Details

Time bar (total: 10.4s)

sample45.0ms

Algorithm
intervals
Results
26.0ms256×body80valid
7.0ms256×pre80true

simplify629.0ms

Counts
1 → 1
Iterations
IterNodes
done2002
5808
4236
388
244
119
08

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.3b

localize13.0ms

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)))))

rewrite25.0ms

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:
9.0ms
(- 1 (* (/ b a) (/ b a)))
13.0ms
(* (/ b a) (/ b a))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series93.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(- 1 (* (/ b a) (/ b a)))
37.0ms
(* (/ b a) (/ b a))
14.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify1.5s

Counts
118 → 118
Iterations
IterNodes
done2000
21597
1496
0167

prune444.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.3b

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

rewrite84.0ms

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:
8.0ms
(- 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)))))

series104.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(- 1 (/ b a))
13.0ms
(+ 1 (/ b a))
56.0ms
(* (+ 1 (/ b a)) (- 1 (/ b a)))
16.0ms
(sqrt (fabs (* (+ 1 (/ b a)) (- 1 (/ b a)))))

simplify1.0s

Counts
225 → 225
Iterations
IterNodes
done2001
11122
0334

prune920.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 8.2b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
53×add-sqr-sqrt
47×times-frac
42×*-un-lft-identity add-cube-cbrt
35×associate-*r*
32×add-cbrt-cube add-exp-log
29×sqrt-prod
12×pow1 prod-exp cbrt-unprod
7×cbrt-undiv div-exp associate-*l*
6×associate-/l*
4×expm1-log1p-u pow-prod-down associate-*r/ insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×associate-/r* div-inv
2×*-commutative
1×frac-times rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-*l/
Counts
4 → 149
Calls
4 calls:
9.0ms
(/ (sqrt b) a)
42.0ms
(* (* (sqrt b) (/ b a)) (/ (sqrt b) a))
15.0ms
(* (sqrt b) (/ b a))
1.0ms
(sqrt (fabs (- 1 (* (* (sqrt b) (/ b a)) (/ (sqrt b) a)))))

series239.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(/ (sqrt b) a)
46.0ms
(* (* (sqrt b) (/ b a)) (/ (sqrt b) a))
75.0ms
(* (sqrt b) (/ b a))
23.0ms
(sqrt (fabs (- 1 (* (* (sqrt b) (/ b a)) (/ (sqrt b) a)))))

simplify679.0ms

Counts
161 → 161
Iterations
IterNodes
done2001
1655
0236

prune771.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 8.2b

localize71.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (posit16->real (real->posit16 (* (sqrt b) (/ b a)))) (/ (sqrt b) a))
0.3b
(* (sqrt b) (/ b a))
8.3b
(sqrt (fabs (- 1 (* (posit16->real (real->posit16 (* (sqrt b) (/ b a)))) (/ (sqrt b) a)))))
54.1b
(posit16->real (real->posit16 (* (sqrt b) (/ b a))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
35×associate-*r*
31×times-frac
28×*-un-lft-identity add-cube-cbrt
18×sqrt-prod
14×add-cbrt-cube add-exp-log
9×pow1 associate-*l*
7×unswap-sqr
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-undiv div-exp pow-prod-down associate-*r/ *-commutative div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2 remove-posit16
Counts
4 → 112
Calls
4 calls:
19.0ms
(* (posit16->real (real->posit16 (* (sqrt b) (/ b a)))) (/ (sqrt b) a))
12.0ms
(* (sqrt b) (/ b a))
1.0ms
(sqrt (fabs (- 1 (* (posit16->real (real->posit16 (* (sqrt b) (/ b a)))) (/ (sqrt b) a)))))
0.0ms
(posit16->real (real->posit16 (* (sqrt b) (/ b a))))

series230.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* (posit16->real (real->posit16 (* (sqrt b) (/ b a)))) (/ (sqrt b) a))
76.0ms
(* (sqrt b) (/ b a))
20.0ms
(sqrt (fabs (- 1 (* (posit16->real (real->posit16 (* (sqrt b) (/ b a)))) (/ (sqrt b) a)))))
72.0ms
(posit16->real (real->posit16 (* (sqrt b) (/ b a))))

simplify834.0ms

Counts
124 → 124
Iterations
IterNodes
done2001
21887
1543
0209

prune1.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 8.2b

regimes178.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done13
113
09

end0.0ms

sample1.3s

Algorithm
intervals
Results
871.0ms8000×body80valid
317.0ms8000×pre80true