Rosa's TurbineBenchmark

Average Accuracy: 79.9% → 98.5%

Time: 18.2s

Precision: binary64

Cost: 1864

Math

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

↓

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -1 \cdot 10^{+54}:\\ \;\;\;\;\left(\left(t_0 + 3\right) + \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot \frac{v \cdot 0.25}{1 - v}\right) + -4.5\\ \mathbf{elif}\;v \leq 3.6 \cdot 10^{+86}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{1 - v}{r \cdot \left(0.375 + v \cdot -0.25\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot 0.25\right)\right)\right)\\ \end{array} \]

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))))
   (if (<= v -1e+54)
     (+ (+ (+ t_0 3.0) (* (* r (* w (* r w))) (/ (* v 0.25) (- 1.0 v)))) -4.5)
     (if (<= v 3.6e+86)
       (+
        t_0
        (- -1.5 (* (* r w) (/ w (/ (- 1.0 v) (* r (+ 0.375 (* v -0.25))))))))
       (+ t_0 (- -1.5 (* (* r w) (* r (* w 0.25)))))))))

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 <= -1e+54) {
		tmp = ((t_0 + 3.0) + ((r * (w * (r * w))) * ((v * 0.25) / (1.0 - v)))) + -4.5;
	} else if (v <= 3.6e+86) {
		tmp = t_0 + (-1.5 - ((r * w) * (w / ((1.0 - v) / (r * (0.375 + (v * -0.25)))))));
	} else {
		tmp = t_0 + (-1.5 - ((r * w) * (r * (w * 0.25))));
	}
	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 <= (-1d+54)) then
        tmp = ((t_0 + 3.0d0) + ((r * (w * (r * w))) * ((v * 0.25d0) / (1.0d0 - v)))) + (-4.5d0)
    else if (v <= 3.6d+86) then
        tmp = t_0 + ((-1.5d0) - ((r * w) * (w / ((1.0d0 - v) / (r * (0.375d0 + (v * (-0.25d0))))))))
    else
        tmp = t_0 + ((-1.5d0) - ((r * w) * (r * (w * 0.25d0))))
    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 <= -1e+54) {
		tmp = ((t_0 + 3.0) + ((r * (w * (r * w))) * ((v * 0.25) / (1.0 - v)))) + -4.5;
	} else if (v <= 3.6e+86) {
		tmp = t_0 + (-1.5 - ((r * w) * (w / ((1.0 - v) / (r * (0.375 + (v * -0.25)))))));
	} else {
		tmp = t_0 + (-1.5 - ((r * w) * (r * (w * 0.25))));
	}
	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 <= -1e+54:
		tmp = ((t_0 + 3.0) + ((r * (w * (r * w))) * ((v * 0.25) / (1.0 - v)))) + -4.5
	elif v <= 3.6e+86:
		tmp = t_0 + (-1.5 - ((r * w) * (w / ((1.0 - v) / (r * (0.375 + (v * -0.25)))))))
	else:
		tmp = t_0 + (-1.5 - ((r * w) * (r * (w * 0.25))))
	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 <= -1e+54)
		tmp = Float64(Float64(Float64(t_0 + 3.0) + Float64(Float64(r * Float64(w * Float64(r * w))) * Float64(Float64(v * 0.25) / Float64(1.0 - v)))) + -4.5);
	elseif (v <= 3.6e+86)
		tmp = Float64(t_0 + Float64(-1.5 - Float64(Float64(r * w) * Float64(w / Float64(Float64(1.0 - v) / Float64(r * Float64(0.375 + Float64(v * -0.25))))))));
	else
		tmp = Float64(t_0 + Float64(-1.5 - Float64(Float64(r * w) * Float64(r * Float64(w * 0.25)))));
	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 <= -1e+54)
		tmp = ((t_0 + 3.0) + ((r * (w * (r * w))) * ((v * 0.25) / (1.0 - v)))) + -4.5;
	elseif (v <= 3.6e+86)
		tmp = t_0 + (-1.5 - ((r * w) * (w / ((1.0 - v) / (r * (0.375 + (v * -0.25)))))));
	else
		tmp = t_0 + (-1.5 - ((r * w) * (r * (w * 0.25))));
	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, -1e+54], N[(N[(N[(t$95$0 + 3.0), $MachinePrecision] + N[(N[(r * N[(w * N[(r * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(v * 0.25), $MachinePrecision] / N[(1.0 - v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -4.5), $MachinePrecision], If[LessEqual[v, 3.6e+86], N[(t$95$0 + N[(-1.5 - N[(N[(r * w), $MachinePrecision] * N[(w / N[(N[(1.0 - v), $MachinePrecision] / N[(r * N[(0.375 + N[(v * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(-1.5 - N[(N[(r * w), $MachinePrecision] * N[(r * N[(w * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if v < -1.0000000000000001e54

