Details

sample108.0ms

Algorithm

intervals

Results

26.0ms	16×	body	640	valid
21.0ms	39×	body	2560	valid
17.0ms	173×	body	80	valid
14.0ms	30×	body	1280	valid
8.0ms	89×	body	80	nan
3.0ms	5×	body	5120	valid
3.0ms	10×	body	320	valid
1.0ms	6×	body	160	valid

simplify166.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	134
7	134
6	132
5	129
4	126
3	103
2	62
1	28
0	14

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
1.2b	(- (* b b) (* 4 (* a c)))
1.4b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
26.8b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`times-frac` `add-cube-cbrt` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 81

Calls

4 calls:

57.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
18.0ms	(- (* b b) (* 4 (* a c)))
20.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
7.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series394.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
54.0ms	(- (* b b) (* 4 (* a c)))
102.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
104.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify2.2s

Counts

93 → 93

Iterations

Iter	Nodes
3	4255
2	1194
1	398
0	154

prune900.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.6b

localize14.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
1	0
0	0

prune75.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.6b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
1.2b	(- (* b b) (* 4 (* a c)))
1.4b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
26.8b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
13×	`associate-r` `add-cube-cbrt`
10×	`times-frac` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`pow1` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`insert-posit16` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log`
2×	`frac-times` `sub-neg` `distribute-rgt-neg-in` `sqrt-div` `associate-*l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `neg-log` `associate-r/` `-commutative` `div-inv`

Counts

4 → 89

Calls

4 calls:

107.0ms	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
15.0ms	(- (* b b) (* 4 (* a c)))
26.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series413.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
63.0ms	(- (* b b) (* 4 (* a c)))
118.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
112.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify2.8s

Counts

101 → 101

Iterations

Iter	Nodes
3	5724
2	1456
1	448
0	177

prune961.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.6b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
1.2b	(- (* b b) (* 4 (* a c)))
1.4b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
26.8b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `div-inv`
4×	`insert-posit16`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `cbrt-unprod` `pow-flip` `inv-pow`

Counts

4 → 129

Calls

4 calls:

72.0ms	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
17.0ms	(- (* b b) (* 4 (* a c)))
31.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series357.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
49.0ms	(- (* b b) (* 4 (* a c)))
99.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
88.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify6.0s

Counts

141 → 141

Iterations

Iter	Nodes
3	6319
2	1703
1	554
0	229

prune994.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.4b

regimes503.0ms

Accuracy

86.7% (3.5b remaining)

Error of 9.0b against oracle of 5.5b and baseline of 31.7b

bsearch429.0ms

Steps

Iters	Range		Point
9	2.662790715355376e+61	3.00977400694497e+66	9.179168538250646e+63
9	-7.863485219732001e-306	1.6702113216735622e-306	-2.396838732613953e-306
9	-229886301330938.94	-710549284.1101115	-6239046376.848015

simplify30.0ms

Iterations

Iter	Nodes
5	73
4	73
3	68
2	56
1	46
0	35

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.4s	5799×	body	80	valid
1.1s	1064×	body	2560	valid
858.0ms	916×	body	1280	valid
466.0ms	2970×	body	80	nan
246.0ms	444×	body	640	valid
150.0ms	120×	body	5120	valid
115.0ms	243×	body	320	valid
56.0ms	125×	body	160	valid