Details

sample42.0ms

Algorithm

intervals

Results

9.0ms	37×	body	2560	valid
7.0ms	177×	body	80	valid
6.0ms	31×	body	1280	valid
3.0ms	92×	body	80	nan
2.0ms	16×	body	640	valid
1.0ms	5×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify56.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	45	16
3	87	16
4	105	16
5	113	16
done	113	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
0.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
0.8b	(- (* b b) (* 4.0 (* a c)))
27.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
135×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
82×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
22×	`associate-/l*`
19×	`prod-diff`
13×	`distribute-lft-out--`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `div-sub`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 183

Calls

4 calls:

37.0ms	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
22.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.0ms	(- (* b b) (* 4.0 (* a c)))
7.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series306.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
80.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
48.0ms	(- (* b b) (* 4.0 (* a c)))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.0s

Counts

195 → 195

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	319	4967
1	759	4592
2	2168	4283
done	5000	4264

prune537.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 1) (/ a (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0)))
0.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
0.8b	(- (* b b) (* 4.0 (* a c)))
27.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

3251×	`times-frac`
1774×	`add-sqr-sqrt`
1519×	`*-un-lft-identity`
1265×	`add-cube-cbrt`
254×	`difference-of-squares`
142×	`sqrt-prod`
129×	`div-inv`
127×	`distribute-lft-out--`
71×	`associate-/r*`
64×	`add-exp-log`
54×	`div-exp`
25×	`add-cbrt-cube`
19×	`prod-diff`
15×	`cbrt-undiv` `1-exp` `associate-/r/`
13×	`associate-/l*`
8×	`add-log-exp`
7×	`fma-neg`
6×	`rec-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 1122

Calls

4 calls:

57.0ms	(/ (/ 1 1) (/ a (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0)))
22.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series346.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (/ 1 1) (/ a (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0)))
76.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
47.0ms	(- (* b b) (* 4.0 (* a c)))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify4.4s

Counts

1134 → 1134

Iterations

Useful iterations: done (4.4s)

Iter	Nodes	Cost
0	1522	48578
1	4522	40803
done	5000	38979

prune777.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ a (/ 1 2.0)))
0.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
0.8b	(- (* b b) (* 4.0 (* a c)))
27.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

726×	`times-frac`
494×	`add-sqr-sqrt`
401×	`*-un-lft-identity`
309×	`add-cube-cbrt`
92×	`difference-of-squares`
61×	`sqrt-prod`
46×	`distribute-lft-out--`
44×	`associate-/r*`
29×	`div-inv`
19×	`add-exp-log` `prod-diff`
13×	`add-cbrt-cube`
11×	`div-exp`
8×	`associate-/r/` `add-log-exp`
7×	`fma-neg`
6×	`cbrt-undiv` `associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`rem-sqrt-square` `rec-exp` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `div-sub` `clear-num`

Counts

4 → 412

Calls

4 calls:

58.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ a (/ 1 2.0)))
23.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series314.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ a (/ 1 2.0)))
83.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
49.0ms	(- (* b b) (* 4.0 (* a c)))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.0s

Counts

424 → 424

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	641	14498
1	1805	13016
done	5000	12417

prune691.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* 4.0 (* a c)))
0.8b	(- (* b b) (* 4.0 (* a c)))
27.3b	(sqrt (- (* b b) (* 4.0 (* a c))))
27.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 66

Calls

4 calls:

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

series234.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* 4.0 (* a c)))
49.0ms	(- (* b b) (* 4.0 (* a c)))
68.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts

78 → 78

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	69	1146
1	168	1050
2	577	952
3	2445	952
done	5000	948

prune297.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.9b

regimes263.0ms

Accuracy

85.2% (4.2b remaining)

Error of 9.8b against oracle of 5.6b and baseline of 33.8b

bsearch129.0ms

Steps

Iters	Range		Point
11	4.489865195692553e-133	5.932607888300091e-106	2.0569776426586135e-106
8	-6.10058349091927e+155	-9.408528429616011e+151	-7.93152454634662e+153

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	40
1	34	40
done	34	40

end0.0ms

sample1.1s

Algorithm

intervals

Results

256.0ms	1046×	body	2560	valid
233.0ms	5918×	body	80	valid
161.0ms	861×	body	1280	valid
103.0ms	2864×	body	80	nan
65.0ms	452×	body	640	valid
34.0ms	113×	body	5120	valid
25.0ms	230×	body	320	valid
7.0ms	100×	body	160	valid