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

Average Error: 0.03% → 0.03%

Time: 1.2s

Precision: binary64

Cost: 6720

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * exp((y * y))
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * exp((y * y))
end function

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.exp((y * y));
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	0.03%
Target	0.02%
Herbie	0.03%

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

Derivation

1. Initial program 0.03

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

2. Final simplification 0.03

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

Alternatives

Alternative 1
Error	1.39%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023089 
(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))))