Rosa's TurbineBenchmark

Average Error: 12.7 → 0.6

Time: 15.2s

Precision: binary64

Cost: 2120

Math

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

↓

\[\begin{array}{l} t_0 := 0.125 \cdot \left(-3 - v \cdot -2\right)\\ t_1 := \frac{2}{r \cdot r} + 3\\ t_2 := -4.5 + \left(t_1 + \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot \frac{t_0}{1 - v}\right)\\ \mathbf{if}\;r \leq -2.6 \cdot 10^{+196}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;r \leq 2.95 \cdot 10^{+231}:\\ \;\;\;\;-4.5 + \left(t_1 + \frac{t_0}{\frac{\frac{\frac{1 - v}{r \cdot w}}{r}}{w}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

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 (* 0.125 (- -3.0 (* v -2.0))))
        (t_1 (+ (/ 2.0 (* r r)) 3.0))
        (t_2 (+ -4.5 (+ t_1 (* (* r (* w (* r w))) (/ t_0 (- 1.0 v)))))))
   (if (<= r -2.6e+196)
     t_2
     (if (<= r 2.95e+231)
       (+ -4.5 (+ t_1 (/ t_0 (/ (/ (/ (- 1.0 v) (* r w)) r) w))))
       t_2))))

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 = 0.125 * (-3.0 - (v * -2.0));
	double t_1 = (2.0 / (r * r)) + 3.0;
	double t_2 = -4.5 + (t_1 + ((r * (w * (r * w))) * (t_0 / (1.0 - v))));
	double tmp;
	if (r <= -2.6e+196) {
		tmp = t_2;
	} else if (r <= 2.95e+231) {
		tmp = -4.5 + (t_1 + (t_0 / ((((1.0 - v) / (r * w)) / r) / w)));
	} else {
		tmp = t_2;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = 0.125d0 * ((-3.0d0) - (v * (-2.0d0)))
    t_1 = (2.0d0 / (r * r)) + 3.0d0
    t_2 = (-4.5d0) + (t_1 + ((r * (w * (r * w))) * (t_0 / (1.0d0 - v))))
    if (r <= (-2.6d+196)) then
        tmp = t_2
    else if (r <= 2.95d+231) then
        tmp = (-4.5d0) + (t_1 + (t_0 / ((((1.0d0 - v) / (r * w)) / r) / w)))
    else
        tmp = t_2
    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 = 0.125 * (-3.0 - (v * -2.0));
	double t_1 = (2.0 / (r * r)) + 3.0;
	double t_2 = -4.5 + (t_1 + ((r * (w * (r * w))) * (t_0 / (1.0 - v))));
	double tmp;
	if (r <= -2.6e+196) {
		tmp = t_2;
	} else if (r <= 2.95e+231) {
		tmp = -4.5 + (t_1 + (t_0 / ((((1.0 - v) / (r * w)) / r) / w)));
	} else {
		tmp = t_2;
	}
	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 = 0.125 * (-3.0 - (v * -2.0))
	t_1 = (2.0 / (r * r)) + 3.0
	t_2 = -4.5 + (t_1 + ((r * (w * (r * w))) * (t_0 / (1.0 - v))))
	tmp = 0
	if r <= -2.6e+196:
		tmp = t_2
	elif r <= 2.95e+231:
		tmp = -4.5 + (t_1 + (t_0 / ((((1.0 - v) / (r * w)) / r) / w)))
	else:
		tmp = t_2
	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(0.125 * Float64(-3.0 - Float64(v * -2.0)))
	t_1 = Float64(Float64(2.0 / Float64(r * r)) + 3.0)
	t_2 = Float64(-4.5 + Float64(t_1 + Float64(Float64(r * Float64(w * Float64(r * w))) * Float64(t_0 / Float64(1.0 - v)))))
	tmp = 0.0
	if (r <= -2.6e+196)
		tmp = t_2;
	elseif (r <= 2.95e+231)
		tmp = Float64(-4.5 + Float64(t_1 + Float64(t_0 / Float64(Float64(Float64(Float64(1.0 - v) / Float64(r * w)) / r) / w))));
	else
		tmp = t_2;
	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 = 0.125 * (-3.0 - (v * -2.0));
	t_1 = (2.0 / (r * r)) + 3.0;
	t_2 = -4.5 + (t_1 + ((r * (w * (r * w))) * (t_0 / (1.0 - v))));
	tmp = 0.0;
	if (r <= -2.6e+196)
		tmp = t_2;
	elseif (r <= 2.95e+231)
		tmp = -4.5 + (t_1 + (t_0 / ((((1.0 - v) / (r * w)) / r) / w)));
	else
		tmp = t_2;
	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[(0.125 * N[(-3.0 - N[(v * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(2.0 / N[(r * r), $MachinePrecision]), $MachinePrecision] + 3.0), $MachinePrecision]}, Block[{t$95$2 = N[(-4.5 + N[(t$95$1 + N[(N[(r * N[(w * N[(r * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 / N[(1.0 - v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[r, -2.6e+196], t$95$2, If[LessEqual[r, 2.95e+231], N[(-4.5 + N[(t$95$1 + N[(t$95$0 / N[(N[(N[(N[(1.0 - v), $MachinePrecision] / N[(r * w), $MachinePrecision]), $MachinePrecision] / r), $MachinePrecision] / w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 2 regimes

