Details

sample96.0ms

Algorithm

intervals

Results

19.0ms	38×	body	2560	valid
17.0ms	190×	body	80	valid
15.0ms	36×	body	1280	valid
6.0ms	79×	body	80	nan
4.0ms	11×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify159.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	87	16
4	120	16
5	129	16
done	129	16

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite156.0ms

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:

86.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
14.0ms	(- (* b b) (* (* 4.0 a) c))
37.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series427.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
68.0ms	(- (* b b) (* (* 4.0 a) c))
98.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
85.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts

102 → 102

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	167	1697
1	451	1588
2	2113	1361
done	5000	1352

prune448.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.9b	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
7.7b	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite602.0ms

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:

48.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
102.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
430.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series685.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
217.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
279.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
93.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts

244 → 244

Iterations

Useful iterations: 2 (800.0ms)

Iter	Nodes	Cost
0	335	10067
1	848	7629
2	4744	6524
done	5000	6524

prune728.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

localize33.0ms

Local error

Found 4 expressions with local error:

14.6b	(/ (* 2.0 a) (* (* 4.0 a) c))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
9×	`prod-exp` `sqrt-prod` `cbrt-unprod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-undiv` `sqrt-div` `div-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 78

Calls

4 calls:

38.0ms	(/ (* 2.0 a) (* (* 4.0 a) c))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (* 2.0 a) (* (* 4.0 a) c))
91.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
95.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
102.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts

90 → 90

Iterations

Useful iterations: 2 (297.0ms)

Iter	Nodes	Cost
0	115	1347
1	347	1207
2	2063	988
done	5000	988

prune506.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize47.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`sqrt-prod`
8×	`add-cube-cbrt`
7×	`pow1` `cbrt-prod`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`distribute-rgt-neg-in` `pow1/3`

Counts

4 → 70

Calls

4 calls:

26.0ms	(cbrt (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series580.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(cbrt (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
100.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
114.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
114.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify947.0ms

Counts

82 → 82

Iterations

Useful iterations: done (943.0ms)

Iter	Nodes	Cost
0	142	1486
1	347	1319
2	1275	1248
done	5001	1231

prune558.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.5b

regimes298.0ms

Accuracy

92.5% (1.8b remaining)

Error of 7.7b against oracle of 5.9b and baseline of 30.1b

bsearch336.0ms

Steps

Iters	Range		Point
8	3932480935863.943	2020002846347102.2	2000198799923726.5
9	4.8236772415131144e-172	7.640585338783926e-164	7.913319087558689e-172
9	-4.955433086253459e+131	-5.661938264600021e+124	-3.4127765686872833e+126

simplify9.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	41	98
1	50	96
2	51	96
done	51	96

end0.0ms

sample3.3s

Algorithm

intervals

Results

952.0ms	5922×	body	80	valid
721.0ms	1053×	body	2560	valid
371.0ms	906×	body	1280	valid
328.0ms	2894×	body	80	nan
167.0ms	458×	body	640	valid
124.0ms	85×	body	5120	valid
47.0ms	220×	body	320	valid
21.0ms	121×	body	160	valid