Average Error: 34.5 → 7.7

Time: 5.3s

Precision: binary64

\[\]

↓

\[\]

Error

The X axis uses an exponential scale — Bits error versus a

The X axis uses an exponential scale — Bits error versus a

The X axis uses an exponential scale — Bits error versus b_2

The X axis uses an exponential scale — Bits error versus b_2

The X axis uses an exponential scale — Bits error versus c

The X axis uses an exponential scale — Bits error versus c

Derivation

Split input into 4 regimes
if b_2 < -1.02765621091724702e121
1. Initial program 60.8
  \[\]
2. Using strategy rm
3. Applied flip--60.8
  \[\leadsto \]
4. Simplified34.7
  \[\leadsto \]
5. Simplified34.7
  \[\leadsto \]
6. Using strategy rm
7. Applied *-un-lft-identity34.7
  \[\leadsto \]
8. Applied *-un-lft-identity34.7
  \[\leadsto \]
9. Applied times-frac34.7
  \[\leadsto \]
10. Simplified34.7
  \[\leadsto \]
11. Simplified33.1
  \[\leadsto \]
12. Taylor expanded around -inf 6.2
  \[\leadsto \]
13. Simplified1.7
  \[\leadsto \]
if -1.02765621091724702e121 < b_2 < 8.28228220137613734e-119
1. Initial program 29.4
  \[\]
2. Using strategy rm
3. Applied flip--30.7
  \[\leadsto \]
4. Simplified17.7
  \[\leadsto \]
5. Simplified17.7
  \[\leadsto \]
6. Using strategy rm
7. Applied *-un-lft-identity17.7
  \[\leadsto \]
8. Applied *-un-lft-identity17.7
  \[\leadsto \]
9. Applied times-frac17.7
  \[\leadsto \]
10. Simplified17.7
  \[\leadsto \]
11. Simplified11.5
  \[\leadsto \]
if 8.28228220137613734e-119 < b_2 < 6.96571265548405628e24
1. Initial program 5.9
  \[\]
2. Using strategy rm
3. Applied div-inv6.1
  \[\leadsto \]
if 6.96571265548405628e24 < b_2
1. Initial program 34.2
  \[\]
2. Using strategy rm
3. Applied flip--60.7
  \[\leadsto \]
4. Simplified60.1
  \[\leadsto \]
5. Simplified60.1
  \[\leadsto \]
6. Taylor expanded around 0 6.7
  \[\leadsto \]
7. Simplified6.7
  \[\leadsto \]
Recombined 4 regimes into one program.
Final simplification7.7
\[\leadsto \]

Reproduce

herbie shell --seed 2020179 
(FPCore (a b_2 c)
  :name "quad2m (problem 3.2.1, negative)"
  :precision binary64
  (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a))