Average Error: 1.8 → 0.2
Time: 10.3s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[a \cdot \left(\left(z - y\right) \cdot \frac{1}{\left(t - z\right) + 1}\right) + x\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
a \cdot \left(\left(z - y\right) \cdot \frac{1}{\left(t - z\right) + 1}\right) + x
double f(double x, double y, double z, double t, double a) {
        double r547559 = x;
        double r547560 = y;
        double r547561 = z;
        double r547562 = r547560 - r547561;
        double r547563 = t;
        double r547564 = r547563 - r547561;
        double r547565 = 1.0;
        double r547566 = r547564 + r547565;
        double r547567 = a;
        double r547568 = r547566 / r547567;
        double r547569 = r547562 / r547568;
        double r547570 = r547559 - r547569;
        return r547570;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r547571 = a;
        double r547572 = z;
        double r547573 = y;
        double r547574 = r547572 - r547573;
        double r547575 = 1.0;
        double r547576 = t;
        double r547577 = r547576 - r547572;
        double r547578 = 1.0;
        double r547579 = r547577 + r547578;
        double r547580 = r547575 / r547579;
        double r547581 = r547574 * r547580;
        double r547582 = r547571 * r547581;
        double r547583 = x;
        double r547584 = r547582 + r547583;
        return r547584;
}

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

Original1.8
Target0.2
Herbie0.2
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 1.8

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

  2. Simplified0.2

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

  4. Applied fma-udef0.2

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

  6. Applied div-inv0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (- x (* (/ (- y z) (+ (- t z) 1)) a))

  (- x (/ (- y z) (/ (+ (- t z) 1) a))))