Details

sample62.0ms

Algorithm

intervals

Results

16.0ms	256×	body	80	valid
7.0ms	255×	pre	80	false
6.0ms	256×	pre	80	true

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	47	11
3	100	11
4	319	11
5	1555	11
done	5000	11

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize27.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
31.5b	(/ (* b b) (* a a))

rewrite31.0ms

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:

2.0ms	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
27.0ms	(/ (* b b) (* a a))

series88.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
56.0ms	(/ (* b b) (* a a))

simplify2.0s

Counts

40 → 40

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	65	498
1	192	462
2	1613	378
done	5000	370

prune205.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (fabs (- 1 (* (fabs (/ b a)) (fabs (/ b a))))))
0.3b	(* (fabs (/ b a)) (fabs (/ b a)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube`
3×	`swap-sqr` `associate-r` `associate-l` `sqrt-prod`
2×	`add-log-exp`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

2 → 38

Calls

2 calls:

2.0ms	(sqrt (fabs (- 1 (* (fabs (/ b a)) (fabs (/ b a))))))
20.0ms	(* (fabs (/ b a)) (fabs (/ b a)))

series44.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify1.7s

Counts

44 → 44

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	51	585
1	114	420
2	888	369
done	5000	363

prune277.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize36.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (fabs (- 1 (log (exp (pow (fabs (/ b a)) 2))))))
0.3b	(pow (fabs (/ b a)) 2)
6.3b	(log (exp (pow (fabs (/ b a)) 2)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `log-pow`
8×	`exp-prod`
6×	`pow1` `unpow-prod-down`
4×	`add-exp-log`
3×	`pow-unpow` `log-prod` `sqrt-prod` `add-cbrt-cube` `add-log-exp`
2×	`unpow2` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `rem-log-exp` `pow-exp`

Counts

3 → 51

Calls

3 calls:

10.0ms	(sqrt (fabs (- 1 (log (exp (pow (fabs (/ b a)) 2))))))
5.0ms	(pow (fabs (/ b a)) 2)
13.0ms	(log (exp (pow (fabs (/ b a)) 2)))

series62.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(sqrt (fabs (- 1 (log (exp (pow (fabs (/ b a)) 2))))))
17.0ms	(pow (fabs (/ b a)) 2)
18.0ms	(log (exp (pow (fabs (/ b a)) 2)))

simplify1.1s

Counts

60 → 60

Iterations

Useful iterations: 2 (136.0ms)

Iter	Nodes	Cost
0	82	674
1	156	533
2	404	485
3	1159	485
done	5001	485

prune406.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (fabs (/ b a)) 2)
0.3b	(pow (fabs (/ b a)) 2)
6.1b	(log (sqrt (exp (pow (fabs (/ b a)) 2))))
6.1b	(log (sqrt (exp (pow (fabs (/ b a)) 2))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

22×	`log-pow`
18×	`sqrt-pow1`
16×	`add-sqr-sqrt` `add-cube-cbrt` `exp-prod` `*-un-lft-identity`
12×	`unpow-prod-down` `log-prod`
10×	`pow1`
8×	`add-exp-log`
6×	`pow-unpow` `sqrt-prod`
4×	`add-cbrt-cube` `unpow2` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `pow-pow` `pow1/2` `rem-log-exp` `pow-exp`

Counts

4 → 86

Calls

4 calls:

5.0ms	(pow (fabs (/ b a)) 2)
5.0ms	(pow (fabs (/ b a)) 2)
19.0ms	(log (sqrt (exp (pow (fabs (/ b a)) 2))))
20.0ms	(log (sqrt (exp (pow (fabs (/ b a)) 2))))

series254.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (fabs (/ b a)) 2)
17.0ms	(pow (fabs (/ b a)) 2)
114.0ms	(log (sqrt (exp (pow (fabs (/ b a)) 2))))
105.0ms	(log (sqrt (exp (pow (fabs (/ b a)) 2))))

simplify1.1s

Counts

98 → 98

Iterations

Useful iterations: 2 (114.0ms)

Iter	Nodes	Cost
0	73	1070
1	136	932
2	345	832
3	1066	832
done	5000	832

prune750.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes127.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	12
1	14	12
done	14	12

end0.0ms

sample1.9s

Algorithm

intervals

Results

527.0ms	8000×	body	80	valid
283.0ms	7987×	pre	80	false
241.0ms	8000×	pre	80	true