Average Error: 0.0 → 0.0
Time: 11.3s
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 2019007 
(FPCore (d1 d2 d3)
  :name "FastMath dist"

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

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

Details

Time bar (total: 10.8s)Debug log

sample38.0ms

Algorithm
intervals

simplify5.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

5.0ms
(+ (* d1 d2) (* d1 d3))

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

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))

series28.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

27.0ms
(* d1 (+ d2 d3))

simplify72.0ms

Counts
10 → 18
Calls

10 calls. Slowest were:

34.0ms
(+ (* d2 d2) (- (* d3 d3) (* d2 d3)))
12.0ms
(cbrt (+ d2 d3))
5.0ms
(+ (* d3 d1) (* d2 d1))

prune174.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

3.1b
(cbrt (* d1 (+ d2 d3)))
3.1b
(cbrt (* d1 (+ d2 d3)))
3.1b
(cbrt (* d1 (+ d2 d3)))
0.4b
(* (cbrt (* d1 (+ d2 d3))) (cbrt (* d1 (+ d2 d3))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Counts
4 → 65
Calls

4 calls. Slowest were:

13.0ms
(* (cbrt (* d1 (+ d2 d3))) (cbrt (* d1 (+ d2 d3))))
2.0ms
(cbrt (* d1 (+ d2 d3)))
2.0ms
(cbrt (* d1 (+ d2 d3)))

series558.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

164.0ms
(* (cbrt (* d1 (+ d2 d3))) (cbrt (* d1 (+ d2 d3))))
154.0ms
(cbrt (* d1 (+ d2 d3)))
133.0ms
(cbrt (* d1 (+ d2 d3)))
107.0ms
(cbrt (* d1 (+ d2 d3)))

simplify4.7s

Counts
49 → 77
Calls

49 calls. Slowest were:

376.0ms
(* (cbrt (* d1 (- (* d2 d2) (* d3 d3)))) (cbrt (* d1 (+ (pow d2 3) (pow d3 3)))))
332.0ms
(* (cbrt (* d1 (- (* d2 d2) (* d3 d3)))) (cbrt (* d1 (- (* d2 d2) (* d3 d3)))))
315.0ms
(exp (* -1/3 (+ (log (/ 1 d1)) (log (/ 1 d2)))))

prune859.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

17.6b
(/ (* d1 (- (* d2 d2) (* d3 d3))) (- d2 d3))
10.8b
(* d1 (- (* d2 d2) (* d3 d3)))
3.4b
(- (* d2 d2) (* d3 d3))

rewrite13.0ms

Algorithm
rewrite-expression-head
Counts
3 → 54
Calls

3 calls. Slowest were:

7.0ms
(/ (* d1 (- (* d2 d2) (* d3 d3))) (- d2 d3))
4.0ms
(* d1 (- (* d2 d2) (* d3 d3)))
2.0ms
(- (* d2 d2) (* d3 d3))

series116.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

60.0ms
(/ (* d1 (- (* d2 d2) (* d3 d3))) (- d2 d3))
39.0ms
(* d1 (- (* d2 d2) (* d3 d3)))
17.0ms
(- (* d2 d2) (* d3 d3))

simplify2.3s

Counts
37 → 63
Calls

37 calls. Slowest were:

426.0ms
(/ (- (* d2 d2) (* d3 d3)) (- d2 d3))
408.0ms
(* d1 (- (* (* d2 d2) (* d2 d2)) (* (* d3 d3) (* d3 d3))))
280.0ms
(* d1 (- (pow (* d2 d2) 3) (pow (* d3 d3) 3)))

prune613.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes179.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample1.1s

Algorithm
intervals