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

Average Error: 0.4 → 0.2

Time: 41.2s

Precision: binary64

Cost: 1088

Math

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

↓

\[\frac{a \cdot 120 + 120 \cdot \left(\frac{x - y}{z - t} + a\right)}{2} \]

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
 (/ (+ (* a 120.0) (* 120.0 (+ (/ (- x y) (- z t)) a))) 2.0))

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 ((a * 120.0) + (120.0 * (((x - y) / (z - t)) + a))) / 2.0;
}

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 = ((a * 120.0d0) + (120.0d0 * (((x - y) / (z - t)) + a))) / 2.0d0
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 ((a * 120.0) + (120.0 * (((x - y) / (z - t)) + a))) / 2.0;
}

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 ((a * 120.0) + (120.0 * (((x - y) / (z - t)) + a))) / 2.0

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(Float64(a * 120.0) + Float64(120.0 * Float64(Float64(Float64(x - y) / Float64(z - t)) + a))) / 2.0)
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 = ((a * 120.0) + (120.0 * (((x - y) / (z - t)) + a))) / 2.0;
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[(N[(a * 120.0), $MachinePrecision] + N[(120.0 * N[(N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $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

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

   [Start] 0.4	\[ \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   rational.json-simplify-2 [=>] 0.4	\[ \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} + a \cdot 120 \]
   rational.json-simplify-49 [=>] 0.2	\[ \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

3. Applied egg-rr 0.2

   \[\leadsto \color{blue}{\frac{a \cdot 120 + 120 \cdot \left(\frac{x - y}{z - t} + a\right)}{2}} \]

4. Final simplification 0.2

   \[\leadsto \frac{a \cdot 120 + 120 \cdot \left(\frac{x - y}{z - t} + a\right)}{2} \]

Alternatives

Alternative 1
Error	15.1
Cost	1876

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -400:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-17}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 50000000000000:\\ \;\;\;\;120 \cdot a + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+18}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{+100}:\\ \;\;\;\;\left(a + y \cdot \frac{0.5}{t}\right) \cdot 120\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 2
Error	25.9
Cost	1768

\[\begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z}\\ t_2 := \frac{x}{z - t} \cdot 60\\ t_3 := -60 \cdot \frac{x - y}{t}\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{-15}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-170}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{-238}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-292}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-303}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-220}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-208}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.4 \cdot 10^{-175}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.25 \cdot 10^{-70}:\\ \;\;\;\;\frac{y}{z - t} \cdot -60\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-17}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 3
Error	14.9
Cost	1616

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -400:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-35}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 50000000000000:\\ \;\;\;\;\left(a + \left(x - y\right) \cdot \frac{0.5}{z}\right) \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{+100}:\\ \;\;\;\;\left(a + y \cdot \frac{0.5}{t}\right) \cdot 120\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 4
Error	25.7
Cost	1240

\[\begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z}\\ t_2 := -60 \cdot \frac{x - y}{t}\\ \mathbf{if}\;a \leq -1.12 \cdot 10^{-14}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-166}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-238}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-287}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-303}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 5
Error	14.6
Cost	1096

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -400:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-17}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 6
Error	29.3
Cost	980

\[\begin{array}{l} t_1 := 60 \cdot \frac{y}{t}\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{-54}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-151}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-257}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 7
Error	10.0
Cost	968

\[\begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{-60}{t} + a \cdot 120\\ \mathbf{if}\;t \leq -6800:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-58}:\\ \;\;\;\;\left(a + \left(x - y\right) \cdot \frac{0.5}{z}\right) \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	6.1
Cost	968

\[\begin{array}{l} t_1 := \frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 800000000:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	6.1
Cost	968

\[\begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+43}:\\ \;\;\;\;\frac{-60 \cdot y}{z - t} + a \cdot 120\\ \mathbf{elif}\;y \leq 1250000000:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \end{array} \]

Alternative 10
Error	0.2
Cost	832

\[\left(a + \left(x - y\right) \cdot \frac{0.5}{z - t}\right) \cdot 120 \]

Alternative 11
Error	0.2
Cost	832

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

Alternative 12
Error	25.7
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-13}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-44}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 13
Error	29.5
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-46}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-109}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 14
Error	29.2
Cost	192

\[120 \cdot a \]

Reproduce

herbie shell --seed 2023074 
(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)))