Average Error: 2.0 → 0.2
Time: 31.8s
Precision: binary64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \frac{y - z}{1 + \left(t - z\right)} \cdot a\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \frac{y - z}{1 + \left(t - z\right)} \cdot a
(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))
↓
(FPCore (x y z t a)
 :precision binary64
 (- x (* (/ (- y z) (+ 1.0 (- t z))) a)))
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) {
	return x - (((y - z) / (1.0 + (t - z))) * a);
}

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

Derivation

  1. Initial program 2.0

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

  3. Applied sub-neg_binary64_130292.0

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

  4. Simplified0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2021076 
(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))))