Average Error: 0.0 → 0.0
Time: 23.2s
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 2018365 +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: 18.6s)Debug log

start140.0ms

Algorithm
intervals

setup137.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

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))

series301.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

258.0ms
(+ (fma b a (* z t)) (fma i c (* x y)))
43.0ms
(fma i c (* x y))

simplify295.0ms

Counts
12 → 35
Calls

12 calls. Slowest were:

146.0ms
(* (exp (fma b a (* z t))) (exp (fma i c (* x y))))
45.0ms
(+ (fma b a (* z t)) (fma i c (* x y)))
30.0ms
(+ (* i c) (+ (* t z) (* x y)))

prune504.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

2.7b
(cbrt (fma b a (* z t)))
2.7b
(cbrt (fma b a (* z t)))
2.7b
(cbrt (fma b a (* z t)))
0.5b
(* (cbrt (fma b a (* z t))) (cbrt (fma b a (* z t))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
4 → 69
Calls

4 calls. Slowest were:

7.0ms
(* (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)))

series524.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

144.0ms
(* (cbrt (fma b a (* z t))) (cbrt (fma b a (* z t))))
139.0ms
(cbrt (fma b a (* z t)))
125.0ms
(cbrt (fma b a (* z t)))
116.0ms
(cbrt (fma b a (* z t)))

simplify3.6s

Counts
41 → 81
Calls

41 calls. Slowest were:

476.0ms
(exp (* -1/3 (+ (* 2 (log (/ -1 a))) (* 2 (log (/ -1 b))))))
432.0ms
(exp (* -1/3 (+ (log (/ 1 b)) (log (/ 1 a)))))
416.0ms
(exp (* -1/3 (+ (log (/ 1 b)) (log (/ 1 a)))))

prune1.5s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

2.7b
(cbrt (fma b a (* z t)))
2.7b
(cbrt (fma b a (* z t)))
2.7b
(cbrt (fma b a (* z t)))
2.7b
(cbrt (fma b a (* z t)))

rewrite3.0ms

Algorithm
rewrite-expression-head
Counts
4 → 52
Calls

4 calls. Slowest were:

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

series518.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

138.0ms
(cbrt (fma b a (* z t)))
130.0ms
(cbrt (fma b a (* z t)))
127.0ms
(cbrt (fma b a (* z t)))
123.0ms
(cbrt (fma b a (* z t)))

simplify3.3s

Counts
24 → 64
Calls

24 calls. Slowest were:

438.0ms
(exp (* -1/3 (+ (log (/ 1 b)) (log (/ 1 a)))))
407.0ms
(exp (* -1/3 (+ (log (/ 1 b)) (log (/ 1 a)))))
397.0ms
(exp (* -1/3 (+ (log (/ 1 b)) (log (/ 1 a)))))

prune1.4s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

2.7b
(cbrt (fma b a (* z t)))
2.7b
(cbrt (fma b a (* z t)))
2.7b
(cbrt (fma b a (* z t)))
2.7b
(cbrt (fma b a (* z t)))

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
4 → 52
Calls

4 calls. Slowest were:

1.0ms
(cbrt (fma b a (* z t)))
0.0ms
(cbrt (fma b a (* z t)))
0.0ms
(cbrt (fma b a (* z t)))

series530.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

150.0ms
(cbrt (fma b a (* z t)))
140.0ms
(cbrt (fma b a (* z t)))
123.0ms
(cbrt (fma b a (* z t)))
116.0ms
(cbrt (fma b a (* z t)))

simplify3.4s

Counts
24 → 64
Calls

24 calls. Slowest were:

423.0ms
(exp (* -1/3 (+ (log (/ 1 b)) (log (/ 1 a)))))
406.0ms
(exp (* -1/3 (+ (log (/ 1 b)) (log (/ 1 a)))))
405.0ms
(exp (* -1/3 (+ (log (/ 1 b)) (log (/ 1 a)))))

prune1.3s

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.0b

regimes1.0s

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms