Details

sample25.0ms

Algorithm

intervals

Results

7.0ms	244×	body	80	valid
2.0ms	18×	body	640	valid
1.0ms	16×	body	320	valid
1.0ms	8×	body	1280	valid
1.0ms	10×	body	160	valid
0.0ms	1×	body	2560	valid

simplify6.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	11	13
1	23	13
2	45	12
3	121	12
4	296	12
5	713	12
6	1457	12
7	2757	12
8	4493	12
done	5000	12

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.8b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
15.9b	(fma (/ (- t x) (- a z)) (- y z) x)

rewrite15.0ms

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:

12.0ms	(/ (- t x) (- a z))
0.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series126.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (- t x) (- a z))
79.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

simplify1.8s

Counts

70 → 70

Iterations

Useful iterations: 4 (984.0ms)

Iter	Nodes	Cost
0	118	918
1	269	890
2	628	838
3	1593	834
4	4635	828
done	5000	828

prune216.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.7b	(+ x (* (- y z) (/ (- t x) (- a z))))
5.7b	(* (- y z) (/ (- t x) (- a z)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 128

Calls

3 calls:

12.0ms	(/ (- t x) (- a z))
3.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
35.0ms	(* (- y z) (/ (- t x) (- a z)))

series323.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ (- t x) (- a z))
147.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
126.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify1.1s

Counts

137 → 137

Iterations

Useful iterations: 2 (270.0ms)

Iter	Nodes	Cost
0	189	1881
1	489	1769
2	1742	1659
done	5000	1659

prune357.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.8b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- t x))
0.5b	(/ 1 (/ (- a z) (- t x)))
15.9b	(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
195×	`add-sqr-sqrt` `*-un-lft-identity`
91×	`add-cube-cbrt`
52×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
6×	`flip3--` `flip--` `div-inv`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `div-sub` `fma-udef` `inv-pow`

Counts

3 → 214

Calls

3 calls:

12.0ms	(/ (- a z) (- t x))
15.0ms	(/ 1 (/ (- a z) (- t x)))
0.0ms	(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

series354.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ (- a z) (- t x))
187.0ms	(/ 1 (/ (- a z) (- t x)))
116.0ms	(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

simplify2.2s

Counts

223 → 223

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	274	3778
1	635	3266
2	1426	2943
3	4053	2863
done	5001	2860

prune386.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a z))
0.0b	(/ 1 (- t x))
0.3b	(/ (/ 1 (- a z)) (/ 1 (- t x)))
15.8b	(fma (/ (/ 1 (- a z)) (/ 1 (- t x))) (- y z) x)

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

1131×	`times-frac`
700×	`add-sqr-sqrt` `*-un-lft-identity`
420×	`add-cube-cbrt`
140×	`distribute-lft-out--` `difference-of-squares`
93×	`associate-/r/`
52×	`add-exp-log`
47×	`div-inv`
46×	`flip3--` `flip--`
36×	`div-exp`
31×	`associate-/r*`
27×	`associate-/l*`
20×	`add-cbrt-cube`
10×	`cbrt-undiv` `rec-exp` `1-exp`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`pow-flip` `inv-pow`
1×	`fma-udef` `associate-/l/`

Counts

4 → 613

Calls

4 calls:

6.0ms	(/ 1 (- a z))
6.0ms	(/ 1 (- t x))
28.0ms	(/ (/ 1 (- a z)) (/ 1 (- t x)))
1.0ms	(fma (/ (/ 1 (- a z)) (/ 1 (- t x))) (- y z) x)

series381.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ 1 (- a z))
33.0ms	(/ 1 (- t x))
196.0ms	(/ (/ 1 (- a z)) (/ 1 (- t x)))
119.0ms	(fma (/ (/ 1 (- a z)) (/ 1 (- t x))) (- y z) x)

simplify1.9s

Counts

625 → 625

Iterations

Useful iterations: 2 (1.4s)

Iter	Nodes	Cost
0	752	15072
1	2218	11230
2	4390	9992
done	5000	9992

prune624.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.8b

regimes357.0ms

Accuracy

22.6% (8.0b remaining)

Error of 12.3b against oracle of 4.2b and baseline of 14.6b

bsearch103.0ms

Steps

Iters	Range		Point
9	6.606479948802491e-148	7.906484867512465e-140	2.816956044142362e-147
8	-1.1766157657047581e-163	-1.090162501590038e-166	-9.166122526810648e-164

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	55
1	35	55
done	35	55

end0.0ms

sample667.0ms

Algorithm

intervals

Results

249.0ms	7829×	body	80	valid
55.0ms	490×	body	640	valid
40.0ms	283×	body	1280	valid
36.0ms	401×	body	320	valid
14.0ms	240×	body	160	valid
3.0ms	18×	body	2560	valid