Details

sample59.0ms

Algorithm

intervals

Results

22.0ms	89×	body	1280	valid
8.0ms	39×	body	640	valid
6.0ms	180×	body	80	valid
4.0ms	25×	body	320	valid
1.0ms	12×	body	160	valid

simplify3.4s

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

prune4.0ms

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)

rewrite41.0ms

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:

8.0ms	(exp (* a x))
31.0ms	(- (exp (* a x)) 1.0)

series82.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(exp (* a x))
58.0ms	(- (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

prune131.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.6b

localize9.0ms

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)

rewrite71.0ms

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:

4.0ms	(exp (* a x))
21.0ms	(pow (- (exp (* a x)) 1.0) 3)
28.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
15.0ms	(- (exp (* a x)) 1.0)

series183.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(exp (* a x))
73.0ms	(pow (- (exp (* a x)) 1.0) 3)
47.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
48.0ms	(- (exp (* a x)) 1.0)

simplify821.0ms

Counts

112 → 112

Iterations

Useful iterations: done (810.0ms)

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

prune677.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/6 (pow a 3))
5.8b	(* (* 1/6 (pow a 3)) x)
11.9b	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))
12.3b	(* (pow x 2) (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
24×	`add-exp-log`
18×	`associate-r`
13×	`prod-exp` `add-cbrt-cube`
12×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
8×	`unpow-prod-down` `unswap-sqr`
6×	`pow1` `add-log-exp`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `cube-prod` `log1p-expm1-u` `sqr-pow`
3×	`pow-to-exp` `pow-exp` `*-commutative`
2×	`flip3-+` `associate-*r/` `flip-+` `unpow2`
1×	`+-commutative` `distribute-rgt-in` `cube-mult` `fma-def` `distribute-lft-in` `unpow3` `pow-prod-down` `sum-log`

Counts

4 → 101

Calls

4 calls:

15.0ms	(* 1/6 (pow a 3))
46.0ms	(* (* 1/6 (pow a 3)) x)
31.0ms	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))
124.0ms	(* (pow x 2) (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))

series431.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* 1/6 (pow a 3))
37.0ms	(* (* 1/6 (pow a 3)) x)
116.0ms	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))
211.0ms	(* (pow x 2) (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))

simplify1.8s

Counts

113 → 113

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	156	1654
1	426	1463
2	1748	1314
done	5001	1313

prune512.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.5b

localize23.0ms

Local error

Found 4 expressions with local error:

3.7b	(* (pow x (/ 2 2)) (* x (fma 1/2 (* a a) (* 1/6 (* (pow a 3) x)))))
5.5b	(* x (fma 1/2 (* a a) (* 1/6 (* (pow a 3) x))))
5.8b	(* (pow a 3) x)
12.0b	(fma 1/2 (* a a) (* 1/6 (* (pow a 3) x)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
22×	`associate-l`
21×	`add-sqr-sqrt`
13×	`prod-exp` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
7×	`unpow-prod-down` `associate-r` `fma-udef`
6×	`pow1`
5×	`distribute-rgt-in` `distribute-lft-in` `cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `cube-prod` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-exp` `*-commutative` `sqr-pow`
1×	`cube-mult` `unpow3` `pow-prod-down`

Counts

4 → 95

Calls

4 calls:

38.0ms	(* (pow x (/ 2 2)) (* x (fma 1/2 (* a a) (* 1/6 (* (pow a 3) x)))))
7.0ms	(* x (fma 1/2 (* a a) (* 1/6 (* (pow a 3) x))))
15.0ms	(* (pow a 3) x)
0.0ms	(fma 1/2 (* a a) (* 1/6 (* (pow a 3) x)))

series465.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(* (pow x (/ 2 2)) (* x (fma 1/2 (* a a) (* 1/6 (* (pow a 3) x)))))
164.0ms	(* x (fma 1/2 (* a a) (* 1/6 (* (pow a 3) x))))
46.0ms	(* (pow a 3) x)
84.0ms	(fma 1/2 (* a a) (* 1/6 (* (pow a 3) x)))

simplify1.5s

Counts

107 → 107

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	145	1762
1	339	1559
2	1082	1344
done	5000	1343

prune478.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.7b

regimes320.0ms

Accuracy

75.2% (5.3b remaining)

Error of 8.0b against oracle of 2.7b and baseline of 24.0b

bsearch1.0ms

simplify9.0ms

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	22	37
1	28	35
2	30	33
done	30	33

end0.0ms

sample1.9s

Algorithm

intervals

Results

778.0ms	2716×	body	1280	valid
332.0ms	1341×	body	640	valid
291.0ms	5450×	body	80	valid
90.0ms	779×	body	320	valid
30.0ms	376×	body	160	valid