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

Average Error: 0.3 → 0.2

Time: 5.6s

Precision: binary64

Math

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

↓

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

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

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

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 = ((120.0d0 * a) + (60.0d0 * (x / (z - t)))) + ((-60.0d0) / ((z - t) / y))
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 ((120.0 * a) + (60.0 * (x / (z - t)))) + (-60.0 / ((z - t) / y));
}

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

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

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	0.3
Target	0.2
Herbie	0.2

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

Derivation

1. Initial program 0.3

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

2. Simplified 0.2

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

3. Taylor expanded in x around 0 0.2

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

4. Applied egg-rr 0.2

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

5. Final simplification 0.2

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

Reproduce

herbie shell --seed 2022166 
(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)))