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

Average Accuracy: 99.4% → 99.8%

Time: 29.5s

Precision: binary64

Cost: 832

Math

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

↓

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

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

Target

Original	99.4%
Target	99.8%
Herbie	99.8%

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

Derivation

1. Initial program 99.4%

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

2. Simplified 99.8%

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

   [Start] 99.4	\[ \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   associate-/l* [=>] 99.8	\[ \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

3. Final simplification 99.8%

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

Alternatives

Alternative 1
Accuracy	74.8%
Cost	1617

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-21}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-55} \lor \neg \left(a \cdot 120 \leq -1 \cdot 10^{-140}\right) \land a \cdot 120 \leq 10^{-81}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 2
Accuracy	61.7%
Cost	1240

\[\begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ t_2 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{-144}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-176}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-180}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-252}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-216}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 3
Accuracy	61.8%
Cost	1240

\[\begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{-142}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-176}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq -1.62 \cdot 10^{-180}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-216}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 4
Accuracy	83.8%
Cost	1225

\[\begin{array}{l} t_1 := \frac{60}{z - t}\\ \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-140} \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{-108}\right):\\ \;\;\;\;x \cdot t_1 + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot t_1\\ \end{array} \]

Alternative 5
Accuracy	55.4%
Cost	1112

\[\begin{array}{l} t_1 := 60 \cdot \frac{x}{z}\\ t_2 := -60 \cdot \frac{y}{z}\\ \mathbf{if}\;a \leq -1.1 \cdot 10^{-144}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-171}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-181}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-244}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-217}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.04 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 6
Accuracy	55.3%
Cost	1112

\[\begin{array}{l} t_1 := 60 \cdot \frac{x}{z}\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{-143}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{-173}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-181}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-218}:\\ \;\;\;\;\frac{-60}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 7
Accuracy	55.2%
Cost	1112

\[\begin{array}{l} t_1 := 60 \cdot \frac{x}{z}\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{-144}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-174}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{-182}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-217}:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 8
Accuracy	60.2%
Cost	1108

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{-143}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -5.1 \cdot 10^{-176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-181}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-241}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 9
Accuracy	61.4%
Cost	1108

\[\begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-144}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-172}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq -2.75 \cdot 10^{-180}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.15 \cdot 10^{-248}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-100}:\\ \;\;\;\;\frac{x - y}{\frac{z}{60}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 10
Accuracy	55.7%
Cost	980

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z}\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{-144}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-201}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-292}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 11
Accuracy	89.2%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+112} \lor \neg \left(y \leq 2.2 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \end{array} \]

Alternative 12
Accuracy	89.2%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+112} \lor \neg \left(y \leq 1.85 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \end{array} \]

Alternative 13
Accuracy	56.2%
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-201}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-234}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 14
Accuracy	54.5%
Cost	192

\[a \cdot 120 \]

Reproduce

herbie shell --seed 2023146 
(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)))