Details

sample51.0ms

Algorithm

intervals

Results

27.0ms	256×	body	80	valid
11.0ms	256×	pre	80	true

simplify8.8s

Counts

1 → 1

Iterations

Iter	Nodes
8	6442
7	1455
6	631
5	341
4	166
3	86
2	44
1	19
0	8

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.5b

localize12.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (/ b a) (/ b a))
4.6b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite35.0ms

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:

27.0ms	(* (/ b a) (/ b a))
6.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series62.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(* (/ b a) (/ b a))
23.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify2.3s

Counts

92 → 92

Iterations

Iter	Nodes
3	4437
2	1250
1	398
0	134

prune893.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 4.5b

localize33.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ b a) b)
4.6b	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))
7.0b	(/ (* (/ b a) b) a)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
17×	`add-cbrt-cube` `add-exp-log`
14×	`*-un-lft-identity` `add-cube-cbrt`
13×	`times-frac` `associate-l`
6×	`pow1`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `associate-/r` `associate-r*` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`associate-*l/` `div-inv` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `-commutative` `associate-/l` `associate-/l/`

Counts

3 → 78

Calls

3 calls:

24.0ms	(* (/ b a) b)
2.0ms	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))
23.0ms	(/ (* (/ b a) b) a)

series99.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(* (/ b a) b)
22.0ms	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))
47.0ms	(/ (* (/ b a) b) a)

simplify3.9s

Counts

87 → 87

Iterations

Iter	Nodes
3	5509
2	950
1	269
0	117

prune899.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 4.4b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fabs (- 1 (log (exp (* (/ b a) (/ b a)))))))
0.0b	(exp (* (/ b a) (/ b a)))
0.4b	(* (/ b a) (/ b a))
5.4b	(log (exp (* (/ b a) (/ b a))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
40×	`times-frac`
34×	`*-un-lft-identity` `add-cube-cbrt`
16×	`add-cbrt-cube` `add-exp-log`
13×	`pow1` `swap-sqr` `associate-r` `associate-l`
7×	`add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv` `unswap-sqr`
3×	`log-prod` `log-pow` `sqrt-prod`
2×	`exp-prod` `exp-to-pow`
1×	`pow2` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `rem-log-exp` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `rem-exp-log`

Counts

4 → 116

Calls

4 calls:

2.0ms	(sqrt (fabs (- 1 (log (exp (* (/ b a) (/ b a)))))))
7.0ms	(exp (* (/ b a) (/ b a)))
26.0ms	(* (/ b a) (/ b a))
8.0ms	(log (exp (* (/ b a) (/ b a))))

series127.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(sqrt (fabs (- 1 (log (exp (* (/ b a) (/ b a)))))))
28.0ms	(exp (* (/ b a) (/ b a)))
32.0ms	(* (/ b a) (/ b a))
45.0ms	(log (exp (* (/ b a) (/ b a))))

simplify2.4s

Counts

128 → 128

Iterations

Iter	Nodes
3	4431
2	1311
1	435
0	161

prune1.4s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 4.4b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ b a) b)
4.6b	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
7.0b	(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
46.5b	(posit16->real (real->posit16 (* (/ b a) b)))

rewrite23.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 92

Calls

4 calls:

15.0ms	(* (/ b a) b)
1.0ms	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
4.0ms	(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
0.0ms	(posit16->real (real->posit16 (* (/ b a) b)))

series102.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (/ b a) b)
13.0ms	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
30.0ms	(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
22.0ms	(posit16->real (real->posit16 (* (/ b a) b)))

simplify1.8s

Counts

104 → 104

Iterations

Iter	Nodes
3	3326
2	750
1	269
0	137

prune2.0s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 4.4b

regimes151.0ms

Accuracy

0% (0.1b remaining)

Error of 7.6b against oracle of 7.5b and baseline of 7.6b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
1	8
0	8

end0.0ms

sample1.4s

Algorithm

intervals

Results

846.0ms	8000×	body	80	valid
388.0ms	8000×	pre	80	true