Details

Time bar (total: 9.8s)

sample66.0ms

Algorithm
intervals
Results
38.0ms256×body80valid
12.0ms256×pre80true

simplify540.0ms

Counts
1 → 1
Iterations
IterNodes
done2000
5753
4228
385
243
118
08

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.3b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b
(- 1 (* (/ b a) (/ b a)))
0.4b
(* (/ b a) (/ b a))
8.3b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite38.0ms

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:
8.0ms
(- 1 (* (/ b a) (/ b a)))
26.0ms
(* (/ b a) (/ b a))
2.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series116.0ms

Counts
3 → 9
Calls
3 calls:
55.0ms
(- 1 (* (/ b a) (/ b a)))
36.0ms
(* (/ b a) (/ b a))
25.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify805.0ms

Counts
106 → 106
Iterations
IterNodes
done2000
21395
1473
0154

prune392.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 1 (/ b a))
0.0b
(+ 1 (/ b a))
0.2b
(* (+ 1 (/ b a)) (- 1 (/ b a)))
8.3b
(sqrt (fabs (* (+ 1 (/ b a)) (- 1 (/ b a)))))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
19×*-un-lft-identity
8×associate-*r* add-log-exp difference-of-squares
7×pow1 add-cube-cbrt
6×add-cbrt-cube add-exp-log
4×frac-times flip3-+ times-frac flip3-- associate-*l* flip-+ insert-posit16 flip--
3×sub-neg sqrt-prod
2×distribute-rgt-in distribute-lft-in associate-*l/ associate-*r/ distribute-lft-out distribute-lft-out--
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 82
Calls
4 calls:
7.0ms
(- 1 (/ b a))
6.0ms
(+ 1 (/ b a))
64.0ms
(* (+ 1 (/ b a)) (- 1 (/ b a)))
2.0ms
(sqrt (fabs (* (+ 1 (/ b a)) (- 1 (/ b a)))))

series113.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(- 1 (/ b a))
18.0ms
(+ 1 (/ b a))
62.0ms
(* (+ 1 (/ b a)) (- 1 (/ b a)))
13.0ms
(sqrt (fabs (* (+ 1 (/ b a)) (- 1 (/ b a)))))

simplify649.0ms

Counts
94 → 94
Iterations
IterNodes
done2002
21105
1305
0109

prune401.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 8.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ b a))
0.2b
(* (* (/ b a) (sqrt (/ b a))) (sqrt (/ b a)))
0.3b
(* (/ b a) (sqrt (/ b a)))
8.3b
(sqrt (fabs (- 1 (* (* (/ b a) (sqrt (/ b a))) (sqrt (/ b a))))))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
46×sqrt-prod
42×times-frac
35×*-un-lft-identity add-cube-cbrt
32×associate-*r*
25×pow1
18×add-cbrt-cube add-exp-log
14×associate-*l*
11×sqrt-div pow-prod-up
7×sqrt-pow1 pow1/2 prod-exp cbrt-unprod
6×frac-times associate-*l/ unswap-sqr
4×pow-prod-down associate-*r/ insert-posit16 div-inv add-log-exp
3×rem-sqrt-square pow3
2×cbrt-undiv div-exp *-commutative
1×pow-plus
Counts
4 → 142
Calls
4 calls:
4.0ms
(sqrt (/ b a))
72.0ms
(* (* (/ b a) (sqrt (/ b a))) (sqrt (/ b a)))
28.0ms
(* (/ b a) (sqrt (/ b a)))
2.0ms
(sqrt (fabs (- 1 (* (* (/ b a) (sqrt (/ b a))) (sqrt (/ b a))))))

series333.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(sqrt (/ b a))
46.0ms
(* (* (/ b a) (sqrt (/ b a))) (sqrt (/ b a)))
181.0ms
(* (/ b a) (sqrt (/ b a)))
24.0ms
(sqrt (fabs (- 1 (* (* (/ b a) (sqrt (/ b a))) (sqrt (/ b a))))))

simplify984.0ms

Counts
154 → 154
Iterations
IterNodes
done2005
21828
1512
0202

prune783.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 8.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (/ b a) (sqrt (/ b a))) (posit16->real (real->posit16 (sqrt (/ b a)))))
0.3b
(* (/ b a) (sqrt (/ b a)))
8.3b
(sqrt (fabs (- 1 (* (* (/ b a) (sqrt (/ b a))) (posit16->real (real->posit16 (sqrt (/ b a))))))))
56.9b
(posit16->real (real->posit16 (sqrt (/ b a))))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
23×times-frac
21×*-un-lft-identity add-cube-cbrt
20×sqrt-prod
19×associate-*r*
18×add-cbrt-cube add-exp-log
15×pow1
14×associate-*l*
7×prod-exp cbrt-unprod
6×unswap-sqr
5×associate-*l/
4×sqrt-div pow-prod-down insert-posit16 add-log-exp
2×frac-times cbrt-undiv sqrt-pow1 pow1/2 div-exp associate-*r/ *-commutative pow-prod-up div-inv
1×rem-sqrt-square pow3 remove-posit16
Counts
4 → 102
Calls
4 calls:
36.0ms
(* (* (/ b a) (sqrt (/ b a))) (posit16->real (real->posit16 (sqrt (/ b a)))))
15.0ms
(* (/ b a) (sqrt (/ b a)))
1.0ms
(sqrt (fabs (- 1 (* (* (/ b a) (sqrt (/ b a))) (posit16->real (real->posit16 (sqrt (/ b a))))))))
0.0ms
(posit16->real (real->posit16 (sqrt (/ b a))))

series297.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (* (/ b a) (sqrt (/ b a))) (posit16->real (real->posit16 (sqrt (/ b a)))))
179.0ms
(* (/ b a) (sqrt (/ b a)))
14.0ms
(sqrt (fabs (- 1 (* (* (/ b a) (sqrt (/ b a))) (posit16->real (real->posit16 (sqrt (/ b a))))))))
68.0ms
(posit16->real (real->posit16 (sqrt (/ b a))))

simplify983.0ms

Counts
114 → 114
Iterations
IterNodes
done2001
21266
1419
0180

prune983.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 8.2b

regimes187.0ms

Accuracy

0% (0.1b remaining)

Error of 7.3b against oracle of 7.2b and baseline of 7.3b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done13
113
09

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.3s8000×body80valid
319.0ms8000×pre80true