Average Error: 20.2 → 17.7
Time: 16.2s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (((double) (((double) (2.0 * ((double) sqrt(x)))) * ((double) cos(((double) (y - ((double) (((double) (z * t)) / 3.0)))))))) - ((double) (a / ((double) (b * 3.0))))));
}

↓
double code(double x, double y, double z, double t, double a, double b) {
	double VAR;
	if ((((double) cos(((double) (y - ((double) (((double) (z * t)) / 3.0)))))) <= 1.0)) {
		VAR = ((double) (((double) (((double) (2.0 * ((double) sqrt(x)))) * ((double) (((double) (((double) cos(y)) * ((double) cos(((double) (t * ((double) (z / 3.0)))))))) + ((double) (((double) sin(y)) * ((double) (((double) (((double) cbrt(((double) sin(((double) (t * ((double) (z * 0.3333333333333333)))))))) * ((double) cbrt(((double) sin(((double) (t * ((double) (z * 0.3333333333333333)))))))))) * ((double) cbrt(((double) (((double) cbrt(((double) sin(((double) (t * ((double) (z * 0.3333333333333333)))))))) * ((double) (((double) cbrt(((double) sin(((double) (t * ((double) (z * 0.3333333333333333)))))))) * ((double) cbrt(((double) sin(((double) (t * ((double) (z * 0.3333333333333333)))))))))))))))))))))) - ((double) (a / ((double) (3.0 * b))))));
	} else {
		VAR = ((double) (((double) log(((double) pow(((double) pow(((double) exp(2.0)), ((double) sqrt(x)))), ((double) (((double) (((double) cos(y)) * ((double) cos(((double) (t * ((double) (z / 3.0)))))))) + ((double) (((double) sin(y)) * ((double) sin(((double) (t * ((double) (z / 3.0)))))))))))))) - ((double) (a / ((double) (3.0 * b))))));
	}
	return VAR;
}

Error
Bits error versus x
Bits error versus y
Bits error versus z
Bits error versus t
Bits error versus a
Bits error versus b
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original20.2
Target18.5
Herbie17.7
\[\]
Derivation
  1. Split input into 2 regimes
  2. if  (cos (- y (/ (* z t) 3.0)))  < 1
    1. Initial program 14.2
      \[\]
    2. Using strategy rm
    3. Applied cos-diff13.7
      \[\leadsto \]
    4. Simplified13.7
      \[\leadsto \]
    5. Simplified13.7
      \[\leadsto \]
    6. Taylor expanded around inf 13.7
      \[\leadsto \]
    7. Simplified13.7
      \[\leadsto \]
    8. Using strategy rm
    9. Applied add-cube-cbrt13.7
      \[\leadsto \]
    10. Using strategy rm
    11. Applied add-cube-cbrt13.7
      \[\leadsto \]
    if 1 <  (cos (- y (/ (* z t) 3.0))) 
    1. Initial program 64.0
      \[\]
    2. Using strategy rm
    3. Applied cos-diff64.0
      \[\leadsto \]
    4. Simplified64.0
      \[\leadsto \]
    5. Simplified63.8
      \[\leadsto \]
    6. Using strategy rm
    7. Applied add-log-exp63.9
      \[\leadsto \]
    8. Simplified46.8
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification17.7
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

  :herbie-target
  (if (< z -1.3793337487235141e+129) (- (* (* 2.0 (sqrt x)) (cos (- (/ 1.0 y) (/ (/ 0.3333333333333333 z) t)))) (/ (/ a 3.0) b)) (if (< z 3.516290613555987e+106) (- (* (* (sqrt x) 2.0) (cos (- y (* (/ t 3.0) z)))) (/ (/ a 3.0) b)) (- (* (cos (- y (/ (/ 0.3333333333333333 z) t))) (* 2.0 (sqrt x))) (/ (/ a b) 3.0))))

  (- (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0)))) (/ a (* b 3.0))))