Details

Time bar (total: 13.1s)

sample74.0ms

Algorithm
intervals
Results
34.0ms862×body80nan
12.0ms256×body80valid

simplify10.0ms

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: 0.3b

localize35.0ms

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)))

rewrite107.0ms

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:
7.0ms
(- 1.0 (* x x))
21.0ms
(/ (sqrt (- 1.0 (* x x))) x)
45.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
29.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series834.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- 1.0 (* x x))
139.0ms
(/ (sqrt (- 1.0 (* x x))) x)
180.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
439.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify1.2s

Counts
107 → 107
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02251840
15281729
222781611
done50011595

prune598.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize25.0ms

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)))))
0.2b
(/ 1.0 (sqrt x))
0.2b
(/ (sqrt (- 1.0 (* x x))) (sqrt x))

rewrite111.0ms

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:
2.0ms
(log (sqrt x))
85.0ms
(+ (- (log (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
6.0ms
(/ 1.0 (sqrt x))
12.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))

series605.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(log (sqrt x))
375.0ms
(+ (- (log (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
46.0ms
(/ 1.0 (sqrt x))
81.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))

simplify1.2s

Counts
179 → 179
Iterations

Useful iterations: done (1.2s)

IterNodesCost
03152913
17082651
227282477
done50012466

prune814.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1.0 x) (/ (/ (sqrt (- 1.0 (* x x))) (sqrt x)) (sqrt x)))
0.2b
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
0.2b
(log (+ (/ 1.0 x) (/ (/ (sqrt (- 1.0 (* x x))) (sqrt x)) (sqrt x))))
0.4b
(/ (/ (sqrt (- 1.0 (* x x))) (sqrt x)) (sqrt x))

rewrite665.0ms

Algorithm
rewrite-expression-head
Rules
616×times-frac
508×sqrt-prod
367×add-sqr-sqrt
330×*-un-lft-identity
318×add-cube-cbrt
53×associate-/l*
49×difference-of-squares
12×associate-/r* add-exp-log
11×add-cbrt-cube
9×div-inv
6×add-log-exp
5×pow1 log-prod
4×cbrt-undiv div-exp distribute-lft-out
3×log-div sqrt-undiv associate-/l/
2×clear-num frac-2neg flip3-+ sqrt-div frac-add flip-+
1×+-commutative sum-log flip3-- rem-log-exp log-pow flip--
Counts
4 → 445
Calls
4 calls:
274.0ms
(+ (/ 1.0 x) (/ (/ (sqrt (- 1.0 (* x x))) (sqrt x)) (sqrt x)))
20.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
274.0ms
(log (+ (/ 1.0 x) (/ (/ (sqrt (- 1.0 (* x x))) (sqrt x)) (sqrt x))))
54.0ms
(/ (/ (sqrt (- 1.0 (* x x))) (sqrt x)) (sqrt x))

series831.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(+ (/ 1.0 x) (/ (/ (sqrt (- 1.0 (* x x))) (sqrt x)) (sqrt x)))
68.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
419.0ms
(log (+ (/ 1.0 x) (/ (/ (sqrt (- 1.0 (* x x))) (sqrt x)) (sqrt x))))
190.0ms
(/ (/ (sqrt (- 1.0 (* x x))) (sqrt x)) (sqrt x))

simplify714.0ms

Counts
457 → 457
Iterations

Useful iterations: done (686.0ms)

IterNodesCost
055011697
1139510119
done50019622

prune1.6s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes176.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01320
11520
done1520

end0.0ms

sample3.5s

Algorithm
intervals
Results
2.1s24038×body80nan
636.0ms8000×body80valid