Details

sample68.0ms

Algorithm

intervals

Results

15.0ms	258×	body	80	nan
14.0ms	514×	pre	80	true
14.0ms	152×	body	160	valid
7.0ms	49×	body	320	valid
3.0ms	55×	body	80	valid

simplify153.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	102
7	102
6	101
5	99
4	91
3	73
2	41
1	22
0	12

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (fma -3 (* c a) (* b b)))
0.1b	(fma -3 (* c a) (* b b))
0.3b	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
36.0b	(- (sqrt (fma -3 (* c a) (* b b))) b)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`prod-diff` `sqrt-prod`
9×	`add-cbrt-cube` `add-exp-log`
6×	`times-frac` `fma-neg` `associate-/l*` `add-log-exp` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 102

Calls

4 calls:

1.0ms	(sqrt (fma -3 (* c a) (* b b)))
0.0ms	(fma -3 (* c a) (* b b))
19.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
8.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

series406.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(sqrt (fma -3 (* c a) (* b b)))
57.0ms	(fma -3 (* c a) (* b b))
119.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
120.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

simplify2.4s

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
3	3990
2	940
1	347
0	152

prune642.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 39.8b

localize74.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b)))
0.3b	(/ (/ (- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (fma (* a c) -3 (* b b)) (* b b)))) (* 3 a))
0.3b	(/ (- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (fma (* a c) -3 (* b b)) (* b b))))
35.2b	(- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b)))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

52×	`times-frac`
48×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `add-cube-cbrt`
23×	`cube-unmult`
20×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
11×	`difference-cubes`
10×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `sqrt-prod` `fma-udef` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`div-sub` `associate-r` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow-plus` `flip3--` `pow1/2` `associate--l+` `pow-prod-up` `flip--` `unswap-sqr`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `*-commutative`

Counts

4 → 145

Calls

4 calls:

15.0ms	(* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b)))
39.0ms	(/ (/ (- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (fma (* a c) -3 (* b b)) (* b b)))) (* 3 a))
42.0ms	(/ (- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (fma (* a c) -3 (* b b)) (* b b))))
21.0ms	(- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b)))

series3.4s

Counts

4 → 12

Calls

4 calls:

1.4s	(* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b)))
485.0ms	(/ (/ (- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (fma (* a c) -3 (* b b)) (* b b)))) (* 3 a))
464.0ms	(/ (- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (fma (* a c) -3 (* b b)) (* b b))))
1.1s	(- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b)))

simplify2.2s

Counts

157 → 157

Iterations

Iter	Nodes
done	5000
2	2103
1	603
0	235

prune1.3s

Pruning

35 alts after pruning (35 fresh and 0 done)

Merged error: 36.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* b b) (sqrt (fma (* a c) -3 (* b b))))
0.3b	(/ (/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (- (* (* b b) (sqrt (fma (* a c) -3 (* b b)))) (* b (* b b)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (fma (* a c) -3 (* b b)) (* b b)))) (* 3 a))
0.3b	(/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (- (* (* b b) (sqrt (fma (* a c) -3 (* b b)))) (* b (* b b)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (fma (* a c) -3 (* b b)) (* b b))))
36.1b	(- (* (* b b) (sqrt (fma (* a c) -3 (* b b)))) (* b (* b b)))

rewrite572.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
30×	`add-sqr-sqrt`
28×	`*-un-lft-identity` `add-cube-cbrt`
23×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/l*`
9×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-r` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-/r*` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`div-sub` `pow-prod-down` `associate-/l/`
2×	`clear-num` `associate-+r-` `frac-2neg` `unswap-sqr`
1×	`sub-neg` `flip3-+` `flip3--` `fma-neg` `diff-log` `associate-l` `prod-diff` `*-commutative` `flip-+` `flip--`

Counts

4 → 126

Calls

4 calls:

