Details

Time bar (total: 22.7s)

sample34.0ms

Algorithm
intervals
Results
18.0ms256×body80valid
7.0ms256×pre80true

simplify2.6s

Counts
1 → 1
Iterations
IterNodes
85093
71204
6512
5299
4159
385
243
118
08

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.5b

localize12.0ms

Local error

Found 2 expressions with local error:

0.4b
(* (/ b a) (/ b a))
8.6b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
40×times-frac
31×*-un-lft-identity add-cube-cbrt
14×add-cbrt-cube add-exp-log
13×swap-sqr associate-*r* associate-*l*
10×pow1
4×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
3×sqrt-prod
2×insert-posit16 add-log-exp
1×pow2 frac-times rem-sqrt-square sqrt-pow1 pow-plus pow1/2 pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
2 → 82
Calls
2 calls:
20.0ms
(* (/ b a) (/ b a))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series50.0ms

Counts
2 → 6
Calls
2 calls:
31.0ms
(* (/ b a) (/ b a))
19.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify1.7s

Counts
88 → 88
Iterations
IterNodes
34268
21217
1393
0130

prune781.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 8.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt b) a)
0.3b
(* (/ (sqrt b) (/ a b)) (/ (sqrt b) a))
0.3b
(/ (sqrt b) (/ a b))
8.6b
(sqrt (fabs (- 1 (* (/ (sqrt b) (/ a b)) (/ (sqrt b) a)))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
337×times-frac
238×add-sqr-sqrt
179×*-un-lft-identity add-cube-cbrt
116×sqrt-prod
83×associate-*l*
32×add-cbrt-cube add-exp-log
22×associate-*r*
17×div-inv
16×associate-/r*
15×unswap-sqr
13×cbrt-undiv div-exp
12×associate-/l*
7×pow1
6×prod-exp cbrt-unprod
4×insert-posit16 add-log-exp
2×clear-num frac-2neg associate-/r/
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 312
Calls
4 calls:
9.0ms
(/ (sqrt b) a)
22.0ms
(* (/ (sqrt b) (/ a b)) (/ (sqrt b) a))
6.0ms
(/ (sqrt b) (/ a b))
1.0ms
(sqrt (fabs (- 1 (* (/ (sqrt b) (/ a b)) (/ (sqrt b) a)))))

series224.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(/ (sqrt b) a)
46.0ms
(* (/ (sqrt b) (/ a b)) (/ (sqrt b) a))
82.0ms
(/ (sqrt b) (/ a b))
20.0ms
(sqrt (fabs (- 1 (* (/ (sqrt b) (/ a b)) (/ (sqrt b) a)))))

simplify1.7s

Counts
324 → 324
Iterations
IterNodes
25166
11191
0397

prune3.6s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 8.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ b a) (/ b a))
0.4b
(* (/ b a) (/ b a))
8.6b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
8.6b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
88×add-sqr-sqrt
80×times-frac
62×*-un-lft-identity add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
20×pow1
8×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
6×sqrt-prod
4×insert-posit16 add-log-exp
2×pow2 frac-times rem-sqrt-square sqrt-pow1 pow-plus pow1/2 pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
4 → 164
Calls
4 calls:
16.0ms
(* (/ b a) (/ b a))
12.0ms
(* (/ b a) (/ b a))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series90.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (/ b a) (/ b a))
30.0ms
(* (/ b a) (/ b a))
19.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
13.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify2.3s

Counts
176 → 176
Iterations
IterNodes
34268
21217
1393
0130

prune2.4s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 8.4b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (posit16->real (real->posit16 (/ (sqrt b) (/ a b)))) (/ (sqrt b) a))
0.3b
(/ (sqrt b) (/ a b))
8.6b
(sqrt (fabs (- 1 (* (posit16->real (real->posit16 (/ (sqrt b) (/ a b)))) (/ (sqrt b) a)))))
55.4b
(posit16->real (real->posit16 (/ (sqrt b) (/ a b))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
161×times-frac
105×add-sqr-sqrt
96×*-un-lft-identity add-cube-cbrt
55×sqrt-prod
22×associate-*r*
14×add-cbrt-cube add-exp-log
13×associate-/r*
9×div-inv
7×pow1
6×associate-/l*
4×cbrt-undiv div-exp insert-posit16 add-log-exp
3×associate-*l* unswap-sqr
2×prod-exp cbrt-unprod
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*r/ associate-/r/ *-commutative remove-posit16
Counts
4 → 179
Calls
4 calls:
10.0ms
(* (posit16->real (real->posit16 (/ (sqrt b) (/ a b)))) (/ (sqrt b) a))
7.0ms
(/ (sqrt b) (/ a b))
1.0ms
(sqrt (fabs (- 1 (* (posit16->real (real->posit16 (/ (sqrt b) (/ a b)))) (/ (sqrt b) a)))))
0.0ms
(posit16->real (real->posit16 (/ (sqrt b) (/ a b))))

series262.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (posit16->real (real->posit16 (/ (sqrt b) (/ a b)))) (/ (sqrt b) a))
86.0ms
(/ (sqrt b) (/ a b))
23.0ms
(sqrt (fabs (- 1 (* (posit16->real (real->posit16 (/ (sqrt b) (/ a b)))) (/ (sqrt b) a)))))
99.0ms
(posit16->real (real->posit16 (/ (sqrt b) (/ a b))))

simplify722.0ms

Counts
191 → 191
Iterations
IterNodes
22610
1779
0315

prune4.4s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 8.4b

regimes170.0ms

Accuracy

0% (0.1b remaining)

Error of 8.1b against oracle of 8.0b and baseline of 8.1b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
210
110
08

end0.0ms

sample1.3s

Algorithm
intervals
Results
771.0ms8000×body80valid
374.0ms8000×pre80true