Details

Time bar (total: 6.3s)

sample67.0ms

Algorithm
intervals
Results
27.0ms64×body1280valid
14.0ms54×body640valid
8.0ms23×body2560valid
4.0ms25×body320valid
3.0ms71×body80valid
2.0ms19×body160valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
079
199
done99

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 52.8b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.9b
(+ x (sqrt (+ (* x x) 1.0)))
5.1b
(log (+ x (sqrt (+ (* x x) 1.0))))
14.7b
(sqrt (+ (* x x) 1.0))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
6×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×add-exp-log log-prod
3×flip3-+ sqrt-prod add-cbrt-cube flip-+
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow
Counts
3 → 42
Calls
3 calls:
6.0ms
(+ x (sqrt (+ (* x x) 1.0)))
6.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
9.0ms
(sqrt (+ (* x x) 1.0))

series19.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ x (sqrt (+ (* x x) 1.0)))
10.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

simplify632.0ms

Counts
51 → 51
Iterations

Useful iterations: 3 (234.0ms)

IterNodesCost
0134761
1310695
2854618
32809600
done5000600

prune141.0ms

Filtered
43 candidates to 51 candidates (-18.6%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New45651
Fresh000
Picked101
Done000
Total46652

Merged error: 0.1b

Counts
52 → 6

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
0.3b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
182×add-sqr-sqrt
140×unpow-prod-down cube-prod
118×add-cube-cbrt *-un-lft-identity
80×sqrt-prod
40×sqr-pow
30×cube-mult unpow3
25×add-exp-log unswap-sqr
10×prod-exp
9×div-exp
7×add-cbrt-cube
6×pow-to-exp pow-exp add-log-exp
4×pow1
3×associate-*r/ associate-*l*
2×diff-log frac-sub cbrt-unprod
1×cbrt-undiv sub-neg flip3-- flip3-+ pow-prod-down associate--l+ sum-log *-commutative flip-- flip-+ div-inv
Counts
2 → 286
Calls
2 calls:
13.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
56.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series30.0ms

Counts
2 → 6
Calls
2 calls:
13.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
17.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify672.0ms

Counts
292 → 292
Iterations

Useful iterations: 2 (246.0ms)

IterNodesCost
03364436
18733464
234872955
done50002955

prune446.0ms

Filtered
111 candidates to 292 candidates (-163.1%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2902292
Fresh055
Picked011
Done000
Total2908298

Merged error: 0.1b

Counts
298 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.0625 (pow x 5))
0.5b
(/ 0.125 (pow x 3))
10.5b
(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
16.8b
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
69×times-frac
68×*-un-lft-identity
66×add-sqr-sqrt
46×add-cube-cbrt
26×unpow-prod-down
19×associate-/r*
15×add-exp-log
12×cube-prod
10×log-prod distribute-lft-out-- sqr-pow
9×add-log-exp
8×frac-sub add-cbrt-cube difference-of-squares
6×div-exp associate-/l*
5×pow1 log-div
4×cube-mult flip3-- unpow3 flip--
3×diff-log
2×cbrt-undiv pow-to-exp sub-neg frac-2neg pow-exp associate--l+ clear-num div-inv
1×associate--l- rem-log-exp log-pow
Counts
4 → 160
Calls
4 calls:
5.0ms
(/ 0.0625 (pow x 5))
6.0ms
(/ 0.125 (pow x 3))
52.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
48.0ms
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

series29.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 0.0625 (pow x 5))
4.0ms
(/ 0.125 (pow x 3))
14.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
6.0ms
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

simplify488.0ms

Counts
172 → 172
Iterations

Useful iterations: 2 (174.0ms)

IterNodesCost
03182874
16682609
221152457
done50002457

prune356.0ms

Filtered
111 candidates to 172 candidates (-55.0%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1720172
Fresh066
Picked011
Done011
Total1728180

Merged error: 0.1b

Counts
180 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (log 2) (/ 0.25 (* x x)))
0.1b
(/ 0.09375 (pow x 4))
0.2b
(/ 0.25 (* x x))
8.1b
(- (+ (log 2) (/ 0.25 (* x x))) (- (/ 0.09375 (pow x 4)) (log x)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
50×*-un-lft-identity
25×add-sqr-sqrt
24×times-frac
23×add-cube-cbrt
15×distribute-lft-out--
14×add-exp-log
13×add-log-exp
12×unpow-prod-down
11×pow1 add-cbrt-cube
8×associate-/r* distribute-lft-out
7×log-pow
6×diff-log associate-/l*
5×div-exp
4×frac-sub sqr-pow
3×cbrt-undiv associate-+l+ log-prod flip3-- flip3-+ sum-log flip-- flip-+
2×sub-neg frac-2neg clear-num div-inv associate--r+
1×+-commutative pow-to-exp pow-exp prod-exp associate--l+ cbrt-unprod associate--r- difference-of-squares
Counts
4 → 115
Calls
4 calls:
6.0ms
(+ (log 2) (/ 0.25 (* x x)))
5.0ms
(/ 0.09375 (pow x 4))
5.0ms
(/ 0.25 (* x x))
24.0ms
(- (+ (log 2) (/ 0.25 (* x x))) (- (/ 0.09375 (pow x 4)) (log x)))

series42.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(+ (log 2) (/ 0.25 (* x x)))
4.0ms
(/ 0.09375 (pow x 4))
3.0ms
(/ 0.25 (* x x))
11.0ms
(- (+ (log 2) (/ 0.25 (* x x))) (- (/ 0.09375 (pow x 4)) (log x)))

simplify486.0ms

Counts
127 → 127
Iterations

Useful iterations: 2 (157.0ms)

IterNodesCost
02272047
15651908
219651780
done50001780

prune226.0ms

Filtered
85 candidates to 127 candidates (-49.4%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1261127
Fresh055
Picked101
Done022
Total1278135

Merged error: 0.1b

Counts
135 → 8

regimes139.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.5b

bsearch35.0ms

Steps
ItersRangePoint
9
0.009971872296741319
901.3230478674768
0.9623652222862653
9
-174458.2165831976
-0.46594774775336223
-0.9999789100910194

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04580
14880
done4880

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.0s2379×body1280valid
412.0ms1562×body640valid
266.0ms798×body2560valid
127.0ms770×body320valid
91.0ms2070×body80valid
47.0ms421×body160valid

Profiling

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