Details

sample64.0ms

Algorithm

intervals

Results

12.0ms	205×	body	80	valid
11.0ms	4×	body	5120	valid
10.0ms	31×	body	2560	valid
8.0ms	31×	body	1280	valid
4.0ms	89×	body	80	nan
2.0ms	12×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify145.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	365
1	28	365
2	64	365
3	115	365
4	142	365
5	152	365
6	156	365
done	156	365

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* a c))
0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

12.0ms	(* 4.0 (* a c))
59.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
29.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series385.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* 4.0 (* a c))
144.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
119.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
98.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts

95 → 95

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	172	32928
1	452	30651
2	1734	29931
done	5000	29771

prune597.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b	(* (* 4.0 a) c)
0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

87.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
16.0ms	(* (* 4.0 a) c)
36.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
25.0ms	(* (* 4.0 a) c)
119.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
113.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts

95 → 95

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	175	32968
1	468	30650
2	2291	29930
done	5000	29770

prune550.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* a c))
0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.7b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

21.0ms	(* 4.0 (* a c))
138.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
29.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
7.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series372.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* 4.0 (* a c))
127.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
116.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
101.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.5s

Counts

103 → 103

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	198	38566
1	524	34134
2	2481	32344
done	5000	32104

prune607.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.5b

localize50.0ms

Local error

Found 4 expressions with local error:

12.2b	(cbrt (* (* 4.0 a) c))
12.2b	(cbrt (* (* 4.0 a) c))
12.2b	(cbrt (* (* 4.0 a) c))
19.5b	(sqrt (- (* b b) (* (* (cbrt (* (* 4.0 a) c)) (cbrt (* (* 4.0 a) c))) (cbrt (* (* 4.0 a) c)))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 42

Calls

4 calls:

19.0ms	(cbrt (* (* 4.0 a) c))
18.0ms	(cbrt (* (* 4.0 a) c))
14.0ms	(cbrt (* (* 4.0 a) c))
16.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 4.0 a) c)) (cbrt (* (* 4.0 a) c))) (cbrt (* (* 4.0 a) c)))))

series687.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(cbrt (* (* 4.0 a) c))
168.0ms	(cbrt (* (* 4.0 a) c))
167.0ms	(cbrt (* (* 4.0 a) c))
216.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 4.0 a) c)) (cbrt (* (* 4.0 a) c))) (cbrt (* (* 4.0 a) c)))))

simplify2.2s

Counts

54 → 54

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	88	17875
1	213	17199
2	628	14039
3	3204	13919
done	5002	12773

prune331.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.5b

regimes370.0ms

Accuracy

85.6% (4.2b remaining)

Error of 9.5b against oracle of 5.3b and baseline of 34.2b

bsearch207.0ms

Steps

Iters	Range		Point
8	2.072994944964499e+129	8.571507078369983e+131	3.087668654677018e+130
8	-8.904680992578465e-52	-2.849527055171251e-56	-4.356959927988237e-56

simplify11.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	29	870
1	37	870
done	37	870

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.1s	5841×	body	80	valid
805.0ms	921×	body	1280	valid
539.0ms	1025×	body	2560	valid
241.0ms	2877×	body	80	nan
126.0ms	457×	body	640	valid
125.0ms	245×	body	320	valid
74.0ms	122×	body	5120	valid
17.0ms	116×	body	160	valid