2. if r < -2.60000000000000012e196 or 2.95e231 < r

   1. Initial program 36.3

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

   2. Simplified 30.4

      \[\leadsto \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \left(r \cdot \left(w \cdot w\right)\right)\right)\right) + -4.5} \]
      Proof
      (+.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (-.f64 1 v)) (*.f64 r (*.f64 r (*.f64 w w))))) -9/2): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (-.f64 1 v)) (*.f64 r (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 w w) r))))) -9/2): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (-.f64 1 v)) (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 (*.f64 w w) r) r)))) -9/2): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) (-.f64 1 v)))) -9/2): 19 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (/.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) (-.f64 1 v))) (Rewrite<= metadata-eval (neg.f64 9/2))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= sub-neg_binary64 (-.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (/.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) (-.f64 1 v))) 9/2)): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in r around 0 30.4

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

   4. Simplified 0.5

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \color{blue}{\left(w \cdot \left(w \cdot r\right)\right)}\right)\right) + -4.5 \]
      Proof
      (*.f64 w (*.f64 w r)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 w w) r)): 56 points increase in error, 45 points decrease in error
      (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 w 2)) r): 0 points increase in error, 0 points decrease in error

   if -2.60000000000000012e196 < r < 2.95e231

   1. Initial program 9.9

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

   2. Simplified 5.7

      \[\leadsto \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 + -2 \cdot v\right)}{\frac{1 - v}{r \cdot \left(r \cdot \left(w \cdot w\right)\right)}}\right) + -4.5} \]
      Proof
      (+.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (/.f64 (*.f64 1/8 (+.f64 3 (*.f64 -2 v))) (/.f64 (-.f64 1 v) (*.f64 r (*.f64 r (*.f64 w w)))))) -9/2): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (/.f64 (*.f64 1/8 (+.f64 3 (*.f64 (Rewrite<= metadata-eval (neg.f64 2)) v))) (/.f64 (-.f64 1 v) (*.f64 r (*.f64 r (*.f64 w w)))))) -9/2): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (/.f64 (*.f64 1/8 (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 3 (*.f64 2 v)))) (/.f64 (-.f64 1 v) (*.f64 r (*.f64 r (*.f64 w w)))))) -9/2): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (/.f64 (-.f64 1 v) (*.f64 r (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 w w) r)))))) -9/2): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (/.f64 (-.f64 1 v) (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 (*.f64 w w) r) r))))) -9/2): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) (-.f64 1 v)))) -9/2): 22 points increase in error, 2 points decrease in error
      (+.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (/.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) (-.f64 1 v))) (Rewrite<= metadata-eval (neg.f64 9/2))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= sub-neg_binary64 (-.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (/.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) (-.f64 1 v))) 9/2)): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in r around 0 5.7

