Details

sample54.0ms

Algorithm

intervals

Results

29.0ms	256×	body	80	valid
12.0ms	256×	pre	80	true

simplify5.0s

Counts

1 → 1

Iterations

Iter	Nodes
8	5935
7	1234
6	515
5	299
4	157
3	83
2	43
1	18
0	8

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.8b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(- 1 (* (/ b a) (/ b a)))
0.4b	(* (/ b a) (/ b a))
7.9b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite35.0ms

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:

9.0ms	(- 1 (* (/ b a) (/ b a)))
22.0ms	(* (/ b a) (/ b a))
1.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series141.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(- 1 (* (/ b a) (/ b a)))
55.0ms	(* (/ b a) (/ b a))
24.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify2.3s

Counts

106 → 106

Iterations

Iter	Nodes
3	5092
2	1379
1	455
0	154

prune668.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 7.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1 (/ (* (/ b a) b) a))
0.1b	(* (/ b a) b)
7.3b	(/ (* (/ b a) b) a)
7.9b	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
18×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log`
15×	`add-cube-cbrt`
13×	`times-frac` `associate-l`
7×	`pow1`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `insert-posit16`
3×	`associate-/r` `associate-r*` `sqrt-prod`
2×	`associate-*l/` `div-inv` `difference-of-squares` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `pow-prod-down` `-commutative` `flip--` `associate-/l` `distribute-lft-out--` `associate-/l/`

Counts

4 → 88

Calls

4 calls:

6.0ms	(- 1 (/ (* (/ b a) b) a))
25.0ms	(* (/ b a) b)
20.0ms	(/ (* (/ b a) b) a)
1.0ms	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))

series128.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- 1 (/ (* (/ b a) b) a))
26.0ms	(* (/ b a) b)
27.0ms	(/ (* (/ b a) b) a)
12.0ms	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))

simplify3.2s

Counts

100 → 100

Iterations

Iter	Nodes
3	4799
2	1042
1	324
0	136

prune637.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 7.7b

localize68.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ b a) b)
7.3b	(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
7.9b	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
45.8b	(posit16->real (real->posit16 (* (/ b a) b)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
13×	`associate-l`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-r` `sqrt-prod` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `-commutative` `remove-posit16`

Counts

4 → 84

Calls

4 calls:

14.0ms	(* (/ b a) b)
9.0ms	(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
2.0ms	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
1.0ms	(posit16->real (real->posit16 (* (/ b a) b)))

series125.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (/ b a) b)
51.0ms	(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
20.0ms	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
21.0ms	(posit16->real (real->posit16 (* (/ b a) b)))

simplify1.8s

Counts

96 → 96

Iterations

Iter	Nodes
3	3658
2	766
1	263
0	129

prune1.6s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 7.7b

localize98.0ms

Local error

Found 4 expressions with local error:

7.9b	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
45.8b	(posit16->real (real->posit16 (* (/ b a) b)))
45.8b	(posit16->real (real->posit16 (* (/ b a) b)))
45.8b	(posit16->real (real->posit16 (* (/ b a) b)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`sqrt-prod` `remove-posit16`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 41

Calls

4 calls:

2.0ms	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
0.0ms	(posit16->real (real->posit16 (* (/ b a) b)))
0.0ms	(posit16->real (real->posit16 (* (/ b a) b)))
1.0ms	(posit16->real (real->posit16 (* (/ b a) b)))

series101.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
20.0ms	(posit16->real (real->posit16 (* (/ b a) b)))
33.0ms	(posit16->real (real->posit16 (* (/ b a) b)))
28.0ms	(posit16->real (real->posit16 (* (/ b a) b)))

simplify7.0s

Counts

53 → 53

Iterations

Iter	Nodes
5	6110
4	1438
3	425
2	135
1	59
0	41

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 7.7b

regimes142.0ms

Accuracy

0% (0.1b remaining)

Error of 7.7b against oracle of 7.6b and baseline of 7.7b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
1	8
0	8

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.2s	8000×	body	80	valid
327.0ms	8000×	pre	80	true