Average Error: 0.4 → 0.2
Time: 17.1s
Precision: binary64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\left(60 \cdot \frac{x}{z - t} - 60 \cdot \frac{y}{z - t}\right) + a \cdot 120\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
\left(60 \cdot \frac{x}{z - t} - 60 \cdot \frac{y}{z - t}\right) + a \cdot 120
(FPCore (x y z t a)
 :precision binary64
 (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))
↓
(FPCore (x y z t a)
 :precision binary64
 (+ (- (* 60.0 (/ x (- z t))) (* 60.0 (/ y (- z t)))) (* a 120.0)))
double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}
↓
double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x / (z - t))) - (60.0 * (y / (z - t)))) + (a * 120.0);
}

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

Original0.4
Target0.2
Herbie0.2
\[\frac{60}{\frac{z - t}{x - y}} + a \cdot 120\]

Derivation

  1. Initial program 0.4

    \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]

  2. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{\left(60 \cdot \frac{x}{z - t} - 60 \cdot \frac{y}{z - t}\right)} + a \cdot 120\]

  3. Final simplification0.2

    \[\leadsto \left(60 \cdot \frac{x}{z - t} - 60 \cdot \frac{y}{z - t}\right) + a \cdot 120\]

Reproduce

herbie shell --seed 2021044 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (+ (/ 60.0 (/ (- z t) (- x y))) (* a 120.0))

  (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))