Average Error: 17.6 → 1.5
Time: 4.9s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{-\frac{v}{t1 + u}}{\frac{t1 + u}{t1}}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{-\frac{v}{t1 + u}}{\frac{t1 + u}{t1}}
double code(double u, double v, double t1) {
	return ((-t1 * v) / ((t1 + u) * (t1 + u)));
}
↓
double code(double u, double v, double t1) {
	return (-(v / (t1 + u)) / ((t1 + u) / t1));
}

Error

Bits error versus u

Bits error versus v

Bits error versus t1

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 17.6

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  2. Using strategy rm

  3. Applied *-commutative17.6

    \[\leadsto \frac{\color{blue}{v \cdot \left(-t1\right)}}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]

  4. Applied times-frac1.4

    \[\leadsto \color{blue}{\frac{v}{t1 + u} \cdot \frac{-t1}{t1 + u}}\]

  5. Simplified1.4

    \[\leadsto \frac{v}{t1 + u} \cdot \color{blue}{\left(-\frac{t1}{t1 + u}\right)}\]
  6. Using strategy rm

  7. Applied clear-num1.6

    \[\leadsto \frac{v}{t1 + u} \cdot \left(-\color{blue}{\frac{1}{\frac{t1 + u}{t1}}}\right)\]

  8. Applied distribute-neg-frac1.6

    \[\leadsto \frac{v}{t1 + u} \cdot \color{blue}{\frac{-1}{\frac{t1 + u}{t1}}}\]

  9. Applied associate-*r/1.5

    \[\leadsto \color{blue}{\frac{\frac{v}{t1 + u} \cdot \left(-1\right)}{\frac{t1 + u}{t1}}}\]

  10. Simplified1.5

    \[\leadsto \frac{\color{blue}{-\frac{v}{t1 + u}}}{\frac{t1 + u}{t1}}\]

  11. Final simplification1.5

    \[\leadsto \frac{-\frac{v}{t1 + u}}{\frac{t1 + u}{t1}}\]

Reproduce

herbie shell --seed 2020066 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))