Average Error: 20.4 → 5.4
Time: 9.0s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((double) (((double) (((double) (((double) (((double) (x * 9.0)) * y)) - ((double) (((double) (((double) (z * 4.0)) * t)) * a)))) + b)) / ((double) (z * c))));
}

↓
double code(double x, double y, double z, double t, double a, double b, double c) {
	double VAR;
	if ((((double) (((double) (((double) (((double) (((double) (x * 9.0)) * y)) - ((double) (((double) (((double) (z * 4.0)) * t)) * a)))) + b)) / ((double) (z * c)))) <= -inf.0)) {
		VAR = ((double) (((double) (b / ((double) (z * c)))) + ((double) (((double) (9.0 * ((double) (y * ((double) (x / ((double) (z * c)))))))) - ((double) (4.0 * ((double) (((double) cbrt(((double) (a / c)))) * ((double) (t * ((double) (((double) cbrt(((double) (a / c)))) * ((double) cbrt(((double) (a / c))))))))))))))));
	} else {
		double VAR_1;
		if ((((double) (((double) (((double) (((double) (((double) (x * 9.0)) * y)) - ((double) (((double) (((double) (z * 4.0)) * t)) * a)))) + b)) / ((double) (z * c)))) <= -1537084935579.915)) {
			VAR_1 = ((double) (((double) (((double) (((double) (((double) (x * 9.0)) * y)) - ((double) (((double) (((double) (z * 4.0)) * t)) * a)))) + b)) / ((double) (z * c))));
		} else {
			double VAR_2;
			if ((((double) (((double) (((double) (((double) (((double) (x * 9.0)) * y)) - ((double) (((double) (((double) (z * 4.0)) * t)) * a)))) + b)) / ((double) (z * c)))) <= 1.530413490682389e+22)) {
				VAR_2 = ((double) (1.0 / ((double) (c / ((double) (((double) (((double) (b + ((double) (x * ((double) (9.0 * y)))))) / z)) - ((double) (4.0 * ((double) (t * a))))))))));
			} else {
				double VAR_3;
				if ((((double) (((double) (((double) (((double) (((double) (x * 9.0)) * y)) - ((double) (((double) (((double) (z * 4.0)) * t)) * a)))) + b)) / ((double) (z * c)))) <= +inf.0)) {
					VAR_3 = ((double) (((double) (b / ((double) (z * c)))) + ((double) (((double) (9.0 * ((double) (y * ((double) (x / ((double) (z * c)))))))) - ((double) (4.0 * ((double) (((double) cbrt(((double) (a / c)))) * ((double) (t * ((double) (((double) cbrt(((double) (a / c)))) * ((double) cbrt(((double) (a / c))))))))))))))));
				} else {
					VAR_3 = ((double) (((double) (((double) (((double) (9.0 * ((double) (y * ((double) (x / z)))))) + ((double) (b / z)))) - ((double) (4.0 * ((double) (t * a)))))) / c));
				}
				VAR_2 = VAR_3;
			}
			VAR_1 = VAR_2;
		}
		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
Bits error versus b
Bits error versus c
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original20.4
Target14.6
Herbie5.4
\[\]
Derivation
  1. Split input into 4 regimes
  2. if  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))  < -inf.0 or 1.53041349068238902e22 <  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))  < +inf.0
    1. Initial program 26.8
      \[\]
    2. Simplified19.3
      \[\leadsto \]
    3. Taylor expanded around 0 15.2
      \[\leadsto \]
    4. Simplified8.3
      \[\leadsto \]
    5. Using strategy rm
    6. Applied add-cube-cbrt8.6
      \[\leadsto \]
    7. Applied associate-*r*8.7
      \[\leadsto \]
    if -inf.0 <  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))  < -1537084935579.915
    1. Initial program 0.6
      \[\]
    if -1537084935579.915 <  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))  < 1.53041349068238902e22
    1. Initial program 12.7
      \[\]
    2. Simplified1.1
      \[\leadsto \]
    3. Using strategy rm
    4. Applied clear-num1.7
      \[\leadsto \]
    if +inf.0 <  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 
    1. Initial program 64.0
      \[\]
    2. Simplified29.1
      \[\leadsto \]
    3. Taylor expanded around 0 29.1
      \[\leadsto \]
    4. Simplified16.0
      \[\leadsto \]
  3. Recombined 4 regimes into one program.
  4. Final simplification5.4
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :herbie-target
  (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -1.1001567408041051e-171) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -0.0) (/ (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9.0 (/ y c)) (/ x z)) (/ b (* c z))) (* 4.0 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (- (+ (* 9.0 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4.0 (/ (* a t) c))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))