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

Average Error: 0.4 → 0.4

Time: 19.2s

Precision: binary64

Cost: 832

Math

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

↓

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

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

Target

Original	0.4
Target	0.2
Herbie	0.4

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

Derivation

1. Initial program 0.4

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

2. Final simplification 0.4

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

Alternatives

Alternative 1
Error	19.5
Cost	1500

\[\begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ t_2 := 120 \cdot a + 60 \cdot \frac{y}{t}\\ t_3 := 120 \cdot a + -60 \cdot \frac{y}{z}\\ \mathbf{if}\;t \leq -2.15 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -0.014:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-190}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-101}:\\ \;\;\;\;120 \cdot a + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-5}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	10.6
Cost	1224

\[\begin{array}{l} t_1 := \frac{-60 \cdot y}{z - t} + a \cdot 120\\ \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-102}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	24.9
Cost	976

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -1.5 \cdot 10^{-90}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-131}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-104}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 4
Error	24.9
Cost	976

\[\begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{-87}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-306}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-122}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-106}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 5
Error	6.5
Cost	968

\[\begin{array}{l} t_1 := \frac{-60 \cdot y}{z - t} + a \cdot 120\\ \mathbf{if}\;y \leq -5 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+21}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	15.3
Cost	840

\[\begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+39}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-28}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 7
Error	27.9
Cost	716

\[\begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{-179}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-307}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-197}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 8
Error	27.7
Cost	716

\[\begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-179}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-230}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-192}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 9
Error	24.5
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-89}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-101}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 10
Error	27.9
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-188}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{-197}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 11
Error	28.7
Cost	192

\[120 \cdot a \]

Reproduce

herbie shell --seed 2023090 
(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)))