Details

Time bar (total: 7.0s)

sample9.0ms

Algorithm
intervals
Results
4.0ms256×body80valid

simplify2.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
057
167
done67

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.7b

localize4.0ms

Local error

Found 1 expressions with local error:

15.7b
(/ x (+ (* x x) 1.0))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
3×add-exp-log associate-/r* add-cbrt-cube associate-/l*
2×associate-/r/
1×pow1 cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+ div-inv add-log-exp
Counts
1 → 29
Calls
1 calls:
6.0ms
(/ x (+ (* x x) 1.0))

series58.0ms

Counts
1 → 3
Calls
1 calls:
58.0ms
(/ x (+ (* x x) 1.0))

simplify1.5s

Counts
32 → 32
Iterations

Useful iterations: 3 (164.0ms)

IterNodesCost
074428
1167413
2404375
3951373
42588373
done5000373

prune62.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ 1 (+ (* x x) 1.0))
15.6b
(* x (/ 1 (+ (* x x) 1.0)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
20×times-frac
19×*-un-lft-identity
18×add-cube-cbrt
15×add-exp-log associate-*r*
9×add-cbrt-cube
5×pow1
4×div-exp prod-exp associate-/r/
3×associate-*l* associate-/r* associate-/l* unswap-sqr
2×cbrt-undiv rec-exp flip3-+ 1-exp cbrt-unprod flip-+ div-inv add-log-exp
1×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num un-div-inv *-commutative inv-pow
Counts
2 → 71
Calls
2 calls:
6.0ms
(/ 1 (+ (* x x) 1.0))
16.0ms
(* x (/ 1 (+ (* x x) 1.0)))

series98.0ms

Counts
2 → 6
Calls
2 calls:
41.0ms
(/ 1 (+ (* x x) 1.0))
57.0ms
(* x (/ 1 (+ (* x x) 1.0)))

simplify1.7s

Counts
77 → 77
Iterations

Useful iterations: 3 (576.0ms)

IterNodesCost
0128985
1315827
2722727
32196725
done5000725

prune106.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (+ (* x x) 1.0))
0.2b
(/ 1 (+ (* x x) 1.0))
15.6b
(sqrt (/ 1 (+ (* x x) 1.0)))
15.6b
(sqrt (/ 1 (+ (* x x) 1.0)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
40×times-frac
36×*-un-lft-identity
34×add-cube-cbrt
30×sqrt-prod
12×add-exp-log
10×pow1
8×associate-/r/ add-cbrt-cube
6×rem-sqrt-square sqrt-pow1 associate-/r* associate-/l*
4×pow-flip flip3-+ div-exp flip-+ div-inv inv-pow add-log-exp
2×cbrt-undiv rec-exp frac-2neg pow1/2 sqrt-div 1-exp clear-num
Counts
4 → 126
Calls
4 calls:
6.0ms
(/ 1 (+ (* x x) 1.0))
7.0ms
(/ 1 (+ (* x x) 1.0))
10.0ms
(sqrt (/ 1 (+ (* x x) 1.0)))
7.0ms
(sqrt (/ 1 (+ (* x x) 1.0)))

series238.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(/ 1 (+ (* x x) 1.0))
39.0ms
(/ 1 (+ (* x x) 1.0))
77.0ms
(sqrt (/ 1 (+ (* x x) 1.0)))
77.0ms
(sqrt (/ 1 (+ (* x x) 1.0)))

simplify1.2s

Counts
138 → 138
Iterations

Useful iterations: 3 (421.0ms)

IterNodesCost
01381850
12851598
26881464
323261446
done50001446

prune247.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1.0 (pow x 5))
0.1b
(/ 1.0 (pow x 3))
16.5b
(+ (- (/ 1 x) (/ 1.0 (pow x 3))) (/ 1.0 (pow x 5)))

rewrite243.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
57×*-un-lft-identity
44×add-sqr-sqrt add-cube-cbrt
24×unpow-prod-down
19×associate-/r*
13×add-exp-log
12×cube-prod
8×add-log-exp sqr-pow
7×add-cbrt-cube
6×div-exp associate-/l*
4×cube-mult unpow3 distribute-lft-out
3×pow1 frac-add div-inv distribute-lft-out--
2×cbrt-undiv pow-to-exp associate-+l+ frac-2neg pow-exp clear-num sum-log
1×+-commutative associate-+l- sub-neg flip3-- flip3-+ diff-log frac-sub flip-- flip-+
Counts
3 → 132
Calls
3 calls:
3.0ms
(/ 1.0 (pow x 5))
4.0ms
(/ 1.0 (pow x 3))
230.0ms
(+ (- (/ 1 x) (/ 1.0 (pow x 3))) (/ 1.0 (pow x 5)))

series132.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(/ 1.0 (pow x 5))
40.0ms
(/ 1.0 (pow x 3))
45.0ms
(+ (- (/ 1 x) (/ 1.0 (pow x 3))) (/ 1.0 (pow x 5)))

simplify732.0ms

Counts
141 → 141
Iterations

Useful iterations: done (729.0ms)

IterNodesCost
02171853
14641621
213971547
done50001543

prune267.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes21.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.8b

bsearch51.0ms

Steps
ItersRangePoint
7
179.5191949529741
4368.076441928604
897.3710299305061
8
-3540160029299381.0
-131863331651.28616
-6092285729639.722

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
02247
13033
done3033

end0.0ms

sample227.0ms

Algorithm
intervals
Results
142.0ms8000×body80valid