Details

sample34.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1561
4	319
3	100
2	47
1	18
0	8

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.8b

localize18.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (/ b a) (/ b a))
7.4b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite40.0ms

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×	`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 → 80

Calls

2 calls:

33.0ms	(* (/ b a) (/ b a))
1.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series67.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(* (/ b a) (/ b a))
26.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify1.6s

Counts

86 → 86

Iterations

Iter	Nodes
done	5001
2	2815
1	412
0	128

prune355.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 7.8b

localize27.0ms

Local error

Found 3 expressions with local error:

0.2b	(* b (/ b a))
7.4b	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
7.5b	(/ (* b (/ b a)) a)

rewrite48.0ms

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-r`
6×	`pow1`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod`
3×	`associate-/r` `associate-l*` `sqrt-prod` `add-log-exp`
2×	`associate-*r/` `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 → 69

Calls

3 calls:

22.0ms	(* b (/ b a))
2.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
19.0ms	(/ (* b (/ b a)) a)

series113.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(* b (/ b a))
29.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
51.0ms	(/ (* b (/ b a)) a)

simplify1.2s

Counts

78 → 78

Iterations

Iter	Nodes
done	5001
2	1676
1	294
0	113

prune447.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 7.8b

localize70.0ms

Local error

Found 4 expressions with local error:

7.5b	(/ (cbrt (/ (* (/ (* b (* b b)) a) (/ (* b (* b b)) a)) a)) a)
12.4b	(/ (* b (* b b)) a)
12.4b	(/ (* b (* b b)) a)
27.3b	(cbrt (/ (* (/ (* b (* b b)) a) (/ (* b (* b b)) a)) a))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

51×	`times-frac`
35×	`cbrt-prod`
33×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
24×	`add-exp-log`
23×	`add-cbrt-cube`
12×	`associate-/l*`
9×	`associate-/r*`
8×	`div-inv`
7×	`cbrt-undiv` `div-exp`
6×	`prod-exp` `cbrt-unprod`
4×	`pow1` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`cbrt-div`
1×	`pow1/3` `associate-/l/`

Counts

4 → 118

Calls

4 calls:

14.0ms	(/ (cbrt (/ (* (/ (* b (* b b)) a) (/ (* b (* b b)) a)) a)) a)
32.0ms	(/ (* b (* b b)) a)
17.0ms	(/ (* b (* b b)) a)
92.0ms	(cbrt (/ (* (/ (* b (* b b)) a) (/ (* b (* b b)) a)) a))

series208.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (cbrt (/ (* (/ (* b (* b b)) a) (/ (* b (* b b)) a)) a)) a)
34.0ms	(/ (* b (* b b)) a)
44.0ms	(/ (* b (* b b)) a)
58.0ms	(cbrt (/ (* (/ (* b (* b b)) a) (/ (* b (* b b)) a)) a))

simplify2.6s

Counts

130 → 130

Iterations

Iter	Nodes
done	5002
2	3244
1	376
0	165

prune792.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 7.7b

localize72.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (fabs (- 1 (/ (cbrt (/ (* (log (exp (/ (* b (* b b)) a))) (/ (* b (* b b)) a)) a)) a))))
2.2b	(log (exp (/ (* b (* b b)) a)))
12.4b	(/ (* b (* b b)) a)
12.4b	(/ (* b (* b b)) a)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

2.0ms	(sqrt (fabs (- 1 (/ (cbrt (/ (* (log (exp (/ (* b (* b b)) a))) (/ (* b (* b b)) a)) a)) a))))
9.0ms	(log (exp (/ (* b (* b b)) a)))
16.0ms	(/ (* b (* b b)) a)
16.0ms	(/ (* b (* b b)) a)

series115.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (fabs (- 1 (/ (cbrt (/ (* (log (exp (/ (* b (* b b)) a))) (/ (* b (* b b)) a)) a)) a))))
23.0ms	(log (exp (/ (* b (* b b)) a)))
23.0ms	(/ (* b (* b b)) a)
35.0ms	(/ (* b (* b b)) a)

simplify2.7s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	2649
1	285
0	119

prune620.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 7.7b

regimes121.0ms

Accuracy

0% (0.1b remaining)

Error of 8.3b against oracle of 8.2b and baseline of 8.3b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	10
1	10
0	8

end0.0ms

sample1.3s

Algorithm

intervals

Results

960.0ms	8000×	body	80	valid
163.0ms	8000×	pre	80	true