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

Average Error: 0.5 → 0.1

Time: 17.5s

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	15.9
Cost	1496

\[\begin{array}{l} t_1 := a \cdot 120 + 60 \cdot \frac{y}{t}\\ t_2 := \left(x - y\right) \cdot \frac{60}{z - t}\\ t_3 := \frac{60}{\frac{z}{x - y}} + a \cdot 120\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{-83}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-134}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-134}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 24000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 2
Error	19.9
Cost	1369

\[\begin{array}{l} t_1 := a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -1.22 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-308}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-61}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+20}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+127} \lor \neg \left(t \leq 5.8 \cdot 10^{+230}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \end{array} \]

Alternative 3
Error	28.9
Cost	1108

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{+159}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-122}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-105}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+167}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	28.9
Cost	1108

\[\begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+160}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+61}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-122}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-105}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+163}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \end{array} \]

Alternative 5
Error	29.2
Cost	1108

\[\begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+160}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+61}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-122}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-93}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+170}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \end{array} \]

Alternative 6
Error	9.9
Cost	1100

\[\begin{array}{l} t_1 := \frac{x - y}{\frac{t}{-60}} + a \cdot 120\\ \mathbf{if}\;t \leq -4.3 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-90}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{elif}\;t \leq 10^{+35}:\\ \;\;\;\;\frac{60}{\frac{z}{x - y}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	9.9
Cost	1100

\[\begin{array}{l} t_1 := \frac{x - y}{\frac{t}{-60}} + a \cdot 120\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-90}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+37}:\\ \;\;\;\;\frac{x - y}{\frac{z}{60}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	11.6
Cost	969

\[\begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-90} \lor \neg \left(t \leq 1.05 \cdot 10^{-83}\right):\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z}{x - y}} + a \cdot 120\\ \end{array} \]

Alternative 9
Error	28.7
Cost	845

\[\begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+159} \lor \neg \left(y \leq -9.8 \cdot 10^{+60}\right) \land y \leq 4.8 \cdot 10^{+167}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]

Alternative 10
Error	15.1
Cost	840

\[\begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+33}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-37}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 11
Error	0.2
Cost	832

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

Alternative 12
Error	0.5
Cost	832

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

Alternative 13
Error	29.2
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -3.65 \cdot 10^{-65}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 9.4 \cdot 10^{-266}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 14
Error	29.2
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -3.65 \cdot 10^{-65}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-268}:\\ \;\;\;\;\frac{x}{t \cdot -0.016666666666666666}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 15
Error	29.1
Cost	192

\[a \cdot 120 \]

Reproduce

herbie shell --seed 2023187 
(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)))