Details

Time bar (total: 13.8s)

sample87.0ms

Algorithm
intervals
Results
53.0ms660×body80nan
20.0ms256×body80valid

simplify7.0ms

Counts
1 → 1
Iterations
IterNodes
done18
218
114
09

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
0.0b
(sqrt (- 1 (* x x)))
0.0b
(/ (sqrt (- 1 (* x x))) x)
0.2b
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
66×*-un-lft-identity
50×times-frac
43×add-sqr-sqrt
31×add-cube-cbrt sqrt-prod
16×distribute-lft-out
15×log-prod
13×div-inv
10×difference-of-squares
8×associate-/l*
7×add-exp-log
6×pow1 distribute-rgt-out add-cbrt-cube add-log-exp
4×sqrt-div insert-posit16
3×log-div associate-/r*
2×flip3-+ flip3-- frac-add distribute-rgt1-in flip-+ flip-- associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp log-pow
Counts
4 → 121
Calls
4 calls:
16.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
4.0ms
(sqrt (- 1 (* x x)))
10.0ms
(/ (sqrt (- 1 (* x x))) x)
22.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

series545.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
74.0ms
(sqrt (- 1 (* x x)))
146.0ms
(/ (sqrt (- 1 (* x x))) x)
235.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

simplify803.0ms

Counts
133 → 133
Iterations
IterNodes
done2005
21402
1525
0239

prune497.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (sqrt (- 1 (* x x))) 1)
0.0b
(sqrt (- 1 (* x x)))
0.2b
(log (* (+ (sqrt (- 1 (* x x))) 1) (/ 1 x)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log
8×*-un-lft-identity
7×add-sqr-sqrt pow1
6×log-div sqrt-prod
5×rem-log-exp add-log-exp
4×prod-exp add-cube-cbrt
3×flip3-+ add-cbrt-cube flip-+ insert-posit16
2×frac-times sqrt-div div-exp associate-*l/ log-pow distribute-lft-out difference-of-squares
1×+-commutative rem-sqrt-square rec-exp log-prod sum-log sqrt-pow1 flip3-- pow1/2 1-exp pow-prod-down associate-*r/ un-div-inv flip--
Counts
3 → 54
Calls
3 calls:
31.0ms
(+ (sqrt (- 1 (* x x))) 1)
7.0ms
(sqrt (- 1 (* x x)))
29.0ms
(log (* (+ (sqrt (- 1 (* x x))) 1) (/ 1 x)))

series298.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(+ (sqrt (- 1 (* x x))) 1)
46.0ms
(sqrt (- 1 (* x x)))
212.0ms
(log (* (+ (sqrt (- 1 (* x x))) 1) (/ 1 x)))

simplify510.0ms

Counts
63 → 63
Iterations
IterNodes
done2000
2864
1328
0140

prune261.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (sqrt (- 1 (* x x))) 1)
0.0b
(sqrt (- 1 (* x x)))
0.0b
(log (+ (sqrt (- 1 (* x x))) 1))
0.2b
(- (log (+ (sqrt (- 1 (* x x))) 1)) (log x))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
15×add-sqr-sqrt
13×log-prod
10×pow1
8×add-cube-cbrt sqrt-prod
6×distribute-lft-out add-log-exp
5×associate--l+ add-exp-log log-pow
4×log-div add-cbrt-cube insert-posit16 distribute-lft-out--
3×flip3-+ flip-+ associate--r+ difference-of-squares
2×associate--l- flip3-- sqrt-div flip--
1×+-commutative rem-sqrt-square sum-log sub-neg sqrt-pow1 pow1/2 diff-log rem-log-exp
Counts
4 → 77
Calls
4 calls:
18.0ms
(+ (sqrt (- 1 (* x x))) 1)
4.0ms
(sqrt (- 1 (* x x)))
18.0ms
(log (+ (sqrt (- 1 (* x x))) 1))
28.0ms
(- (log (+ (sqrt (- 1 (* x x))) 1)) (log x))

series489.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(+ (sqrt (- 1 (* x x))) 1)
79.0ms
(sqrt (- 1 (* x x)))
148.0ms
(log (+ (sqrt (- 1 (* x x))) 1))
212.0ms
(- (log (+ (sqrt (- 1 (* x x))) 1)) (log x))

