Details

Time bar (total: 11.8s)

sample113.0ms

Algorithm
intervals
Results
66.0ms816×body80nan
15.0ms256×body80valid

simplify13.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0913
11213
21613
done1613

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- 1.0 (* x x)))
0.0b
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.0b
(/ (sqrt (- 1.0 (* x x))) x)
0.0b
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
33×times-frac
32×add-sqr-sqrt
26×add-cube-cbrt
20×sqrt-prod
8×log-prod distribute-lft-out
7×add-exp-log associate-/l*
6×pow1 add-cbrt-cube add-log-exp
5×div-inv difference-of-squares
4×sqrt-div
3×log-div associate-/r*
2×distribute-rgt-out flip3-- flip3-+ frac-add flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp clear-num sum-log log-pow
Counts
4 → 98
Calls
4 calls:
11.0ms
(sqrt (- 1.0 (* x x)))
58.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
19.0ms
(/ (sqrt (- 1.0 (* x x))) x)
63.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

series845.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(sqrt (- 1.0 (* x x)))
387.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
231.0ms
(/ (sqrt (- 1.0 (* x x))) x)
168.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

simplify960.0ms

Counts
110 → 110
Iterations

Useful iterations: done (955.0ms)

IterNodesCost
02261924
15101798
214331665
done50001638

prune400.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- 1.0 (* x x)))
0.0b
(log (+ (/ 1.0 x) (/ (* 1 (sqrt (- 1.0 (* x x)))) x)))
0.0b
(/ (* 1 (sqrt (- 1.0 (* x x)))) x)
0.0b
(+ (/ 1.0 x) (/ (* 1 (sqrt (- 1.0 (* x x)))) x))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
15×times-frac
14×add-sqr-sqrt
12×add-exp-log add-cube-cbrt
9×add-cbrt-cube
8×log-prod distribute-lft-out
6×pow1 add-log-exp
5×div-inv
4×sqrt-div sqrt-prod
3×log-div div-exp associate-/r*
2×cbrt-undiv distribute-rgt-out flip3-- flip3-+ associate-*r/ frac-add prod-exp flip-- flip-+ associate-/l/
1×+-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 1-exp rem-log-exp clear-num sum-log log-pow cbrt-unprod associate-/l* difference-of-squares
Counts
4 → 77
Calls
4 calls:
9.0ms
(sqrt (- 1.0 (* x x)))
19.0ms
(log (+ (/ 1.0 x) (/ (* 1 (sqrt (- 1.0 (* x x)))) x)))
14.0ms
(/ (* 1 (sqrt (- 1.0 (* x x)))) x)
44.0ms
(+ (/ 1.0 x) (/ (* 1 (sqrt (- 1.0 (* x x)))) x))

series927.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(sqrt (- 1.0 (* x x)))
464.0ms
(log (+ (/ 1.0 x) (/ (* 1 (sqrt (- 1.0 (* x x)))) x)))
211.0ms
(/ (* 1 (sqrt (- 1.0 (* x x)))) x)
164.0ms
(+ (/ 1.0 x) (/ (* 1 (sqrt (- 1.0 (* x x)))) x))

simplify1.2s

Counts
89 → 89
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02141683
15101436
215701297
done50001270

prune426.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (sqrt x))
0.2b
(+ (- (log (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
0.3b
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
0.3b
(/ 1.0 (sqrt x))

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
83×*-un-lft-identity
78×sqrt-prod
76×times-frac
69×add-sqr-sqrt
58×add-cube-cbrt
25×log-prod
15×distribute-lft-out
13×associate-+r+
12×associate-/r*
11×pow1
10×associate-/l*
9×add-exp-log
8×log-pow add-cbrt-cube
7×difference-of-squares
6×associate-+l+ distribute-neg-in
5×add-log-exp
4×distribute-rgt-neg-in div-inv
3×associate-+r- log-div
2×cbrt-undiv frac-2neg flip3-+ sqrt-div div-exp clear-num sum-log flip-+ associate-/l/
1×+-commutative neg-sub0 associate-+l- sqrt-undiv distribute-rgt-out flip3-- sqrt-pow1 pow1/2 rem-log-exp neg-log frac-add flip--
Counts
4 → 167
Calls
4 calls:
4.0ms
(log (sqrt x))
131.0ms
(+ (- (log (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
14.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
6.0ms
(/ 1.0 (sqrt x))

series780.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(log (sqrt x))
515.0ms
(+ (- (log (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
122.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
70.0ms
(/ 1.0 (sqrt x))

simplify1.4s

Counts
179 → 179
Iterations

Useful iterations: done (1.4s)

IterNodesCost
03312943
17102681
217552491
done50002456

prune662.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes27.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01115
11513
done1513

end0.0ms

sample3.5s

Algorithm
intervals
Results
2.1s23585×body80nan
630.0ms8000×body80valid