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

Average Accuracy: 99.3% → 99.8%

Time: 24.5s

Precision: binary64

Cost: 7104

Math

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

↓

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

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

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

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

   \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60}{z - t} \cdot \left(x - y\right)\right)} \]
   Proof

   [Start] 99.3	\[ \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   +-commutative [=>] 99.3	\[ \color{blue}{a \cdot 120 + \frac{60 \cdot \left(x - y\right)}{z - t}} \]
   fma-def [=>] 99.3	\[ \color{blue}{\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(x - y\right)}{z - t}\right)} \]
   associate-*l/ [<=] 99.8	\[ \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)}\right) \]

3. Final simplification 99.8%

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

Alternatives

Alternative 1
Accuracy	61.0%
Cost	1636

\[\begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z}\\ \mathbf{if}\;a \leq -4.6 \cdot 10^{+19}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -0.007:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-131}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{-306}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-290}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-270}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-219}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 2
Accuracy	61.0%
Cost	1636

\[\begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{if}\;a \leq -1.22 \cdot 10^{+21}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -0.0027:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-127}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-227}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-306}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-291}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-271}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-219}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 3
Accuracy	61.1%
Cost	1636

\[\begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{+20}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -0.007:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-133}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-227}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-306}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-291}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{-269}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-219}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-105}:\\ \;\;\;\;\frac{x - y}{z \cdot 0.016666666666666666}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 4
Accuracy	74.6%
Cost	1616

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+27}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq -0.5:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-47}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 20000000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 5
Accuracy	74.2%
Cost	1616

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+38}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-47}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x}}\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-123}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 20000000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 6
Accuracy	74.2%
Cost	1616

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+38}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-47}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x}}\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-123}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 20000000000:\\ \;\;\;\;\frac{x - y}{\frac{z - t}{60}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 7
Accuracy	60.0%
Cost	1240

\[\begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;a \leq -4.6 \cdot 10^{+19}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -0.000155:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-125}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-220}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{-297}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 8
Accuracy	89.7%
Cost	1234

\[\begin{array}{l} \mathbf{if}\;x \leq -3000000000 \lor \neg \left(x \leq 2.6 \cdot 10^{+14}\right) \land \left(x \leq 3.1 \cdot 10^{+69} \lor \neg \left(x \leq 3.2 \cdot 10^{+127}\right)\right):\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \end{array} \]

Alternative 9
Accuracy	83.1%
Cost	1225

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-123} \lor \neg \left(a \cdot 120 \leq 0.0002\right):\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{\frac{z - t}{60}}\\ \end{array} \]

Alternative 10
Accuracy	76.6%
Cost	1104

\[\begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{+19}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -0.0056:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-49}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 800000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 11
Accuracy	55.2%
Cost	980

\[\begin{array}{l} t_1 := 60 \cdot \frac{x}{z}\\ \mathbf{if}\;a \leq -1.75 \cdot 10^{-133}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{-294}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-214}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 12
Accuracy	60.8%
Cost	976

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -1 \cdot 10^{-58}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-269}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-245}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 13
Accuracy	60.4%
Cost	976

\[\begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{-125}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -5.1 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-297}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 14
Accuracy	55.2%
Cost	848

\[\begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-129}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-227}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-297}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-219}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 15
Accuracy	55.3%
Cost	848

\[\begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{-132}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-227}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-296}:\\ \;\;\;\;\frac{60 \cdot y}{t}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-218}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 16
Accuracy	99.8%
Cost	832

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

Alternative 17
Accuracy	99.8%
Cost	832

\[\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666} + a \cdot 120 \]

Alternative 18
Accuracy	55.5%
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{-218}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-218}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 19
Accuracy	54.1%
Cost	192

\[a \cdot 120 \]

Reproduce

herbie shell --seed 2023151 
(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)))