Details

sample40.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5004
6	2324
5	753
4	228
3	85
2	43
1	18
0	8

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.1b

localize13.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (/ b a) (/ b a))
7.2b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

84×	`add-sqr-sqrt`
81×	`frac-times`
72×	`*-un-lft-identity`
71×	`add-cube-cbrt`
61×	`associate-/l*`
60×	`associate-/r*`
40×	`times-frac`
21×	`clear-num`
20×	`frac-2neg`
14×	`add-cbrt-cube` `add-exp-log`
13×	`swap-sqr` `associate-r` `associate-l`
10×	`pow1`
9×	`associate-l/` `associate-r/`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
3×	`sqrt-prod`
2×	`un-div-inv` `insert-posit16` `add-log-exp`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

2 → 180

Calls

2 calls:

42.0ms	(* (/ b a) (/ b a))
1.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series52.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(* (/ b a) (/ b a))
15.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify2.4s

Counts

186 → 186

Iterations

Iter	Nodes
done	5001
2	3339
1	869
0	257

prune732.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 7.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ b a) b)
7.2b	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))
7.2b	(/ (* (/ b a) b) a)

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

119×	`times-frac`
102×	`add-sqr-sqrt`
76×	`*-un-lft-identity` `add-cube-cbrt`
65×	`associate-l`
29×	`associate-/l*`
18×	`associate-*l/`
17×	`add-cbrt-cube` `add-exp-log`
15×	`associate-r`
10×	`unswap-sqr`
9×	`associate-/r*` `associate-/l/`
6×	`pow1` `div-inv`
5×	`cbrt-undiv` `div-exp` `*-commutative`
4×	`prod-exp` `cbrt-unprod`
3×	`clear-num` `frac-2neg` `sqrt-prod` `insert-posit16` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down`

Counts

3 → 176

Calls

3 calls:

30.0ms	(* (/ b a) b)
1.0ms	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))
37.0ms	(/ (* (/ b a) b) a)

series88.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(* (/ b a) b)
16.0ms	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))
45.0ms	(/ (* (/ b a) b) a)

simplify1.7s

Counts

185 → 185

Iterations

Iter	Nodes
done	5000
2	1929
1	647
0	252

prune888.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 7.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ b a) (/ b a))
0.4b	(* (/ b a) (/ b a))
7.2b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
11.6b	(cbrt (* (fabs (- 1 (* (/ b a) (/ b a)))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

175×	`add-sqr-sqrt`
162×	`frac-times`
147×	`*-un-lft-identity`
145×	`add-cube-cbrt`
122×	`associate-/l*`
120×	`associate-/r*`
80×	`times-frac`
42×	`clear-num`
40×	`frac-2neg`
32×	`associate-r`
29×	`associate-l`
28×	`add-cbrt-cube` `add-exp-log`
26×	`swap-sqr`
19×	`pow1`
18×	`associate-l/` `associate-r/`
16×	`cbrt-prod`
10×	`unswap-sqr`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
7×	`sqrt-prod`
4×	`un-div-inv` `insert-posit16` `add-log-exp`
3×	`*-commutative`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 372

Calls

4 calls:

59.0ms	(* (/ b a) (/ b a))
56.0ms	(* (/ b a) (/ b a))
1.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
8.0ms	(cbrt (* (fabs (- 1 (* (/ b a) (/ b a)))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))

series127.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (/ b a) (/ b a))
32.0ms	(* (/ b a) (/ b a))
14.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
32.0ms	(cbrt (* (fabs (- 1 (* (/ b a) (/ b a)))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))

simplify1.9s

Counts

384 → 384

Iterations

Iter	Nodes
done	5098
2	3134
1	900
0	290

prune1.8s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 7.0b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* a a) (* b b))
7.2b	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
21.9b	(/ (- (* a a) (* b b)) (* a a))

rewrite328.0ms

Algorithm

rewrite-expression-head

Rules

1109×	`add-sqr-sqrt`
495×	`times-frac`
425×	`difference-of-squares`
394×	`*-un-lft-identity`
306×	`swap-sqr`
204×	`*-commutative` `unswap-sqr`
190×	`add-cube-cbrt`
170×	`associate-l`
102×	`associate-r`
85×	`distribute-lft-out--`
33×	`associate-/l*`
15×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
4×	`pow1`
3×	`sqrt-prod` `insert-posit16`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

3 → 618

Calls

3 calls:

73.0ms	(- (* a a) (* b b))
1.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
209.0ms	(/ (- (* a a) (* b b)) (* a a))

series168.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(- (* a a) (* b b))
36.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
74.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify1.9s

Counts

627 → 627

Iterations

Iter	Nodes
done	5001
2	3440
1	1173
0	404

prune947.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 7.0b

regimes332.0ms

Accuracy

0% (0.1b remaining)

Error of 7.5b against oracle of 7.4b and baseline of 7.5b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	10
1	10
0	8

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.2s	8000×	body	80	valid
352.0ms	8000×	pre	80	true