Details

sample335.0ms

Algorithm

intervals

Results

6.0ms	186×	body	80	valid
6.0ms	30×	body	1280	valid
5.0ms	28×	body	2560	valid
3.0ms	16×	body	640	valid
3.0ms	85×	body	80	nan
1.0ms	3×	body	5120	valid
0.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify52.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite139.0ms

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:

74.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* b_2 b_2) (* a c))
35.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
36.0ms	(- (* b_2 b_2) (* a c))
74.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify952.0ms

Counts

183 → 183

Iterations

Useful iterations: done (945.0ms)

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

prune345.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
2.1b	(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
8.6b	(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
25.0b	(sqrt (fma b_2 b_2 (- (* c a))))

rewrite97.0ms

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:

11.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
45.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
30.0ms	(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
2.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

series525.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
165.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
199.0ms	(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
76.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

simplify1.5s

Counts

229 → 229

Iterations

Useful iterations: done (1.5s)

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

prune551.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
0.8b	(fma b_2 b_2 (- (* c a)))
1.2b	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
25.0b	(sqrt (fma b_2 b_2 (- (* c a))))

rewrite31.0ms

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:

15.0ms	(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
0.0ms	(fma b_2 b_2 (- (* c a)))
11.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
2.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

series390.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
41.0ms	(fma b_2 b_2 (- (* c a)))
83.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
73.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

simplify1.5s

Counts

121 → 121

Iterations

Useful iterations: done (1.5s)

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

prune272.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* c (/ 1 (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)))
0.8b	(fma b_2 b_2 (- (* c a)))
1.2b	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
25.0b	(sqrt (fma b_2 b_2 (- (* c a))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
30×	`add-cube-cbrt`
24×	`associate-r`
20×	`times-frac`
19×	`sqrt-prod`
18×	`prod-diff`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`difference-of-squares`
7×	`pow1`
6×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out--`
3×	`associate-l` `unswap-sqr`
2×	`flip3--` `div-exp` `associate-/r/` `flip--` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `fma-udef` `div-inv`

Counts

4 → 115

Calls

4 calls:

38.0ms	(* c (/ 1 (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)))
0.0ms	(fma b_2 b_2 (- (* c a)))
14.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
2.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

series404.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(* c (/ 1 (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)))
42.0ms	(fma b_2 b_2 (- (* c a)))
87.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
75.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

simplify1.6s

Counts

127 → 127

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	190	2204
1	421	1813
2	838	1550
3	2166	1472
done	5000	1417

prune267.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.9b

regimes168.0ms

Accuracy

95.5% (1.1b remaining)

Error of 7.1b against oracle of 6.0b and baseline of 29.9b

bsearch132.0ms

Steps

Iters	Range	Point
9	8.777746745010686e+110	1.2290467223415774e+117	1.1407450360752811e+117
9	-5.951265309377375e-290	-1.5896185090842948e-298	-1.6162133210491554e-298
7	-8.517839832020836e+86	-7.169178603400426e+84	-2.3026006569991443e+85

Iters

Range

Point

8.777746745010686e+110

1.2290467223415774e+117

1.1407450360752811e+117

-5.951265309377375e-290

-1.5896185090842948e-298

-1.6162133210491554e-298

-8.517839832020836e+86

-7.169178603400426e+84

-2.3026006569991443e+85

simplify7.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	38	59
1	50	51
2	52	51
done	52	51

end0.0ms

sample1.1s

Algorithm

intervals

Results

204.0ms	1108×	body	2560	valid
186.0ms	5896×	body	80	valid
130.0ms	886×	body	1280	valid
86.0ms	2950×	body	80	nan
53.0ms	446×	body	640	valid
31.0ms	110×	body	5120	valid
22.0ms	229×	body	320	valid
6.0ms	106×	body	160	valid