Details

sample75.0ms

Algorithm

intervals

Results

21.0ms	24×	body	1280	valid
11.0ms	31×	body	2560	valid
10.0ms	203×	body	80	valid
4.0ms	78×	body	80	nan
4.0ms	18×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	1×	body	160	valid

simplify24.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	13
1	18	13
2	32	13
3	40	13
4	42	13
done	42	13

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 32.5b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
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 → 91

Calls

4 calls:

16.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
9.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
15.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(- (* b_2 b_2) (* a c))
24.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts

103 → 103

Iterations

Useful iterations: 3 (946.0ms)

Iter	Nodes	Cost
0	153	1823
1	360	1730
2	981	1618
3	3283	1602
done	5000	1602

prune159.0ms

Filtered

72 candidates to 103 candidates (-43.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	93	10	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	10	104

Merged error: 6.2b

Counts

104 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.6b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac`
130×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
77×	`add-cube-cbrt`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `inv-pow`

Counts

4 → 177

Calls

4 calls:

15.0ms	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
9.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
18.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts

189 → 189

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	265	4484
1	589	3937
2	1418	3622
3	4437	3510
done	5001	3510

prune138.0ms

Filtered

85 candidates to 189 candidates (-122.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	186	3	189
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	190	9	199

Merged error: 6.1b

Counts

199 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
1.5b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0b	(/ (+ (* a c) 0) a)
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`associate-/r` `sqrt-prod` `associate-/l`
2×	`flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 71

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(/ (+ (* a c) 0) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.0ms	(/ (+ (* a c) 0) a)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts

83 → 83

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	143	1085
1	336	916
2	1069	828
3	4261	788
done	5000	788

prune127.0ms

Filtered

67 candidates to 83 candidates (-23.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	83	9	92

Merged error: 6.1b

Counts

92 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
1.0b	(- (* b_2 b_2) (* a c))
1.5b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/r*`
3×	`sqrt-prod` `associate-/l*`
2×	`flip3--` `flip3-+` `sqrt-div` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 79

Calls

4 calls:

10.0ms	(/ c (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series89.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ c (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
8.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

91 → 91

Iterations

Useful iterations: 3 (475.0ms)

Iter	Nodes	Cost
0	142	1488
1	323	1386
2	870	1219
3	2528	1201
done	5000	1201

prune87.0ms

Filtered

67 candidates to 91 candidates (-35.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	91	9	100

Merged error: 6.1b

Counts

100 → 9

regimes311.0ms

Accuracy

95.5% (1.1b remaining)

Error of 6.8b against oracle of 5.8b and baseline of 29.8b

bsearch115.0ms

Steps

Iters	Range	Point
10	1.1487243557305423e+102	3.920821933018458e+112	9.421054264015979e+109
9	4.8461344139268896e-188	1.768914724278288e-182	4.8980015245867535e-188
10	-8.003596903883499e+165	-5.641302321031635e+152	-5.266991299595048e+153

Iters

Range

Point

1.1487243557305423e+102

3.920821933018458e+112

9.421054264015979e+109

4.8461344139268896e-188

1.768914724278288e-182

4.8980015245867535e-188

-8.003596903883499e+165

-5.641302321031635e+152

-5.266991299595048e+153

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	50
1	33	50
done	33	50

end0.0ms

sample1.5s

Algorithm

intervals

Results

296.0ms	1062×	body	2560	valid
284.0ms	5949×	body	80	valid
198.0ms	856×	body	1280	valid
141.0ms	2987×	body	80	nan
83.0ms	460×	body	640	valid
38.0ms	117×	body	5120	valid
33.0ms	232×	body	320	valid
10.0ms	112×	body	160	valid

Details

sample75.0ms

simplify24.0ms

prune5.0ms

localize11.0ms

rewrite39.0ms

series65.0ms

simplify1.7s

prune159.0ms

localize11.0ms

rewrite42.0ms

series71.0ms

simplify2.3s

prune138.0ms

localize12.0ms

rewrite25.0ms

series38.0ms

simplify2.8s

prune127.0ms

localize9.0ms

rewrite29.0ms

series89.0ms

simplify1.3s

prune87.0ms

regimes311.0ms

bsearch115.0ms

simplify3.0ms

end0.0ms

sample1.5s

Profiling