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

Average Error: 0.4 → 0.1

Time: 19.1s

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	0.4
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

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

   [Start] 0.4	\[ \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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	25.0
Cost	1372

\[\begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ t_2 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -1.95 \cdot 10^{-29}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-172}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-248}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-43}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 2
Error	25.1
Cost	1372

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ t_2 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;a \leq -2.25 \cdot 10^{-29}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-105}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-172}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-304}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{-152}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 3
Error	25.3
Cost	1372

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ t_2 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{-21}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-83}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-172}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-304}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 4
Error	25.2
Cost	1372

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{-28}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-82}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-172}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-304}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-147}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 5
Error	25.3
Cost	1372

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -9.4 \cdot 10^{-24}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-82}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-172}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-304}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-142}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;a \leq 3.25 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 6
Error	24.9
Cost	1372

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -7.5 \cdot 10^{-28}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-95}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-127}:\\ \;\;\;\;\frac{x - y}{\frac{t}{-60}}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-304}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-144}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 7
Error	10.4
Cost	1225

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-17} \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{-151}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]

Alternative 8
Error	26.5
Cost	1108

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -2.25 \cdot 10^{-29}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-200}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-304}:\\ \;\;\;\;\frac{60}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 9
Error	14.1
Cost	1096

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-17}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-29}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 10
Error	7.2
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+15} \lor \neg \left(y \leq 2.9 \cdot 10^{+122}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \end{array} \]

Alternative 11
Error	28.0
Cost	848

\[\begin{array}{l} t_1 := 60 \cdot \frac{x}{z}\\ \mathbf{if}\;a \leq -2.6 \cdot 10^{-198}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-189}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 12
Error	28.0
Cost	848

\[\begin{array}{l} t_1 := 60 \cdot \frac{x}{z}\\ \mathbf{if}\;a \leq -2.55 \cdot 10^{-199}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-189}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 13
Error	28.0
Cost	848

\[\begin{array}{l} t_1 := \frac{60}{\frac{z}{x}}\\ \mathbf{if}\;a \leq -2.16 \cdot 10^{-200}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-189}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 14
Error	0.2
Cost	832

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

Alternative 15
Error	28.1
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{-230}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-135}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 16
Error	29.0
Cost	192

\[a \cdot 120 \]

Reproduce

herbie shell --seed 2023040 
(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)))