Details

sample311.0ms

Algorithm

intervals

Results

50.0ms	31×	body	2560	valid
37.0ms	12×	body	640	valid
24.0ms	205×	body	80	valid
15.0ms	31×	body	1280	valid
8.0ms	89×	body	80	nan
4.0ms	4×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify59.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	10	283
1	18	283
2	32	283
3	41	283
4	44	283
done	44	283

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize79.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite669.0ms

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-cbrt-cube` `add-exp-log`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 91

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
89.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
546.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series414.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b_2 b_2) (* a c))
127.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
134.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
109.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

103 → 103

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	158	39129
1	393	35913
2	1530	35553
done	5000	35393

prune496.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

6.0ms	(- (* b_2 b_2) (* a c))
96.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
18.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (* b_2 b_2) (* a c))
115.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
104.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
85.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.5s

Counts

101 → 101

Iterations

Useful iterations: done (4.5s)

Iter	Nodes	Cost
0	177	36970
1	462	31750
2	2879	30158
done	5000	29717

prune485.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
0.1b	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
0.5b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
19.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
84.0ms	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (* b_2 b_2) (* a c))
126.0ms	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
102.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts

118 → 118

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	186	45260
1	447	41631
2	1836	41391
done	5001	41311

prune602.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (exp (log (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))) a)
0.5b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
3.4b	(exp (log (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
19.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
54×	`times-frac`
47×	`add-sqr-sqrt`
46×	`add-cube-cbrt`
36×	`log-prod` `exp-sum`
28×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
18×	`associate-/l*`
10×	`distribute-lft-out`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`log-div` `exp-prod` `neg-mul-1` `exp-diff`
3×	`associate-/r*` `flip3-+` `sqrt-prod` `flip-+`
2×	`sqrt-div` `distribute-neg-frac` `associate-/l/`
1×	`neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `div-sub` `div-exp` `distribute-frac-neg` `log-pow` `div-inv` `flip--` `rem-exp-log`

Counts

4 → 136

Calls

4 calls:

79.0ms	(/ (- (exp (log (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))) a)
19.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
14.0ms	(exp (log (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (- (exp (log (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))) a)
103.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
104.0ms	(exp (log (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
103.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts

148 → 148

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	243	82605
1	530	57504
2	1928	57184
done	5001	57024

prune714.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.5b

regimes396.0ms

Accuracy

87.2% (3.7b remaining)

Error of 8.9b against oracle of 5.2b and baseline of 34.1b

bsearch327.0ms

Steps

Iters	Range		Point
8	2.072994944964499e+129	8.571507078369983e+131	2.8233354537966034e+131
8	-8.904680992578465e-52	-2.849527055171251e-56	-5.546621280225112e-56
5	-1.0933554809811831e-44	-3.3311956001427126e-45	-3.4083546428522886e-45
7	-5.856362438573669e+138	-1.280729871585891e+137	-2.1229423973235387e+137

simplify29.0ms

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	37	1251
1	48	1210
2	50	1210
done	50	1210

end0.0ms

sample2.8s

Algorithm

intervals

Results

875.0ms	1029×	body	2560	valid
488.0ms	5835×	body	80	valid
486.0ms	922×	body	1280	valid
203.0ms	2877×	body	80	nan
184.0ms	455×	body	640	valid
66.0ms	122×	body	5120	valid
44.0ms	242×	body	320	valid
19.0ms	123×	body	160	valid