Average Error: 20.8 → 9.9
Time: 32.6s
Precision: binary64
\[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -1.1248003357302601 \cdot 10^{-17}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{\frac{z \cdot c}{y}}\right) - 4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;a \le -4.19304622018763957 \cdot 10^{-144}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}\\ \mathbf{elif}\;a \le -5.15422094316753991 \cdot 10^{-151}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + \left(9 \cdot \frac{x}{z}\right) \cdot \frac{y}{c}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;a \le -1.00978527387666522 \cdot 10^{-265}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + \left(\sqrt[3]{9} \cdot \sqrt[3]{9}\right) \cdot \left(\sqrt[3]{9} \cdot \frac{x \cdot y}{z \cdot c}\right)\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;a \le 2.4746682039209063 \cdot 10^{-210}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;a \le 554395.268607782316:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + \left(\sqrt[3]{9} \cdot \sqrt[3]{9}\right) \cdot \left(\sqrt[3]{9} \cdot \frac{x \cdot y}{z \cdot c}\right)\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;a \le 1.68517251305351882 \cdot 10^{66}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{z \cdot \frac{c}{y}}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{\frac{z \cdot c}{y}}\right) - 4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array}\]
\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}\;a \le -1.1248003357302601 \cdot 10^{-17}:\\
\;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{\frac{z \cdot c}{y}}\right) - 4 \cdot \left(a \cdot \frac{t}{c}\right)\\

\mathbf{elif}\;a \le -4.19304622018763957 \cdot 10^{-144}:\\
\;\;\;\;\frac{1}{z} \cdot \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}\\

\mathbf{elif}\;a \le -5.15422094316753991 \cdot 10^{-151}:\\
\;\;\;\;\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{elif}\;a \le -1.00978527387666522 \cdot 10^{-265}:\\
\;\;\;\;\left(\frac{b}{z \cdot c} + \left(\sqrt[3]{9} \cdot \sqrt[3]{9}\right) \cdot \left(\sqrt[3]{9} \cdot \frac{x \cdot y}{z \cdot c}\right)\right) - 4 \cdot \frac{a \cdot t}{c}\\

\mathbf{elif}\;a \le 2.4746682039209063 \cdot 10^{-210}:\\
\;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\right) - 4 \cdot \frac{a \cdot t}{c}\\

\mathbf{elif}\;a \le 554395.268607782316:\\
\;\;\;\;\left(\frac{b}{z \cdot c} + \left(\sqrt[3]{9} \cdot \sqrt[3]{9}\right) \cdot \left(\sqrt[3]{9} \cdot \frac{x \cdot y}{z \cdot c}\right)\right) - 4 \cdot \frac{a \cdot t}{c}\\

\mathbf{elif}\;a \le 1.68517251305351882 \cdot 10^{66}:\\
\;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{z \cdot \frac{c}{y}}\right) - 4 \cdot \frac{a \cdot t}{c}\\

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

\end{array}
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 ((a <= -1.12480033573026e-17)) {
		VAR = ((double) (((double) (((double) (b / ((double) (z * c)))) + ((double) (9.0 * ((double) (x / ((double) (((double) (z * c)) / y)))))))) - ((double) (4.0 * ((double) (a * ((double) (t / c))))))));
	} else {
		double VAR_1;
		if ((a <= -4.1930462201876396e-144)) {
			VAR_1 = ((double) (((double) (1.0 / z)) * ((double) (((double) (((double) (((double) (((double) (x * 9.0)) * y)) - ((double) (((double) (((double) (z * 4.0)) * t)) * a)))) + b)) / c))));
		} else {
			double VAR_2;
			if ((a <= -5.15422094316754e-151)) {
				VAR_2 = ((double) (((double) (((double) (b / ((double) (z * c)))) + ((double) (((double) (9.0 * ((double) (x / z)))) * ((double) (y / c)))))) - ((double) (4.0 * ((double) (((double) (a * t)) / c))))));
			} else {
				double VAR_3;
				if ((a <= -1.0097852738766652e-265)) {
					VAR_3 = ((double) (((double) (((double) (b / ((double) (z * c)))) + ((double) (((double) (((double) cbrt(9.0)) * ((double) cbrt(9.0)))) * ((double) (((double) cbrt(9.0)) * ((double) (((double) (x * y)) / ((double) (z * c)))))))))) - ((double) (4.0 * ((double) (((double) (a * t)) / c))))));
				} else {
					double VAR_4;
					if ((a <= 2.4746682039209063e-210)) {
						VAR_4 = ((double) (((double) (((double) (b / ((double) (z * c)))) + ((double) (9.0 * ((double) (((double) (x / z)) * ((double) (y / c)))))))) - ((double) (4.0 * ((double) (((double) (a * t)) / c))))));
					} else {
						double VAR_5;
						if ((a <= 554395.2686077823)) {
							VAR_5 = ((double) (((double) (((double) (b / ((double) (z * c)))) + ((double) (((double) (((double) cbrt(9.0)) * ((double) cbrt(9.0)))) * ((double) (((double) cbrt(9.0)) * ((double) (((double) (x * y)) / ((double) (z * c)))))))))) - ((double) (4.0 * ((double) (((double) (a * t)) / c))))));
						} else {
							double VAR_6;
							if ((a <= 1.685172513053519e+66)) {
								VAR_6 = ((double) (((double) (((double) (b / ((double) (z * c)))) + ((double) (9.0 * ((double) (x / ((double) (z * ((double) (c / y)))))))))) - ((double) (4.0 * ((double) (((double) (a * t)) / c))))));
							} else {
								VAR_6 = ((double) (((double) (((double) (b / ((double) (z * c)))) + ((double) (9.0 * ((double) (x / ((double) (((double) (z * c)) / y)))))))) - ((double) (4.0 * ((double) (a * ((double) (t / c))))))));
							}
							VAR_5 = VAR_6;
						}
						VAR_4 = VAR_5;
					}
					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

