Rosa's TurbineBenchmark

Average Error: 12.5 → 1.1

Time: 16.2s

Precision: binary64

Cost: 1864

Math

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

↓

\[\begin{array}{l} t_0 := 3 + \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -2.0533200165948094 \cdot 10^{+24}:\\ \;\;\;\;\left(t_0 + \left(r \cdot w\right) \cdot \left(\left(r \cdot w\right) \cdot -0.25\right)\right) + -4.5\\ \mathbf{elif}\;v \leq 4.2140857039136757 \cdot 10^{-10}:\\ \;\;\;\;\left(t_0 + \left(r \cdot w\right) \cdot \left(\left(r \cdot w\right) \cdot \left(-0.375 + v \cdot -0.125\right)\right)\right) + -4.5\\ \mathbf{else}:\\ \;\;\;\;\left(t_0 + \left(r \cdot w\right) \cdot \left(\left(r \cdot w\right) \cdot \left(0.125 \cdot \left(-2 - \frac{-1}{v}\right)\right)\right)\right) + -4.5\\ \end{array} \]

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
 (let* ((t_0 (+ 3.0 (/ 2.0 (* r r)))))
   (if (<= v -2.0533200165948094e+24)
     (+ (+ t_0 (* (* r w) (* (* r w) -0.25))) -4.5)
     (if (<= v 4.2140857039136757e-10)
       (+ (+ t_0 (* (* r w) (* (* r w) (+ -0.375 (* v -0.125))))) -4.5)
       (+
        (+ t_0 (* (* r w) (* (* r w) (* 0.125 (- -2.0 (/ -1.0 v))))))
        -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 t_0 = 3.0 + (2.0 / (r * r));
	double tmp;
	if (v <= -2.0533200165948094e+24) {
		tmp = (t_0 + ((r * w) * ((r * w) * -0.25))) + -4.5;
	} else if (v <= 4.2140857039136757e-10) {
		tmp = (t_0 + ((r * w) * ((r * w) * (-0.375 + (v * -0.125))))) + -4.5;
	} else {
		tmp = (t_0 + ((r * w) * ((r * w) * (0.125 * (-2.0 - (-1.0 / v)))))) + -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) :: t_0
    real(8) :: tmp
    t_0 = 3.0d0 + (2.0d0 / (r * r))
    if (v <= (-2.0533200165948094d+24)) then
        tmp = (t_0 + ((r * w) * ((r * w) * (-0.25d0)))) + (-4.5d0)
    else if (v <= 4.2140857039136757d-10) then
        tmp = (t_0 + ((r * w) * ((r * w) * ((-0.375d0) + (v * (-0.125d0)))))) + (-4.5d0)
    else
        tmp = (t_0 + ((r * w) * ((r * w) * (0.125d0 * ((-2.0d0) - ((-1.0d0) / v)))))) + (-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 t_0 = 3.0 + (2.0 / (r * r));
	double tmp;
	if (v <= -2.0533200165948094e+24) {
		tmp = (t_0 + ((r * w) * ((r * w) * -0.25))) + -4.5;
	} else if (v <= 4.2140857039136757e-10) {
		tmp = (t_0 + ((r * w) * ((r * w) * (-0.375 + (v * -0.125))))) + -4.5;
	} else {
		tmp = (t_0 + ((r * w) * ((r * w) * (0.125 * (-2.0 - (-1.0 / v)))))) + -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):
	t_0 = 3.0 + (2.0 / (r * r))
	tmp = 0
	if v <= -2.0533200165948094e+24:
		tmp = (t_0 + ((r * w) * ((r * w) * -0.25))) + -4.5
	elif v <= 4.2140857039136757e-10:
		tmp = (t_0 + ((r * w) * ((r * w) * (-0.375 + (v * -0.125))))) + -4.5
	else:
		tmp = (t_0 + ((r * w) * ((r * w) * (0.125 * (-2.0 - (-1.0 / v)))))) + -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)
	t_0 = Float64(3.0 + Float64(2.0 / Float64(r * r)))
	tmp = 0.0
	if (v <= -2.0533200165948094e+24)
		tmp = Float64(Float64(t_0 + Float64(Float64(r * w) * Float64(Float64(r * w) * -0.25))) + -4.5);
	elseif (v <= 4.2140857039136757e-10)
		tmp = Float64(Float64(t_0 + Float64(Float64(r * w) * Float64(Float64(r * w) * Float64(-0.375 + Float64(v * -0.125))))) + -4.5);
	else
		tmp = Float64(Float64(t_0 + Float64(Float64(r * w) * Float64(Float64(r * w) * Float64(0.125 * Float64(-2.0 - Float64(-1.0 / v)))))) + -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)
	t_0 = 3.0 + (2.0 / (r * r));
	tmp = 0.0;
	if (v <= -2.0533200165948094e+24)
		tmp = (t_0 + ((r * w) * ((r * w) * -0.25))) + -4.5;
	elseif (v <= 4.2140857039136757e-10)
		tmp = (t_0 + ((r * w) * ((r * w) * (-0.375 + (v * -0.125))))) + -4.5;
	else
		tmp = (t_0 + ((r * w) * ((r * w) * (0.125 * (-2.0 - (-1.0 / v)))))) + -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_] := Block[{t$95$0 = N[(3.0 + N[(2.0 / N[(r * r), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[v, -2.0533200165948094e+24], N[(N[(t$95$0 + N[(N[(r * w), $MachinePrecision] * N[(N[(r * w), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -4.5), $MachinePrecision], If[LessEqual[v, 4.2140857039136757e-10], N[(N[(t$95$0 + N[(N[(r * w), $MachinePrecision] * N[(N[(r * w), $MachinePrecision] * N[(-0.375 + N[(v * -0.125), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -4.5), $MachinePrecision], N[(N[(t$95$0 + N[(N[(r * w), $MachinePrecision] * N[(N[(r * w), $MachinePrecision] * N[(0.125 * N[(-2.0 - N[(-1.0 / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -4.5), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if v < -2.0533200165948094e24

