Average Error: 0.0 → 0.0
Time: 13.0s
Precision: 64
Internal Precision: 128
\[d1 \cdot d2 + d1 \cdot d3\]
↓
\[\left(d3 + d2\right) \cdot d1\]

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019007 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist"

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

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

Details

Time bar (total: 12.5s)Debug log

sample26.0ms

Algorithm
intervals

simplify11.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

11.0ms
(+ (* d1 d2) (* d1 d3))

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (+ d2 d3) d1)

rewrite3.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

3.0ms
(* (+ d2 d3) d1)

series16.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

15.0ms
(* (+ d2 d3) d1)

simplify272.0ms

Counts
7 → 18
Calls

7 calls. Slowest were:

201.0ms
(* (- (* d2 d2) (* d3 d3)) d1)
42.0ms
(* (+ (pow d2 3) (pow d3 3)) d1)
13.0ms
(* (cbrt (+ d2 d3)) (cbrt (+ d2 d3)))

prune124.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite15.0ms

Algorithm
rewrite-expression-head
Counts
4 → 73
Calls

4 calls. Slowest were:

9.0ms
(* (cbrt (* (+ d2 d3) d1)) (cbrt (* (+ d2 d3) d1)))
2.0ms
(cbrt (* (+ d2 d3) d1))
2.0ms
(cbrt (* (+ d2 d3) d1))

series433.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

112.0ms
(* (cbrt (* (+ d2 d3) d1)) (cbrt (* (+ d2 d3) d1)))
111.0ms
(cbrt (* (+ d2 d3) d1))
107.0ms
(cbrt (* (+ d2 d3) d1))
103.0ms
(cbrt (* (+ d2 d3) d1))

simplify5.5s

Counts
49 → 85
Calls

49 calls. Slowest were:

400.0ms
(exp (* -1/3 (+ (log (/ 1 d1)) (log (/ 1 d2)))))
394.0ms
(exp (* -1/3 (+ (* 2 (log (/ -1 d1))) (* 2 (log (/ -1 d2))))))
393.0ms
(exp (* -1/3 (+ (log (/ 1 d1)) (log (/ 1 d2)))))

prune831.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize31.0ms

Local error

Found 3 expressions with local error:

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

rewrite27.0ms

Algorithm
rewrite-expression-head
Counts
3 → 58
Calls

3 calls. Slowest were:

14.0ms
(/ (* (- (* d2 d2) (* d3 d3)) d1) (- d2 d3))
9.0ms
(* (- (* d2 d2) (* d3 d3)) d1)
4.0ms
(- (* d2 d2) (* d3 d3))

series131.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

57.0ms
(/ (* (- (* d2 d2) (* d3 d3)) d1) (- d2 d3))
46.0ms
(* (- (* d2 d2) (* d3 d3)) d1)
27.0ms
(- (* d2 d2) (* d3 d3))

simplify3.4s

Counts
35 → 67
Calls

35 calls. Slowest were:

643.0ms
(* (- (* (* d2 d2) (* d2 d2)) (* (* d3 d3) (* d3 d3))) d1)
562.0ms
(* (- (* (* d2 d2) (* d2 d2)) (* (* d3 d3) (* d3 d3))) d1)
344.0ms
(- (log (* (- (* d2 d2) (* d3 d3)) d1)) (log (- d2 d3)))

prune555.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes137.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample893.0ms

Algorithm
intervals