Details

sample52.0ms

Algorithm

intervals

Results

14.0ms	54×	body	1280	valid
10.0ms	44×	body	640	valid
8.0ms	132×	body	80	valid
3.0ms	19×	body	320	valid
1.0ms	7×	body	160	valid

simplify2.8s

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	79	13
9	183	13
10	535	13
11	1745	13
12	4085	13
done	5000	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite271.0ms

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-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 596

Calls

3 calls:

9.0ms	(/ x (+ x 1.0))
34.0ms	(/ (+ x 1.0) (- x 1.0))
158.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series256.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ x (+ x 1.0))
41.0ms	(/ (+ x 1.0) (- x 1.0))
172.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.1s

Counts

605 → 605

Iterations

Useful iterations: 2 (923.0ms)

Iter	Nodes	Cost
0	523	34216
1	1252	30943
2	4599	23743
done	5000	23743

prune1.8s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

15.0b	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
15.0b	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
15.0b	(/ x (- (* x x) (* 1.0 1.0)))
29.6b	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

rewrite98.0ms

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-cbrt-cube` `add-exp-log` `distribute-lft-out`
6×	`associate-/r/`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp` `associate-/l/`
3×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `div-inv` `flip--`
2×	`flip3-+` `flip-+`
1×	`fma-udef`

Counts

4 → 129

Calls

4 calls:

42.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
31.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
17.0ms	(/ x (- (* 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))))))

series510.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
55.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
100.0ms	(/ x (- (* x x) (* 1.0 1.0)))
292.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

simplify1.8s

Counts

141 → 141

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	168	2601
1	424	2525
2	2206	2296
done	5001	2294

prune781.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
2.7b	(fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ (cbrt x) (cbrt (+ x 1.0))) (/ (- (+ x 1.0)) (- x 1.0)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
0.0ms	(fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ (cbrt x) (cbrt (+ x 1.0))) (/ (- (+ x 1.0)) (- x 1.0)))

series1.5s

Counts

4 → 12

Calls

4 calls:

273.0ms	(cbrt x)
263.0ms	(cbrt x)
249.0ms	(cbrt x)
701.0ms	(fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ (cbrt x) (cbrt (+ x 1.0))) (/ (- (+ x 1.0)) (- x 1.0)))

simplify703.0ms

Counts

61 → 61

Iterations

Useful iterations: done (700.0ms)

Iter	Nodes	Cost
0	101	794
1	270	772
2	1031	620
done	5001	487

prune376.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- (+ x 1.0)) (- x 1.0))
0.0b	(/ 1 (+ x 1.0))
29.6b	(fma x (/ 1 (+ x 1.0)) (/ (- (+ x 1.0)) (- x 1.0)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
72×	`times-frac`
69×	`add-sqr-sqrt`
43×	`add-cube-cbrt`
24×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
16×	`distribute-lft-out`
15×	`associate-/l*`
13×	`distribute-lft-out--` `difference-of-squares`
9×	`associate-/r*` `add-exp-log`
7×	`add-cbrt-cube`
6×	`neg-mul-1`
4×	`pow1` `associate-/r/`
3×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip-+` `div-inv` `distribute-neg-frac` `associate-/l/`
1×	`neg-sub0` `rec-exp` `flip3--` `1-exp` `div-sub` `distribute-frac-neg` `fma-udef` `pow-flip` `flip--` `inv-pow`

Counts

3 → 146

Calls

3 calls:

37.0ms	(/ (- (+ x 1.0)) (- x 1.0))
15.0ms	(/ 1 (+ x 1.0))
0.0ms	(fma x (/ 1 (+ x 1.0)) (/ (- (+ x 1.0)) (- x 1.0)))

series279.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(/ (- (+ x 1.0)) (- x 1.0))
31.0ms	(/ 1 (+ x 1.0))
169.0ms	(fma x (/ 1 (+ x 1.0)) (/ (- (+ x 1.0)) (- x 1.0)))

simplify1.4s

Counts

155 → 155

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	220	2158
1	509	2009
2	2194	1889
done	5000	1882

prune497.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes93.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 28.6b

bsearch114.0ms

Steps

Iters	Range		Point
9	2205.5689030668646	4825064884.677679	10454.066790945864
10	-185496355225.45163	-22.8286883066892	-13946.27375560417

simplify13.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	25	55
1	39	40
2	40	40
done	40	40

end0.0ms

sample1.3s

Algorithm

intervals

Results

358.0ms	1659×	body	1280	valid
342.0ms	4183×	body	80	valid
337.0ms	1242×	body	640	valid
85.0ms	629×	body	320	valid
25.0ms	287×	body	160	valid