Data.Number.Erf:$dmerfcx from erf-2.0.0.0

Average Error: 0.0 → 0.0

Time: 2.6s

Precision: binary64

Cost: 13120

Math

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

↓

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

FPCore

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

↓

(FPCore (x y) :precision binary64 (* x (pow E (* y y))))

C

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

function code(x, y)
	return Float64(x * (exp(1) ^ Float64(y * y)))
end

MATLAB

function tmp = code(x, y)
	tmp = x * exp((y * y));
end

↓

function tmp = code(x, y)
	tmp = x * (2.71828182845904523536 ^ (y * y));
end

Wolfram

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

↓

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

Target

Original	0.0
Target	0.0
Herbie	0.0

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

Derivation

1. Initial program 0.0

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

2. Applied egg-rr 0.0

   \[\leadsto x \cdot \color{blue}{{\left(e^{1}\right)}^{\left(y \cdot y\right)}} \]

3. Simplified 0.0

   \[\leadsto x \cdot \color{blue}{{e}^{\left(y \cdot y\right)}} \]
   Proof

   [Start] 0.0	\[ x \cdot {\left(e^{1}\right)}^{\left(y \cdot y\right)} \]
   exp-1-e [=>] 0.0	\[ x \cdot {\color{blue}{e}}^{\left(y \cdot y\right)} \]

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	0.0
Cost	13056

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

Alternative 2
Error	0.0
Cost	6720

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

Alternative 3
Error	0.6
Cost	448

\[x \cdot \left(y \cdot y + 1\right) \]

Alternative 4
Error	0.9
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023031 
(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))))