Average Error: 44.3 → 44.3
Time: 31.5s
Precision: 64
Internal Precision: 576
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]
↓
\[\frac{\left(-b\right) + \sqrt{b \cdot b - (e^{\log_* (1 + \left(3 \cdot a\right) \cdot c)} - 1)^*}}{3 \cdot a}\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 44.3

    \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]
  2. Using strategy rm

  3. Applied expm1-log1p-u44.3

    \[\leadsto \frac{\left(-b\right) + \sqrt{b \cdot b - \color{blue}{(e^{\log_* (1 + \left(3 \cdot a\right) \cdot c)} - 1)^*}}}{3 \cdot a}\]

Runtime

Time bar (total: 31.5s)Debug logProfile

herbie shell --seed 2018214 +o rules:numerics
(FPCore (a b c d)
  :name "Cubic critical, medium range"
  :pre (and (< 1.1102230246251565e-16 a 9007199254740992.0) (< 1.1102230246251565e-16 b 9007199254740992.0) (< 1.1102230246251565e-16 c 9007199254740992.0))
  (/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a)))