Details

sample41.0ms

Algorithm

intervals

Results

8.0ms	201×	body	80	valid
7.0ms	35×	body	1280	valid
6.0ms	27×	body	2560	valid
3.0ms	87×	body	80	nan
2.0ms	12×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify90.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	28	17
2	63	17
3	114	17
4	130	17
5	136	17
6	139	17
done	139	17

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
20.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite58.0ms

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:

37.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
12.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series289.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
77.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
48.0ms	(- (* b b) (* 4.0 (* a c)))
67.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify952.0ms

Counts

89 → 89

Iterations

Useful iterations: done (950.0ms)

Iter	Nodes	Cost
0	157	1750
1	405	1650
2	1328	1474
done	5000	1459

prune260.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.4b

localize13.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.7b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
10.3b	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
20.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
78×	`times-frac`
58×	`*-un-lft-identity`
36×	`add-cube-cbrt`
27×	`associate-/l*`
22×	`difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-lft-out--`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`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` `diff-log` `flip-+`

Counts

4 → 141

Calls

4 calls:

19.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
45.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
27.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series531.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
172.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
204.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify839.0ms

Counts

153 → 153

Iterations

Useful iterations: done (833.0ms)

Iter	Nodes	Cost
0	250	4579
1	626	4057
2	2390	3753
done	5000	3751

prune415.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.3b

localize16.0ms

Local error

Found 4 expressions with local error:

6.4b	(/ (/ (* 4.0 (* a c)) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) a)
6.7b	(/ (* 4.0 (* a c)) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
20.5b	(sqrt (- (* b b) (* 4.0 (* a c))))
20.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
64×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
48×	`sqrt-prod`
38×	`add-cube-cbrt`
27×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/l*`
14×	`sqrt-div`
12×	`associate-/r*` `difference-of-squares`
10×	`cbrt-undiv` `div-exp` `associate-/r/`
7×	`flip3--` `flip--`
6×	`pow1` `prod-exp` `cbrt-unprod` `div-inv` `distribute-lft-out--`
4×	`add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 149

Calls

4 calls:

41.0ms	(/ (/ (* 4.0 (* a c)) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) a)
29.0ms	(/ (* 4.0 (* a c)) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series1.4s

Counts

4 → 12

Calls

4 calls:

734.0ms	(/ (/ (* 4.0 (* a c)) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) a)
544.0ms	(/ (* 4.0 (* a c)) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.0s

Counts

161 → 161

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	277	4644
1	710	4174
2	2646	3898
done	5001	3894

prune497.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
20.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

57.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
13.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
6.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series294.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
77.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
49.0ms	(- (* b b) (* 4.0 (* a c)))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify842.0ms

Counts

97 → 97

Iterations

Useful iterations: done (840.0ms)

Iter	Nodes	Cost
0	183	2003
1	468	1793
2	1570	1565
done	5000	1564

prune224.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 5.3b

regimes291.0ms

Accuracy

81.8% (4.8b remaining)

Error of 10.5b against oracle of 5.8b and baseline of 31.9b

bsearch100.0ms

Steps

Iters	Range		Point
8	2.1878188410446244e+107	3.8616146939177386e+111	3.6627135292415903e+111
8	-4.854151311909829e-126	-9.294658666337375e-130	-4.7828589349284326e-126

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	37
1	31	37
done	31	37

end0.0ms

sample1.2s

Algorithm

intervals

Results

266.0ms	1110×	body	2560	valid
234.0ms	5789×	body	80	valid
171.0ms	885×	body	1280	valid
109.0ms	2998×	body	80	nan
69.0ms	448×	body	640	valid
31.0ms	253×	body	320	valid
29.0ms	101×	body	5120	valid
15.0ms	126×	body	160	valid