Average Error: 0.0 → 0.0
Time: 6.2s
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 2019002 
(FPCore (d1 d2 d3)
  :name "FastMath dist"

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

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

Details

Time bar (total: 5.8s)Debug log

sample52.0ms

Algorithm
intervals

simplify10.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

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

prune18.0ms

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))

series27.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

27.0ms
(* d1 (+ d2 d3))

simplify65.0ms

Counts
10 → 18
Calls

10 calls. Slowest were:

40.0ms
(+ (* d2 d2) (- (* d3 d3) (* d2 d3)))
7.0ms
(+ (* d3 d1) (* d2 d1))
5.0ms
(+ (* d2 d1) (* d3 d1))

prune164.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 1 expressions with local error:

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

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
1 → 12
Calls

1 calls. Slowest were:

4.0ms
(+ (* d1 d2) (* d1 d3))

series31.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

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

simplify53.0ms

Counts
5 → 15
Calls

5 calls. Slowest were:

19.0ms
(* (exp (* d1 d2)) (exp (* d1 d3)))
12.0ms
(+ (* d3 d1) (* d2 d1))
10.0ms
(+ (* d3 d1) (* d2 d1))

prune115.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize5.0ms

Local error

Found 4 expressions with local error:

3.7b
(sqrt (* d1 (+ d2 d3)))
3.7b
(sqrt (* d1 (+ d2 d3)))
0.2b
(* (sqrt (* d1 (+ d2 d3))) (sqrt (* d1 (+ d2 d3))))
0.0b
(* d1 (+ d2 d3))

rewrite9.0ms

Algorithm
rewrite-expression-head
Counts
4 → 71
Calls

4 calls. Slowest were:

6.0ms
(* (sqrt (* d1 (+ d2 d3))) (sqrt (* d1 (+ d2 d3))))
1.0ms
(* d1 (+ d2 d3))
1.0ms
(sqrt (* d1 (+ d2 d3)))

series124.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

46.0ms
(sqrt (* d1 (+ d2 d3)))
40.0ms
(sqrt (* d1 (+ d2 d3)))
21.0ms
(* (sqrt (* d1 (+ d2 d3))) (sqrt (* d1 (+ d2 d3))))
17.0ms
(* d1 (+ d2 d3))

simplify3.1s

Counts
55 → 83
Calls

55 calls. Slowest were:

434.0ms
(* (sqrt (* d1 (+ (pow d2 3) (pow d3 3)))) (sqrt (* d1 (- (* d2 d2) (* d3 d3)))))
364.0ms
(* (* (* (sqrt (* d1 (+ d2 d3))) (sqrt (* d1 (+ d2 d3)))) (sqrt (* d1 (+ d2 d3)))) (* (* (sqrt (* d1 (+ d2 d3))) (sqrt (* d1 (+ d2 d3)))) (sqrt (* d1 (+ d2 d3)))))
329.0ms
(* (* d1 (+ d2 d3)) (* d1 (+ d2 d3)))

prune742.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes166.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.0s

Algorithm
intervals