Average Error: 10.9 → 1.2
Time: 3.4s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y + x\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y + x
double f(double x, double y, double z, double t, double a) {
        double r511577 = x;
        double r511578 = y;
        double r511579 = z;
        double r511580 = t;
        double r511581 = r511579 - r511580;
        double r511582 = r511578 * r511581;
        double r511583 = a;
        double r511584 = r511583 - r511580;
        double r511585 = r511582 / r511584;
        double r511586 = r511577 + r511585;
        return r511586;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r511587 = z;
        double r511588 = a;
        double r511589 = t;
        double r511590 = r511588 - r511589;
        double r511591 = r511587 / r511590;
        double r511592 = r511589 / r511590;
        double r511593 = r511591 - r511592;
        double r511594 = y;
        double r511595 = r511593 * r511594;
        double r511596 = x;
        double r511597 = r511595 + r511596;
        return r511597;
}

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

Original10.9
Target1.1
Herbie1.2
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.9

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

  2. Simplified2.7

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

  4. Applied clear-num2.9

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

  6. Applied fma-udef2.9

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

  7. Simplified2.8

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

  9. Applied associate-/r/1.2

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

  11. Applied div-sub1.2

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

  12. Final simplification1.2

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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