Details

sample59.0ms

Algorithm

intervals

Results

35.0ms	278×	body	80	valid
9.0ms	77×	body	80	nan

simplify168.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	168
7	168
6	166
5	160
4	151
3	125
2	75
1	38
0	20

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.8b

localize116.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4 a) c))
1.6b	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
22.6b	(sqrt (- (* b b) (* (* 4 a) c)))
22.6b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-log-exp`
7×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `flip--`
3×	`diff-log`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `distribute-rgt-neg-in` `neg-log`

Counts

4 → 64

Calls

4 calls:

14.0ms	(- (* b b) (* (* 4 a) c))
29.0ms	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
12.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b b) (* (* 4 a) c))
104.0ms	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
105.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
132.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.1s

Counts

76 → 76

Iterations

Iter	Nodes
3	2593
2	742
1	237
0	99

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

localize194.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4 a) c))
4.8b	(/ (* (- (/ a (/ b c)) b) 2) (* 2 a))
4.9b	(/ a (/ b c))
22.6b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity` `add-cube-cbrt`
21×	`add-cbrt-cube` `add-exp-log`
14×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `associate-/l*`
3×	`flip3--` `sqrt-prod` `flip--`
2×	`clear-num` `frac-2neg` `sqrt-div` `associate-*l/` `associate-/l/`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-/r/`

Counts

4 → 124

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4 a) c))
47.0ms	(/ (* (- (/ a (/ b c)) b) 2) (* 2 a))
11.0ms	(/ a (/ b c))
15.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (* b b) (* (* 4 a) c))
52.0ms	(/ (* (- (/ a (/ b c)) b) 2) (* 2 a))
26.0ms	(/ a (/ b c))
107.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.6s

Counts

136 → 136

Iterations

Iter	Nodes
2	2484
1	689
0	260

prune2.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

localize176.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 2 c) (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.2b	(- (* b b) (* (* 4 a) c))
22.6b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite64.0ms

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` `associate-/r*` `times-frac`
4×	`insert-posit16`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `sum-log` `flip3-+` `flip3--` `sqrt-div` `div-exp` `associate-/r/` `flip-+` `flip--`
1×	`neg-sub0` `+-commutative` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `prod-exp` `associate-+l-` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 73

Calls

4 calls:

34.0ms	(/ (* 2 c) (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))))
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
7.0ms	(- (* b b) (* (* 4 a) c))
8.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series567.0ms

Counts

4 → 12

Calls

4 calls:

279.0ms	(/ (* 2 c) (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))))
122.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
82.0ms	(- (* b b) (* (* 4 a) c))
84.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify3.0s

Counts

85 → 85

Iterations

Iter	Nodes
3	4917
2	1277
1	381
0	147

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.4b

localize190.0ms

Local error

Found 4 expressions with local error:

13.9b	(cbrt (/ b c))
13.9b	(cbrt (/ b c))
13.9b	(cbrt (/ b c))
22.6b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
27×	`add-sqr-sqrt` `times-frac`
26×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`cbrt-div` `pow1/3` `sqrt-prod` `div-inv`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 85

Calls

4 calls:

3.0ms	(cbrt (/ b c))
3.0ms	(cbrt (/ b c))
3.0ms	(cbrt (/ b c))
14.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series371.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(cbrt (/ b c))
83.0ms	(cbrt (/ b c))
95.0ms	(cbrt (/ b c))
113.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify3.9s

Counts

97 → 97

Iterations

Iter	Nodes
4	6291
3	1846
2	601
1	235
0	126

prune2.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.4b

regimes615.0ms

Accuracy

93.1% (1.1b remaining)

Error of 6.6b against oracle of 5.5b and baseline of 21.3b

bsearch299.0ms

Steps

Iters	Range		Point
7	1.602087361235081e+82	9.448026055101687e+83	6.431123294932864e+83
8	-5.520406447692031e+155	-1.5529738836716088e+153	-7.66098576995581e+153

simplify21.0ms

Iterations

Iter	Nodes
2	54
1	54
0	45

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.1s	8756×	body	80	valid
630.0ms	2920×	body	80	nan