Average Error: 24.0 → 7.8
Time: 27.3s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[y \cdot \frac{1}{\frac{a - t}{z - t}} - \left(\frac{x}{\frac{a - t}{z - t}} - x\right)\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
y \cdot \frac{1}{\frac{a - t}{z - t}} - \left(\frac{x}{\frac{a - t}{z - t}} - x\right)
double f(double x, double y, double z, double t, double a) {
        double r27476235 = x;
        double r27476236 = y;
        double r27476237 = r27476236 - r27476235;
        double r27476238 = z;
        double r27476239 = t;
        double r27476240 = r27476238 - r27476239;
        double r27476241 = r27476237 * r27476240;
        double r27476242 = a;
        double r27476243 = r27476242 - r27476239;
        double r27476244 = r27476241 / r27476243;
        double r27476245 = r27476235 + r27476244;
        return r27476245;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r27476246 = y;
        double r27476247 = 1.0;
        double r27476248 = a;
        double r27476249 = t;
        double r27476250 = r27476248 - r27476249;
        double r27476251 = z;
        double r27476252 = r27476251 - r27476249;
        double r27476253 = r27476250 / r27476252;
        double r27476254 = r27476247 / r27476253;
        double r27476255 = r27476246 * r27476254;
        double r27476256 = x;
        double r27476257 = r27476256 / r27476253;
        double r27476258 = r27476257 - r27476256;
        double r27476259 = r27476255 - r27476258;
        return r27476259;
}

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

Original24.0
Target9.5
Herbie7.8
\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Initial program 24.0

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

  2. Simplified12.0

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

  4. Applied clear-num12.1

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

  6. Applied fma-udef12.1

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

  7. Simplified12.0

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

  9. Applied div-sub12.0

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

  10. Applied associate-+l-7.7

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

  12. Applied div-inv7.8

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

  13. Final simplification7.8

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t))))))

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