Details

sample36.0ms

Algorithm

intervals

Results

7.0ms	34×	body	2560	valid
6.0ms	41×	body	1280	valid
5.0ms	173×	body	80	valid
3.0ms	94×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	7×	body	160	valid

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	13
1	18	13
2	32	13
3	40	13
4	42	13
done	42	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
2.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
26.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite59.0ms

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:

34.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms	(- (* b_2 b_2) (* a c))
69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts

103 → 103

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	156	1821
1	368	1727
2	997	1611
3	3176	1595
done	5000	1594

prune252.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
2.5b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.3b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
26.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite85.0ms

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:

3.0ms	(- (* b_2 b_2) (* a c))
45.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
25.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* b_2 b_2) (* a c))
154.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
191.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

196 → 196

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	302	5540
1	722	4791
2	2531	4615
done	5001	4613

prune502.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
2.6b	(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
9.3b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
26.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
52×	`times-frac`
49×	`*-un-lft-identity`
33×	`add-cube-cbrt`
28×	`add-exp-log`
24×	`associate-l`
18×	`add-cbrt-cube`
14×	`difference-of-squares`
13×	`associate-r`
10×	`sqrt-prod`
9×	`div-exp`
8×	`prod-exp`
7×	`pow1` `distribute-lft-out--`
6×	`associate-/r*` `add-log-exp` `unswap-sqr`
5×	`cbrt-undiv`
4×	`flip3--` `associate-/r/` `flip--` `cbrt-unprod`
3×	`div-inv` `associate-/l*`
2×	`rec-exp` `sqrt-div` `1-exp` `associate-/l/`
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 → 138

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
64.0ms	(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
25.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* b_2 b_2) (* a c))
152.0ms	(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
187.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify972.0ms

Counts

150 → 150

Iterations

Useful iterations: done (968.0ms)

Iter	Nodes	Cost
0	248	3414
1	693	2905
2	2273	2589
done	5000	2587

prune377.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
12.9b	(/ (* a c) a)
26.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

19.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms	(- (* b_2 b_2) (* a c))
3.0ms	(/ (* a c) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series174.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
39.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(/ (* a c) a)
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts

75 → 75

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	125	880
1	282	798
2	927	698
3	3420	694
done	5001	694

prune191.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.0b

regimes210.0ms

Accuracy

94.5% (1.3b remaining)

Error of 6.8b against oracle of 5.5b and baseline of 28.8b

bsearch135.0ms

Steps

Iters	Range	Point
9	2.944023772201993e+37	9.447687191993962e+42	9.347996314154137e+42
8	-5.096416236867507e-226	-1.8943734949279783e-228	-1.9151734797750612e-228
8	-6.10058349091927e+155	-9.408528429616011e+151	-1.0245899460467552e+154

Iters

Range

Point

2.944023772201993e+37

9.447687191993962e+42

9.347996314154137e+42

-5.096416236867507e-226

-1.8943734949279783e-228

-1.9151734797750612e-228

-6.10058349091927e+155

-9.408528429616011e+151

-1.0245899460467552e+154

simplify3.0ms

Iterations

Useful iterations: done (3.0ms)

Iter	Nodes	Cost
0	34	51
1	40	49
done	40	47

end0.0ms

sample991.0ms

Algorithm

intervals

Results

206.0ms	1077×	body	2560	valid
191.0ms	5775×	body	80	valid
148.0ms	972×	body	1280	valid
86.0ms	2867×	body	80	nan
54.0ms	456×	body	640	valid
25.0ms	109×	body	5120	valid
23.0ms	234×	body	320	valid
7.0ms	111×	body	160	valid