Average Error: 0.3 → 0.4
Time: 7.2m
Precision: 64
Internal Precision: 384
\[\begin{array}{l} \mathbf{if}\;a \lt b:\\ \;\;\;\;\frac{\sqrt{\left(\left(\left(c + \left(b + a\right)\right) \cdot \left(a - \left(c - b\right)\right)\right) \cdot \left(a + \left(c - b\right)\right)\right) \cdot \left(c + \left(b - a\right)\right)}}{4.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{\left(\left(\left(c + \left(a + b\right)\right) \cdot \left(b - \left(c - a\right)\right)\right) \cdot \left(b + \left(c - a\right)\right)\right) \cdot \left(c + \left(a - b\right)\right)}}{4.0}\\ \end{array}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \lt b:\\ \;\;\;\;\frac{\sqrt{\left(\left(\left(c + \left(b + a\right)\right) \cdot \left(a - \left(c - b\right)\right)\right) \cdot \left(a + \left(c - b\right)\right)\right) \cdot \left(c + \left(b - a\right)\right)}}{4.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{\sqrt[3]{\left({\left(a - \left(b - c\right)\right)}^{3} \cdot {\left(\left(c - a\right) + b\right)}^{3}\right) \cdot \left({\left(\left(b - c\right) + a\right)}^{3} \cdot {\left(c + \left(a + b\right)\right)}^{3}\right)}}}{4.0}\\ \end{array}\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Derivation

  1. Initial program 0.3

    \[\begin{array}{l} \mathbf{if}\;a \lt b:\\ \;\;\;\;\frac{\sqrt{\left(\left(\left(c + \left(b + a\right)\right) \cdot \left(a - \left(c - b\right)\right)\right) \cdot \left(a + \left(c - b\right)\right)\right) \cdot \left(c + \left(b - a\right)\right)}}{4.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{\left(\left(\left(c + \left(a + b\right)\right) \cdot \left(b - \left(c - a\right)\right)\right) \cdot \left(b + \left(c - a\right)\right)\right) \cdot \left(c + \left(a - b\right)\right)}}{4.0}\\ \end{array}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \lt b:\\ \;\;\;\;\frac{\sqrt{\left(\left(\left(c + \left(b + a\right)\right) \cdot \left(a - \left(c - b\right)\right)\right) \cdot \left(a + \left(c - b\right)\right)\right) \cdot \left(c + \left(b - a\right)\right)}}{4.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{\left(\left(\left(c + \left(a + b\right)\right) \cdot \left(b - \left(c - a\right)\right)\right) \cdot \left(b + \left(c - a\right)\right)\right) \cdot \sqrt[3]{\left(\left(c + \left(a - b\right)\right) \cdot \left(c + \left(a - b\right)\right)\right) \cdot \left(c + \left(a - b\right)\right)}}}{4.0}\\ \end{array}\]

  4. Applied add-cbrt-cube0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \lt b:\\ \;\;\;\;\frac{\sqrt{\left(\left(\left(c + \left(b + a\right)\right) \cdot \left(a - \left(c - b\right)\right)\right) \cdot \left(a + \left(c - b\right)\right)\right) \cdot \left(c + \left(b - a\right)\right)}}{4.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{\left(\left(\left(c + \left(a + b\right)\right) \cdot \left(b - \left(c - a\right)\right)\right) \cdot \sqrt[3]{\left(\left(b + \left(c - a\right)\right) \cdot \left(b + \left(c - a\right)\right)\right) \cdot \left(b + \left(c - a\right)\right)}\right) \cdot \sqrt[3]{\left(\left(c + \left(a - b\right)\right) \cdot \left(c + \left(a - b\right)\right)\right) \cdot \left(c + \left(a - b\right)\right)}}}{4.0}\\ \end{array}\]

  5. Applied add-cbrt-cube0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \lt b:\\ \;\;\;\;\frac{\sqrt{\left(\left(\left(c + \left(b + a\right)\right) \cdot \left(a - \left(c - b\right)\right)\right) \cdot \left(a + \left(c - b\right)\right)\right) \cdot \left(c + \left(b - a\right)\right)}}{4.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{\left(\left(\left(c + \left(a + b\right)\right) \cdot \sqrt[3]{\left(\left(b - \left(c - a\right)\right) \cdot \left(b - \left(c - a\right)\right)\right) \cdot \left(b - \left(c - a\right)\right)}\right) \cdot \sqrt[3]{\left(\left(b + \left(c - a\right)\right) \cdot \left(b + \left(c - a\right)\right)\right) \cdot \left(b + \left(c - a\right)\right)}\right) \cdot \sqrt[3]{\left(\left(c + \left(a - b\right)\right) \cdot \left(c + \left(a - b\right)\right)\right) \cdot \left(c + \left(a - b\right)\right)}}}{4.0}\\ \end{array}\]

  6. Applied add-cbrt-cube0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \lt b:\\ \;\;\;\;\frac{\sqrt{\left(\left(\left(c + \left(b + a\right)\right) \cdot \left(a - \left(c - b\right)\right)\right) \cdot \left(a + \left(c - b\right)\right)\right) \cdot \left(c + \left(b - a\right)\right)}}{4.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{\left(\left(\sqrt[3]{\left(\left(c + \left(a + b\right)\right) \cdot \left(c + \left(a + b\right)\right)\right) \cdot \left(c + \left(a + b\right)\right)} \cdot \sqrt[3]{\left(\left(b - \left(c - a\right)\right) \cdot \left(b - \left(c - a\right)\right)\right) \cdot \left(b - \left(c - a\right)\right)}\right) \cdot \sqrt[3]{\left(\left(b + \left(c - a\right)\right) \cdot \left(b + \left(c - a\right)\right)\right) \cdot \left(b + \left(c - a\right)\right)}\right) \cdot \sqrt[3]{\left(\left(c + \left(a - b\right)\right) \cdot \left(c + \left(a - b\right)\right)\right) \cdot \left(c + \left(a - b\right)\right)}}}{4.0}\\ \end{array}\]

