Details

sample106.0ms

Algorithm

intervals

Results

24.0ms	44×	body	2560	valid
16.0ms	167×	body	80	valid
15.0ms	32×	body	1280	valid
9.0ms	100×	body	80	nan
5.0ms	14×	body	640	valid
2.0ms	3×	body	5120	valid
2.0ms	7×	body	320	valid
1.0ms	3×	body	160	valid

simplify174.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	102	16
5	111	16
done	111	16

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
0.8b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.0b	(- (* b b) (* 4.0 (* a c)))
25.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

107.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
50.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
9.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series464.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
107.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
68.0ms	(- (* b b) (* 4.0 (* a c)))
105.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.0s

Counts

84 → 84

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	152	1592
1	403	1496
2	1596	1332
done	5001	1326

prune388.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
0.8b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.0b	(- (* b b) (* 4.0 (* a c)))
25.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
47×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
26×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`div-exp` `associate-/r*`
10×	`difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod` `add-log-exp`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv` `distribute-lft-out--`
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 → 118

Calls

4 calls:

83.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
78.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
10.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series503.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
111.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
70.0ms	(- (* b b) (* 4.0 (* a c)))
108.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts

130 → 130

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	218	3137
1	566	2809
2	2636	2613
done	5000	2611

prune411.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* 2.0 a))
0.8b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.0b	(- (* b b) (* 4.0 (* a c)))
25.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-exp-log`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cbrt-cube`
8×	`pow1` `add-log-exp`
7×	`add-cube-cbrt`
4×	`div-exp` `sqrt-prod`
3×	`flip3--` `times-frac` `prod-exp` `flip--` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `rec-exp` `pow-flip` `sqrt-div` `diff-log` `1-exp` `difference-of-squares`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv` `distribute-lft-out--` `inv-pow`

Counts

4 → 70

Calls

4 calls:

12.0ms	(/ 1 (* 2.0 a))
47.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
9.0ms	(- (* b b) (* 4.0 (* a c)))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ 1 (* 2.0 a))
122.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
60.0ms	(- (* b b) (* 4.0 (* a c)))
88.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify901.0ms

Counts

82 → 82

Iterations

Useful iterations: done (899.0ms)

Iter	Nodes	Cost
0	136	1051
1	332	938
2	1370	850
done	5001	848

prune283.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.7b

localize34.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (* b b) (* 4.0 (* a c)))
25.3b	(sqrt (- (* b b) (* 4.0 (* a c))))
25.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 54

Calls

4 calls:

13.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
19.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series332.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (* b b) (* 4.0 (* a c)))
70.0ms	(- (* b b) (* 4.0 (* a c)))
102.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
105.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.3s

Counts

66 → 66

Iterations

Useful iterations: 2 (112.0ms)

Iter	Nodes	Cost
0	60	1010
1	160	930
2	631	834
3	3660	834
done	5000	834

prune275.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 6.7b

regimes352.0ms

Accuracy

84.9% (4.4b remaining)

Error of 10.1b against oracle of 5.7b and baseline of 35.0b

bsearch228.0ms

Steps

Iters	Range		Point
8	2.5460852775314814e-33	4.614087934274923e-30	3.116683443156572e-33
10	-8.097032161796104e+150	-8.691973301260876e+137	-2.322469259707236e+143

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	42
1	32	42
done	32	42

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.2s	1127×	body	2560	valid
597.0ms	5717×	body	80	valid
491.0ms	223×	body	320	valid
450.0ms	936×	body	1280	valid
368.0ms	2905×	body	80	nan
181.0ms	448×	body	640	valid
68.0ms	111×	body	5120	valid
17.0ms	112×	body	160	valid