Details

Time bar (total: 6.0s)

sample18.0ms

Algorithm
intervals
Results
9.0ms274×body80valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0215
1375
2615
3915
41155
51215
61215

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 6.4b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

3.9b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
4.3b
(* y (+ 1.0 (* z z)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
20×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity
16×add-exp-log add-cbrt-cube
13×associate-/l*
6×cbrt-undiv div-exp
4×pow1 associate-*r/
3×associate-*r* associate-*l* prod-exp cbrt-unprod div-inv
2×flip3-+ associate-/r/ flip-+ add-log-exp
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num associate-/r* *-commutative associate-/l/ unswap-sqr
Counts
2 → 70
Calls
2 calls:
8.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
5.0ms
(* y (+ 1.0 (* z z)))

series109.0ms

Counts
2 → 6
Calls
2 calls:
54.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
55.0ms
(* y (+ 1.0 (* z z)))

simplify48.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0409511
11963443
25001443

prune156.0ms

Filtered
76 candidates to 56 candidates (73.7%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New70676
Fresh000
Picked101
Done000
Total71677

Merged error: 4.8b

Counts
77 → 6

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (/ 1.0 y) x)
5.6b
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
468×times-frac
228×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
56×associate-/l*
22×div-inv
16×add-exp-log add-cbrt-cube
9×cbrt-undiv div-exp
6×associate-/r*
2×pow1 frac-2neg clear-num associate-/r/ associate-/l/ add-log-exp
1×flip3-+ flip-+
Counts
2 → 264
Calls
2 calls:
6.0ms
(/ (/ 1.0 y) x)
14.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

series78.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(/ (/ 1.0 y) x)
59.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

simplify107.0ms

Algorithm
egg-herbie
Counts
270 → 270
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
011322994
145722919
250022919

prune712.0ms

Filtered
270 candidates to 233 candidates (86.3%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2682270
Fresh235
Picked011
Done000
Total2706276

Merged error: 4.8b

Counts
276 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 x) (sqrt (+ 1.0 (* z z))))
0.8b
(* (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
16.6b
(sqrt (+ 1.0 (* z z)))
16.6b
(sqrt (+ 1.0 (* z z)))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
497×times-frac
375×add-sqr-sqrt
231×*-un-lft-identity
221×add-cube-cbrt
155×sqrt-prod
84×associate-*r* associate-*l*
73×add-exp-log
45×add-cbrt-cube
39×div-exp
35×unswap-sqr
22×div-inv
21×cbrt-undiv
15×prod-exp
13×associate-/l*
10×sqrt-div
9×cbrt-unprod
8×pow1
6×associate-/r* associate-/r/
5×flip3-+ flip-+
4×rec-exp 1-exp add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 385
Calls
4 calls:
9.0ms
(/ (/ 1 x) (sqrt (+ 1.0 (* z z))))
106.0ms
(* (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
2.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series434.0ms

Counts
4 → 12
Calls
4 calls:
261.0ms
(/ (/ 1 x) (sqrt (+ 1.0 (* z z))))
63.0ms
(* (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
63.0ms
(sqrt (+ 1.0 (* z z)))
46.0ms
(sqrt (+ 1.0 (* z z)))

simplify91.0ms

Algorithm
egg-herbie
Counts
397 → 397
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
015705406
150015036

prune826.0ms

Filtered
397 candidates to 230 candidates (57.9%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New3961397
Fresh134
Picked011
Done011
Total3976403

Merged error: 4.8b

Counts
403 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (/ (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) x) (/ 1 (sqrt (+ 1.0 (* z z)))))
1.6b
(/ (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) x)
16.6b
(sqrt (+ 1.0 (* z z)))
16.6b
(sqrt (+ 1.0 (* z z)))

rewrite212.0ms

Algorithm
rewrite-expression-head
Rules
1525×times-frac
801×add-sqr-sqrt
684×*-un-lft-identity
672×add-cube-cbrt
310×sqrt-prod
256×associate-*l*
84×associate-/l*
73×add-exp-log
52×div-inv
45×add-cbrt-cube
38×div-exp
30×unswap-sqr
24×associate-*r*
22×cbrt-undiv
20×sqrt-div
16×prod-exp associate-/r/
10×flip3-+ flip-+
8×pow1 cbrt-unprod
4×rec-exp 1-exp add-log-exp
3×associate-/r*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative associate-/l/
Counts
4 → 733
Calls
4 calls:
112.0ms
(* (/ (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) x) (/ 1 (sqrt (+ 1.0 (* z z)))))
26.0ms
(/ (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) x)
2.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series238.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* (/ (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) x) (/ 1 (sqrt (+ 1.0 (* z z)))))
84.0ms
(/ (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) x)
46.0ms
(sqrt (+ 1.0 (* z z)))
42.0ms
(sqrt (+ 1.0 (* z z)))

simplify149.0ms

Algorithm
egg-herbie
Counts
745 → 745
Iterations

Useful iterations: 1 (50.0ms)

IterNodesCost
0282810678
1500110106

prune2.0s

Filtered
745 candidates to 526 candidates (70.6%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New7450745
Fresh033
Picked011
Done022
Total7456751

Merged error: 4.8b

Counts
751 → 6

regimes176.0ms

Accuracy

0% (1.1b remaining)

Error of 5.9b against oracle of 4.8b and baseline of 5.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01711
11711

end0.0ms

sample408.0ms

Algorithm
intervals
Results
238.0ms8629×body80valid