Details

sample73.0ms

Algorithm

intervals

Results

14.0ms	40×	body	2560	valid
11.0ms	181×	body	80	valid
8.0ms	7×	body	5120	valid
7.0ms	27×	body	1280	valid
5.0ms	92×	body	80	nan
3.0ms	13×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	3×	body	160	valid

simplify37.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite594.0ms

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:

447.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
18.0ms	(- (* b_2 b_2) (* a c))
65.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
50.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
41.0ms	(- (* b_2 b_2) (* a c))
85.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
93.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts

183 → 183

Iterations

Useful iterations: done (1.7s)

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

prune524.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize30.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
2.9b	(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
8.4b	(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
23.4b	(sqrt (fma b_2 b_2 (- (* c a))))

rewrite178.0ms

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:

24.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
71.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
55.0ms	(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
4.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

series745.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
225.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
290.0ms	(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
94.0ms	(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

prune917.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
0.3b	(fma b_2 b_2 (- (* c a)))
1.1b	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
23.4b	(sqrt (fma b_2 b_2 (- (* c a))))

rewrite57.0ms

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:

26.0ms	(/ 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)
2.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

series537.0ms

Counts

4 → 12

Calls

4 calls:

258.0ms	(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
63.0ms	(fma b_2 b_2 (- (* c a)))
114.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
102.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

simplify2.5s

Counts

121 → 121

Iterations

Useful iterations: done (2.5s)

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

prune471.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma b_2 b_2 (- (* c a)))
0.7b	(/ (/ 1 1) (* (/ (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2) c) 1))
1.1b	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
23.4b	(sqrt (fma b_2 b_2 (- (* c a))))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

97×	`add-exp-log`
69×	`div-exp`
39×	`1-exp`
38×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
33×	`add-cube-cbrt`
31×	`times-frac`
28×	`prod-exp`
25×	`add-cbrt-cube`
18×	`prod-diff`
16×	`sqrt-prod`
13×	`associate-/l*`
11×	`cbrt-undiv`
10×	`rec-exp`
6×	`fma-neg` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u`
3×	`div-inv`
2×	`difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `flip--` `fma-udef` `associate-/l/` `distribute-lft-out--`

Counts

4 → 148

Calls

4 calls:

1.0ms	(fma b_2 b_2 (- (* c a)))
59.0ms	(/ (/ 1 1) (* (/ (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2) c) 1))
24.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
4.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

series473.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(fma b_2 b_2 (- (* c a)))
190.0ms	(/ (/ 1 1) (* (/ (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2) c) 1))
117.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
109.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

simplify2.8s

Counts

160 → 160

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	264	3300
1	520	2513
2	1016	2099
3	3030	1924
done	5000	1914

prune373.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.3b

regimes253.0ms

Accuracy

95.8% (1.0b remaining)

Error of 6.3b against oracle of 5.3b and baseline of 29.5b

bsearch240.0ms

Steps

Iters	Range	Point
10	4.61796087672408e+142	1.3206820209921783e+153	1.1043857160155008e+144
4	1.096458200021764e-161	2.1348066422084948e-161	1.123334719424155e-161
9	-6.354265220965125e+156	-1.769171722317776e+149	-2.4466612317601678e+151

Iters

Range

Point

4.61796087672408e+142

1.3206820209921783e+153

1.1043857160155008e+144

1.096458200021764e-161

2.1348066422084948e-161

1.123334719424155e-161

-6.354265220965125e+156

-1.769171722317776e+149

-2.4466612317601678e+151

simplify8.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	37	58
1	46	54
2	48	54
done	48	54

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.1s	1098×	body	2560	valid
585.0ms	5724×	body	80	valid
406.0ms	959×	body	1280	valid
250.0ms	2913×	body	80	nan
172.0ms	456×	body	640	valid
64.0ms	119×	body	5120	valid
49.0ms	242×	body	320	valid
16.0ms	116×	body	160	valid