Details

Time bar (total: 22.8s)

sample55.0ms

Algorithm
intervals
Results
30.0ms256×body80valid
12.0ms256×pre80true

simplify4.7s

Counts
1 → 1
Iterations
IterNodes
85653
71499
6631
5347
4168
388
244
119
08

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.5b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite16.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u 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 → 86
Calls
2 calls:
14.0ms
(* (/ b a) (/ b a))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series59.0ms

Counts
2 → 6
Calls
2 calls:
38.0ms
(* (/ b a) (/ b a))
21.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify2.0s

Counts
92 → 92
Iterations
IterNodes
34450
21254
1399
0134

prune900.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 8.5b

localize20.0ms

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)))))

rewrite44.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u 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 → 172
Calls
4 calls:
23.0ms
(* (/ b a) (/ b a))
13.0ms
(* (/ b a) (/ b a))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series127.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (/ b a) (/ b a))
40.0ms
(* (/ b a) (/ b a))
19.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
28.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify2.1s

Counts
184 → 184
Iterations
IterNodes
34450
21254
1399
0134

prune2.7s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 8.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt b) a)
0.3b
(* (/ (* b (sqrt b)) a) (/ (sqrt b) a))
8.6b
(sqrt (fabs (- 1 (* (/ (* b (sqrt b)) a) (/ (sqrt b) a)))))
13.3b
(/ (* b (sqrt b)) a)

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
44×times-frac
37×*-un-lft-identity add-cube-cbrt
32×add-cbrt-cube add-exp-log
25×sqrt-prod
22×associate-*r*
10×cbrt-undiv div-exp
9×prod-exp cbrt-unprod
7×pow1 associate-*l* associate-/l*
6×associate-/r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
3×unswap-sqr
2×clear-num frac-2neg
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 141
Calls
4 calls:
8.0ms
(/ (sqrt b) a)
24.0ms
(* (/ (* b (sqrt b)) a) (/ (sqrt b) a))
1.0ms
(sqrt (fabs (- 1 (* (/ (* b (sqrt b)) a) (/ (sqrt b) a)))))
24.0ms
(/ (* b (sqrt b)) a)

series281.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(/ (sqrt b) a)
47.0ms
(* (/ (* b (sqrt b)) a) (/ (sqrt b) a))
24.0ms
(sqrt (fabs (- 1 (* (/ (* b (sqrt b)) a) (/ (sqrt b) a)))))
98.0ms
(/ (* b (sqrt b)) a)

simplify615.0ms

Counts
153 → 153
Iterations
IterNodes
22302
1622
0227

prune1.9s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 8.4b

localize67.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (posit16->real (real->posit16 (/ (* b (sqrt b)) a))) (/ (sqrt b) a))
8.6b
(sqrt (fabs (- 1 (* (posit16->real (real->posit16 (/ (* b (sqrt b)) a))) (/ (sqrt b) a)))))
13.3b
(/ (* b (sqrt b)) a)
55.4b
(posit16->real (real->posit16 (/ (* b (sqrt b)) a)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
23×times-frac
22×associate-*r*
21×*-un-lft-identity add-cube-cbrt
14×add-cbrt-cube add-exp-log
13×sqrt-prod
7×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv associate-/r* div-exp associate-*l* prod-exp cbrt-unprod unswap-sqr
2×div-inv
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*r/ *-commutative remove-posit16 associate-/l*
Counts
4 → 96
Calls
4 calls:
18.0ms
(* (posit16->real (real->posit16 (/ (* b (sqrt b)) a))) (/ (sqrt b) a))
1.0ms
(sqrt (fabs (- 1 (* (posit16->real (real->posit16 (/ (* b (sqrt b)) a))) (/ (sqrt b) a)))))
16.0ms
(/ (* b (sqrt b)) a)
0.0ms
(posit16->real (real->posit16 (/ (* b (sqrt b)) a)))

series269.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* (posit16->real (real->posit16 (/ (* b (sqrt b)) a))) (/ (sqrt b) a))
31.0ms
(sqrt (fabs (- 1 (* (posit16->real (real->posit16 (/ (* b (sqrt b)) a))) (/ (sqrt b) a)))))
69.0ms
(/ (* b (sqrt b)) a)
113.0ms
(posit16->real (real->posit16 (/ (* b (sqrt b)) a)))

simplify2.7s

Counts
108 → 108
Iterations
IterNodes
36395
21510
1468
0194

prune2.6s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 8.4b

regimes220.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations
IterNodes
210
110
08

end0.0ms

sample1.3s

Algorithm
intervals
Results
849.0ms8000×body80valid
277.0ms8000×pre80true