Average Error: 24.9 → 0.7
Time: 2.1s
Precision: binary64
\[x \cdot \sqrt{y \cdot y - z \cdot z} \]
↓
\[x \cdot \mathsf{hypot}\left(y, z\right) \]
(FPCore (x y z) :precision binary64 (* x (sqrt (- (* y y) (* z z)))))
↓
(FPCore (x y z) :precision binary64 (* x (hypot y z)))
double code(double x, double y, double z) {
	return x * sqrt(((y * y) - (z * z)));
}
↓
double code(double x, double y, double z) {
	return x * hypot(y, z);
}

public static double code(double x, double y, double z) {
	return x * Math.sqrt(((y * y) - (z * z)));
}
↓
public static double code(double x, double y, double z) {
	return x * Math.hypot(y, z);
}

def code(x, y, z):
	return x * math.sqrt(((y * y) - (z * z)))
↓
def code(x, y, z):
	return x * math.hypot(y, z)

function code(x, y, z)
	return Float64(x * sqrt(Float64(Float64(y * y) - Float64(z * z))))
end
↓
function code(x, y, z)
	return Float64(x * hypot(y, z))
end

function tmp = code(x, y, z)
	tmp = x * sqrt(((y * y) - (z * z)));
end
↓
function tmp = code(x, y, z)
	tmp = x * hypot(y, z);
end

code[x_, y_, z_] := N[(x * N[Sqrt[N[(N[(y * y), $MachinePrecision] - N[(z * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_] := N[(x * N[Sqrt[y ^ 2 + z ^ 2], $MachinePrecision]), $MachinePrecision]

x \cdot \sqrt{y \cdot y - z \cdot z}
↓
x \cdot \mathsf{hypot}\left(y, z\right)

Error

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original24.9
Target0.6
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;y < 2.5816096488251695 \cdot 10^{-278}:\\ \;\;\;\;-x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\sqrt{y + z} \cdot \sqrt{y - z}\right)\\ \end{array} \]

Derivation

  1. Initial program 24.9

    \[x \cdot \sqrt{y \cdot y - z \cdot z} \]

  2. Simplified24.9

    \[\leadsto \color{blue}{x \cdot \sqrt{\mathsf{fma}\left(y, y, z \cdot \left(-z\right)\right)}} \]

  3. Applied egg-rr0.7

    \[\leadsto x \cdot \color{blue}{\mathsf{hypot}\left(y, z\right)} \]

  4. Final simplification0.7

    \[\leadsto x \cdot \mathsf{hypot}\left(y, z\right) \]

Reproduce

herbie shell --seed 2022210 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:initialConfig from diagrams-contrib-1.3.0.5, B"
  :precision binary64

  :herbie-target
  (if (< y 2.5816096488251695e-278) (- (* x y)) (* x (* (sqrt (+ y z)) (sqrt (- y z)))))

  (* x (sqrt (- (* y y) (* z z)))))