Average Error: 2.0 → 1.8
Time: 42.7s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \left(y - z\right) \cdot \frac{a}{1 + \left(t - z\right)}\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \left(y - z\right) \cdot \frac{a}{1 + \left(t - z\right)}
double f(double x, double y, double z, double t, double a) {
        double r28247466 = x;
        double r28247467 = y;
        double r28247468 = z;
        double r28247469 = r28247467 - r28247468;
        double r28247470 = t;
        double r28247471 = r28247470 - r28247468;
        double r28247472 = 1.0;
        double r28247473 = r28247471 + r28247472;
        double r28247474 = a;
        double r28247475 = r28247473 / r28247474;
        double r28247476 = r28247469 / r28247475;
        double r28247477 = r28247466 - r28247476;
        return r28247477;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r28247478 = x;
        double r28247479 = y;
        double r28247480 = z;
        double r28247481 = r28247479 - r28247480;
        double r28247482 = a;
        double r28247483 = 1.0;
        double r28247484 = t;
        double r28247485 = r28247484 - r28247480;
        double r28247486 = r28247483 + r28247485;
        double r28247487 = r28247482 / r28247486;
        double r28247488 = r28247481 * r28247487;
        double r28247489 = r28247478 - r28247488;
        return r28247489;
}

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

Original2.0
Target0.2
Herbie1.8
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 2.0

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
  2. Using strategy rm

  3. Applied div-inv2.0

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

  4. Simplified1.8

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

  5. Final simplification1.8

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"

  :herbie-target
  (- x (* (/ (- y z) (+ (- t z) 1.0)) a))

  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))