   1. Initial program 17.8

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

   2. Taylor expanded in v around inf 17.2

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

   3. Simplified 17.2

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\left(w \cdot w\right) \cdot \left(\left(r \cdot r\right) \cdot 0.25\right)}\right) - 4.5 \]
      Proof
      (*.f64 (*.f64 w w) (*.f64 (*.f64 r r) 1/4)): 0 points increase in error, 0 points decrease in error
      (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 w 2)) (*.f64 (*.f64 r r) 1/4)): 0 points increase in error, 0 points decrease in error
      (*.f64 (pow.f64 w 2) (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 r 2)) 1/4)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (pow.f64 w 2) (pow.f64 r 2)) 1/4)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= *-commutative_binary64 (*.f64 1/4 (*.f64 (pow.f64 w 2) (pow.f64 r 2)))): 0 points increase in error, 0 points decrease in error

   4. Taylor expanded in w around 0 17.2

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

   5. Simplified 0.3

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\left(w \cdot r\right) \cdot \left(0.25 \cdot \left(w \cdot r\right)\right)}\right) - 4.5 \]
      Proof
      (*.f64 (*.f64 w r) (*.f64 1/4 (*.f64 w r))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 w r) (Rewrite=> *-commutative_binary64 (*.f64 (*.f64 w r) 1/4))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 w r) (*.f64 w r)) 1/4)): 0 points increase in error, 0 points decrease in error
      (*.f64 (Rewrite<= unswap-sqr_binary64 (*.f64 (*.f64 w w) (*.f64 r r))) 1/4): 97 points increase in error, 54 points decrease in error
      (*.f64 (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 w 2)) (*.f64 r r)) 1/4): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 (pow.f64 w 2) (Rewrite<= unpow2_binary64 (pow.f64 r 2))) 1/4): 0 points increase in error, 0 points decrease in error
      (Rewrite<= *-commutative_binary64 (*.f64 1/4 (*.f64 (pow.f64 w 2) (pow.f64 r 2)))): 0 points increase in error, 0 points decrease in error

