Average Error: 0.0 → 0.0
Time: 2.6min
Precision: binary64
Cost: 960
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i
↓
\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i
(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
↓
(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((x * y) + (z * t)) + (a * b)) + (c * i);
}
↓
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((x * y) + (z * t)) + (a * b)) + (c * i);
}

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

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error6.4
Cost1288
\[\begin{array}{l} \mathbf{if}\;z \cdot t \leq -4.4753191735844233 \cdot 10^{-35} \lor \neg \left(z \cdot t \leq 3.005768827235306 \cdot 10^{-19}\right):\\ \;\;\;\;c \cdot i + \left(z \cdot t + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \end{array}\]
Alternative 2
Error6.3
Cost1288
\[\begin{array}{l} \mathbf{if}\;z \cdot t \leq -876.4149557637376 \lor \neg \left(z \cdot t \leq 2.8835041158773195 \cdot 10^{+42}\right):\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \end{array}\]
Alternative 3
Error8.8
Cost1288
\[\begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.0953330280262287 \cdot 10^{+65} \lor \neg \left(a \cdot b \leq 2.903160141591779 \cdot 10^{+26}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) + c \cdot i\\ \end{array}\]
Alternative 4
Error22.0
Cost3142
\[\begin{array}{l} \mathbf{if}\;z \cdot t \leq -876.4149557637376:\\ \;\;\;\;z \cdot t + c \cdot i\\ \mathbf{elif}\;z \cdot t \leq -4.949272516952354 \cdot 10^{-196}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;z \cdot t \leq 2.4737080334763 \cdot 10^{-316}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;z \cdot t \leq 2.1581452307212927 \cdot 10^{-149}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;z \cdot t \leq 5.635453931134026 \cdot 10^{-38}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;z \cdot t \leq 2.8835041158773195 \cdot 10^{+42}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;z \cdot t + c \cdot i\\ \end{array}\]
Alternative 5
Error22.8
Cost3142
\[\begin{array}{l} \mathbf{if}\;z \cdot t \leq -26.57269911161113:\\ \;\;\;\;z \cdot t + c \cdot i\\ \mathbf{elif}\;z \cdot t \leq -1.9466096945774426 \cdot 10^{-196}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;z \cdot t \leq -4.242490964351764 \cdot 10^{-263}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \cdot t \leq 1.7024475142077485 \cdot 10^{-52}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;z \cdot t \leq 3.723468280179997 \cdot 10^{-33}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \cdot t \leq 4.6954354245452426 \cdot 10^{+42}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;z \cdot t + c \cdot i\\ \end{array}\]
Alternative 6
Error25.7
Cost3142
\[\begin{array}{l} \mathbf{if}\;z \cdot t \leq -1.4682424816772405 \cdot 10^{+47}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \cdot t \leq -1.4594106300492162 \cdot 10^{-196}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;z \cdot t \leq -2.9042922117227954 \cdot 10^{-266}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \cdot t \leq 2.42177553232811 \cdot 10^{-52}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;z \cdot t \leq 5.765917962725551 \cdot 10^{-38}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \cdot t \leq 8.939617775903697 \cdot 10^{+48}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array}\]
Alternative 7
Error38.7
Cost4368
\[\begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.3427785174985994 \cdot 10^{+120}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -5.02835631197913 \cdot 10^{+41}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -6.171056146212279 \cdot 10^{+34}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -4.562143479425966 \cdot 10^{-197}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 2.0966161334014614 \cdot 10^{-244}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 8.132991851105379 \cdot 10^{-123}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 0.018460399255693722:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 9.833871218930718 \cdot 10^{+24}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 4.671990953245658 \cdot 10^{+70} \lor \neg \left(c \cdot i \leq 1.7535445578822088 \cdot 10^{+142}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array}\]
Alternative 8
Error37.9
Cost3784
\[\begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.3427785174985994 \cdot 10^{+120}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -7.02076980251134 \cdot 10^{+40}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -1.3078305081244203 \cdot 10^{+35}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.8082365074153387 \cdot 10^{-198}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 1.0653981193321036 \cdot 10^{-241}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 8.510170755152069 \cdot 10^{-125}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 1.9507792172644677 \cdot 10^{-07}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 5.987164468623569 \cdot 10^{+24}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array}\]
Alternative 9
Error37.5
Cost776
\[\begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.0200710793183858 \cdot 10^{+35} \lor \neg \left(c \cdot i \leq 2.3849187735444016 \cdot 10^{+24}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array}\]
Alternative 10
Error47.4
Cost192
\[c \cdot i\]
Alternative 11
Error62.0
Cost64
\[1\]

Error

Time

Derivation

  1. Initial program 0.0

    \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
  2. Using strategy rm

  3. Applied pow1_binary64_21850.0

    \[\leadsto \left(\color{blue}{{\left(x \cdot y + z \cdot t\right)}^{1}} + a \cdot b\right) + c \cdot i\]
  4. Using strategy rm

  5. Applied pow1_binary64_21850.0

    \[\leadsto \color{blue}{{\left({\left(x \cdot y + z \cdot t\right)}^{1} + a \cdot b\right)}^{1}} + c \cdot i\]

  6. Simplified0.0

    \[\leadsto \color{blue}{\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i}\]

  7. Final simplification0.0

    \[\leadsto \left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]

Reproduce

herbie shell --seed 2021040 
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3, C"
  :precision binary64
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))