simplify817.0ms

Counts
89 → 89
Iterations
IterNodes
done2000
21082
1398
0177

prune352.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b
(log (/ (+ (/ 1 (* (* x x) x)) (* (/ (- 1 (* x x)) x) (/ (sqrt (- 1 (* x x))) (* x x)))) (+ (* (/ (sqrt (- 1 (* x x))) x) (- (/ (sqrt (- 1 (* x x))) x) (/ 1 x))) (/ (/ 1 x) x))))
0.3b
(* (/ (sqrt (- 1 (* x x))) x) (- (/ (sqrt (- 1 (* x x))) x) (/ 1 x)))
2.0b
(- (/ (sqrt (- 1 (* x x))) x) (/ 1 x))
40.3b
(/ (+ (/ 1 (* (* x x) x)) (* (/ (- 1 (* x x)) x) (/ (sqrt (- 1 (* x x))) (* x x)))) (+ (* (/ (sqrt (- 1 (* x x))) x) (- (/ (sqrt (- 1 (* x x))) x) (/ 1 x))) (/ (/ 1 x) x)))

rewrite545.0ms

Algorithm
rewrite-expression-head
Rules
114×add-sqr-sqrt
94×times-frac
82×*-un-lft-identity
43×add-cube-cbrt
28×associate-*l* sqrt-prod
24×log-prod difference-of-squares
23×associate-*r*
22×associate-/r/
21×frac-add
16×distribute-lft-out--
14×add-exp-log
13×frac-times associate-*r/ div-inv
11×add-cbrt-cube
7×pow1 flip3-- frac-sub flip-- sub-div
6×distribute-rgt-out-- add-log-exp
5×associate-/l/
4×associate-*l/ insert-posit16
3×associate-/r* sub-neg flip3-+ div-exp flip-+ associate-/l* unswap-sqr
2×distribute-rgt-in cbrt-undiv distribute-lft-in rem-log-exp prod-exp cbrt-unprod
1×log-div clear-num frac-2neg diff-log pow-prod-down log-pow *-commutative
Counts
4 → 196
Calls
4 calls:
91.0ms
(log (/ (+ (/ 1 (* (* x x) x)) (* (/ (- 1 (* x x)) x) (/ (sqrt (- 1 (* x x))) (* x x)))) (+ (* (/ (sqrt (- 1 (* x x))) x) (- (/ (sqrt (- 1 (* x x))) x) (/ 1 x))) (/ (/ 1 x) x))))
137.0ms
(* (/ (sqrt (- 1 (* x x))) x) (- (/ (sqrt (- 1 (* x x))) x) (/ 1 x)))
32.0ms
(- (/ (sqrt (- 1 (* x x))) x) (/ 1 x))
281.0ms
(/ (+ (/ 1 (* (* x x) x)) (* (/ (- 1 (* x x)) x) (/ (sqrt (- 1 (* x x))) (* x x)))) (+ (* (/ (sqrt (- 1 (* x x))) x) (- (/ (sqrt (- 1 (* x x))) x) (/ 1 x))) (/ (/ 1 x) x)))

series1.0s

Counts
4 → 12
Calls
4 calls:
434.0ms
(log (/ (+ (/ 1 (* (* x x) x)) (* (/ (- 1 (* x x)) x) (/ (sqrt (- 1 (* x x))) (* x x)))) (+ (* (/ (sqrt (- 1 (* x x))) x) (- (/ (sqrt (- 1 (* x x))) x) (/ 1 x))) (/ (/ 1 x) x))))
239.0ms
(* (/ (sqrt (- 1 (* x x))) x) (- (/ (sqrt (- 1 (* x x))) x) (/ 1 x)))
95.0ms
(- (/ (sqrt (- 1 (* x x))) x) (/ 1 x))
242.0ms
(/ (+ (/ 1 (* (* x x) x)) (* (/ (- 1 (* x x)) x) (/ (sqrt (- 1 (* x x))) (* x x)))) (+ (* (/ (sqrt (- 1 (* x x))) x) (- (/ (sqrt (- 1 (* x x))) x) (/ 1 x))) (/ (/ 1 x) x)))

simplify858.0ms

Counts
208 → 208
Iterations
IterNodes
done2004
11137
0413

prune1.0s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes21.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done12
112
09

end0.0ms

sample5.4s

Algorithm
intervals
Results
3.7s23875×body80nan
1.1s8000×body80valid