exp neg sub

Average Error: 0.0 → 0.0

Time: 2.2s

Precision: binary64

Cost: 6720

Math

\[e^{-\left(1 - x \cdot x\right)} \]

↓

\[e^{-1 + x \cdot x} \]

FPCore

(FPCore (x) :precision binary64 (exp (- (- 1.0 (* x x)))))

↓

(FPCore (x) :precision binary64 (exp (+ -1.0 (* x x))))

C

double code(double x) {
	return exp(-(1.0 - (x * x)));
}

↓

double code(double x) {
	return exp((-1.0 + (x * x)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = exp(-(1.0d0 - (x * x)))
end function

↓

real(8) function code(x)
    real(8), intent (in) :: x
    code = exp(((-1.0d0) + (x * x)))
end function

Java

public static double code(double x) {
	return Math.exp(-(1.0 - (x * x)));
}

↓

public static double code(double x) {
	return Math.exp((-1.0 + (x * x)));
}

Python

def code(x):
	return math.exp(-(1.0 - (x * x)))

↓

def code(x):
	return math.exp((-1.0 + (x * x)))

Julia

function code(x)
	return exp(Float64(-Float64(1.0 - Float64(x * x))))
end

↓

function code(x)
	return exp(Float64(-1.0 + Float64(x * x)))
end

MATLAB

function tmp = code(x)
	tmp = exp(-(1.0 - (x * x)));
end

↓

function tmp = code(x)
	tmp = exp((-1.0 + (x * x)));
end

Wolfram

code[x_] := N[Exp[(-N[(1.0 - N[(x * x), $MachinePrecision]), $MachinePrecision])], $MachinePrecision]

↓

code[x_] := N[Exp[N[(-1.0 + N[(x * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 0.0

   \[e^{-\left(1 - x \cdot x\right)} \]

2. Applied egg-rr 0.0

   \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(e^{-1 + x \cdot x}\right)\right)} \]

3. Applied egg-rr 0.0

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

4. Applied egg-rr 0.0

   \[\leadsto \color{blue}{e^{-1 + x \cdot x}} \]

5. Final simplification 0.0

   \[\leadsto e^{-1 + x \cdot x} \]

Alternatives

Alternative 1
Error	1.0
Cost	6464

\[e^{-1} \]

Reproduce

herbie shell --seed 2022295 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1.0 (* x x)))))