Average Error: 0.1 → 0.0

Time: 4.3s

Precision: binary64

Cost: 6848

\[x \cdot e^{y \cdot y} \]

↓

\[x + x \cdot \mathsf{expm1}\left(y \cdot y\right) \]

(FPCore (x y) :precision binary64 (* x (exp (* y y))))

↓

(FPCore (x y) :precision binary64 (+ x (* x (expm1 (* y y)))))

double code(double x, double y) {
	return x * exp((y * y));
}

↓

double code(double x, double y) {
	return x + (x * expm1((y * y)));
}

public static double code(double x, double y) {
	return x * Math.exp((y * y));
}

↓

public static double code(double x, double y) {
	return x + (x * Math.expm1((y * y)));
}

def code(x, y):
	return x * math.exp((y * y))

↓

def code(x, y):
	return x + (x * math.expm1((y * y)))

function code(x, y)
	return Float64(x * exp(Float64(y * y)))
end

↓

function code(x, y)
	return Float64(x + Float64(x * expm1(Float64(y * y))))
end

code[x_, y_] := N[(x * N[Exp[N[(y * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[(x + N[(x * N[(Exp[N[(y * y), $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

x \cdot e^{y \cdot y}

↓

x + x \cdot \mathsf{expm1}\left(y \cdot y\right)

Try it out

In
Out

Enter valid numbers for all inputs

Target

Original	0.1
Target	0.0
Herbie	0.0

\[x \cdot {\left(e^{y}\right)}^{y} \]

Derivation

Initial program 0.1
\[x \cdot e^{y \cdot y} \]
Applied egg-rr0.1
\[\leadsto x \cdot \color{blue}{\left(\left(1 + e^{y \cdot y}\right) - 1\right)} \]
Applied egg-rr0.0
\[\leadsto \color{blue}{x + \mathsf{expm1}\left(y \cdot y\right) \cdot x} \]
Final simplification0.0
\[\leadsto x + x \cdot \mathsf{expm1}\left(y \cdot y\right) \]

Alternatives

Alternative 1
Error	0.1
Cost	6720

\[x \cdot e^{y \cdot y} \]

Alternative 2
Error	0.5
Cost	448

\[x + y \cdot \left(x \cdot y\right) \]

Alternative 3
Error	0.8
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022318 
(FPCore (x y)
  :name "Data.Number.Erf:$dmerfcx from erf-2.0.0.0"
  :precision binary64

  :herbie-target
  (* x (pow (exp y) y))

  (* x (exp (* y y))))