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

   4. Simplified 2.6

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 + -2 \cdot v\right)}{\frac{1 - v}{r \cdot \color{blue}{\left(w \cdot \left(w \cdot r\right)\right)}}}\right) + -4.5 \]
      Proof
      (*.f64 w (*.f64 w r)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 w w) r)): 56 points increase in error, 45 points decrease in error
      (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 w 2)) r): 0 points increase in error, 0 points decrease in error

   5. Applied egg-rr 0.3

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

   6. Applied egg-rr 0.6

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

4. Final simplification 0.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;r \leq -2.6 \cdot 10^{+196}:\\ \;\;\;\;-4.5 + \left(\left(\frac{2}{r \cdot r} + 3\right) + \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot \frac{0.125 \cdot \left(-3 - v \cdot -2\right)}{1 - v}\right)\\ \mathbf{elif}\;r \leq 2.95 \cdot 10^{+231}:\\ \;\;\;\;-4.5 + \left(\left(\frac{2}{r \cdot r} + 3\right) + \frac{0.125 \cdot \left(-3 - v \cdot -2\right)}{\frac{\frac{\frac{1 - v}{r \cdot w}}{r}}{w}}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 + \left(\left(\frac{2}{r \cdot r} + 3\right) + \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot \frac{0.125 \cdot \left(-3 - v \cdot -2\right)}{1 - v}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	0.3
Cost	7872

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

Alternative 2
Error	0.3
Cost	7872

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

Alternative 3
Error	1.1
Cost	2116

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r} + 3\\ \mathbf{if}\;w \cdot w \leq 10^{+302}:\\ \;\;\;\;-4.5 + \left(t_0 + \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot \frac{0.125 \cdot \left(-3 - v \cdot -2\right)}{1 - v}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 + \left(t_0 - \frac{r}{\frac{1 - v}{w}} \cdot \left(\left(r \cdot w\right) \cdot \left(0.375 + v \cdot -0.25\right)\right)\right)\\ \end{array} \]

Alternative 4
Error	0.4
Cost	1984

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

Alternative 5
Error	2.0
Cost	1732

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -4 \cdot 10^{+21}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) \cdot 0.25\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \frac{\left(r \cdot w\right) \cdot \left(0.375 + v \cdot -0.25\right)}{v + -1}\right)\\ \end{array} \]

Alternative 6
Error	1.0
Cost	1352

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ t_1 := \left(r \cdot w\right) \cdot \left(r \cdot w\right)\\ t_2 := t_0 + \left(-1.5 - t_1 \cdot 0.25\right)\\ \mathbf{if}\;v \leq -170000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;v \leq 2.1 \cdot 10^{-17}:\\ \;\;\;\;t_0 + \left(-1.5 + t_1 \cdot -0.375\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	0.9
Cost	1352

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ t_1 := t_0 + \left(-1.5 - \left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) \cdot 0.25\right)\\ \mathbf{if}\;v \leq -170000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;v \leq 4.5 \cdot 10^{-10}:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot -0.375\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	21.6
Cost	1096

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r} + -1.5\\ \mathbf{if}\;w \cdot w \leq 8 \cdot 10^{+91}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;w \cdot w \leq 2.8 \cdot 10^{+157}:\\ \;\;\;\;\left(r \cdot r\right) \cdot \left(\left(w \cdot w\right) \cdot -0.375\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 9
Error	21.5
Cost	1096

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r} + -1.5\\ \mathbf{if}\;w \cdot w \leq 8.5 \cdot 10^{+91}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;w \cdot w \leq 2.9 \cdot 10^{+152}:\\ \;\;\;\;-0.375 \cdot \left(\left(r \cdot r\right) \cdot \left(w \cdot w\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 10
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 11
Error	20.9
Cost	448

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

Alternative 12
Error	37.7
Cost	320

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

Alternative 13
Error	37.7
Cost	320

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

Reproduce

herbie shell --seed 2022338 
(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))