Average Error: 18.2 → 1.3
Time: 6.1s
Precision: binary64
Cost: 704
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{v}{u + t1}}{-1 - \frac{u}{t1}}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\frac{v}{u + t1}}{-1 - \frac{u}{t1}}
(FPCore (u v t1) :precision binary64 (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))
↓
(FPCore (u v t1) :precision binary64 (/ (/ v (+ u t1)) (- -1.0 (/ u 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 / (u + t1)) / (-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

Alternatives

Alternative 1
Error3.3
Cost704
\[\frac{v}{\left(u + t1\right) \cdot \left(-1 - \frac{u}{t1}\right)}\]
Alternative 2
Error14.2
Cost904
\[\begin{array}{l} \mathbf{if}\;t1 \leq -0.0007085118757943032 \lor \neg \left(t1 \leq 1.825414605180934 \cdot 10^{-123}\right):\\ \;\;\;\;\frac{v}{u \cdot -2 - t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{v}{u}}{-1 - \frac{u}{t1}}\\ \end{array}\]
Alternative 3
Error14.1
Cost840
\[\begin{array}{l} \mathbf{if}\;t1 \leq -1.6279607611381128 \lor \neg \left(t1 \leq 1.901358804695172 \cdot 10^{-114}\right):\\ \;\;\;\;\frac{v}{u \cdot -2 - t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-v}{\frac{u}{t1}}}{u}\\ \end{array}\]
Alternative 4
Error14.0
Cost840
\[\begin{array}{l} \mathbf{if}\;t1 \leq -0.2140300373321104 \lor \neg \left(t1 \leq 2.4916353317115206 \cdot 10^{-89}\right):\\ \;\;\;\;\frac{v}{u \cdot -2 - t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{u \cdot \frac{u}{t1}}\\ \end{array}\]
Alternative 5
Error21.6
Cost776
\[\begin{array}{l} \mathbf{if}\;t1 \leq -1.0132433850623741 \cdot 10^{-175} \lor \neg \left(t1 \leq 1.4778993763372515 \cdot 10^{-209}\right):\\ \;\;\;\;\frac{v}{u \cdot -2 - t1}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]
Alternative 6
Error21.3
Cost898
\[\begin{array}{l} \mathbf{if}\;u \leq -10310.711087361351:\\ \;\;\;\;0\\ \mathbf{elif}\;u \leq 1.758383268694475 \cdot 10^{+131}:\\ \;\;\;\;\frac{-v}{t1}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]
Alternative 7
Error39.6
Cost64
\[0\]
Alternative 8
Error61.8
Cost64
\[1\]

Error

Derivation

  1. Initial program 18.2

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

  2. Simplified1.3

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

  3. Simplified1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2021044 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))