Average Error: 2.1 → 2.2
Time: 11.5s
Precision: binary64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\frac{t}{\frac{z - y}{x}} - \frac{t}{\frac{z - y}{y}}\]
\frac{x - y}{z - y} \cdot t
↓
\frac{t}{\frac{z - y}{x}} - \frac{t}{\frac{z - y}{y}}
(FPCore (x y z t) :precision binary64 (* (/ (- x y) (- z y)) t))
↓
(FPCore (x y z t)
 :precision binary64
 (- (/ t (/ (- z y) x)) (/ t (/ (- z y) 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 - y) / x)) - (t / ((z - y) / 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

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

Derivation

  1. Initial program 2.1

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

  2. Taylor expanded around 0 11.6

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

  3. Simplified2.2

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

  4. Final simplification2.2

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

Reproduce

herbie shell --seed 2021176 
(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))