Details

sample68.0ms

Algorithm

intervals

Results

12.0ms	206×	body	80	valid
10.0ms	29×	body	2560	valid
10.0ms	96×	body	80	nan
8.0ms	28×	body	1280	valid
3.0ms	12×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	3×	body	160	valid
0.0ms	1×	body	5120	valid

simplify259.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	28	17
2	64	17
3	114	17
4	130	17
5	137	17
6	141	17
done	141	17

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b	(- (* b b) (* 4.0 (* a c)))
24.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt` `times-frac` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `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` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

111.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
36.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series467.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
138.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
77.0ms	(- (* b b) (* 4.0 (* a c)))
108.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.2s

Counts

89 → 89

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	157	1750
1	402	1650
2	1322	1474
3	4955	1459
done	5000	1459

prune441.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.7b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b	(- (* b b) (* 4.0 (* a c)))
24.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite113.0ms

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`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 125

Calls

4 calls:

55.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
30.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series492.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
102.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms	(- (* b b) (* 4.0 (* a c)))
107.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts

137 → 137

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	226	3421
1	518	3066
2	1541	2794
done	5001	2684

prune415.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
1.2b	(- (* b b) (* 4.0 (* a c)))
5.1b	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
24.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

24.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
91.0ms	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
19.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series542.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
77.0ms	(- (* b b) (* 4.0 (* a c)))
169.0ms	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
127.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts

88 → 88

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	165	1798
1	417	1643
2	1302	1511
done	5000	1506

prune321.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.6b

localize26.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* 4.0 (* a c)))
2.0b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.1b	(/ (+ 0 (* (* 4.0 a) c)) (* 2.0 a))
24.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
5×	`pow1`
3×	`times-frac` `sqrt-prod` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 65

Calls

4 calls:

18.0ms	(- (* b b) (* 4.0 (* a c)))
35.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
38.0ms	(/ (+ 0 (* (* 4.0 a) c)) (* 2.0 a))
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series283.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (* b b) (* 4.0 (* a c)))
97.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms	(/ (+ 0 (* (* 4.0 a) c)) (* 2.0 a))
112.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.0s

Counts

77 → 77

Iterations

Useful iterations: 2 (316.0ms)

Iter	Nodes	Cost
0	147	1241
1	375	1068
2	1670	950
done	5001	950

prune360.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.6b

regimes259.0ms

Accuracy

94.7% (1.3b remaining)

Error of 6.8b against oracle of 5.5b and baseline of 29.4b

bsearch297.0ms

Steps

Iters	Range		Point
9	1.2073698495971617e+61	8.75865749938149e+67	5.099089738165329e+67
10	1.610059141238142e-239	1.618698210595833e-224	2.094358742794728e-239
10	-3.742210988141449e+103	-1.0235731023437291e+92	-3.359953003549157e+103

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	64
1	43	64
done	43	64

end0.0ms

sample3.2s

Algorithm

intervals

Results

604.0ms	1047×	body	2560	valid
592.0ms	5837×	body	80	valid
550.0ms	2844×	body	80	nan
499.0ms	897×	body	1280	valid
201.0ms	466×	body	640	valid
100.0ms	112×	body	5120	valid
57.0ms	106×	body	160	valid
49.0ms	241×	body	320	valid