Average Error: 0.0 → 0.0
Time: 5.4s
Precision: 64
Internal Precision: 128
\[d1 \cdot d2 + d1 \cdot d3\]
↓
\[\left(d2 + d3\right) \cdot d1\]

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019004 
(FPCore (d1 d2 d3)
  :name "FastMath dist"

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

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

Details

Time bar (total: 4.9s)Debug log

sample55.0ms

Algorithm
intervals

simplify9.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

9.0ms
(+ (* d1 d2) (* d1 d3))

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 1 expressions with local error:

0.0b
(* d1 (+ d2 d3))

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

2.0ms
(* d1 (+ d2 d3))

series29.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

29.0ms
(* d1 (+ d2 d3))

simplify122.0ms

Counts
10 → 18
Calls

10 calls. Slowest were:

76.0ms
(+ (* d2 d2) (- (* d3 d3) (* d2 d3)))
9.0ms
(+ (* d3 d1) (* d2 d1))
9.0ms
(+ (* d2 d1) (* d3 d1))

prune124.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
1 → 12
Calls

1 calls. Slowest were:

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

series27.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

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

simplify56.0ms

Counts
5 → 15
Calls

5 calls. Slowest were:

19.0ms
(* (exp (* d2 d1)) (exp (* d3 d1)))
13.0ms
(+ (* d3 d1) (* d2 d1))
10.0ms
(+ (* d3 d1) (* d2 d1))

prune170.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize27.0ms

Local error

Found 3 expressions with local error:

18.6b
(/ (* d1 (- (* d2 d2) (* d3 d3))) (- d2 d3))
9.1b
(* d1 (- (* d2 d2) (* d3 d3)))
3.0b
(- (* d2 d2) (* d3 d3))

rewrite12.0ms

Algorithm
rewrite-expression-head
Counts
3 → 54
Calls

3 calls. Slowest were:

6.0ms
(/ (* d1 (- (* d2 d2) (* d3 d3))) (- d2 d3))
3.0ms
(* d1 (- (* d2 d2) (* d3 d3)))
2.0ms
(- (* d2 d2) (* d3 d3))

series171.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

83.0ms
(/ (* d1 (- (* d2 d2) (* d3 d3))) (- d2 d3))
61.0ms
(* d1 (- (* d2 d2) (* d3 d3)))
26.0ms
(- (* d2 d2) (* d3 d3))

simplify2.2s

Counts
37 → 63
Calls

37 calls. Slowest were:

385.0ms
(* d1 (- (* (* d2 d2) (* d2 d2)) (* (* d3 d3) (* d3 d3))))
361.0ms
(/ (- (* d2 d2) (* d3 d3)) (- d2 d3))
314.0ms
(* d1 (- (pow (* d2 d2) 3) (pow (* d3 d3) 3)))

prune465.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes105.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.3s

Algorithm
intervals