Average Error: 10.4 → 1.5
Time: 20.5s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\frac{z - t}{a - t} \cdot y + x\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\frac{z - t}{a - t} \cdot y + x
double f(double x, double y, double z, double t, double a) {
        double r24753519 = x;
        double r24753520 = y;
        double r24753521 = z;
        double r24753522 = t;
        double r24753523 = r24753521 - r24753522;
        double r24753524 = r24753520 * r24753523;
        double r24753525 = a;
        double r24753526 = r24753525 - r24753522;
        double r24753527 = r24753524 / r24753526;
        double r24753528 = r24753519 + r24753527;
        return r24753528;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r24753529 = z;
        double r24753530 = t;
        double r24753531 = r24753529 - r24753530;
        double r24753532 = a;
        double r24753533 = r24753532 - r24753530;
        double r24753534 = r24753531 / r24753533;
        double r24753535 = y;
        double r24753536 = r24753534 * r24753535;
        double r24753537 = x;
        double r24753538 = r24753536 + r24753537;
        return r24753538;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.4
Target1.3
Herbie1.5
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.4

    \[x + \frac{y \cdot \left(z - t\right)}{a - t}\]

  2. Simplified3.2

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)}\]
  3. Using strategy rm

  4. Applied clear-num3.4

    \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{a - t}{y}}}, z - t, x\right)\]
  5. Using strategy rm

  6. Applied add-cube-cbrt3.9

    \[\leadsto \mathsf{fma}\left(\frac{1}{\color{blue}{\left(\sqrt[3]{\frac{a - t}{y}} \cdot \sqrt[3]{\frac{a - t}{y}}\right) \cdot \sqrt[3]{\frac{a - t}{y}}}}, z - t, x\right)\]
  7. Using strategy rm

  8. Applied fma-udef3.9

    \[\leadsto \color{blue}{\frac{1}{\left(\sqrt[3]{\frac{a - t}{y}} \cdot \sqrt[3]{\frac{a - t}{y}}\right) \cdot \sqrt[3]{\frac{a - t}{y}}} \cdot \left(z - t\right) + x}\]

  9. Simplified3.3

    \[\leadsto \color{blue}{\frac{z - t}{\frac{a - t}{y}}} + x\]
  10. Using strategy rm

  11. Applied associate-/r/1.5

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

  12. Final simplification1.5

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"

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

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