   1. Initial program 68.6%

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

   2. Simplified 85.8%

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

      [Start] 68.6	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]
      sub-neg [=>] 68.6	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(-4.5\right)} \]
      associate-*l/ [<=] 85.8	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}\right) + \left(-4.5\right) \]
      *-commutative [=>] 85.8	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \color{blue}{\left(r \cdot \left(\left(w \cdot w\right) \cdot r\right)\right)}\right) + \left(-4.5\right) \]
      *-commutative [=>] 85.8	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \color{blue}{\left(r \cdot \left(w \cdot w\right)\right)}\right)\right) + \left(-4.5\right) \]
      metadata-eval [=>] 85.8	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \left(r \cdot \left(w \cdot w\right)\right)\right)\right) + \color{blue}{-4.5} \]

   3. Taylor expanded in v around inf 86.0%

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\color{blue}{-0.25 \cdot v}}{1 - v} \cdot \left(r \cdot \left(r \cdot \left(w \cdot w\right)\right)\right)\right) + -4.5 \]

   4. Taylor expanded in r around 0 86.0%

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{-0.25 \cdot v}{1 - v} \cdot \left(r \cdot \color{blue}{\left({w}^{2} \cdot r\right)}\right)\right) + -4.5 \]

   5. Simplified 96.2%

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{-0.25 \cdot v}{1 - v} \cdot \left(r \cdot \color{blue}{\left(w \cdot \left(w \cdot r\right)\right)}\right)\right) + -4.5 \]
      Proof

      [Start] 86.0	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{-0.25 \cdot v}{1 - v} \cdot \left(r \cdot \left({w}^{2} \cdot r\right)\right)\right) + -4.5 \]
      unpow2 [=>] 86.0	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{-0.25 \cdot v}{1 - v} \cdot \left(r \cdot \left(\color{blue}{\left(w \cdot w\right)} \cdot r\right)\right)\right) + -4.5 \]
      associate-*l* [=>] 96.2	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{-0.25 \cdot v}{1 - v} \cdot \left(r \cdot \color{blue}{\left(w \cdot \left(w \cdot r\right)\right)}\right)\right) + -4.5 \]

   if -1.0000000000000001e54 < v < 3.60000000000000005e86

   1. Initial program 86.4%

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

   2. Simplified 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] 86.4	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]
      sub-neg [=>] 86.4	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)\right)} - 4.5 \]
      +-commutative [=>] 86.4	\[ \color{blue}{\left(\left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(3 + \frac{2}{r \cdot r}\right)\right)} - 4.5 \]
      associate--l+ [=>] 86.4	\[ \color{blue}{\left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right)} \]
      +-commutative [=>] 86.4	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)} \]
      sub-neg [=>] 86.4	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) + \left(-4.5\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      +-commutative [=>] 86.4	\[ \color{blue}{\left(\left(-4.5\right) + \left(3 + \frac{2}{r \cdot r}\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      associate-+r+ [=>] 86.4	\[ \color{blue}{\left(\left(\left(-4.5\right) + 3\right) + \frac{2}{r \cdot r}\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      +-commutative [<=] 86.4	\[ \color{blue}{\left(\frac{2}{r \cdot r} + \left(\left(-4.5\right) + 3\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      associate-+r+ [<=] 86.4	\[ \color{blue}{\frac{2}{r \cdot r} + \left(\left(\left(-4.5\right) + 3\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)\right)} \]

   3. Taylor expanded in r around 0 99.1%

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

   if 3.60000000000000005e86 < v

   1. Initial program 70.5%

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

   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] 70.5	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]
      sub-neg [=>] 70.5	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)\right)} - 4.5 \]
      +-commutative [=>] 70.5	\[ \color{blue}{\left(\left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(3 + \frac{2}{r \cdot r}\right)\right)} - 4.5 \]
      associate--l+ [=>] 70.5	\[ \color{blue}{\left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right)} \]
      +-commutative [=>] 70.5	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)} \]
      sub-neg [=>] 70.5	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) + \left(-4.5\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      +-commutative [=>] 70.5	\[ \color{blue}{\left(\left(-4.5\right) + \left(3 + \frac{2}{r \cdot r}\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      associate-+r+ [=>] 70.5	\[ \color{blue}{\left(\left(\left(-4.5\right) + 3\right) + \frac{2}{r \cdot r}\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      +-commutative [<=] 70.5	\[ \color{blue}{\left(\frac{2}{r \cdot r} + \left(\left(-4.5\right) + 3\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      associate-+r+ [<=] 70.5	\[ \color{blue}{\frac{2}{r \cdot r} + \left(\left(\left(-4.5\right) + 3\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)\right)} \]

