Details

sample78.0ms

Algorithm

intervals

Results

34.0ms	58×	body	1280	valid
15.0ms	59×	body	640	valid
4.0ms	29×	body	320	valid
4.0ms	95×	body	80	valid
4.0ms	90×	body	80	overflowed
2.0ms	16×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	19	12
2	28	12
3	40	12
4	74	12
5	170	12
6	464	12
7	1490	12
done	5000	12

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: 40.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.2b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
5.7b	(- (exp (* 2.0 x)) 1.0)
5.7b	(- (exp x) 1.0)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
51×	`times-frac`
31×	`sqrt-prod`
27×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`associate-/r/`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 123

Calls

4 calls:

17.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
10.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
4.0ms	(- (exp (* 2.0 x)) 1.0)
6.0ms	(- (exp x) 1.0)

series35.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
12.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
3.0ms	(- (exp (* 2.0 x)) 1.0)
11.0ms	(- (exp x) 1.0)

simplify1.1s

Counts

135 → 135

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	189	2376
1	388	2279
2	898	2167
3	2400	2156
done	5000	2154

prune373.0ms

Filtered

92 candidates to 135 candidates (-46.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	2	136

Merged error: 0.2b

Counts

136 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))) (* 0.5 (/ x (sqrt 2.0))))
0.2b	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
0.3b	(/ (pow x 2) (sqrt 2.0))
0.4b	(/ x (sqrt 2.0))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac`
108×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
81×	`add-cube-cbrt`
67×	`sqrt-prod`
52×	`associate-l`
41×	`unpow-prod-down`
21×	`add-exp-log`
15×	`unpow2` `sqr-pow`
13×	`add-cbrt-cube`
12×	`associate-/r*`
11×	`associate-/l*`
9×	`associate-*r/` `unswap-sqr`
7×	`div-exp`
6×	`pow1` `associate-r` `add-log-exp`
5×	`frac-add`
4×	`distribute-rgt-in` `frac-times` `sub-neg` `associate-+l+` `flip3--` `distribute-lft-in` `prod-exp` `flip--`
3×	`cbrt-undiv` `div-inv`
2×	`pow-to-exp` `frac-2neg` `associate-*l/` `pow-exp` `clear-num` `cbrt-unprod` `difference-of-squares`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+` `distribute-lft-out--`

Counts

4 → 226

Calls

4 calls:

16.0ms	(+ (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))) (* 0.5 (/ x (sqrt 2.0))))
22.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
7.0ms	(/ (pow x 2) (sqrt 2.0))
5.0ms	(/ x (sqrt 2.0))

series42.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+ (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))) (* 0.5 (/ x (sqrt 2.0))))
7.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
8.0ms	(/ (pow x 2) (sqrt 2.0))
10.0ms	(/ x (sqrt 2.0))

simplify1.0s

Counts

238 → 238

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	291	3592
1	683	3327
2	2417	3025
done	5001	3005

prune532.0ms

Filtered

151 candidates to 238 candidates (-57.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	236	2	238
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	237	3	240

Merged error: 0.2b

Counts

240 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (pow x 2) (sqrt 2.0))
0.4b	(/ x (sqrt 2.0))
3.1b	(exp (log (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
27.8b	(log (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
52×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
39×	`sqrt-prod`
22×	`add-exp-log`
21×	`unpow-prod-down`
12×	`associate-/r*`
11×	`associate-/l*`
10×	`pow1` `log-div`
8×	`add-cbrt-cube`
7×	`div-exp` `unpow2` `sqr-pow`
5×	`exp-prod` `exp-diff` `rem-log-exp`
4×	`frac-times` `flip3--` `associate-*r/` `prod-exp` `log-pow` `flip--` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `log-prod` `frac-2neg` `pow-prod-down` `associate-*l/` `pow-exp` `clear-num` `div-inv`
1×	`exp-sum` `rem-exp-log`

Counts

4 → 154

Calls

4 calls:

7.0ms	(/ (pow x 2) (sqrt 2.0))
5.0ms	(/ x (sqrt 2.0))
19.0ms	(exp (log (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
14.0ms	(log (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))

series41.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ (pow x 2) (sqrt 2.0))
6.0ms	(/ x (sqrt 2.0))
7.0ms	(exp (log (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
21.0ms	(log (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))

simplify1.7s

Counts

166 → 166

Iterations

Useful iterations: 3 (882.0ms)

Iter	Nodes	Cost
0	231	2119
1	414	1883
2	1129	1706
3	4279	1701
done	5000	1701

prune371.0ms

Filtered

98 candidates to 166 candidates (-69.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	166	3	169

Merged error: 0.2b

Counts

169 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
0.2b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))))
5.7b	(- (exp (* 2.0 x)) 1.0)
5.7b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

253×	`times-frac`
208×	`*-un-lft-identity`
178×	`add-sqr-sqrt`
135×	`sqrt-prod`
92×	`add-cube-cbrt`
79×	`difference-of-squares`
31×	`distribute-lft-out`
27×	`distribute-lft-out--`
26×	`exp-sum`
13×	`associate-/r/`
8×	`add-log-exp`
7×	`div-inv`
6×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
5×	`pow1` `associate-/l*`
4×	`associate-/r*`
3×	`rem-sqrt-square` `flip3--` `flip--`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 222

Calls

4 calls:

13.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
26.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))))
4.0ms	(- (exp (* 2.0 x)) 1.0)
8.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series32.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
19.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))))
3.0ms	(- (exp (* 2.0 x)) 1.0)
3.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify959.0ms

Counts

234 → 234

Iterations

Useful iterations: 2 (389.0ms)

Iter	Nodes	Cost
0	510	7530
1	1087	7251
2	3183	6927
done	5000	6927

prune544.0ms

Filtered

158 candidates to 234 candidates (-48.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	233	1	234
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	233	4	237

Merged error: 0.2b

Counts

237 → 4

regimes47.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.0b

bsearch19.0ms

Steps

Iters	Range		Point
9	-0.0001616040529746431	-1.1951251334293225e-11	-4.599158930389739e-07

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	49
1	40	49
done	40	49

end0.0ms

sample1.6s

Algorithm

intervals

Results

716.0ms	2297×	body	1280	valid
346.0ms	1663×	body	640	valid
120.0ms	2864×	body	80	valid
112.0ms	802×	body	320	valid
100.0ms	2519×	body	80	overflowed
40.0ms	423×	body	160	valid

Details

sample78.0ms

simplify1.5s

prune5.0ms

localize11.0ms

rewrite44.0ms

series35.0ms

simplify1.1s

prune373.0ms

localize13.0ms

rewrite60.0ms

series42.0ms

simplify1.0s

prune532.0ms

localize17.0ms

rewrite52.0ms

series41.0ms

simplify1.7s

prune371.0ms

localize14.0ms

rewrite70.0ms

series32.0ms

simplify959.0ms

prune544.0ms

regimes47.0ms

bsearch19.0ms

simplify3.0ms

end0.0ms

sample1.6s

Profiling