Average Error: 0.0 → 0.0
Time: 13.9s
Precision: binary64
Cost: 960
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[c \cdot i + \left(a \cdot b + \left(z \cdot t + x \cdot y\right)\right)\]
\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i
↓
c \cdot i + \left(a \cdot b + \left(z \cdot t + x \cdot y\right)\right)
(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
 (+ (* c i) (+ (* a b) (+ (* z t) (* x y)))))
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 (c * i) + ((a * b) + ((z * t) + (x * y)));
}

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
Error5.8
Cost1602
\[\begin{array}{l} \mathbf{if}\;z \cdot t \leq -2.7129334744167018 \cdot 10^{+17}:\\ \;\;\;\;z \cdot t + \left(c \cdot i + a \cdot b\right)\\ \mathbf{elif}\;z \cdot t \leq 5.4601817202938685 \cdot 10^{+37}:\\ \;\;\;\;x \cdot y + \left(c \cdot i + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \left(c \cdot i + z \cdot t\right)\\ \end{array}\]
Alternative 2
Error5.9
Cost1288
\[\begin{array}{l} \mathbf{if}\;z \cdot t \leq -4.0563271152084345 \cdot 10^{+56} \lor \neg \left(z \cdot t \leq 7.278883847136083 \cdot 10^{+35}\right):\\ \;\;\;\;x \cdot y + \left(c \cdot i + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \left(c \cdot i + a \cdot b\right)\\ \end{array}\]
Alternative 3
Error8.8
Cost1288
\[\begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.686821135771392 \cdot 10^{+150} \lor \neg \left(a \cdot b \leq 2.0258307511909915 \cdot 10^{+51}\right):\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \left(c \cdot i + z \cdot t\right)\\ \end{array}\]
Alternative 4
Error21.9
Cost3142
\[\begin{array}{l} \mathbf{if}\;z \cdot t \leq -3617.6822000964817:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;z \cdot t \leq -7.665063518406412 \cdot 10^{-75}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;z \cdot t \leq 5.0192236041753155 \cdot 10^{-295}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{elif}\;z \cdot t \leq 1.1394012057089724 \cdot 10^{-92}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;z \cdot t \leq 15.50754778208336:\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{elif}\;z \cdot t \leq 1.12637621579885 \cdot 10^{+90}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array}\]
Alternative 5
Error21.9
Cost2244
\[\begin{array}{l} \mathbf{if}\;z \cdot t \leq -8.921018102024512 \cdot 10^{+54}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;z \cdot t \leq 1.3390339677214344 \cdot 10^{-176}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{elif}\;z \cdot t \leq 1.9362121089733716 \cdot 10^{-146}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \cdot t \leq 3.535054415999451 \cdot 10^{+35}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array}\]
Alternative 6
Error24.5
Cost2244
\[\begin{array}{l} \mathbf{if}\;z \cdot t \leq -1.3735403014533352 \cdot 10^{+125}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \cdot t \leq 1.303385695566023 \cdot 10^{-176}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{elif}\;z \cdot t \leq 1.8753648367927177 \cdot 10^{-146}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \cdot t \leq 8.036089838350377 \cdot 10^{+53}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array}\]
Alternative 7
Error38.9
Cost3730
\[\begin{array}{l} \mathbf{if}\;a \cdot b \leq -2161035170348433.5:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.9127922628299423 \cdot 10^{-112}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 0:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2.508347268279416 \cdot 10^{-161}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 6.451850220937613 \cdot 10^{-71}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 4.194571575027767 \cdot 10^{-28}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 3.802218275024958 \cdot 10^{+18} \lor \neg \left(a \cdot b \leq 3.8202017739384467 \cdot 10^{+130}\right) \land a \cdot b \leq 4.0013104649089415 \cdot 10^{+189}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array}\]
Alternative 8
Error38.0
Cost3784
\[\begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.4290688400102296 \cdot 10^{+94}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.3396180967583755 \cdot 10^{-14}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -7.719004521702518 \cdot 10^{-105}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 5.7816080669312 \cdot 10^{-209}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 3.9286844900081155 \cdot 10^{-133}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 4.590367693747697 \cdot 10^{-79}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 7.504842694095727 \cdot 10^{+49}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 1.3902746931727136 \cdot 10^{+66}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array}\]
Alternative 9
Error38.7
Cost1297
\[\begin{array}{l} \mathbf{if}\;a \cdot b \leq -570401006626526.9 \lor \neg \left(a \cdot b \leq 5.258383448328799 \cdot 10^{+18} \lor \neg \left(a \cdot b \leq 4.03525028849407 \cdot 10^{+130}\right) \land a \cdot b \leq 4.0013104649089415 \cdot 10^{+189}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array}\]
Alternative 10
Error47.5
Cost192
\[c \cdot i\]
Alternative 11
Error62.0
Cost64
\[-1\]
Alternative 12
Error62.0
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2021044 
(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)))