exp neg sub

Average Error: 0.0 → 0.0

Time: 3.1s

Precision: binary64

Cost: 13120

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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((x * x)) * exp((-1.0d0))
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((x * x)) * Math.exp(-1.0);
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Simplified 0.0

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

   [Start] 0.0	\[ e^{-\left(1 - x \cdot x\right)} \]
   rational_best-simplify-10 [=>] 0.0	\[ e^{\color{blue}{0 - \left(1 - x \cdot x\right)}} \]
   rational_best-simplify-49 [=>] 0.0	\[ e^{\color{blue}{x \cdot x + \left(0 - 1\right)}} \]
   metadata-eval [=>] 0.0	\[ e^{x \cdot x + \color{blue}{-1}} \]

3. Applied egg-rr 0.0

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

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	0.0
Cost	6720

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

Alternative 2
Error	0.9
Cost	6464

\[e^{-1} \]

Reproduce

herbie shell --seed 2023096 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1.0 (* x x)))))