Average Error: 1.4 → 1.3
Time: 25.1s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\frac{y}{\frac{a - t}{z - t}} + x\]
x + y \cdot \frac{z - t}{a - t}
↓
\frac{y}{\frac{a - t}{z - t}} + x
double f(double x, double y, double z, double t, double a) {
        double r396188 = x;
        double r396189 = y;
        double r396190 = z;
        double r396191 = t;
        double r396192 = r396190 - r396191;
        double r396193 = a;
        double r396194 = r396193 - r396191;
        double r396195 = r396192 / r396194;
        double r396196 = r396189 * r396195;
        double r396197 = r396188 + r396196;
        return r396197;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r396198 = y;
        double r396199 = a;
        double r396200 = t;
        double r396201 = r396199 - r396200;
        double r396202 = z;
        double r396203 = r396202 - r396200;
        double r396204 = r396201 / r396203;
        double r396205 = r396198 / r396204;
        double r396206 = x;
        double r396207 = r396205 + r396206;
        return r396207;
}

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

Original1.4
Target0.4
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;y \lt -8.508084860551241069024247453646278348229 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Initial program 1.4

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

  2. Simplified1.4

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

  4. Applied clear-num1.4

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

  6. Applied fma-udef1.4

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

  7. Simplified1.3

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

  8. Final simplification1.3

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

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.50808486055124107e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.8944268627920891e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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