Details

Time bar (total: 3.0s)

sample27.0ms

Algorithm
intervals
Results
14.0ms280×body80valid

simplify19.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0215
1375
2615
3915
41155
51215
61215

prune3.0ms

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

localize16.0ms

Local error

Found 2 expressions with local error:

3.3b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
4.0b
(* y (+ 1.0 (* z z)))

rewrite26.0ms

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:
14.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
9.0ms
(* y (+ 1.0 (* z z)))

series121.0ms

Counts
2 → 6
Calls
2 calls:
59.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
62.0ms
(* y (+ 1.0 (* z z)))

simplify47.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0409511
11963443
25001443

prune155.0ms

Filtered
76 candidates to 56 candidates (73.7%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New67976
Fresh000
Picked101
Done000
Total68977

Merged error: 4.8b

Counts
77 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
3.3b
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
14.7b
(sqrt (+ 1.0 (* z z)))
14.7b
(sqrt (+ 1.0 (* z z)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
30×add-exp-log add-cbrt-cube
28×sqrt-div
24×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
16×associate-*r/
14×flip3-+ flip-+
13×associate-/l*
11×pow1
9×cbrt-undiv div-exp prod-exp sqrt-prod cbrt-unprod
8×frac-times associate-/r/
6×associate-*r*
4×associate-*l/ add-log-exp
3×pow-prod-down div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-2neg associate-*l* clear-num associate-/r* *-commutative associate-/l/
Counts
4 → 117
Calls
4 calls:
10.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
14.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series210.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
57.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
48.0ms
(sqrt (+ 1.0 (* z z)))
48.0ms
(sqrt (+ 1.0 (* z z)))

simplify69.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
06101242
128861023
250021005

prune251.0ms

Filtered
129 candidates to 93 candidates (72.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1281129
Fresh178
Picked101
Done000
Total1308138

Merged error: 4.8b

Counts
138 → 8

localize7.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ 1.0 (* (* y (+ 1.0 (* z z))) x))
3.2b
(* (* y (+ 1.0 (* z z))) x)
4.0b
(* y (+ 1.0 (* z z)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log add-cbrt-cube
10×pow1 add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
7×prod-exp cbrt-unprod
6×associate-*r/ associate-*r*
4×associate-*l* pow-prod-down associate-*l/
3×cbrt-undiv flip3-+ times-frac div-exp flip-+ associate-/l* add-log-exp
2×associate-/r/ *-commutative
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r* div-inv unswap-sqr
Counts
3 → 67
Calls
3 calls:
7.0ms
(/ 1.0 (* (* y (+ 1.0 (* z z))) x))
6.0ms
(* (* y (+ 1.0 (* z z))) x)
5.0ms
(* y (+ 1.0 (* z z)))

series172.0ms

Counts
3 → 9
Calls
3 calls:
68.0ms
(/ 1.0 (* (* y (+ 1.0 (* z z))) x))
48.0ms
(* (* y (+ 1.0 (* z z))) x)
57.0ms
(* y (+ 1.0 (* z z)))

simplify51.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0367480
12077394
25002394

prune119.0ms

Filtered
76 candidates to 51 candidates (67.1%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New75176
Fresh167
Picked011
Done000
Total76884

Merged error: 4.8b

Counts
84 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ (/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z))))) (sqrt (+ 1.0 (* z z))))
2.6b
(/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z)))))
14.7b
(sqrt (+ 1.0 (* z z)))
14.7b
(sqrt (+ 1.0 (* z z)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
299×times-frac
118×add-sqr-sqrt
116×add-cube-cbrt *-un-lft-identity
66×sqrt-prod
34×add-exp-log add-cbrt-cube
32×associate-/l*
22×sqrt-div
18×associate-/r/ div-inv
17×cbrt-undiv div-exp
16×associate-*r/
11×flip3-+ flip-+
7×associate-/r*
6×pow1
4×prod-exp cbrt-unprod add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 240
Calls
4 calls:
20.0ms
(/ (/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z))))) (sqrt (+ 1.0 (* z z))))
9.0ms
(/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z)))))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series248.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(/ (/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z))))) (sqrt (+ 1.0 (* z z))))
92.0ms
(/ (/ 1.0 x) (* y (sqrt (+ 1.0 (* z z)))))
50.0ms
(sqrt (+ 1.0 (* z z)))
44.0ms
(sqrt (+ 1.0 (* z z)))

simplify106.0ms

Algorithm
egg-herbie
Counts
252 → 252
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
09633413
140853172
250023077

prune495.0ms

Filtered
252 candidates to 176 candidates (69.8%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2520252
Fresh066
Picked011
Done011
Total2528260

Merged error: 4.8b

Counts
260 → 8

regimes241.0ms

Accuracy

31.2% (1.1b remaining)

Error of 5.9b against oracle of 4.7b and baseline of 6.4b

bsearch2.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02312
12312

end0.0ms

sample512.0ms

Algorithm
intervals
Results
333.0ms8599×body80valid

Profiling

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