Average Error: 0.0 → 0.0
Time: 5.8s
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 2019005 
(FPCore (d1 d2 d3)
  :name "FastMath dist"

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

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

Details

Time bar (total: 5.4s)Debug log

sample29.0ms

Algorithm
intervals

simplify9.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

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

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 1 expressions with local error:

0.0b
(* d1 (+ d2 d3))

rewrite3.0ms

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))

simplify100.0ms

Counts
10 → 18
Calls

10 calls. Slowest were:

58.0ms
(+ (* d2 d2) (- (* d3 d3) (* d2 d3)))
10.0ms
(+ (* d3 d1) (* d2 d1))
6.0ms
(+ (* d3 d1) (* d2 d1))

prune205.0ms

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
1 → 12
Calls

1 calls. Slowest were:

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

series33.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

33.0ms
(+ (* d2 d1) (* d3 d1))

simplify55.0ms

Counts
5 → 15
Calls

5 calls. Slowest were:

21.0ms
(* (exp (* d2 d1)) (exp (* d3 d1)))
10.0ms
(+ (* d2 d1) (* d3 d1))
10.0ms
(+ (* d3 d1) (* d2 d1))

prune130.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ d2 d3))
0.6b
(cbrt (+ d2 d3))
0.6b
(cbrt (+ d2 d3))
0.5b
(* (cbrt (+ d2 d3)) (cbrt (+ d2 d3)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
4 → 75
Calls

4 calls. Slowest were:

5.0ms
(* (cbrt (+ d2 d3)) (cbrt (+ d2 d3)))
1.0ms
(cbrt (+ d2 d3))
1.0ms
(cbrt (+ d2 d3))

series604.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

187.0ms
(* (cbrt (+ d2 d3)) (cbrt (+ d2 d3)))
153.0ms
(cbrt (+ d2 d3))
149.0ms
(cbrt (+ d2 d3))
116.0ms
(cbrt (+ d2 d3))

simplify1.6s

Counts
59 → 87
Calls

59 calls. Slowest were:

172.0ms
(- (+ (pow d3 1/3) (* 1/3 (* (pow (/ 1 (pow d3 2)) 1/3) d2))) (* 1/9 (* (pow (/ 1 (pow d3 5)) 1/3) (pow d2 2))))
160.0ms
(- (+ (pow d3 1/3) (* 1/3 (* (pow (/ 1 (pow d3 2)) 1/3) d2))) (* 1/9 (* (pow (/ 1 (pow d3 5)) 1/3) (pow d2 2))))
153.0ms
(- (+ (* 2/3 (* (pow (/ 1 d3) 1/3) d2)) (pow d3 2/3)) (* 1/9 (* (pow (/ 1 (pow d3 4)) 1/3) (pow d2 2))))

prune979.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes167.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.4s

Algorithm
intervals