31.0ms	(* (* b b) (sqrt (fma (* a c) -3 (* b b))))
297.0ms	(/ (/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (- (* (* b b) (sqrt (fma (* a c) -3 (* b b)))) (* b (* b b)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (fma (* a c) -3 (* b b)) (* b b)))) (* 3 a))
213.0ms	(/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (- (* (* b b) (sqrt (fma (* a c) -3 (* b b)))) (* b (* b b)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (fma (* a c) -3 (* b b)) (* b b))))
28.0ms	(- (* (* b b) (sqrt (fma (* a c) -3 (* b b)))) (* b (* b b)))

series1.2s

Counts

4 → 12

Calls

4 calls:

166.0ms	(* (* b b) (sqrt (fma (* a c) -3 (* b b))))
504.0ms	(/ (/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (- (* (* b b) (sqrt (fma (* a c) -3 (* b b)))) (* b (* b b)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (fma (* a c) -3 (* b b)) (* b b)))) (* 3 a))
397.0ms	(/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (- (* (* b b) (sqrt (fma (* a c) -3 (* b b)))) (* b (* b b)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (fma (* a c) -3 (* b b)) (* b b))))
143.0ms	(- (* (* b b) (sqrt (fma (* a c) -3 (* b b)))) (* b (* b b)))

simplify2.2s

Counts

138 → 138

Iterations

Iter	Nodes
done	5011
2	2282
1	631
0	243

prune1.2s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 4.6b

localize67.0ms

Local error

Found 4 expressions with local error:

0.3b	(* a (* b c))
0.3b	(* -3/2 (* a (* b c)))
0.4b	(/ (/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (* -3/2 (* a (* b c)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (fma (* a c) -3 (* b b)) (* b b)))) (* 3 a))
0.4b	(/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (* -3/2 (* a (* b c)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (fma (* a c) -3 (* b b)) (* b b))))

rewrite458.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
32×	`add-cbrt-cube` `add-exp-log`
28×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`pow1`
16×	`associate-/l*`
11×	`prod-exp` `cbrt-unprod`
9×	`pow-prod-down`
7×	`cbrt-undiv` `div-exp`
6×	`associate-l`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `associate-r` `*-commutative`
1×	`flip3-+` `flip-+`

Counts

4 → 126

Calls

4 calls:

14.0ms	(* a (* b c))
56.0ms	(* -3/2 (* a (* b c)))
150.0ms	(/ (/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (* -3/2 (* a (* b c)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (fma (* a c) -3 (* b b)) (* b b)))) (* 3 a))
236.0ms	(/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (* -3/2 (* a (* b c)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (fma (* a c) -3 (* b b)) (* b b))))

series1.0s

Counts

4 → 12

Calls

4 calls:

42.0ms	(* a (* b c))
39.0ms	(* -3/2 (* a (* b c)))
517.0ms	(/ (/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (* -3/2 (* a (* b c)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (fma (* a c) -3 (* b b)) (* b b)))) (* 3 a))
424.0ms	(/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (* -3/2 (* a (* b c)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (fma (* a c) -3 (* b b)) (* b b))))

simplify2.5s

Counts

138 → 138

Iterations

Iter	Nodes
done	5001
2	1925
1	505
0	202

prune1.2s

Pruning

44 alts after pruning (44 fresh and 0 done)

Merged error: 4.2b

regimes1.3s

Accuracy

-7.1% (7.6b remaining)

Error of 12.0b against oracle of 4.4b and baseline of 11.5b

bsearch42.0ms

Steps

Iters	Range		Point
2	57.94671676530687	64.00467477206256	58.70366934289741

simplify34.0ms

Iterations

Iter	Nodes
done	81
3	81
2	77
1	64
0	43

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.1s	8276×	body	80	nan
848.0ms	4828×	body	160	valid
848.0ms	16276×	pre	80	true
370.0ms	1393×	body	320	valid
202.0ms	1779×	body	80	valid