Average Error: 12.9 → 0.5
Time: 17.0s
Precision: binary64
Cost: 8264
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]
↓
\[\begin{array}{l} t_0 := 3 + \frac{2}{r \cdot r}\\ t_1 := \frac{\mathsf{fma}\left(v, -0.25, 0.375\right)}{1 - v}\\ t_2 := \left(t_0 - t_1 \cdot \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right)\right) + -4.5\\ \mathbf{if}\;r \leq -1.3384447166039757 \cdot 10^{-53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;r \leq 10^{+42}:\\ \;\;\;\;\left(t_0 - t_1 \cdot \left(w \cdot \left(r \cdot \left(r \cdot w\right)\right)\right)\right) + -4.5\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
(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))))
        (t_1 (/ (fma v -0.25 0.375) (- 1.0 v)))
        (t_2 (+ (- t_0 (* t_1 (* r (* w (* r w))))) -4.5)))
   (if (<= r -1.3384447166039757e-53)
     t_2
     (if (<= r 1e+42) (+ (- t_0 (* t_1 (* w (* r (* r w))))) -4.5) t_2))))
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 t_1 = fma(v, -0.25, 0.375) / (1.0 - v);
	double t_2 = (t_0 - (t_1 * (r * (w * (r * w))))) + -4.5;
	double tmp;
	if (r <= -1.3384447166039757e-53) {
		tmp = t_2;
	} else if (r <= 1e+42) {
		tmp = (t_0 - (t_1 * (w * (r * (r * w))))) + -4.5;
	} else {
		tmp = t_2;
	}
	return tmp;
}

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)))
	t_1 = Float64(fma(v, -0.25, 0.375) / Float64(1.0 - v))
	t_2 = Float64(Float64(t_0 - Float64(t_1 * Float64(r * Float64(w * Float64(r * w))))) + -4.5)
	tmp = 0.0
	if (r <= -1.3384447166039757e-53)
		tmp = t_2;
	elseif (r <= 1e+42)
		tmp = Float64(Float64(t_0 - Float64(t_1 * Float64(w * Float64(r * Float64(r * w))))) + -4.5);
	else
		tmp = t_2;
	end
	return tmp
end

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]}, Block[{t$95$1 = N[(N[(v * -0.25 + 0.375), $MachinePrecision] / N[(1.0 - v), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$0 - N[(t$95$1 * N[(r * N[(w * N[(r * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -4.5), $MachinePrecision]}, If[LessEqual[r, -1.3384447166039757e-53], t$95$2, If[LessEqual[r, 1e+42], N[(N[(t$95$0 - N[(t$95$1 * N[(w * N[(r * N[(r * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -4.5), $MachinePrecision], t$95$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
↓
\begin{array}{l}
t_0 := 3 + \frac{2}{r \cdot r}\\
t_1 := \frac{\mathsf{fma}\left(v, -0.25, 0.375\right)}{1 - v}\\
t_2 := \left(t_0 - t_1 \cdot \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right)\right) + -4.5\\
\mathbf{if}\;r \leq -1.3384447166039757 \cdot 10^{-53}:\\
\;\;\;\;t_2\\

\mathbf{elif}\;r \leq 10^{+42}:\\
\;\;\;\;\left(t_0 - t_1 \cdot \left(w \cdot \left(r \cdot \left(r \cdot w\right)\right)\right)\right) + -4.5\\

\mathbf{else}:\\
\;\;\;\;t_2\\


\end{array}

Error

Derivation

  1. Split input into 2 regimes

  2. if r < -1.3384447166039757e-53 or 1.00000000000000004e42 < r

    1. Initial program 14.2

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

    2. Taylor expanded in w around 0 27.4

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

    3. Simplified13.0

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \color{blue}{\left(w \cdot \left(\left(w \cdot r\right) \cdot r\right)\right)}}{1 - v}\right) - 4.5 \]
      Proof
      (*.f64 w (*.f64 (*.f64 w r) r)): 0 points increase in error, 0 points decrease in error
      (*.f64 w (Rewrite<= associate-*r*_binary64 (*.f64 w (*.f64 r r)))): 55 points increase in error, 26 points decrease in error
      (*.f64 w (*.f64 w (Rewrite<= unpow2_binary64 (pow.f64 r 2)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 w w) (pow.f64 r 2))): 40 points increase in error, 30 points decrease in error
      (*.f64 (Rewrite<= unpow2_binary64 (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 27.4

