Details

sample79.0ms

Algorithm

intervals

Results

18.0ms	178×	body	80	valid
18.0ms	41×	body	2560	valid
10.0ms	29×	body	1280	valid
6.0ms	93×	body	80	nan
5.0ms	17×	body	640	valid
1.0ms	5×	body	160	valid
0.0ms	1×	body	5120	valid
0.0ms	2×	body	320	valid

simplify87.0ms

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

localize37.0ms

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)))

rewrite123.0ms

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:

73.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
28.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series505.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
146.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
78.0ms	(- (* b b) (* (* 4.0 a) c))
105.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

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

localize36.0ms

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))))

rewrite177.0ms

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:

60.0ms	(/ 1 (/ a (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0)))
51.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series452.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(/ 1 (/ a (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0)))
94.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
64.0ms	(- (* b b) (* 4.0 (* a c)))
102.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.0s

Counts

366 → 366

Iterations

Iter	Nodes
done	5050
2	4474
1	1573
0	569

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 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))))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

116.0ms	(* (/ 1 a) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0))
52.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
7.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series465.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(* (/ 1 a) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0))
101.0ms	(- (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))))

simplify1.9s

Counts

119 → 119

Iterations

Iter	Nodes
done	5001
2	1864
1	577
0	206

prune689.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.0b

localize53.0ms

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))))

rewrite36.0ms

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 b) (* 4.0 (* a c)))
10.0ms	(- (* b b) (* 4.0 (* a c)))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
7.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series345.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (* b b) (* 4.0 (* a c)))
82.0ms	(- (* b b) (* 4.0 (* a c)))
103.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
98.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts

66 → 66

Iterations

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

prune392.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.0b

regimes368.0ms

Accuracy

85.3% (4.3b remaining)

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

bsearch264.0ms

Steps

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

simplify36.0ms

Iterations

Iter	Nodes
done	35
1	35
0	28

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.0s	1115×	body	2560	valid
906.0ms	5809×	body	80	valid
519.0ms	902×	body	1280	valid
450.0ms	2954×	body	80	nan
192.0ms	454×	body	640	valid
63.0ms	105×	body	5120	valid
51.0ms	210×	body	320	valid
19.0ms	126×	body	160	valid