Average Error: 25.2 → 7.3
Time: 6.2s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x, double y, double z, double t, double a) {
	return ((double) (((double) (((double) (x * y)) * z)) / ((double) sqrt(((double) (((double) (z * z)) - ((double) (t * a))))))));
}

↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if ((z <= -6.57733640771942e+56)) {
		VAR = ((double) (((double) (x * y)) * ((double) (z / ((double) (((double) (0.5 * ((double) (t * ((double) (a / z)))))) - z))))));
	} else {
		double VAR_1;
		if ((z <= 3.430719117234428e+68)) {
			VAR_1 = ((double) (x * ((double) (((double) (z * y)) * ((double) (1.0 / ((double) sqrt(((double) (((double) (z * z)) - ((double) (t * a))))))))))));
		} else {
			VAR_1 = ((double) (x * y));
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error
Bits error versus x
Bits error versus y
Bits error versus z
Bits error versus t
Bits error versus a
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original25.2
Target8.2
Herbie7.3
\[\]
Derivation
  1. Split input into 3 regimes
  2. if  z  < -6.5773364077194196e56
    1. Initial program 38.0
      \[\]
    2. Simplified35.2
      \[\leadsto \]
    3. Using strategy rm
    4. Applied associate-*r*35.2
      \[\leadsto \]
    5. Taylor expanded around -inf 6.2
      \[\leadsto \]
    6. Simplified3.6
      \[\leadsto \]
    if -6.5773364077194196e56 <  z  < 3.43071911723442781e68
    1. Initial program 11.7
      \[\]
    2. Simplified10.2
      \[\leadsto \]
    3. Using strategy rm
    4. Applied div-inv10.3
      \[\leadsto \]
    5. Applied associate-*r*11.1
      \[\leadsto \]
    6. Simplified11.1
      \[\leadsto \]
    if 3.43071911723442781e68 <  z 
    1. Initial program 40.7
      \[\]
    2. Simplified37.3
      \[\leadsto \]
    3. Taylor expanded around inf 3.2
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification7.3
    \[\leadsto \]
Reproduce
herbie shell --seed 2020190 
(FPCore (x y z t a)
  :name "Statistics.Math.RootFinding:ridders from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (if (< z -3.1921305903852764e+46) (neg (* y x)) (if (< z 5.976268120920894e+90) (/ (* x z) (/ (sqrt (- (* z z) (* a t))) y)) (* y x)))

  (/ (* (* x y) z) (sqrt (- (* z z) (* t a)))))