Details

sample26.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
4.0ms	296×	pre	80	false
3.0ms	256×	pre	80	true

simplify10.4s

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	47	11
3	107	11
4	238	11
5	625	11
6	3257	11
done	5001	11

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.6b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
27.7b	(/ (* b b) (* a a))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
4×	`cbrt-undiv` `add-sqr-sqrt` `div-exp` `prod-exp` `cbrt-unprod`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
2×	`add-log-exp`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

2 → 34

Calls

2 calls:

1.0ms	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
5.0ms	(/ (* b b) (* a a))

series43.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
29.0ms	(/ (* b b) (* a a))

simplify4.1s

Counts

40 → 40

Iterations

Useful iterations: 3 (357.0ms)

Iter	Nodes	Cost
0	65	498
1	164	462
2	664	370
3	4769	355
done	5000	355

prune80.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
0.1b	(* b (/ b a))
11.6b	(/ (* b (/ b a)) a)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 69

Calls

3 calls:

1.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
7.0ms	(* b (/ b a))
5.0ms	(/ (* b (/ b a)) a)

series60.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
18.0ms	(* b (/ b a))
27.0ms	(/ (* b (/ b a)) a)

simplify553.0ms

Counts

78 → 78

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	113	789
1	281	734
2	1321	623
done	5000	623

prune164.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (exp (sqrt (fabs (- 1 (/ (* b (/ b a)) a))))))
0.0b	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
0.1b	(* b (/ b a))
11.6b	(/ (* b (/ b a)) a)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
18×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
13×	`times-frac` `associate-r`
8×	`pow1`
7×	`log-pow`
6×	`exp-prod` `sqrt-prod`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`log-prod` `associate-l` `associate-/r*`
2×	`associate-*r/` `div-inv` `unswap-sqr`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `rem-log-exp` `pow-prod-down` `clear-num` `-commutative` `associate-/l/` `associate-/l`

Counts

4 → 87

Calls

4 calls:

2.0ms	(log (exp (sqrt (fabs (- 1 (/ (* b (/ b a)) a))))))
1.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
7.0ms	(* b (/ b a))
5.0ms	(/ (* b (/ b a)) a)

series70.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(log (exp (sqrt (fabs (- 1 (/ (* b (/ b a)) a))))))
14.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
18.0ms	(* b (/ b a))
25.0ms	(/ (* b (/ b a)) a)

simplify576.0ms

Counts

99 → 99

Iterations

Useful iterations: 2 (104.0ms)

Iter	Nodes	Cost
0	138	1148
1	311	1030
2	1372	898
done	5000	898

prune239.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(* b (/ b a))
0.1b	(* b (/ b a))
11.6b	(/ (* b (/ b a)) a)
11.6b	(/ (* b (/ b a)) a)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
32×	`add-exp-log` `add-cbrt-cube`
26×	`times-frac` `associate-r`
24×	`add-cube-cbrt` `*-un-lft-identity`
10×	`cbrt-undiv` `div-exp`
8×	`pow1` `prod-exp` `cbrt-unprod`
6×	`associate-l` `associate-/r*`
4×	`associate-*r/` `div-inv` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `associate-/l/` `associate-/l`

Counts

4 → 112

Calls

4 calls:

7.0ms	(* b (/ b a))
7.0ms	(* b (/ b a))
5.0ms	(/ (* b (/ b a)) a)
7.0ms	(/ (* b (/ b a)) a)

series90.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* b (/ b a))
21.0ms	(* b (/ b a))
25.0ms	(/ (* b (/ b a)) a)
26.0ms	(/ (* b (/ b a)) a)

simplify543.0ms

Counts

124 → 124

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	94	1120
1	255	1066
2	1280	862
done	5000	862

prune388.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes32.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	12	11
done	12	11

end0.0ms

sample630.0ms

Algorithm

intervals

Results

202.0ms	8000×	body	80	valid
100.0ms	8113×	pre	80	false
94.0ms	8000×	pre	80	true