Average Error: 3.7 → 2.7
Time: 2.6m
Precision: 64
Internal Precision: 320
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2.0 \cdot \frac{\left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(\left(3.0 \cdot t\right) \cdot \left(c + b\right)\right)\right) \cdot \left(\sqrt{a + t} \cdot z\right) - \left(\left(\left(c + b\right) \cdot t\right) \cdot \left(b - c\right)\right) \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(\left(\frac{5.0}{6.0} + a\right) \cdot \left(3.0 \cdot t\right) - 2.0\right)\right)}{t \cdot \left(\left(b + c\right) \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right)\right)}}} \le 1.0000000022309354:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2.0 \cdot \frac{\left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(\left(3.0 \cdot t\right) \cdot \left(c + b\right)\right)\right) \cdot \left(\sqrt{a + t} \cdot z\right) - \left(\left(\left(c + b\right) \cdot t\right) \cdot \left(b - c\right)\right) \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(\left(\frac{5.0}{6.0} + a\right) \cdot \left(3.0 \cdot t\right) - 2.0\right)\right)}{t \cdot \left(\left(b + c\right) \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right)\right)}}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\\ \end{array}\]

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if (/ x (+ x (* y (exp (* 2.0 (/ (- (* (* (- a (/ 5.0 6.0)) (* (* 3.0 t) (+ c b))) (* (sqrt (+ a t)) z)) (* (* (* (+ c b) t) (- b c)) (* (- a (/ 5.0 6.0)) (- (* (+ (/ 5.0 6.0) a) (* 3.0 t)) 2.0)))) (* t (* (+ b c) (* (- a (/ 5.0 6.0)) (* t 3.0)))))))))) < 1.0000000022309354

    1. Initial program 2.2

      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
    2. Using strategy rm

    3. Applied flip-+4.0

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\color{blue}{\frac{a \cdot a - \frac{5.0}{6.0} \cdot \frac{5.0}{6.0}}{a - \frac{5.0}{6.0}}} - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]

    4. Applied frac-sub4.1

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \color{blue}{\frac{\left(a \cdot a - \frac{5.0}{6.0} \cdot \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0}{\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)}}\right)}}\]

    5. Applied flip--7.3

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \color{blue}{\frac{b \cdot b - c \cdot c}{b + c}} \cdot \frac{\left(a \cdot a - \frac{5.0}{6.0} \cdot \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0}{\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)}\right)}}\]

    6. Applied frac-times7.4

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \color{blue}{\frac{\left(b \cdot b - c \cdot c\right) \cdot \left(\left(a \cdot a - \frac{5.0}{6.0} \cdot \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0\right)}{\left(b + c\right) \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right)}}\right)}}\]

    7. Applied frac-sub6.1

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \color{blue}{\frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(b + c\right) \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right)\right) - t \cdot \left(\left(b \cdot b - c \cdot c\right) \cdot \left(\left(a \cdot a - \frac{5.0}{6.0} \cdot \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0\right)\right)}{t \cdot \left(\left(b + c\right) \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right)\right)}}}}\]

    8. Applied simplify0.3

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \frac{\color{blue}{\left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(\left(3.0 \cdot t\right) \cdot \left(c + b\right)\right)\right) \cdot \left(\sqrt{a + t} \cdot z\right) - \left(\left(\left(c + b\right) \cdot t\right) \cdot \left(b - c\right)\right) \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(\left(\frac{5.0}{6.0} + a\right) \cdot \left(3.0 \cdot t\right) - 2.0\right)\right)}}{t \cdot \left(\left(b + c\right) \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right)\right)}}}\]

    if 1.0000000022309354 < (/ x (+ x (* y (exp (* 2.0 (/ (- (* (* (- a (/ 5.0 6.0)) (* (* 3.0 t) (+ c b))) (* (sqrt (+ a t)) z)) (* (* (* (+ c b) t) (- b c)) (* (- a (/ 5.0 6.0)) (- (* (+ (/ 5.0 6.0) a) (* 3.0 t)) 2.0)))) (* t (* (+ b c) (* (- a (/ 5.0 6.0)) (* t 3.0))))))))))

    1. Initial program 5.2

      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
    2. Using strategy rm

    3. Applied div-inv5.3

      \[\leadsto \color{blue}{x \cdot \frac{1}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}}\]
  3. Recombined 2 regimes into one program.

Runtime

Time bar (total: 2.6m)Debug logProfile

herbie shell --seed 2020178 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2"
  (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))