Details

sample40.0ms

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

simplify45.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	90	16
5	98	16
done	98	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 4.0 a) c)
0.8b	(- (* b b) (* (* 4.0 a) c))
1.3b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod`
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 → 60

Calls

4 calls:

6.0ms	(* (* 4.0 a) c)
3.0ms	(- (* b b) (* (* 4.0 a) c))
20.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 4.0 a) c)
48.0ms	(- (* b b) (* (* 4.0 a) c))
77.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts

72 → 72

Iterations

Useful iterations: 3 (849.0ms)

Iter	Nodes	Cost
0	120	1001
1	279	903
2	994	825
3	3828	821
done	5000	821

prune198.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 12.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))) b) 2.0) a)
0.8b	(- (* b b) (pow (* 4.0 (* a c)) 1))
1.3b	(- (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))) b)
21.1b	(sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
123×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
30×	`difference-of-squares`
22×	`associate-/l*`
18×	`sqrt-prod`
13×	`distribute-lft-out--`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
5×	`pow1` `div-inv`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `div-sub` `sqr-pow`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 153

Calls

4 calls:

58.0ms	(/ (/ (- (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))) b) 2.0) a)
3.0ms	(- (* b b) (pow (* 4.0 (* a c)) 1))
30.0ms	(- (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))) b)
9.0ms	(sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (/ (- (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))) b) 2.0) a)
45.0ms	(- (* b b) (pow (* 4.0 (* a c)) 1))
82.0ms	(- (sqrt (- (* b b) (pow (* 4.0 (* a c)) 1))) b)
73.0ms	(sqrt (- (* b b) (pow (* 4.0 (* a c)) 1)))

simplify775.0ms

Counts

165 → 165

Iterations

Useful iterations: done (769.0ms)

Iter	Nodes	Cost
0	289	4633
1	670	3975
2	1939	3813
done	5000	3812

prune470.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

71×	`times-frac`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
43×	`associate-r`
41×	`add-cube-cbrt`
19×	`add-exp-log`
13×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`div-exp` `associate-l`
5×	`flip3--` `prod-exp` `sqrt-prod` `flip--`
4×	`div-inv` `difference-of-squares` `unswap-sqr`
3×	`cbrt-undiv` `cbrt-unprod`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `associate-*l/` `distribute-lft-out--`
1×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `-commutative`

Counts

4 → 117

Calls

4 calls:

75.0ms	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (/ 1 2.0) a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
7.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series312.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (/ 1 2.0) a))
45.0ms	(- (* b b) (* 4.0 (* a c)))
83.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify770.0ms

Counts

129 → 129

Iterations

Useful iterations: done (766.0ms)

Iter	Nodes	Cost
0	263	2757
1	698	2456
2	2128	2210
done	5000	2201

prune353.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
0.8b	(- (* b b) (* 4.0 (* a c)))
1.3b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/l*`
16×	`sqrt-prod`
13×	`distribute-lft-out--`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
5×	`pow1` `div-inv`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `div-sub`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 149

Calls

4 calls:

37.0ms	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
3.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series321.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
51.0ms	(- (* b b) (* 4.0 (* a c)))
83.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify732.0ms

Counts

161 → 161

Iterations

Useful iterations: done (722.0ms)

Iter	Nodes	Cost
0	278	4083
1	663	3911
2	1940	3753
done	5000	3752

prune381.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.4b

regimes180.0ms

Accuracy

83.7% (4.6b remaining)

Error of 10.1b against oracle of 5.4b and baseline of 33.8b

bsearch111.0ms

Steps

Iters	Range		Point
8	1.3679096689958957e-81	5.608239720335765e-77	3.84613441880261e-81
7	-3.550313394724354e+57	-2.3888623512096697e+55	-3.124283374205192e+57

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	38
1	30	38
done	30	38

end0.0ms

sample1.1s

Algorithm

intervals

Results

248.0ms	1074×	body	2560	valid
229.0ms	5844×	body	80	valid
167.0ms	907×	body	1280	valid
109.0ms	2890×	body	80	nan
65.0ms	452×	body	640	valid
35.0ms	102×	body	5120	valid
25.0ms	234×	body	320	valid
11.0ms	119×	body	160	valid