Average Error: 59.9 → 0.3
Time: 16.8s
Precision: binary64
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\[\]
↓
\[\]
↓
double code(double x) {
	return ((double) (((double) (1.0 / x)) - ((double) (1.0 / ((double) tan(x))))));
}

↓
double code(double x) {
	return ((double) (((double) (0.022222222222222223 * ((double) pow(x, 3.0)))) + ((double) (((double) (0.0021164021164021165 * ((double) pow(x, 5.0)))) + ((double) (x * 0.3333333333333333))))));
}

Error
Bits error versus x
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original59.9
Target0.1
Herbie0.3
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Derivation
  1. Initial program 59.9
    \[\]
  2. Taylor expanded around 0 0.3
    \[\leadsto \]
  3. Simplified0.3
    \[\leadsto \]
  4. Final simplification0.3
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (x)
  :name "invcot (example 3.9)"
  :precision binary64
  :pre (and (< -0.026 x) (< x 0.026))

  :herbie-target
  (if (< (fabs x) 0.026) (* (/ x 3.0) (+ 1.0 (/ (* x x) 15.0))) (- (/ 1.0 x) (/ 1.0 (tan x))))

  (- (/ 1.0 x) (/ 1.0 (tan x))))