Details

sample147.0ms

Algorithm

intervals

Results

86.0ms	103×	body	1280	valid
35.0ms	88×	body	640	valid
8.0ms	41×	body	320	valid
4.0ms	256×	pre	80	true
2.0ms	16×	body	160	valid
0.0ms	8×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	9
1	10	9
2	11	9
done	11	9

prune3.0ms

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: 61.3b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
4.8b	(log (+ 1.0 x))
5.0b	(log (- 1.0 x))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
16×	`times-frac`
15×	`pow1` `add-cube-cbrt`
12×	`log-pow`
9×	`log-prod`
7×	`add-exp-log`
6×	`log-div`
5×	`add-cbrt-cube`
4×	`associate-/r` `associate-/l`
3×	`add-log-exp`
2×	`flip3--` `div-sub` `rem-log-exp` `flip--`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 69

Calls

3 calls:

7.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
3.0ms	(log (+ 1.0 x))
4.0ms	(log (- 1.0 x))

series22.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
3.0ms	(log (+ 1.0 x))
3.0ms	(log (- 1.0 x))

simplify491.0ms

Counts

78 → 78

Iterations

Useful iterations: done (488.0ms)

Iter	Nodes	Cost
0	214	1397
1	523	1298
2	1866	1131
done	5000	1127

prune181.0ms

Filtered

56 candidates to 78 candidates (-39.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	72	6	78
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	72	7	79

Merged error: 58.9b

Counts

79 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow x 2)
0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(/ (log (- 1.0 x)) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
5.0b	(log (- 1.0 x))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

92×	`times-frac`
86×	`add-sqr-sqrt`
68×	`associate-r`
59×	`unpow-prod-down`
52×	`*-un-lft-identity`
50×	`add-cube-cbrt`
31×	`add-exp-log`
25×	`unpow2` `sqr-pow`
17×	`unswap-sqr`
12×	`pow1`
11×	`add-cbrt-cube`
10×	`div-exp` `prod-exp`
7×	`pow-to-exp` `pow-exp`
5×	`log-prod` `log-pow`
4×	`log-div` `associate-/r/` `associate-/l*` `add-log-exp`
3×	`pow-unpow` `flip3--` `associate-r/` `associate-l` `associate-/r` `flip--`
2×	`cbrt-undiv` `div-sub` `frac-sub` `cbrt-unprod` `div-inv`
1×	`pow-pow` `frac-2neg` `flip3-+` `rem-log-exp` `pow-prod-down` `clear-num` `*-commutative` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 181

Calls

4 calls:

2.0ms	(pow x 2)
21.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
10.0ms	(/ (log (- 1.0 x)) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
4.0ms	(log (- 1.0 x))

series24.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(pow x 2)
6.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
12.0ms	(/ (log (- 1.0 x)) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
3.0ms	(log (- 1.0 x))

simplify772.0ms

Counts

193 → 193

Iterations

Useful iterations: done (762.0ms)

Iter	Nodes	Cost
0	432	3343
1	1077	3088
2	3577	2650
done	5000	2645

prune494.0ms

Filtered

131 candidates to 193 candidates (-47.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	196	4	200

Merged error: 0.0b

Counts

200 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow x 2)
0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(/ (- (log 1.0) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1.0 x))) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

178×	`times-frac`
161×	`add-sqr-sqrt`
136×	`associate-r`
115×	`unpow-prod-down`
97×	`*-un-lft-identity`
85×	`add-cube-cbrt`
53×	`add-exp-log`
49×	`unpow2` `sqr-pow`
34×	`unswap-sqr`
20×	`prod-exp`
19×	`div-exp`
16×	`add-cbrt-cube`
13×	`pow1` `pow-to-exp` `pow-exp`
8×	`distribute-lft-out--`
6×	`associate-l` `associate-/l*`
4×	`associate-*r/` `associate-/r/` `log-pow` `cbrt-unprod` `add-log-exp` `difference-of-squares`
3×	`cbrt-undiv` `pow-unpow` `associate-/r*` `div-inv`
2×	`flip3--` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `associate-/l/`
1×	`pow-pow` `frac-2neg` `flip3-+` `div-sub` `clear-num` `flip-+`

