Details

sample94.0ms

Algorithm

intervals

Results

21.0ms	193×	body	80	valid
20.0ms	30×	body	2560	valid
13.0ms	26×	body	1280	valid
10.0ms	99×	body	80	nan
6.0ms	12×	body	640	valid
3.0ms	5×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	1×	body	160	valid

simplify147.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	98
7	98
6	97
5	95
4	87
3	70
2	43
1	24
0	14

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
0.2b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
0.6b	(- (* b b) (* (* 4 a) c))
24.5b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite104.0ms

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*`
4×	`insert-posit16`
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 → 74

Calls

4 calls:

59.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
17.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
14.0ms	(- (* b b) (* (* 4 a) c))
13.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
100.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
63.0ms	(- (* b b) (* (* 4 a) c))
98.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.9s

Counts

86 → 86

Iterations

Iter	Nodes
3	4960
2	1314
1	402
0	153

prune823.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

localize64.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 4 a) c))
0.6b	(- (* b b) (* (* 4 a) c))
24.5b	(sqrt (- (* b b) (* (* 4 a) c)))
24.5b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite39.0ms

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` `insert-posit16` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 58

Calls

4 calls:

15.0ms	(- (* b b) (* (* 4 a) c))
8.0ms	(- (* b b) (* (* 4 a) c))
8.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
8.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (* b b) (* (* 4 a) c))
52.0ms	(- (* b b) (* (* 4 a) c))
85.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
87.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify4.7s

Counts

70 → 70

Iterations

Iter	Nodes
4	7462
3	1987
2	522
1	156
0	63

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.8b

localize80.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 4 a) c))
24.5b	(sqrt (- (* b b) (* (* 4 a) c)))
24.5b	(sqrt (- (* b b) (* (* 4 a) c)))
24.5b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log`

Counts

4 → 61

Calls

4 calls:

7.0ms	(- (* b b) (* (* 4 a) c))
7.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
8.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
8.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- (* b b) (* (* 4 a) c))
106.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
112.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
91.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify5.1s

Counts

73 → 73

Iterations

Iter	Nodes
4	7462
3	1987
2	522
1	156
0	63

prune971.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.8b

localize52.0ms

Local error

Found 4 expressions with local error:

24.5b	(sqrt (- (* b b) (* (* 4 a) c)))
25.3b	(cbrt (- (* b b) (* (* 4 a) c)))
25.3b	(cbrt (- (* b b) (* (* 4 a) c)))
25.3b	(cbrt (- (* b b) (* (* 4 a) c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
5×	`pow1`
4×	`flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `flip--` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

8.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
12.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
10.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
8.0ms	(cbrt (- (* b b) (* (* 4 a) c)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
104.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
123.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
108.0ms	(cbrt (- (* b b) (* (* 4 a) c)))

simplify3.4s

Counts

70 → 70

Iterations

Iter	Nodes
4	6322
3	1876
2	580
1	200
0	89

prune1.1s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.8b

regimes295.0ms

Accuracy

82.5% (4.9b remaining)

Error of 10.6b against oracle of 5.7b and baseline of 33.5b

bsearch209.0ms

Steps

Iters	Range		Point
6	3.7222086374392734e-21	4.963951531010332e-20	3.821014310434392e-21
10	-3.568388406125044e+108	-3.585760457965514e+97	-3.5748480491313226e+106

simplify6.0ms

Iterations

Iter	Nodes
2	32
1	32
0	26

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.1s	5860×	body	80	valid
853.0ms	1029×	body	2560	valid
574.0ms	889×	body	1280	valid
379.0ms	2862×	body	80	nan
240.0ms	469×	body	640	valid
169.0ms	107×	body	5120	valid
86.0ms	199×	body	320	valid
29.0ms	141×	body	160	valid