Details

sample39.0ms

Algorithm

intervals

Results

8.0ms	39×	body	2560	valid
6.0ms	36×	body	1280	valid
6.0ms	165×	body	80	valid
3.0ms	86×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	4×	body	160	valid

simplify53.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	12	17
1	21	17
2	41	16
3	75	16
4	87	16
5	95	16
done	95	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
1.0b	(- (* b b) (* (* 3.0 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
3×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-l` `neg-log` `*-commutative` `flip-+`

Counts

4 → 60

Calls

4 calls:

7.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series228.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* 3.0 a) c)
51.0ms	(- (* b b) (* (* 3.0 a) c))
87.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.9s

Counts

72 → 72

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	122	1001
1	307	907
2	1084	805
3	4598	795
done	5000	795

prune202.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 3.0 (* a c))
1.0b	(- (* b b) (* 3.0 (* a c)))
1.4b	(+ (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
22.6b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
3×	`associate-l` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r` `neg-log` `*-commutative` `flip-+`

Counts

4 → 60

Calls

4 calls:

6.0ms	(* 3.0 (* a c))
3.0ms	(- (* b b) (* 3.0 (* a c)))
14.0ms	(+ (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series221.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* 3.0 (* a c))
49.0ms	(- (* b b) (* 3.0 (* a c)))
82.0ms	(+ (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
70.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify1.9s

Counts

72 → 72

Iterations

Useful iterations: 3 (794.0ms)

Iter	Nodes	Cost
0	119	998
1	297	906
2	929	804
3	3554	794
done	5000	794

prune187.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt 3.0) (* (sqrt 3.0) (* a c)))
1.0b	(- (* b b) (* (sqrt 3.0) (* (sqrt 3.0) (* a c))))
1.4b	(+ (- b) (sqrt (- (* b b) (* (sqrt 3.0) (* (sqrt 3.0) (* a c))))))
22.6b	(sqrt (- (* b b) (* (sqrt 3.0) (* (sqrt 3.0) (* a c)))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1`
13×	`add-exp-log` `add-cbrt-cube`
11×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`associate-l` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r` `neg-log` `*-commutative` `flip-+`

Counts

4 → 66

Calls

4 calls:

20.0ms	(* (sqrt 3.0) (* (sqrt 3.0) (* a c)))
3.0ms	(- (* b b) (* (sqrt 3.0) (* (sqrt 3.0) (* a c))))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (sqrt 3.0) (* (sqrt 3.0) (* a c))))))
4.0ms	(sqrt (- (* b b) (* (sqrt 3.0) (* (sqrt 3.0) (* a c)))))

series669.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (sqrt 3.0) (* (sqrt 3.0) (* a c)))
122.0ms	(- (* b b) (* (sqrt 3.0) (* (sqrt 3.0) (* a c))))
234.0ms	(+ (- b) (sqrt (- (* b b) (* (sqrt 3.0) (* (sqrt 3.0) (* a c))))))
235.0ms	(sqrt (- (* b b) (* (sqrt 3.0) (* (sqrt 3.0) (* a c)))))

simplify865.0ms

Counts

78 → 78

Iterations

Useful iterations: done (862.0ms)

Iter	Nodes	Cost
0	134	1482
1	348	989
2	1171	865
done	5000	860

prune216.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 14.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt c)
1.0b	(- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))))
22.6b	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity` `add-log-exp`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube`
3×	`cbrt-prod` `sqrt-prod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `diff-log` `neg-log` `flip-+`

Counts

4 → 53

Calls

4 calls:

0.0ms	(cbrt c)
3.0ms	(- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))))
4.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

series430.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt c)
63.0ms	(- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))
98.0ms	(+ (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))))
91.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

simplify2.6s

Counts

65 → 65

Iterations

Useful iterations: 3 (917.0ms)

Iter	Nodes	Cost
0	116	1364
1	281	1232
2	934	735
3	4848	725
done	5000	725

prune191.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 14.3b

regimes313.0ms

Accuracy

95.8% (0.9b remaining)

Error of 13.0b against oracle of 12.1b and baseline of 33.7b

bsearch155.0ms

Steps

Iters	Range	Point
4	1.2086931281044804e+136	2.364246562673592e+136	2.0964838406867355e+136
9	2.365685850767504e-168	1.2053288471691685e-161	1.7270734494037783e-162
10	-2.699314103090194e+180	-2.227381996671495e+165	-2.272454186637281e+165

Iters

Range

Point

1.2086931281044804e+136

2.364246562673592e+136

2.0964838406867355e+136

2.365685850767504e-168

1.2053288471691685e-161

1.7270734494037783e-162

-2.699314103090194e+180

-2.227381996671495e+165

-2.272454186637281e+165

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	87
1	60	87
2	63	87
3	70	87
done	70	87

end0.0ms

sample1.1s

Algorithm

intervals

Results

219.0ms	5915×	body	80	valid
214.0ms	1025×	body	2560	valid
158.0ms	893×	body	1280	valid
104.0ms	2995×	body	80	nan
64.0ms	447×	body	640	valid
28.0ms	107×	body	5120	valid
21.0ms	210×	body	320	valid
7.0ms	103×	body	160	valid