Data.Colour.RGB:hslsv from colour-2.3.3, B

?

Percentage Accurate: 99.3% → 99.8%
Time: 19.9s
Precision: binary64
Cost: 7104

?

\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
↓
\[\mathsf{fma}\left(a, 120, \frac{60}{z - t} \cdot \left(x - y\right)\right) \]
(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
 (fma a 120.0 (* (/ 60.0 (- z t)) (- x y))))
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(a, 120.0, ((60.0 / (z - t)) * (x - y)));
}

function code(x, y, z, t, a)
	return Float64(Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t)) + Float64(a * 120.0))
end
↓
function code(x, y, z, t, a)
	return fma(a, 120.0, Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y)))
end

code[x_, y_, z_, t_, a_] := N[(N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_, t_, a_] := N[(a * 120.0 + N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

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

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Herbie found 20 alternatives:

AlternativeAccuracySpeedup

Accuracy vs Speed

The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Bogosity?

Bogosity

Target

Original99.3%
Target99.8%
Herbie99.8%
\[\frac{60}{\frac{z - t}{x - y}} + a \cdot 120 \]

Derivation?

  1. Initial program 99.4%

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

  2. Simplified99.8%

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

    [Start]99.4%

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

    +-commutative [=>]99.4%

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

    fma-def [=>]99.4%

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

    associate-*l/ [<=]99.8%

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

  3. Final simplification99.8%

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

Alternatives

Alternative 1
Accuracy99.8%
Cost7104
\[\mathsf{fma}\left(a, 120, \frac{60}{z - t} \cdot \left(x - y\right)\right) \]
Alternative 2
Accuracy74.8%
Cost1232
\[\begin{array}{l} t_1 := a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-296}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-121}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+20}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 3
Accuracy59.1%
Cost1108
\[\begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-79}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-210}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-273}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-173}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-41}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
Alternative 4
Accuracy59.1%
Cost1108
\[\begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-79}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-211}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-270}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-171}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-41}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
Alternative 5
Accuracy59.1%
Cost1108
\[\begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-79}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-211}:\\ \;\;\;\;\frac{x - y}{\frac{z}{60}}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-274}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-173}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-42}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
Alternative 6
Accuracy59.0%
Cost1108
\[\begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-79}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-210}:\\ \;\;\;\;\frac{x - y}{\frac{z}{60}}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-274}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-176}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-38}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
Alternative 7
Accuracy59.2%
Cost1108
\[\begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{-79}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-212}:\\ \;\;\;\;\frac{x - y}{\frac{z}{60}}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-274}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-173}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-43}:\\ \;\;\;\;\frac{60}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
Alternative 8
Accuracy74.6%
Cost1096
\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -50:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+69}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
Alternative 9
Accuracy56.5%
Cost976
\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -2.45 \cdot 10^{-176}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-207}:\\ \;\;\;\;\frac{60 \cdot x}{z}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
Alternative 10
Accuracy83.8%
Cost969
\[\begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-12} \lor \neg \left(t \leq 9.5 \cdot 10^{-95}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x - y}}\\ \end{array} \]
Alternative 11
Accuracy89.0%
Cost969
\[\begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+94} \lor \neg \left(y \leq 0.048\right):\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \end{array} \]
Alternative 12
Accuracy89.3%
Cost969
\[\begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+94} \lor \neg \left(y \leq 0.052\right):\\ \;\;\;\;\frac{60}{\frac{t - z}{y}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \end{array} \]
Alternative 13
Accuracy74.6%
Cost840
\[\begin{array}{l} \mathbf{if}\;a \leq -0.09:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+67}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
Alternative 14
Accuracy99.8%
Cost832
\[\frac{60}{z - t} \cdot \left(x - y\right) + a \cdot 120 \]
Alternative 15
Accuracy99.8%
Cost832
\[\frac{60}{\frac{z - t}{x - y}} + a \cdot 120 \]
Alternative 16
Accuracy59.2%
Cost713
\[\begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+160} \lor \neg \left(x \leq 2.5 \cdot 10^{+170}\right):\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
Alternative 17
Accuracy49.6%
Cost584
\[\begin{array}{l} \mathbf{if}\;z \leq 1.75 \cdot 10^{-266}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-86}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
Alternative 18
Accuracy49.5%
Cost584
\[\begin{array}{l} \mathbf{if}\;z \leq 7.2 \cdot 10^{-268}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-86}:\\ \;\;\;\;\frac{60}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
Alternative 19
Accuracy52.0%
Cost452
\[\begin{array}{l} \mathbf{if}\;x \leq 2.2 \cdot 10^{+230}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \end{array} \]
Alternative 20
Accuracy51.1%
Cost192
\[a \cdot 120 \]

Reproduce?

herbie shell --seed 2023272 
(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)))