Details

Time bar (total: 16.8s)

sample142.0ms

Algorithm
intervals
Results
56.0ms77×body1280valid
27.0ms25×body2560valid
23.0ms53×body640valid
8.0ms28×body320valid
5.0ms61×body80valid
2.0ms12×body160valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
199
done99

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.9b

localize20.0ms

Local error

Found 3 expressions with local error:

0.3b
(+ x (sqrt (+ (* x x) 1.0)))
3.5b
(log (+ x (sqrt (+ (* x x) 1.0))))
15.2b
(sqrt (+ (* x x) 1.0))

rewrite89.0ms

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:
42.0ms
(+ x (sqrt (+ (* x x) 1.0)))
29.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
17.0ms
(sqrt (+ (* x x) 1.0))

series436.0ms

Counts
3 → 9
Calls
3 calls:
92.0ms
(+ x (sqrt (+ (* x x) 1.0)))
280.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
65.0ms
(sqrt (+ (* x x) 1.0))

simplify1.0s

Counts
51 → 51
Iterations

Useful iterations: done (1.0s)

IterNodesCost
0133761
1319691
21350618
done5002606

prune351.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 1 expressions with local error:

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

rewrite225.0ms

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:
175.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series262.0ms

Counts
1 → 3
Calls
1 calls:
261.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify785.0ms

Counts
273 → 273
Iterations

Useful iterations: done (770.0ms)

IterNodesCost
02933830
18542926
done50012645

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.0625 (pow x 5))
0.2b
(/ 0.125 (pow x 3))
12.9b
(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
18.7b
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

rewrite1.3s

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:
16.0ms
(/ 0.0625 (pow x 5))
17.0ms
(/ 0.125 (pow x 3))
397.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
856.0ms
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

series621.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(/ 0.0625 (pow x 5))
80.0ms
(/ 0.125 (pow x 3))
337.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
109.0ms
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

simplify2.3s

Counts
172 → 172
Iterations

Useful iterations: 2 (945.0ms)

IterNodesCost
03202874
17022609
231272481
done50022481

prune932.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize26.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ 0.125 (pow x 3))
10.2b
(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

rewrite611.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
36×times-frac
28×add-sqr-sqrt add-cube-cbrt
12×unpow-prod-down cube-prod associate-/r*
8×add-exp-log
6×log-prod
5×distribute-lft-out
4×cube-mult unpow3 add-cbrt-cube sqr-pow
3×pow1 div-exp associate-/l*
2×log-div add-log-exp
1×cbrt-undiv pow-to-exp frac-2neg flip3-+ rem-log-exp pow-exp clear-num log-pow flip-+ div-inv distribute-lft-out--
Counts
2 → 82
Calls
2 calls:
17.0ms
(/ 0.125 (pow x 3))
588.0ms
(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

series356.0ms

Counts
2 → 6
Calls
2 calls:
68.0ms
(/ 0.125 (pow x 3))
288.0ms
(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

simplify1.4s

Counts
88 → 88
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01641209
13621046
21640980
done5002972

prune777.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes71.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.4b

bsearch142.0ms

Steps
ItersRangePoint
10
2.8868360106527892e-08
453261925.93168354
0.8960040298281693
9
-4.26929226401081
-3.26160511802404e-08
-1.0390866699268784

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03457
13857
done3857

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.8s2277×body1280valid
787.0ms1538×body640valid
416.0ms822×body2560valid
234.0ms815×body320valid
182.0ms2158×body80valid
57.0ms390×body160valid