Details

Time bar (total: 25.7s)

sample291.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
8.0ms259×body80nan

simplify16.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0911
11611
21911
32111
done2111

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
0.0b
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b
(/ (- 1.0 x) (+ 1.0 x))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
64×*-un-lft-identity
45×add-sqr-sqrt
41×times-frac
26×sqrt-prod
24×add-cube-cbrt
11×distribute-lft-out
9×distribute-lft-out-- difference-of-squares
5×add-exp-log add-cbrt-cube associate-/l*
4×pow1 associate-/r* associate-/r/
3×add-log-exp
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv flip3-- frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub div-exp clear-num flip--
Counts
3 → 91
Calls
3 calls:
0.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
9.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
13.0ms
(/ (- 1.0 x) (+ 1.0 x))

series147.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
94.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
49.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify1.1s

Counts
100 → 100
Iterations

Useful iterations: 3 (476.0ms)

IterNodesCost
01671451
13521376
28451324
322571268
done50011268

prune212.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
529×sqrt-prod
456×*-un-lft-identity
422×add-sqr-sqrt
416×times-frac
162×add-cube-cbrt
138×swap-sqr
64×distribute-lft-out
62×associate-*r* associate-*l*
60×distribute-lft-out--
38×difference-of-squares
25×unswap-sqr
21×pow1
16×add-exp-log add-cbrt-cube
15×sqrt-div
8×sqrt-pow1 associate-/r/
4×cbrt-undiv sqrt-undiv flip3-+ div-exp prod-exp cbrt-unprod flip-+ div-inv add-log-exp
3×rem-sqrt-square pow1/2
2×pow2 frac-times flip3-- pow-plus associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up flip--
1×sqrt-unprod rem-square-sqrt *-commutative
Counts
4 → 366
Calls
4 calls:
22.0ms
(sqrt (* (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))
3.0ms
(sqrt (- 1.0 x))
4.0ms
(sqrt (- 1.0 x))
103.0ms
(* (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))

series196.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(sqrt (* (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))
32.0ms
(sqrt (- 1.0 x))
32.0ms
(sqrt (- 1.0 x))
40.0ms
(* (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))

simplify1.1s

Counts
378 → 378
Iterations

Useful iterations: done (1.1s)

IterNodesCost
031711040
19689329
230137435
done50007329

prune542.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite9.3s

Algorithm
rewrite-expression-head
Rules
33127×sqrt-prod
22704×times-frac
17434×add-sqr-sqrt
15572×*-un-lft-identity
6238×add-cube-cbrt
4002×swap-sqr
2277×distribute-lft-out
1628×distribute-lft-out--
980×difference-of-squares
866×associate-*r* associate-*l*
484×unswap-sqr
300×sqrt-div
148×associate-/r/
102×associate-/l*
74×flip3-+ flip-+ div-inv
49×add-exp-log add-cbrt-cube
30×associate-/r*
23×cbrt-undiv div-exp
12×sqrt-undiv
11×pow1
9×prod-exp cbrt-unprod
5×associate-/l/
4×add-log-exp
3×frac-2neg clear-num
2×flip3-- flip--
1×pow2 frac-times pow-plus sqrt-unprod associate-*r/ pow-prod-down associate-*l/ rem-square-sqrt pow-sqr *-commutative pow-prod-up
Counts
4 → 7458
Calls
4 calls:
48.0ms
(/ (/ (sqrt (- 1.0 x)) (sqrt (sqrt (+ 1.0 x)))) (sqrt (sqrt (+ 1.0 x))))
162.0ms
(/ (sqrt (- 1.0 x)) (sqrt (sqrt (+ 1.0 x))))
13.0ms
(/ (sqrt (- 1.0 x)) (sqrt (sqrt (+ 1.0 x))))
7.5s
(* (/ (/ (sqrt (- 1.0 x)) (sqrt (sqrt (+ 1.0 x)))) (sqrt (sqrt (+ 1.0 x)))) (/ (/ (sqrt (- 1.0 x)) (sqrt (sqrt (+ 1.0 x)))) (sqrt (sqrt (+ 1.0 x)))))

series631.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(/ (/ (sqrt (- 1.0 x)) (sqrt (sqrt (+ 1.0 x)))) (sqrt (sqrt (+ 1.0 x))))
251.0ms
(/ (sqrt (- 1.0 x)) (sqrt (sqrt (+ 1.0 x))))
251.0ms
(/ (sqrt (- 1.0 x)) (sqrt (sqrt (+ 1.0 x))))
41.0ms
(* (/ (/ (sqrt (- 1.0 x)) (sqrt (sqrt (+ 1.0 x)))) (sqrt (sqrt (+ 1.0 x)))) (/ (/ (sqrt (- 1.0 x)) (sqrt (sqrt (+ 1.0 x)))) (sqrt (sqrt (+ 1.0 x)))))

simplify2.0s

Counts
7470 → 7470
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01797438812
done5000438804

prune9.2s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes16.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01223
11423
done1423

end0.0ms

sample718.0ms

Algorithm
intervals
Results
308.0ms8000×body80valid
219.0ms8082×body80nan