Average Error: 18.8 → 1.4
Time: 2.9s
Precision: binary64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{v}{t1 + u}}{-1 - \frac{u}{t1}}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\frac{v}{t1 + u}}{-1 - \frac{u}{t1}}
(FPCore (u v t1) :precision binary64 (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))
↓
(FPCore (u v t1) :precision binary64 (/ (/ v (+ t1 u)) (- -1.0 (/ u t1))))
double code(double u, double v, double t1) {
	return (((double) (((double) -(t1)) * v)) / ((double) (((double) (t1 + u)) * ((double) (t1 + u)))));
}
↓
double code(double u, double v, double t1) {
	return ((v / ((double) (t1 + u))) / ((double) (-1.0 - (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 Error: 18.8 bits

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

  2. SimplifiedError: 3.6 bits

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

  4. Applied associate-/r*Error: 1.4 bits

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

  5. Final simplificationError: 1.4 bits

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

Reproduce

herbie shell --seed 2020204 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))