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

Average Error: 0.4 → 0.4

Time: 40.1s

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	11.0
Cost	1364

\[\begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{-60}{t} + a \cdot 120\\ t_2 := \left(x - y\right) \cdot \frac{60}{z} + a \cdot 120\\ t_3 := \left(\frac{x}{z - t} + a \cdot 2\right) \cdot 60\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{-40}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+24}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+164}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	11.0
Cost	1364

\[\begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{60}{z} + a \cdot 120\\ t_2 := \left(\frac{x}{z - t} + a \cdot 2\right) \cdot 60\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{-40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+132}:\\ \;\;\;\;\frac{-60}{\frac{t}{x - y}} + a \cdot 120\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+164}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t} + a \cdot 120\\ \end{array} \]

Alternative 3
Error	11.0
Cost	1364

\[\begin{array}{l} t_1 := \left(\frac{x}{z - t} + a \cdot 2\right) \cdot 60\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-91}:\\ \;\;\;\;\frac{60}{\frac{z}{x - y}} + a \cdot 120\\ \mathbf{elif}\;t \leq 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+132}:\\ \;\;\;\;\frac{-60}{\frac{t}{x - y}} + a \cdot 120\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+164}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t} + a \cdot 120\\ \end{array} \]

Alternative 4
Error	29.6
Cost	1240

\[\begin{array}{l} t_1 := -60 \cdot \frac{x - y}{t}\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{-215}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-234}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-288}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-263}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-151}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 5
Error	12.3
Cost	1100

\[\begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+109}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+192}:\\ \;\;\;\;\left(\frac{x}{z - t} + a \cdot 2\right) \cdot 60\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+234}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z} + a \cdot 120\\ \end{array} \]

Alternative 6
Error	15.1
Cost	1096

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-99}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \cdot 120 \leq 0.04:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 7
Error	24.5
Cost	976

\[\begin{array}{l} t_1 := \frac{x}{z - t} \cdot 60\\ \mathbf{if}\;a \leq -1.08 \cdot 10^{-101}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-198}:\\ \;\;\;\;\frac{y}{z - t} \cdot -60\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 8
Error	12.5
Cost	972

\[\begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+109}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+192}:\\ \;\;\;\;\left(\frac{x}{z - t} + a \cdot 2\right) \cdot 60\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+233}:\\ \;\;\;\;120 \cdot a + 60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z} + a \cdot 120\\ \end{array} \]

Alternative 9
Error	7.1
Cost	968

\[\begin{array}{l} t_1 := \left(\frac{x}{z - t} + a \cdot 2\right) \cdot 60\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+135}:\\ \;\;\;\;\frac{-60 \cdot y}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	7.2
Cost	968

\[\begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+70}:\\ \;\;\;\;\left(\frac{x}{z - t} + a \cdot 2\right) \cdot 60\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+135}:\\ \;\;\;\;\frac{-60 \cdot y}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \end{array} \]

Alternative 11
Error	0.1
Cost	832

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

Alternative 12
Error	0.1
Cost	832

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

Alternative 13
Error	0.2
Cost	832

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

Alternative 14
Error	24.3
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -2.16 \cdot 10^{-103}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-127}:\\ \;\;\;\;\frac{x}{z - t} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 15
Error	28.6
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{-302}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-138}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 16
Error	28.5
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{-290}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-154}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 17
Error	28.0
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -1.18 \cdot 10^{-238}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-135}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 18
Error	27.9
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{-153}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-168}:\\ \;\;\;\;\frac{x}{z} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]

Alternative 19
Error	29.0
Cost	192

\[120 \cdot a \]

Reproduce

herbie shell --seed 2023075 
(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)))