Average Error: 5.2 → 2.2
Time: 3.0m
Precision: 64
Internal Precision: 576
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot z \le -2.030585386610541 \cdot 10^{+287}:\\ \;\;\;\;\left(c \cdot b + \left(z \cdot 18.0\right) \cdot \left(t \cdot \left(y \cdot x\right)\right)\right) - \left(4.0 \cdot \left(x \cdot i + t \cdot a\right) + \left(k \cdot j\right) \cdot 27.0\right)\\ \mathbf{if}\;y \cdot z \le 4.5158876310708284 \cdot 10^{+268}:\\ \;\;\;\;t \cdot \left(\left(18.0 \cdot x\right) \cdot \left(y \cdot z\right) - 4.0 \cdot a\right) + \left(\left(b \cdot c - i \cdot \left(x \cdot 4.0\right)\right) - \left(j \cdot k\right) \cdot 27.0\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot \left(z \cdot t\right) - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\\ \end{array}\]

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

Derivation

  1. Split input into 3 regimes

  2. if (* y z) < -2.030585386610541e+287

    1. Initial program 19.6

      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]

    2. Taylor expanded around inf 3.8

      \[\leadsto \left(\color{blue}{\left(\left(18.0 \cdot \left(z \cdot \left(y \cdot \left(t \cdot x\right)\right)\right) + b \cdot c\right) - 4.0 \cdot \left(a \cdot t\right)\right)} - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]

    3. Applied simplify3.5

      \[\leadsto \color{blue}{\left(c \cdot b + z \cdot \left(\left(18.0 \cdot t\right) \cdot \left(y \cdot x\right)\right)\right) - \left(4.0 \cdot \left(x \cdot i + t \cdot a\right) + \left(k \cdot j\right) \cdot 27.0\right)}\]
    4. Using strategy rm

    5. Applied associate-*l*3.6

      \[\leadsto \left(c \cdot b + z \cdot \color{blue}{\left(18.0 \cdot \left(t \cdot \left(y \cdot x\right)\right)\right)}\right) - \left(4.0 \cdot \left(x \cdot i + t \cdot a\right) + \left(k \cdot j\right) \cdot 27.0\right)\]
    6. Using strategy rm

    7. Applied associate-*r*4.2

      \[\leadsto \left(c \cdot b + \color{blue}{\left(z \cdot 18.0\right) \cdot \left(t \cdot \left(y \cdot x\right)\right)}\right) - \left(4.0 \cdot \left(x \cdot i + t \cdot a\right) + \left(k \cdot j\right) \cdot 27.0\right)\]

    if -2.030585386610541e+287 < (* y z) < 4.5158876310708284e+268

    1. Initial program 3.9

      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]

    2. Taylor expanded around 0 3.8

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \color{blue}{27.0 \cdot \left(j \cdot k\right)}\]

    3. Applied simplify1.9

      \[\leadsto \color{blue}{t \cdot \left(\left(18.0 \cdot x\right) \cdot \left(y \cdot z\right) - 4.0 \cdot a\right) + \left(\left(b \cdot c - i \cdot \left(x \cdot 4.0\right)\right) - \left(j \cdot k\right) \cdot 27.0\right)}\]

    if 4.5158876310708284e+268 < (* y z)

    1. Initial program 18.5

      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
    2. Using strategy rm

    3. Applied associate-*l*7.3

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
  3. Recombined 3 regimes into one program.

Runtime

Time bar (total: 3.0m)Debug logProfile

herbie shell --seed 2018206 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1"
  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))