Details

sample30.0ms

Algorithm

intervals

Results

12.0ms	76×	body	1280	valid
6.0ms	55×	body	640	valid
3.0ms	167×	body	80	valid
1.0ms	19×	body	320	valid
1.0ms	19×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	5	6
1	10	6
2	13	6
3	15	6
done	15	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.2b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.9b	(- (exp x) 1.0)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

11.0ms	(/ (- (exp x) 1.0) x)
4.0ms	(- (exp x) 1.0)

series56.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ (- (exp x) 1.0) x)
15.0ms	(- (exp x) 1.0)

simplify1.1s

Counts

58 → 58

Iterations

Useful iterations: 3 (227.0ms)

Iter	Nodes	Cost
0	99	596
1	221	572
2	607	542
3	2390	537
done	5000	537

prune116.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 2 expressions with local error:

0.1b	(* x (+ 1/2 (* 1/6 x)))
0.4b	(* 1/6 x)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*` `add-cbrt-cube`
2×	`associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `add-log-exp` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+`

Counts

2 → 40

Calls

2 calls:

7.0ms	(* x (+ 1/2 (* 1/6 x)))
3.0ms	(* 1/6 x)

series74.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(* x (+ 1/2 (* 1/6 x)))
14.0ms	(* 1/6 x)

simplify2.6s

Counts

46 → 46

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	70	356
1	189	328
2	746	298
3	3213	298
done	5001	298

prune73.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* x (+ 1/2 (* 1/6 x))))
0.1b	(* x (+ 1/2 (* 1/6 x)))
0.4b	(* 1/6 x)
5.0b	(log (exp (* x (+ 1/2 (* 1/6 x)))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`associate-r` `associate-l`
5×	`log-prod`
4×	`exp-sum`
3×	`distribute-rgt-in` `distribute-lft-in` `log-pow`
2×	`exp-prod` `exp-to-pow` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`flip3-+` `rem-log-exp` `flip-+` `rem-exp-log`

Counts

4 → 68

Calls

4 calls:

2.0ms	(exp (* x (+ 1/2 (* 1/6 x))))
7.0ms	(* x (+ 1/2 (* 1/6 x)))
3.0ms	(* 1/6 x)
2.0ms	(log (exp (* x (+ 1/2 (* 1/6 x)))))

series146.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(exp (* x (+ 1/2 (* 1/6 x))))
58.0ms	(* x (+ 1/2 (* 1/6 x)))
14.0ms	(* 1/6 x)
59.0ms	(log (exp (* x (+ 1/2 (* 1/6 x)))))

simplify2.9s

Counts

80 → 80

Iterations

Useful iterations: 3 (460.0ms)

Iter	Nodes	Cost
0	105	722
1	240	648
2	860	579
3	3758	577
done	5001	577

prune156.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) x)
4.1b	(- (/ (exp x) x) (/ 1.0 x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
19×	`times-frac`
12×	`add-cube-cbrt`
4×	`add-cbrt-cube` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`add-exp-log` `associate-/r` `div-inv` `associate-/l`
2×	`pow1`
1×	`cbrt-undiv` `sub-neg` `flip3--` `distribute-rgt-out--` `frac-2neg` `diff-log` `div-exp` `clear-num` `frac-sub` `flip--` `sub-div`

Counts

2 → 50

Calls

2 calls:

3.0ms	(/ (exp x) x)
19.0ms	(- (/ (exp x) x) (/ 1.0 x))

series75.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(/ (exp x) x)
46.0ms	(- (/ (exp x) x) (/ 1.0 x))

simplify1.1s

Counts

56 → 56

Iterations

Useful iterations: 3 (220.0ms)

Iter	Nodes	Cost
0	105	581
1	217	530
2	593	507
3	2198	505
done	5001	505

prune101.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes23.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 22.1b

bsearch21.0ms

Steps

Iters	Range		Point
7	-0.0009113054925467739	-1.3606912768451591e-05	-0.00019061484402488725

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	23
1	24	23
done	24	23

end0.0ms

sample859.0ms

Algorithm

intervals

Results

385.0ms	2306×	body	1280	valid
165.0ms	1617×	body	640	valid
105.0ms	5519×	body	80	valid
52.0ms	798×	body	320	valid
17.0ms	391×	body	160	valid