Average Error: 2.3 → 2.3
Time: 15.4s
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 r350010 = x;
        double r350011 = y;
        double r350012 = r350010 - r350011;
        double r350013 = z;
        double r350014 = r350013 - r350011;
        double r350015 = r350012 / r350014;
        double r350016 = t;
        double r350017 = r350015 * r350016;
        return r350017;
}
↓
double f(double x, double y, double z, double t) {
        double r350018 = x;
        double r350019 = y;
        double r350020 = r350018 - r350019;
        double r350021 = z;
        double r350022 = r350021 - r350019;
        double r350023 = r350020 / r350022;
        double r350024 = t;
        double r350025 = r350023 * r350024;
        return r350025;
}

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 
(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))