Details

Time bar (total: 6.2s)

sample23.0ms

Algorithm
intervals
Results
10.0ms273×body80valid

simplify49.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0911
12111
23611
35611
48211
59911
done9911

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 6.1b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

3.2b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
4.1b
(* y (+ 1.0 (* z z)))

rewrite16.0ms

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))))
6.0ms
(* y (+ 1.0 (* z z)))

series29.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
10.0ms
(* y (+ 1.0 (* z z)))

simplify915.0ms

Counts
76 → 76
Iterations

Useful iterations: 2 (201.0ms)

IterNodesCost
01561062
14081035
21361887
done5000887

prune135.0ms

Filtered
58 candidates to 76 candidates (-31.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New69776
Fresh000
Picked101
Done000
Total70777

Merged error: 4.7b

Counts
77 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
3.2b
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
18.2b
(sqrt (+ 1.0 (* z z)))
18.2b
(sqrt (+ 1.0 (* z z)))

rewrite37.0ms

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:
11.0ms
(* (* 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)))

series36.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
18.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
4.0ms
(sqrt (+ 1.0 (* z z)))
4.0ms
(sqrt (+ 1.0 (* z z)))

simplify1.2s

Counts
129 → 129
Iterations

Useful iterations: 2 (646.0ms)

IterNodesCost
02172776
16082060
223891728
done50001728

prune214.0ms

Filtered
92 candidates to 129 candidates (-40.2%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1272129
Fresh246
Picked101
Done000
Total1306136

Merged error: 4.7b

Counts
136 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
3.3b
(/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt x) (cbrt x))) (* y (sqrt (+ 1.0 (* z z)))))
18.2b
(sqrt (+ 1.0 (* z z)))
18.2b
(sqrt (+ 1.0 (* z z)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log
29×add-cbrt-cube
18×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
7×times-frac
6×pow1 sqrt-div sqrt-prod
5×associate-/l*
4×add-log-exp
3×cbrt-prod flip3-+ flip-+ div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ associate-/r/
1×frac-2neg pow1/3 clear-num associate-/r* associate-/l/
Counts
4 → 85
Calls
4 calls:
1.0ms
(cbrt x)
15.0ms
(/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt x) (cbrt x))) (* y (sqrt (+ 1.0 (* z z)))))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series98.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(cbrt x)
68.0ms
(/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt x) (cbrt x))) (* y (sqrt (+ 1.0 (* z z)))))
4.0ms
(sqrt (+ 1.0 (* z z)))
4.0ms
(sqrt (+ 1.0 (* z z)))

simplify788.0ms

Counts
97 → 97
Iterations

Useful iterations: 2 (249.0ms)

IterNodesCost
02121923
15971692
224901368
done50001368

prune240.0ms

Filtered
70 candidates to 97 candidates (-38.6%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New97097
Fresh055
Picked011
Done000
Total976103

Merged error: 4.7b

Counts
103 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1.0 (* (sqrt (+ 1.0 (* z z))) x))
1.1b
(* (/ 1 (* y (sqrt (+ 1.0 (* z z))))) (/ 1.0 (* (sqrt (+ 1.0 (* z z))) x)))
18.2b
(sqrt (+ 1.0 (* z z)))
18.2b
(sqrt (+ 1.0 (* z z)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
87×add-exp-log
45×add-cbrt-cube
38×prod-exp
28×div-exp
16×add-sqr-sqrt cbrt-unprod
14×cbrt-undiv
12×add-cube-cbrt *-un-lft-identity
10×sqrt-div
9×times-frac associate-*r* associate-*l*
8×pow1
6×rec-exp 1-exp sqrt-prod associate-/r/
5×flip3-+ associate-*l/ flip-+
4×add-log-exp
3×associate-*r/ div-inv associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg pow-prod-down clear-num associate-/r* *-commutative unswap-sqr
Counts
4 → 114
Calls
4 calls:
7.0ms
(/ 1.0 (* (sqrt (+ 1.0 (* z z))) x))
17.0ms
(* (/ 1 (* y (sqrt (+ 1.0 (* z z))))) (/ 1.0 (* (sqrt (+ 1.0 (* z z))) x)))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series43.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(/ 1.0 (* (sqrt (+ 1.0 (* z z))) x))
18.0ms
(* (/ 1 (* y (sqrt (+ 1.0 (* z z))))) (/ 1.0 (* (sqrt (+ 1.0 (* z z))) x)))
4.0ms
(sqrt (+ 1.0 (* z z)))
7.0ms
(sqrt (+ 1.0 (* z z)))

simplify975.0ms

Counts
126 → 126
Iterations

Useful iterations: done (972.0ms)

IterNodesCost
02252720
16532338
224061590
done50011574

prune185.0ms

Filtered
82 candidates to 126 candidates (-53.7%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1242126
Fresh224
Picked011
Done011
Total1266132

Merged error: 4.7b

Counts
132 → 6

regimes373.0ms

Accuracy

0% (1.2b remaining)

Error of 6.3b against oracle of 5.1b and baseline of 6.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01733
12033
done2033

end0.0ms

sample656.0ms

Algorithm
intervals
Results
330.0ms8596×body80valid

Profiling

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