Details

sample180.0ms

Algorithm

intervals

Results

14.0ms	41×	body	2560	valid
10.0ms	186×	body	80	valid
7.0ms	28×	body	1280	valid
6.0ms	108×	body	80	nan
4.0ms	17×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify46.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	10	13
1	19	13
2	33	13
3	46	13
4	49	13
done	49	13

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize26.0ms

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))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite228.0ms

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-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
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 → 171

Calls

4 calls:

117.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
9.0ms	(- (* b_2 b_2) (* a c))
58.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
26.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
44.0ms	(- (* b_2 b_2) (* a c))
95.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
138.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts

183 → 183

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	242	5993
1	546	4313
2	1408	3549
done	5000	3001

prune469.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize23.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
5.1b	(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
10.3b	(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
24.0b	(sqrt (fma b_2 b_2 (- (* c a))))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

164×	`add-sqr-sqrt`
162×	`times-frac`
129×	`*-un-lft-identity`
95×	`add-cube-cbrt`
34×	`difference-of-squares`
32×	`sqrt-prod`
27×	`associate-/l*`
18×	`prod-diff`
17×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
6×	`flip3--` `fma-neg` `flip--` `div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`associate-/l/`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 217

Calls

4 calls:

26.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
65.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
49.0ms	(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
2.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

series705.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
258.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
247.0ms	(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
93.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

simplify2.6s

Counts

229 → 229

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	329	6395
1	757	5450
2	2207	5130
done	5002	5015

prune870.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
1.0b	(fma b_2 b_2 (- (* c a)))
1.4b	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
24.0b	(sqrt (fma b_2 b_2 (- (* c a))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
18×	`times-frac` `prod-diff`
10×	`difference-of-squares`
6×	`add-exp-log` `fma-neg` `associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/l*`
2×	`flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

4 → 109

Calls

4 calls:

31.0ms	(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
1.0ms	(fma b_2 b_2 (- (* c a)))
25.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
4.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

series576.0ms

Counts

4 → 12

Calls

4 calls:

290.0ms	(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
69.0ms	(fma b_2 b_2 (- (* c a)))
112.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
105.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

simplify2.3s

Counts

121 → 121

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	167	2224
1	334	1950
2	702	1731
3	1968	1653
done	5000	1598

prune412.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.1b

localize4.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune0.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 5.1b

regimes272.0ms

Accuracy

77.2% (5.5b remaining)

Error of 11.3b against oracle of 5.8b and baseline of 30.0b

bsearch124.0ms

Steps

Iters	Range		Point
6	1.6855676195581707e-170	7.565529323099765e-170	7.455592343308264e-170
5	-2.3823986784004295e+101	-6.644598008915225e+100	-1.8696623466311214e+101

simplify13.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	26	39
1	36	35
2	38	35
done	38	35

end0.0ms

sample2.8s

Algorithm

intervals

Results

700.0ms	2996×	body	80	nan
476.0ms	1051×	body	2560	valid
428.0ms	5894×	body	80	valid
320.0ms	835×	body	1280	valid
139.0ms	450×	body	640	valid
116.0ms	135×	body	5120	valid
60.0ms	119×	body	160	valid
41.0ms	226×	body	320	valid