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

    5. Simplified27.0

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \color{blue}{\left(w \cdot \left(w \cdot \left(r \cdot r\right)\right)\right)}}{1 - v}\right) - 4.5 \]
      Proof
      (*.f64 w (*.f64 w (*.f64 r r))): 0 points increase in error, 0 points decrease in error
      (*.f64 w (*.f64 w (Rewrite<= unpow2_binary64 (pow.f64 r 2)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 w w) (pow.f64 r 2))): 40 points increase in error, 30 points decrease in error
      (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 w 2)) (pow.f64 r 2)): 0 points increase in error, 0 points decrease in error

    6. Taylor expanded in w around 0 27.4

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

    7. Simplified0.6

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\frac{\mathsf{fma}\left(v, -0.25, 0.375\right)}{1 - v} \cdot \left(r \cdot \left(\left(w \cdot r\right) \cdot w\right)\right)}\right) - 4.5 \]
      Proof
      (*.f64 (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)) (*.f64 r (*.f64 (*.f64 w r) w))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 v -1/4) 3/8)) (-.f64 1 v)) (*.f64 r (*.f64 (*.f64 w r) w))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 -1/4 v)) 3/8) (-.f64 1 v)) (*.f64 r (*.f64 (*.f64 w r) w))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (+.f64 (*.f64 (Rewrite<= metadata-eval (*.f64 1/8 -2)) v) 3/8) (-.f64 1 v)) (*.f64 r (*.f64 (*.f64 w r) w))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (+.f64 (Rewrite<= associate-*r*_binary64 (*.f64 1/8 (*.f64 -2 v))) 3/8) (-.f64 1 v)) (*.f64 r (*.f64 (*.f64 w r) w))): 1 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (+.f64 (*.f64 1/8 (*.f64 (Rewrite<= metadata-eval (neg.f64 2)) v)) 3/8) (-.f64 1 v)) (*.f64 r (*.f64 (*.f64 w r) w))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (+.f64 (*.f64 1/8 (Rewrite<= distribute-lft-neg-in_binary64 (neg.f64 (*.f64 2 v)))) 3/8) (-.f64 1 v)) (*.f64 r (*.f64 (*.f64 w r) w))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (+.f64 (*.f64 1/8 (neg.f64 (*.f64 2 v))) (Rewrite<= metadata-eval (*.f64 1/8 3))) (-.f64 1 v)) (*.f64 r (*.f64 (*.f64 w r) w))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (Rewrite<= distribute-lft-in_binary64 (*.f64 1/8 (+.f64 (neg.f64 (*.f64 2 v)) 3))) (-.f64 1 v)) (*.f64 r (*.f64 (*.f64 w r) w))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (*.f64 1/8 (Rewrite<= +-commutative_binary64 (+.f64 3 (neg.f64 (*.f64 2 v))))) (-.f64 1 v)) (*.f64 r (*.f64 (*.f64 w r) w))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (*.f64 1/8 (Rewrite<= sub-neg_binary64 (-.f64 3 (*.f64 2 v)))) (-.f64 1 v)) (*.f64 r (*.f64 (*.f64 w r) w))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (-.f64 1 v)) (*.f64 r (*.f64 (Rewrite=> *-commutative_binary64 (*.f64 r w)) w))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (-.f64 1 v)) (*.f64 r (Rewrite<= associate-*r*_binary64 (*.f64 r (*.f64 w w))))): 30 points increase in error, 49 points decrease in error
      (*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (-.f64 1 v)) (*.f64 r (*.f64 r (Rewrite<= unpow2_binary64 (pow.f64 w 2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (-.f64 1 v)) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 r r) (pow.f64 w 2)))): 73 points increase in error, 22 points decrease in error
      (*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (-.f64 1 v)) (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 r 2)) (pow.f64 w 2))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (-.f64 1 v)) (Rewrite<= *-commutative_binary64 (*.f64 (pow.f64 w 2) (pow.f64 r 2)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/r/_binary64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (/.f64 (-.f64 1 v) (*.f64 (pow.f64 w 2) (pow.f64 r 2))))): 18 points increase in error, 15 points decrease in error
      (Rewrite<= associate-*r/_binary64 (*.f64 1/8 (/.f64 (-.f64 3 (*.f64 2 v)) (/.f64 (-.f64 1 v) (*.f64 (pow.f64 w 2) (pow.f64 r 2)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 1/8 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 3 (*.f64 2 v)) (*.f64 (pow.f64 w 2) (pow.f64 r 2))) (-.f64 1 v)))): 30 points increase in error, 17 points decrease in error

