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

Average Error: 0.4 → 0.2

Time: 40.4s

Precision: binary64

Cost: 960

Math

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

↓

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

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
 (+ (/ (* (- x y) 0.5) (/ (- t z) -120.0)) (* 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 (((x - y) * 0.5) / ((t - z) / -120.0)) + (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 = (((x - y) * 0.5d0) / ((t - z) / (-120.0d0))) + (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 (((x - y) * 0.5) / ((t - z) / -120.0)) + (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 (((x - y) * 0.5) / ((t - z) / -120.0)) + (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(Float64(Float64(x - y) * 0.5) / Float64(Float64(t - z) / -120.0)) + 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 = (((x - y) * 0.5) / ((t - z) / -120.0)) + (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[(N[(N[(x - y), $MachinePrecision] * 0.5), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] / -120.0), $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

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

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

3. Applied egg-rr 0.2

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

4. Final simplification 0.2

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

Alternatives

Alternative 1
Error	27.7
Cost	1504

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+181}:\\ \;\;\;\;\frac{-60 \cdot y}{z - t}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+110}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{+51}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-137}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-160}:\\ \;\;\;\;\frac{x \cdot 60}{z - t}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+148}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+210}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	27.7
Cost	1504

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;y \leq -2.25 \cdot 10^{+181}:\\ \;\;\;\;\frac{-60 \cdot y}{z - t}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+107}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{+51}:\\ \;\;\;\;\frac{x - y}{t \cdot -0.016666666666666666}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-137}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-160}:\\ \;\;\;\;\frac{x \cdot 60}{z - t}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+146}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+211}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	15.3
Cost	1368

\[\begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;a \leq -6.4 \cdot 10^{+19}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-116}:\\ \;\;\;\;\left(-0.5 \cdot \frac{x}{t} + a\right) \cdot 120\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 23500:\\ \;\;\;\;120 \cdot a + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+19}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 4
Error	15.2
Cost	1368

\[\begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+20}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-79}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-115}:\\ \;\;\;\;\left(-0.5 \cdot \frac{x}{t} + a\right) \cdot 120\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-17}:\\ \;\;\;\;\frac{x - y}{\left(t - z\right) \cdot -0.016666666666666666}\\ \mathbf{elif}\;a \leq 32000000:\\ \;\;\;\;120 \cdot a + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+19}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 5
Error	15.2
Cost	1368

\[\begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+20}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-78}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-115}:\\ \;\;\;\;\left(-0.5 \cdot \frac{x}{t} + a\right) \cdot 120\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-17}:\\ \;\;\;\;\frac{x - y}{\left(t - z\right) \cdot -0.016666666666666666}\\ \mathbf{elif}\;a \leq 4600000:\\ \;\;\;\;60 \cdot \left(\left(-\frac{y}{z}\right) + \left(a + a\right)\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+19}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 6
Error	27.3
Cost	1240

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+180}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{+130}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+147}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+210}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	27.5
Cost	1240

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+180}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+107}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{+51}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+148}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+210}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	15.2
Cost	1236

\[\begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;a \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-115}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-118}:\\ \;\;\;\;\frac{-60 \cdot y}{z - t}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 9
Error	14.9
Cost	1104

\[\begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;a \leq -8 \cdot 10^{+20}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-115}:\\ \;\;\;\;\left(-0.5 \cdot \frac{x}{t} + a\right) \cdot 120\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 10
Error	10.7
Cost	968

\[\begin{array}{l} t_1 := 60 \cdot \left(\frac{y}{t - z} + \left(a + a\right)\right)\\ \mathbf{if}\;a \leq -2.25 \cdot 10^{-141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-112}:\\ \;\;\;\;\frac{x - y}{\left(t - z\right) \cdot -0.016666666666666666}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	6.8
Cost	968

\[\begin{array}{l} t_1 := 60 \cdot \left(\frac{y}{t - z} + \left(a + a\right)\right)\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+125}:\\ \;\;\;\;120 \cdot \left(a + \frac{0.5}{z - t} \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	6.8
Cost	968

\[\begin{array}{l} t_1 := 60 \cdot \left(\frac{y}{t - z} + \left(a + a\right)\right)\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+125}:\\ \;\;\;\;\left(0.5 \cdot \frac{x}{z - t} + a\right) \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	6.9
Cost	968

\[\begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{+72}:\\ \;\;\;\;\frac{-60 \cdot y}{z - t} + a \cdot 120\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+124}:\\ \;\;\;\;\left(0.5 \cdot \frac{x}{z - t} + a\right) \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \left(\frac{y}{t - z} + \left(a + a\right)\right)\\ \end{array} \]

Alternative 14
Error	28.5
Cost	848

\[\begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{-185}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-267}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-242}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-117}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 15
Error	24.9
Cost	844

\[\begin{array}{l} \mathbf{if}\;a \leq -2.25 \cdot 10^{-141}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-269}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-116}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 16
Error	24.9
Cost	844

\[\begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-141}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-269}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-115}:\\ \;\;\;\;\frac{-60 \cdot y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 17
Error	0.2
Cost	832

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

Alternative 18
Error	0.1
Cost	832

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

Alternative 19
Error	28.7
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{-220}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-120}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 20
Error	28.4
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-206}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-118}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 21
Error	29.2
Cost	192

\[120 \cdot a \]

Reproduce

herbie shell --seed 2023064 
(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)))