Details

sample41.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
5.0ms	282×	pre	80	false
4.0ms	256×	pre	80	true

simplify5.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
15.6b	(/ (- (* a a) (* b b)) (* a a))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 43

Calls

2 calls:

2.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
28.0ms	(/ (- (* a a) (* b b)) (* a a))

series103.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
67.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify2.3s

Counts

49 → 49

Iterations

Useful iterations: 3 (845.0ms)

Iter	Nodes	Cost
0	84	765
1	193	647
2	571	569
3	2813	560
done	5001	560

prune195.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
13×	`associate-l`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `associate-r` `prod-diff` `associate-/r` `sqrt-prod` `associate-/l`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

4 → 101

Calls

4 calls:

13.0ms	(- a (* (/ b a) b))
3.0ms	(sqrt (fabs (/ (- a (* (/ b a) b)) a)))
30.0ms	(/ (- a (* (/ b a) b)) a)
38.0ms	(* (/ b a) b)

series178.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- a (* (/ b a) b))
24.0ms	(sqrt (fabs (/ (- a (* (/ b a) b)) a)))
77.0ms	(/ (- a (* (/ b a) b)) a)
35.0ms	(* (/ b a) b)

simplify2.8s

Counts

113 → 113

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	157	1323
1	334	1250
2	902	1144
3	3151	1131
done	5000	1127

prune430.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

328×	`add-sqr-sqrt`
296×	`times-frac`
282×	`sqrt-prod`
164×	`add-cube-cbrt` `*-un-lft-identity`
68×	`swap-sqr`
66×	`associate-l`
46×	`associate-r`
29×	`unswap-sqr`
28×	`add-exp-log` `add-cbrt-cube`
15×	`pow1`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp` `div-inv`
6×	`associate-/r` `associate-/l`
5×	`sqrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `associate-l/` `-commutative`
2×	`sqrt-div` `associate-/l/`
1×	`pow2` `frac-times` `flip3--` `frac-2neg` `pow-plus` `sqrt-unprod` `associate-*r/` `clear-num` `rem-square-sqrt` `pow-sqr` `pow-prod-up` `flip--`

Counts

4 → 334

Calls

4 calls:

25.0ms	(/ (sqrt (- a (* (/ b a) b))) (sqrt a))
96.0ms	(* (/ (sqrt (- a (* (/ b a) b))) (sqrt a)) (/ (sqrt (- a (* (/ b a) b))) (sqrt a)))
22.0ms	(* (/ b a) b)
16.0ms	(* (/ b a) b)

series316.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(/ (sqrt (- a (* (/ b a) b))) (sqrt a))
88.0ms	(* (/ (sqrt (- a (* (/ b a) b))) (sqrt a)) (/ (sqrt (- a (* (/ b a) b))) (sqrt a)))
36.0ms	(* (/ b a) b)
25.0ms	(* (/ b a) b)

simplify2.2s

Counts

346 → 346

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	294	9807
1	825	8627
2	2515	6949
done	5000	6499

prune1.1s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes30.0ms

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	8	11
1	9	11
done	9	11

end0.0ms

sample1.9s

Algorithm

intervals

Results

919.0ms	8000×	body	80	valid
201.0ms	8000×	pre	80	true
200.0ms	7938×	pre	80	false