Average Error: 18.5 → 1.6
Time: 9.9s
Precision: binary64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{v}{t1 + u}}{-1 + u \cdot \frac{-1}{t1}}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\frac{v}{t1 + u}}{-1 + u \cdot \frac{-1}{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 (/ -1.0 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)) / (-1.0 + (u * (-1.0 / 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 18.5

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

  2. Simplified1.6

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

  4. Applied div-inv_binary64_751.6

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

  5. Applied cancel-sign-sub-inv_binary64_441.6

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

  6. Final simplification1.6

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

Reproduce

herbie shell --seed 2021047 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))