Counts

4 → 284

Calls

4 calls:

3.0ms	(pow x 2)
26.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
21.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
20.0ms	(/ (- (log 1.0) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1.0 x))) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

series25.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(pow x 2)
6.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
6.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
10.0ms	(/ (- (log 1.0) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1.0 x))) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

simplify672.0ms

Counts

296 → 296

Iterations

Useful iterations: done (656.0ms)

Iter	Nodes	Cost
0	343	5503
1	886	5056
2	2927	4310
done	5001	4308

prune1.0s

Filtered

186 candidates to 296 candidates (-59.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	293	3	296
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	295	5	300

Merged error: 0.0b

Counts

300 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cbrt (/ (- (log 1.0) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1.0 x))) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))) (cbrt (/ (- (log 1.0) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1.0 x))) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
0.0b	(/ (- (log 1.0) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1.0 x))) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
0.0b	(/ (- (log 1.0) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1.0 x))) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
0.0b	(/ (- (log 1.0) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1.0 x))) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

213×	`*-un-lft-identity`
168×	`times-frac`
165×	`add-sqr-sqrt`
152×	`cbrt-prod`
93×	`add-cube-cbrt`
72×	`distribute-lft-out--`
47×	`pow1` `swap-sqr`
36×	`log-pow`
29×	`associate-r` `associate-l`
28×	`associate-/r/`
24×	`difference-of-squares`
18×	`associate-/l*`
15×	`associate-*r/`
14×	`frac-sub`
12×	`add-exp-log`
10×	`flip3--` `add-cbrt-cube` `flip--`
9×	`associate-/r*` `unswap-sqr`
7×	`flip3-+` `flip-+` `div-inv`
6×	`pow1/3` `associate-/l/`
4×	`cbrt-div` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod`

Counts

4 → 273

Calls

4 calls:

53.0ms	(* (cbrt (/ (- (log 1.0) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1.0 x))) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))) (cbrt (/ (- (log 1.0) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1.0 x))) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
21.0ms	(/ (- (log 1.0) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1.0 x))) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
24.0ms	(/ (- (log 1.0) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1.0 x))) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
21.0ms	(/ (- (log 1.0) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1.0 x))) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

series50.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (cbrt (/ (- (log 1.0) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1.0 x))) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))) (cbrt (/ (- (log 1.0) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1.0 x))) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
10.0ms	(/ (- (log 1.0) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1.0 x))) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
11.0ms	(/ (- (log 1.0) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1.0 x))) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
10.0ms	(/ (- (log 1.0) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1.0 x))) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

simplify629.0ms

Counts

285 → 285

Iterations

Useful iterations: done (604.0ms)

Iter	Nodes	Cost
0	290	19863
1	646	19320
2	2447	18553
done	5000	18529

prune5.1s

Filtered

184 candidates to 285 candidates (-54.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	283	2	285
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	284	6	290

Merged error: 0.0b

Counts

290 → 6

regimes173.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	104
1	23	104
done	23	104

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.8s	3441×	body	1280	valid
982.0ms	2473×	body	640	valid
258.0ms	1233×	body	320	valid
132.0ms	8000×	pre	80	true
78.0ms	618×	body	160	valid
13.0ms	235×	body	80	valid

Details

sample147.0ms

simplify4.0ms

prune3.0ms

localize7.0ms

rewrite16.0ms

series22.0ms

simplify491.0ms

prune181.0ms

localize17.0ms

rewrite46.0ms

series24.0ms

simplify772.0ms

prune494.0ms

localize14.0ms

rewrite85.0ms

series25.0ms

simplify672.0ms

prune1.0s

localize19.0ms

rewrite140.0ms

series50.0ms

simplify629.0ms

prune5.1s

regimes173.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample4.4s

Profiling