Details

sample70.0ms

Algorithm

intervals

Results

17.0ms	41×	body	2560	valid
12.0ms	178×	body	80	valid
10.0ms	29×	body	1280	valid
6.0ms	93×	body	80	nan
5.0ms	17×	body	640	valid
1.0ms	1×	body	5120	valid
1.0ms	5×	body	160	valid
0.0ms	2×	body	320	valid

simplify89.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	98
7	98
6	97
5	95
4	87
3	72
2	42
1	24
0	14

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.7b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0b	(- (* b b) (* (* 4.0 a) c))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`neg-sub0` `cbrt-undiv` `sum-log` `flip3-+` `flip3--` `sqrt-div` `div-exp` `associate-+l-` `flip-+` `flip--` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

106.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
35.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms	(- (* b b) (* (* 4.0 a) c))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
118.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
65.0ms	(- (* b b) (* (* 4.0 a) c))
104.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	1364
1	411
0	154

prune541.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ a (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0)))
1.7b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.0b	(- (* b b) (* 4.0 (* a c)))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

693×	`times-frac`
438×	`add-sqr-sqrt`
363×	`*-un-lft-identity`
289×	`add-cube-cbrt`
74×	`difference-of-squares`
71×	`associate-/r*`
40×	`sqrt-prod`
37×	`distribute-lft-out--`
25×	`add-exp-log`
17×	`div-inv`
15×	`div-exp`
13×	`add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `cbrt-undiv`
5×	`associate-/r/`
3×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-flip` `inv-pow`

Counts

4 → 354

Calls

4 calls:

99.0ms	(/ 1 (/ a (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0)))
39.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
8.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series551.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(/ 1 (/ a (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0)))
131.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
87.0ms	(- (* b b) (* 4.0 (* a c)))
123.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.9s

Counts

366 → 366

Iterations

Iter	Nodes
done	5050
2	4474
1	1573
0	569

prune1.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ 1 (* a 2.0)))
1.7b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.0b	(- (* b b) (* 4.0 (* a c)))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite266.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

201.0ms	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ 1 (* a 2.0)))
41.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
7.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series463.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ 1 (* a 2.0)))
133.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
60.0ms	(- (* b b) (* 4.0 (* a c)))
120.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.1s

Counts

93 → 93

Iterations

Iter	Nodes
done	5018
2	1694
1	464
0	178

prune507.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.0b

localize84.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (* b b) (* 4.0 (* a c)))
2.0b	(- (* b b) (* 4.0 (* a c)))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

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:

7.0ms	(- (* b b) (* 4.0 (* a c)))
7.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series344.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (* b b) (* 4.0 (* a c)))
71.0ms	(- (* b b) (* 4.0 (* a c)))
90.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
112.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.8s

Counts

66 → 66

Iterations

Iter	Nodes
done	5003
3	1892
2	471
1	152
0	60

prune443.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.0b

regimes377.0ms

Accuracy

85.3% (4.3b remaining)

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

bsearch229.0ms

Steps

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

simplify10.0ms

Iterations

Iter	Nodes
done	36
1	36
0	28

end0.0ms

sample3.0s

Algorithm

intervals

Results

691.0ms	1115×	body	2560	valid
610.0ms	5809×	body	80	valid
603.0ms	2954×	body	80	nan
367.0ms	902×	body	1280	valid
218.0ms	454×	body	640	valid
60.0ms	105×	body	5120	valid
44.0ms	210×	body	320	valid
18.0ms	126×	body	160	valid