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

Average Accuracy: 99.2% → 99.2%

Time: 23.5s

Precision: binary64

Cost: 832

Math

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

↓

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

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

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

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

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

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

Target

Original	99.2%
Target	99.8%
Herbie	99.2%

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

Derivation

1. Initial program 99.2%

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

2. Final simplification 99.2%

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

Alternatives

Alternative 1
Accuracy	72.4%
Cost	2137

\[\begin{array}{l} t_1 := a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{+21}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-83} \lor \neg \left(a \cdot 120 \leq -5 \cdot 10^{-128}\right) \land a \cdot 120 \leq 4 \cdot 10^{-79}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 2
Accuracy	72.3%
Cost	2137

\[\begin{array}{l} t_1 := a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{+21}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-83} \lor \neg \left(a \cdot 120 \leq -5 \cdot 10^{-128}\right) \land a \cdot 120 \leq 4 \cdot 10^{-79}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 3
Accuracy	73.0%
Cost	2025

\[\begin{array}{l} t_1 := a \cdot 120 + 60 \cdot \frac{x}{z}\\ t_2 := a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-39}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-274}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-167}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 10^{-24} \lor \neg \left(t \leq 1.35 \cdot 10^{+41}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \end{array} \]

Alternative 4
Accuracy	72.8%
Cost	2025

\[\begin{array}{l} t_1 := a \cdot 120 + 60 \cdot \frac{x}{z}\\ t_2 := \frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-39}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-273}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-167}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-25} \lor \neg \left(t \leq 4.2 \cdot 10^{+39}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \end{array} \]

Alternative 5
Accuracy	87.4%
Cost	1233

\[\begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+140}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-97} \lor \neg \left(y \leq 360000\right) \land y \leq 1.85 \cdot 10^{+61}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \end{array} \]

Alternative 6
Accuracy	75.1%
Cost	1105

\[\begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-43}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-89} \lor \neg \left(a \leq -7.2 \cdot 10^{-130}\right) \land a \leq 4.6 \cdot 10^{-78}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 7
Accuracy	60.9%
Cost	976

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -2.15 \cdot 10^{-134}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.95 \cdot 10^{-209}:\\ \;\;\;\;\frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-128}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 8
Accuracy	61.2%
Cost	976

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{-134}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-109}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 9
Accuracy	61.3%
Cost	976

\[\begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-139}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-226}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-109}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-77}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 10
Accuracy	56.0%
Cost	848

\[\begin{array}{l} t_1 := 60 \cdot \frac{x}{z}\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{-145}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.18 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-269}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.15 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 11
Accuracy	54.3%
Cost	848

\[\begin{array}{l} t_1 := 60 \cdot \frac{y}{t}\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+227}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+267}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+294}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 12
Accuracy	54.3%
Cost	848

\[\begin{array}{l} t_1 := 60 \cdot \frac{y}{t}\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+216}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+291}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \end{array} \]

Alternative 13
Accuracy	54.3%
Cost	848

\[\begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+232}:\\ \;\;\;\;\frac{y}{\frac{t}{60}}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+221}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+276}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+291}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \end{array} \]

Alternative 14
Accuracy	61.0%
Cost	844

\[\begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{-139}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-220}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-120}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 15
Accuracy	60.9%
Cost	844

\[\begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-136}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-220}:\\ \;\;\;\;\frac{\frac{y}{-0.016666666666666666}}{z - t}\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{-121}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 16
Accuracy	99.8%
Cost	832

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

Alternative 17
Accuracy	56.4%
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -3.45 \cdot 10^{-208}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-185}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 18
Accuracy	55.9%
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -8.1 \cdot 10^{-144}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-235}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 19
Accuracy	54.8%
Cost	192

\[a \cdot 120 \]

Reproduce

herbie shell --seed 2023138 
(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)))