Average Error: 0.0 → 0.0
Time: 2.6s
Precision: 64
Internal Precision: 128
\[d1 \cdot d2 + d1 \cdot d3\]
↓
\[(d1 \cdot d2 + \left(d1 \cdot d3\right))_*\]

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Target

Original0.0
Target0.0
Herbie0.0
\[d1 \cdot \left(d2 + d3\right)\]

Derivation

  1. Initial program 0.0

    \[d1 \cdot d2 + d1 \cdot d3\]
  2. Using strategy rm

  3. Applied fma-def0.0

    \[\leadsto \color{blue}{(d1 \cdot d2 + \left(d1 \cdot d3\right))_*}\]

  4. Final simplification0.0

    \[\leadsto (d1 \cdot d2 + \left(d1 \cdot d3\right))_*\]

Reproduce

herbie shell --seed 2019008 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist"

  :herbie-target
  (* d1 (+ d2 d3))

  (+ (* d1 d2) (* d1 d3)))

Details

Time bar (total: 2.2s)Debug log

sample39.0ms

Algorithm
intervals

simplify12.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

12.0ms
(+ (* d1 d2) (* d1 d3))

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (+ d2 d3) d1)

rewrite3.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

3.0ms
(* (+ d2 d3) d1)

series19.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

19.0ms
(* (+ d2 d3) d1)

simplify264.0ms

Counts
7 → 18
Calls

7 calls. Slowest were:

199.0ms
(* (- (* d2 d2) (* d3 d3)) d1)
43.0ms
(* (+ (pow d2 3) (pow d3 3)) d1)
7.0ms
(+ (* d3 d1) (* d2 d1))

prune145.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b
(+ (* d1 d2) (* d1 d3))

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

2.0ms
(+ (* d1 d2) (* d1 d3))

series27.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

27.0ms
(+ (* d1 d2) (* d1 d3))

simplify31.0ms

Counts
5 → 18
Calls

5 calls. Slowest were:

11.0ms
(* (exp (* d1 d2)) (exp (* d1 d3)))
6.0ms
(+ (* d3 d1) (* d2 d1))
6.0ms
(+ (* d3 d1) (* d2 d1))

prune205.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b
(fma d1 d2 (* d1 d3))

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

0.0ms
(fma d1 d2 (* d1 d3))

series35.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

35.0ms
(fma d1 d2 (* d1 d3))

simplify23.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

10.0ms
(+ (* d2 d1) (* d3 d1))
6.0ms
(+ (* d3 d1) (* d2 d1))
6.0ms
(+ (* d3 d1) (* d2 d1))

prune124.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes86.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.2s

Algorithm
intervals