Average Error: 0.0 → 0.0
Time: 3.2s
Precision: 64
Internal Precision: 128
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
↓
\[(\left(d3 + d2\right) \cdot d1 + \left(d1 \cdot 37\right))_*\]

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Target

Original0.0
Target0.0
Herbie0.0
\[d1 \cdot \left(\left(37 + d3\right) + d2\right)\]

Derivation

  1. Initial program 0.0

    \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]

  2. Simplified0.0

    \[\leadsto \color{blue}{(\left(d2 + d3\right) \cdot d1 + \left(d1 \cdot 37\right))_*}\]

  3. Final simplification0.0

    \[\leadsto (\left(d3 + d2\right) \cdot d1 + \left(d1 \cdot 37\right))_*\]

Reproduce

herbie shell --seed 2019004 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist3"

  :herbie-target
  (* d1 (+ (+ 37 d3) d2))

  (+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32)))

Details

Time bar (total: 2.9s)Debug log

sample70.0ms

Algorithm
intervals

simplify493.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

493.0ms
(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 1 expressions with local error:

0.0b
(fma (+ d2 d3) d1 (* d1 37))

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

0.0ms
(fma (+ d2 d3) d1 (* d1 37))

series31.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

31.0ms
(fma (+ d2 d3) d1 (* d1 37))

simplify172.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

68.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 37 d1)))
56.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 37 d1)))
47.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 37 d1)))

prune108.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b
(fma d1 (+ 37 d2) (* d3 d1))

rewrite0.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

0.0ms
(fma d1 (+ 37 d2) (* d3 d1))

series27.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

27.0ms
(fma d1 (+ 37 d2) (* d3 d1))

simplify196.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

76.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 37 d1)))
72.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 37 d1)))
47.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 37 d1)))

prune115.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes148.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample1.5s

Algorithm
intervals