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

Average Error: 0.4 → 0.1

Time: 14.3s

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	0.4
Target	0.2
Herbie	0.1

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

Derivation

1. Initial program 0.4

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

2. Simplified 0.1

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

   [Start] 0.4	\[ \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   +-commutative [=>] 0.4	\[ \color{blue}{a \cdot 120 + \frac{60 \cdot \left(x - y\right)}{z - t}} \]
   fma-def [=>] 0.4	\[ \color{blue}{\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(x - y\right)}{z - t}\right)} \]
   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	0.1
Cost	7104

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

Alternative 2
Error	15.6
Cost	1616

\[\begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-20}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-38}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 3
Error	25.7
Cost	1372

\[\begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ t_2 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -4.1 \cdot 10^{-110}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-240}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-37}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 4
Error	10.5
Cost	1225

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-155} \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{-116}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 5
Error	26.2
Cost	976

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{-109}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-201}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 6
Error	7.5
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-121} \lor \neg \left(y \leq 1.2 \cdot 10^{+38}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \end{array} \]

Alternative 7
Error	7.4
Cost	968

\[\begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-120}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+38}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t - z}{y}}\\ \end{array} \]

Alternative 8
Error	15.4
Cost	840

\[\begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-23}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+29}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 9
Error	0.2
Cost	832

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

Alternative 10
Error	28.6
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-252}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-118}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 11
Error	28.5
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-248}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-118}:\\ \;\;\;\;\frac{-60}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 12
Error	28.9
Cost	192

\[a \cdot 120 \]

Reproduce

herbie shell --seed 2023018 
(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)))