?

Average Accuracy: 99.3% → 99.8%
Time: 23.2s
Precision: binary64
Cost: 7104

?

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

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

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]

\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)

Error?

Target

Original99.3%
Target99.7%
Herbie99.8%
\[\frac{60}{\frac{z - t}{x - y}} + a \cdot 120 \]

Derivation?

  1. Initial program 99.3%

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

  2. Simplified99.8%

    \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60}{z - t} \cdot \left(x - y\right)\right)} \]
    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 simplification99.8%

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

Alternatives

Alternative 1
Accuracy99.8%
Cost7104
\[\mathsf{fma}\left(60, \frac{x - y}{z - t}, a \cdot 120\right) \]
Alternative 2
Accuracy80.9%
Cost1746
\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-19} \lor \neg \left(a \cdot 120 \leq -4 \cdot 10^{-56}\right) \land \left(a \cdot 120 \leq -5 \cdot 10^{-90} \lor \neg \left(a \cdot 120 \leq 4 \cdot 10^{+53}\right)\right):\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \]
Alternative 3
Accuracy58.6%
Cost1504
\[\begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ t_2 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{-22}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-92}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-295}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-253}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{-11}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
Alternative 4
Accuracy58.6%
Cost1504
\[\begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{-22}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-93}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-295}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-253}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
Alternative 5
Accuracy58.7%
Cost1504
\[\begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;a \leq -3.7 \cdot 10^{-22}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-61}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-93}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-253}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
Alternative 6
Accuracy58.7%
Cost1504
\[\begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;a \leq -7.2 \cdot 10^{-22}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-63}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-92}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-294}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-253}:\\ \;\;\;\;\frac{y}{\frac{z - t}{-60}}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
Alternative 7
Accuracy76.5%
Cost1496
\[\begin{array}{l} t_1 := a \cdot 120 + -60 \cdot \frac{x}{t}\\ t_2 := a \cdot 120 + 60 \cdot \frac{y}{t}\\ t_3 := \frac{60}{\frac{z}{x - y}} + a \cdot 120\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{-11}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-94}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-147}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 8
Accuracy54.8%
Cost980
\[\begin{array}{l} t_1 := 60 \cdot \frac{x}{z}\\ \mathbf{if}\;a \leq -5.5 \cdot 10^{-96}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.06 \cdot 10^{-232}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-258}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
Alternative 9
Accuracy89.0%
Cost969
\[\begin{array}{l} \mathbf{if}\;x \leq -2.95 \cdot 10^{-12} \lor \neg \left(x \leq 1.25 \cdot 10^{+97}\right):\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \end{array} \]
Alternative 10
Accuracy54.5%
Cost848
\[\begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-131}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.95 \cdot 10^{-242}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-245}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-123}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
Alternative 11
Accuracy54.4%
Cost848
\[\begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-101}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-187}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-120}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-100}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
Alternative 12
Accuracy54.5%
Cost848
\[\begin{array}{l} \mathbf{if}\;a \leq -3.75 \cdot 10^{-103}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-186}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-121}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-101}:\\ \;\;\;\;\frac{-60}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
Alternative 13
Accuracy75.2%
Cost841
\[\begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+64} \lor \neg \left(a \leq 6 \cdot 10^{+52}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \]
Alternative 14
Accuracy99.7%
Cost832
\[\frac{60}{\frac{z - t}{x - y}} + a \cdot 120 \]
Alternative 15
Accuracy99.3%
Cost832
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
Alternative 16
Accuracy59.3%
Cost712
\[\begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{-107}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+17}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
Alternative 17
Accuracy54.4%
Cost585
\[\begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-136} \lor \neg \left(a \leq 4.2 \cdot 10^{-202}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]
Alternative 18
Accuracy53.6%
Cost192
\[a \cdot 120 \]

Error

Reproduce?

herbie shell --seed 2023133 
(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)))