Details

Time bar (total: 13.6s)

sample115.0ms

Algorithm
intervals
Results
59.0ms862×body80nan
21.0ms256×body80valid

simplify5.0ms

Counts
1 → 1
Iterations
IterNodes
done16
216
112
09

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
41×*-un-lft-identity
33×times-frac
30×add-sqr-sqrt
25×add-cube-cbrt
16×sqrt-prod
8×log-prod distribute-lft-out add-log-exp
7×add-exp-log associate-/l*
6×add-cbrt-cube
5×pow1 div-inv difference-of-squares
3×log-div associate-/r*
2×flip3-+ distribute-rgt-out flip3-- sqrt-div frac-add flip-+ flip-- associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg diff-log div-exp rem-log-exp log-pow
Counts
4 → 95
Calls
4 calls:
8.0ms
(- 1.0 (* x x))
20.0ms
(/ (sqrt (- 1.0 (* x x))) x)
45.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
46.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series1.2s

Counts
4 → 12
Calls
4 calls:
446.0ms
(- 1.0 (* x x))
159.0ms
(/ (sqrt (- 1.0 (* x x))) x)
169.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
440.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify993.0ms

Counts
107 → 107
Iterations
IterNodes
done5001
22278
1528
0225

prune560.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite158.0ms

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×add-cbrt-cube log-pow
7×difference-of-squares
6×associate-+l+ distribute-neg-in
5×add-log-exp
4×distribute-rgt-neg-in div-inv
3×log-div associate-+r-
2×cbrt-undiv clear-num sum-log frac-2neg flip3-+ sqrt-div div-exp flip-+ associate-/l/
1×neg-sub0 +-commutative sqrt-undiv sqrt-pow1 distribute-rgt-out flip3-- pow1/2 rem-log-exp neg-log frac-add associate-+l- flip--
Counts
4 → 167
Calls
4 calls:
3.0ms
(log (sqrt x))
109.0ms
(+ (- (log (sqrt x))) (log (+ (/ (sqrt (- 1.0 (* x x))) (sqrt x)) (/ 1.0 (sqrt x)))))
10.0ms
(/ 1.0 (sqrt x))
21.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))

series593.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(log (sqrt x))
370.0ms
(+ (- (log (sqrt x))) (log (+ (/ (sqrt (- 1.0 (* x x))) (sqrt x)) (/ 1.0 (sqrt x)))))
47.0ms
(/ 1.0 (sqrt x))
88.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))

simplify1.2s

Counts
179 → 179
Iterations
IterNodes
done5000
22728
1708
0315

prune940.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x))
0.2b
(/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x))
0.2b
(log (+ (/ 1.0 x) (* (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)) (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)))))
0.6b
(* (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)) (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)))

rewrite270.0ms

Algorithm
rewrite-expression-head
Rules
938×sqrt-prod
667×add-sqr-sqrt
580×times-frac
283×*-un-lft-identity add-cube-cbrt
132×swap-sqr
64×associate-*r* associate-*l*
49×unswap-sqr
42×difference-of-squares
21×add-exp-log
20×add-cbrt-cube associate-/l*
12×pow1 associate-/r*
8×sqrt-div
6×cbrt-undiv sqrt-undiv div-exp div-inv
5×log-div
4×prod-exp cbrt-unprod add-log-exp associate-/l/
3×log-prod frac-add
2×frac-times clear-num frac-2neg flip3-- associate-*l/ associate-*r/ flip--
1×pow2 rem-square-sqrt flip3-+ pow-plus sqrt-unprod rem-log-exp pow-prod-down pow-sqr log-pow *-commutative pow-prod-up flip-+
Counts
4 → 534
Calls
4 calls:
13.0ms
(/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x))
24.0ms
(/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x))
18.0ms
(log (+ (/ 1.0 x) (* (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)) (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)))))
152.0ms
(* (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)) (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)))

series914.0ms

Counts
4 → 12
Calls
4 calls:
218.0ms
(/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x))
192.0ms
(/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x))
342.0ms
(log (+ (/ 1.0 x) (* (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)) (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)))))
163.0ms
(* (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)) (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)))

simplify802.0ms

Counts
546 → 546
Iterations
IterNodes
done5000
11524
0473

prune1.7s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes121.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done15
115
013

end0.0ms

sample3.7s

Algorithm
intervals
Results
2.2s24038×body80nan
749.0ms8000×body80valid