Details

Time bar (total: 10.8s)

sample57.0ms

Algorithm
intervals
Results
30.0ms256×body80valid
12.0ms256×pre80true

simplify835.0ms

Counts
1 → 1
Iterations
IterNodes
done2012
62012
5753
4228
385
243
118
08

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.2b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(- 1 (* (/ b a) (/ b a)))
0.4b
(* (/ b a) (/ b a))
9.2b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
40×times-frac
33×*-un-lft-identity
32×add-cube-cbrt
15×add-cbrt-cube add-exp-log
13×swap-sqr associate-*r* associate-*l*
11×pow1
5×add-log-exp
4×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
3×sqrt-prod insert-posit16
2×difference-of-squares
1×pow2 frac-times rem-sqrt-square sub-neg sqrt-pow1 pow-plus flip3-- pow1/2 diff-log pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip--
Counts
3 → 97
Calls
3 calls:
9.0ms
(- 1 (* (/ b a) (/ b a)))
15.0ms
(* (/ b a) (/ b a))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series80.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(- 1 (* (/ b a) (/ b a)))
30.0ms
(* (/ b a) (/ b a))
13.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify1.3s

Counts
106 → 106
Iterations
IterNodes
done2000
32000
21395
1473
0154

prune467.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 9.2b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1 (/ b a))
0.2b
(* (+ 1 (/ b a)) (- 1 (/ b a)))
9.2b
(sqrt (fabs (* (+ 1 (/ b a)) (- 1 (/ b a)))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
14×*-un-lft-identity
8×associate-*r*
6×pow1 add-cube-cbrt
5×add-cbrt-cube add-exp-log add-log-exp
4×frac-times flip3-+ associate-*l* flip-+ difference-of-squares
3×flip3-- sqrt-prod insert-posit16 flip--
2×distribute-rgt-in sub-neg distribute-lft-in times-frac associate-*l/ associate-*r/ distribute-lft-out
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out-- unswap-sqr
Counts
3 → 64
Calls
3 calls:
12.0ms
(+ 1 (/ b a))
52.0ms
(* (+ 1 (/ b a)) (- 1 (/ b a)))
1.0ms
(sqrt (fabs (* (+ 1 (/ b a)) (- 1 (/ b a)))))

series122.0ms

Counts
3 → 9
Calls
3 calls:
22.0ms
(+ 1 (/ b a))
75.0ms
(* (+ 1 (/ b a)) (- 1 (/ b a)))
25.0ms
(sqrt (fabs (* (+ 1 (/ b a)) (- 1 (/ b a)))))

simplify1.1s

Counts
73 → 73
Iterations
IterNodes
done2003
32003
21073
1288
0102

prune413.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 9.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ b a))
0.3b
(* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a)))
0.3b
(* (sqrt (/ b a)) (/ b a))
9.2b
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a))))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
46×sqrt-prod
42×times-frac
35×*-un-lft-identity add-cube-cbrt
32×associate-*l*
30×pow1
18×add-cbrt-cube add-exp-log
15×pow-prod-up
14×associate-*r*
12×sqrt-pow1 pow1/2
11×sqrt-div
7×prod-exp cbrt-unprod
6×frac-times pow-plus associate-*r/ unswap-sqr
4×pow-prod-down associate-*l/ insert-posit16 div-inv add-log-exp
3×rem-sqrt-square
2×cbrt-undiv cube-unmult div-exp *-commutative
Counts
4 → 147
Calls
4 calls:
2.0ms
(sqrt (/ b a))
53.0ms
(* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a)))
15.0ms
(* (sqrt (/ b a)) (/ b a))
1.0ms
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a))))))

series283.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(sqrt (/ b a))
35.0ms
(* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a)))
173.0ms
(* (sqrt (/ b a)) (/ b a))
13.0ms
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a))))))

simplify1.4s

Counts
159 → 159
Iterations
IterNodes
done2000
32000
21432
1507
0199

prune752.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 9.1b

localize33.0ms

Local error

Found 4 expressions with local error:

9.2b
(sqrt (fabs (* (* (cbrt (- 1 (* (/ b a) (/ b a)))) (cbrt (- 1 (* (/ b a) (/ b a))))) (cbrt (- 1 (* (/ b a) (/ b a)))))))
9.5b
(cbrt (- 1 (* (/ b a) (/ b a))))
9.5b
(cbrt (- 1 (* (/ b a) (/ b a))))
9.5b
(cbrt (- 1 (* (/ b a) (/ b a))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
12×add-sqr-sqrt
11×*-un-lft-identity
8×add-cube-cbrt
6×cbrt-div difference-of-squares
5×pow1
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×flip3-- pow1/3 sqrt-prod flip--
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 62
Calls
4 calls:
1.0ms
(sqrt (fabs (* (* (cbrt (- 1 (* (/ b a) (/ b a)))) (cbrt (- 1 (* (/ b a) (/ b a))))) (cbrt (- 1 (* (/ b a) (/ b a)))))))
3.0ms
(cbrt (- 1 (* (/ b a) (/ b a))))
3.0ms
(cbrt (- 1 (* (/ b a) (/ b a))))
3.0ms
(cbrt (- 1 (* (/ b a) (/ b a))))

series644.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(sqrt (fabs (* (* (cbrt (- 1 (* (/ b a) (/ b a)))) (cbrt (- 1 (* (/ b a) (/ b a))))) (cbrt (- 1 (* (/ b a) (/ b a)))))))
198.0ms
(cbrt (- 1 (* (/ b a) (/ b a))))
219.0ms
(cbrt (- 1 (* (/ b a) (/ b a))))
202.0ms
(cbrt (- 1 (* (/ b a) (/ b a))))

simplify1.2s

Counts
74 → 74
Iterations
IterNodes
done2002
42002
3973
2344
1163
088

prune504.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 9.1b

regimes113.0ms

Accuracy

0% (0.1b remaining)

Error of 7.5b against oracle of 7.4b and baseline of 7.5b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done13
113
09

end0.0ms

sample1.3s

Algorithm
intervals
Results
806.0ms8000×body80valid
373.0ms8000×pre80true