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

Average Accuracy: 99.4% → 99.8%

Time: 22.8s

Precision: binary64

Cost: 7104

Math

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

↓

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

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

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(60.0, ((x - y) / (z - t)), (a * 120.0));
}

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(60.0, Float64(Float64(x - y) / Float64(z - t)), Float64(a * 120.0))
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[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $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 99.8%

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

   [Start] 99.4	\[ \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   associate-*r/ [<=] 99.8	\[ \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]
   fma-def [=>] 99.8	\[ \color{blue}{\mathsf{fma}\left(60, \frac{x - y}{z - t}, a \cdot 120\right)} \]

3. Final simplification 99.8%

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

Alternatives

Alternative 1
Accuracy	61.6%
Cost	2268

\[\begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z}\\ \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-51}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-149}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-208}:\\ \;\;\;\;\frac{x - y}{t \cdot -0.016666666666666666}\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-288}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-18}:\\ \;\;\;\;\frac{y}{z - t} \cdot -60\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 2
Accuracy	61.1%
Cost	2008

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-51}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-149}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-202}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-288}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-104}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-18}:\\ \;\;\;\;\frac{y}{z - t} \cdot -60\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 3
Accuracy	99.8%
Cost	1728

\[\begin{array}{l} t_1 := \frac{y}{z - t}\\ \left(a \cdot 120 + \left(-120 \cdot t_1 + 60 \cdot \frac{x}{z - t}\right)\right) - t_1 \cdot -60 \end{array} \]

Alternative 4
Accuracy	60.8%
Cost	1372

\[\begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z}\\ t_2 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;a \leq -9 \cdot 10^{-56}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-151}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-204}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-242}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-17}:\\ \;\;\;\;\frac{y}{z - t} \cdot -60\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 5
Accuracy	60.8%
Cost	1372

\[\begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z}\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{-55}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-151}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-204}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-242}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-298}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-19}:\\ \;\;\;\;\frac{y}{z - t} \cdot -60\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 6
Accuracy	83.3%
Cost	1225

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-155} \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{-18}\right):\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{\frac{z - t}{60}}\\ \end{array} \]

Alternative 7
Accuracy	54.8%
Cost	1112

\[\begin{array}{l} t_1 := x \cdot \frac{60}{z}\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{-206}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-297}:\\ \;\;\;\;\frac{-60}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-126}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-24}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 8
Accuracy	77.7%
Cost	1096

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-35}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+15}:\\ \;\;\;\;\frac{x - y}{\frac{z - t}{60}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 9
Accuracy	89.8%
Cost	969

\[\begin{array}{l} \mathbf{if}\;x \leq -1.52 \cdot 10^{+15} \lor \neg \left(x \leq 2.65 \cdot 10^{+113}\right):\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{z - t}{y}}\\ \end{array} \]

Alternative 10
Accuracy	61.5%
Cost	844

\[\begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{-54}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-295}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-20}:\\ \;\;\;\;\frac{y}{z - t} \cdot -60\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 11
Accuracy	99.8%
Cost	832

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

Alternative 12
Accuracy	61.5%
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{-157}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-20}:\\ \;\;\;\;\frac{y}{z - t} \cdot -60\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 13
Accuracy	54.2%
Cost	584

\[\begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+92}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+54}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 14
Accuracy	56.5%
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{-209}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{-176}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 15
Accuracy	55.3%
Cost	192

\[a \cdot 120 \]

Reproduce

herbie shell --seed 2023147 
(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)))