Details

Time bar (total: 14.1s)

sample148.0ms

Algorithm
intervals
Results
23.0ms256×body80valid
22.0ms283×body80nan

simplify83.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
0911
11611
21911
32111
done2111

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 3 expressions with local error:

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

rewrite105.0ms

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:
38.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
1.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
42.0ms
(/ (- 1.0 x) (+ 1.0 x))

series207.0ms

Counts
3 → 9
Calls
3 calls:
131.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
6.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
69.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify1.1s

Counts
100 → 100
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01621425
13541350
213911264
done50011262

prune558.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
85×sqrt-prod
78×*-un-lft-identity
60×add-sqr-sqrt
56×times-frac
40×add-cube-cbrt
10×distribute-lft-out
9×distribute-lft-out-- difference-of-squares
8×sqrt-div associate-/l*
7×associate-/r*
6×pow1 add-exp-log add-cbrt-cube
4×add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv sqrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 128
Calls
4 calls:
13.0ms
(sqrt (+ 1.0 x))
1.0ms
(atan (fabs (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))
12.0ms
(sqrt (- 1.0 x))
53.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

series251.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(sqrt (+ 1.0 x))
5.0ms
(atan (fabs (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))
49.0ms
(sqrt (- 1.0 x))
133.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

simplify938.0ms

Counts
140 → 140
Iterations

Useful iterations: done (930.0ms)

IterNodesCost
01842180
13441951
211481877
done50001848

prune719.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 2 expressions with local error:

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

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
36×*-un-lft-identity
28×times-frac
20×add-sqr-sqrt add-cube-cbrt sqrt-prod
8×distribute-lft-out
7×associate-/l*
5×difference-of-squares
4×add-exp-log associate-/r* add-cbrt-cube
2×pow1 sqrt-div associate-/r/ associate-/l/ add-log-exp
1×cbrt-undiv flip3-- frac-2neg flip3-+ div-exp clear-num flip-- flip-+ div-inv
Counts
2 → 62
Calls
2 calls:
1.0ms
(atan (fabs (/ (sqrt (- (* 1.0 1.0) (* x x))) (+ 1.0 x))))
47.0ms
(/ (sqrt (- (* 1.0 1.0) (* x x))) (+ 1.0 x))

series148.0ms

Counts
2 → 6
Calls
2 calls:
11.0ms
(atan (fabs (/ (sqrt (- (* 1.0 1.0) (* x x))) (+ 1.0 x))))
137.0ms
(/ (sqrt (- (* 1.0 1.0) (* x x))) (+ 1.0 x))

simplify908.0ms

Counts
68 → 68
Iterations

Useful iterations: done (902.0ms)

IterNodesCost
01371429
12881330
210701249
done50001238

prune399.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite278.0ms

Algorithm
rewrite-expression-head
Rules
1068×sqrt-prod
940×times-frac
668×*-un-lft-identity
428×add-sqr-sqrt
426×add-cube-cbrt
121×distribute-lft-out
97×difference-of-squares
56×sqrt-div associate-/r*
25×associate-/r/
14×flip3-- flip-- associate-/l*
13×div-inv
11×add-exp-log add-cbrt-cube
6×pow1
4×cbrt-undiv sqrt-pow1 div-exp associate-/l/ add-log-exp
2×rem-sqrt-square frac-2neg pow1/2 clear-num
1×flip3-+ flip-+
Counts
4 → 632
Calls
4 calls:
18.0ms
(sqrt (sqrt (- (* 1.0 1.0) (* x x))))
1.0ms
(atan (fabs (/ (sqrt (sqrt (- (* 1.0 1.0) (* x x)))) (/ (+ 1.0 x) (sqrt (sqrt (- (* 1.0 1.0) (* x x))))))))
108.0ms
(/ (sqrt (sqrt (- (* 1.0 1.0) (* x x)))) (/ (+ 1.0 x) (sqrt (sqrt (- (* 1.0 1.0) (* x x))))))
54.0ms
(/ (+ 1.0 x) (sqrt (sqrt (- (* 1.0 1.0) (* x x)))))

series653.0ms

Counts
4 → 12
Calls
4 calls:
331.0ms
(sqrt (sqrt (- (* 1.0 1.0) (* x x))))
10.0ms
(atan (fabs (/ (sqrt (sqrt (- (* 1.0 1.0) (* x x)))) (/ (+ 1.0 x) (sqrt (sqrt (- (* 1.0 1.0) (* x x))))))))
135.0ms
(/ (sqrt (sqrt (- (* 1.0 1.0) (* x x)))) (/ (+ 1.0 x) (sqrt (sqrt (- (* 1.0 1.0) (* x x))))))
177.0ms
(/ (+ 1.0 x) (sqrt (sqrt (- (* 1.0 1.0) (* x x)))))

simplify1.6s

Counts
644 → 644
Iterations

Useful iterations: done (1.5s)

IterNodesCost
066527458
1174724577
done500123956

prune3.1s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes58.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01216
11416
done1416

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.4s8000×body80valid
685.0ms8118×body80nan