Details

sample94.0ms

Algorithm

intervals

Results

33.0ms	71×	body	1280	valid
25.0ms	75×	body	10240	exit
12.0ms	45×	body	640	valid
7.0ms	36×	body	320	valid
5.0ms	91×	body	80	valid
2.0ms	13×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
2	11
1	10
0	5

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.9b

localize15.0ms

Local error

Found 2 expressions with local error:

1.0b	(/ (exp x) (- (exp x) 1))
4.7b	(- (exp x) 1)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
21×	`times-frac`
14×	`add-cube-cbrt`
10×	`difference-of-squares`
7×	`associate-/r*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `insert-posit16` `flip--`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

2 → 63

Calls

2 calls:

22.0ms	(/ (exp x) (- (exp x) 1))
14.0ms	(- (exp x) 1)

series71.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(/ (exp x) (- (exp x) 1))
34.0ms	(- (exp x) 1)

simplify2.0s

Counts

69 → 69

Iterations

Iter	Nodes
done	5010
3	1632
2	502
1	203
0	101

prune243.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.9b

localize27.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
0.4b	(* 1/12 x)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-log-exp`
6×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`sum-log` `associate-r` `associate-l`
2×	`insert-posit16`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

2 → 33

Calls

2 calls:

43.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
11.0ms	(* 1/12 x)

series59.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
30.0ms	(* 1/12 x)

simplify1.8s

Counts

39 → 39

Iterations

Iter	Nodes
done	5006
3	1777
2	480
1	156
0	60

prune119.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.9b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp x) (+ 1 (exp x)))
0.8b	(/ (exp x) (/ (- (exp (* 3 x)) 1) (+ (* (exp x) (+ 1 (exp x))) 1)))
0.9b	(/ (- (exp (* 3 x)) 1) (+ (* (exp x) (+ 1 (exp x))) 1))
5.1b	(- (exp (* 3 x)) 1)

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
160×	`add-sqr-sqrt`
143×	`*-un-lft-identity`
90×	`add-cube-cbrt`
34×	`difference-of-squares`
30×	`associate-/r*`
17×	`difference-of-sqr-1` `distribute-lft-out--`
13×	`add-cbrt-cube`
11×	`associate-/r/`
10×	`add-exp-log` `associate-/l*`
6×	`pow1` `flip3-+` `flip-+` `div-inv` `add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-r` `insert-posit16`
3×	`associate-l`
2×	`clear-num` `frac-2neg` `flip3--` `associate-*r/` `flip--` `associate-/l/`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `diff-log` `div-sub` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

4 → 217

Calls

4 calls:

24.0ms	(* (exp x) (+ 1 (exp x)))
47.0ms	(/ (exp x) (/ (- (exp (* 3 x)) 1) (+ (* (exp x) (+ 1 (exp x))) 1)))
69.0ms	(/ (- (exp (* 3 x)) 1) (+ (* (exp x) (+ 1 (exp x))) 1))
11.0ms	(- (exp (* 3 x)) 1)

series220.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (exp x) (+ 1 (exp x)))
89.0ms	(/ (exp x) (/ (- (exp (* 3 x)) 1) (+ (* (exp x) (+ 1 (exp x))) 1)))
72.0ms	(/ (- (exp (* 3 x)) 1) (+ (* (exp x) (+ 1 (exp x))) 1))
24.0ms	(- (exp (* 3 x)) 1)

simplify3.0s

Counts

229 → 229

Iterations

Iter	Nodes
done	5023
2	3393
1	910
0	325

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
0.0b	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
0.4b	(* 1/12 x)
2.1b	(exp (log (+ (* 1/12 x) (+ (/ 1 x) 1/2))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
8×	`pow1`
7×	`add-exp-log`
6×	`log-prod` `add-cbrt-cube`
4×	`log-div` `exp-prod` `insert-posit16`
3×	`sum-log` `flip3-+` `associate-r` `associate-l` `exp-sum` `flip-+`
2×	`exp-diff` `log-pow`
1×	`+-commutative` `associate-+r+` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`

Counts

4 → 66

Calls

4 calls:

20.0ms	(log (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
32.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
11.0ms	(* 1/12 x)
28.0ms	(exp (log (+ (* 1/12 x) (+ (/ 1 x) 1/2))))

series105.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(log (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
26.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
16.0ms	(* 1/12 x)
22.0ms	(exp (log (+ (* 1/12 x) (+ (/ 1 x) 1/2))))

simplify2.0s

Counts

78 → 78

Iterations

Iter	Nodes
done	5002
3	2977
2	711
1	264
0	118

prune291.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.9b

regimes86.0ms

Accuracy

99% (0.2b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 20.6b

bsearch52.0ms

Steps

Iters	Range		Point
9	-101227.54480913779	-0.0005350557287305616	-0.0014285877116162612

simplify7.0ms

Iterations

Iter	Nodes
done	30
1	30
0	21

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.1s	2262×	body	1280	valid
1.0s	2513×	body	10240	exit
632.0ms	2763×	body	80	valid
484.0ms	1624×	body	640	valid
233.0ms	891×	body	320	valid
59.0ms	460×	body	160	valid