Average Error: 0.0 → 0.0
Time: 6.3s
Precision: 64
Internal Precision: 128
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[(b \cdot a + \left(z \cdot t\right))_* + (i \cdot c + \left(y \cdot x\right))_*\]

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

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019004 +o rules:numerics
(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: 5.7s)Debug log

sample91.0ms

Algorithm
intervals

simplify111.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

111.0ms
(+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 2 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
2 → 29
Calls

2 calls. Slowest were:

7.0ms
(+ (fma b a (* z t)) (fma i c (* x y)))
0.0ms
(fma i c (* x y))

series258.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

210.0ms
(+ (fma b a (* z t)) (fma i c (* x y)))
48.0ms
(fma i c (* x y))

simplify299.0ms

Counts
12 → 35
Calls

12 calls. Slowest were:

135.0ms
(* (exp (fma b a (* z t))) (exp (fma i c (* x y))))
47.0ms
(+ (fma b a (* z t)) (fma i c (* x y)))
30.0ms
(+ (* i c) (+ (* t z) (* x y)))

prune472.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma x y (fma i c (* t z)))
0.0b
(fma i c (* t z))

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
2 → 20
Calls

2 calls. Slowest were:

0.0ms
(fma i c (* t z))
0.0ms
(fma x y (fma i c (* t z)))

series106.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

63.0ms
(fma x y (fma i c (* t z)))
43.0ms
(fma i c (* t z))

simplify83.0ms

Counts
6 → 26
Calls

6 calls. Slowest were:

30.0ms
(+ (* i c) (+ (* t z) (* x y)))
29.0ms
(+ (* i c) (+ (* t z) (* x y)))
11.0ms
(+ (* t z) (* i c))

prune315.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes690.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample3.2s

Algorithm
intervals