Average Error: 3.8 → 2.6
Time: 9.5m
Precision: 64
Internal Precision: 320
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot e^{2.0 \cdot \frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(a \cdot a + \left(\frac{5.0}{6.0} \cdot \frac{5.0}{6.0} - a \cdot \frac{5.0}{6.0}\right)\right) \cdot \left(t \cdot 3.0\right)\right) - t \cdot \left(\left(b - c\right) \cdot \left(\left({a}^{3} + {\left(\frac{5.0}{6.0}\right)}^{3}\right) \cdot \left(t \cdot 3.0\right) - \left(a \cdot a + \left(\frac{5.0}{6.0} \cdot \frac{5.0}{6.0} - a \cdot \frac{5.0}{6.0}\right)\right) \cdot 2.0\right)\right)}{\left(\frac{5.0}{6.0} \cdot \frac{5.0}{6.0} - \left(\frac{5.0}{6.0} - a\right) \cdot a\right) \cdot \left(t \cdot \left(t \cdot 3.0\right)\right)}} \le 3.61122253937575 \cdot 10^{-310}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2.0 \cdot \frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(a \cdot a + \left(\frac{5.0}{6.0} \cdot \frac{5.0}{6.0} - a \cdot \frac{5.0}{6.0}\right)\right) \cdot \left(t \cdot 3.0\right)\right) - t \cdot \left(\left(b - c\right) \cdot \left(\left({a}^{3} + {\left(\frac{5.0}{6.0}\right)}^{3}\right) \cdot \left(t \cdot 3.0\right) - \left(a \cdot a + \left(\frac{5.0}{6.0} \cdot \frac{5.0}{6.0} - a \cdot \frac{5.0}{6.0}\right)\right) \cdot 2.0\right)\right)}{\left(\frac{5.0}{6.0} \cdot \frac{5.0}{6.0} - \left(\frac{5.0}{6.0} - a\right) \cdot a\right) \cdot \left(t \cdot \left(t \cdot 3.0\right)\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z}{\frac{t}{\sqrt{t + a}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\\ \end{array}\]

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 (* y (exp (* 2.0 (/ (- (* (* z (sqrt (+ t a))) (* (+ (* a a) (- (* (/ 5.0 6.0) (/ 5.0 6.0)) (* a (/ 5.0 6.0)))) (* t 3.0))) (* t (* (- b c) (- (* (+ (pow a 3) (pow (/ 5.0 6.0) 3)) (* t 3.0)) (* (+ (* a a) (- (* (/ 5.0 6.0) (/ 5.0 6.0)) (* a (/ 5.0 6.0)))) 2.0))))) (* (- (* (/ 5.0 6.0) (/ 5.0 6.0)) (* (- (/ 5.0 6.0) a) a)) (* t (* t 3.0))))))) < 3.61122253937575e-310

    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 flip3-+3.5

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\color{blue}{\frac{{a}^{3} + {\left(\frac{5.0}{6.0}\right)}^{3}}{a \cdot a + \left(\frac{5.0}{6.0} \cdot \frac{5.0}{6.0} - a \cdot \frac{5.0}{6.0}\right)}} - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]

    4. Applied frac-sub3.5

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \color{blue}{\frac{\left({a}^{3} + {\left(\frac{5.0}{6.0}\right)}^{3}\right) \cdot \left(t \cdot 3.0\right) - \left(a \cdot a + \left(\frac{5.0}{6.0} \cdot \frac{5.0}{6.0} - a \cdot \frac{5.0}{6.0}\right)\right) \cdot 2.0}{\left(a \cdot a + \left(\frac{5.0}{6.0} \cdot \frac{5.0}{6.0} - a \cdot \frac{5.0}{6.0}\right)\right) \cdot \left(t \cdot 3.0\right)}}\right)}}\]

    5. Applied associate-*r/3.6

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \color{blue}{\frac{\left(b - c\right) \cdot \left(\left({a}^{3} + {\left(\frac{5.0}{6.0}\right)}^{3}\right) \cdot \left(t \cdot 3.0\right) - \left(a \cdot a + \left(\frac{5.0}{6.0} \cdot \frac{5.0}{6.0} - a \cdot \frac{5.0}{6.0}\right)\right) \cdot 2.0\right)}{\left(a \cdot a + \left(\frac{5.0}{6.0} \cdot \frac{5.0}{6.0} - a \cdot \frac{5.0}{6.0}\right)\right) \cdot \left(t \cdot 3.0\right)}}\right)}}\]

    6. Applied frac-sub1.5

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \color{blue}{\frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(a \cdot a + \left(\frac{5.0}{6.0} \cdot \frac{5.0}{6.0} - a \cdot \frac{5.0}{6.0}\right)\right) \cdot \left(t \cdot 3.0\right)\right) - t \cdot \left(\left(b - c\right) \cdot \left(\left({a}^{3} + {\left(\frac{5.0}{6.0}\right)}^{3}\right) \cdot \left(t \cdot 3.0\right) - \left(a \cdot a + \left(\frac{5.0}{6.0} \cdot \frac{5.0}{6.0} - a \cdot \frac{5.0}{6.0}\right)\right) \cdot 2.0\right)\right)}{t \cdot \left(\left(a \cdot a + \left(\frac{5.0}{6.0} \cdot \frac{5.0}{6.0} - a \cdot \frac{5.0}{6.0}\right)\right) \cdot \left(t \cdot 3.0\right)\right)}}}}\]

    7. Applied simplify1.5

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(a \cdot a + \left(\frac{5.0}{6.0} \cdot \frac{5.0}{6.0} - a \cdot \frac{5.0}{6.0}\right)\right) \cdot \left(t \cdot 3.0\right)\right) - t \cdot \left(\left(b - c\right) \cdot \left(\left({a}^{3} + {\left(\frac{5.0}{6.0}\right)}^{3}\right) \cdot \left(t \cdot 3.0\right) - \left(a \cdot a + \left(\frac{5.0}{6.0} \cdot \frac{5.0}{6.0} - a \cdot \frac{5.0}{6.0}\right)\right) \cdot 2.0\right)\right)}{\color{blue}{\left(\frac{5.0}{6.0} \cdot \frac{5.0}{6.0} - \left(\frac{5.0}{6.0} - a\right) \cdot a\right) \cdot \left(t \cdot \left(t \cdot 3.0\right)\right)}}}}\]

    if 3.61122253937575e-310 < (* y (exp (* 2.0 (/ (- (* (* z (sqrt (+ t a))) (* (+ (* a a) (- (* (/ 5.0 6.0) (/ 5.0 6.0)) (* a (/ 5.0 6.0)))) (* t 3.0))) (* t (* (- b c) (- (* (+ (pow a 3) (pow (/ 5.0 6.0) 3)) (* t 3.0)) (* (+ (* a a) (- (* (/ 5.0 6.0) (/ 5.0 6.0)) (* a (/ 5.0 6.0)))) 2.0))))) (* (- (* (/ 5.0 6.0) (/ 5.0 6.0)) (* (- (/ 5.0 6.0) a) a)) (* t (* t 3.0)))))))

    1. Initial program 4.8

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

    3. Applied associate-/l*3.3

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

Runtime

Time bar (total: 9.5m)Debug logProfile

herbie shell --seed 2018198 
(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)))))))))))