Average Error: 8.4 → 3.3
Time: 2.3s
Precision: binary64
\[\]
\[\]
↓
\[\]
↓
double code(double x0, double x1) {
	return ((double) (((double) (x0 / ((double) (1.0 - x1)))) - x0));
}

↓
double code(double x0, double x1) {
	double VAR;
	if ((x1 <= 0.00021208908081054686)) {
		VAR = ((double) (((double) (x0 * ((double) (((double) log(((double) cbrt(((double) exp(((double) (((double) (x0 / ((double) (1.0 + ((double) (x1 * ((double) (x1 - 2.0)))))))) - x0)))))))) + ((double) (((double) log(((double) cbrt(((double) exp(((double) (((double) (x0 / ((double) (1.0 + ((double) (x1 * ((double) (x1 - 2.0)))))))) - x0)))))))) * 2.0)))))) / ((double) (x0 + ((double) (x0 / ((double) (1.0 - x1))))))));
	} else {
		VAR = ((double) (((double) (x0 * ((double) log(((double) exp(((double) (((double) (x0 / ((double) (1.0 + ((double) (x1 * ((double) (x1 - 2.0)))))))) - x0)))))))) / ((double) (x0 + ((double) (1.0 / ((double) (((double) (1.0 - x1)) / x0))))))));
	}
	return VAR;
}

Error
Bits error versus x0
Bits error versus x1
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original8.4
Target0.5
Herbie3.3
\[\]
Derivation
  1. Split input into 2 regimes
  2. if  x1  < 2.12089080810546861e-4
    1. Initial program 11.3
      \[\]
    2. Using strategy rm
    3. Applied flip--11.4
      \[\leadsto \]
    4. Simplified9.1
      \[\leadsto \]
    5. Simplified9.1
      \[\leadsto \]
    6. Taylor expanded around 0 11.3
      \[\leadsto \]
    7. Simplified9.1
      \[\leadsto \]
    8. Using strategy rm
    9. Applied add-log-exp9.1
      \[\leadsto \]
    10. Applied add-log-exp9.1
      \[\leadsto \]
    11. Applied diff-log8.9
      \[\leadsto \]
    12. Simplified8.9
      \[\leadsto \]
    13. Using strategy rm
    14. Applied add-cube-cbrt10.6
      \[\leadsto \]
    15. Applied log-prod9.9
      \[\leadsto \]
    16. Simplified6.6
      \[\leadsto \]
    if 2.12089080810546861e-4 <  x1 
    1. Initial program 5.5
      \[\]
    2. Using strategy rm
    3. Applied flip--4.0
      \[\leadsto \]
    4. Simplified4.7
      \[\leadsto \]
    5. Simplified4.7
      \[\leadsto \]
    6. Taylor expanded around 0 2.8
      \[\leadsto \]
    7. Simplified2.8
      \[\leadsto \]
    8. Using strategy rm
    9. Applied add-log-exp2.8
      \[\leadsto \]
    10. Applied add-log-exp2.8
      \[\leadsto \]
    11. Applied diff-log3.9
      \[\leadsto \]
    12. Simplified1.0
      \[\leadsto \]
    13. Using strategy rm
    14. Applied clear-num0
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification3.3
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (x0 x1)
  :name "(- (/ x0 (- 1 x1)) x0)"
  :precision binary64
  :pre (or (and (== x0 1.855) (== x1 0.000209)) (and (== x0 2.985) (== x1 0.0186)))

  :herbie-target
  (/ (* x0 x1) (- 1.0 x1))

  (- (/ x0 (- 1.0 x1)) x0))