Details

Time bar (total: 18.5s)

sample119.0ms

Algorithm
intervals
Results
49.0ms505×body80nan
33.0ms248×body160nan
19.0ms256×body80valid

simplify5.6s

Counts
1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize20.0ms

Local error

Found 4 expressions with local error:

29.9b
(sqrt (- (* x x) 1))
0.0b
(+ x (sqrt (- (* x x) 1)))
0.0b
(- (* x x) 1)
0.0b
(log (+ x (sqrt (- (* x x) 1))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
9×add-sqr-sqrt
8×add-log-exp
6×pow1 add-cube-cbrt sqrt-prod
5×add-exp-log
4×log-prod add-cbrt-cube insert-posit16 difference-of-squares
2×log-div flip3-+ flip3-- sqrt-div difference-of-sqr-1 flip-+ flip-- distribute-lft-out
1×+-commutative rem-sqrt-square sum-log sub-neg sqrt-pow1 pow1/2 diff-log rem-log-exp log-pow
Counts
4 → 64
Calls
4 calls:
Slowest
12.0ms
(+ x (sqrt (- (* x x) 1)))
11.0ms
(log (+ x (sqrt (- (* x x) 1))))
8.0ms
(sqrt (- (* x x) 1))
7.0ms
(- (* x x) 1)

series428.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
195.0ms
(log (+ x (sqrt (- (* x x) 1))))
99.0ms
(+ x (sqrt (- (* x x) 1)))
74.0ms
(sqrt (- (* x x) 1))
59.0ms
(- (* x x) 1)

simplify1.1s

Counts
76 → 76

prune741.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 3 expressions with local error:

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

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
15×sqrt-prod
13×*-un-lft-identity
12×sqrt-div
10×associate-*r*
8×pow1 add-cube-cbrt
7×associate-*l*
6×add-exp-log
5×flip3-+ add-cbrt-cube flip-+ add-log-exp
4×frac-times unswap-sqr
3×log-prod flip3-- pow-prod-down insert-posit16 flip--
2×log-div sqrt-pow1 pow1/2 associate-*l/ associate-*r/ difference-of-squares
1×+-commutative sum-log sqrt-unprod difference-of-sqr-1 rem-log-exp prod-exp log-pow *-commutative cbrt-unprod distribute-lft-out distribute-lft-out--
Counts
3 → 71
Calls
3 calls:
Slowest
26.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
5.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
3.0ms
(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))

series457.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
233.0ms
(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
120.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
104.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))

simplify1.2s

Counts
80 → 80

prune838.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (sqrt (+ x 1)))
0.5b
(cbrt (sqrt (+ x 1)))
0.5b
(cbrt (sqrt (+ x 1)))
0.4b
(* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
69×cbrt-prod
44×add-sqr-sqrt
42×*-un-lft-identity
40×sqrt-prod
22×add-cube-cbrt
18×cbrt-div sqrt-div
14×swap-sqr
11×pow1
10×associate-*r* associate-*l*
9×flip3-+ pow1/3 flip-+ distribute-lft-out unswap-sqr
6×add-exp-log
4×frac-times add-cbrt-cube insert-posit16 add-log-exp
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 124
Calls
4 calls:
Slowest
29.0ms
(* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))
3.0ms
(cbrt (sqrt (+ x 1)))
3.0ms
(cbrt (sqrt (+ x 1)))
3.0ms
(cbrt (sqrt (+ x 1)))

series210.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
65.0ms
(cbrt (sqrt (+ x 1)))
55.0ms
(* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))
52.0ms
(cbrt (sqrt (+ x 1)))
38.0ms
(cbrt (sqrt (+ x 1)))

simplify1.8s

Counts
136 → 136

prune1.7s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes25.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.8s7691×body160nan
1.2s16542×body80nan
695.0ms8000×body80valid