Details

sample54.0ms

Algorithm

intervals

Results

22.0ms	227×	body	80	valid
3.0ms	15×	body	640	valid
2.0ms	13×	body	320	valid
2.0ms	6×	body	1280	valid
1.0ms	11×	body	160	valid
0.0ms	1×	body	2560	valid

simplify12.1s

Counts

1 → 1

Iterations

Useful iterations: 4 (57.0ms)

Iter	Nodes	Cost
0	11	13
1	22	13
2	52	13
3	109	13
4	203	12
5	451	12
6	748	12
7	1078	12
8	1400	12
9	1655	12
10	2153	12
11	2683	12
12	3847	12
done	5001	12

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.8b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t z) (- a t))
3.8b	(fma (/ (- t z) (- a t)) y (+ x y))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

47.0ms	(/ (- t z) (- a t))
1.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

series317.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(/ (- t z) (- a t))
255.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

simplify1.3s

Counts

70 → 70

Iterations

Useful iterations: 3 (427.0ms)

Iter	Nodes	Cost
0	113	906
1	258	878
2	622	826
3	1643	824
done	5000	824

prune205.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ t (- a t)) (/ z (- a t)))
0.0b	(/ t (- a t))
0.0b	(/ z (- a t))
3.8b	(fma (- (/ t (- a t)) (/ z (- a t))) y (+ x y))

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

713×	`*-un-lft-identity`
703×	`add-sqr-sqrt`
693×	`times-frac`
441×	`prod-diff`
413×	`add-cube-cbrt`
149×	`distribute-lft-out--`
143×	`difference-of-squares`
94×	`associate-/r/`
48×	`flip3--` `flip--`
47×	`div-inv`
21×	`fma-neg`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-rgt-out--`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `diff-log` `frac-sub` `fma-udef` `sub-div`

Counts

4 → 581

Calls

4 calls:

159.0ms	(- (/ t (- a t)) (/ z (- a t)))
26.0ms	(/ t (- a t))
17.0ms	(/ z (- a t))
0.0ms	(fma (- (/ t (- a t)) (/ z (- a t))) y (+ x y))

series504.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(- (/ t (- a t)) (/ z (- a t)))
52.0ms	(/ t (- a t))
32.0ms	(/ z (- a t))
279.0ms	(fma (- (/ t (- a t)) (/ z (- a t))) y (+ x y))

simplify2.3s

Counts

593 → 593

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	569	28424
1	1228	25525
2	2593	19569
done	5002	14988

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt t)
0.5b	(cbrt t)
0.5b	(cbrt t)
8.0b	(fma (+ (fma (* (cbrt t) (cbrt t)) (/ (cbrt t) (- a t)) (/ (- z) (- a t))) 0) y (+ x y))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt t)
1.0ms	(cbrt t)
2.0ms	(cbrt t)
1.0ms	(fma (+ (fma (* (cbrt t) (cbrt t)) (/ (cbrt t) (- a t)) (/ (- z) (- a t))) 0) y (+ x y))

series904.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(cbrt t)
208.0ms	(cbrt t)
217.0ms	(cbrt t)
272.0ms	(fma (+ (fma (* (cbrt t) (cbrt t)) (/ (cbrt t) (- a t)) (/ (- z) (- a t))) 0) y (+ x y))

simplify2.0s

Counts

61 → 61

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	52	568
1	85	530
2	187	422
3	585	378
4	2998	378
done	5000	378

prune265.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ (fma y (- (/ t (- a t)) (/ z (- a t))) y) x))
4.1b	(fma y (- (/ t (- a t)) (/ z (- a t))) y)
4.1b	(fma y (- (/ t (- a t)) (/ z (- a t))) y)
4.1b	(fma y (- (/ t (- a t)) (/ z (- a t))) y)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
5×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `cbrt-prod` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
2×	`cbrt-div`
1×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`

Counts

4 → 46

Calls

4 calls:

6.0ms	(cbrt (+ (fma y (- (/ t (- a t)) (/ z (- a t))) y) x))
0.0ms	(fma y (- (/ t (- a t)) (/ z (- a t))) y)
0.0ms	(fma y (- (/ t (- a t)) (/ z (- a t))) y)
1.0ms	(fma y (- (/ t (- a t)) (/ z (- a t))) y)

series1.4s

Counts

4 → 12

Calls

4 calls:

940.0ms	(cbrt (+ (fma y (- (/ t (- a t)) (/ z (- a t))) y) x))
159.0ms	(fma y (- (/ t (- a t)) (/ z (- a t))) y)
160.0ms	(fma y (- (/ t (- a t)) (/ z (- a t))) y)
170.0ms	(fma y (- (/ t (- a t)) (/ z (- a t))) y)

simplify1.2s

Counts

58 → 58

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	93	1145
1	197	1050
2	492	1012
3	1628	992
done	5000	980

prune228.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.9b

regimes367.0ms

Accuracy

39.6% (3.4b remaining)

Error of 6.6b against oracle of 3.1b and baseline of 8.8b

bsearch3.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	33	251
1	38	251
done	38	251

end0.0ms

sample1.5s

Algorithm

intervals

Results

601.0ms	7376×	body	80	valid
131.0ms	462×	body	640	valid
65.0ms	402×	body	320	valid
62.0ms	228×	body	1280	valid
56.0ms	245×	body	160	valid
4.0ms	10×	body	2560	valid