Details

sample26.0ms

Algorithm

intervals

Results

7.0ms	218×	body	80	valid
2.0ms	22×	body	320	valid
2.0ms	17×	body	640	valid
2.0ms	13×	body	1280	valid
0.0ms	5×	body	160	valid

simplify8.4s

Counts

1 → 1

Iterations

Useful iterations: 4 (29.0ms)

Iter	Nodes	Cost
0	11	13
1	22	13
2	51	13
3	104	13
4	214	12
5	481	12
6	937	12
7	1715	12
8	2446	12
9	4989	12
done	5000	12

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.8b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t z) (- a t))
2.9b	(fma (/ (- t z) (- a t)) y y)

rewrite20.0ms

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:

17.0ms	(/ (- t z) (- a t))
0.0ms	(fma (/ (- t z) (- a t)) y y)

series153.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (- t z) (- a t))
107.0ms	(fma (/ (- t z) (- a t)) y y)

simplify941.0ms

Counts

70 → 70

Iterations

Useful iterations: done (939.0ms)

Iter	Nodes	Cost
0	110	876
1	253	848
2	665	800
3	2131	800
done	5000	798

prune221.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.9b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ z (- a t))
0.0b	(/ t (- a t))
2.9b	(fma (- (/ t (- a t)) (/ z (- a t))) y y)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`times-frac`
23×	`add-cube-cbrt`
10×	`associate-/r*`
8×	`distribute-lft-out--` `difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`associate-/r/`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`
1×	`fma-udef`

Counts

3 → 88

Calls

3 calls:

6.0ms	(/ z (- a t))
5.0ms	(/ t (- a t))
0.0ms	(fma (- (/ t (- a t)) (/ z (- a t))) y y)

series231.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ z (- a t))
47.0ms	(/ t (- a t))
150.0ms	(fma (- (/ t (- a t)) (/ z (- a t))) y y)

simplify1.2s

Counts

97 → 97

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	132	988
1	248	952
2	701	886
3	2341	886
done	5000	884

prune321.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a t))
0.0b	(/ t (- a t))
0.2b	(* z (/ 1 (- a t)))
2.9b	(fma (- (/ t (- a t)) (* z (/ 1 (- a t)))) y y)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
47×	`times-frac`
34×	`add-cube-cbrt`
21×	`associate-r`
19×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r*`
7×	`pow1`
6×	`associate-/r/` `associate-/l*`
5×	`div-exp`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `flip3--` `associate-l` `flip--` `div-inv` `unswap-sqr`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `cbrt-unprod`
1×	`pow-flip` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `fma-udef` `inv-pow`

Counts

4 → 138

Calls

4 calls:

6.0ms	(/ 1 (- a t))
5.0ms	(/ t (- a t))
19.0ms	(* z (/ 1 (- a t)))
0.0ms	(fma (- (/ t (- a t)) (* z (/ 1 (- a t)))) y y)

series259.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 1 (- a t))
47.0ms	(/ t (- a t))
32.0ms	(* z (/ 1 (- a t)))
142.0ms	(fma (- (/ t (- a t)) (* z (/ 1 (- a t)))) y y)

simplify2.7s

Counts

150 → 150

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	172	1493
1	367	1298
2	1215	1142
3	3386	1142
done	5000	1140

prune411.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
0.6b	(* (cbrt (- a t)) (cbrt (- a t)))
15.6b	(fma (- (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ t (cbrt (- a t)))) (/ z (- a t))) y y)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

38×	`cbrt-prod`
34×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
16×	`cbrt-div`
14×	`add-cube-cbrt`
11×	`pow1`
10×	`swap-sqr`
8×	`flip3--` `pow1/3` `associate-r` `associate-l` `flip--` `distribute-lft-out--`
6×	`add-exp-log` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 102

Calls

4 calls:

2.0ms	(cbrt (- a t))
2.0ms	(cbrt (- a t))
21.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
0.0ms	(fma (- (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ t (cbrt (- a t)))) (/ z (- a t))) y y)

series591.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(cbrt (- a t))
165.0ms	(cbrt (- a t))
138.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
130.0ms	(fma (- (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ t (cbrt (- a t)))) (/ z (- a t))) y y)

simplify3.4s

Counts

114 → 114

Iterations

Useful iterations: 3 (717.0ms)

Iter	Nodes	Cost
0	157	1615
1	313	1519
2	1128	1381
3	4763	1171
done	5000	1171

prune447.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.9b

regimes328.0ms

Accuracy

28.9% (2.7b remaining)

Error of 6.6b against oracle of 3.9b and baseline of 7.7b

bsearch5.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	27	75
1	38	58
done	38	58

end0.0ms

sample694.0ms

Algorithm

intervals

Results

248.0ms	7307×	body	80	valid
66.0ms	462×	body	640	valid
44.0ms	288×	body	1280	valid
35.0ms	376×	body	320	valid
17.0ms	273×	body	160	valid
3.0ms	16×	body	2560	valid