Average Error: 18.3 → 1.5
Time: 3.9s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{-t1}{t1 + u} \cdot \left(v \cdot \frac{1}{t1 + u}\right)\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{-t1}{t1 + u} \cdot \left(v \cdot \frac{1}{t1 + u}\right)
double f(double u, double v, double t1) {
        double r29208 = t1;
        double r29209 = -r29208;
        double r29210 = v;
        double r29211 = r29209 * r29210;
        double r29212 = u;
        double r29213 = r29208 + r29212;
        double r29214 = r29213 * r29213;
        double r29215 = r29211 / r29214;
        return r29215;
}
↓
double f(double u, double v, double t1) {
        double r29216 = t1;
        double r29217 = -r29216;
        double r29218 = u;
        double r29219 = r29216 + r29218;
        double r29220 = r29217 / r29219;
        double r29221 = v;
        double r29222 = 1.0;
        double r29223 = r29222 / r29219;
        double r29224 = r29221 * r29223;
        double r29225 = r29220 * r29224;
        return r29225;
}

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 18.3

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  2. Using strategy rm

  3. Applied times-frac1.4

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

  5. Applied div-inv1.5

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

  6. Final simplification1.5

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

Reproduce

herbie shell --seed 2020035 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))