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

Average Error: 0.5 → 0.1

Time: 20.3s

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	0.5
Target	0.2
Herbie	0.1

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

Derivation

1. Initial program 0.5

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

2. Simplified 0.1

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

   [Start] 0.5	\[ \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   +-commutative [=>] 0.5	\[ \color{blue}{a \cdot 120 + \frac{60 \cdot \left(x - y\right)}{z - t}} \]
   fma-def [=>] 0.5	\[ \color{blue}{\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(x - y\right)}{z - t}\right)} \]
   associate-*l/ [<=] 0.1	\[ \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)}\right) \]

3. Final simplification 0.1

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

Alternatives

Alternative 1
Error	15.3
Cost	1616

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-48}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-60}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-107}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-27}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 2
Error	15.1
Cost	1616

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-48}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-60}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-107}:\\ \;\;\;\;a \cdot 120 + \frac{y}{\frac{t}{60}}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-27}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 3
Error	15.3
Cost	1616

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-48}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-60}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-107}:\\ \;\;\;\;a \cdot 120 + \frac{y}{\frac{t}{60}}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-27}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 4
Error	10.9
Cost	1225

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-153} \lor \neg \left(a \cdot 120 \leq 10^{-80}\right):\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \end{array} \]

Alternative 5
Error	28.0
Cost	1112

\[\begin{array}{l} t_1 := 60 \cdot \frac{y}{t}\\ \mathbf{if}\;a \leq -2 \cdot 10^{-109}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-263}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-255}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-195}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 6
Error	28.0
Cost	1112

\[\begin{array}{l} t_1 := 60 \cdot \frac{y}{t}\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{-109}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-263}:\\ \;\;\;\;\frac{-60}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-251}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-193}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 7
Error	28.0
Cost	1112

\[\begin{array}{l} t_1 := 60 \cdot \frac{y}{t}\\ \mathbf{if}\;a \leq -2.55 \cdot 10^{-110}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-263}:\\ \;\;\;\;\frac{-60}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-256}:\\ \;\;\;\;\frac{x \cdot -60}{t}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-194}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 8
Error	15.4
Cost	1105

\[\begin{array}{l} \mathbf{if}\;a \leq -4.9 \cdot 10^{-51}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-64} \lor \neg \left(a \leq -7.6 \cdot 10^{-109}\right) \land a \leq 4 \cdot 10^{-29}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 9
Error	25.7
Cost	976

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{-109}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-303}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-212}:\\ \;\;\;\;\frac{x \cdot -60}{t}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 10
Error	7.6
Cost	969

\[\begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+55} \lor \neg \left(x \leq 7 \cdot 10^{+154}\right):\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \end{array} \]

Alternative 11
Error	28.0
Cost	848

\[\begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-146}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-304}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-252}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-197}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 12
Error	24.7
Cost	844

\[\begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{-110}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-305}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-80}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 13
Error	24.7
Cost	844

\[\begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-109}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-308}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-83}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 14
Error	24.6
Cost	844

\[\begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-109}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-304}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-82}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 15
Error	24.7
Cost	844

\[\begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-109}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-307}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-82}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 16
Error	24.7
Cost	844

\[\begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-109}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-303}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-83}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 17
Error	0.2
Cost	832

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

Alternative 18
Error	30.6
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-148}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-251}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 19
Error	28.4
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-152}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{-303}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 20
Error	28.9
Cost	192

\[a \cdot 120 \]

Reproduce

herbie shell --seed 2023054 
(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)))