Average Error: 58.7 → 58.7

Time: 1.4s

Precision: binary64

Cost: 6592

\[-0.00017 < x\]

\[e^{x} - 1\]

↓

\[e^{x} - 1\]

e^{x} - 1

↓

e^{x} - 1

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

↓

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

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

↓

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

Error

The X axis uses an exponential scale — Bits error versus `x`

Try it out

In
Out

Enter valid numbers for all inputs

Target

Original	58.7
Target	0.5
Herbie	58.7

\[x \cdot \left(\left(1 + \frac{x}{2}\right) + \frac{x \cdot x}{6}\right)\]

Derivation

Initial program 58.7
\[e^{x} - 1\]

Reproduce

herbie shell --seed 2021044 
(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))