Average Error: 0.0 → 0.0
Time: 13.9s
Precision: 64
Internal Precision: 128
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[c \cdot i + \left(\left(z \cdot t + x \cdot y\right) + a \cdot b\right)\]

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

Derivation

  1. Initial program 0.0

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

  2. Final simplification0.0

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

Reproduce

herbie shell --seed 2019004 
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3"
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))

Details

Time bar (total: 13.3s)Debug log

sample127.0ms

Algorithm
intervals

simplify67.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

67.0ms
(+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x y) (* z t))
0.0b
(+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))

rewrite75.0ms

Algorithm
rewrite-expression-head
Counts
2 → 25
Calls

2 calls. Slowest were:

72.0ms
(+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))
2.0ms
(+ (* x y) (* z t))

series309.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

275.0ms
(+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))
33.0ms
(+ (* x y) (* z t))

simplify930.0ms

Counts
11 → 31
Calls

11 calls. Slowest were:

522.0ms
(* (* (exp (+ (* x y) (* z t))) (exp (* a b))) (exp (* c i)))
205.0ms
(* (* (* (exp (* x y)) (exp (* z t))) (exp (* a b))) (exp (* c i)))
147.0ms
(* (exp (+ (+ (* x y) (* z t)) (* a b))) (exp (* c i)))

prune512.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

1.2b
(sqrt (+ (* x y) (* z t)))
1.2b
(sqrt (+ (* x y) (* z t)))
0.2b
(* (sqrt (+ (* x y) (* z t))) (sqrt (+ (* x y) (* z t))))
0.0b
(+ (+ (* (sqrt (+ (* x y) (* z t))) (sqrt (+ (* x y) (* z t)))) (* a b)) (* c i))

rewrite74.0ms

Algorithm
rewrite-expression-head
Counts
4 → 79
Calls

4 calls. Slowest were:

48.0ms
(+ (+ (* (sqrt (+ (* x y) (* z t))) (sqrt (+ (* x y) (* z t)))) (* a b)) (* c i))
17.0ms
(* (sqrt (+ (* x y) (* z t))) (sqrt (+ (* x y) (* z t))))
4.0ms
(sqrt (+ (* x y) (* z t)))

series383.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

240.0ms
(+ (+ (* (sqrt (+ (* x y) (* z t))) (sqrt (+ (* x y) (* z t)))) (* a b)) (* c i))
57.0ms
(sqrt (+ (* x y) (* z t)))
49.0ms
(sqrt (+ (* x y) (* z t)))
37.0ms
(* (sqrt (+ (* x y) (* z t))) (sqrt (+ (* x y) (* z t))))

simplify4.9s

Counts
62 → 91
Calls

62 calls. Slowest were:

451.0ms
(* (sqrt (- (* x y) (* z t))) (sqrt (+ (* (* x y) (* x y)) (- (* (* z t) (* z t)) (* (* x y) (* z t))))))
376.0ms
(* (sqrt (+ (pow (* x y) 3) (pow (* z t) 3))) (sqrt (- (* (* x y) (* x y)) (* (* z t) (* z t)))))
352.0ms
(* (sqrt (+ (* (* x y) (* x y)) (- (* (* z t) (* z t)) (* (* x y) (* z t))))) (sqrt (+ (* (* x y) (* x y)) (- (* (* z t) (* z t)) (* (* x y) (* z t))))))

prune1.4s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes1.1s

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch2.0ms

end0.0ms

sample3.4s

Algorithm
intervals