Average Error: 0.5 → 0.5
Time: 15.6s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x1, double x2) {
	return ((double) (x1 + ((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (2.0 * x1)) * ((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))))) * ((double) (((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))) - 3.0)))) + ((double) (((double) (x1 * x1)) * ((double) (((double) (4.0 * ((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))))) - 6.0)))))) * ((double) (((double) (x1 * x1)) + 1.0)))) + ((double) (((double) (((double) (3.0 * x1)) * x1)) * ((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))))))) + ((double) (((double) (x1 * x1)) * x1)))) + x1)) + ((double) (3.0 * ((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) - ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0))))))))));
}

↓
double code(double x1, double x2) {
	return ((double) (x1 + ((double) (x1 + ((double) (((double) (((double) (((double) (x1 * x1)) + 1.0)) * ((double) (((double) (((double) (1.0 / ((double) sqrt(((double) (((double) (x1 * x1)) + 1.0)))))) * ((double) (((double) (x1 * ((double) (((double) (2.0 * ((double) (((double) (((double) (((double) (x1 * ((double) (x1 * 3.0)))) + ((double) (((double) (2.0 * x2)) - x1)))) / ((double) (((double) (x1 * x1)) + 1.0)))) - 3.0)))) + ((double) (x1 * 4.0)))))) * ((double) (((double) (((double) (x1 * ((double) (x1 * 3.0)))) + ((double) (((double) (2.0 * x2)) - x1)))) / ((double) sqrt(((double) (((double) (x1 * x1)) + 1.0)))))))))) - ((double) (((double) (x1 * x1)) * 6.0)))))) + ((double) (((double) (x1 * ((double) (x1 * ((double) (x1 + ((double) (3.0 * ((double) (((double) (((double) (x1 * ((double) (x1 * 3.0)))) + ((double) (((double) (2.0 * x2)) - x1)))) / ((double) (((double) (x1 * x1)) + 1.0)))))))))))) + ((double) (3.0 * ((double) (((double) (((double) (x1 * ((double) (x1 * 3.0)))) - ((double) (x1 + ((double) (2.0 * x2)))))) / ((double) (((double) (x1 * x1)) + 1.0))))))))))))));
}

Error
Bits error versus x1
Bits error versus x2
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Initial program 0.5
    \[\]
  2. Simplified0.5
    \[\leadsto \]
  3. Using strategy rm
  4. Applied add-sqr-sqrt0.5
    \[\leadsto \]
  5. Applied *-un-lft-identity0.5
    \[\leadsto \]
  6. Applied times-frac0.5
    \[\leadsto \]
  7. Applied associate-*l*0.5
    \[\leadsto \]
  8. Simplified0.5
    \[\leadsto \]
  9. Final simplification0.5
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (x1 x2)
  :name "Rosa's FloatVsDoubleBenchmark"
  :precision binary64
  (+ x1 (+ (+ (+ (+ (* (+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)) (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0))) (+ (* x1 x1) 1.0)) (* (* (* 3.0 x1) x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))) (* (* x1 x1) x1)) x1) (* 3.0 (/ (- (- (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))))))