Details

sample34.0ms

Algorithm

intervals

Results

10.0ms	246×	body	80	valid
3.0ms	19×	body	640	valid
2.0ms	17×	body	320	valid
1.0ms	6×	body	1280	valid
1.0ms	8×	body	160	valid

simplify3.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	1890
5	788
4	299
3	108
2	43
1	20
0	11

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.8b

localize28.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- z t) (- a t))
2.7b	(fma (/ (- z t) (- a t)) (- y x) x)

rewrite23.0ms

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-cbrt-cube` `add-exp-log`
2×	`expm1-log1p-u` `pow1` `flip3--` `associate-/r/` `log1p-expm1-u` `flip--` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

20.0ms	(/ (- z t) (- a t))
0.0ms	(fma (/ (- z t) (- a t)) (- y x) x)

series319.0ms

Counts

2 → 6

Calls

2 calls:

93.0ms	(/ (- z t) (- a t))
225.0ms	(fma (/ (- z t) (- a t)) (- y x) x)

simplify1.9s

Counts

70 → 70

Iterations

Iter	Nodes
done	5002
3	2154
2	678
1	272
0	116

prune466.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.7b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* (- z t) (/ 1 (- a t)))
4.7b	(fma (* (- z t) (/ 1 (- a t))) (- y x) x)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
32×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
16×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-/r` `associate-l*`
4×	`flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

3 → 105

Calls

3 calls:

10.0ms	(/ 1 (- a t))
41.0ms	(* (- z t) (/ 1 (- a t)))
0.0ms	(fma (* (- z t) (/ 1 (- a t))) (- y x) x)

series262.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ 1 (- a t))
60.0ms	(* (- z t) (/ 1 (- a t)))
159.0ms	(fma (* (- z t) (/ 1 (- a t))) (- y x) x)

simplify2.3s

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
3	3870
2	1216
1	360
0	152

prune728.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.7b

localize68.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ 1 (- a t)))
0.6b	(cbrt (/ 1 (- a t)))
0.6b	(cbrt (/ 1 (- a t)))
10.3b	(fma (* (* (- z t) (* (cbrt (/ 1 (- a t))) (cbrt (/ 1 (- a t))))) (cbrt (/ 1 (- a t)))) (- y x) x)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

63×	`cbrt-prod`
49×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
31×	`add-cube-cbrt`
9×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `flip3--` `pow1/3` `div-inv` `flip--`
1×	`fma-udef`

Counts

4 → 106

Calls

4 calls:

9.0ms	(cbrt (/ 1 (- a t)))
9.0ms	(cbrt (/ 1 (- a t)))
9.0ms	(cbrt (/ 1 (- a t)))
1.0ms	(fma (* (* (- z t) (* (cbrt (/ 1 (- a t))) (cbrt (/ 1 (- a t))))) (cbrt (/ 1 (- a t)))) (- y x) x)

series836.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(cbrt (/ 1 (- a t)))
234.0ms	(cbrt (/ 1 (- a t)))
198.0ms	(cbrt (/ 1 (- a t)))
179.0ms	(fma (* (* (- z t) (* (cbrt (/ 1 (- a t))) (cbrt (/ 1 (- a t))))) (cbrt (/ 1 (- a t)))) (- y x) x)

simplify1.6s

Counts

118 → 118

Iterations

Iter	Nodes
done	5002
3	1585
2	544
1	263
0	144

prune1.0s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 4.7b

localize62.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt (/ 1 (- a t))) (/ 1 (cbrt (- a t))))
0.6b	(cbrt (/ 1 (- a t)))
0.6b	(cbrt (/ 1 (- a t)))
9.5b	(fma (* (* (- z t) (* (cbrt (/ 1 (- a t))) (/ 1 (cbrt (- a t))))) (cbrt (/ 1 (- a t)))) (- y x) x)

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

124×	`add-sqr-sqrt`
101×	`cbrt-prod`
95×	`times-frac`
84×	`*-un-lft-identity`
47×	`add-cube-cbrt`
30×	`associate-r`
24×	`associate-l`
20×	`unswap-sqr`
13×	`add-exp-log`
12×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-/r/`
6×	`pow1` `cbrt-div` `add-cbrt-cube`
4×	`expm1-log1p-u` `flip3--` `prod-exp` `log1p-expm1-u` `div-inv` `flip--` `add-log-exp`
2×	`pow1/3` `div-exp` `cbrt-unprod`
1×	`frac-times` `cbrt-undiv` `rec-exp` `1-exp` `pow-prod-down` `associate-l/` `associate-r/` `un-div-inv` `*-commutative` `fma-udef`

Counts

4 → 169

Calls

4 calls:

96.0ms	(* (cbrt (/ 1 (- a t))) (/ 1 (cbrt (- a t))))
10.0ms	(cbrt (/ 1 (- a t)))
11.0ms	(cbrt (/ 1 (- a t)))
1.0ms	(fma (* (* (- z t) (* (cbrt (/ 1 (- a t))) (/ 1 (cbrt (- a t))))) (cbrt (/ 1 (- a t)))) (- y x) x)

series869.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(* (cbrt (/ 1 (- a t))) (/ 1 (cbrt (- a t))))
251.0ms	(cbrt (/ 1 (- a t)))
226.0ms	(cbrt (/ 1 (- a t)))
184.0ms	(fma (* (* (- z t) (* (cbrt (/ 1 (- a t))) (/ 1 (cbrt (- a t))))) (cbrt (/ 1 (- a t)))) (- y x) x)

simplify2.6s

Counts

181 → 181

Iterations

Iter	Nodes
done	5001
3	3332
2	1401
1	672
0	286

prune1.7s

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 4.7b

regimes1.3s

Accuracy

34.3% (5.5b remaining)

Error of 9.0b against oracle of 3.6b and baseline of 11.9b

bsearch4.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	35
1	35
0	26

end0.0ms

sample1.9s

Algorithm

intervals

Results

662.0ms	7782×	body	80	valid
551.0ms	518×	body	640	valid
102.0ms	376×	body	320	valid
87.0ms	288×	body	1280	valid
40.0ms	11×	body	2560	valid
30.0ms	251×	body	160	valid