Average Error: 0.1 → 0.0
Time: 11.3s
Precision: binary64
Cost: 7104
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
↓
\[\mathsf{fma}\left(y, 5, x \cdot \left(t + \left(y + z\right) \cdot 2\right)\right) \]
(FPCore (x y z t)
 :precision binary64
 (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))
↓
(FPCore (x y z t) :precision binary64 (fma y 5.0 (* x (+ t (* (+ y z) 2.0)))))
double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}
↓
double code(double x, double y, double z, double t) {
	return fma(y, 5.0, (x * (t + ((y + z) * 2.0))));
}

function code(x, y, z, t)
	return Float64(Float64(x * Float64(Float64(Float64(Float64(y + z) + z) + y) + t)) + Float64(y * 5.0))
end
↓
function code(x, y, z, t)
	return fma(y, 5.0, Float64(x * Float64(t + Float64(Float64(y + z) * 2.0))))
end

code[x_, y_, z_, t_] := N[(N[(x * N[(N[(N[(N[(y + z), $MachinePrecision] + z), $MachinePrecision] + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_, t_] := N[(y * 5.0 + N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
\mathsf{fma}\left(y, 5, x \cdot \left(t + \left(y + z\right) \cdot 2\right)\right)

Error

Derivation

  1. Initial program 0.1

    \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]

  2. Applied egg-rr0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(y + z\right) \cdot 2 + t\right)\right)} \]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(t + \left(y + z\right) \cdot 2\right)\right) \]

Alternatives

Alternative 1
Error10.2
Cost1760
\[\begin{array}{l} t_1 := x \cdot t + y \cdot 5\\ t_2 := x \cdot \left(t + z \cdot 2\right)\\ t_3 := \left(y + z\right) \cdot 2\\ t_4 := x \cdot t_3 + y \cdot 5\\ t_5 := x \cdot \left(t + t_3\right)\\ \mathbf{if}\;x \leq -62000000:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-26}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-130}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-241}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-265}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-10}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]
Alternative 2
Error26.1
Cost1637
\[\begin{array}{l} t_1 := \left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{if}\;x \leq -20000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-71}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-95}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-17}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-6} \lor \neg \left(x \leq 9 \cdot 10^{+61}\right) \land x \leq 4.6 \cdot 10^{+212}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \]
Alternative 3
Error10.5
Cost1497
\[\begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right) + x \cdot t\\ t_2 := x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -2500:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-95}:\\ \;\;\;\;x \cdot t + y \cdot 5\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-35} \lor \neg \left(x \leq 1.02 \cdot 10^{-16}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 4
Error10.7
Cost1369
\[\begin{array}{l} t_1 := x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -155:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-5}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-95} \lor \neg \left(x \leq 2.5 \cdot 10^{-35}\right) \land x \leq 1.02 \cdot 10^{-16}:\\ \;\;\;\;x \cdot t + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 5
Error10.7
Cost1369
\[\begin{array}{l} t_1 := x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{if}\;x \leq -155:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-11}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(y \cdot 2\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-96} \lor \neg \left(x \leq 3.4 \cdot 10^{-35}\right) \land x \leq 8.2 \cdot 10^{-17}:\\ \;\;\;\;x \cdot t + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 6
Error25.0
Cost1240
\[\begin{array}{l} t_1 := \left(y + z\right) \cdot \left(x \cdot 2\right)\\ t_2 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{-26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-261}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-136}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 1.66 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 7
Error31.2
Cost1112
\[\begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{-26}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-259}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-134}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
Alternative 8
Error26.2
Cost978
\[\begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-71} \lor \neg \left(x \leq 2.3 \cdot 10^{-95} \lor \neg \left(x \leq 5 \cdot 10^{-35}\right) \land x \leq 5.8 \cdot 10^{-17}\right):\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
Alternative 9
Error14.8
Cost976
\[\begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ t_2 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -2.05 \cdot 10^{-53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-28}:\\ \;\;\;\;x \cdot t + y \cdot 5\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 10
Error0.1
Cost960
\[x \cdot \left(t + \left(y + \left(z + \left(y + z\right)\right)\right)\right) + y \cdot 5 \]
Alternative 11
Error0.1
Cost960
\[x \cdot \left(t + z \cdot 2\right) + y \cdot \left(5 + x \cdot 2\right) \]
Alternative 12
Error14.8
Cost713
\[\begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-50} \lor \neg \left(y \leq 3.3 \cdot 10^{+51}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]
Alternative 13
Error31.7
Cost456
\[\begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{-105}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+22}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
Alternative 14
Error37.9
Cost192
\[y \cdot 5 \]

Error

Reproduce

herbie shell --seed 2022364 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B"
  :precision binary64
  (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))