   3. Taylor expanded in v around inf 99.6%

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

   4. Simplified 99.6%

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

      [Start] 99.6	\[ \frac{2}{r \cdot r} + \left(-1.5 - \left(0.25 \cdot \left(w \cdot r\right)\right) \cdot \left(r \cdot w\right)\right) \]
      associate-*r* [=>] 99.6	\[ \frac{2}{r \cdot r} + \left(-1.5 - \color{blue}{\left(\left(0.25 \cdot w\right) \cdot r\right)} \cdot \left(r \cdot w\right)\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;v \leq -1 \cdot 10^{+54}:\\ \;\;\;\;\left(\left(\frac{2}{r \cdot r} + 3\right) + \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot \frac{v \cdot 0.25}{1 - v}\right) + -4.5\\ \mathbf{elif}\;v \leq 3.6 \cdot 10^{+86}:\\ \;\;\;\;\frac{2}{r \cdot r} + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{1 - v}{r \cdot \left(0.375 + v \cdot -0.25\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{r \cdot r} + \left(-1.5 - \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot 0.25\right)\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	99.6%
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
Accuracy	99.2%
Cost	1737

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -1.65 \lor \neg \left(v \leq 1\right):\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4 + \frac{2}{v}}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{2.6666666666666665}{r} + \frac{v \cdot -0.8888888888888888}{r}}\right)\\ \end{array} \]

Alternative 3
Accuracy	97.8%
Cost	1736

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -1.55:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4 + \frac{2}{v}}{r}}\right)\\ \mathbf{elif}\;v \leq 2.05:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{2.6666666666666665}{r} + \frac{v \cdot -0.8888888888888888}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \frac{w}{\frac{\frac{\frac{4}{r} + \frac{2}{r \cdot v}}{w}}{r}}\right)\\ \end{array} \]

Alternative 4
Accuracy	97.0%
Cost	1736

\[\begin{array}{l} t_0 := \frac{4}{r} + \frac{2}{r \cdot v}\\ t_1 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -1.8:\\ \;\;\;\;t_1 + \left(-1.5 - \frac{w \cdot \left(r \cdot w\right)}{t_0}\right)\\ \mathbf{elif}\;v \leq 1.7:\\ \;\;\;\;t_1 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{2.6666666666666665}{r} + \frac{v \cdot -0.8888888888888888}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(-1.5 - \frac{w}{\frac{\frac{t_0}{w}}{r}}\right)\\ \end{array} \]

Alternative 5
Accuracy	99.1%
Cost	1609

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

Alternative 6
Accuracy	93.6%
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -1.75 \lor \neg \left(v \leq 3.1\right):\\ \;\;\;\;t_0 + \left(-1.5 - 0.25 \cdot \left(w \cdot \left(r \cdot \left(r \cdot w\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot -0.375\right)\\ \end{array} \]

Alternative 7
Accuracy	95.3%
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -3.7 \lor \neg \left(v \leq 1.95\right):\\ \;\;\;\;t_0 + \left(-1.5 - 0.25 \cdot \left(w \cdot \left(r \cdot \left(r \cdot w\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot 0.375\right)\right)\right)\\ \end{array} \]

Alternative 8
Accuracy	98.9%
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -1.15 \lor \neg \left(v \leq 1\right):\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot 0.25\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot 0.375\right)\right)\right)\\ \end{array} \]

Alternative 9
Accuracy	98.9%
Cost	1352

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -1.15:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r}}\right)\\ \mathbf{elif}\;v \leq 1:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot 0.375\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot 0.25\right)\right)\right)\\ \end{array} \]

Alternative 10
Accuracy	64.7%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;w \cdot w \leq 3.7 \cdot 10^{-31} \lor \neg \left(w \cdot w \leq 1.45 \cdot 10^{+122}\right):\\ \;\;\;\;-1.5 + \frac{\frac{2}{r}}{r}\\ \mathbf{else}:\\ \;\;\;\;\left(r \cdot r\right) \cdot \left(-0.25 \cdot \left(w \cdot w\right)\right)\\ \end{array} \]

Alternative 11
Accuracy	65.1%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;w \cdot w \leq 5 \cdot 10^{-12} \lor \neg \left(w \cdot w \leq 2 \cdot 10^{+122}\right):\\ \;\;\;\;-1.5 + \frac{\frac{2}{r}}{r}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(r \cdot r\right) \cdot \left(w \cdot w\right)\right) \cdot -0.375\\ \end{array} \]

Alternative 12
Accuracy	81.6%
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 13
Accuracy	67.3%
Cost	448

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

Alternative 14
Accuracy	40.9%
Cost	320

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

Alternative 15
Accuracy	40.9%
Cost	320

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

Reproduce

herbie shell --seed 2023129 
(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))