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

Average Error: 0.4 → 0.2

Time: 17.3s

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	0.4
Target	0.2
Herbie	0.2

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

Derivation

1. Initial program 0.4

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

2. Simplified 0.2

   \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]
   Proof
   (+.f64 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))) (*.f64 a 120)): 0 points increase in error, 0 points decrease in error
   (+.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))) (*.f64 a 120)): 18 points increase in error, 14 points decrease in error

3. Final simplification 0.2

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

Alternatives

Alternative 1
Error	26.2
Cost	2916

\[\begin{array}{l} t_1 := \frac{x - y}{z \cdot 0.016666666666666666}\\ t_2 := a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{+108}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-122}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-180}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-288}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-245}:\\ \;\;\;\;\frac{x}{\frac{z - t}{60}}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-171}:\\ \;\;\;\;\frac{x - y}{t \cdot -0.016666666666666666}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	24.9
Cost	1372

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -5 \cdot 10^{-124}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-143}:\\ \;\;\;\;\frac{x - y}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-173}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-291}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-243}:\\ \;\;\;\;\frac{x}{\frac{z - t}{60}}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-220}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-87}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 3
Error	25.0
Cost	1240

\[\begin{array}{l} t_1 := \frac{x - y}{z \cdot 0.016666666666666666}\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{-124}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-200}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-172}:\\ \;\;\;\;\frac{x - y}{t \cdot -0.016666666666666666}\\ \mathbf{elif}\;a \leq 3.15 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 4
Error	10.7
Cost	1224

\[\begin{array}{l} t_1 := x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-92}:\\ \;\;\;\;\frac{x - y}{\frac{z - t}{60}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	25.1
Cost	1108

\[\begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ t_2 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -1.25 \cdot 10^{-173}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-220}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 6
Error	25.0
Cost	1108

\[\begin{array}{l} t_1 := \frac{60}{\frac{z - t}{x}}\\ t_2 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{-173}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-244}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-220}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 7
Error	25.0
Cost	1108

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{-173}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-292}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-244}:\\ \;\;\;\;\frac{x}{\frac{z - t}{60}}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-220}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-67}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 8
Error	20.4
Cost	1104

\[\begin{array}{l} t_1 := a \cdot 120 + x \cdot \frac{-60}{t}\\ t_2 := a \cdot 120 + x \cdot \frac{60}{z}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-217}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 920:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	15.1
Cost	1096

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-9}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-66}:\\ \;\;\;\;\frac{x - y}{\frac{z - t}{60}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 10
Error	28.6
Cost	848

\[\begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-226}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-237}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-219}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-121}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 11
Error	28.6
Cost	848

\[\begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-227}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-238}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-216}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-121}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 12
Error	28.6
Cost	848

\[\begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{-226}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-240}:\\ \;\;\;\;\frac{-60}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-218}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-121}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 13
Error	28.6
Cost	848

\[\begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-227}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-240}:\\ \;\;\;\;\frac{y}{\frac{z}{-60}}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-219}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-121}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 14
Error	25.1
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{-173}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-84}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 15
Error	29.4
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{-290}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-69}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 16
Error	28.7
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-226}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-129}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 17
Error	29.4
Cost	192

\[a \cdot 120 \]

Reproduce

herbie shell --seed 2022325 
(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)))