Average Error: 5.4 → 2.4
Time: 10.8s
Precision: binary64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \leq -1.7713669608055964 \cdot 10^{-119}:\\ \;\;\;\;\sqrt[3]{t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - x \cdot \left(4 \cdot i\right)\right)} \cdot \left(\sqrt[3]{t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - x \cdot \left(4 \cdot i\right)\right)} \cdot \sqrt[3]{t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - x \cdot \left(4 \cdot i\right)\right)}\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 1.389098210761329 \cdot 10^{-101}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(x \cdot 18\right) \cdot \left(y \cdot \left(t \cdot z\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 1.178785463028594 \cdot 10^{-52}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(t \cdot z\right) - t \cdot \left(a \cdot 4\right)\right)\right) - x \cdot \left(4 \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array}\]
\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k
↓
\begin{array}{l}
\mathbf{if}\;t \leq -1.7713669608055964 \cdot 10^{-119}:\\
\;\;\;\;\sqrt[3]{t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - x \cdot \left(4 \cdot i\right)\right)} \cdot \left(\sqrt[3]{t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - x \cdot \left(4 \cdot i\right)\right)} \cdot \sqrt[3]{t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - x \cdot \left(4 \cdot i\right)\right)}\right) - \left(j \cdot 27\right) \cdot k\\

\mathbf{elif}\;t \leq 1.389098210761329 \cdot 10^{-101}:\\
\;\;\;\;\left(\left(b \cdot c + \left(\left(x \cdot 18\right) \cdot \left(y \cdot \left(t \cdot z\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - \left(j \cdot 27\right) \cdot k\\

\mathbf{elif}\;t \leq 1.178785463028594 \cdot 10^{-52}:\\
\;\;\;\;\left(\left(b \cdot c + \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(t \cdot z\right) - t \cdot \left(a \cdot 4\right)\right)\right) - x \cdot \left(4 \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\

\mathbf{else}:\\
\;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - \left(j \cdot 27\right) \cdot k\\

\end{array}
(FPCore (x y z t a b c i j k)
 :precision binary64
 (-
  (-
   (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
   (* (* x 4.0) i))
  (* (* j 27.0) k)))
↓
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -1.7713669608055964e-119)
   (-
    (*
     (cbrt
      (+
       (* t (- (* (* x (* 18.0 y)) z) (* a 4.0)))
       (- (* b c) (* x (* 4.0 i)))))
     (*
      (cbrt
       (+
        (* t (- (* (* x (* 18.0 y)) z) (* a 4.0)))
        (- (* b c) (* x (* 4.0 i)))))
      (cbrt
       (+
        (* t (- (* (* x (* 18.0 y)) z) (* a 4.0)))
        (- (* b c) (* x (* 4.0 i)))))))
    (* (* j 27.0) k))
   (if (<= t 1.389098210761329e-101)
     (-
      (-
       (+ (* b c) (- (* (* x 18.0) (* y (* t z))) (* t (* a 4.0))))
       (* i (* x 4.0)))
      (* (* j 27.0) k))
     (if (<= t 1.178785463028594e-52)
       (-
        (-
         (+ (* b c) (- (* (* x (* 18.0 y)) (* t z)) (* t (* a 4.0))))
         (* x (* 4.0 i)))
        (* (* j 27.0) k))
       (-
        (-
         (+ (* b c) (- (* t (* (* x 18.0) (* y z))) (* t (* a 4.0))))
         (* i (* x 4.0)))
        (* (* j 27.0) k))))))
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return ((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (x * 18.0)) * y)) * z)) * t)) - ((double) (((double) (a * 4.0)) * t)))) + ((double) (b * c)))) - ((double) (((double) (x * 4.0)) * i)))) - ((double) (((double) (j * 27.0)) * k))));
}
↓
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.7713669608055964e-119)) {
		tmp = ((double) (((double) (((double) cbrt(((double) (((double) (t * ((double) (((double) (((double) (x * ((double) (18.0 * y)))) * z)) - ((double) (a * 4.0)))))) + ((double) (((double) (b * c)) - ((double) (x * ((double) (4.0 * i)))))))))) * ((double) (((double) cbrt(((double) (((double) (t * ((double) (((double) (((double) (x * ((double) (18.0 * y)))) * z)) - ((double) (a * 4.0)))))) + ((double) (((double) (b * c)) - ((double) (x * ((double) (4.0 * i)))))))))) * ((double) cbrt(((double) (((double) (t * ((double) (((double) (((double) (x * ((double) (18.0 * y)))) * z)) - ((double) (a * 4.0)))))) + ((double) (((double) (b * c)) - ((double) (x * ((double) (4.0 * i)))))))))))))) - ((double) (((double) (j * 27.0)) * k))));
	} else {
		double tmp_1;
		if ((t <= 1.389098210761329e-101)) {
			tmp_1 = ((double) (((double) (((double) (((double) (b * c)) + ((double) (((double) (((double) (x * 18.0)) * ((double) (y * ((double) (t * z)))))) - ((double) (t * ((double) (a * 4.0)))))))) - ((double) (i * ((double) (x * 4.0)))))) - ((double) (((double) (j * 27.0)) * k))));
		} else {
			double tmp_2;
			if ((t <= 1.178785463028594e-52)) {
				tmp_2 = ((double) (((double) (((double) (((double) (b * c)) + ((double) (((double) (((double) (x * ((double) (18.0 * y)))) * ((double) (t * z)))) - ((double) (t * ((double) (a * 4.0)))))))) - ((double) (x * ((double) (4.0 * i)))))) - ((double) (((double) (j * 27.0)) * k))));
			} else {
				tmp_2 = ((double) (((double) (((double) (((double) (b * c)) + ((double) (((double) (t * ((double) (((double) (x * 18.0)) * ((double) (y * z)))))) - ((double) (t * ((double) (a * 4.0)))))))) - ((double) (i * ((double) (x * 4.0)))))) - ((double) (((double) (j * 27.0)) * k))));
			}
			tmp_1 = tmp_2;
		}
		tmp = tmp_1;
	}
	return tmp;
}

