exp neg sub

Average Error: 0.0 → 0.0

Time: 8.6s

Precision: binary64

Cost: 19392

Math

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

↓

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

FPCore

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

↓

(FPCore (x) :precision binary64 (/ (pow (exp x) x) E))

C

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

↓

double code(double x) {
	return pow(exp(x), x) / ((double) M_E);
}

Java

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

↓

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

Python

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

↓

def code(x):
	return math.pow(math.exp(x), x) / math.e

Julia

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

↓

function code(x)
	return Float64((exp(x) ^ x) / exp(1))
end

MATLAB

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

↓

function tmp = code(x)
	tmp = (exp(x) ^ x) / 2.71828182845904523536;
end

Wolfram

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

↓

code[x_] := N[(N[Power[N[Exp[x], $MachinePrecision], x], $MachinePrecision] / E), $MachinePrecision]

Derivation

1. Initial program 0.0

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

2. Applied egg-rr 0.0

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

3. Applied egg-rr 0.0

   \[\leadsto \frac{\color{blue}{{\left(e^{x}\right)}^{x}}}{e} \]

Alternatives

Alternative 1
Error	0.0
Cost	6720

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

Alternative 2
Error	1.0
Cost	6528

\[\frac{1}{e} \]

Reproduce

herbie shell --seed 2023010 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1.0 (* x x)))))