Details

sample25.0ms

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

simplify150.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	12	13
2	16	13
3	19	13
4	21	13
5	27	13
6	39	13
7	58	13
8	77	13
9	99	13
10	113	13
11	119	13
12	123	13
done	123	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize17.0ms

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)))

rewrite369.0ms

Algorithm

rewrite-expression-head

Rules

981×	`*-un-lft-identity`
736×	`times-frac`
585×	`add-sqr-sqrt`
468×	`prod-diff`
419×	`add-cube-cbrt`
189×	`distribute-lft-out`
94×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
47×	`div-inv`
29×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 596

Calls

3 calls:

23.0ms	(/ x (+ x 1.0))
46.0ms	(/ (+ x 1.0) (- x 1.0))
229.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series313.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ x (+ x 1.0))
49.0ms	(/ (+ x 1.0) (- x 1.0))
213.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify3.6s

Counts

605 → 605

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	523	34216
1	1199	30851
2	2823	22735
done	5000	16848

prune766.0ms

Pruning

7 alts after pruning (7 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)))

rewrite908.0ms

Algorithm

rewrite-expression-head

Rules

1898×	`*-un-lft-identity`
1428×	`times-frac`
1132×	`add-sqr-sqrt`
936×	`prod-diff`
810×	`add-cube-cbrt`
473×	`log-prod`
470×	`exp-sum`
365×	`distribute-lft-out`
182×	`associate-/r/`
175×	`distribute-lft-out--`
157×	`difference-of-squares`
91×	`div-inv`
55×	`flip3-+` `flip-+`
38×	`flip3--` `flip--`
18×	`fma-neg`
17×	`log-pow`
16×	`exp-prod`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l*`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `div-exp` `clear-num` `associate-/l/`
1×	`log-div` `exp-diff` `diff-log` `rem-log-exp` `frac-sub`

Counts

4 → 1097

Calls

4 calls:

26.0ms	(/ (+ x 1.0) (- x 1.0))
18.0ms	(/ x (+ x 1.0))
513.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
155.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series477.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (+ x 1.0) (- x 1.0))
47.0ms	(/ x (+ x 1.0))
166.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
201.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.3s

Counts

1109 → 1109

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	1136	69094
1	1825	60490
2	3748	44278
done	5000	44276

prune2.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

13.2b	(/ x (- (* x x) (* 1.0 1.0)))
13.2b	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
13.2b	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
28.5b	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
44×	`times-frac`
33×	`add-sqr-sqrt` `add-cube-cbrt`
14×	`difference-of-squares`
12×	`associate-/r*`
11×	`associate-/l*`
10×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`associate-/r/`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`
2×	`flip3-+` `flip-+`
1×	`fma-udef`

Counts

4 → 129

Calls

4 calls:

27.0ms	(/ x (- (* x x) (* 1.0 1.0)))
37.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
46.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
0.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

series520.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ x (- (* x x) (* 1.0 1.0)))
67.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
52.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
328.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

simplify3.1s

Counts

141 → 141

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	169	2601
1	392	2521
2	1186	2066
3	4088	1892
done	5000	1887

prune588.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

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)) (fma (/ x (+ x 1.0)) (/ x (+ x 1.0)) (* (/ (+ x 1.0) (- x 1.0)) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))))))

rewrite2.7s

Algorithm

rewrite-expression-head

Rules

5021×	`*-un-lft-identity`
3743×	`times-frac`
3033×	`add-sqr-sqrt`
2438×	`unpow-prod-down` `cube-prod`
2436×	`prod-diff`
2009×	`add-cube-cbrt`
918×	`distribute-lft-out`
556×	`distribute-lft-out--`
488×	`difference-of-squares`
412×	`associate-/r/`
236×	`log-pow`
235×	`exp-prod`
207×	`div-inv`
151×	`sqr-pow`
120×	`flip3-+` `flip-+`
103×	`cube-mult` `unpow3`
87×	`flip3--` `flip--`
42×	`fma-neg`
10×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`pow-unpow` `add-log-exp`
4×	`difference-cubes` `cube-div` `expm1-log1p-u` `pow-exp` `log1p-expm1-u` `rem-cube-cbrt`
3×	`log-prod`
2×	`cbrt-undiv` `pow-to-exp` `pow-pow` `div-exp`
1×	`sub-neg` `log-div` `exp-diff` `diff-log` `div-sub` `rem-log-exp` `frac-sub`

Counts

4 → 2949

Calls

4 calls:

24.0ms	(pow (/ x (+ x 1.0)) 3)
38.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
478.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
1.3s	(log (exp (/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (fma (/ x (+ x 1.0)) (/ x (+ x 1.0)) (* (/ (+ x 1.0) (- x 1.0)) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))))))

series1.4s

Counts

4 → 12

Calls

4 calls:

76.0ms	(pow (/ x (+ x 1.0)) 3)
87.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
433.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
838.0ms	(log (exp (/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (fma (/ x (+ x 1.0)) (/ x (+ x 1.0)) (* (/ (+ x 1.0) (- x 1.0)) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))))))

simplify2.0s

Counts

2961 → 2961

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	1124	225906
1	2416	187351
done	5000	141523

prune2.8s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes57.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.6b

bsearch113.0ms

Steps

Iters	Range		Point
10	1.0194597579740466e-06	20796729.49276672	12455.499002847031
10	-6045414056204.408	-123.41774798665298	-15309.121527086834

simplify11.0ms

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	32	116
1	42	101
done	42	101

end0.0ms

sample1.1s

Algorithm

intervals

Results

354.0ms	1745×	body	1280	valid
281.0ms	4051×	body	80	valid
227.0ms	1246×	body	640	valid
62.0ms	632×	body	320	valid
21.0ms	326×	body	160	valid