Average Error: 2.3 → 2.3
Time: 17.1s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\frac{x - y}{z - y} \cdot t\]
\frac{x - y}{z - y} \cdot t
↓
\frac{x - y}{z - y} \cdot t
double f(double x, double y, double z, double t) {
        double r284169 = x;
        double r284170 = y;
        double r284171 = r284169 - r284170;
        double r284172 = z;
        double r284173 = r284172 - r284170;
        double r284174 = r284171 / r284173;
        double r284175 = t;
        double r284176 = r284174 * r284175;
        return r284176;
}
↓
double f(double x, double y, double z, double t) {
        double r284177 = x;
        double r284178 = y;
        double r284179 = r284177 - r284178;
        double r284180 = z;
        double r284181 = r284180 - r284178;
        double r284182 = r284179 / r284181;
        double r284183 = t;
        double r284184 = r284182 * r284183;
        return r284184;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.3
Target2.2
Herbie2.3
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Initial program 2.3

    \[\frac{x - y}{z - y} \cdot t\]
  2. Using strategy rm

  3. Applied div-inv2.4

    \[\leadsto \color{blue}{\left(\left(x - y\right) \cdot \frac{1}{z - y}\right)} \cdot t\]

  4. Applied associate-*l*10.8

    \[\leadsto \color{blue}{\left(x - y\right) \cdot \left(\frac{1}{z - y} \cdot t\right)}\]

  5. Simplified10.7

    \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{t}{z - y}}\]
  6. Using strategy rm

  7. Applied clear-num11.4

    \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{1}{\frac{z - y}{t}}}\]
  8. Using strategy rm

  9. Applied associate-/r/10.8

    \[\leadsto \left(x - y\right) \cdot \color{blue}{\left(\frac{1}{z - y} \cdot t\right)}\]

  10. Applied associate-*r*2.4

    \[\leadsto \color{blue}{\left(\left(x - y\right) \cdot \frac{1}{z - y}\right) \cdot t}\]

  11. Simplified2.3

    \[\leadsto \color{blue}{\frac{x - y}{z - y}} \cdot t\]

  12. Final simplification2.3

    \[\leadsto \frac{x - y}{z - y} \cdot t\]

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

  (* (/ (- x y) (- z y)) t))