   if -2.0533200165948094e24 < v < 4.21408570391367566e-10

   1. Initial program 8.1

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

   2. Applied egg-rr 0.4

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

   3. Applied egg-rr 0.4

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

   4. Applied egg-rr 0.3

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

   5. Taylor expanded in v around 0 1.4

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

   6. Simplified 1.4

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \left(w \cdot r\right) \cdot \color{blue}{\left(\left(w \cdot r\right) \cdot \left(0.125 \cdot v + 0.375\right)\right)}\right) - 4.5 \]
      Proof
      (*.f64 (*.f64 w r) (+.f64 (*.f64 1/8 v) 3/8)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 (*.f64 1/8 v) (*.f64 w r)) (*.f64 3/8 (*.f64 w r)))): 0 points increase in error, 2 points decrease in error
      (+.f64 (*.f64 (*.f64 1/8 v) (Rewrite<= *-rgt-identity_binary64 (*.f64 (*.f64 w r) 1))) (*.f64 3/8 (*.f64 w r))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (*.f64 1/8 v) (*.f64 (*.f64 w r) (Rewrite<= metadata-eval (-.f64 -2 -3)))) (*.f64 3/8 (*.f64 w r))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (*.f64 1/8 v) (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 -2 (*.f64 w r)) (*.f64 -3 (*.f64 w r))))) (*.f64 3/8 (*.f64 w r))): 30 points increase in error, 23 points decrease in error
      (+.f64 (Rewrite<= associate-*r*_binary64 (*.f64 1/8 (*.f64 v (-.f64 (*.f64 -2 (*.f64 w r)) (*.f64 -3 (*.f64 w r)))))) (*.f64 3/8 (*.f64 w r))): 0 points increase in error, 0 points decrease in error

   if 4.21408570391367566e-10 < v

   1. Initial program 17.0

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

   2. Applied egg-rr 12.4

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

   3. Applied egg-rr 0.4

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

   4. Applied egg-rr 0.4

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

   5. Taylor expanded in v around inf 0.9

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

4. Final simplification 1.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;v \leq -2.0533200165948094 \cdot 10^{+24}:\\ \;\;\;\;\left(\left(3 + \frac{2}{r \cdot r}\right) + \left(r \cdot w\right) \cdot \left(\left(r \cdot w\right) \cdot -0.25\right)\right) + -4.5\\ \mathbf{elif}\;v \leq 4.2140857039136757 \cdot 10^{-10}:\\ \;\;\;\;\left(\left(3 + \frac{2}{r \cdot r}\right) + \left(r \cdot w\right) \cdot \left(\left(r \cdot w\right) \cdot \left(-0.375 + v \cdot -0.125\right)\right)\right) + -4.5\\ \mathbf{else}:\\ \;\;\;\;\left(\left(3 + \frac{2}{r \cdot r}\right) + \left(r \cdot w\right) \cdot \left(\left(r \cdot w\right) \cdot \left(0.125 \cdot \left(-2 - \frac{-1}{v}\right)\right)\right)\right) + -4.5\\ \end{array} \]

Alternatives

Alternative 1
Error	0.4
Cost	7936

\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{{\left(r \cdot w\right)}^{2}}{\frac{1 - v}{v \cdot -0.25 + 0.375}}\right) + -4.5 \]

