Average Error: 18.6 → 1.5
Time: 3.4s
Precision: binary64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{v}{t1 + u} \cdot \frac{-1}{\frac{u}{t1} - -1}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{v}{t1 + u} \cdot \frac{-1}{\frac{u}{t1} - -1}
(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) -1.0))))
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 ((double) ((v / ((double) (t1 + u))) * (-1.0 / ((double) ((u / t1) - -1.0)))));
}

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 18.6

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

  2. Simplified1.5

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

  4. Applied div-inv_binary641.5

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

  5. Simplified1.5

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

  6. Final simplification1.5

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

Reproduce

herbie shell --seed 2020205 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))