Average Error: 12.4 → 0.3
Time: 6.9s
Precision: binary64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \left(0.375 + \left(v \cdot -2\right) \cdot 0.125\right) \cdot \frac{r \cdot w}{\frac{1 - v}{r \cdot w}}\right) + -4.5 \]
(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
 (+
  (-
   (+ 3.0 (/ 2.0 (* r r)))
   (* (+ 0.375 (* (* v -2.0) 0.125)) (/ (* r w) (/ (- 1.0 v) (* r w)))))
  -4.5))
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) {
	return ((3.0 + (2.0 / (r * r))) - ((0.375 + ((v * -2.0) * 0.125)) * ((r * w) / ((1.0 - v) / (r * w))))) + -4.5;
}

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
    code = ((3.0d0 + (2.0d0 / (r * r))) - ((0.375d0 + ((v * (-2.0d0)) * 0.125d0)) * ((r * w) / ((1.0d0 - v) / (r * w))))) + (-4.5d0)
end function

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) {
	return ((3.0 + (2.0 / (r * r))) - ((0.375 + ((v * -2.0) * 0.125)) * ((r * w) / ((1.0 - v) / (r * w))))) + -4.5;
}

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):
	return ((3.0 + (2.0 / (r * r))) - ((0.375 + ((v * -2.0) * 0.125)) * ((r * w) / ((1.0 - v) / (r * w))))) + -4.5

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)
	return Float64(Float64(Float64(3.0 + Float64(2.0 / Float64(r * r))) - Float64(Float64(0.375 + Float64(Float64(v * -2.0) * 0.125)) * Float64(Float64(r * w) / Float64(Float64(1.0 - v) / Float64(r * w))))) + -4.5)
end

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 = code(v, w, r)
	tmp = ((3.0 + (2.0 / (r * r))) - ((0.375 + ((v * -2.0) * 0.125)) * ((r * w) / ((1.0 - v) / (r * w))))) + -4.5;
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_] := N[(N[(N[(3.0 + N[(2.0 / N[(r * r), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(0.375 + N[(N[(v * -2.0), $MachinePrecision] * 0.125), $MachinePrecision]), $MachinePrecision] * N[(N[(r * w), $MachinePrecision] / N[(N[(1.0 - v), $MachinePrecision] / N[(r * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -4.5), $MachinePrecision]

\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
↓
\left(\left(3 + \frac{2}{r \cdot r}\right) - \left(0.375 + \left(v \cdot -2\right) \cdot 0.125\right) \cdot \frac{r \cdot w}{\frac{1 - v}{r \cdot w}}\right) + -4.5

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 12.4

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

  2. Applied egg-rr0.4

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\left(0.375 + \left(v \cdot -2\right) \cdot 0.125\right) \cdot \left({\left(w \cdot r\right)}^{2} \cdot \frac{1}{1 - v}\right)}\right) - 4.5 \]

  3. Applied egg-rr0.3

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \left(0.375 + \left(v \cdot -2\right) \cdot 0.125\right) \cdot \color{blue}{\frac{w \cdot r}{\frac{1 - v}{w \cdot r}}}\right) - 4.5 \]

  4. Final simplification0.3

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \left(0.375 + \left(v \cdot -2\right) \cdot 0.125\right) \cdot \frac{r \cdot w}{\frac{1 - v}{r \cdot w}}\right) + -4.5 \]

Reproduce

herbie shell --seed 2022211 
(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))