Average Error: 18.0 → 1.4
Time: 3.5s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{-1}{\frac{t1 + u}{t1}} \cdot \frac{v}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{-1}{\frac{t1 + u}{t1}} \cdot \frac{v}{t1 + u}
double code(double u, double v, double t1) {
	return ((-t1 * v) / ((t1 + u) * (t1 + u)));
}
↓
double code(double u, double v, double t1) {
	return ((-1.0 / ((t1 + u) / t1)) * (v / (t1 + u)));
}

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 18.0

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

  3. Applied times-frac1.3

    \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity1.3

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

  6. Applied distribute-lft-neg-in1.3

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

  7. Applied associate-/l*1.4

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

  8. Final simplification1.4

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

Reproduce

herbie shell --seed 2020049 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))