Average Error: 18.5 → 1.3
Time: 23.3s
Precision: binary64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{-1}{t1 + u} \cdot \frac{\frac{v}{t1 + u}}{\frac{1}{t1}}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{-1}{t1 + u} \cdot \frac{\frac{v}{t1 + u}}{\frac{1}{t1}}
(FPCore (u v t1) :precision binary64 (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))
↓
(FPCore (u v t1)
 :precision binary64
 (* (/ -1.0 (+ t1 u)) (/ (/ v (+ t1 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 (-1.0 / (t1 + u)) * ((v / (t1 + 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

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

  4. Applied div-inv_binary64_751.7

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

  5. Applied *-un-lft-identity_binary64_781.7

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

  6. Applied neg-mul-1_binary64_741.7

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

  7. Applied times-frac_binary64_841.7

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

  8. Applied times-frac_binary64_841.3

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

  9. Final simplification1.3

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

Reproduce

herbie shell --seed 2021176 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))