[ \frac{2}{r \cdot r} + \left(-1.5 - \frac{w}{\frac{4 + \frac{\color{blue}{2}}{v}}{r}} \cdot \left(r \cdot w\right)\right) \]

   if -2.5e10 < v < 1.7000000000000001e-19

   1. Initial program 86.2

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

   2. Simplified 99.6

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

      [Start] 86.2	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]
      sub-neg [=>] 86.2	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)\right)} - 4.5 \]
      +-commutative [=>] 86.2	\[ \color{blue}{\left(\left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(3 + \frac{2}{r \cdot r}\right)\right)} - 4.5 \]
      associate--l+ [=>] 86.2	\[ \color{blue}{\left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right)} \]
      +-commutative [=>] 86.2	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)} \]
      sub-neg [=>] 86.2	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) + \left(-4.5\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      +-commutative [=>] 86.2	\[ \color{blue}{\left(\left(-4.5\right) + \left(3 + \frac{2}{r \cdot r}\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      associate-+r+ [=>] 86.2	\[ \color{blue}{\left(\left(\left(-4.5\right) + 3\right) + \frac{2}{r \cdot r}\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      +-commutative [<=] 86.2	\[ \color{blue}{\left(\frac{2}{r \cdot r} + \left(\left(-4.5\right) + 3\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      associate-+r+ [<=] 86.2	\[ \color{blue}{\frac{2}{r \cdot r} + \left(\left(\left(-4.5\right) + 3\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)\right)} \]

   3. Taylor expanded in v around 0 98.9

      \[\leadsto \frac{2}{r \cdot r} + \left(-1.5 - \frac{w}{\color{blue}{2.6666666666666665 \cdot \frac{1}{r} + -0.8888888888888888 \cdot \frac{v}{r}}} \cdot \left(r \cdot w\right)\right) \]

   4. Simplified 98.9

      \[\leadsto \frac{2}{r \cdot r} + \left(-1.5 - \frac{w}{\color{blue}{\frac{2.6666666666666665}{r} + \frac{-0.8888888888888888 \cdot v}{r}}} \cdot \left(r \cdot w\right)\right) \]
      Proof

      [Start] 98.9	\[ \frac{2}{r \cdot r} + \left(-1.5 - \frac{w}{2.6666666666666665 \cdot \frac{1}{r} + -0.8888888888888888 \cdot \frac{v}{r}} \cdot \left(r \cdot w\right)\right) \]
      associate-*r/ [=>] 98.9	\[ \frac{2}{r \cdot r} + \left(-1.5 - \frac{w}{\color{blue}{\frac{2.6666666666666665 \cdot 1}{r}} + -0.8888888888888888 \cdot \frac{v}{r}} \cdot \left(r \cdot w\right)\right) \]
      metadata-eval [=>] 98.9	\[ \frac{2}{r \cdot r} + \left(-1.5 - \frac{w}{\frac{\color{blue}{2.6666666666666665}}{r} + -0.8888888888888888 \cdot \frac{v}{r}} \cdot \left(r \cdot w\right)\right) \]
      associate-*r/ [=>] 98.9	\[ \frac{2}{r \cdot r} + \left(-1.5 - \frac{w}{\frac{2.6666666666666665}{r} + \color{blue}{\frac{-0.8888888888888888 \cdot v}{r}}} \cdot \left(r \cdot w\right)\right) \]

3. Recombined 2 regimes into one program.

4. Final simplification 98.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;v \leq -25000000000 \lor \neg \left(v \leq 1.7 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{2}{r \cdot r} + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4 + \frac{2}{v}}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{r \cdot r} + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{2.6666666666666665}{r} + \frac{v \cdot -0.8888888888888888}{r}}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	99.6%
Cost	7872.00

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

Alternative 2
Error	97.0%
Cost	1988.00

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -7.1 \cdot 10^{+87}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 + \left(\left(t_0 + 3\right) - \frac{r \cdot w}{8 \cdot \frac{1 - v}{\left(r \cdot w\right) \cdot \left(3 + v \cdot -2\right)}}\right)\\ \end{array} \]

Alternative 3
Error	99.5%
Cost	1856.00

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

Alternative 4
Error	97.1%
Cost	1732.00

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -1 \cdot 10^{+95}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{\left(r \cdot w\right) \cdot \left(0.375 + v \cdot -0.25\right)}{1 - v}\right)\\ \end{array} \]

Alternative 5
Error	98.6%
Cost	1609.00

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -25000000000 \lor \neg \left(v \leq 1.7 \cdot 10^{-19}\right):\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4 + \frac{2}{v}}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{2.6666666666666665}{r}}\right)\\ \end{array} \]

Alternative 6
Error	74.4%
Cost	1360.00

\[\begin{array}{l} t_0 := -4.5 + \left(3 + \left(r \cdot r\right) \cdot \left(-0.25 \cdot \left(w \cdot w\right)\right)\right)\\ t_1 := -4.5 + -0.25 \cdot \left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right)\\ \mathbf{if}\;r \leq -1.32 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;r \leq -1900:\\ \;\;\;\;t_0\\ \mathbf{elif}\;r \leq 130:\\ \;\;\;\;\frac{2}{r \cdot r} + -1.5\\ \mathbf{elif}\;r \leq 4.8 \cdot 10^{+135}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	98.5%
Cost	1353.00

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -25000000000 \lor \neg \left(v \leq 1.7 \cdot 10^{-19}\right):\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot -0.25\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot 0.375\right)\right)\right)\\ \end{array} \]

Alternative 8
Error	98.5%
Cost	1353.00

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -25000000000 \lor \neg \left(v \leq 1.7 \cdot 10^{-19}\right):\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot -0.25\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot 0.375\right)\right)\right)\\ \end{array} \]

Alternative 9
Error	98.5%
Cost	1353.00

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -25000000000 \lor \neg \left(v \leq 1.7 \cdot 10^{-19}\right):\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot -0.25\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{2.6666666666666665}{r}}\right)\\ \end{array} \]

Alternative 10
Error	98.5%
Cost	1353.00

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -25000000000 \lor \neg \left(v \leq 1.7 \cdot 10^{-19}\right):\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{2.6666666666666665}{r}}\right)\\ \end{array} \]

Alternative 11
Error	65.8%
Cost	1096.00

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;w \cdot w \leq 2 \cdot 10^{-67}:\\ \;\;\;\;t_0 + -1.5\\ \mathbf{elif}\;w \cdot w \leq 2 \cdot 10^{-19}:\\ \;\;\;\;\left(r \cdot r\right) \cdot \left(w \cdot \left(w \cdot -0.25\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + -4.5\\ \end{array} \]

Alternative 12
Error	84.0%
Cost	1088.00

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

Alternative 13
Error	86.4%
Cost	1088.00

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

Alternative 14
Error	68.7%
Cost	969.00

\[\begin{array}{l} \mathbf{if}\;r \leq -3.4 \cdot 10^{+200} \lor \neg \left(r \leq 4.2 \cdot 10^{+135}\right):\\ \;\;\;\;-4.5 + -0.25 \cdot \left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{r \cdot r} + -1.5\\ \end{array} \]

Alternative 15
Error	45.2%
Cost	448.00

\[\frac{2}{r \cdot r} + -4.5 \]

Alternative 16
Error	67.3%
Cost	448.00

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

Alternative 17
Error	40.2%
Cost	320.00

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

Reproduce

herbie shell --seed 2023093 
(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))