Average Error: 1.8 → 0.2
Time: 5.7s
Precision: binary64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
↓
\[\begin{array}{l} t_1 := \left(1 + t\right) - z\\ x - a \cdot \left(\frac{y}{t_1} - \frac{z}{t_1}\right) \end{array} \]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
\begin{array}{l}
t_1 := \left(1 + t\right) - z\\
x - a \cdot \left(\frac{y}{t_1} - \frac{z}{t_1}\right)
\end{array}

(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))
↓
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ 1.0 t) z))) (- x (* a (- (/ y t_1) (/ z t_1))))))
double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}
↓
double code(double x, double y, double z, double t, double a) {
	double t_1 = (1.0 + t) - z;
	return x - (a * ((y / t_1) - (z / t_1)));
}

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. Applied egg-rr0.2

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

  3. Taylor expanded in y around 0 0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2022130 
(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) 1.0)) a))

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