Average Error: 0.4 → 0.4
Time: 4.3s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\mathsf{fma}\left(120, a, \frac{60 \cdot x + 60 \cdot \left(-y\right)}{z - t}\right)\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
\mathsf{fma}\left(120, a, \frac{60 \cdot x + 60 \cdot \left(-y\right)}{z - t}\right)
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 fma(120.0, a, (((60.0 * x) + (60.0 * -y)) / (z - t)));
}

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
Target0.1
Herbie0.4
\[\frac{60}{\frac{z - t}{x - y}} + a \cdot 120\]

Derivation

  1. Initial program 0.4

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

  2. Simplified0.4

    \[\leadsto \color{blue}{\mathsf{fma}\left(120, a, \frac{60 \cdot \left(x - y\right)}{z - t}\right)}\]
  3. Using strategy rm

  4. Applied sub-neg0.4

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

  5. Applied distribute-lft-in0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2020066 +o rules:numerics
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (+ (/ 60 (/ (- z t) (- x y))) (* a 120))

  (+ (/ (* 60 (- x y)) (- z t)) (* a 120)))