Average Error: 20.6 → 10.4
Time: 5.6s
Precision: 64
\[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -9.1777242374334205 \cdot 10^{59}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{1}{\frac{z \cdot \frac{c}{y}}{x}}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;y \le 1.2889311644196529 \cdot 10^{-7}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;y \le 8.81398444710026263 \cdot 10^{115}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{\frac{x}{z \cdot c}}{\frac{1}{y}}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;y \le 5.87751849036165333 \cdot 10^{168}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;y \le 6.1051022150981975 \cdot 10^{253}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + \left(9 \cdot \frac{x}{z}\right) \cdot \frac{y}{c}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \left(\left(\sqrt[3]{\frac{x}{\frac{z \cdot c}{y}}} \cdot \sqrt[3]{\frac{x}{\frac{z \cdot c}{y}}}\right) \cdot \sqrt[3]{\frac{x}{\frac{z \cdot c}{y}}}\right)\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array}\]
\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}
↓
\begin{array}{l}
\mathbf{if}\;y \le -9.1777242374334205 \cdot 10^{59}:\\
\;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{1}{\frac{z \cdot \frac{c}{y}}{x}}\right) - 4 \cdot \frac{a \cdot t}{c}\\

\mathbf{elif}\;y \le 1.2889311644196529 \cdot 10^{-7}:\\
\;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a}{\frac{c}{t}}\\

\mathbf{elif}\;y \le 8.81398444710026263 \cdot 10^{115}:\\
\;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{\frac{x}{z \cdot c}}{\frac{1}{y}}\right) - 4 \cdot \frac{a \cdot t}{c}\\

\mathbf{elif}\;y \le 5.87751849036165333 \cdot 10^{168}:\\
\;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \left(a \cdot \frac{t}{c}\right)\\

\mathbf{elif}\;y \le 6.1051022150981975 \cdot 10^{253}:\\
\;\;\;\;\left(\frac{b}{z \cdot c} + \left(9 \cdot \frac{x}{z}\right) \cdot \frac{y}{c}\right) - 4 \cdot \frac{a \cdot t}{c}\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \left(\left(\sqrt[3]{\frac{x}{\frac{z \cdot c}{y}}} \cdot \sqrt[3]{\frac{x}{\frac{z \cdot c}{y}}}\right) \cdot \sqrt[3]{\frac{x}{\frac{z \cdot c}{y}}}\right)\right) - 4 \cdot \frac{a \cdot t}{c}\\

\end{array}
double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c));
}
↓
double code(double x, double y, double z, double t, double a, double b, double c) {
	double VAR;
	if ((y <= -9.17772423743342e+59)) {
		VAR = (((b / (z * c)) + (9.0 * (1.0 / ((z * (c / y)) / x)))) - (4.0 * ((a * t) / c)));
	} else {
		double VAR_1;
		if ((y <= 1.2889311644196529e-07)) {
			VAR_1 = (((b / (z * c)) + (9.0 * ((x * y) / (z * c)))) - (4.0 * (a / (c / t))));
		} else {
			double VAR_2;
			if ((y <= 8.813984447100263e+115)) {
				VAR_2 = (((b / (z * c)) + (9.0 * ((x / (z * c)) / (1.0 / y)))) - (4.0 * ((a * t) / c)));
			} else {
				double VAR_3;
				if ((y <= 5.877518490361653e+168)) {
					VAR_3 = (((b / (z * c)) + (9.0 * ((x * y) / (z * c)))) - (4.0 * (a * (t / c))));
				} else {
					double VAR_4;
					if ((y <= 6.105102215098197e+253)) {
						VAR_4 = (((b / (z * c)) + ((9.0 * (x / z)) * (y / c))) - (4.0 * ((a * t) / c)));
					} else {
						VAR_4 = (((b / (z * c)) + (9.0 * ((cbrt((x / ((z * c) / y))) * cbrt((x / ((z * c) / y)))) * cbrt((x / ((z * c) / y)))))) - (4.0 * ((a * t) / c)));
					}
					VAR_3 = VAR_4;
				}
				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

Original20.6
Target14.4
Herbie10.4
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt -1.10015674080410512 \cdot 10^{-171}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt -0.0:\\ \;\;\;\;\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 1.17088779117474882 \cdot 10^{-53}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 2.8768236795461372 \cdot 10^{130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 1.3838515042456319 \cdot 10^{158}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array}\]

Derivation

  1. Split input into 6 regimes

  2. if y < -9.17772423743342e+59

    1. Initial program 26.8

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]

    2. Taylor expanded around 0 18.8

      \[\leadsto \color{blue}{\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}}\]
    3. Using strategy rm

    4. Applied associate-/l*15.1

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \color{blue}{\frac{x}{\frac{z \cdot c}{y}}}\right) - 4 \cdot \frac{a \cdot t}{c}\]
    5. Using strategy rm

    6. Applied *-un-lft-identity15.1

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{\frac{z \cdot c}{\color{blue}{1 \cdot y}}}\right) - 4 \cdot \frac{a \cdot t}{c}\]