  7. Applied cbrt-unprod0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \lt b:\\ \;\;\;\;\frac{\sqrt{\left(\left(\left(c + \left(b + a\right)\right) \cdot \left(a - \left(c - b\right)\right)\right) \cdot \left(a + \left(c - b\right)\right)\right) \cdot \left(c + \left(b - a\right)\right)}}{4.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{\left(\sqrt[3]{\left(\left(\left(c + \left(a + b\right)\right) \cdot \left(c + \left(a + b\right)\right)\right) \cdot \left(c + \left(a + b\right)\right)\right) \cdot \left(\left(\left(b - \left(c - a\right)\right) \cdot \left(b - \left(c - a\right)\right)\right) \cdot \left(b - \left(c - a\right)\right)\right)} \cdot \sqrt[3]{\left(\left(b + \left(c - a\right)\right) \cdot \left(b + \left(c - a\right)\right)\right) \cdot \left(b + \left(c - a\right)\right)}\right) \cdot \sqrt[3]{\left(\left(c + \left(a - b\right)\right) \cdot \left(c + \left(a - b\right)\right)\right) \cdot \left(c + \left(a - b\right)\right)}}}{4.0}\\ \end{array}\]

  8. Applied cbrt-unprod0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \lt b:\\ \;\;\;\;\frac{\sqrt{\left(\left(\left(c + \left(b + a\right)\right) \cdot \left(a - \left(c - b\right)\right)\right) \cdot \left(a + \left(c - b\right)\right)\right) \cdot \left(c + \left(b - a\right)\right)}}{4.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{\sqrt[3]{\left(\left(\left(\left(c + \left(a + b\right)\right) \cdot \left(c + \left(a + b\right)\right)\right) \cdot \left(c + \left(a + b\right)\right)\right) \cdot \left(\left(\left(b - \left(c - a\right)\right) \cdot \left(b - \left(c - a\right)\right)\right) \cdot \left(b - \left(c - a\right)\right)\right)\right) \cdot \left(\left(\left(b + \left(c - a\right)\right) \cdot \left(b + \left(c - a\right)\right)\right) \cdot \left(b + \left(c - a\right)\right)\right)} \cdot \sqrt[3]{\left(\left(c + \left(a - b\right)\right) \cdot \left(c + \left(a - b\right)\right)\right) \cdot \left(c + \left(a - b\right)\right)}}}{4.0}\\ \end{array}\]

  9. Applied cbrt-unprod0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \lt b:\\ \;\;\;\;\frac{\sqrt{\left(\left(\left(c + \left(b + a\right)\right) \cdot \left(a - \left(c - b\right)\right)\right) \cdot \left(a + \left(c - b\right)\right)\right) \cdot \left(c + \left(b - a\right)\right)}}{4.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{\sqrt[3]{\left(\left(\left(\left(\left(c + \left(a + b\right)\right) \cdot \left(c + \left(a + b\right)\right)\right) \cdot \left(c + \left(a + b\right)\right)\right) \cdot \left(\left(\left(b - \left(c - a\right)\right) \cdot \left(b - \left(c - a\right)\right)\right) \cdot \left(b - \left(c - a\right)\right)\right)\right) \cdot \left(\left(\left(b + \left(c - a\right)\right) \cdot \left(b + \left(c - a\right)\right)\right) \cdot \left(b + \left(c - a\right)\right)\right)\right) \cdot \left(\left(\left(c + \left(a - b\right)\right) \cdot \left(c + \left(a - b\right)\right)\right) \cdot \left(c + \left(a - b\right)\right)\right)}}}{4.0}\\ \end{array}\]

  10. Applied simplify0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \lt b:\\ \;\;\;\;\frac{\sqrt{\left(\left(\left(c + \left(b + a\right)\right) \cdot \left(a - \left(c - b\right)\right)\right) \cdot \left(a + \left(c - b\right)\right)\right) \cdot \left(c + \left(b - a\right)\right)}}{4.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{\sqrt[3]{\left({\left(a - \left(b - c\right)\right)}^{3} \cdot {\left(\left(c - a\right) + b\right)}^{3}\right) \cdot \left({\left(\left(b - c\right) + a\right)}^{3} \cdot {\left(c + \left(a + b\right)\right)}^{3}\right)}}}{4.0}\\ \end{array}\]

Runtime

Time bar (total: 7.2m)Debug log

herbie shell --seed '#(1743936871 1855164119 3668777427 1254258049 132811564 1366975197)' 
(FPCore (a b c)
  :name "triangleSorted"
  :pre (and (<= 1 a 9) (<= 1 b 9) (<= 1 c 9) (> (+ a b) (+ c 1e-06)) (> (+ a c) (+ b 1e-06)) (> (+ b c) (+ a 1e-06)) (< a c) (< b c))
  (if (< a b) (/ (sqrt (* (* (* (+ c (+ b a)) (- a (- c b))) (+ a (- c b))) (+ c (- b a)))) 4.0) (/ (sqrt (* (* (* (+ c (+ a b)) (- b (- c a))) (+ b (- c a))) (+ c (- a b)))) 4.0)))