?

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

↓

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

(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)

Original	0.4
Target	0.2
Herbie	0.1

[Start]0.4	\[ \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
+-commutative [=>]0.4	\[ \color{blue}{a \cdot 120 + \frac{60 \cdot \left(x - y\right)}{z - t}} \]
fma-def [=>]0.4	\[ \color{blue}{\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(x - y\right)}{z - t}\right)} \]
associate-*l/ [<=]0.1	\[ \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)}\right) \]

Alternatives

Alternative 1
Error	0.1
Cost	7104

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

Alternative 2
Error	25.5
Cost	1108

\[\begin{array}{l} \mathbf{if}\;a \leq -5.3 \cdot 10^{-24}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-287}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-123}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-17}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 0.14:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 3
Error	25.6
Cost	1108

\[\begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{-24}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-290}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-124}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-17}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 0.21:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 4
Error	25.5
Cost	1108

\[\begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-25}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-290}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{-123}:\\ \;\;\;\;\frac{\frac{x - y}{z}}{0.016666666666666666}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-17}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 0.096:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 5
Error	15.1
Cost	1100

\[\begin{array}{l} t_1 := a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-29}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-45}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	9.9
Cost	1100

\[\begin{array}{l} t_1 := a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-30}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-45}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	15.9
Cost	1096

\[\begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -500000:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 20:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 8
Error	29.4
Cost	980

\[\begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-26}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-77}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-124}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{-237}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-124}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 9
Error	29.3
Cost	980

\[\begin{array}{l} \mathbf{if}\;a \leq -1.22 \cdot 10^{-26}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-80}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-128}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-238}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-122}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 10
Error	29.4
Cost	980

\[\begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-26}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-77}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-127}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-236}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-122}:\\ \;\;\;\;\frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 11
Error	29.4
Cost	980

\[\begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-26}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-77}:\\ \;\;\;\;\frac{-60}{\frac{-t}{y}}\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-122}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-238}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \mathbf{elif}\;a \leq 1.46 \cdot 10^{-124}:\\ \;\;\;\;\frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 12
Error	25.8
Cost	976

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{-24}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-262}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-202}:\\ \;\;\;\;\frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 13
Error	6.9
Cost	969

\[\begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-49} \lor \neg \left(x \leq 5.8 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \end{array} \]

Alternative 14
Error	26.1
Cost	844

\[\begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-26}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-263}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 0.096:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 15
Error	14.9
Cost	840

\[\begin{array}{l} \mathbf{if}\;a \leq -6200000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 4.6:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 16
Error	0.2
Cost	832

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

Alternative 17
Error	28.5
Cost	716

\[\begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{-126}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-233}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 10^{-123}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 18
Error	28.4
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-108}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-246}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 19
Error	28.1
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-124}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-165}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 20
Error	29.1
Cost	192

\[a \cdot 120 \]

?

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Error?

Target

Derivation?

Alternatives

Error

Reproduce?