Details

Time bar (total: 15.5s)

sample96.0ms

Algorithm
intervals
Results
47.0ms81×body1280valid
18.0ms52×body640valid
10.0ms26×body2560valid
5.0ms24×body320valid
3.0ms56×body80valid
2.0ms17×body160valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
079
1108
done108

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.7b

localize13.0ms

Local error

Found 3 expressions with local error:

1.0b
(+ x (sqrt (+ (* x x) 1.0)))
3.6b
(log (+ x (sqrt (+ (* x x) 1.0))))
12.2b
(sqrt (+ (* x x) 1.0))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-sqr-sqrt
6×add-cube-cbrt
5×pow1 add-log-exp
4×add-exp-log log-prod
3×expm1-log1p-u fma-def flip3-+ sqrt-prod add-cbrt-cube flip-+ log1p-expm1-u
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow hypot-def
Counts
3 → 52
Calls
3 calls:
28.0ms
(+ x (sqrt (+ (* x x) 1.0)))
27.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
16.0ms
(sqrt (+ (* x x) 1.0))

series346.0ms

Counts
3 → 9
Calls
3 calls:
85.0ms
(+ x (sqrt (+ (* x x) 1.0)))
204.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
57.0ms
(sqrt (+ (* x x) 1.0))

simplify1.7s

Counts
61 → 61
Iterations

Useful iterations: done (1.7s)

IterNodesCost
0139813
1329677
2938609
33024595
done5000593

prune245.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
0.0ms
(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

series179.0ms

Counts
1 → 3
Calls
1 calls:
178.0ms
(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

simplify914.0ms

Counts
13 → 13
Iterations

Useful iterations: done (913.0ms)

IterNodesCost
025295
151295
2171256
3989256
done5000255

prune53.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.0625 (pow x 5))
0.4b
(/ 0.125 (pow x 3))
10.9b
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
20.7b
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite505.0ms

Algorithm
rewrite-expression-head
Rules
480×*-un-lft-identity
367×times-frac
244×add-sqr-sqrt
218×add-cube-cbrt
200×prod-diff
84×distribute-lft-out
80×unpow-prod-down
68×cube-prod
40×fma-neg
28×sqr-pow
22×cube-mult unpow3
19×associate-/r*
15×add-exp-log
11×log-prod
10×difference-of-squares
9×add-log-exp
8×add-cbrt-cube div-inv
6×div-exp frac-sub associate-/l* distribute-lft-out--
5×pow1 log-div
4×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv pow-to-exp flip3-- frac-2neg flip3-+ diff-log frac-add pow-exp clear-num flip-- flip-+
1×sub-neg rem-log-exp sum-log log-pow associate--r+
Counts
4 → 408
Calls
4 calls:
8.0ms
(/ 0.0625 (pow x 5))
14.0ms
(/ 0.125 (pow x 3))
233.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
220.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series464.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(/ 0.0625 (pow x 5))
54.0ms
(/ 0.125 (pow x 3))
264.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
73.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify1.8s

Counts
420 → 420
Iterations

Useful iterations: done (1.8s)

IterNodesCost
046617336
1101511891
227829369
done50008909

prune834.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

13.2b
(cbrt (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
13.2b
(cbrt (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
20.7b
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))
20.7b
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite738.0ms

Algorithm
rewrite-expression-head
Rules
874×*-un-lft-identity
620×times-frac
402×add-sqr-sqrt
400×prod-diff
350×add-cube-cbrt
168×distribute-lft-out
112×unpow-prod-down cube-prod
80×fma-neg
40×sqr-pow
36×cube-mult unpow3
22×cbrt-prod
20×difference-of-squares
14×add-log-exp
12×frac-sub div-inv distribute-lft-out--
10×cbrt-div
4×pow1 add-exp-log expm1-log1p-u flip3-- flip3-+ diff-log frac-add add-cbrt-cube flip-- flip-+ log1p-expm1-u
2×sub-neg pow1/3 sum-log associate--r+
Counts
4 → 586
Calls
4 calls:
121.0ms
(cbrt (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
109.0ms
(cbrt (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
181.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))
230.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series1.2s

Counts
4 → 12
Calls
4 calls:
716.0ms
(cbrt (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
365.0ms
(cbrt (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
61.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))
93.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify1.4s

Counts
598 → 598
Iterations

Useful iterations: done (1.3s)

IterNodesCost
038432328
189421856
2248516924
done500015966

prune1.5s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes46.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.8b

bsearch97.0ms

Steps
ItersRangePoint
9
0.0030847216915828425
5729.342694487068
0.8864725828659493
11
-30636816361710.875
-9.292394687435822e-10
-1.014356783985294

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03355
13555
done3555

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.4s2302×body1280valid
693.0ms800×body2560valid
607.0ms1576×body640valid
185.0ms788×body320valid
99.0ms2110×body80valid
95.0ms424×body160valid