Details

Time bar (total: 4.6s)

sample25.0ms

Algorithm
intervals
Results
10.0ms273×body80valid

simplify46.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0911
12111
23611
35711
48511
510611
done10611

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)))

rewrite17.0ms

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:
9.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
6.0ms
(* y (+ 1.0 (* z z)))

series35.0ms

Counts
2 → 6
Calls
2 calls:
20.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
15.0ms
(* y (+ 1.0 (* z z)))

simplify418.0ms

Counts
76 → 76
Iterations

Useful iterations: 2 (120.0ms)

IterNodesCost
01561062
14101035
21513887
done5000887

prune142.0ms

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))))
15.0ms
(/ (/ 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)))

series40.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
20.0ms
(/ (/ 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)))

simplify566.0ms

Counts
129 → 129
Iterations

Useful iterations: 2 (192.0ms)

IterNodesCost
02172776
16102090
224941728
done50001728

prune231.0ms

Filtered
95 candidates to 129 candidates (-35.8%)
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)))

rewrite26.0ms

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)
16.0ms
(/ (/ (* (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)))

series111.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(cbrt x)
76.0ms
(/ (/ (* (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)))

simplify557.0ms

Counts
97 → 97
Iterations

Useful iterations: 2 (191.0ms)

IterNodesCost
02121923
15991698
225701368
done50011368

prune252.0ms

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

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log add-cbrt-cube
20×add-sqr-sqrt
18×times-frac sqrt-prod
16×add-cube-cbrt *-un-lft-identity prod-exp cbrt-unprod
14×cbrt-undiv div-exp
12×associate-*r* associate-*l*
10×sqrt-div
8×pow1
6×associate-/r/ associate-/l*
5×flip3-+ associate-*l/ flip-+
4×add-log-exp
3×associate-*r/ div-inv
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:
9.0ms
(/ (sqrt 1.0) (* (sqrt (+ 1.0 (* z z))) x))
23.0ms
(* (/ (sqrt 1.0) (* y (sqrt (+ 1.0 (* z z))))) (/ (sqrt 1.0) (* (sqrt (+ 1.0 (* z z))) x)))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series56.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(/ (sqrt 1.0) (* (sqrt (+ 1.0 (* z z))) x))
30.0ms
(* (/ (sqrt 1.0) (* y (sqrt (+ 1.0 (* z z))))) (/ (sqrt 1.0) (* (sqrt (+ 1.0 (* z z))) x)))
4.0ms
(sqrt (+ 1.0 (* z z)))
4.0ms
(sqrt (+ 1.0 (* z z)))

simplify618.0ms

Counts
126 → 126
Iterations

Useful iterations: done (614.0ms)

IterNodesCost
02172825
16302389
228811715
done50011651

prune257.0ms

Filtered
89 candidates to 126 candidates (-41.6%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1242126
Fresh224
Picked011
Done011
Total1266132

Merged error: 4.7b

Counts
132 → 6

regimes419.0ms

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

sample691.0ms

Algorithm
intervals
Results
336.0ms8596×body80valid

Profiling

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