Alternative 2
Error	1.1
Cost	1736

\[\begin{array}{l} t_0 := 3 + \frac{2}{r \cdot r}\\ t_1 := \left(t_0 + \left(r \cdot w\right) \cdot \left(\left(r \cdot w\right) \cdot -0.25\right)\right) + -4.5\\ \mathbf{if}\;v \leq -2.0533200165948094 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;v \leq 4.2140857039136757 \cdot 10^{-10}:\\ \;\;\;\;\left(t_0 + \left(r \cdot w\right) \cdot \left(\left(r \cdot w\right) \cdot \left(-0.375 + v \cdot -0.125\right)\right)\right) + -4.5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	13.9
Cost	1616

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ t_1 := t_0 + -1.5\\ t_2 := \left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot -0.25\right)\right)\\ \mathbf{if}\;r \leq -1.05 \cdot 10^{+237}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;r \leq -6.5 \cdot 10^{+198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;r \leq -1 \cdot 10^{+150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;r \leq 1.4 \cdot 10^{+153}:\\ \;\;\;\;t_0 + \left(-1.5 + w \cdot \left(-0.25 \cdot \left(\left(r \cdot r\right) \cdot w\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	3.1
Cost	1480

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ t_1 := t_0 + \left(-1.5 + r \cdot \left(w \cdot \left(\left(r \cdot w\right) \cdot -0.25\right)\right)\right)\\ \mathbf{if}\;v \leq -2.0533200165948094 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;v \leq 4.2140857039136757 \cdot 10^{-10}:\\ \;\;\;\;\left(\left(3 + t_0\right) + \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot -0.375\right) + -4.5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	2.1
Cost	1480

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ t_1 := t_0 + \left(-1.5 + r \cdot \left(w \cdot \left(\left(r \cdot w\right) \cdot -0.25\right)\right)\right)\\ \mathbf{if}\;v \leq -2.0533200165948094 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;v \leq 4.2140857039136757 \cdot 10^{-10}:\\ \;\;\;\;\left(\left(3 + t_0\right) + \left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot -0.375\right)\right)\right) + -4.5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	1.0
Cost	1480

\[\begin{array}{l} t_0 := 3 + \frac{2}{r \cdot r}\\ t_1 := \left(t_0 + \left(r \cdot w\right) \cdot \left(\left(r \cdot w\right) \cdot -0.25\right)\right) + -4.5\\ \mathbf{if}\;v \leq -2.0533200165948094 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;v \leq 4.2140857039136757 \cdot 10^{-10}:\\ \;\;\;\;\left(t_0 + \left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot -0.375\right)\right)\right) + -4.5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	9.3
Cost	1352

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ t_1 := t_0 + \left(-1.5 + r \cdot \left(w \cdot \left(\left(r \cdot w\right) \cdot -0.25\right)\right)\right)\\ \mathbf{if}\;r \leq -1 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;r \leq 20000000000000:\\ \;\;\;\;t_0 + \left(-1.5 + w \cdot \left(-0.25 \cdot \left(\left(r \cdot r\right) \cdot w\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	15.9
Cost	1224

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ t_1 := t_0 + -0.25 \cdot \left(w \cdot \left(\left(r \cdot r\right) \cdot w\right)\right)\\ \mathbf{if}\;w \leq -8.4 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;w \leq 10^{-90}:\\ \;\;\;\;t_0 + -1.5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	20.8
Cost	972

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r} + -1.5\\ t_1 := \left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot -0.25\right)\right)\\ \mathbf{if}\;r \leq -1.05 \cdot 10^{+237}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;r \leq -6.5 \cdot 10^{+198}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;r \leq -2 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 10
Error	21.7
Cost	840

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r} + -1.5\\ \mathbf{if}\;v \leq 9.412523568426364 \cdot 10^{+208}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;v \leq 4.1221945554169586 \cdot 10^{+239}:\\ \;\;\;\;r \cdot \left(r \cdot \left(-0.25 \cdot \left(w \cdot w\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 11
Error	21.1
Cost	448

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

Alternative 12
Error	38.1
Cost	320

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

Reproduce

herbie shell --seed 2022300 
(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))