Average Error: 2.1 → 0.3
Time: 24.7s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x + \frac{a}{\frac{t + \left(1 - z\right)}{z - y}}\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x + \frac{a}{\frac{t + \left(1 - z\right)}{z - y}}
double f(double x, double y, double z, double t, double a) {
        double r24136674 = x;
        double r24136675 = y;
        double r24136676 = z;
        double r24136677 = r24136675 - r24136676;
        double r24136678 = t;
        double r24136679 = r24136678 - r24136676;
        double r24136680 = 1.0;
        double r24136681 = r24136679 + r24136680;
        double r24136682 = a;
        double r24136683 = r24136681 / r24136682;
        double r24136684 = r24136677 / r24136683;
        double r24136685 = r24136674 - r24136684;
        return r24136685;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r24136686 = x;
        double r24136687 = a;
        double r24136688 = t;
        double r24136689 = 1.0;
        double r24136690 = z;
        double r24136691 = r24136689 - r24136690;
        double r24136692 = r24136688 + r24136691;
        double r24136693 = y;
        double r24136694 = r24136690 - r24136693;
        double r24136695 = r24136692 / r24136694;
        double r24136696 = r24136687 / r24136695;
        double r24136697 = r24136686 + r24136696;
        return r24136697;
}

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

Original2.1
Target0.3
Herbie0.3
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 2.1

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

  2. Simplified0.2

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

  4. Applied div-inv0.3

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

  6. Applied fma-udef0.3

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

  7. Simplified0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019172 +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))))