?

Average Error: 91.85% → 0%
Time: 1.7s
Precision: binary64
Cost: 6464

?

\[-0.00017 < x\]
\[e^{x} - 1 \]
↓
\[\mathsf{expm1}\left(x\right) \]
(FPCore (x) :precision binary64 (- (exp x) 1.0))
↓
(FPCore (x) :precision binary64 (expm1 x))
double code(double x) {
	return exp(x) - 1.0;
}
↓
double code(double x) {
	return expm1(x);
}

public static double code(double x) {
	return Math.exp(x) - 1.0;
}
↓
public static double code(double x) {
	return Math.expm1(x);
}

def code(x):
	return math.exp(x) - 1.0
↓
def code(x):
	return math.expm1(x)

function code(x)
	return Float64(exp(x) - 1.0)
end
↓
function code(x)
	return expm1(x)
end

code[x_] := N[(N[Exp[x], $MachinePrecision] - 1.0), $MachinePrecision]
↓
code[x_] := N[(Exp[x] - 1), $MachinePrecision]

e^{x} - 1
↓
\mathsf{expm1}\left(x\right)

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original91.85%
Target0.71%
Herbie0%
\[x \cdot \left(\left(1 + \frac{x}{2}\right) + \frac{x \cdot x}{6}\right) \]

Derivation?

  1. Initial program 91.85

    \[e^{x} - 1 \]

  2. Simplified0

    \[\leadsto \color{blue}{\mathsf{expm1}\left(x\right)} \]
    Proof

    [Start]91.85

    \[ e^{x} - 1 \]

    expm1-def [=>]0

    \[ \color{blue}{\mathsf{expm1}\left(x\right)} \]

  3. Final simplification0

    \[\leadsto \mathsf{expm1}\left(x\right) \]

Reproduce?

herbie shell --seed 2023089 
(FPCore (x)
  :name "expm1 (example 3.7)"
  :precision binary64
  :pre (< -0.00017 x)

  :herbie-target
  (* x (+ (+ 1.0 (/ x 2.0)) (/ (* x x) 6.0)))

  (- (exp x) 1.0))