Details

Time bar (total: 15.2s)

sample105.0ms

Algorithm
intervals
Results
38.0ms513×body80nan
33.0ms261×body160nan
18.0ms256×body80valid

simplify1.7s

Counts
1 → 1
Iterations
IterNodes
done2000
82000
71825
6472
5156
460
335
219
116
07

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1)))
31.9b
(sqrt (- (* x x) 1))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
6×*-un-lft-identity sqrt-prod
5×add-sqr-sqrt
4×add-log-exp
3×pow1 add-cube-cbrt
2×add-cbrt-cube sqrt-div add-exp-log insert-posit16 difference-of-squares
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 flip3-+ flip3-- pow1/2 difference-of-sqr-1 flip-+ flip-- distribute-lft-out
Counts
2 → 32
Calls
2 calls:
15.0ms
(+ x (sqrt (- (* x x) 1)))
17.0ms
(sqrt (- (* x x) 1))

series113.0ms

Counts
2 → 6
Calls
2 calls:
72.0ms
(+ x (sqrt (- (* x x) 1)))
41.0ms
(sqrt (- (* x x) 1))

simplify1.1s

Counts
38 → 38
Iterations
IterNodes
done2000
42000
31427
2508
1208
091

prune242.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1))
0.0b
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
0.5b
(* (sqrt (+ x 1)) (sqrt (- x 1)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×sqrt-prod
15×*-un-lft-identity
14×sqrt-div
10×associate-*r*
8×pow1 add-cube-cbrt
7×associate-*l*
5×flip3-+ add-cbrt-cube add-exp-log flip-+ add-log-exp
4×frac-times unswap-sqr
3×sqrt-pow1 flip3-- pow1/2 pow-prod-down insert-posit16 flip--
2×associate-*l/ associate-*r/ distribute-lft-out difference-of-squares
1×+-commutative rem-sqrt-square sum-log sqrt-unprod difference-of-sqr-1 prod-exp *-commutative cbrt-unprod distribute-lft-out--
Counts
3 → 73
Calls
3 calls:
4.0ms
(sqrt (+ x 1))
7.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
41.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))

series222.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(sqrt (+ x 1))
89.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
105.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))

simplify1.0s

Counts
82 → 82
Iterations
IterNodes
done2008
32008
2745
1321
0142

prune705.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (* (sqrt (+ x 1)) (sqrt (- x 1)))) (cbrt (* (sqrt (+ x 1)) (sqrt (- x 1)))))
0.5b
(cbrt (* (sqrt (+ x 1)) (sqrt (- x 1))))
0.5b
(cbrt (* (sqrt (+ x 1)) (sqrt (- x 1))))
0.5b
(cbrt (* (sqrt (+ x 1)) (sqrt (- x 1))))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
252×sqrt-div
168×cbrt-div
148×frac-times
63×flip3-+ flip3-- flip-+ flip--
50×associate-*l/ associate-*r/
11×pow1
10×add-sqr-sqrt
9×pow1/3
8×*-un-lft-identity add-cube-cbrt
7×cbrt-prod
6×add-exp-log
4×add-cbrt-cube swap-sqr associate-*r* associate-*l* insert-posit16 add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 166
Calls
4 calls:
45.0ms
(* (cbrt (* (sqrt (+ x 1)) (sqrt (- x 1)))) (cbrt (* (sqrt (+ x 1)) (sqrt (- x 1)))))
27.0ms
(cbrt (* (sqrt (+ x 1)) (sqrt (- x 1))))
20.0ms
(cbrt (* (sqrt (+ x 1)) (sqrt (- x 1))))
20.0ms
(cbrt (* (sqrt (+ x 1)) (sqrt (- x 1))))

series845.0ms

Counts
4 → 12
Calls
4 calls:
219.0ms
(* (cbrt (* (sqrt (+ x 1)) (sqrt (- x 1)))) (cbrt (* (sqrt (+ x 1)) (sqrt (- x 1)))))
214.0ms
(cbrt (* (sqrt (+ x 1)) (sqrt (- x 1))))
197.0ms
(cbrt (* (sqrt (+ x 1)) (sqrt (- x 1))))
214.0ms
(cbrt (* (sqrt (+ x 1)) (sqrt (- x 1))))

simplify1.4s

Counts
178 → 178
Iterations
IterNodes
done2001
32001
21103
1558
0308

prune3.1s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes44.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done18
118
012

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.8s7723×body160nan
1.3s16421×body80nan
719.0ms8000×body80valid