Details

sample78.0ms

Algorithm

intervals

Results

15.0ms	36×	body	2560	valid
14.0ms	189×	body	80	valid
10.0ms	25×	body	1280	valid
7.0ms	104×	body	80	nan
5.0ms	16×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	3×	body	160	valid

simplify63.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	49
4	49
3	46
2	33
1	19
0	10

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
26.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `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 → 171

Calls

4 calls:

119.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
56.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(- (* b_2 b_2) (* a c))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series370.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
106.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
60.0ms	(- (* b_2 b_2) (* a c))
85.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

183 → 183

Iterations

Iter	Nodes
done	5000
2	2149
1	583
0	244

prune912.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.5b

localize43.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
2.8b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.9b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
26.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite210.0ms

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-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 194

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
123.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
64.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series653.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b_2 b_2) (* a c))
231.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
264.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
110.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.5s

Counts

206 → 206

Iterations

Iter	Nodes
done	5000
2	4614
1	804
0	315

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
26.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`associate-r` `add-exp-log`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `neg-mul-1` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `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 → 169

Calls

4 calls:

111.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
39.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series412.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
126.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms	(- (* b_2 b_2) (* a c))
103.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.4s

Counts

181 → 181

Iterations

Iter	Nodes
done	5001
2	3576
1	652
0	263

prune899.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
26.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `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 → 171

Calls

4 calls:

92.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
41.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
106.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
59.0ms	(- (* b_2 b_2) (* a c))
89.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts

183 → 183

Iterations

Iter	Nodes
done	5000
2	2149
1	583
0	244

prune770.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.4b

regimes613.0ms

Accuracy

86.1% (4.0b remaining)

Error of 9.6b against oracle of 5.6b and baseline of 34.4b

bsearch165.0ms

Steps

Iters	Range		Point
6	5.84949006905106e+100	6.027833473435204e+101	5.878879592304488e+101
6	-3.94223749317518e-93	-9.247487777844521e-94	-1.2208633566514056e-93
6	-3.687013704912239e+33	-6.257941608560553e+32	-2.7267558266977494e+33

simplify13.0ms

Iterations

Iter	Nodes
done	41
1	41
0	35

end0.0ms

sample2.3s

Algorithm

intervals

Results

510.0ms	1063×	body	2560	valid
470.0ms	2885×	body	80	nan
447.0ms	5821×	body	80	valid
273.0ms	950×	body	1280	valid
143.0ms	475×	body	640	valid
75.0ms	239×	body	320	valid
50.0ms	116×	body	5120	valid
11.0ms	105×	body	160	valid