Details

sample93.0ms

Algorithm

intervals

Results

26.0ms	167×	body	80	valid
17.0ms	44×	body	2560	valid
11.0ms	32×	body	1280	valid
6.0ms	100×	body	80	nan
4.0ms	14×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	3×	body	160	valid

simplify91.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	12	17
1	22	17
2	42	16
3	83	16
4	112	16
5	120	16
done	120	16

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* 3.0 a) c)
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b	(- (* b b) (* (* 3.0 a) c))
25.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`pow1` `add-sqr-sqrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `neg-log` `*-commutative` `flip-+`

Counts

4 → 80

Calls

4 calls:

18.0ms	(* (* 3.0 a) c)
42.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(- (* b b) (* (* 3.0 a) c))
12.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series400.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (* 3.0 a) c)
145.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
90.0ms	(- (* b b) (* (* 3.0 a) c))
129.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.0s

Counts

92 → 92

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	135	1109
1	361	1010
2	1922	900
done	5000	893

prune392.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.8b

localize37.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
3.4b	(/ (/ (+ 0 (* c (* 3.0 a))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
11.3b	(/ (+ 0 (* c (* 3.0 a))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
25.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite365.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 158

Calls

4 calls:

19.0ms	(- (* b b) (* (* 3.0 a) c))
177.0ms	(/ (/ (+ 0 (* c (* 3.0 a))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
130.0ms	(/ (+ 0 (* c (* 3.0 a))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series651.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (* b b) (* (* 3.0 a) c))
228.0ms	(/ (/ (+ 0 (* c (* 3.0 a))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
266.0ms	(/ (+ 0 (* c (* 3.0 a))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
95.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.5s

Counts

170 → 170

Iterations

Useful iterations: 2 (1.1s)

Iter	Nodes	Cost
0	262	5076
1	689	4517
2	4643	4197
done	5000	4197

prune710.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.4b

localize24.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
3.4b	(/ (/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
11.3b	(/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
25.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
54×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
29×	`add-cube-cbrt`
27×	`add-exp-log` `add-cbrt-cube`
14×	`associate-/l*`
12×	`distribute-lft-out--` `difference-of-squares`
10×	`cbrt-undiv` `div-exp` `associate-/r*` `associate-/r/`
9×	`sqrt-prod`
7×	`flip3--` `flip--`
6×	`distribute-rgt-neg-in` `prod-exp` `cbrt-unprod` `div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `associate-/l/`

Counts

4 → 144

Calls

4 calls:

9.0ms	(- (* b b) (* (* 3.0 a) c))
82.0ms	(/ (/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
61.0ms	(/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
19.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series549.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* (* 3.0 a) c))
188.0ms	(/ (/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
218.0ms	(/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
94.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.2s

Counts

156 → 156

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	266	4241
1	733	3999
2	4199	3606
done	5000	3604

prune732.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 12.4b

localize44.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
3.4b	(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 (* a c)))) (* 3.0 a))
11.5b	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 (* a c)))
25.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite264.0ms

Algorithm

rewrite-expression-head

Rules

153×	`times-frac`
122×	`add-exp-log`
76×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
63×	`div-exp`
58×	`add-cbrt-cube`
45×	`associate-/l*`
43×	`add-cube-cbrt`
34×	`prod-exp`
27×	`cbrt-undiv`
16×	`distribute-lft-out--` `difference-of-squares`
14×	`cbrt-unprod`
11×	`sqrt-prod`
10×	`div-inv`
8×	`rec-exp` `distribute-rgt-neg-in` `1-exp`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `flip--` `associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/r*` `associate-/r/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff`

Counts

4 → 195

Calls

4 calls:

11.0ms	(- (* b b) (* (* 3.0 a) c))
113.0ms	(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 (* a c)))) (* 3.0 a))
101.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 (* a c)))
20.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series486.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (* b b) (* (* 3.0 a) c))
176.0ms	(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 (* a c)))) (* 3.0 a))
131.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 (* a c)))
99.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify687.0ms

Counts

207 → 207

Iterations

Useful iterations: done (677.0ms)

Iter	Nodes	Cost
0	393	6101
1	1177	5758
done	5001	4984

prune767.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.6b

regimes596.0ms

Accuracy

88.2% (3.2b remaining)

Error of 8.9b against oracle of 5.7b and baseline of 32.9b

bsearch288.0ms

Steps

Iters	Range		Point
7	517946.10598021303	17102963.46615162	12147289.827179085
10	-8.138706044250008e-279	-2.4810350231976038e-293	-7.563947638607336e-293
10	-8.097032161796104e+150	-8.691973301260876e+137	-8.996672738587564e+142

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	83
1	51	83
done	51	83

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.1s	1127×	body	2560	valid
683.0ms	5718×	body	80	valid
399.0ms	2902×	body	80	nan
380.0ms	936×	body	1280	valid
140.0ms	448×	body	640	valid
70.0ms	111×	body	5120	valid
46.0ms	223×	body	320	valid
16.0ms	111×	body	160	valid