Details

Time bar (total: 4.7s)

sample10.0ms

Algorithm
intervals
Results
4.0ms256×body80valid

simplify3.0ms

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: 13.8b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) 1.0)
13.8b
(/ x (+ (* x x) 1.0))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×pow1 flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 40
Calls
2 calls:
3.0ms
(+ (* x x) 1.0)
6.0ms
(/ x (+ (* x x) 1.0))

series90.0ms

Counts
2 → 6
Calls
2 calls:
31.0ms
(+ (* x x) 1.0)
59.0ms
(/ x (+ (* x x) 1.0))

simplify1.2s

Counts
46 → 46
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
085552
1193530
2573474
32679474
done5001474

prune84.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
0.0b
(/ 1 (sqrt (+ (* x x) 1.0)))
13.8b
(sqrt (+ (* x x) 1.0))
13.8b
(sqrt (+ (* x x) 1.0))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
30×add-exp-log
24×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
10×pow1 sqrt-div div-exp
8×prod-exp
6×associate-/r* associate-/r/
5×cbrt-undiv flip3-+ flip-+
4×cbrt-unprod add-log-exp
3×rec-exp pow-flip sqrt-pow1 pow1/2 1-exp div-inv associate-/l*
2×rem-sqrt-square
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative inv-pow
Counts
4 → 164
Calls
4 calls:
48.0ms
(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
8.0ms
(/ 1 (sqrt (+ (* x x) 1.0)))
4.0ms
(sqrt (+ (* x x) 1.0))
5.0ms
(sqrt (+ (* x x) 1.0))

series221.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
74.0ms
(/ 1 (sqrt (+ (* x x) 1.0)))
46.0ms
(sqrt (+ (* x x) 1.0))
43.0ms
(sqrt (+ (* x x) 1.0))

simplify900.0ms

Counts
176 → 176
Iterations

Useful iterations: 2 (283.0ms)

IterNodesCost
02253329
16252901
219952399
done50002399

prune303.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1.0 (pow x 5))
0.9b
(/ 1.0 (pow x 3))
20.7b
(- (+ (/ 1.0 (pow x 5)) (/ 1 x)) (/ 1.0 (pow x 3)))

rewrite267.0ms

Algorithm
rewrite-expression-head
Rules
64×times-frac
57×add-sqr-sqrt *-un-lft-identity
44×add-cube-cbrt
25×unpow-prod-down
19×associate-/r*
13×add-exp-log cube-prod
9×sqr-pow
8×add-log-exp
7×add-cbrt-cube
6×div-exp associate-/l*
5×difference-of-squares
4×cube-mult unpow3 distribute-lft-out--
3×pow1 frac-sub div-inv distribute-lft-out
2×cbrt-undiv pow-to-exp frac-2neg diff-log pow-exp clear-num
1×sub-neg flip3-- flip3-+ frac-add associate--l+ sum-log flip-- flip-+
Counts
3 → 136
Calls
3 calls:
4.0ms
(/ 1.0 (pow x 5))
5.0ms
(/ 1.0 (pow x 3))
251.0ms
(- (+ (/ 1.0 (pow x 5)) (/ 1 x)) (/ 1.0 (pow x 3)))

series125.0ms

Counts
3 → 9
Calls
3 calls:
45.0ms
(/ 1.0 (pow x 5))
37.0ms
(/ 1.0 (pow x 3))
41.0ms
(- (+ (/ 1.0 (pow x 5)) (/ 1 x)) (/ 1.0 (pow x 3)))

simplify790.0ms

Counts
145 → 145
Iterations

Useful iterations: done (786.0ms)

IterNodesCost
02252019
14781783
219451709
done50001705

prune273.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes44.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 14.9b

bsearch1.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
02569
13353
done3353

end0.0ms

sample235.0ms

Algorithm
intervals
Results
142.0ms8000×body80valid