Average Error: 0.0 → 0.0
Time: 41.9s
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 2019002 +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: 40.8s)Debug log

sample98.0ms

Algorithm
intervals

simplify99.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

99.0ms
(+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
3 → 39
Calls

3 calls. Slowest were:

4.0ms
(+ (fma b a (* z t)) (fma i c (* x y)))
0.0ms
(fma b a (* z t))
0.0ms
(fma i c (* x y))

series308.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

238.0ms
(+ (fma b a (* z t)) (fma i c (* x y)))
37.0ms
(fma b a (* z t))
34.0ms
(fma i c (* x y))

simplify276.0ms

Counts
15 → 48
Calls

15 calls. Slowest were:

128.0ms
(* (exp (fma b a (* z t))) (exp (fma i c (* x y))))
51.0ms
(+ (fma b a (* z t)) (fma i c (* x y)))
27.0ms
(+ (* i c) (+ (* t z) (* x y)))

prune630.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

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

series93.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

59.0ms
(fma x y (fma i c (* t z)))
33.0ms
(fma i c (* t z))

simplify48.0ms

Counts
6 → 26
Calls

6 calls. Slowest were:

22.0ms
(+ (* i c) (+ (* t z) (* x y)))
15.0ms
(+ (* i c) (+ (* t z) (* x y)))
5.0ms
(+ (* t z) (* i c))

prune387.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

1.3b
(sqrt (fma b a (* z t)))
1.3b
(sqrt (fma b a (* z t)))
0.1b
(fma (sqrt (fma b a (* z t))) (sqrt (fma b a (* z t))) (fma i c (* x y)))
0.0b
(fma b a (* z t))

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
4 → 48
Calls

4 calls. Slowest were:

2.0ms
(sqrt (fma b a (* z t)))
2.0ms
(sqrt (fma b a (* z t)))
0.0ms
(fma (sqrt (fma b a (* z t))) (sqrt (fma b a (* z t))) (fma i c (* x y)))

series12.4s

Counts
4 → 12
Calls

4 calls. Slowest were:

12.2s
(fma (sqrt (fma b a (* z t))) (sqrt (fma b a (* z t))) (fma i c (* x y)))
70.0ms
(sqrt (fma b a (* z t)))
55.0ms
(sqrt (fma b a (* z t)))
25.0ms
(fma b a (* z t))

simplify86.0ms

Counts
20 → 60
Calls

20 calls. Slowest were:

14.0ms
(sqrt (sqrt (fma b a (* z t))))
12.0ms
(sqrt (fma b a (* z t)))
8.0ms
(sqrt (* (cbrt (fma b a (* z t))) (cbrt (fma b a (* z t)))))

prune1.0s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm
rewrite-expression-head
Counts
4 → 97
Calls

4 calls. Slowest were:

19.0ms
(* (sqrt (+ (fma b a (* z t)) (fma i c (* x y)))) (sqrt (+ (fma b a (* z t)) (fma i c (* x y)))))
8.0ms
(sqrt (+ (fma b a (* z t)) (fma i c (* x y))))
8.0ms
(sqrt (+ (fma b a (* z t)) (fma i c (* x y))))

series10.7s

Counts
4 → 12
Calls

4 calls. Slowest were:

5.1s
(sqrt (+ (fma b a (* z t)) (fma i c (* x y))))
5.0s
(sqrt (+ (fma b a (* z t)) (fma i c (* x y))))
310.0ms
(+ (fma b a (* z t)) (fma i c (* x y)))
264.0ms
(* (sqrt (+ (fma b a (* z t)) (fma i c (* x y)))) (sqrt (+ (fma b a (* z t)) (fma i c (* x y)))))

simplify8.4s

Counts
71 → 109
Calls

71 calls. Slowest were:

633.0ms
(* (* (* (sqrt (+ (fma b a (* z t)) (fma i c (* x y)))) (sqrt (+ (fma b a (* z t)) (fma i c (* x y))))) (sqrt (+ (fma b a (* z t)) (fma i c (* x y))))) (* (* (sqrt (+ (fma b a (* z t)) (fma i c (* x y)))) (sqrt (+ (fma b a (* z t)) (fma i c (* x y))))) (sqrt (+ (fma b a (* z t)) (fma i c (* x y))))))
630.0ms
(* (sqrt (- (* (fma b a (* z t)) (fma b a (* z t))) (* (fma i c (* x y)) (fma i c (* x y))))) (sqrt (+ (fma b a (* z t)) (fma i c (* x y)))))
557.0ms
(* (+ (fma b a (* z t)) (fma i c (* x y))) (+ (fma b a (* z t)) (fma i c (* x y))))

prune1.9s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes887.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample3.4s

Algorithm
intervals