Details

sample68.0ms

Algorithm

intervals

Results

28.0ms	84×	body	1280	valid
9.0ms	43×	body	640	valid
7.0ms	158×	body	80	valid
4.0ms	34×	body	320	valid
1.0ms	14×	body	160	valid

simplify3.8s

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	118	6
6	453	6
7	3607	6
done	5002	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.9b	(- (exp (* a x)) 1.0)

rewrite33.0ms

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:

4.0ms	(exp (* a x))
28.0ms	(- (exp (* a x)) 1.0)

series55.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(exp (* a x))
37.0ms	(- (exp (* a x)) 1.0)

simplify2.4s

Counts

46 → 46

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	79	557
1	183	460
2	598	386
3	3356	328
done	5000	325

prune136.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.7b

localize17.0ms

Local error

Found 3 expressions with local error:

0.3b	(* 1/6 (pow a 3))
9.8b	(fma (pow x 2) (fma x (* 1/6 (pow a 3)) (* 1/2 (pow a 2))) (* a x))
13.9b	(fma x (* 1/6 (pow a 3)) (* 1/2 (pow a 2)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

21.0ms	(* 1/6 (pow a 3))
0.0ms	(fma (pow x 2) (fma x (* 1/6 (pow a 3)) (* 1/2 (pow a 2))) (* a x))
0.0ms	(fma x (* 1/6 (pow a 3)) (* 1/2 (pow a 2)))

series321.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(* 1/6 (pow a 3))
111.0ms	(fma (pow x 2) (fma x (* 1/6 (pow a 3)) (* 1/2 (pow a 2))) (* a x))
159.0ms	(fma x (* 1/6 (pow a 3)) (* 1/2 (pow a 2)))

simplify754.0ms

Counts

62 → 62

Iterations

Useful iterations: done (752.0ms)

Iter	Nodes	Cost
0	94	792
1	216	745
2	815	669
done	5001	626

prune250.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* a a) (+ (* (* x 1/6) a) 1/2))
0.4b	(* x 1/6)
1.4b	(* x (+ a (* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x)))
7.5b	(* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x)

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1` `add-exp-log` `add-cbrt-cube`
15×	`add-sqr-sqrt`
12×	`associate-r`
11×	`pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-l`
6×	`associate-*r/`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `flip-+` `unswap-sqr`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/`

Counts

4 → 94

Calls

4 calls:

73.0ms	(* (* a a) (+ (* (* x 1/6) a) 1/2))
7.0ms	(* x 1/6)
16.0ms	(* x (+ a (* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x)))
138.0ms	(* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x)

series317.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (* a a) (+ (* (* x 1/6) a) 1/2))
23.0ms	(* x 1/6)
139.0ms	(* x (+ a (* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x)))
89.0ms	(* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x)

simplify2.9s

Counts

106 → 106

Iterations

Useful iterations: 2 (868.0ms)

Iter	Nodes	Cost
0	160	1663
1	513	1472
2	3967	1271
done	5000	1271

prune545.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.1b

localize42.0ms

Local error

Found 4 expressions with local error:

7.5b	(* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x)
18.7b	(cbrt (* x (+ a (* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x))))
18.7b	(cbrt (* x (+ a (* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x))))
18.7b	(cbrt (* x (+ a (* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x))))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`associate-*r/`
6×	`cbrt-div` `pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `associate-r`
2×	`associate-*l/`
1×	`associate-l` `*-commutative`

Counts

4 → 64

Calls

4 calls:

191.0ms	(* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x)
6.0ms	(cbrt (* x (+ a (* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x))))
6.0ms	(cbrt (* x (+ a (* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x))))
6.0ms	(cbrt (* x (+ a (* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x))))

series1.3s

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x)
395.0ms	(cbrt (* x (+ a (* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x))))
419.0ms	(cbrt (* x (+ a (* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x))))
410.0ms	(cbrt (* x (+ a (* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x))))

simplify2.7s

Counts

76 → 76

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	144	2170
1	439	1928
2	2829	1707
done	5002	1641

prune887.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.1b

regimes340.0ms

Accuracy

96.5% (0.8b remaining)

Error of 3.2b against oracle of 2.4b and baseline of 23.9b

bsearch1.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	33
1	31	33
done	31	33

end0.0ms

sample2.1s

Algorithm

intervals

Results

860.0ms	2748×	body	1280	valid
360.0ms	5280×	body	80	valid
243.0ms	1346×	body	640	valid
91.0ms	754×	body	320	valid
75.0ms	415×	body	160	valid