Details

sample40.0ms

Algorithm

intervals

Results

9.0ms	180×	body	80	valid
6.0ms	34×	body	2560	valid
5.0ms	30×	body	1280	valid
3.0ms	85×	body	80	nan
2.0ms	16×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify68.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	12	17
1	22	17
2	42	16
3	82	16
4	104	16
5	112	16
done	112	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.6b	(- (* b b) (* (* 3.0 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite113.0ms

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:

67.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms	(- (* b b) (* (* 3.0 a) c))
24.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
11.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
46.0ms	(- (* b b) (* (* 3.0 a) c))
83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
74.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.1s

Counts

102 → 102

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	167	1697
1	427	1586
2	1445	1363
done	5001	1349

prune268.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.4b	(/ (/ (+ 0 (* (* c 3.0) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
9.0b	(/ (+ 0 (* (* c 3.0) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite198.0ms

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:

30.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
88.0ms	(/ (/ (+ 0 (* (* c 3.0) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
59.0ms	(/ (+ 0 (* (* c 3.0) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
11.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series523.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
187.0ms	(/ (/ (+ 0 (* (* c 3.0) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
181.0ms	(/ (+ 0 (* (* c 3.0) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
74.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.3s

Counts

244 → 244

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	337	10067
1	808	7605
2	3024	6508
done	5000	6422

prune500.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.6b	(- (* b b) (* (* 3.0 a) c))
1.4b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
24.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`prod-diff`
16×	`sqrt-prod`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 94

Calls

4 calls:

17.0ms	(* (* 3.0 a) c)
9.0ms	(- (* b b) (* (* 3.0 a) c))
51.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
11.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (* 3.0 a) c)
47.0ms	(- (* b b) (* (* 3.0 a) c))
84.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
76.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.6s

Counts

106 → 106

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	161	1863
1	367	1562
2	1128	1333
3	4517	1245
done	5000	1245

prune240.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c))) b))
0.6b	(- (* b b) (* (* 3.0 a) c))
1.4b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
24.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

49.0ms	(/ (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c))) b))
9.0ms	(- (* b b) (* (* 3.0 a) c))
52.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
11.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(/ (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c))) b))
51.0ms	(- (* b b) (* (* 3.0 a) c))
81.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
79.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify938.0ms

Counts

117 → 117

Iterations

Useful iterations: done (934.0ms)

Iter	Nodes	Cost
0	186	2435
1	437	2126
2	1342	1820
done	5001	1750

prune252.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 6.0b

regimes324.0ms

Accuracy

81.5% (5.0b remaining)

Error of 11.1b against oracle of 6.0b and baseline of 33.2b

bsearch85.0ms

Steps

Iters	Range		Point
8	1.7227097696114035e-146	1.4073942755830443e-143	1.3880700472259379e-143
7	-1.6239005782062206e+154	-7.680972122048022e+152	-2.6152573735422387e+153

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	42
1	35	42
done	35	42

end0.0ms

sample1.1s

Algorithm

intervals

Results

213.0ms	1092×	body	2560	valid
206.0ms	5861×	body	80	valid
146.0ms	917×	body	1280	valid
94.0ms	2943×	body	80	nan
65.0ms	458×	body	640	valid
32.0ms	116×	body	5120	valid
20.0ms	213×	body	320	valid
6.0ms	103×	body	160	valid