Average Error: 2.2 → 2.1
Time: 5.9s
Precision: binary64
\[\frac{x - y}{z - y} \cdot t \]
↓
\[\frac{t}{\frac{z}{x - y} - \frac{y}{x - y}} \]
\frac{x - y}{z - y} \cdot t
↓
\frac{t}{\frac{z}{x - y} - \frac{y}{x - y}}

(FPCore (x y z t) :precision binary64 (* (/ (- x y) (- z y)) t))
↓
(FPCore (x y z t) :precision binary64 (/ t (- (/ z (- x y)) (/ y (- x y)))))
double code(double x, double y, double z, double t) {
	return ((x - y) / (z - y)) * t;
}
↓
double code(double x, double y, double z, double t) {
	return t / ((z / (x - y)) - (y / (x - y)));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.2
Target2.1
Herbie2.1
\[\frac{t}{\frac{z - y}{x - y}} \]

Derivation

  1. Initial program 2.2

    \[\frac{x - y}{z - y} \cdot t \]

  2. Applied clear-num_binary642.4

    \[\leadsto \color{blue}{\frac{1}{\frac{z - y}{x - y}}} \cdot t \]

  3. Applied associate-*l/_binary642.1

    \[\leadsto \color{blue}{\frac{1 \cdot t}{\frac{z - y}{x - y}}} \]

  4. Simplified2.1

    \[\leadsto \frac{\color{blue}{t}}{\frac{z - y}{x - y}} \]

  5. Taylor expanded in z around 0 2.1

    \[\leadsto \frac{t}{\color{blue}{\frac{z}{x - y} - \frac{y}{x - y}}} \]

  6. Final simplification2.1

    \[\leadsto \frac{t}{\frac{z}{x - y} - \frac{y}{x - y}} \]

Reproduce

herbie shell --seed 2021340 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

  (* (/ (- x y) (- z y)) t))