Details

sample125.0ms

Algorithm

intervals

Results

43.0ms	758×	body	80	nan
17.0ms	167×	body	80	valid
10.0ms	16×	body	1280	valid
10.0ms	28×	body	640	valid
6.0ms	27×	body	320	valid
2.0ms	19×	body	160	valid

simplify367.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (fma x (log y) (* z (log (- 1.0 y)))) t)
0.0b	(* z (log (- 1.0 y)))
0.2b	(fma x (log y) (* z (log (- 1.0 y))))
6.3b	(log (- 1.0 y))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

13.0ms	(- (fma x (log y) (* z (log (- 1.0 y)))) t)
29.0ms	(* z (log (- 1.0 y)))
1.0ms	(fma x (log y) (* z (log (- 1.0 y))))
12.0ms	(log (- 1.0 y))

series432.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(- (fma x (log y) (* z (log (- 1.0 y)))) t)
107.0ms	(* z (log (- 1.0 y)))
129.0ms	(fma x (log y) (* z (log (- 1.0 y))))
61.0ms	(log (- 1.0 y))

simplify2.4s

Counts

100 → 100

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	204	1528
1	458	1378
2	1069	1218
3	2848	1112
done	5000	1079

prune327.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma x (log y) (fma z (- (log 1.0) (* 1.0 y)) (* (/ (* z (pow y 2)) (pow 1.0 2)) -1/2)))
8.7b	(* z (pow y 2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 39

Calls

2 calls:

1.0ms	(fma x (log y) (fma z (- (log 1.0) (* 1.0 y)) (* (/ (* z (pow y 2)) (pow 1.0 2)) -1/2)))
19.0ms	(* z (pow y 2))

series195.0ms

Counts

2 → 6

Calls

2 calls:

163.0ms	(fma x (log y) (fma z (- (log 1.0) (* 1.0 y)) (* (/ (* z (pow y 2)) (pow 1.0 2)) -1/2)))
32.0ms	(* z (pow y 2))

simplify1.3s

Counts

45 → 45

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	82	587
1	174	561
2	418	482
3	1305	478
done	5000	467

prune481.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma x (log y) (fma z (- (log 1.0) (* 1.0 y)) (* (/ (* z (pow y 2)) (pow 1.0 2)) -1/2))))
8.7b	(* z (pow y 2))
8.7b	(* z (pow y 2))
8.7b	(* z (pow y 2))

rewrite55.0ms

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 z (- (log 1.0) (* 1.0 y)) (* (/ (* z (pow y 2)) (pow 1.0 2)) -1/2))))
14.0ms	(* z (pow y 2))
12.0ms	(* 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 z (- (log 1.0) (* 1.0 y)) (* (/ (* z (pow y 2)) (pow 1.0 2)) -1/2))))
38.0ms	(* z (pow y 2))
46.0ms	(* z (pow y 2))
37.0ms	(* z (pow y 2))

simplify1.4s

Counts

112 → 112

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	121	1263
1	255	1188
2	592	1037
3	1724	1027
done	5000	1004

prune770.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

8.7b	(* z (pow y 2))
8.7b	(* z (pow y 2))
8.7b	(* z (pow y 2))
8.7b	(* z (pow y 2))

rewrite61.0ms

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:

12.0ms	(* z (pow y 2))
20.0ms	(* z (pow y 2))
12.0ms	(* z (pow y 2))
12.0ms	(* z (pow y 2))

series139.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* z (pow y 2))
39.0ms	(* z (pow y 2))
36.0ms	(* z (pow y 2))
32.0ms	(* z (pow y 2))

simplify3.3s

Counts

128 → 128

Iterations

Useful iterations: 4 (1.3s)

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

prune941.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

regimes184.0ms

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

sample6.2s

Algorithm

intervals

Results

3.2s	24052×	body	80	nan
598.0ms	5518×	body	80	valid
409.0ms	862×	body	640	valid
389.0ms	416×	body	1280	valid
237.0ms	749×	body	320	valid
126.0ms	495×	body	160	valid