    if -1.3384447166039757e-53 < r < 1.00000000000000004e42

    1. Initial program 11.1

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

    2. Applied egg-rr9.5

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

    3. Taylor expanded in w around 0 11.1

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

    4. Simplified0.3

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\frac{\mathsf{fma}\left(v, -0.25, 0.375\right)}{1 - v} \cdot \left(w \cdot \left(\left(w \cdot r\right) \cdot r\right)\right)}\right) - 4.5 \]
      Proof
      (*.f64 (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)) (*.f64 w (*.f64 (*.f64 w r) r))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 v -1/4) 3/8)) (-.f64 1 v)) (*.f64 w (*.f64 (*.f64 w r) r))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 -1/4 v)) 3/8) (-.f64 1 v)) (*.f64 w (*.f64 (*.f64 w r) r))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 3/8 (*.f64 -1/4 v))) (-.f64 1 v)) (*.f64 w (*.f64 (*.f64 w r) r))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (+.f64 3/8 (*.f64 (Rewrite<= metadata-eval (*.f64 1/8 -2)) v)) (-.f64 1 v)) (*.f64 w (*.f64 (*.f64 w r) r))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (+.f64 3/8 (Rewrite<= associate-*r*_binary64 (*.f64 1/8 (*.f64 -2 v)))) (-.f64 1 v)) (*.f64 w (*.f64 (*.f64 w r) r))): 1 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (+.f64 (Rewrite<= metadata-eval (*.f64 1/8 3)) (*.f64 1/8 (*.f64 -2 v))) (-.f64 1 v)) (*.f64 w (*.f64 (*.f64 w r) r))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (Rewrite<= distribute-lft-in_binary64 (*.f64 1/8 (+.f64 3 (*.f64 -2 v)))) (-.f64 1 v)) (*.f64 w (*.f64 (*.f64 w r) r))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (*.f64 1/8 (+.f64 3 (*.f64 -2 v))) (-.f64 1 v)) (*.f64 w (Rewrite<= associate-*r*_binary64 (*.f64 w (*.f64 r r))))): 53 points increase in error, 24 points decrease in error
      (*.f64 (/.f64 (*.f64 1/8 (+.f64 3 (*.f64 -2 v))) (-.f64 1 v)) (*.f64 w (*.f64 w (Rewrite<= unpow2_binary64 (pow.f64 r 2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (*.f64 1/8 (+.f64 3 (*.f64 -2 v))) (-.f64 1 v)) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 w w) (pow.f64 r 2)))): 40 points increase in error, 29 points decrease in error
      (*.f64 (/.f64 (*.f64 1/8 (+.f64 3 (*.f64 -2 v))) (-.f64 1 v)) (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 w 2)) (pow.f64 r 2))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/r/_binary64 (/.f64 (*.f64 1/8 (+.f64 3 (*.f64 -2 v))) (/.f64 (-.f64 1 v) (*.f64 (pow.f64 w 2) (pow.f64 r 2))))): 18 points increase in error, 15 points decrease in error
      (Rewrite<= associate-*r/_binary64 (*.f64 1/8 (/.f64 (+.f64 3 (*.f64 -2 v)) (/.f64 (-.f64 1 v) (*.f64 (pow.f64 w 2) (pow.f64 r 2)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 1/8 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (+.f64 3 (*.f64 -2 v)) (*.f64 (pow.f64 w 2) (pow.f64 r 2))) (-.f64 1 v)))): 30 points increase in error, 17 points decrease in error
  3. Recombined 2 regimes into one program.

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;r \leq -1.3384447166039757 \cdot 10^{-53}:\\ \;\;\;\;\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\mathsf{fma}\left(v, -0.25, 0.375\right)}{1 - v} \cdot \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right)\right) + -4.5\\ \mathbf{elif}\;r \leq 10^{+42}:\\ \;\;\;\;\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\mathsf{fma}\left(v, -0.25, 0.375\right)}{1 - v} \cdot \left(w \cdot \left(r \cdot \left(r \cdot w\right)\right)\right)\right) + -4.5\\ \mathbf{else}:\\ \;\;\;\;\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\mathsf{fma}\left(v, -0.25, 0.375\right)}{1 - v} \cdot \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right)\right) + -4.5\\ \end{array} \]

