Details

sample41.0ms

Algorithm

intervals

Results

8.0ms	37×	body	2560	valid
7.0ms	177×	body	80	valid
6.0ms	31×	body	1280	valid
3.0ms	92×	body	80	nan
2.0ms	16×	body	640	valid
1.0ms	5×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify222.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	90	16
5	98	16
done	98	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b	(- (* b b) (* (* 4.0 a) c))
27.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

36.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
74.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms	(- (* b b) (* (* 4.0 a) c))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify702.0ms

Counts

82 → 82

Iterations

Useful iterations: done (699.0ms)

Iter	Nodes	Cost
0	154	1565
1	406	1461
2	1359	1245
done	5000	1235

prune250.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.0b

localize18.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.5b	(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
8.5b	(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
27.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

14.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms	(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
35.0ms	(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
125.0ms	(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
165.0ms	(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify948.0ms

Counts

166 → 166

Iterations

Useful iterations: done (942.0ms)

Iter	Nodes	Cost
0	261	5855
1	677	5304
2	2366	4558
done	5000	4556

prune435.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
2.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.5b	(/ (+ (* 4.0 (* a c)) 0) a)
27.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

2.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms	(/ (+ (* 4.0 (* a c)) 0) a)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series194.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* (* 4.0 a) c))
73.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(/ (+ (* 4.0 (* a c)) 0) a)
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify788.0ms

Counts

86 → 86

Iterations

Useful iterations: done (785.0ms)

Iter	Nodes	Cost
0	154	1396
1	354	1206
2	1302	1116
done	5000	1114

prune262.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 4.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.8b	(- (* b b) (* (* 4.0 a) c))
2.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
27.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite44.0ms

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-/r*`
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-/r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 76

Calls

4 calls:

21.0ms	(/ (* 4.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ (* 4.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
44.0ms	(- (* b b) (* (* 4.0 a) c))
77.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify703.0ms

Counts

88 → 88

Iterations

Useful iterations: done (700.0ms)

Iter	Nodes	Cost
0	150	1693
1	364	1585
2	1241	1413
done	5000	1405

prune200.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 3.9b

regimes194.0ms

Accuracy

95.2% (1.2b remaining)

Error of 6.7b against oracle of 5.5b and baseline of 30.2b

bsearch147.0ms

Steps

Iters	Range		Point
10	9.447687191993962e+42	3.6320219268964787e+53	1.770319343989097e+52
3	-5.414215960318802e-301	-3.7291721340186856e-301	-5.09754230413862e-301
8	-6.10058349091927e+155	-9.408528429616011e+151	-7.93152454634662e+153

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	64
1	46	64
done	46	64

end0.0ms

sample1.1s

Algorithm

intervals

Results

230.0ms	1046×	body	2560	valid
224.0ms	5918×	body	80	valid
159.0ms	861×	body	1280	valid
113.0ms	2864×	body	80	nan
64.0ms	452×	body	640	valid
33.0ms	113×	body	5120	valid
24.0ms	230×	body	320	valid
7.0ms	100×	body	160	valid