Details

sample39.0ms

Algorithm

intervals

Results

9.0ms	40×	body	2560	valid
7.0ms	187×	body	80	valid
4.0ms	23×	body	1280	valid
3.0ms	86×	body	80	nan
2.0ms	16×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	5×	body	160	valid

simplify48.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	45	16
3	87	16
4	106	16
5	114	16
done	114	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b	(- (* b b) (* (* 4.0 a) c))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

33.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
44.0ms	(- (* b b) (* (* 4.0 a) c))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify481.0ms

Counts

102 → 102

Iterations

Useful iterations: done (478.0ms)

Iter	Nodes	Cost
0	167	1697
1	449	1584
2	1600	1361
done	5000	1351

prune280.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.6b

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
6.0b	(/ (/ (+ (* (* 4.0 a) c) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
8.8b	(/ (+ (* (* 4.0 a) c) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 232

Calls

4 calls:

16.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
55.0ms	(/ (/ (+ (* (* 4.0 a) c) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
38.0ms	(/ (+ (* (* 4.0 a) c) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series478.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
149.0ms	(/ (/ (+ (* (* 4.0 a) c) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
182.0ms	(/ (+ (* (* 4.0 a) c) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts

244 → 244

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	337	10795
1	843	8234
2	3052	6673
done	5001	6650

prune533.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (- b) (sqrt (- (pow b 2) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (pow b 2) (* 4.0 (* a c)))
1.3b	(+ (- b) (sqrt (- (pow b 2) (* 4.0 (* a c)))))
21.1b	(sqrt (- (pow b 2) (* 4.0 (* a c))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
10×	`fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`fma-neg` `prod-diff`
6×	`unpow-prod-down` `distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/` `unpow2` `sqr-pow`
1×	`+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 104

Calls

4 calls:

53.0ms	(/ (+ (- b) (sqrt (- (pow b 2) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (pow b 2) (* 4.0 (* a c)))
19.0ms	(+ (- b) (sqrt (- (pow b 2) (* 4.0 (* a c)))))
12.0ms	(sqrt (- (pow b 2) (* 4.0 (* a c))))

series303.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (+ (- b) (sqrt (- (pow b 2) (* 4.0 (* a c))))) (* 2.0 a))
47.0ms	(- (pow b 2) (* 4.0 (* a c)))
77.0ms	(+ (- b) (sqrt (- (pow b 2) (* 4.0 (* a c)))))
72.0ms	(sqrt (- (pow b 2) (* 4.0 (* a c))))

simplify585.0ms

Counts

116 → 116

Iterations

Useful iterations: done (581.0ms)

Iter	Nodes	Cost
0	182	1925
1	474	1793
2	1671	1543
done	5000	1542

prune322.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ 2.0 (/ (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) a)))
0.8b	(- (pow b 2) (* 4.0 (* a c)))
1.3b	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
21.1b	(sqrt (- (pow b 2) (* 4.0 (* a c))))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

693×	`times-frac`
456×	`add-sqr-sqrt`
381×	`*-un-lft-identity`
307×	`add-cube-cbrt`
74×	`difference-of-squares`
71×	`associate-/r*`
52×	`sqrt-prod`
37×	`distribute-lft-out--`
26×	`prod-diff`
25×	`add-exp-log`
17×	`div-inv`
15×	`div-exp`
14×	`fma-neg`
13×	`add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `cbrt-undiv` `unpow-prod-down`
5×	`associate-/r/`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log` `unpow2` `sqr-pow`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 402

Calls

4 calls:

51.0ms	(/ 1 (/ 2.0 (/ (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) a)))
9.0ms	(- (pow b 2) (* 4.0 (* a c)))
46.0ms	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
10.0ms	(sqrt (- (pow b 2) (* 4.0 (* a c))))

series310.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ 1 (/ 2.0 (/ (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) a)))
45.0ms	(- (pow b 2) (* 4.0 (* a c)))
79.0ms	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
76.0ms	(sqrt (- (pow b 2) (* 4.0 (* a c))))

simplify565.0ms

Counts

414 → 414

Iterations

Useful iterations: done (549.0ms)

Iter	Nodes	Cost
0	637	13093
1	1531	11820
done	5001	11142

prune689.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.3b

regimes184.0ms

Accuracy

85.1% (4.2b remaining)

Error of 9.5b against oracle of 5.3b and baseline of 33.8b

bsearch139.0ms

Steps

Iters	Range		Point
8	1.9086145032856143e-23	7.928945926733413e-19	1.0486964725483499e-20
4	5.373368029867189e-105	8.528584395310529e-105	6.785925920671322e-105
7	-3.550313394724354e+57	-2.3888623512096697e+55	-3.124283374205192e+57

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	70
1	54	70
done	54	70

end0.0ms

sample1.1s

Algorithm

intervals

Results

242.0ms	1074×	body	2560	valid
228.0ms	5844×	body	80	valid
163.0ms	907×	body	1280	valid
106.0ms	2890×	body	80	nan
63.0ms	452×	body	640	valid
28.0ms	102×	body	5120	valid
25.0ms	234×	body	320	valid
8.0ms	119×	body	160	valid