Details

sample97.0ms

Algorithm

intervals

Results

27.0ms	40×	body	2560	valid
21.0ms	186×	body	80	valid
14.0ms	28×	body	1280	valid
10.0ms	91×	body	80	nan
4.0ms	10×	body	640	valid
3.0ms	8×	body	320	valid
2.0ms	3×	body	5120	valid
1.0ms	4×	body	160	valid

simplify109.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	95
7	95
6	94
5	92
4	84
3	67
2	43
1	24
0	14

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
1.0b	(- (* b b) (* (* 4 a) c))
1.3b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
21.9b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite129.0ms

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--` `insert-posit16` `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 → 88

Calls

4 calls:

72.0ms	(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
13.0ms	(- (* b b) (* (* 4 a) c))
35.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
54.0ms	(- (* b b) (* (* 4 a) c))
100.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
87.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.5s

Counts

100 → 100

Iterations

Iter	Nodes
3	3816
2	1126
1	392
0	161

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.8b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* (* 4 a) c))) b) (/ 1 a))
1.0b	(- (* b b) (* (* 4 a) c))
1.3b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
21.9b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite227.0ms

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` `insert-posit16` `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 → 89

Calls

4 calls:

142.0ms	(* (- (sqrt (- (* b b) (* (* 4 a) c))) b) (/ 1 a))
7.0ms	(- (* b b) (* (* 4 a) c))
62.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
14.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(* (- (sqrt (- (* b b) (* (* 4 a) c))) b) (/ 1 a))
60.0ms	(- (* b b) (* (* 4 a) c))
92.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
110.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.7s

Counts

101 → 101

Iterations

Iter	Nodes
3	4837
2	1437
1	455
0	181

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (+ (* -4 (* a c)) (* b b))) b) a)
1.0b	(+ (* -4 (* a c)) (* b b))
1.3b	(- (sqrt (+ (* -4 (* a c)) (* b b))) b)
21.9b	(sqrt (+ (* -4 (* a c)) (* b b)))

rewrite303.0ms

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×	`insert-posit16`
3×	`associate-/r*`
2×	`flip3-+` `flip3--` `sqrt-div` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

4 → 87

Calls

4 calls:

164.0ms	(/ (- (sqrt (+ (* -4 (* a c)) (* b b))) b) a)
23.0ms	(+ (* -4 (* a c)) (* b b))
99.0ms	(- (sqrt (+ (* -4 (* a c)) (* b b))) b)
15.0ms	(sqrt (+ (* -4 (* a c)) (* b b)))

series396.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (- (sqrt (+ (* -4 (* a c)) (* b b))) b) a)
66.0ms	(+ (* -4 (* a c)) (* b b))
102.0ms	(- (sqrt (+ (* -4 (* a c)) (* b b))) b)
91.0ms	(sqrt (+ (* -4 (* a c)) (* b b)))

simplify1.6s

Counts

99 → 99

Iterations

Iter	Nodes
3	3527
2	930
1	328
0	137

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.8b

localize18.0ms

Local error

Found 1 expressions with local error:

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

rewrite24.0ms

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` `insert-posit16` `div-inv` `add-log-exp`

Counts

1 → 33

Calls

1 calls:

23.0ms

(* -2 (/ c b))

series20.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

(* -2 (/ c b))

simplify6.9s

Counts

36 → 36

Iterations

Iter	Nodes
4	3714
3	1054
2	425
1	169
0	69

prune285.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 4.8b

regimes467.0ms

Accuracy

85.1% (4.2b remaining)

Error of 9.6b against oracle of 5.4b and baseline of 33.6b

bsearch272.0ms

Steps

Iters	Range		Point
8	6.256891986679925e-86	3.543466061308676e-83	5.9878793504095505e-84
10	-1.0499721897563905e+163	-8.354690034354516e+151	-9.768773924260542e+151

simplify9.0ms

Iterations

Iter	Nodes
2	32
1	32
0	27

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.2s	935×	body	1280	valid
1.1s	5845×	body	80	valid
1.0s	1106×	body	2560	valid
493.0ms	2919×	body	80	nan
273.0ms	453×	body	640	valid
176.0ms	111×	body	5120	valid
92.0ms	212×	body	320	valid
28.0ms	113×	body	160	valid