Average Error: 22.9 → 23.0
Time: 6.7s
Precision: binary64
\[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\]
↓
\[\frac{1}{\frac{y + z \cdot \left(b - y\right)}{y \cdot x + z \cdot \left(t - a\right)}}\]
\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}
↓
\frac{1}{\frac{y + z \cdot \left(b - y\right)}{y \cdot x + z \cdot \left(t - a\right)}}
(FPCore (x y z t a b)
 :precision binary64
 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))
↓
(FPCore (x y z t a b)
 :precision binary64
 (/ 1.0 (/ (+ y (* z (- b y))) (+ (* y x) (* z (- t a))))))
double code(double x, double y, double z, double t, double a, double b) {
	return (((double) (((double) (x * y)) + ((double) (z * ((double) (t - a)))))) / ((double) (y + ((double) (z * ((double) (b - y)))))));
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	return (1.0 / (((double) (y + ((double) (z * ((double) (b - y)))))) / ((double) (((double) (y * x)) + ((double) (z * ((double) (t - a))))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original22.9
Target17.7
Herbie23.0
\[\frac{z \cdot t + y \cdot x}{y + z \cdot \left(b - y\right)} - \frac{a}{\left(b - y\right) + \frac{y}{z}}\]

Derivation

  1. Initial program Error: 22.9 bits

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

  3. Applied clear-numError: 23.0 bits

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

  4. Final simplificationError: 23.0 bits

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

Reproduce

herbie shell --seed 2020203 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

  (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))