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

Average Accuracy: 99.3% → 99.8%

Time: 19.1s

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	99.3%
Target	99.8%
Herbie	99.8%

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

Derivation

1. Initial program 99.3%

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

2. Simplified 99.8%

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

   [Start] 99.3	\[ \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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	54.8%
Cost	1505

\[\begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{+105}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-122}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq 17000000000:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+66} \lor \neg \left(x \leq 1.25 \cdot 10^{+127}\right) \land x \leq 3.5 \cdot 10^{+186}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Accuracy	84.1%
Cost	1225

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-89} \lor \neg \left(a \cdot 120 \leq 5 \cdot 10^{-145}\right):\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \end{array} \]

Alternative 3
Accuracy	84.1%
Cost	1225

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-82} \lor \neg \left(a \cdot 120 \leq 5 \cdot 10^{-145}\right):\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \end{array} \]

Alternative 4
Accuracy	60.4%
Cost	1108

\[\begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{-89}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-220}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 2.12 \cdot 10^{-128}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-69}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 9.1 \cdot 10^{-29}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 5
Accuracy	60.4%
Cost	1108

\[\begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-87}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-219}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-129}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-36}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 9.1 \cdot 10^{-29}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 6
Accuracy	60.4%
Cost	1108

\[\begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-87}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-219}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-127}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{\frac{z - t}{60}}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-29}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 7
Accuracy	60.4%
Cost	1108

\[\begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-87}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-219}:\\ \;\;\;\;\frac{x - y}{\frac{t}{-60}}\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{-127}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{\frac{z - t}{60}}\\ \mathbf{elif}\;a \leq 10^{-28}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 8
Accuracy	76.6%
Cost	1096

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-82}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 0.005:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 9
Accuracy	76.6%
Cost	1096

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-82}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 0.005:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 10
Accuracy	60.1%
Cost	976

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{-90}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-243}:\\ \;\;\;\;\frac{x}{t \cdot -0.016666666666666666}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 11
Accuracy	60.7%
Cost	976

\[\begin{array}{l} t_1 := -60 \cdot \frac{x - y}{t}\\ \mathbf{if}\;a \leq -7.8 \cdot 10^{-87}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-220}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-138}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 12
Accuracy	89.5%
Cost	969

\[\begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+60} \lor \neg \left(x \leq 23000000000\right):\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \end{array} \]

Alternative 13
Accuracy	76.6%
Cost	840

\[\begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-84}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-5}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 14
Accuracy	55.0%
Cost	716

\[\begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-91}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-297}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-146}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 15
Accuracy	54.9%
Cost	716

\[\begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{-88}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-293}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-146}:\\ \;\;\;\;\frac{x}{t \cdot -0.016666666666666666}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 16
Accuracy	54.9%
Cost	716

\[\begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{-88}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-297}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-147}:\\ \;\;\;\;\frac{x \cdot -60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 17
Accuracy	54.7%
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{-87}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 10^{-146}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 18
Accuracy	54.2%
Cost	192

\[a \cdot 120 \]

Reproduce

herbie shell --seed 2023129 
(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)))