Details

sample84.0ms

Algorithm

intervals

Results

16.0ms	34×	body	2560	valid
16.0ms	196×	body	80	valid
8.0ms	20×	body	1280	valid
6.0ms	78×	body	80	nan
5.0ms	15×	body	640	valid
3.0ms	6×	body	5120	valid
2.0ms	7×	body	320	valid
0.0ms	2×	body	160	valid

simplify63.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	13
1	18	13
2	32	13
3	41	13
4	44	13
done	44	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (* b_2 b_2) (* a c))
0.4b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 91

Calls

4 calls:

99.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* b_2 b_2) (* a c))
24.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series412.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
63.0ms	(- (* b_2 b_2) (* a c))
89.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
103.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.0s

Counts

103 → 103

Iterations

Useful iterations: done (1000.0ms)

Iter	Nodes	Cost
0	156	1821
1	387	1727
2	1508	1613
done	5001	1603

prune407.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b_2 b_2) (* a c))
0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.4b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
13×	`add-exp-log` `add-cube-cbrt` `associate-r`
11×	`times-frac`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `distribute-rgt-neg-in` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 89

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
149.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
36.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b_2 b_2) (* a c))
151.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
77.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
101.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify5.9s

Counts

101 → 101

Iterations

Useful iterations: done (5.9s)

Iter	Nodes	Cost
0	175	1741
1	456	1582
2	2994	1379
done	5000	1357

prune291.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (* b_2 b_2) (* a c))
0.4b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 91

Calls

4 calls:

119.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* b_2 b_2) (* a c))
43.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series397.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
63.0ms	(- (* b_2 b_2) (* a c))
95.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
92.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify998.0ms

Counts

103 → 103

Iterations

Useful iterations: done (994.0ms)

Iter	Nodes	Cost
0	156	1821
1	387	1727
2	1508	1613
done	5001	1603

prune339.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b_2 b_2) (* a c))
0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.4b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac`
130×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
77×	`add-cube-cbrt`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `inv-pow`

Counts

4 → 177

Calls

4 calls:

17.0ms	(- (* b_2 b_2) (* a c))
68.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
56.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b_2 b_2) (* a c))
149.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
134.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
80.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts

189 → 189

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	266	4484
1	661	3936
2	3609	3788
done	5001	3786

prune416.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.4b

regimes425.0ms

Accuracy

85.9% (4.0b remaining)

Error of 9.8b against oracle of 5.8b and baseline of 34.3b

bsearch247.0ms

Steps

Iters	Range		Point
8	3932480935863.943	2020002846347102.2	1920982614230223.5
10	-1.3330344523059006e-149	-1.6749016460307825e-159	-1.3943257168792356e-154
6	-2.350179250111568e+55	-1.828939172749339e+54	-7.359940312872037e+54

simplify8.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	36	63
1	44	59
2	46	59
done	46	59

end0.0ms

sample3.0s

Algorithm

intervals

Results

861.0ms	5763×	body	80	valid
549.0ms	1057×	body	2560	valid
369.0ms	933×	body	1280	valid
261.0ms	2859×	body	80	nan
210.0ms	445×	body	640	valid
108.0ms	116×	body	5120	valid
45.0ms	234×	body	320	valid
14.0ms	119×	body	160	valid