Details

sample57.0ms

Algorithm

intervals

Results

15.0ms	85×	body	10240	exit
14.0ms	63×	body	1280	valid
10.0ms	69×	body	640	valid
3.0ms	92×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	13×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
2	8
1	7
0	5

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.7b

localize11.0ms

Local error

Found 2 expressions with local error:

0.7b	(/ (exp x) (- (exp x) 1.0))
3.0b	(- (exp x) 1.0)

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 51

Calls

2 calls:

23.0ms	(/ (exp x) (- (exp x) 1.0))
13.0ms	(- (exp x) 1.0)

series69.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (exp x) (- (exp x) 1.0))
24.0ms	(- (exp x) 1.0)

simplify1.3s

Counts

57 → 57

Iterations

Iter	Nodes
done	5002
3	1479
2	540
1	191
0	91

prune217.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite67.0ms

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`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

2 → 31

Calls

2 calls:

56.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
9.0ms	(* 1/12 x)

series45.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
27.0ms	(* 1/12 x)

simplify1.4s

Counts

37 → 37

Iterations

Iter	Nodes
done	5002
3	1810
2	477
1	154
0	58

prune140.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (* 1/12 (sqrt x)) (sqrt x)) (+ (/ 1 x) 1/2))
0.1b	(* 1/12 (sqrt x))
0.2b	(* (* 1/12 (sqrt x)) (sqrt x))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 56

Calls

3 calls:

64.0ms	(+ (* (* 1/12 (sqrt x)) (sqrt x)) (+ (/ 1 x) 1/2))
12.0ms	(* 1/12 (sqrt x))
26.0ms	(* (* 1/12 (sqrt x)) (sqrt x))

series133.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(+ (* (* 1/12 (sqrt x)) (sqrt x)) (+ (/ 1 x) 1/2))
59.0ms	(* 1/12 (sqrt x))
27.0ms	(* (* 1/12 (sqrt x)) (sqrt x))

simplify3.3s

Counts

65 → 65

Iterations

Iter	Nodes
done	5013
3	4442
2	1029
1	295
0	104

prune246.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `pow1` `add-log-exp`
6×	`add-cube-cbrt`
5×	`exp-prod` `add-cbrt-cube` `add-exp-log` `distribute-lft-out`
3×	`sum-log` `associate-r` `associate-l`
2×	`pow-prod-down` `log-pow`
1×	`+-commutative` `associate-+r+` `log-prod` `flip3-+` `exp-sum` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr` `rem-exp-log`

Counts

3 → 48

Calls

3 calls:

65.0ms	(+ (exp (log (* 1/12 x))) (+ (/ 1 x) 1/2))
10.0ms	(* 1/12 x)
18.0ms	(exp (log (* 1/12 x)))

series71.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (exp (log (* 1/12 x))) (+ (/ 1 x) 1/2))
25.0ms	(* 1/12 x)
19.0ms	(exp (log (* 1/12 x)))

simplify1.6s

Counts

57 → 57

Iterations

Iter	Nodes
done	5012
3	1951
2	522
1	182
0	75

prune244.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.7b

regimes160.0ms

Accuracy

97.8% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 21.7b

bsearch1.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	34
1	34
0	23

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.1s	2547×	body	10240	exit
716.0ms	2251×	body	1280	valid
299.0ms	1626×	body	640	valid
139.0ms	833×	body	320	valid
138.0ms	2888×	body	80	valid
31.0ms	402×	body	160	valid