Average Error: 0.0 → 0.0
Time: 5.5s
Precision: 64
Internal Precision: 128
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
↓
\[(d1 \cdot \left(37 + d2\right) + \left(d3 \cdot d1\right))_*\]

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. Taylor expanded around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019008 +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: 5.1s)Debug log

sample78.0ms

Algorithm
intervals

simplify554.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

554.0ms
(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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))

series28.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

28.0ms
(fma (+ d2 d3) d1 (* d1 37))

simplify178.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

77.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 37 d1)))
51.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 37 d1)))
50.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 37 d1)))

prune145.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

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

series23.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

23.0ms
(fma d1 (+ 37 d2) (* d3 d1))

simplify187.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

75.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 37 d1)))
62.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 37 d1)))
50.0ms
(+ (* d2 d1) (+ (* d3 d1) (* 37 d1)))

prune123.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))
0.0b
(+ (* d1 d2) (* (+ d3 5) d1))
0.0b
(* (+ d3 5) d1)

rewrite25.0ms

Algorithm
rewrite-expression-head
Counts
3 → 47
Calls

3 calls. Slowest were:

14.0ms
(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))
5.0ms
(+ (* d1 d2) (* (+ d3 5) d1))
5.0ms
(* (+ d3 5) d1)

series100.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

41.0ms
(+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32))
36.0ms
(+ (* d1 d2) (* (+ d3 5) d1))
24.0ms
(* (+ d3 5) d1)

simplify1.3s

Counts
19 → 56
Calls

19 calls. Slowest were:

226.0ms
(* (exp (+ (* d1 d2) (* (+ d3 5) d1))) (exp (* d1 32)))
193.0ms
(* (* (exp (* d1 d2)) (exp (* (+ d3 5) d1))) (exp (* d1 32)))
161.0ms
(* (exp (* d1 d2)) (exp (* (+ d3 5) d1)))

prune511.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes198.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample1.6s

Algorithm
intervals