Details

Time bar (total: 15.4s)

sample40.0ms

Algorithm
intervals
Results
17.0ms256×body80valid
9.0ms256×pre80true

simplify1.4s

Counts
1 → 1
Iterations
IterNodes
done5004
62324
5753
4228
385
243
118
08

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.7b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(- 1 (* (/ b a) (/ b a)))
0.4b
(* (/ b a) (/ b a))
5.7b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite28.0ms

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)))
16.0ms
(* (/ b a) (/ b a))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series117.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(- 1 (* (/ b a) (/ b a)))
39.0ms
(* (/ b a) (/ b a))
24.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify1.4s

Counts
106 → 106
Iterations
IterNodes
done5000
21395
1473
0154

prune479.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.7b

localize22.0ms

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)))
5.7b
(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:
6.0ms
(+ 1 (/ b a))
7.0ms
(- 1 (/ b a))
62.0ms
(* (+ 1 (/ b a)) (- 1 (/ b a)))
2.0ms
(sqrt (fabs (* (+ 1 (/ b a)) (- 1 (/ b a)))))

series161.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(+ 1 (/ b a))
34.0ms
(- 1 (/ b a))
89.0ms
(* (+ 1 (/ b a)) (- 1 (/ b a)))
18.0ms
(sqrt (fabs (* (+ 1 (/ b a)) (- 1 (/ b a)))))

simplify2.6s

Counts
94 → 94
Iterations
IterNodes
done5001
32936
21106
1305
0109

prune465.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 5.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ b a) (/ b a))
0.4b
(* (/ b a) (/ b a))
5.7b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
14.2b
(cbrt (* (fabs (- 1 (* (/ b a) (/ b a)))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
87×add-sqr-sqrt
80×times-frac
61×*-un-lft-identity add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
19×pow1
8×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
4×insert-posit16 add-log-exp
3×sqrt-prod
2×pow2 frac-times pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
1×cbrt-prod rem-sqrt-square sqrt-pow1 pow1/2 pow1/3 pow3 rem-cbrt-cube
Counts
4 → 161
Calls
4 calls:
13.0ms
(* (/ b a) (/ b a))
20.0ms
(* (/ b a) (/ b a))
9.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
8.0ms
(cbrt (* (fabs (- 1 (* (/ b a) (/ b a)))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))

series133.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (/ b a) (/ b a))
42.0ms
(* (/ b a) (/ b a))
22.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
16.0ms
(cbrt (* (fabs (- 1 (* (/ b a) (/ b a)))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))

simplify2.7s

Counts
173 → 173
Iterations
IterNodes
done5022
34017
21328
1421
0140

prune879.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 5.6b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1 (/ b a))
0.2b
(* (posit16->real (real->posit16 (+ 1 (/ b a)))) (- 1 (/ b a)))
5.7b
(sqrt (fabs (* (posit16->real (real->posit16 (+ 1 (/ b a)))) (- 1 (/ b a)))))
29.8b
(posit16->real (real->posit16 (+ 1 (/ b a))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
13×*-un-lft-identity
8×associate-*r*
7×pow1 add-cube-cbrt
6×add-cbrt-cube add-exp-log add-log-exp
4×insert-posit16 difference-of-squares
3×associate-*l* sqrt-prod
2×distribute-rgt-in sub-neg distribute-lft-in times-frac associate-*r/
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 flip3-+ flip3-- pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ remove-posit16 flip-- distribute-lft-out distribute-lft-out-- unswap-sqr
Counts
4 → 66
Calls
4 calls:
12.0ms
(+ 1 (/ b a))
43.0ms
(* (posit16->real (real->posit16 (+ 1 (/ b a)))) (- 1 (/ b a)))
1.0ms
(sqrt (fabs (* (posit16->real (real->posit16 (+ 1 (/ b a)))) (- 1 (/ b a)))))
0.0ms
(posit16->real (real->posit16 (+ 1 (/ b a))))

series155.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(+ 1 (/ b a))
87.0ms
(* (posit16->real (real->posit16 (+ 1 (/ b a)))) (- 1 (/ b a)))
26.0ms
(sqrt (fabs (* (posit16->real (real->posit16 (+ 1 (/ b a)))) (- 1 (/ b a)))))
27.0ms
(posit16->real (real->posit16 (+ 1 (/ b a))))

simplify2.3s

Counts
78 → 78
Iterations
IterNodes
done5003
32592
2898
1244
0102

prune657.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 5.6b

regimes138.0ms

Accuracy

0% (0.1b remaining)

Error of 7.6b against oracle of 7.5b and baseline of 7.6b

bsearch0.0ms

simplify1.0ms

Iterations
IterNodes
done13
113
09

end0.0ms

sample1.3s

Algorithm
intervals
Results
708.0ms8000×pre80true
509.0ms8000×body80valid