Details

sample44.0ms

Algorithm

intervals

Results

8.0ms	34×	body	2560	valid
7.0ms	180×	body	80	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

simplify78.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	86	16
4	108	16
5	116	16
done	116	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite125.0ms

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:

72.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
9.0ms	(- (* b b) (* (* 4.0 a) c))
25.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
52.0ms	(- (* b b) (* (* 4.0 a) c))
97.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
86.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify971.0ms

Counts

102 → 102

Iterations

Useful iterations: done (968.0ms)

Iter	Nodes	Cost
0	167	1697
1	433	1584
2	1488	1361
done	5000	1347

prune339.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.4b	(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.0b	(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite220.0ms

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:

34.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
95.0ms	(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
67.0ms	(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series601.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
213.0ms	(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
212.0ms	(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
88.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

244 → 244

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	338	10067
1	811	7605
2	3063	6508
done	5000	6422

prune582.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
60×	`times-frac`
50×	`*-un-lft-identity`
40×	`add-cube-cbrt`
25×	`add-exp-log`
20×	`sqrt-prod`
19×	`prod-diff`
13×	`add-cbrt-cube`
12×	`div-exp` `associate-/r*`
10×	`difference-of-squares`
9×	`associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 152

Calls

4 calls:

62.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
10.0ms	(- (* b b) (* (* 4.0 a) c))
52.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
56.0ms	(- (* b b) (* (* 4.0 a) c))
93.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
81.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify974.0ms

Counts

164 → 164

Iterations

Useful iterations: done (969.0ms)

Iter	Nodes	Cost
0	261	4025
1	587	3484
2	1656	3082
done	5001	2938

prune337.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) (* a 2.0))
0.6b	(- (pow b 2) (* 4.0 (* a c)))
1.4b	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
24.3b	(sqrt (- (pow b 2) (* 4.0 (* a c))))

rewrite270.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
26×	`prod-diff`
25×	`add-cube-cbrt`
18×	`sqrt-prod`
14×	`fma-neg`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`unpow-prod-down` `times-frac` `associate-/l*` `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-/l/` `unpow2` `sqr-pow`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 120

Calls

4 calls:

145.0ms	(/ (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) (* a 2.0))
18.0ms	(- (pow b 2) (* 4.0 (* a c)))
85.0ms	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
18.0ms	(sqrt (- (pow b 2) (* 4.0 (* a c))))

series334.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) (* a 2.0))
48.0ms	(- (pow b 2) (* 4.0 (* a c)))
89.0ms	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
80.0ms	(sqrt (- (pow b 2) (* 4.0 (* a c))))

simplify1.2s

Counts

132 → 132

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	208	2704
1	514	2376
2	1445	2037
done	5001	1957

prune328.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 6.0b

regimes145.0ms

Accuracy

81.9% (4.9b remaining)

Error of 10.9b against oracle of 6.0b and baseline of 33.2b

bsearch102.0ms

Steps

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

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	31	44
1	41	38
done	41	38

end0.0ms

sample1.2s

Algorithm

intervals

Results

230.0ms	1092×	body	2560	valid
224.0ms	5865×	body	80	valid
164.0ms	916×	body	1280	valid
107.0ms	2944×	body	80	nan
68.0ms	460×	body	640	valid
32.0ms	116×	body	5120	valid
21.0ms	209×	body	320	valid
7.0ms	105×	body	160	valid