Details

sample55.0ms

Algorithm

intervals

Results

24.0ms	84×	body	1280	valid
6.0ms	39×	body	640	valid
5.0ms	166×	body	80	valid
2.0ms	23×	body	320	valid
1.0ms	18×	body	160	valid

simplify3.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	153
1	11	153
2	16	153
3	24	153
4	45	153
5	94	153
6	218	153
7	747	153
8	2971	153
done	5090	153

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize16.0ms

Local error

Found 2 expressions with local error:

0.1b	(exp (* a x))
5.2b	(- (exp (* a x)) 1.0)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 40

Calls

2 calls:

3.0ms	(exp (* a x))
14.0ms	(- (exp (* a x)) 1.0)

series67.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(exp (* a x))
43.0ms	(- (exp (* a x)) 1.0)

simplify1.8s

Counts

46 → 46

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	79	13351
1	182	10880
2	412	9103
3	1456	8983
done	5002	8415

prune175.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* a x) (* a x))
0.3b	(* (* a x) (* a x))
5.2b	(fma 1/2 (* (* a x) (* a x)) (* a x))
12.3b	(fma 1/6 (* (* a x) (* (* a x) (* a x))) (fma 1/2 (* (* a x) (* a x)) (* a x)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

82×	`pow1`
34×	`pow-prod-down`
28×	`add-cbrt-cube` `add-exp-log`
16×	`prod-exp` `cbrt-unprod`
8×	`pow-sqr` `pow-prod-up`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `pow-plus` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `swap-sqr` `associate-r` `associate-l` `*-commutative` `fma-udef`

Counts

4 → 92

Calls

4 calls:

46.0ms	(* (* a x) (* a x))
43.0ms	(* (* a x) (* a x))
1.0ms	(fma 1/2 (* (* a x) (* a x)) (* a x))
1.0ms	(fma 1/6 (* (* a x) (* (* a x) (* a x))) (fma 1/2 (* (* a x) (* a x)) (* a x)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (* a x) (* a x))
65.0ms	(* (* a x) (* a x))
85.0ms	(fma 1/2 (* (* a x) (* a x)) (* a x))
167.0ms	(fma 1/6 (* (* a x) (* (* a x) (* a x))) (fma 1/2 (* (* a x) (* a x)) (* a x)))

simplify4.8s

Counts

104 → 104

Iterations

Useful iterations: done (4.8s)

Iter	Nodes	Cost
0	74	20882
1	176	14121
2	683	12686
3	4103	12686
done	5001	12246

prune343.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (* (* a x) (* a x)) (fma 1/6 (* a x) 1/2) (* a x))
0.1b	(fma 1/6 (* a x) 1/2)
0.3b	(* (* a x) (* a x))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

42×	`pow1`
17×	`pow-prod-down`
15×	`add-cbrt-cube` `add-exp-log`
8×	`prod-exp` `cbrt-unprod`
4×	`pow-sqr` `pow-prod-up`
3×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
2×	`pow-plus` `fma-udef`
1×	`pow2` `swap-sqr` `associate-r` `associate-l` `*-commutative`

Counts

3 → 56

Calls

3 calls:

0.0ms	(fma (* (* a x) (* a x)) (fma 1/6 (* a x) 1/2) (* a x))
1.0ms	(fma 1/6 (* a x) 1/2)
44.0ms	(* (* a x) (* a x))

series252.0ms

Counts

3 → 9

Calls

3 calls:

137.0ms	(fma (* (* a x) (* a x)) (fma 1/6 (* a x) 1/2) (* a x))
61.0ms	(fma 1/6 (* a x) 1/2)
54.0ms	(* (* a x) (* a x))

simplify4.0s

Counts

65 → 65

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	74	13368
1	170	9431
2	677	8526
3	4053	8446
done	5000	8446

prune306.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (* (* (- (exp (* a x)) 1.0) (- (exp (* a x)) 1.0)) (- (exp (* a x)) 1.0)))
5.2b	(- (exp (* a x)) 1.0)
5.2b	(- (exp (* a x)) 1.0)
5.2b	(- (exp (* a x)) 1.0)

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`flip3--` `flip--`
28×	`frac-times`
27×	`prod-diff`
26×	`cbrt-div`
25×	`add-cube-cbrt`
14×	`associate-*l/`
10×	`add-log-exp`
9×	`fma-neg`
8×	`associate-*r/`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`sub-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 122

Calls

4 calls:

87.0ms	(cbrt (* (* (- (exp (* a x)) 1.0) (- (exp (* a x)) 1.0)) (- (exp (* a x)) 1.0)))
16.0ms	(- (exp (* a x)) 1.0)
21.0ms	(- (exp (* a x)) 1.0)
15.0ms	(- (exp (* a x)) 1.0)

series202.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(cbrt (* (* (- (exp (* a x)) 1.0) (- (exp (* a x)) 1.0)) (- (exp (* a x)) 1.0)))
59.0ms	(- (exp (* a x)) 1.0)
45.0ms	(- (exp (* a x)) 1.0)
52.0ms	(- (exp (* a x)) 1.0)

simplify2.8s

Counts

134 → 134

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	169	67259
1	376	53553
2	1368	48267
done	5004	46091

prune632.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes325.0ms

Accuracy

98.3% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 20.8b

bsearch1.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	612
1	20	612
done	20	612

end0.0ms

sample2.3s

Algorithm

intervals

Results

828.0ms	2704×	body	1280	valid
730.0ms	5420×	body	80	valid
254.0ms	1353×	body	640	valid
95.0ms	794×	body	320	valid
35.0ms	391×	body	160	valid