Details

sample55.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
6.0ms	252×	pre	80	false
6.0ms	256×	pre	80	true

simplify5.8s

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* a a) (* b b))
0.0b	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
13.8b	(/ (- (* a a) (* b b)) (* a a))

rewrite82.0ms

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:

16.0ms	(- (* a a) (* b b))
3.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
62.0ms	(/ (- (* a a) (* b b)) (* a a))

series175.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(- (* a a) (* b b))
39.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
74.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify2.7s

Counts

69 → 69

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	99	979
1	230	843
2	698	744
3	3365	735
done	5001	735

prune296.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize24.0ms

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))

rewrite95.0ms

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:

15.0ms	(/ a (- a (* b (/ b a))))
3.0ms	(sqrt (fabs (/ 1 (/ a (- a (* b (/ b a)))))))
35.0ms	(/ 1 (/ a (- a (* b (/ b a)))))
35.0ms	(* b (/ b a))

series198.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ a (- a (* b (/ b a))))
18.0ms	(sqrt (fabs (/ 1 (/ a (- a (* b (/ b a)))))))
84.0ms	(/ 1 (/ a (- a (* b (/ b a)))))
36.0ms	(* b (/ b a))

simplify3.2s

Counts

178 → 178

Iterations

Useful iterations: done (3.2s)

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

prune589.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite471.0ms

Algorithm

rewrite-expression-head

Rules

4760×	`times-frac`
3066×	`sqrt-prod`
2158×	`add-sqr-sqrt`
2148×	`add-cube-cbrt` `*-un-lft-identity`
88×	`div-inv`
84×	`sqrt-div`
83×	`associate-/r/`
48×	`associate-/r*`
46×	`associate-/l*`
42×	`flip3--` `flip--`
28×	`add-exp-log` `add-cbrt-cube`
26×	`associate-r`
11×	`cbrt-undiv` `div-exp`
8×	`pow1`
6×	`associate-l`
4×	`expm1-log1p-u` `sqrt-undiv` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/l/`
2×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 1918

Calls

4 calls:

115.0ms	(/ (/ (sqrt (- a (* b (/ b a)))) (sqrt a)) (/ (sqrt a) (sqrt (- a (* b (/ b a))))))
15.0ms	(/ (sqrt (- a (* b (/ b a)))) (sqrt a))
15.0ms	(* b (/ b a))
21.0ms	(* b (/ b a))

series707.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (/ (sqrt (- a (* b (/ b a)))) (sqrt a)) (/ (sqrt a) (sqrt (- a (* b (/ b a))))))
128.0ms	(/ (sqrt (- a (* b (/ b a)))) (sqrt a))
468.0ms	(* b (/ b a))
26.0ms	(* b (/ b a))

simplify3.6s

Counts

1930 → 1930

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	1592	96547
1	4408	85337
done	5000	82885

prune4.3s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes41.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	13	13
done	13	13

end0.0ms

sample1.5s

Algorithm

intervals

Results

429.0ms	8000×	body	80	valid
198.0ms	7823×	pre	80	false
195.0ms	8000×	pre	80	true