Details

Time bar (total: 26.6s)

sample132.0ms

Algorithm
intervals
Results
37.0ms260×body160nan
35.0ms510×body80nan
21.0ms256×body80valid

simplify37.0ms

Counts
1 → 1
Iterations
IterNodes
done11
211
110
07

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize97.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
0.0b
(log (+ x (sqrt (- (* x x) 1.0))))
30.4b
(sqrt (- (* x x) 1.0))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
7×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×log-prod add-exp-log sqrt-prod
3×add-cbrt-cube insert-posit16
2×log-div flip3-+ sqrt-div flip-+ distribute-lft-out
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 flip3-- pow1/2 rem-log-exp log-pow flip-- difference-of-squares
Counts
3 → 46
Calls
3 calls:
51.0ms
(+ x (sqrt (- (* x x) 1.0)))
46.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
23.0ms
(sqrt (- (* x x) 1.0))

series523.0ms

Counts
3 → 9
Calls
3 calls:
127.0ms
(+ x (sqrt (- (* x x) 1.0)))
299.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
97.0ms
(sqrt (- (* x x) 1.0))

simplify5.8s

Counts
55 → 55
Iterations
IterNodes
done5017
33266
2908
1320
0142

prune564.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize135.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- x (sqrt 1.0)))
0.0b
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.0b
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.5b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite234.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
22×sqrt-prod
16×*-un-lft-identity
14×sqrt-div
10×pow1 add-cube-cbrt
9×associate-*r*
7×associate-*l* add-exp-log
6×add-cbrt-cube add-log-exp
5×flip3-+ flip-+
4×frac-times flip3-- insert-posit16 flip-- difference-of-squares unswap-sqr
3×log-prod sqrt-pow1 pow1/2 pow-prod-down
2×log-div associate-*l/ associate-*r/ distribute-lft-out--
1×+-commutative rem-sqrt-square sum-log sqrt-unprod rem-log-exp prod-exp log-pow *-commutative cbrt-unprod distribute-lft-out
Counts
4 → 89
Calls
4 calls:
39.0ms
(sqrt (- x (sqrt 1.0)))
26.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
17.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
145.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series1.1s

Counts
4 → 12
Calls
4 calls:
90.0ms
(sqrt (- x (sqrt 1.0)))
276.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
470.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
282.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify3.8s

Counts
101 → 101
Iterations
IterNodes
done5002
21498
1511
0218

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize191.0ms

Local error

Found 4 expressions with local error:

0.2b
(sqrt (log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))))
0.5b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
0.5b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
0.6b
(* (sqrt (log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))) (sqrt (log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))))

rewrite413.0ms

Algorithm
rewrite-expression-head
Rules
60×sqrt-prod
58×add-sqr-sqrt
35×pow1
31×*-un-lft-identity
25×associate-*r*
24×sqrt-div
21×associate-*l* add-cube-cbrt
13×sqrt-pow1 pow1/2
12×unswap-sqr
11×swap-sqr
10×add-cbrt-cube add-exp-log
9×pow-prod-down
8×frac-times
7×log-pow
6×flip3-+ flip3-- flip-+ flip--
5×pow-prod-up
4×associate-*l/ associate-*r/ insert-posit16 add-log-exp difference-of-squares
3×sqrt-unprod prod-exp pow-sqr *-commutative cbrt-unprod
2×distribute-lft-out distribute-lft-out--
1×pow2 rem-sqrt-square rem-square-sqrt pow-plus
Counts
4 → 156
Calls
4 calls:
7.0ms
(sqrt (log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))))
140.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
179.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
62.0ms
(* (sqrt (log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))) (sqrt (log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))))

series1.6s

Counts
4 → 12
Calls
4 calls:
524.0ms
(sqrt (log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))))
293.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
296.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
472.0ms
(* (sqrt (log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))) (sqrt (log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))))

simplify4.1s

Counts
168 → 168
Iterations
IterNodes
done5002
21749
1611
0255

prune1.5s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes267.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify10.0ms

Iterations
IterNodes
done13
113
010

end0.0ms

sample4.9s

Algorithm
intervals
Results
2.1s15928×body80nan
1.4s7666×body160nan
669.0ms8000×body80valid