Details

sample127.0ms

Algorithm

intervals

Results

43.0ms	799×	body	80	nan
11.0ms	186×	body	80	valid
9.0ms	28×	body	640	valid
8.0ms	11×	body	1280	valid
4.0ms	23×	body	320	valid
1.0ms	11×	body	160	valid

simplify361.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	12	13
1	22	12
2	38	12
3	52	12
4	60	12
5	77	12
6	105	12
7	154	12
8	198	12
9	221	12
10	239	12
11	240	12
done	240	12

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(* z (log (- 1.0 y)))
0.3b	(fma x (log y) (* z (log (- 1.0 y))))
4.5b	(log (- 1.0 y))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`log-prod`
14×	`*-un-lft-identity`
8×	`add-cube-cbrt`
7×	`pow1`
6×	`add-exp-log`
5×	`distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
4×	`associate-r`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`log-div` `log-pow`
1×	`flip3--` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

3 → 59

Calls

3 calls:

15.0ms	(* z (log (- 1.0 y)))
0.0ms	(fma x (log y) (* z (log (- 1.0 y))))
6.0ms	(log (- 1.0 y))

series267.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(* z (log (- 1.0 y)))
118.0ms	(fma x (log y) (* z (log (- 1.0 y))))
51.0ms	(log (- 1.0 y))

simplify3.0s

Counts

68 → 68

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	148	786
1	325	751
2	771	672
3	1745	655
4	4610	646
done	5000	645

prune321.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma -1/2 (/ (* z (pow y 2)) (pow 1.0 2)) (* z (- (log 1.0) (* 1.0 y))))
0.2b	(fma x (log y) (fma -1/2 (/ (* z (pow y 2)) (pow 1.0 2)) (* z (- (log 1.0) (* 1.0 y)))))
6.9b	(* z (pow y 2))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`add-exp-log` `associate-r`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube`
4×	`unpow-prod-down` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `associate-l` `prod-exp` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef` `unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 49

Calls

3 calls:

0.0ms	(fma -1/2 (/ (* z (pow y 2)) (pow 1.0 2)) (* z (- (log 1.0) (* 1.0 y))))
1.0ms	(fma x (log y) (fma -1/2 (/ (* z (pow y 2)) (pow 1.0 2)) (* z (- (log 1.0) (* 1.0 y)))))
16.0ms	(* z (pow y 2))

series365.0ms

Counts

3 → 9

Calls

3 calls:

150.0ms	(fma -1/2 (/ (* z (pow y 2)) (pow 1.0 2)) (* z (- (log 1.0) (* 1.0 y))))
164.0ms	(fma x (log y) (fma -1/2 (/ (* z (pow y 2)) (pow 1.0 2)) (* z (- (log 1.0) (* 1.0 y)))))
51.0ms	(* z (pow y 2))

simplify1.2s

Counts

58 → 58

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	92	892
1	185	863
2	443	746
3	1476	739
done	5001	716

prune393.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize49.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma x (log y) (fma -1/2 (/ (* z (pow y 2)) (pow 1.0 2)) (* z (- (log 1.0) (* 1.0 y))))))
6.9b	(* z (pow y 2))
6.9b	(* z (pow y 2))
6.9b	(* z (pow y 2))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`associate-r`
19×	`add-exp-log`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `unswap-sqr`
10×	`add-cbrt-cube`
9×	`associate-l` `prod-exp`
6×	`unpow2` `sqr-pow`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`pow1/3`

Counts

4 → 100

Calls

4 calls:

1.0ms	(cbrt (fma x (log y) (fma -1/2 (/ (* z (pow y 2)) (pow 1.0 2)) (* z (- (log 1.0) (* 1.0 y))))))
16.0ms	(* z (pow y 2))
25.0ms	(* z (pow y 2))
25.0ms	(* z (pow y 2))

series1.3s

Counts

4 → 12

Calls

4 calls:

1.2s	(cbrt (fma x (log y) (fma -1/2 (/ (* z (pow y 2)) (pow 1.0 2)) (* z (- (log 1.0) (* 1.0 y))))))
32.0ms	(* z (pow y 2))
32.0ms	(* z (pow y 2))
39.0ms	(* z (pow y 2))

simplify1.5s

Counts

112 → 112

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	121	1263
1	253	1188
2	579	1037
3	1673	1027
done	5001	1004

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.2b

localize69.0ms

Local error

Found 4 expressions with local error:

6.9b	(* z (pow y 2))
6.9b	(* z (pow y 2))
6.9b	(* z (pow y 2))
6.9b	(* z (pow y 2))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
32×	`associate-r`
24×	`add-exp-log`
16×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity` `unswap-sqr`
12×	`associate-l` `prod-exp` `add-cbrt-cube`
8×	`unpow2` `sqr-pow`
4×	`pow1` `expm1-log1p-u` `pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`

Counts

4 → 116

Calls

4 calls:

18.0ms	(* z (pow y 2))
25.0ms	(* z (pow y 2))
33.0ms	(* z (pow y 2))
25.0ms	(* z (pow y 2))

series174.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* z (pow y 2))
49.0ms	(* z (pow y 2))
43.0ms	(* z (pow y 2))
40.0ms	(* z (pow y 2))

simplify3.8s

Counts

128 → 128

Iterations

Useful iterations: 4 (1.7s)

Iter	Nodes	Cost
0	53	976
1	109	884
2	237	752
3	672	752
4	3356	740
done	5001	740

prune902.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.2b

regimes312.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	25
1	22	25
done	22	25

end0.0ms

sample6.8s

Algorithm

intervals

Results

3.1s	24209×	body	80	nan
695.0ms	5516×	body	80	valid
483.0ms	900×	body	640	valid
423.0ms	446×	body	1280	valid
219.0ms	723×	body	320	valid
77.0ms	449×	body	160	valid