Average Error: 0.0 → 0.1
Time: 3.7s
Precision: binary64
\[\frac{x + 1}{1 - x}\]
↓
\[\frac{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1}}{\sqrt[3]{1 - x} \cdot \sqrt[3]{1 - x}} \cdot \frac{\sqrt[3]{x + 1}}{\sqrt[3]{1 - x}}\]
\frac{x + 1}{1 - x}
↓
\frac{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1}}{\sqrt[3]{1 - x} \cdot \sqrt[3]{1 - x}} \cdot \frac{\sqrt[3]{x + 1}}{\sqrt[3]{1 - x}}
(FPCore (x) :precision binary64 (/ (+ x 1.0) (- 1.0 x)))
↓
(FPCore (x)
 :precision binary64
 (*
  (/
   (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
   (* (cbrt (- 1.0 x)) (cbrt (- 1.0 x))))
  (/ (cbrt (+ x 1.0)) (cbrt (- 1.0 x)))))
double code(double x) {
	return (x + 1.0) / (1.0 - x);
}
↓
double code(double x) {
	return ((cbrt(x + 1.0) * cbrt(x + 1.0)) / (cbrt(1.0 - x) * cbrt(1.0 - x))) * (cbrt(x + 1.0) / cbrt(1.0 - x));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  3. Applied add-cube-cbrt_binary64_23760.7

    \[\leadsto \frac{x + 1}{\color{blue}{\left(\sqrt[3]{1 - x} \cdot \sqrt[3]{1 - x}\right) \cdot \sqrt[3]{1 - x}}}\]

  4. Applied add-cube-cbrt_binary64_23760.1

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1}\right) \cdot \sqrt[3]{x + 1}}}{\left(\sqrt[3]{1 - x} \cdot \sqrt[3]{1 - x}\right) \cdot \sqrt[3]{1 - x}}\]

  5. Applied times-frac_binary64_24000.1

    \[\leadsto \color{blue}{\frac{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1}}{\sqrt[3]{1 - x} \cdot \sqrt[3]{1 - x}} \cdot \frac{\sqrt[3]{x + 1}}{\sqrt[3]{1 - x}}}\]

  6. Final simplification0.1

    \[\leadsto \frac{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1}}{\sqrt[3]{1 - x} \cdot \sqrt[3]{1 - x}} \cdot \frac{\sqrt[3]{x + 1}}{\sqrt[3]{1 - x}}\]

Reproduce

herbie shell --seed 2020270 
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  :precision binary64
  (/ (+ x 1.0) (- 1.0 x)))