Details

Time bar (total: 13.9s)

sample118.0ms

Algorithm
intervals
Results
61.0ms91×body1280valid
15.0ms37×body640valid
12.0ms27×body2560valid
6.0ms23×body320valid
4.0ms59×body80valid
2.0ms19×body160valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
079
199
done99

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.8b

localize17.0ms

Local error

Found 3 expressions with local error:

0.9b
(+ x (sqrt (+ (* x x) 1.0)))
4.2b
(log (+ x (sqrt (+ (* x x) 1.0))))
14.3b
(sqrt (+ (* x x) 1.0))

rewrite97.0ms

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:
29.0ms
(+ x (sqrt (+ (* x x) 1.0)))
50.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
17.0ms
(sqrt (+ (* x x) 1.0))

series420.0ms

Counts
3 → 9
Calls
3 calls:
96.0ms
(+ x (sqrt (+ (* x x) 1.0)))
272.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
52.0ms
(sqrt (+ (* x x) 1.0))

simplify851.0ms

Counts
51 → 51
Iterations

Useful iterations: done (849.0ms)

IterNodesCost
0133761
1319691
21350618
done5002606

prune265.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 1 expressions with local error:

0.1b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
181×add-sqr-sqrt
140×unpow-prod-down cube-prod
117×add-cube-cbrt *-un-lft-identity
80×sqrt-prod
40×sqr-pow
30×cube-mult unpow3
25×unswap-sqr
24×add-exp-log
10×prod-exp
9×div-exp
6×pow-to-exp pow-exp add-cbrt-cube
3×pow1 associate-*l*
2×cbrt-unprod
1×cbrt-undiv associate-*r/ pow-prod-down *-commutative div-inv add-log-exp
Counts
1 → 270
Calls
1 calls:
104.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series251.0ms

Counts
1 → 3
Calls
1 calls:
251.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify617.0ms

Counts
273 → 273
Iterations

Useful iterations: done (603.0ms)

IterNodesCost
02933830
18542926
done50012645

prune627.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 0.0625 (pow x 5))
0.4b
(/ 0.125 (pow x 3))
12.9b
(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
19.9b
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

rewrite983.0ms

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:
14.0ms
(/ 0.0625 (pow x 5))
15.0ms
(/ 0.125 (pow x 3))
265.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
679.0ms
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

series477.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(/ 0.0625 (pow x 5))
70.0ms
(/ 0.125 (pow x 3))
273.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
64.0ms
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

simplify2.0s

Counts
172 → 172
Iterations

Useful iterations: 2 (731.0ms)

IterNodesCost
03202874
17022609
231272481
done50022481

prune527.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.4b
(/ 0.125 (pow x 3))
11.7b
(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

rewrite519.0ms

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
51×times-frac
44×*-un-lft-identity
29×add-cube-cbrt
14×unpow-prod-down cube-prod
12×associate-/r*
10×difference-of-squares
9×add-exp-log
6×log-prod sqr-pow
5×add-cbrt-cube distribute-lft-out add-log-exp
4×pow1 cube-mult unpow3
3×div-exp associate-/l* distribute-lft-out--
2×log-div
1×cbrt-undiv pow-to-exp sub-neg flip3-- frac-2neg flip3-+ diff-log rem-log-exp pow-exp clear-num log-pow frac-sub flip-- flip-+ div-inv
Counts
3 → 107
Calls
3 calls:
65.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
11.0ms
(/ 0.125 (pow x 3))
439.0ms
(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

series454.0ms

Counts
3 → 9
Calls
3 calls:
123.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
64.0ms
(/ 0.125 (pow x 3))
267.0ms
(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

simplify1.4s

Counts
116 → 116
Iterations

Useful iterations: 2 (451.0ms)

IterNodesCost
02091723
14751535
221851447
done50021447

prune329.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes54.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.6b

bsearch113.0ms

Steps
ItersRangePoint
11
0.022891638200552334
5.118117448855024e+31
0.8969537796209996
10
-911936.9907706906
-4.3470241882695893e-07
-1.0205349568144453

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03457
13857
done3857

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.9s2409×body1280valid
605.0ms1557×body640valid
381.0ms786×body2560valid
239.0ms764×body320valid
178.0ms2059×body80valid
54.0ms425×body160valid