Details

sample41.0ms

Algorithm

intervals

Results

9.0ms	36×	body	1280	valid
8.0ms	39×	body	2560	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

simplify46.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	12	17
1	22	17
2	42	16
3	82	16
4	100	16
5	108	16
done	108	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`prod-diff`
16×	`sqrt-prod`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 94

Calls

4 calls:

6.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
21.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
49.0ms	(- (* b b) (* (* 3.0 a) c))
81.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify591.0ms

Counts

106 → 106

Iterations

Useful iterations: 2 (157.0ms)

Iter	Nodes	Cost
0	161	1863
1	362	1562
2	1336	1315
done	5001	1315

prune253.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.4b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`prod-diff`
16×	`sqrt-prod`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative` `distribute-lft-out--`

Counts

4 → 94

Calls

4 calls:

6.0ms	(* 3.0 (* a c))
3.0ms	(- (* b b) (* 3.0 (* a c)))
21.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series216.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 3.0 (* a c))
42.0ms	(- (* b b) (* 3.0 (* a c)))
80.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
70.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify512.0ms

Counts

106 → 106

Iterations

Useful iterations: done (509.0ms)

Iter	Nodes	Cost
0	158	1860
1	356	1561
2	1188	1314
done	5000	1312

prune240.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.4b

localize16.0ms

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	(- (sqrt (- (* b b) (* (sqrt 3.0) (* (sqrt 3.0) (* a c))))) b)
22.6b	(sqrt (- (* b b) (* (sqrt 3.0) (* (sqrt 3.0) (* a c)))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff` `sqrt-prod`
14×	`pow1`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
6×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative` `distribute-lft-out--`

Counts

4 → 100

Calls

4 calls:

19.0ms	(* (sqrt 3.0) (* (sqrt 3.0) (* a c)))
3.0ms	(- (* b b) (* (sqrt 3.0) (* (sqrt 3.0) (* a c))))
21.0ms	(- (sqrt (- (* b b) (* (sqrt 3.0) (* (sqrt 3.0) (* a c))))) b)
4.0ms	(sqrt (- (* b b) (* (sqrt 3.0) (* (sqrt 3.0) (* a c)))))

series670.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (sqrt 3.0) (* (sqrt 3.0) (* a c)))
130.0ms	(- (* b b) (* (sqrt 3.0) (* (sqrt 3.0) (* a c))))
235.0ms	(- (sqrt (- (* b b) (* (sqrt 3.0) (* (sqrt 3.0) (* a c))))) b)
226.0ms	(sqrt (- (* b b) (* (sqrt 3.0) (* (sqrt 3.0) (* a c)))))

simplify578.0ms

Counts

112 → 112

Iterations

Useful iterations: done (575.0ms)

Iter	Nodes	Cost
0	173	2540
1	403	1646
2	1453	1379
done	5000	1377

prune456.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 14.3b

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
1.4b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
22.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))
22.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
32×	`sqrt-prod`
12×	`fma-neg`
8×	`add-log-exp`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 116

Calls

4 calls:

21.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
79.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
68.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
68.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify890.0ms

Counts

128 → 128

Iterations

Useful iterations: done (886.0ms)

Iter	Nodes	Cost
0	113	2856
1	262	2310
2	899	1912
done	5000	1702

prune313.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 14.3b

regimes258.0ms

Accuracy

84.9% (3.3b remaining)

Error of 15.5b against oracle of 12.2b and baseline of 33.8b

bsearch144.0ms

Steps

Iters	Range		Point
9	7.760624497279612e-54	8.046870571685393e-47	2.5407141653924318e-51
10	-2.699314103090194e+180	-2.227381996671495e+165	-2.272454186637281e+165

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	53
1	35	53
done	35	53

end0.0ms

sample1.1s

Algorithm

intervals

Results

230.0ms	5915×	body	80	valid
227.0ms	1025×	body	2560	valid
163.0ms	893×	body	1280	valid
107.0ms	2995×	body	80	nan
63.0ms	447×	body	640	valid
29.0ms	107×	body	5120	valid
22.0ms	210×	body	320	valid
7.0ms	103×	body	160	valid