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

Average Accuracy: 99.3% → 99.8%

Time: 27.7s

Precision: binary64

Cost: 7104

Math

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

↓

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

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

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

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

3. Final simplification 99.8%

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

Alternatives

Alternative 1
Accuracy	70.0%
Cost	2136

\[\begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+83}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-50}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{-154}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 2
Accuracy	70.0%
Cost	2136

\[\begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+83}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{+18}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-50}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{-154}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 3
Accuracy	53.7%
Cost	1504

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ t_2 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;x \leq -3 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-109}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.42 \cdot 10^{-239}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8.4 \cdot 10^{-83}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+231}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Accuracy	47.9%
Cost	1376

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ t_2 := x \cdot \frac{60}{z}\\ \mathbf{if}\;x \leq -3.1 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-109}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-239}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-81}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+232}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Accuracy	58.4%
Cost	1372

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ t_2 := 60 \cdot \frac{x - y}{z}\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{-54}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-139}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 10^{-161}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 220:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 510000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 6
Accuracy	58.5%
Cost	1372

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -7.2 \cdot 10^{-54}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-139}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 3.55 \cdot 10^{-162}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;a \leq 230:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3500000:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 7
Accuracy	58.4%
Cost	1372

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -4.6 \cdot 10^{-54}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-139}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;a \leq 10^{-161}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;a \leq 230:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 64000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 8
Accuracy	61.4%
Cost	1372

\[\begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-117}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-139}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{-162}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-144}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-137}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-82}:\\ \;\;\;\;\frac{x - y}{\frac{t}{-60}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 9
Accuracy	72.3%
Cost	1371

\[\begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+75} \lor \neg \left(a \leq -45000000000\right) \land \left(a \leq -8.8 \cdot 10^{-53} \lor \neg \left(a \leq 10^{-161} \lor \neg \left(a \leq 2 \cdot 10^{-150}\right) \land a \leq 1.25 \cdot 10^{+82}\right)\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 10
Accuracy	72.1%
Cost	1368

\[\begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{+73}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -245000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-53}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-156}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 11
Accuracy	75.6%
Cost	1236

\[\begin{array}{l} t_1 := a \cdot 120 + 60 \cdot \frac{x}{z}\\ t_2 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;z \leq -1.56 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{-125}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+106}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 12
Accuracy	83.8%
Cost	1225

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-115} \lor \neg \left(a \cdot 120 \leq 5 \cdot 10^{-191}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 13
Accuracy	85.5%
Cost	1100

\[\begin{array}{l} t_1 := \frac{x - y}{\frac{z}{60}} + a \cdot 120\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-135}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+41}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Accuracy	99.8%
Cost	832

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

Alternative 15
Accuracy	55.4%
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-64}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-241}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 16
Accuracy	56.4%
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{-119}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-228}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 17
Accuracy	56.4%
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-121}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-221}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 18
Accuracy	55.1%
Cost	192

\[a \cdot 120 \]

Reproduce

herbie shell --seed 2023137 
(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)))