Average Error: 58.6 → 0.0
Time: 2.1s
Precision: binary64
\[-0.00017 < x\]
\[e^{x} - 1 \]
↓
\[\mathsf{expm1}\left(x\right) \]
(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

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original58.6
Target0.5
Herbie0.0
\[x \cdot \left(\left(1 + \frac{x}{2}\right) + \frac{x \cdot x}{6}\right) \]

Derivation

  1. Initial program 58.6

    \[e^{x} - 1 \]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2022151 
(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))