Average Error: 0.0 → 0.0
Time: 2.1s
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 2019016 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist"

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

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

Details

Time bar (total: 1.8s)Debug log

sample26.0ms

Algorithm
intervals
Results
330×(pre true 80)
330×(body real 80)

simplify6.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
6.0ms
(+ (* d1 d2) (* d1 d3))

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
3×add-log-exp
1×distribute-lft-out
1×log1p-expm1-u
1×flip-+
1×add-cube-cbrt
1×add-exp-log
1×add-cbrt-cube
1×flip3-+
1×*-un-lft-identity
1×fma-def
1×sum-log
1×+-commutative
1×pow1
1×expm1-log1p-u
1×add-sqr-sqrt
Counts
1 → 15
Calls
1 calls:
Slowest
2.0ms
(+ (* d1 d2) (* d1 d3))

series20.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
20.0ms
(+ (* d1 d2) (* d1 d3))

simplify37.0ms

Counts
5 → 18
Calls
5 calls:
Slowest
14.0ms
(* (exp (* d1 d2)) (exp (* d1 d3)))
7.0ms
(+ (* d2 d1) (* d3 d1))
6.0ms
(+ (* d3 d1) (* d2 d1))
6.0ms
(+ (* d3 d1) (* d2 d1))
3.0ms
(+ d2 d3)

prune155.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×add-log-exp
1×log1p-expm1-u
1×fma-udef
1×add-cube-cbrt
1×add-exp-log
1×add-cbrt-cube
1×*-un-lft-identity
1×pow1
1×expm1-log1p-u
1×add-sqr-sqrt
Counts
1 → 10
Calls
1 calls:
Slowest
0.0ms
(fma d1 d2 (* d1 d3))

series34.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
34.0ms
(fma d1 d2 (* d1 d3))

simplify38.0ms

Counts
3 → 13
Calls
3 calls:
Slowest
14.0ms
(+ (* d2 d1) (* d3 d1))
12.0ms
(+ (* d3 d1) (* d2 d1))
11.0ms
(+ (* d3 d1) (* d2 d1))

prune125.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0.0b

end0.0ms

sample1.3s

Algorithm
intervals
Results
10125×(pre true 80)
10125×(body real 80)