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

Average Error: 0.5 → 0.1

Time: 26.3s

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	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

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

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

3. Final simplification 0.1

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

Alternatives

Alternative 1
Error	21.4
Cost	1632

\[\begin{array}{l} t_1 := a \cdot 120 + -60 \cdot \frac{x}{t}\\ t_2 := a \cdot 120 + -60 \cdot \frac{y}{z}\\ t_3 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-22}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-173}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 15000000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+84}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+118}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	21.2
Cost	1632

\[\begin{array}{l} t_1 := a \cdot 120 + -60 \cdot \frac{x}{t}\\ t_2 := a \cdot 120 + -60 \cdot \frac{y}{z}\\ t_3 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.66 \cdot 10^{-21}:\\ \;\;\;\;\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-174}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 750000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+84}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+120}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	21.2
Cost	1632

\[\begin{array}{l} t_1 := a \cdot 120 + -60 \cdot \frac{y}{z}\\ t_2 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;z \leq -4 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-21}:\\ \;\;\;\;\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-174}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-100}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 110000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+51}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{-t}{x}}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+118}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	21.2
Cost	1500

\[\begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ t_2 := a \cdot 120 + -60 \cdot \frac{y}{z}\\ t_3 := a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-21}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-100}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 190000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+51}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+118}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	16.5
Cost	1500

\[\begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ t_2 := a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-19}:\\ \;\;\;\;\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-99}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;z \leq 480000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+51}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{-t}{x}}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+120}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	24.9
Cost	1372

\[\begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{-24}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-122}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-302}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-186}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-126}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 7
Error	24.8
Cost	1372

\[\begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;a \leq -2.35 \cdot 10^{-24}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-126}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-305}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-186}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-126}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 8
Error	24.9
Cost	1372

\[\begin{array}{l} \mathbf{if}\;a \leq -3.15 \cdot 10^{-24}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-119}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-303}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-186}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-163}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-126}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 9
Error	24.9
Cost	1372

\[\begin{array}{l} \mathbf{if}\;a \leq -2.35 \cdot 10^{-24}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{\frac{z - t}{60}}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-117}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-303}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-185}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-162}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-127}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 10
Error	24.9
Cost	1372

\[\begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-21}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{\frac{z - t}{60}}\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-116}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-305}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 3.55 \cdot 10^{-186}:\\ \;\;\;\;\frac{x - y}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-166}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-127}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 11
Error	9.8
Cost	1225

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-112} \lor \neg \left(a \cdot 120 \leq 10^{-125}\right):\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 12
Error	24.7
Cost	1108

\[\begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;a \leq -2.4 \cdot 10^{-24}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-155}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-126}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 13
Error	15.9
Cost	1105

\[\begin{array}{l} \mathbf{if}\;a \leq -520000000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-65} \lor \neg \left(a \leq -1.35 \cdot 10^{-114}\right) \land a \leq 2.2 \cdot 10^{-37}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 14
Error	15.9
Cost	1104

\[\begin{array}{l} \mathbf{if}\;a \leq -460000000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-65}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-114}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-30}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 15
Error	6.9
Cost	969

\[\begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+50} \lor \neg \left(x \leq 4.5 \cdot 10^{-58}\right):\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \end{array} \]

Alternative 16
Error	28.0
Cost	848

\[\begin{array}{l} t_1 := -60 \cdot \frac{x}{t}\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{-153}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-182}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-171}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 17
Error	28.1
Cost	848

\[\begin{array}{l} \mathbf{if}\;a \leq -5.9 \cdot 10^{-154}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-296}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-181}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-137}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 18
Error	16.7
Cost	840

\[\begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-114}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-37}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 19
Error	0.2
Cost	832

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

Alternative 20
Error	25.0
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -5.35 \cdot 10^{-160}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-126}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 21
Error	24.5
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-125}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-130}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 22
Error	28.2
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-156}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-254}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 23
Error	29.1
Cost	192

\[a \cdot 120 \]

Reproduce

herbie shell --seed 2023046 
(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)))