Details

Time bar (total: 19.3s)

sample51.0ms

Algorithm
intervals
Results
25.0ms256×body80valid
11.0ms256×pre80true

simplify2.3s

Counts
1 → 1
Iterations
IterNodes
done5216
62493
5808
4236
388
244
119
08

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.7b

localize15.0ms

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)))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
40×times-frac
35×*-un-lft-identity
34×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×expm1-log1p-u fma-neg prod-diff sqrt-prod insert-posit16 log1p-expm1-u
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 → 109
Calls
3 calls:
10.0ms
(- 1 (* (/ b a) (/ b a)))
20.0ms
(* (/ b a) (/ b a))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series120.0ms

Counts
3 → 9
Calls
3 calls:
51.0ms
(- 1 (* (/ b a) (/ b a)))
46.0ms
(* (/ b a) (/ b a))
23.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify3.3s

Counts
118 → 118
Iterations
IterNodes
done5000
34909
21597
1496
0167

prune461.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.7b

localize16.0ms

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)))))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
130×add-sqr-sqrt
123×*-un-lft-identity
117×prod-diff
111×add-cube-cbrt
85×times-frac
41×distribute-rgt-in distribute-lft-in
9×div-inv
8×associate-*r* add-log-exp difference-of-squares
7×pow1
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u frac-times flip3-+ flip3-- associate-*l* flip-+ insert-posit16 log1p-expm1-u flip--
3×sub-neg fma-def fma-neg sqrt-prod
2×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 → 213
Calls
4 calls:
6.0ms
(+ 1 (/ b a))
8.0ms
(- 1 (/ b a))
52.0ms
(* (+ 1 (/ b a)) (- 1 (/ b a)))
1.0ms
(sqrt (fabs (* (+ 1 (/ b a)) (- 1 (/ b a)))))

series107.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(+ 1 (/ b a))
21.0ms
(- 1 (/ b a))
51.0ms
(* (+ 1 (/ b a)) (- 1 (/ b a)))
21.0ms
(sqrt (fabs (* (+ 1 (/ b a)) (- 1 (/ b a)))))

simplify3.1s

Counts
225 → 225
Iterations
IterNodes
done5001
22689
11122
0334

prune835.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 5.6b

localize19.0ms

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)))))))

rewrite45.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u 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 → 169
Calls
4 calls:
13.0ms
(* (/ b a) (/ b a))
24.0ms
(* (/ b a) (/ b a))
2.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
4.0ms
(cbrt (* (fabs (- 1 (* (/ b a) (/ b a)))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))

series119.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (/ b a) (/ b a))
43.0ms
(* (/ b a) (/ b a))
22.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
22.0ms
(cbrt (* (fabs (- 1 (* (/ b a) (/ b a)))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))

simplify2.6s

Counts
181 → 181
Iterations
IterNodes
done5349
34030
21407
1428
0146

prune894.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 5.6b

localize64.0ms

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))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
87×add-sqr-sqrt
82×*-un-lft-identity
78×prod-diff
76×add-cube-cbrt
56×times-frac
41×distribute-rgt-in distribute-lft-in
8×associate-*r*
7×pow1
6×add-cbrt-cube add-exp-log div-inv add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u difference-of-squares
3×fma-def associate-*l* sqrt-prod
2×sub-neg 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 → 155
Calls
4 calls:
12.0ms
(+ 1 (/ b a))
31.0ms
(* (posit16->real (real->posit16 (+ 1 (/ b a)))) (- 1 (/ b a)))
2.0ms
(sqrt (fabs (* (posit16->real (real->posit16 (+ 1 (/ b a)))) (- 1 (/ b a)))))
1.0ms
(posit16->real (real->posit16 (+ 1 (/ b a))))

series118.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(+ 1 (/ b a))
72.0ms
(* (posit16->real (real->posit16 (+ 1 (/ b a)))) (- 1 (/ b a)))
12.0ms
(sqrt (fabs (* (posit16->real (real->posit16 (+ 1 (/ b a)))) (- 1 (/ b a)))))
20.0ms
(posit16->real (real->posit16 (+ 1 (/ b a))))

simplify2.0s

Counts
167 → 167
Iterations
IterNodes
done5001
21790
1751
0327

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.6b

regimes555.0ms

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
782.0ms8000×body80valid
385.0ms8000×pre80true