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

Percentage Accurate: 99.4% → 99.8%

Time: 24.8s

Precision: binary64

Cost: 7104

Math

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

↓

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

FPCore

(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))))

C

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)));
}

Julia

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

Wolfram

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]

Target

Original	99.4%
Target	99.8%
Herbie	99.8%

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

Derivation

1. Initial program 99.4%

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

2. Simplified 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60}{z - t} \cdot \left(x - y\right)\right)} \]
   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/ [<=] 99.9	\[ \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)}\right) \]

3. Final simplification 99.9%

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

Alternatives

Alternative 1
Accuracy	60.6%
Cost	1764

\[\begin{array}{l} t_1 := a \cdot 120 + -60 \cdot \frac{x}{t}\\ t_2 := a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7 \cdot 10^{+132}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-100}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-140}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-190}:\\ \;\;\;\;\frac{x - y}{t \cdot -0.016666666666666666}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-188}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-109}:\\ \;\;\;\;\frac{x - y}{\frac{z}{60}}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-10}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Accuracy	57.9%
Cost	1372

\[\begin{array}{l} t_1 := \frac{-60}{\frac{t}{x - y}}\\ t_2 := 60 \cdot \frac{x - y}{z}\\ \mathbf{if}\;a \leq -40:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-130}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-229}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-19}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 3
Accuracy	57.9%
Cost	1372

\[\begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z}\\ t_2 := \frac{-60}{\frac{t}{x - y}}\\ \mathbf{if}\;a \leq -32:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-126}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -9.6 \cdot 10^{-268}:\\ \;\;\;\;\frac{x - y}{t \cdot -0.016666666666666666}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 4
Accuracy	61.9%
Cost	1368

\[\begin{array}{l} t_1 := a \cdot 120 + \frac{60}{\frac{z}{x}}\\ t_2 := a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{if}\;y \leq -7 \cdot 10^{+104}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-283}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \end{array} \]

Alternative 5
Accuracy	82.6%
Cost	1225

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-124} \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{-71}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \end{array} \]

Alternative 6
Accuracy	74.0%
Cost	1096

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+60}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-6}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 7
Accuracy	57.8%
Cost	976

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-12}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-35}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+146}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	88.9%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+57} \lor \neg \left(y \leq 3.8 \cdot 10^{+137}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \end{array} \]

Alternative 9
Accuracy	99.8%
Cost	832

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

Alternative 10
Accuracy	52.0%
Cost	716

\[\begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-242}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-238}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-92}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 11
Accuracy	58.4%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+99} \lor \neg \left(y \leq 1.45 \cdot 10^{+149}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 12
Accuracy	51.4%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+99} \lor \neg \left(y \leq 1.4 \cdot 10^{+156}\right):\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 13
Accuracy	51.4%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+99} \lor \neg \left(y \leq 4.2 \cdot 10^{+156}\right):\\ \;\;\;\;y \cdot \frac{60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 14
Accuracy	52.0%
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-249}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-92}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 15
Accuracy	51.3%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+99}:\\ \;\;\;\;\frac{60 \cdot y}{t}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+155}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \end{array} \]

Alternative 16
Accuracy	50.8%
Cost	192

\[a \cdot 120 \]

Reproduce

herbie shell --seed 2023160 
(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)))