Details

sample142.0ms

Algorithm

intervals

Results

47.0ms	156×	body	160	valid
27.0ms	260×	body	80	nan
24.0ms	516×	pre	80	true
16.0ms	50×	body	320	valid
5.0ms	50×	body	80	valid

simplify122.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	105
7	105
6	104
5	102
4	94
3	77
2	44
1	25
0	14

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 46.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4 a) c)))
0.1b	(- (* b b) (* (* 4 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
40.5b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

483×	`add-sqr-sqrt`
330×	`associate-l` `prod-diff`
309×	`*-un-lft-identity`
229×	`add-cube-cbrt`
177×	`associate-r`
125×	`unswap-sqr`
75×	`swap-sqr`
65×	`*-commutative`
60×	`times-frac`
30×	`difference-of-squares`
28×	`distribute-lft-out`
24×	`sqrt-prod`
17×	`distribute-rgt-neg-in`
15×	`fma-neg`
12×	`associate-/r*` `distribute-lft-out--`
10×	`fma-def` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in`
2×	`neg-sub0` `cbrt-undiv` `sum-log` `flip3-+` `flip3--` `sqrt-div` `div-exp` `associate-+l-` `flip-+` `flip--` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `neg-mul-1` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 545

Calls

4 calls:

205.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
108.0ms	(- (* b b) (* (* 4 a) c))
837.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
261.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))

series393.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
61.0ms	(- (* b b) (* (* 4 a) c))
139.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
105.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))

simplify2.7s

Counts

557 → 557

Iterations

Iter	Nodes
done	5000
2	3979
1	1514
0	630

prune2.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.0b

localize5.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune59.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (* -2 (/ (* a c) b)) (* 2 a))
0.3b	(/ (* a c) b)

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

1142×	`times-frac`
808×	`add-sqr-sqrt` `associate-r`
501×	`*-un-lft-identity`
499×	`add-cube-cbrt`
328×	`associate-l`
148×	`unswap-sqr`
109×	`*-commutative`
77×	`associate-/l*`
39×	`add-cbrt-cube` `add-exp-log`
21×	`associate-/l/`
18×	`associate-/r` `associate-r/`
15×	`div-inv`
14×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod`
4×	`clear-num`
3×	`frac-2neg` `un-div-inv`
2×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

2 → 793

Calls

2 calls:

127.0ms	(/ (* -2 (/ (* a c) b)) (* 2 a))
17.0ms	(/ (* a c) b)

series56.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ (* -2 (/ (* a c) b)) (* 2 a))
21.0ms	(/ (* a c) b)

simplify2.9s

Counts

799 → 799

Iterations

Iter	Nodes
done	5000
1	4340
0	1215

prune3.1s

Pruning

33 alts after pruning (32 fresh and 1 done)

Merged error: 3.9b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt a) (cbrt a))
0.6b	(cbrt a)
0.6b	(cbrt a)
0.6b	(cbrt a)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
8×	`add-cbrt-cube`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative`

Counts

4 → 88

Calls

4 calls:

11.0ms	(* (cbrt a) (cbrt a))
1.0ms	(cbrt a)
2.0ms	(cbrt a)
2.0ms	(cbrt a)

series1.0s

Counts

4 → 12

Calls

4 calls:

268.0ms	(* (cbrt a) (cbrt a))
221.0ms	(cbrt a)
282.0ms	(cbrt a)
249.0ms	(cbrt a)

simplify3.3s

Counts

100 → 100

Iterations

Iter	Nodes
done	5001
4	4292
3	1164
2	420
1	155
0	70

prune480.0ms

Pruning

33 alts after pruning (32 fresh and 1 done)

Merged error: 3.9b

regimes906.0ms

Accuracy

28.3% (4.8b remaining)

Error of 9.9b against oracle of 5.2b and baseline of 11.8b

bsearch6.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	40
1	40
0	30

end0.0ms

sample5.1s

Algorithm

intervals

Results

1.6s	16170×	pre	80	true
1.3s	4880×	body	160	valid
962.0ms	8170×	body	80	nan
503.0ms	1367×	body	320	valid
287.0ms	1753×	body	80	valid