Details

sample64.0ms

Algorithm

intervals

Results

12.0ms	6×	body	320	valid
12.0ms	38×	body	2560	valid
9.0ms	178×	body	80	valid
7.0ms	28×	body	1280	valid
4.0ms	79×	body	80	nan
2.0ms	11×	body	640	valid
1.0ms	3×	body	5120	valid
0.0ms	2×	body	160	valid

simplify112.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	91	16
5	99	16
done	99	16

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
0.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
0.6b	(- (* b b) (* 4.0 (* a c)))
20.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite239.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

132.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
68.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
19.0ms	(- (* b b) (* 4.0 (* a c)))
19.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series468.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
109.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
88.0ms	(- (* b b) (* 4.0 (* a c)))
89.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.1s

Counts

84 → 84

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	152	1592
1	385	1488
2	1206	1332
3	4422	1324
done	5000	1324

prune374.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ 1 (* 2.0 a)))
0.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
0.6b	(- (* b b) (* 4.0 (* a c)))
20.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite336.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

233.0ms	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ 1 (* 2.0 a)))
73.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
16.0ms	(- (* b b) (* 4.0 (* a c)))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series445.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ 1 (* 2.0 a)))
134.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
79.0ms	(- (* b b) (* 4.0 (* a c)))
103.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.9s

Counts

93 → 93

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	178	1851
1	441	1643
2	1459	1437
done	5000	1431

prune380.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
0.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
0.6b	(- (* b b) (* 4.0 (* a c)))
20.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

69.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
64.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
9.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series492.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
128.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
60.0ms	(- (* b b) (* 4.0 (* a c)))
107.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.3s

Counts

130 → 130

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	218	3137
1	494	2801
2	1433	2561
done	5001	2481

prune314.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (/ 1 2.0) a) (/ 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
0.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
0.6b	(- (* b b) (* 4.0 (* a c)))
20.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite384.0ms

Algorithm

rewrite-expression-head

Rules

3474×	`times-frac`
1853×	`add-sqr-sqrt`
1586×	`*-un-lft-identity`
1320×	`add-cube-cbrt`
266×	`difference-of-squares`
145×	`div-inv`
136×	`sqrt-prod`
133×	`distribute-lft-out--`
89×	`associate-/r/`
69×	`add-exp-log`
54×	`div-exp`
47×	`flip3--` `flip--`
43×	`associate-/l*`
25×	`add-cbrt-cube`
24×	`associate-/r*`
15×	`cbrt-undiv`
9×	`rec-exp` `1-exp`
8×	`add-log-exp`
5×	`pow1`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 1179

Calls

4 calls:

135.0ms	(/ (/ (/ 1 2.0) a) (/ 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
53.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
9.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series414.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(/ (/ (/ 1 2.0) a) (/ 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
92.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
57.0ms	(- (* b b) (* 4.0 (* a c)))
108.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.5s

Counts

1191 → 1191

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	1578	54089
1	4342	45253
done	5002	43676

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.1b

regimes283.0ms

Accuracy

83.9% (4.6b remaining)

Error of 10.2b against oracle of 5.5b and baseline of 34.3b

bsearch189.0ms

Steps

Iters	Range		Point
8	4.924640387312937e-45	5.473977791176249e-42	5.2024432226242543e-45
8	-6.990724105819741e+111	-2.6156774686163576e+108	-1.569310777886352e+111

simplify31.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	40
1	35	40
done	35	40

end0.0ms

sample3.2s

Algorithm

intervals

Results

881.0ms	930×	body	1280	valid
621.0ms	1087×	body	2560	valid
549.0ms	5806×	body	80	valid
232.0ms	2994×	body	80	nan
133.0ms	117×	body	5120	valid
119.0ms	446×	body	640	valid
85.0ms	210×	body	320	valid
16.0ms	116×	body	160	valid