Details

sample129.0ms

Algorithm

intervals

Results

38.0ms	29×	body	1280	valid
10.0ms	41×	body	2560	valid
8.0ms	179×	body	80	valid
4.0ms	92×	body	80	nan
3.0ms	17×	body	640	valid
0.0ms	4×	body	160	valid
0.0ms	3×	body	320	valid
0.0ms	1×	body	5120	valid

simplify25.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	29
5	29
4	27
3	25
2	22
1	14
0	10

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.2b	(- (* b_2 b_2) (* a c))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

133.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
55.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
6.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
101.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
55.0ms	(- (* b_2 b_2) (* a c))
84.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts

96 → 96

Iterations

Iter	Nodes
done	5008
3	4099
2	1023
1	374
0	154

prune684.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
1.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.2b	(- (* b_2 b_2) (* a c))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite255.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

165.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
60.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
90.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
57.0ms	(- (* b_2 b_2) (* a c))
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.0s

Counts

97 → 97

Iterations

Iter	Nodes
done	5003
3	4611
2	1338
1	443
0	174

prune480.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.3b

localize45.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (* b_2 b_2) (* a c))
2.2b	(- (* b_2 b_2) (* a c))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

6.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(- (* b_2 b_2) (* a c))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (* b_2 b_2) (* a c))
39.0ms	(- (* b_2 b_2) (* a c))
88.0ms	(sqrt (- (* b_2 b_2) (* a c)))
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.3s

Counts

66 → 66

Iterations

Iter	Nodes
done	5000
4	4824
3	1339
2	413
1	147
0	58

prune523.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.3b

localize12.0ms

Local error

Found 1 expressions with local error:

0.0b	(* -1/2 (/ c b_2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-r`
10×	`times-frac`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log`
3×	`pow1` `associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `div-inv` `add-log-exp`

Counts

1 → 32

Calls

1 calls:

20.0ms

(* -1/2 (/ c b_2))

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

(* -1/2 (/ c b_2))

simplify1.6s

Counts

35 → 35

Iterations

Iter	Nodes
done	5000
3	1422
2	508
1	172
0	68

prune138.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.3b

regimes465.0ms

Accuracy

85.5% (4.2b remaining)

Error of 10.1b against oracle of 5.8b and baseline of 34.9b

bsearch148.0ms

Steps

Iters	Range		Point
10	8.767897341253802e-114	4.657027509742155e-104	4.6129908231112306e-104
9	-6.117539429929052e+154	-3.6285784997486435e+148	-3.6803290429888884e+148

simplify5.0ms

Iterations

Iter	Nodes
done	31
1	31
0	25

end0.0ms

sample3.0s

Algorithm

intervals

Results

612.0ms	1119×	body	2560	valid
601.0ms	5807×	body	80	valid
453.0ms	125×	body	160	valid
372.0ms	899×	body	1280	valid
264.0ms	2952×	body	80	nan
132.0ms	453×	body	640	valid
56.0ms	106×	body	5120	valid
45.0ms	213×	body	320	valid