Details

sample27.0ms

Algorithm

intervals

Results

7.0ms	53×	body	1280	valid
4.0ms	138×	body	80	valid
3.0ms	33×	body	320	valid
3.0ms	25×	body	640	valid
0.0ms	7×	body	160	valid

simplify237.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	14	13
2	16	13
3	21	13
4	51	13
5	68	13
6	126	13
7	188	13
8	204	13
9	208	13
done	208	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.8b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
52×	`times-frac`
45×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`distribute-lft-out` `distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 104

Calls

3 calls:

23.0ms	(/ x (+ x 1.0))
52.0ms	(/ (+ x 1.0) (- x 1.0))
152.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series330.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(/ x (+ x 1.0))
74.0ms	(/ (+ x 1.0) (- x 1.0))
194.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.9s

Counts

113 → 113

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	176	1584
1	1197	1477
done	5002	1423

prune334.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
2.8b	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
2.8b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite585.0ms

Algorithm

rewrite-expression-head

Rules

148×	`*-un-lft-identity`
72×	`times-frac`
60×	`add-sqr-sqrt`
31×	`distribute-lft-out--`
26×	`add-cube-cbrt` `distribute-lft-out`
17×	`log-pow`
16×	`exp-prod`
13×	`difference-of-squares`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l*`
6×	`add-log-exp`
5×	`pow1` `log-prod`
4×	`associate-/r/`
2×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `div-exp` `exp-sum` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`log-div` `exp-diff` `diff-log` `rem-log-exp` `frac-sub`

Counts

4 → 135

Calls

4 calls:

26.0ms	(/ (+ x 1.0) (- x 1.0))
12.0ms	(/ x (+ x 1.0))
408.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
129.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series553.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ (+ x 1.0) (- x 1.0))
43.0ms	(/ x (+ x 1.0))
243.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
199.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.8s

Counts

147 → 147

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	211	2126
1	1255	1908
done	5001	1828

prune487.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.8b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
52×	`times-frac`
45×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`distribute-lft-out` `distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 104

Calls

3 calls:

12.0ms	(/ x (+ x 1.0))
35.0ms	(/ (+ x 1.0) (- x 1.0))
136.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series303.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(/ x (+ x 1.0))
50.0ms	(/ (+ x 1.0) (- x 1.0))
195.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.9s

Counts

113 → 113

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	176	1584
1	1197	1477
done	5002	1423

prune301.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ x (+ x 1.0)) 3)
0.0b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
2.8b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
2.8b	(log (exp (/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (+ (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))))))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

916×	`*-un-lft-identity`
647×	`times-frac`
476×	`add-sqr-sqrt`
284×	`unpow-prod-down` `cube-prod`
259×	`log-pow`
258×	`exp-prod`
220×	`distribute-lft-out--`
152×	`difference-of-squares`
144×	`distribute-lft-out`
124×	`add-cube-cbrt`
50×	`sqr-pow`
31×	`associate-/r/`
27×	`frac-add`
16×	`frac-times` `associate-*r/`
10×	`add-exp-log` `associate-*l/` `add-cbrt-cube`
9×	`flip3-+` `flip-+`
7×	`pow1`
6×	`pow-unpow` `add-log-exp`
5×	`div-inv`
4×	`difference-cubes` `cube-div` `pow-exp` `rem-cube-cbrt`
3×	`log-prod` `flip3--` `flip--`
2×	`cbrt-undiv` `cube-mult` `pow-to-exp` `pow-pow` `unpow3` `div-exp`
1×	`sub-neg` `log-div` `exp-diff` `diff-log` `div-sub` `rem-log-exp` `frac-sub`

Counts

4 → 486

Calls

4 calls:

18.0ms	(pow (/ x (+ x 1.0)) 3)
42.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
367.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
1.4s	(log (exp (/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (+ (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

73.0ms	(pow (/ x (+ x 1.0)) 3)
70.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
451.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
889.0ms	(log (exp (/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (+ (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))))))

simplify971.0ms

Counts

498 → 498

Iterations

Useful iterations: done (949.0ms)

Iter	Nodes	Cost
0	669	19414
done	5000	17322

prune1.3s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes71.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 29.7b

bsearch1.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	45
1	28	45
2	34	45
3	37	45
done	37	45

end0.0ms

sample1.9s

Algorithm

intervals

Results

715.0ms	1246×	body	640	valid
568.0ms	1745×	body	1280	valid
323.0ms	4051×	body	80	valid
92.0ms	632×	body	320	valid
31.0ms	326×	body	160	valid