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

Bits error versus i

Bits error versus j

Bits error versus k

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.4
Target1.3
Herbie2.4
\[\begin{array}{l} \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if t < -1.7713669608055964e-119

    1. Initial program 3.0

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    2. Using strategy rm

    3. Applied associate-*l*_binary647.3

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    4. Using strategy rm

    5. Applied associate-*l*_binary647.4

      \[\leadsto \left(\left(\left(\color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)} \cdot \left(z \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    6. Using strategy rm

    7. Applied associate-*l*_binary647.4

      \[\leadsto \left(\left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \color{blue}{x \cdot \left(4 \cdot i\right)}\right) - \left(j \cdot 27\right) \cdot k\]
    8. Using strategy rm

    9. Applied add-cube-cbrt_binary648.2

      \[\leadsto \color{blue}{\left(\sqrt[3]{\left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - x \cdot \left(4 \cdot i\right)} \cdot \sqrt[3]{\left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - x \cdot \left(4 \cdot i\right)}\right) \cdot \sqrt[3]{\left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - x \cdot \left(4 \cdot i\right)}} - \left(j \cdot 27\right) \cdot k\]

    10. Simplified9.1

      \[\leadsto \color{blue}{\left(\sqrt[3]{t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - x \cdot \left(4 \cdot i\right)\right)} \cdot \sqrt[3]{t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - x \cdot \left(4 \cdot i\right)\right)}\right)} \cdot \sqrt[3]{\left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - x \cdot \left(4 \cdot i\right)} - \left(j \cdot 27\right) \cdot k\]

    11. Simplified4.0

      \[\leadsto \left(\sqrt[3]{t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - x \cdot \left(4 \cdot i\right)\right)} \cdot \sqrt[3]{t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - x \cdot \left(4 \cdot i\right)\right)}\right) \cdot \color{blue}{\sqrt[3]{t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - x \cdot \left(4 \cdot i\right)\right)}} - \left(j \cdot 27\right) \cdot k\]

    if -1.7713669608055964e-119 < t < 1.38909821076132898e-101

    1. Initial program 8.9

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    2. Using strategy rm

    3. Applied associate-*l*_binary644.6

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    4. Using strategy rm

    5. Applied associate-*l*_binary641.0

      \[\leadsto \left(\left(\left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

    if 1.38909821076132898e-101 < t < 1.17878546302859394e-52

    1. Initial program 7.1

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    2. Using strategy rm

    3. Applied associate-*l*_binary643.4

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    4. Using strategy rm

    5. Applied associate-*l*_binary643.4

      \[\leadsto \left(\left(\left(\color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)} \cdot \left(z \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    6. Using strategy rm

    7. Applied associate-*l*_binary643.4

      \[\leadsto \left(\left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \color{blue}{x \cdot \left(4 \cdot i\right)}\right) - \left(j \cdot 27\right) \cdot k\]

    if 1.17878546302859394e-52 < t

    1. Initial program 2.0

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    2. Using strategy rm

    3. Applied associate-*l*_binary642.6

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)} \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
  3. Recombined 4 regimes into one program.

  4. Final simplification2.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7713669608055964 \cdot 10^{-119}:\\ \;\;\;\;\sqrt[3]{t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - x \cdot \left(4 \cdot i\right)\right)} \cdot \left(\sqrt[3]{t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - x \cdot \left(4 \cdot i\right)\right)} \cdot \sqrt[3]{t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - x \cdot \left(4 \cdot i\right)\right)}\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 1.389098210761329 \cdot 10^{-101}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(x \cdot 18\right) \cdot \left(y \cdot \left(t \cdot z\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 1.178785463028594 \cdot 10^{-52}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(t \cdot z\right) - t \cdot \left(a \cdot 4\right)\right)\right) - x \cdot \left(4 \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array}\]

Reproduce

herbie shell --seed 2020205 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :herbie-target
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18.0 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4.0)) (- (* c b) (* 27.0 (* k j)))) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b)))))

  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))