Details

sample59.0ms

Algorithm

intervals

Results

17.0ms	244×	body	80	valid
5.0ms	18×	body	640	valid
3.0ms	11×	body	1280	valid
2.0ms	9×	body	320	valid
1.0ms	11×	body	160	valid

simplify3.6s

Counts

1 → 1

Iterations

Useful iterations: 3 (26.0ms)

Iter	Nodes	Cost
0	11	13
1	20	13
2	45	13
3	116	12
4	326	12
5	1014	12
6	4061	12
done	5000	12

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.5b

localize28.0ms

Local error

Found 2 expressions with local error:

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

rewrite63.0ms

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:

57.0ms	(/ (- y z) (- a z))
1.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

series310.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(/ (- y z) (- a z))
223.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify3.3s

Counts

70 → 70

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	116	918
1	271	890
2	855	840
3	4496	834
done	5000	834

prune640.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.8b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
0.9b	(* (/ (- y z) (- a z)) (- t x))
3.3b	(+ (* (/ (- y z) (- a z)) (- t x)) x)

rewrite245.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-sqr-sqrt`
97×	`*-un-lft-identity`
51×	`add-cube-cbrt` `times-frac`
36×	`prod-diff`
31×	`associate-l`
23×	`distribute-lft-out--` `difference-of-squares`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-r` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`sub-neg` `associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `fma-def` `frac-2neg` `flip3-+` `div-sub` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 170

Calls

3 calls:

46.0ms	(/ (- y z) (- a z))
126.0ms	(* (/ (- y z) (- a z)) (- t x))
58.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)

series987.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(/ (- y z) (- a z))
554.0ms	(* (/ (- y z) (- a z)) (- t x))
334.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)

simplify2.5s

Counts

179 → 179

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	255	3085
1	716	2731
2	3222	2494
done	5000	2468

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.8b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- y z) (- a z))
0.0b	(/ (- y z) (- a z))
0.8b	(* t (/ (- y z) (- a z)))
3.5b	(fma (/ (- y z) (- a z)) (- x) x)

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
76×	`times-frac`
40×	`add-cube-cbrt`
34×	`distribute-lft-out--` `difference-of-squares`
31×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r` `associate-/l`
6×	`pow1` `associate-/r/`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`frac-2neg` `div-sub` `prod-exp` `clear-num` `cbrt-unprod` `unswap-sqr`
1×	`associate-r/` `pow-prod-down` `-commutative` `fma-udef`

Counts

4 → 170

Calls

4 calls:

46.0ms	(/ (- y z) (- a z))
43.0ms	(/ (- y z) (- a z))
91.0ms	(* t (/ (- y z) (- a z)))
1.0ms	(fma (/ (- y z) (- a z)) (- x) x)

series496.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (- y z) (- a z))
84.0ms	(/ (- y z) (- a z))
129.0ms	(* t (/ (- y z) (- a z)))
186.0ms	(fma (/ (- y z) (- a z)) (- x) x)

simplify1.3s

Counts

182 → 182

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	157	2244
1	406	2155
2	1597	2021
done	5000	2015

prune1.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.8b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- y z) (- a z))
0.1b	(/ 1 (/ (- a z) (- y z)))
0.8b	(* t (/ (- y z) (- a z)))
3.5b	(fma (/ 1 (/ (- a z) (- y z))) (- x) x)

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

244×	`times-frac`
233×	`add-sqr-sqrt`
228×	`*-un-lft-identity`
104×	`add-cube-cbrt`
62×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
31×	`associate-r`
22×	`add-exp-log`
16×	`add-cbrt-cube`
13×	`associate-/r/`
9×	`div-exp`
8×	`associate-/l*`
7×	`pow1` `flip3--` `flip--` `div-inv`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
2×	`rec-exp` `frac-2neg` `1-exp` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`pow-flip` `div-sub` `associate-r/` `pow-prod-down` `-commutative` `fma-udef` `inv-pow`

Counts

4 → 266

Calls

4 calls:

48.0ms	(/ (- y z) (- a z))
58.0ms	(/ 1 (/ (- a z) (- y z)))
102.0ms	(* t (/ (- y z) (- a z)))
1.0ms	(fma (/ 1 (/ (- a z) (- y z))) (- x) x)

series692.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (- y z) (- a z))
263.0ms	(/ 1 (/ (- a z) (- y z)))
130.0ms	(* t (/ (- y z) (- a z)))
208.0ms	(fma (/ 1 (/ (- a z) (- y z))) (- x) x)

simplify3.5s

Counts

278 → 278

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	350	4388
1	919	3843
2	4707	3612
done	5001	3602

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.8b

regimes899.0ms

Accuracy

6.7% (4.1b remaining)

Error of 7.6b against oracle of 3.5b and baseline of 7.9b

bsearch233.0ms

Steps

Iters	Range		Point
9	1.363931741773715e-218	8.197993687946751e-213	1.3751750426910988e-213
10	-5.4135962025315565e-166	-5.143081329042359e-179	-9.207084913440813e-179

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	25	69
1	34	45
done	34	45

end0.0ms

sample2.1s

Algorithm

intervals

Results

820.0ms	7718×	body	80	valid
174.0ms	499×	body	640	valid
140.0ms	286×	body	1280	valid
89.0ms	292×	body	160	valid
85.0ms	395×	body	320	valid
7.0ms	16×	body	2560	valid