Average Error: 5.3 → 0.1
Time: 13.3s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (((double) (((double) sqrt(((double) (x + 1.0)))) - ((double) sqrt(x)))) + ((double) (((double) sqrt(((double) (y + 1.0)))) - ((double) sqrt(y)))))) + ((double) (((double) sqrt(((double) (z + 1.0)))) - ((double) sqrt(z)))))) + ((double) (((double) sqrt(((double) (t + 1.0)))) - ((double) sqrt(t))))));
}

↓
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (((double) (1.0 / ((double) (((double) sqrt(((double) (1.0 + x)))) + ((double) sqrt(x)))))) + ((double) (1.0 / ((double) (((double) sqrt(((double) (1.0 + y)))) + ((double) sqrt(y)))))))) + ((double) (1.0 / ((double) (((double) sqrt(((double) (1.0 + z)))) + ((double) sqrt(z)))))))) + ((double) (1.0 / ((double) (((double) sqrt(((double) (1.0 + t)))) + ((double) sqrt(t))))))));
}

Error
Bits error versus x
Bits error versus y
Bits error versus z
Bits error versus t
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original5.3
Target1.3
Herbie0.1
\[\]
Derivation
  1. Initial program 5.3
    \[\]
  2. Using strategy rm
  3. Applied flip--5.2
    \[\leadsto \]
  4. Simplified4.0
    \[\leadsto \]
  5. Simplified4.0
    \[\leadsto \]
  6. Using strategy rm
  7. Applied flip--3.9
    \[\leadsto \]
  8. Simplified2.9
    \[\leadsto \]
  9. Simplified2.9
    \[\leadsto \]
  10. Using strategy rm
  11. Applied flip--2.8
    \[\leadsto \]
  12. Simplified1.6
    \[\leadsto \]
  13. Using strategy rm
  14. Applied flip--1.5
    \[\leadsto \]
  15. Simplified0.1
    \[\leadsto \]
  16. Final simplification0.1
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (x y z t)
  :name "Main:z from "
  :precision binary64

  :herbie-target
  (+ (+ (+ (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))) (/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))) (/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))) (- (sqrt (+ t 1.0)) (sqrt t)))

  (+ (+ (+ (- (sqrt (+ x 1.0)) (sqrt x)) (- (sqrt (+ y 1.0)) (sqrt y))) (- (sqrt (+ z 1.0)) (sqrt z))) (- (sqrt (+ t 1.0)) (sqrt t))))