Details

Time bar (total: 17.7s)

sample180.0ms

Algorithm
intervals
Results
49.0ms256×body80valid
13.0ms276×body80nan

simplify209.0ms

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

localize29.0ms

Local error

Found 3 expressions with local error:

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

rewrite111.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 97
Calls
3 calls:
29.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
62.0ms
(/ (- 1.0 x) (+ 1.0 x))
3.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

series180.0ms

Counts
3 → 9
Calls
3 calls:
122.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
40.0ms
(/ (- 1.0 x) (+ 1.0 x))
18.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify2.2s

Counts
106 → 106
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01731505
13721422
29201333
323331320
done50001300

prune445.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite359.0ms

Algorithm
rewrite-expression-head
Rules
670×sqrt-prod
586×*-un-lft-identity
528×times-frac
514×add-sqr-sqrt
228×add-cube-cbrt
138×swap-sqr
82×distribute-lft-out
74×distribute-lft-out--
62×associate-*r* associate-*l*
52×difference-of-squares
25×unswap-sqr
20×add-exp-log add-cbrt-cube
16×sqrt-div associate-/l*
14×associate-/r*
12×associate-/r/
11×pow1
6×cbrt-undiv sqrt-undiv flip3-+ div-exp flip-+ div-inv
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u associate-/l/ add-log-exp
2×flip3-- frac-2neg clear-num 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 → 504
Calls
4 calls:
1.0ms
(atan (sqrt (* (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))))
49.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
26.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
231.0ms
(* (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))

series320.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(atan (sqrt (* (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))))
150.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
118.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
45.0ms
(* (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))

simplify2.7s

Counts
516 → 516
Iterations

Useful iterations: done (2.7s)

IterNodesCost
031613994
191311942
227459995
done50009578

prune1.6s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b
(/ (- 1.0 x) (+ 1.0 x))
0.0b
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
0.0b
(expm1 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x)))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
65×*-un-lft-identity
46×add-sqr-sqrt
41×times-frac
26×sqrt-prod
25×add-cube-cbrt
11×distribute-lft-out
9×distribute-lft-out-- difference-of-squares
6×add-exp-log add-cbrt-cube
5×pow1 log1p-expm1-u associate-/l*
4×expm1-log1p-u associate-/r* associate-/r/ add-log-exp
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv expm1-log1p flip3-- frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub div-exp clear-num flip-- expm1-udef
Counts
4 → 108
Calls
4 calls:
33.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
31.0ms
(/ (- 1.0 x) (+ 1.0 x))
1.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
1.0ms
(expm1 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x)))))

series250.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
55.0ms
(/ (- 1.0 x) (+ 1.0 x))
3.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
72.0ms
(expm1 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x)))))

simplify2.2s

Counts
120 → 120
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01841683
13871592
29531483
324331470
done50011450

prune539.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))
0.0b
(cbrt (+ 1.0 x))
0.0b
(cbrt (+ 1.0 x))
0.0b
(cbrt (+ 1.0 x))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
36×cbrt-prod
35×*-un-lft-identity
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 swap-sqr flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 103
Calls
4 calls:
79.0ms
(* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))
4.0ms
(cbrt (+ 1.0 x))
4.0ms
(cbrt (+ 1.0 x))
5.0ms
(cbrt (+ 1.0 x))

series551.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))
124.0ms
(cbrt (+ 1.0 x))
110.0ms
(cbrt (+ 1.0 x))
150.0ms
(cbrt (+ 1.0 x))

simplify2.9s

Counts
115 → 115
Iterations

Useful iterations: done (2.9s)

IterNodesCost
01431535
13231385
28381323
321831174
done50001140

prune744.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes161.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01223
11423
done1423

end0.0ms

sample1.7s

Algorithm
intervals
Results
690.0ms8000×body80valid
586.0ms7937×body80nan