Average Error: 1.9 → 0.3
Time: 23.9s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[a \cdot \frac{z - y}{\left(t - z\right) + 1} + x\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
a \cdot \frac{z - y}{\left(t - z\right) + 1} + x
double f(double x, double y, double z, double t, double a) {
        double r455525 = x;
        double r455526 = y;
        double r455527 = z;
        double r455528 = r455526 - r455527;
        double r455529 = t;
        double r455530 = r455529 - r455527;
        double r455531 = 1.0;
        double r455532 = r455530 + r455531;
        double r455533 = a;
        double r455534 = r455532 / r455533;
        double r455535 = r455528 / r455534;
        double r455536 = r455525 - r455535;
        return r455536;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r455537 = a;
        double r455538 = z;
        double r455539 = y;
        double r455540 = r455538 - r455539;
        double r455541 = t;
        double r455542 = r455541 - r455538;
        double r455543 = 1.0;
        double r455544 = r455542 + r455543;
        double r455545 = r455540 / r455544;
        double r455546 = r455537 * r455545;
        double r455547 = x;
        double r455548 = r455546 + r455547;
        return r455548;
}

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

Original1.9
Target0.3
Herbie0.3
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 1.9

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

  2. Simplified0.3

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

  4. Applied fma-udef0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019199 +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))))