Original20.8
Target14.3
Herbie9.9
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt -1.10015674080410512 \cdot 10^{-171}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt -0.0:\\ \;\;\;\;\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 1.17088779117474882 \cdot 10^{-53}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 2.8768236795461372 \cdot 10^{130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 1.3838515042456319 \cdot 10^{158}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array}\]

Derivation

  1. Split input into 6 regimes

  2. if a < -1.1248003357302601e-17 or 1.68517251305351882e66 < a

    1. Initial program 24.5

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

    2. Taylor expanded around 0 15.8

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

    4. Applied associate-/l*14.5

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

    6. Applied *-un-lft-identity14.5

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

    7. Applied times-frac7.9

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

    8. Simplified7.9

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

    if -1.1248003357302601e-17 < a < -4.19304622018763957e-144

    1. Initial program 18.2

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

    3. Applied *-un-lft-identity18.2

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

    4. Applied times-frac18.7

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

    if -4.19304622018763957e-144 < a < -5.15422094316753991e-151

    1. Initial program 20.4

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

    2. Taylor expanded around 0 9.2

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

    4. Applied times-frac6.9

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

    5. Applied associate-*r*6.9

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

    if -5.15422094316753991e-151 < a < -1.00978527387666522e-265 or 2.4746682039209063e-210 < a < 554395.268607782316

    1. Initial program 17.9

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

    2. Taylor expanded around 0 8.8

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

    4. Applied add-cube-cbrt8.8

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

    5. Applied associate-*l*8.8

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

    if -1.00978527387666522e-265 < a < 2.4746682039209063e-210

    1. Initial program 18.9

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

    2. Taylor expanded around 0 10.2

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

    4. Applied times-frac11.6

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

    if 554395.268607782316 < a < 1.68517251305351882e66

    1. Initial program 19.4

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

    2. Taylor expanded around 0 9.1

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

    4. Applied associate-/l*8.6

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

    6. Applied *-un-lft-identity8.6

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

    7. Applied times-frac9.4

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

    8. Simplified9.4

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

  4. Final simplification9.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -1.1248003357302601 \cdot 10^{-17}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{\frac{z \cdot c}{y}}\right) - 4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;a \le -4.19304622018763957 \cdot 10^{-144}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}\\ \mathbf{elif}\;a \le -5.15422094316753991 \cdot 10^{-151}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + \left(9 \cdot \frac{x}{z}\right) \cdot \frac{y}{c}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;a \le -1.00978527387666522 \cdot 10^{-265}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + \left(\sqrt[3]{9} \cdot \sqrt[3]{9}\right) \cdot \left(\sqrt[3]{9} \cdot \frac{x \cdot y}{z \cdot c}\right)\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;a \le 2.4746682039209063 \cdot 10^{-210}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;a \le 554395.268607782316:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + \left(\sqrt[3]{9} \cdot \sqrt[3]{9}\right) \cdot \left(\sqrt[3]{9} \cdot \frac{x \cdot y}{z \cdot c}\right)\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;a \le 1.68517251305351882 \cdot 10^{66}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{z \cdot \frac{c}{y}}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{\frac{z \cdot c}{y}}\right) - 4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020173 
(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)))