    7. Applied times-frac14.9

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{\color{blue}{\frac{z}{1} \cdot \frac{c}{y}}}\right) - 4 \cdot \frac{a \cdot t}{c}\]

    8. Simplified14.9

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{\color{blue}{z} \cdot \frac{c}{y}}\right) - 4 \cdot \frac{a \cdot t}{c}\]
    9. Using strategy rm

    10. Applied clear-num15.0

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \color{blue}{\frac{1}{\frac{z \cdot \frac{c}{y}}{x}}}\right) - 4 \cdot \frac{a \cdot t}{c}\]

    if -9.17772423743342e+59 < y < 1.2889311644196529e-07

    1. Initial program 17.0

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]

    2. Taylor expanded around 0 8.0

      \[\leadsto \color{blue}{\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}}\]
    3. Using strategy rm

    4. Applied associate-/l*7.8

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}}\]

    if 1.2889311644196529e-07 < y < 8.813984447100263e+115

    1. Initial program 20.0

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]

    2. Taylor expanded around 0 12.0

      \[\leadsto \color{blue}{\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}}\]
    3. Using strategy rm

    4. Applied associate-/l*9.4

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \color{blue}{\frac{x}{\frac{z \cdot c}{y}}}\right) - 4 \cdot \frac{a \cdot t}{c}\]
    5. Using strategy rm

    6. Applied div-inv9.4

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{\color{blue}{\left(z \cdot c\right) \cdot \frac{1}{y}}}\right) - 4 \cdot \frac{a \cdot t}{c}\]

    7. Applied associate-/r*9.4

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \color{blue}{\frac{\frac{x}{z \cdot c}}{\frac{1}{y}}}\right) - 4 \cdot \frac{a \cdot t}{c}\]

    if 8.813984447100263e+115 < y < 5.877518490361653e+168

    1. Initial program 27.6

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]

    2. Taylor expanded around 0 17.2

      \[\leadsto \color{blue}{\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}}\]
    3. Using strategy rm

    4. Applied *-un-lft-identity17.2

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{\color{blue}{1 \cdot c}}\]

    5. Applied times-frac17.0

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \color{blue}{\left(\frac{a}{1} \cdot \frac{t}{c}\right)}\]

    6. Simplified17.0

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \left(\color{blue}{a} \cdot \frac{t}{c}\right)\]

    if 5.877518490361653e+168 < y < 6.105102215098197e+253

    1. Initial program 28.2

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]

    2. Taylor expanded around 0 20.0

      \[\leadsto \color{blue}{\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}}\]
    3. Using strategy rm

    4. Applied times-frac14.2

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \color{blue}{\left(\frac{x}{z} \cdot \frac{y}{c}\right)}\right) - 4 \cdot \frac{a \cdot t}{c}\]

    5. Applied associate-*r*14.2

      \[\leadsto \left(\frac{b}{z \cdot c} + \color{blue}{\left(9 \cdot \frac{x}{z}\right) \cdot \frac{y}{c}}\right) - 4 \cdot \frac{a \cdot t}{c}\]

    if 6.105102215098197e+253 < y

    1. Initial program 33.1

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]

    2. Taylor expanded around 0 23.9

      \[\leadsto \color{blue}{\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}}\]
    3. Using strategy rm

    4. Applied associate-/l*21.5

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \color{blue}{\frac{x}{\frac{z \cdot c}{y}}}\right) - 4 \cdot \frac{a \cdot t}{c}\]
    5. Using strategy rm

    6. Applied add-cube-cbrt21.7

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \color{blue}{\left(\left(\sqrt[3]{\frac{x}{\frac{z \cdot c}{y}}} \cdot \sqrt[3]{\frac{x}{\frac{z \cdot c}{y}}}\right) \cdot \sqrt[3]{\frac{x}{\frac{z \cdot c}{y}}}\right)}\right) - 4 \cdot \frac{a \cdot t}{c}\]
  3. Recombined 6 regimes into one program.

  4. Final simplification10.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -9.1777242374334205 \cdot 10^{59}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{1}{\frac{z \cdot \frac{c}{y}}{x}}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;y \le 1.2889311644196529 \cdot 10^{-7}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;y \le 8.81398444710026263 \cdot 10^{115}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{\frac{x}{z \cdot c}}{\frac{1}{y}}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;y \le 5.87751849036165333 \cdot 10^{168}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;y \le 6.1051022150981975 \cdot 10^{253}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + \left(9 \cdot \frac{x}{z}\right) \cdot \frac{y}{c}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \left(\left(\sqrt[3]{\frac{x}{\frac{z \cdot c}{y}}} \cdot \sqrt[3]{\frac{x}{\frac{z \cdot c}{y}}}\right) \cdot \sqrt[3]{\frac{x}{\frac{z \cdot c}{y}}}\right)\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array}\]

Reproduce

herbie shell --seed 2020102 
(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) y) (* (* (* z 4) t) a)) b) (* z c)) -1.1001567408041051e-171) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) -0.0) (/ (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9 (/ y c)) (/ x z)) (/ b (* c z))) (* 4 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (- (+ (* 9 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4 (/ (* a t) c))))))))

  (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)))