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

Average Error: 0.5 → 0.1

Time: 45.1s

Precision: binary64

Cost: 1216

Math

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

↓

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

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 (/ y (- z t))) (* 60.0 (/ x (- 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 ((-60.0 * (y / (z - t))) + (60.0 * (x / (z - t)))) + (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) * (y / (z - t))) + (60.0d0 * (x / (z - t)))) + (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 * (y / (z - t))) + (60.0 * (x / (z - t)))) + (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 * (y / (z - t))) + (60.0 * (x / (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 Float64(Float64(Float64(-60.0 * Float64(y / Float64(z - t))) + Float64(60.0 * Float64(x / Float64(z - t)))) + 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 * (y / (z - t))) + (60.0 * (x / (z - t)))) + (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[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Target

Original	0.5
Target	0.2
Herbie	0.1

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

Derivation

1. Initial program 0.5

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

2. Taylor expanded in x around 0 0.1

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

3. Final simplification 0.1

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

Alternatives

Alternative 1
Error	29.5
Cost	1504

\[\begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ t_2 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;y \leq -6.3 \cdot 10^{+137}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-23}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.32 \cdot 10^{-211}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-246}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1000:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+220}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	16.1
Cost	972

\[\begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+43}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-121}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+94}:\\ \;\;\;\;120 \cdot a + 60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 3
Error	13.1
Cost	968

\[\begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+141}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+214}:\\ \;\;\;\;120 \cdot a + 60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a + -60 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 4
Error	6.8
Cost	968

\[\begin{array}{l} t_1 := \frac{-60 \cdot y}{z - t} + a \cdot 120\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+61}:\\ \;\;\;\;120 \cdot a + 60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	30.3
Cost	848

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+145}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+220}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+257}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 6
Error	15.1
Cost	840

\[\begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+43}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-30}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 7
Error	0.5
Cost	832

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

Alternative 8
Error	27.0
Cost	712

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+220}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	25.3
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-69}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-121}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 10
Error	29.1
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-262}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-121}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 11
Error	29.4
Cost	192

\[120 \cdot a \]

Reproduce

herbie shell --seed 2023077 
(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)))