Details

sample525.0ms

Algorithm

intervals

Results

91.0ms	39×	body	2560	valid
78.0ms	166×	body	80	valid
17.0ms	36×	body	1280	valid
9.0ms	89×	body	80	nan
7.0ms	18×	body	640	valid
3.0ms	10×	body	320	valid
3.0ms	4×	body	5120	valid
0.0ms	2×	body	160	valid

simplify115.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	10	13
1	18	13
2	32	13
3	41	13
4	44	13
done	44	13

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite254.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

129.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
72.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0ms	(- (* b_2 b_2) (* a c))
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
97.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
55.0ms	(- (* b_2 b_2) (* a c))
138.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify831.0ms

Counts

103 → 103

Iterations

Useful iterations: done (818.0ms)

Iter	Nodes	Cost
0	156	1821
1	388	1727
2	1501	1611
done	5000	1603

prune432.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.4b

localize18.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
4.4b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.8b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 184

Calls

4 calls:

9.0ms	(- (* b_2 b_2) (* a c))
105.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
94.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series651.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* b_2 b_2) (* a c))
237.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
258.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
105.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts

196 → 196

Iterations

Useful iterations: 2 (801.0ms)

Iter	Nodes	Cost
0	302	5540
1	770	4801
2	4236	4619
done	5001	4619

prune739.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.4b

localize18.0ms

Local error

Found 4 expressions with local error:

6.6b	(/ (/ (* a c) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
7.3b	(/ (* a c) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite262.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 145

Calls

4 calls:

147.0ms	(/ (/ (* a c) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
83.0ms	(/ (* a c) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series1.7s

Counts

4 → 12

Calls

4 calls:

734.0ms	(/ (/ (* a c) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
735.0ms	(/ (* a c) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
98.0ms	(sqrt (- (* b_2 b_2) (* a c)))
109.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

157 → 157

Iterations

Useful iterations: 2 (696.0ms)

Iter	Nodes	Cost
0	260	3735
1	670	3366
2	3331	3180
done	5002	3180

prune665.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.4b

localize41.0ms

Local error

Found 4 expressions with local error:

6.6b	(/ (* (/ a (sqrt (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))) (/ c (sqrt (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))) a)
22.6b	(sqrt (- (* b_2 b_2) (* a c)))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
9×	`cbrt-undiv` `add-cube-cbrt` `*-un-lft-identity` `div-exp` `sqrt-prod`
7×	`pow1`
6×	`sqrt-div`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `times-frac` `pow1/2` `associate-/r*` `flip--` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 75

Calls

4 calls:

149.0ms	(/ (* (/ a (sqrt (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))) (/ c (sqrt (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))) a)
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series801.0ms

Counts

4 → 12

Calls

4 calls:

544.0ms	(/ (* (/ a (sqrt (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))) (/ c (sqrt (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))) a)
84.0ms	(sqrt (- (* b_2 b_2) (* a c)))
92.0ms	(sqrt (- (* b_2 b_2) (* a c)))
80.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts

87 → 87

Iterations

Useful iterations: 2 (416.0ms)

Iter	Nodes	Cost
0	154	2093
1	458	1919
2	2626	1543
done	5001	1543

prune497.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.4b

regimes380.0ms

Accuracy

86.1% (3.7b remaining)

Error of 9.5b against oracle of 5.7b and baseline of 32.4b

bsearch251.0ms

Steps

Iters	Range		Point
11	8.182113676652236e-12	2116652649.122401	2098867031.9345784
11	9.132164512921457e-291	8.018752023592085e-262	9.282718576312558e-291
8	-5.545092253462458e+82	-2.14594256023029e+80	-1.113821654949689e+81

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	86
1	46	86
done	46	86

end0.0ms

sample2.9s

Algorithm

intervals

Results

933.0ms	1015×	body	2560	valid
451.0ms	912×	body	1280	valid
440.0ms	5936×	body	80	valid
255.0ms	2930×	body	80	nan
152.0ms	438×	body	640	valid
47.0ms	100×	body	5120	valid
42.0ms	232×	body	320	valid
18.0ms	123×	body	160	valid