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

Average Error: 0.65% → 0.24%

Time: 22.6s

Precision: binary64

Cost: 832

Math

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

↓

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

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
 (+ (/ 60.0 (/ (- z t) (- x y))) (* 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 (60.0 / ((z - t) / (x - y))) + (a * 120.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((60.0d0 * (x - y)) / (z - t)) + (a * 120.0d0)
end function

↓

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (60.0d0 / ((z - t) / (x - y))) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

↓

public static double code(double x, double y, double z, double t, double a) {
	return (60.0 / ((z - t) / (x - y))) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0)

↓

def code(x, y, z, t, a):
	return (60.0 / ((z - t) / (x - y))) + (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 Float64(Float64(60.0 / Float64(Float64(z - t) / Float64(x - y))) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
end

↓

function tmp = code(x, y, z, t, a)
	tmp = (60.0 / ((z - t) / (x - y))) + (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[(N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Target

Original	0.65%
Target	0.24%
Herbie	0.24%

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

Derivation

1. Initial program 0.65

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

2. Simplified 0.24

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

   [Start] 0.65	\[ \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   associate-/l* [=>] 0.24	\[ \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

3. Final simplification 0.24

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

Alternatives

Alternative 1
Error	39.19%
Cost	2657

\[\begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{60}{z - t}\\ t_2 := a \cdot 120 + \frac{60}{\frac{z}{x}}\\ \mathbf{if}\;z - t \leq -2 \cdot 10^{+149}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq -1 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z - t \leq -2 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z - t \leq 2 \cdot 10^{-165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z - t \leq 2 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z - t \leq 10^{+134} \lor \neg \left(z - t \leq 4 \cdot 10^{+172}\right) \land z - t \leq 5 \cdot 10^{+201}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 2
Error	27.61%
Cost	2136

\[\begin{array}{l} t_1 := a \cdot 120 + \frac{60}{\frac{z}{x}}\\ t_2 := \frac{60}{\frac{z - t}{x - y}}\\ \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{+120}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-79}:\\ \;\;\;\;\frac{y}{\frac{t}{60}} + a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-74}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 3
Error	23.71%
Cost	1628

\[\begin{array}{l} t_1 := \frac{60}{\frac{z - t}{x}} + a \cdot 120\\ t_2 := \frac{60}{\frac{z}{x - y}} + a \cdot 120\\ t_3 := \frac{y}{\frac{t}{60}} + a \cdot 120\\ \mathbf{if}\;z \leq -1 \cdot 10^{-59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-144}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-163}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-55}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+14}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	27.13%
Cost	1616

\[\begin{array}{l} t_1 := a \cdot 120 + \frac{60}{\frac{z}{x}}\\ \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-79}:\\ \;\;\;\;\frac{y}{\frac{t}{60}} + a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-74}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 5
Error	38.29%
Cost	1372

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ t_2 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;a \leq -3 \cdot 10^{-22}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-118}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-264}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-77}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 6
Error	38.61%
Cost	1372

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ t_2 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{-22}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-118}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.56 \cdot 10^{-264}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-77}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 7
Error	38.53%
Cost	1372

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ t_2 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;a \leq -2.05 \cdot 10^{-22}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-119}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-264}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-77}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 8
Error	38.48%
Cost	1372

\[\begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;a \leq -1.96 \cdot 10^{-22}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-119}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-249}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-145}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-77}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 9
Error	38.58%
Cost	1372

\[\begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{-22}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-118}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-246}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-146}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-77}:\\ \;\;\;\;\frac{60}{\frac{z}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 10
Error	38.67%
Cost	1372

\[\begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-22}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-44}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-118}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-249}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-264}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-145}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-77}:\\ \;\;\;\;\frac{60}{\frac{z}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 11
Error	24.04%
Cost	1232

\[\begin{array}{l} t_1 := \frac{60}{\frac{z}{x - y}} + a \cdot 120\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-144}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-55}:\\ \;\;\;\;\frac{y}{\frac{t}{60}} + a \cdot 120\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+14}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	44.75%
Cost	1112

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z}\\ t_2 := 60 \cdot \frac{x}{z}\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{-234}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-289}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-283}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 13
Error	44.74%
Cost	1112

\[\begin{array}{l} t_1 := \frac{-60}{\frac{z}{y}}\\ t_2 := 60 \cdot \frac{x}{z}\\ \mathbf{if}\;a \leq -1.16 \cdot 10^{-234}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-290}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-283}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 14
Error	44.76%
Cost	1112

\[\begin{array}{l} t_1 := \frac{-60}{\frac{z}{y}}\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{-235}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-289}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-283}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-91}:\\ \;\;\;\;\frac{60 \cdot x}{z}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 15
Error	10.24%
Cost	1096

\[\begin{array}{l} t_1 := \frac{z - t}{x}\\ \mathbf{if}\;x \leq -30500000000000:\\ \;\;\;\;\frac{60}{t_1} + a \cdot 120\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+80}:\\ \;\;\;\;\frac{y}{\frac{z - t}{-60}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{1}{t_1} + a \cdot 120\\ \end{array} \]

Alternative 16
Error	10.24%
Cost	969

\[\begin{array}{l} \mathbf{if}\;x \leq -11000000000000 \lor \neg \left(x \leq 3.2 \cdot 10^{+77}\right):\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z - t}{-60}} + a \cdot 120\\ \end{array} \]

Alternative 17
Error	23.5%
Cost	841

\[\begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{-22} \lor \neg \left(a \leq 4.6 \cdot 10^{-75}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 18
Error	38.2%
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-118}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-78}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 19
Error	44.29%
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-194}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-79}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 20
Error	44.91%
Cost	192

\[a \cdot 120 \]

Reproduce

herbie shell --seed 2023102 
(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)))