Details

sample41.0ms

Algorithm

intervals

Results

7.0ms	179×	body	80	valid
7.0ms	38×	body	1280	valid
5.0ms	24×	body	2560	valid
2.0ms	73×	body	80	nan
2.0ms	15×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	7×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	9
done	148	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.1b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite103.0ms

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:

62.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms	(- (* b b) (* 4.0 (* a c)))
22.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series294.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
45.0ms	(- (* b b) (* 4.0 (* a c)))
79.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Counts

89 → 89

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	404	890
1	1481	801
2	5001	796
done	5001	796

prune235.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.1b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite144.0ms

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:

101.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
10.0ms	(- (* b b) (* 4.0 (* a c)))
22.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series299.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
46.0ms	(- (* b b) (* 4.0 (* a c)))
80.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify59.0ms

Counts

97 → 97

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	469	991
1	2048	866
2	5002	857
done	5002	857

prune230.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* 4.0 (* a c)))
3.0b	(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
8.2b	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
22.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
61×	`*-un-lft-identity`
52×	`times-frac`
51×	`add-exp-log`
30×	`add-cube-cbrt` `associate-l`
27×	`add-cbrt-cube`
20×	`prod-exp`
18×	`difference-of-squares`
16×	`div-exp`
13×	`distribute-lft-out`
12×	`sqrt-prod`
9×	`distribute-lft-out--`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`pow1` `associate-r`
6×	`associate-/r*` `add-log-exp`
4×	`rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--` `associate-/l*`
3×	`div-inv`
2×	`sqrt-div` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 149

Calls

4 calls:

9.0ms	(- (* b b) (* 4.0 (* a c)))
132.0ms	(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
65.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series507.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* 4.0 (* a c)))
173.0ms	(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
210.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
76.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify115.0ms

Counts

161 → 161

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	760	2359
1	3742	2008
2	5001	1985
done	5001	1985

prune379.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
0.8b	(- (* b b) (* 4.0 (* a c)))
11.2b	(/ (* 4.0 (* a c)) (* 2.0 a))
22.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

40.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
8.0ms	(- (* b b) (* 4.0 (* a c)))
22.0ms	(/ (* 4.0 (* a c)) (* 2.0 a))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series211.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
46.0ms	(- (* b b) (* 4.0 (* a c)))
11.0ms	(/ (* 4.0 (* a c)) (* 2.0 a))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify55.0ms

Counts

79 → 79

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	403	577
1	2221	498
2	5001	498
done	5001	498

prune163.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.7b

regimes211.0ms

Accuracy

96.1% (0.9b remaining)

Error of 6.5b against oracle of 5.6b and baseline of 29.8b

bsearch188.0ms

Steps

Iters	Range	Point
9	1.4800420954007604e+99	2.6367850541344314e+108	3.631578693473388e+102
10	1.0693689171863556e-172	3.0813629188746354e-157	1.0856062432929024e-172
10	-6.90058054258779e+154	-1.4735496756669211e+144	-1.4267509350112253e+149

Iters

Range

Point

1.4800420954007604e+99

2.6367850541344314e+108

3.631578693473388e+102

1.0693689171863556e-172

3.0813629188746354e-157

1.0856062432929024e-172

-6.90058054258779e+154

-1.4735496756669211e+144

-1.4267509350112253e+149

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	31
1	41	31
done	41	31

end0.0ms

sample1.2s

Algorithm

intervals

Results

235.0ms	1023×	body	2560	valid
220.0ms	5918×	body	80	valid
164.0ms	896×	body	1280	valid
102.0ms	2904×	body	80	nan
67.0ms	451×	body	640	valid
33.0ms	117×	body	5120	valid
25.0ms	234×	body	320	valid
9.0ms	129×	body	160	valid