Alternatives

Alternative 1
Error0.4
Cost14336
\[\left(\left(3 + \frac{2}{r \cdot r}\right) + {\left(r \cdot w\right)}^{2} \cdot \frac{\mathsf{fma}\left(v, -2, 3\right) \cdot -0.125}{1 - v}\right) + -4.5 \]
Alternative 2
Error0.8
Cost7624
\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ t_1 := \left(r \cdot w\right) \cdot \left(r \cdot w\right)\\ t_2 := t_0 - \mathsf{fma}\left(t_1, 0.25, 1.5\right)\\ \mathbf{if}\;v \leq -16729169308.064728:\\ \;\;\;\;t_2\\ \mathbf{elif}\;v \leq 2.1672639611814287 \cdot 10^{-9}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(0.375 + 0.125 \cdot v\right) \cdot t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 3
Error14.1
Cost1996
\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ t_1 := \left(\left(3 + t_0\right) + w \cdot \left(w \cdot \left(\left(r \cdot r\right) \cdot -0.25\right)\right)\right) + -4.5\\ \mathbf{if}\;w \cdot w \leq 5 \cdot 10^{-283}:\\ \;\;\;\;t_0 + -1.5\\ \mathbf{elif}\;w \cdot w \leq 5 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;w \cdot w \leq 10^{+213}:\\ \;\;\;\;\left(\left(3 + \frac{\frac{2}{r}}{r}\right) + \left(w \cdot \left(\left(r \cdot r\right) \cdot w\right)\right) \cdot -0.375\right) + -4.5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 4
Error14.2
Cost1996
\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ t_1 := 3 + t_0\\ t_2 := \left(t_1 + w \cdot \left(w \cdot \left(\left(r \cdot r\right) \cdot -0.25\right)\right)\right) + -4.5\\ \mathbf{if}\;w \cdot w \leq 5 \cdot 10^{-283}:\\ \;\;\;\;t_0 + -1.5\\ \mathbf{elif}\;w \cdot w \leq 5 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;w \cdot w \leq 10^{+213}:\\ \;\;\;\;\left(t_1 + w \cdot \left(w \cdot \left(\left(r \cdot r\right) \cdot -0.375\right)\right)\right) + -4.5\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 5
Error9.6
Cost1996
\[\begin{array}{l} t_0 := 3 + \frac{2}{r \cdot r}\\ t_1 := \left(t_0 + w \cdot \left(w \cdot \left(\left(r \cdot r\right) \cdot -0.25\right)\right)\right) + -4.5\\ \mathbf{if}\;w \cdot w \leq 2 \cdot 10^{-114}:\\ \;\;\;\;\left(t_0 + \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot -0.375\right) + -4.5\\ \mathbf{elif}\;w \cdot w \leq 5 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;w \cdot w \leq 10^{+213}:\\ \;\;\;\;\left(t_0 + w \cdot \left(w \cdot \left(\left(r \cdot r\right) \cdot -0.375\right)\right)\right) + -4.5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 6
Error0.9
Cost1608
\[\begin{array}{l} t_0 := \left(r \cdot w\right) \cdot \left(r \cdot w\right)\\ t_1 := \frac{2}{r \cdot r}\\ t_2 := \left(\left(3 + t_1\right) + -0.25 \cdot t_0\right) + -4.5\\ \mathbf{if}\;v \leq -16729169308.064728:\\ \;\;\;\;t_2\\ \mathbf{elif}\;v \leq 2.1672639611814287 \cdot 10^{-9}:\\ \;\;\;\;t_1 + \left(-1.5 - \left(0.375 + 0.125 \cdot v\right) \cdot t_0\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 7
Error14.1
Cost1480
\[\begin{array}{l} t_0 := \left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot -0.375\right)\right)\\ \mathbf{if}\;r \leq -1 \cdot 10^{+122}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;r \leq 10^{+150}:\\ \;\;\;\;\left(\left(3 + \frac{2}{r \cdot r}\right) + w \cdot \left(w \cdot \left(\left(r \cdot r\right) \cdot -0.25\right)\right)\right) + -4.5\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 8
Error2.2
Cost1480
\[\begin{array}{l} t_0 := 3 + \frac{2}{r \cdot r}\\ t_1 := \left(t_0 + -0.25 \cdot \left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right)\right) + -4.5\\ \mathbf{if}\;v \leq -16729169308.064728:\\ \;\;\;\;t_1\\ \mathbf{elif}\;v \leq 2.1236282881432422 \cdot 10^{-33}:\\ \;\;\;\;\left(t_0 + \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot -0.375\right) + -4.5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 9
Error21.8
Cost840
\[\begin{array}{l} t_0 := \frac{2}{r \cdot r} + -1.5\\ \mathbf{if}\;r \leq -9 \cdot 10^{+153}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;r \leq -1.2 \cdot 10^{+112}:\\ \;\;\;\;r \cdot \left(r \cdot \left(\left(w \cdot w\right) \cdot -0.375\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 10
Error21.3
Cost840
\[\begin{array}{l} t_0 := \frac{2}{r \cdot r} + -1.5\\ \mathbf{if}\;r \leq 6.6 \cdot 10^{+173}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;r \leq 2.3 \cdot 10^{+227}:\\ \;\;\;\;\left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot -0.375\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 11
Error21.1
Cost448
\[\frac{2}{r \cdot r} + -1.5 \]
Alternative 12
Error39.0
Cost320
\[\frac{\frac{2}{r}}{r} \]
Alternative 13
Error39.0
Cost320
\[\frac{2}{r \cdot r} \]

Error

Reproduce

herbie shell --seed 2022298 
(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))