Details

Time bar (total: 13.4s)

sample72.0ms

Algorithm
intervals
Results
36.0ms79×body1280valid
12.0ms44×body640valid
5.0ms30×body320valid
5.0ms14×body2560valid
3.0ms81×body80valid
1.0ms8×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
199
done99

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.4b
(+ x (sqrt (+ (* x x) 1.0)))
3.3b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.1b
(sqrt (+ (* x x) 1.0))

rewrite72.0ms

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:
18.0ms
(+ x (sqrt (+ (* x x) 1.0)))
39.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
15.0ms
(sqrt (+ (* x x) 1.0))

series307.0ms

Counts
3 → 9
Calls
3 calls:
58.0ms
(+ x (sqrt (+ (* x x) 1.0)))
201.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
48.0ms
(sqrt (+ (* x x) 1.0))

simplify568.0ms

Counts
51 → 51
Iterations

Useful iterations: done (566.0ms)

IterNodesCost
0133761
1319691
21350618
done5002606

prune192.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

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

rewrite441.0ms

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:
284.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
117.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series359.0ms

Counts
2 → 6
Calls
2 calls:
185.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
173.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify531.0ms

Counts
292 → 292
Iterations

Useful iterations: done (519.0ms)

IterNodesCost
03364436
19903368
done50003059

prune666.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ 0.125 (pow x 3))
9.2b
(log (- (+ (* 2 x) (/ 0.5 x)) (/ 0.125 (pow x 3))))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
40×times-frac
30×*-un-lft-identity
28×add-cube-cbrt
13×unpow-prod-down cube-prod
12×associate-/r*
9×log-prod
8×add-exp-log
5×difference-of-squares sqr-pow
4×cube-mult log-div unpow3 add-cbrt-cube
3×pow1 div-exp associate-/l*
2×frac-sub add-log-exp
1×cbrt-undiv pow-to-exp flip3-- frac-2neg flip3-+ rem-log-exp pow-exp clear-num log-pow flip-- flip-+ div-inv distribute-lft-out--
Counts
2 → 87
Calls
2 calls:
8.0ms
(/ 0.125 (pow x 3))
78.0ms
(log (- (+ (* 2 x) (/ 0.5 x)) (/ 0.125 (pow x 3))))

series267.0ms

Counts
2 → 6
Calls
2 calls:
51.0ms
(/ 0.125 (pow x 3))
216.0ms
(log (- (+ (* 2 x) (/ 0.5 x)) (/ 0.125 (pow x 3))))

simplify950.0ms

Counts
93 → 93
Iterations

Useful iterations: 2 (350.0ms)

IterNodesCost
02041459
14631276
219731220
done50001220

prune289.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 1/36 (pow (/ x (sqrt 1.0)) 6))
0.1b
(* (pow (/ x (sqrt 1.0)) 3) 1/6)
14.1b
(- (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))) (* 1/36 (pow (/ x (sqrt 1.0)) 6)))
39.0b
(/ (- (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))) (* 1/36 (pow (/ x (sqrt 1.0)) 6))) (+ (log (sqrt 1.0)) (+ (/ x (sqrt 1.0)) (* (pow (/ x (sqrt 1.0)) 3) 1/6))))

rewrite407.0ms

Algorithm
rewrite-expression-head
Rules
87×add-sqr-sqrt
75×times-frac
69×*-un-lft-identity
57×add-cube-cbrt
53×associate-*l*
50×unpow-prod-down
30×sqrt-prod
29×associate-*r*
25×cube-prod
22×add-exp-log
13×unswap-sqr
10×add-cbrt-cube
8×pow1 prod-exp distribute-lft-out
6×add-log-exp
5×associate-/r*
4×pow-exp log-pow div-inv sqr-pow
3×div-exp associate-/l*
2×pow-to-exp flip3-- associate--l+ associate-/r/ *-commutative flip-- cbrt-unprod associate-/l/
1×cbrt-undiv cube-div distribute-rgt-in cube-mult sub-neg frac-2neg distribute-lft-in flip3-+ diff-log unpow3 div-sub associate-*l/ clear-num flip-+
Counts
4 → 176
Calls
4 calls:
37.0ms
(* 1/36 (pow (/ x (sqrt 1.0)) 6))
53.0ms
(* (pow (/ x (sqrt 1.0)) 3) 1/6)
59.0ms
(- (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))) (* 1/36 (pow (/ x (sqrt 1.0)) 6)))
246.0ms
(/ (- (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))) (* 1/36 (pow (/ x (sqrt 1.0)) 6))) (+ (log (sqrt 1.0)) (+ (/ x (sqrt 1.0)) (* (pow (/ x (sqrt 1.0)) 3) 1/6))))

series1.1s

Counts
4 → 12
Calls
4 calls:
179.0ms
(* 1/36 (pow (/ x (sqrt 1.0)) 6))
134.0ms
(* (pow (/ x (sqrt 1.0)) 3) 1/6)
315.0ms
(- (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))) (* 1/36 (pow (/ x (sqrt 1.0)) 6)))
514.0ms
(/ (- (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))) (* 1/36 (pow (/ x (sqrt 1.0)) 6))) (+ (log (sqrt 1.0)) (+ (/ x (sqrt 1.0)) (* (pow (/ x (sqrt 1.0)) 3) 1/6))))

simplify2.7s

Counts
188 → 188
Iterations

Useful iterations: 2 (848.0ms)

IterNodesCost
02984793
18034595
244714258
done50004258

prune677.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes167.0ms

Accuracy

99.4% (0.2b remaining)

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

bsearch105.0ms

Steps
ItersRangePoint
8
0.0004268116563047139
15.006088268796836
0.8844350792771517
8
-101.50163225226844
-0.031678663534995
-1.0087686302909924

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03557
13957
done3957

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.4s2228×body1280valid
629.0ms1591×body640valid
479.0ms2227×body80valid
406.0ms758×body2560valid
162.0ms796×body320valid
48.0ms400×body160valid