Average Error: 0.0 → 0.0
Time: 26.4s
Precision: binary64
Cost: 448
\[\frac{x + 1}{1 - x}\]
↓
\[\frac{x + 1}{1 - x}\]
\frac{x + 1}{1 - x}
↓
\frac{x + 1}{1 - x}
(FPCore (x) :precision binary64 (/ (+ x 1.0) (- 1.0 x)))
↓
(FPCore (x) :precision binary64 (/ (+ x 1.0) (- 1.0 x)))
double code(double x) {
	return (x + 1.0) / (1.0 - x);
}
↓
double code(double x) {
	return (x + 1.0) / (1.0 - x);
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs
Alternative 1
Accuracy0.0
Cost640
\[\sqrt[3]{{\left(\frac{x + 1}{1 - x}\right)}^{3}}\]
Alternative 2
Accuracy0.1
Cost1664
\[\sqrt[3]{\frac{x + 1}{1 - x}} \cdot \left(\sqrt[3]{\frac{x + 1}{1 - x}} \cdot \sqrt[3]{\frac{x + 1}{1 - x}}\right)\]
Alternative 3
Accuracy32.2
Cost1088
\[\sqrt{\frac{x + 1}{1 - x}} \cdot \sqrt{\frac{x + 1}{1 - x}}\]

Derivation

  1. Initial program 0.0

    \[\frac{x + 1}{1 - x}\]
  2. Using strategy rm

  3. Applied pow1_binary64_8210.0

    \[\leadsto \color{blue}{{\left(\frac{x + 1}{1 - x}\right)}^{1}}\]

  4. Final simplification0.0

    \[\leadsto \frac{x + 1}{1 - x}\]

Reproduce

herbie shell --seed 2020322 
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  :precision binary64
  (/ (+ x 1.0) (- 1.0 x)))