Details

sample73.0ms

Algorithm

intervals

Results

31.0ms	89×	body	1280	valid
10.0ms	39×	body	640	valid
9.0ms	180×	body	80	valid
4.0ms	25×	body	320	valid
1.0ms	12×	body	160	valid

simplify3.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	11	6
2	18	6
3	27	6
4	51	6
5	116	6
6	273	6
7	807	6
8	2954	6
done	5000	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.8b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.1b	(- (exp (* a x)) 1.0)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
6×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `exp-prod` `flip3--` `exp-to-pow` `diff-log` `flip--` `rem-exp-log` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

5.0ms	(exp (* a x))
29.0ms	(- (exp (* a x)) 1.0)

series56.0ms

Counts

2 → 6

Calls

2 calls:

15.0ms	(exp (* a x))
42.0ms	(- (exp (* a x)) 1.0)

simplify2.3s

Counts

46 → 46

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	79	557
1	175	457
2	393	386
3	1277	346
done	5000	316

prune127.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.0b	(pow (- (exp (* a x)) 1.0) 3)
0.1b	(cbrt (pow (- (exp (* a x)) 1.0) 3))
3.1b	(- (exp (* a x)) 1.0)

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`cbrt-prod`
10×	`unpow-prod-down` `cube-prod`
9×	`prod-diff`
8×	`add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `flip3--` `fma-neg` `flip--`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `exp-prod` `exp-to-pow` `pow-pow` `pow1/3` `diff-log` `pow-exp` `rem-cbrt-cube` `rem-exp-log` `rem-cube-cbrt`

Counts

4 → 100

Calls

4 calls:

8.0ms	(exp (* a x))
39.0ms	(pow (- (exp (* a x)) 1.0) 3)
17.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
15.0ms	(- (exp (* a x)) 1.0)

series190.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(exp (* a x))
54.0ms	(pow (- (exp (* a x)) 1.0) 3)
61.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
60.0ms	(- (exp (* a x)) 1.0)

simplify987.0ms

Counts

112 → 112

Iterations

Useful iterations: done (984.0ms)

Iter	Nodes	Cost
0	146	1566
1	334	1253
2	910	1117
done	5000	1085

prune314.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.6b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (pow a 2))
0.1b	(* 1/6 (pow a 3))
8.1b	(fma (pow x 2) (fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2))) (* a x))
17.0b	(fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`associate-r`
14×	`add-exp-log`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `expm1-log1p-u` `cube-prod` `log1p-expm1-u` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unpow2`
1×	`cube-mult` `unpow3`

Counts

4 → 82

Calls

4 calls:

19.0ms	(* 1/2 (pow a 2))
27.0ms	(* 1/6 (pow a 3))
1.0ms	(fma (pow x 2) (fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2))) (* a x))
1.0ms	(fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* 1/2 (pow a 2))
40.0ms	(* 1/6 (pow a 3))
115.0ms	(fma (pow x 2) (fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2))) (* a x))
98.0ms	(fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2)))

simplify3.5s

Counts

94 → 94

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	137	1036
1	282	962
2	737	846
3	3838	827
done	5001	814

prune460.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.7b

localize9.0ms

Local error

Found 2 expressions with local error:

1.9b	(* x (fma 1/2 (* x (pow a 2)) a))
6.4b	(* x (pow a 2))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 51

Calls

2 calls:

13.0ms	(* x (fma 1/2 (* x (pow a 2)) a))
15.0ms	(* x (pow a 2))

series124.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(* x (fma 1/2 (* x (pow a 2)) a))
40.0ms	(* x (pow a 2))

simplify1.4s

Counts

57 → 57

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	87	574
1	179	546
2	437	469
3	1517	469
done	5001	466

prune124.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes230.0ms

Accuracy

76.3% (5.0b remaining)

Error of 5.3b against oracle of 0.3b and baseline of 21.5b

bsearch1.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	31
1	27	31
done	27	31

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.4s	2716×	body	1280	valid
301.0ms	1341×	body	640	valid
269.0ms	5450×	body	80	valid
102.0ms	779×	body	320	valid
77.0ms	376×	body	160	valid