Details

sample24.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	244×	pre	80	false

simplify3.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	48	11
3	101	11
4	198	11
5	376	11
6	618	11
7	1653	11
done	5001	11

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
0.0b	(- (* a a) (* b b))
13.7b	(/ (- (* a a) (* b b)) (* a a))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-log-exp`
4×	`pow1` `times-frac` `associate-/l*`
3×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u` `difference-of-squares`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

3 → 60

Calls

3 calls:

1.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
8.0ms	(- (* a a) (* b b))
22.0ms	(/ (- (* a a) (* b b)) (* a a))

series106.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
32.0ms	(- (* a a) (* b b))
53.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify1.7s

Counts

69 → 69

Iterations

Useful iterations: 3 (737.0ms)

Iter	Nodes	Cost
0	99	979
1	230	843
2	700	744
3	3380	735
done	5000	735

prune168.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b	(sqrt (fabs (fma (/ b a) (- (/ b a)) 1)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
1×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

1 → 15

Calls

1 calls:

2.0ms

(sqrt (fabs (fma (/ b a) (- (/ b a)) 1)))

series12.0ms

Counts

1 → 3

Calls

1 calls:

12.0ms

(sqrt (fabs (fma (/ b a) (- (/ b a)) 1)))

simplify1.5s

Counts

18 → 18

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	24	253
1	33	225
2	44	216
3	66	216
4	89	216
5	116	216
6	151	216
7	224	216
8	519	216
9	1944	216
done	5000	216

prune40.0ms

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

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

100×	`times-frac`
71×	`add-sqr-sqrt`
65×	`add-cube-cbrt` `*-un-lft-identity`
22×	`add-exp-log`
18×	`associate-/r*`
16×	`add-cbrt-cube`
13×	`associate-r`
11×	`associate-/r/`
9×	`div-exp`
8×	`pow1`
7×	`div-inv`
6×	`associate-/l*`
5×	`cbrt-undiv` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `sqrt-prod`
2×	`rec-exp` `frac-2neg` `1-exp` `prod-exp` `clear-num` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `-commutative` `inv-pow`

Counts

4 → 166

Calls

4 calls:

9.0ms	(/ a (- a (* b (/ b a))))
1.0ms	(sqrt (fabs (/ 1 (/ a (- a (* b (/ b a)))))))
15.0ms	(/ 1 (/ a (- a (* b (/ b a)))))
14.0ms	(* b (/ b a))

series139.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ a (- a (* b (/ b a))))
15.0ms	(sqrt (fabs (/ 1 (/ a (- a (* b (/ b a)))))))
50.0ms	(/ 1 (/ a (- a (* b (/ b a)))))
24.0ms	(* b (/ b a))

simplify2.0s

Counts

178 → 178

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	253	2948
1	538	2634
2	1260	2356
3	3876	2305
done	5000	2288

prune339.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (fabs (expm1 (log1p (- 1 (* (/ b a) (/ b a)))))))
0.1b	(expm1 (log1p (- 1 (* (/ b a) (/ b a)))))
0.4b	(* (/ b a) (/ b a))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
40×	`times-frac`
32×	`add-cube-cbrt` `*-un-lft-identity`
15×	`add-exp-log` `add-cbrt-cube`
13×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
3×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `frac-times` `rem-sqrt-square` `expm1-log1p` `sqrt-pow1` `pow-plus` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `expm1-udef`

Counts

3 → 95

Calls

3 calls:

1.0ms	(sqrt (fabs (expm1 (log1p (- 1 (* (/ b a) (/ b a)))))))
0.0ms	(expm1 (log1p (- 1 (* (/ b a) (/ b a)))))
25.0ms	(* (/ b a) (/ b a))

series179.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(sqrt (fabs (expm1 (log1p (- 1 (* (/ b a) (/ b a)))))))
130.0ms	(expm1 (log1p (- 1 (* (/ b a) (/ b a)))))
28.0ms	(* (/ b a) (/ b a))

simplify1.3s

Counts

104 → 104

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	167	1355
1	415	1166
2	1305	1016
done	5000	956

prune250.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes26.0ms

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	10	13
1	12	13
done	12	13

end0.0ms

sample657.0ms

Algorithm

intervals

Results

181.0ms	8000×	body	80	valid
90.0ms	8088×	pre	80	false
81.0ms	8000×	pre	80	true