Average Error: 18.2 → 1.3
Time: 3.6s
Precision: binary64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{1}{t1 + u} \cdot \left(v \cdot \frac{-1}{1 + \frac{u}{t1}}\right)\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{1}{t1 + u} \cdot \left(v \cdot \frac{-1}{1 + \frac{u}{t1}}\right)
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) ((1.0 / ((double) (t1 + u))) * ((double) (v * (-1.0 / ((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 18.2

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

  2. Simplified3.3

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

  4. Applied *-un-lft-identity3.3

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

  5. Applied times-frac1.3

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

  7. Applied div-inv1.3

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

  8. Simplified1.3

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

  9. Final simplification1.3

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

Reproduce

herbie shell --seed 2020196 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))