Average Error: 0.0 → 0.0
Time: 12.3s
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. Initial simplification0.0

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

  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 2018362 +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: 8.0s)Debug log

start107.0ms

Algorithm
intervals

setup148.0ms

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

series288.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

244.0ms
(+ (fma b a (* z t)) (fma i c (* x y)))
44.0ms
(fma i c (* x y))

simplify323.0ms

Counts
12 → 35
Calls

12 calls. Slowest were:

158.0ms
(* (exp (fma b a (* z t))) (exp (fma i c (* x y))))
52.0ms
(+ (fma b a (* z t)) (fma i c (* x y)))
29.0ms
(+ (* i c) (+ (* t z) (* x y)))

prune595.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

1.4b
(cbrt (fma b a (* z t)))
1.4b
(cbrt (fma b a (* z t)))
1.4b
(cbrt (fma b a (* z t)))
0.5b
(* (cbrt (fma b a (* z t))) (cbrt (fma b a (* z t))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Counts
4 → 69
Calls

4 calls. Slowest were:

5.0ms
(* (cbrt (fma b a (* z t))) (cbrt (fma b a (* z t))))
1.0ms
(cbrt (fma b a (* z t)))
1.0ms
(cbrt (fma b a (* z t)))

series566.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

169.0ms
(* (cbrt (fma b a (* z t))) (cbrt (fma b a (* z t))))
142.0ms
(cbrt (fma b a (* z t)))
128.0ms
(cbrt (fma b a (* z t)))
127.0ms
(cbrt (fma b a (* z t)))

simplify3.4s

Counts
41 → 81
Calls

41 calls. Slowest were:

421.0ms
(exp (* -1/3 (+ (log (/ 1 b)) (log (/ 1 a)))))
383.0ms
(exp (* -1/3 (+ (* 2 (log (/ -1 a))) (* 2 (log (/ -1 b))))))
357.0ms
(exp (* -1/3 (+ (log (/ 1 b)) (log (/ 1 a)))))

prune1.4s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

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

series42.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

42.0ms
(fma i c (* t z))

simplify10.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

5.0ms
(+ (* t z) (* i c))
4.0ms
(+ (* t z) (* i c))
0.0ms
0

prune149.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes833.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms