Details

sample56.0ms

Algorithm

intervals

Results

30.0ms	256×	body	80	valid
12.0ms	256×	pre	80	true

simplify2.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5216
6	2493
5	808
4	236
3	88
2	44
1	19
0	8

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.1b

localize29.0ms

Local error

Found 2 expressions with local error:

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

rewrite40.0ms

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×	`expm1-log1p-u` `un-div-inv` `insert-posit16` `log1p-expm1-u` `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 → 184

Calls

2 calls:

31.0ms	(* (/ b a) (/ b a))
2.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series63.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(* (/ b a) (/ b a))
27.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify1.8s

Counts

190 → 190

Iterations

Iter	Nodes
done	5009
2	3014
1	872
0	261

prune660.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 7.1b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

119×	`times-frac`
102×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
76×	`add-cube-cbrt`
65×	`associate-r`
31×	`associate-/l*`
18×	`associate-*r/`
17×	`add-cbrt-cube` `add-exp-log`
15×	`associate-l`
11×	`associate-/l/`
10×	`unswap-sqr`
9×	`associate-/r*`
6×	`pow1` `div-inv`
5×	`cbrt-undiv` `clear-num` `div-exp` `*-commutative`
4×	`prod-exp` `un-div-inv` `cbrt-unprod`
3×	`expm1-log1p-u` `frac-2neg` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down`

Counts

3 → 186

Calls

3 calls:

35.0ms	(* b (/ b a))
3.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
64.0ms	(/ (* b (/ b a)) a)

series114.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* b (/ b a))
27.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
51.0ms	(/ (* b (/ b a)) a)

simplify1.5s

Counts

195 → 195

Iterations

Iter	Nodes
done	5010
2	2052
1	668
0	263

prune895.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 7.0b

localize44.0ms

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)))))))

rewrite121.0ms

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×	`expm1-log1p-u` `un-div-inv` `insert-posit16` `log1p-expm1-u` `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 → 380

Calls

4 calls:

51.0ms	(* (/ b a) (/ b a))
38.0ms	(* (/ b a) (/ b a))
3.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
18.0ms	(cbrt (* (fabs (- 1 (* (/ b a) (/ b a)))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))

series141.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (/ b a) (/ b a))
54.0ms	(* (/ b a) (/ b a))
26.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
25.0ms	(cbrt (* (fabs (- 1 (* (/ b a) (/ b a)))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))

simplify2.1s

Counts

392 → 392

Iterations

Iter	Nodes
done	5007
2	3210
1	940
0	296

prune2.0s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 7.0b

localize33.0ms

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))

rewrite356.0ms

Algorithm

rewrite-expression-head

Rules

1326×	`add-sqr-sqrt`
549×	`*-un-lft-identity`
495×	`times-frac`
425×	`difference-of-squares`
399×	`swap-sqr`
345×	`add-cube-cbrt`
263×	`associate-l`
235×	`*-commutative` `unswap-sqr`
225×	`prod-diff`
195×	`associate-r`
85×	`distribute-lft-out--`
33×	`associate-/l*`
15×	`associate-/r*` `fma-neg`
8×	`add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `sqrt-prod` `insert-posit16` `log1p-expm1-u`
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 → 864

Calls

3 calls:

77.0ms	(- (* a a) (* b b))
1.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
194.0ms	(/ (- (* a a) (* b b)) (* a a))

series157.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(- (* a a) (* b b))
27.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
89.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify3.2s

Counts

873 → 873

Iterations

Iter	Nodes
done	5002
2	3616
1	1521
0	607

prune1.3s

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 7.0b

regimes351.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	10
1	10
0	8

end0.0ms

sample1.4s

Algorithm

intervals

Results

850.0ms	8000×	body	80	valid
328.0ms	8000×	pre	80	true