Details

sample71.0ms

Algorithm

intervals

Results

25.0ms	88×	body	1280	valid
21.0ms	90×	body	10240	exit
9.0ms	50×	body	640	valid
4.0ms	31×	body	320	valid
3.0ms	79×	body	80	valid
1.0ms	9×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
2	11
1	10
0	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.7b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) (- (exp x) 1))
3.3b	(- (exp x) 1)

rewrite38.0ms

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:

28.0ms	(/ (exp x) (- (exp x) 1))
9.0ms	(- (exp x) 1)

series43.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(/ (exp x) (- (exp x) 1))
16.0ms	(- (exp x) 1)

simplify1.3s

Counts

69 → 69

Iterations

Iter	Nodes
done	2018
3	1632
2	502
1	203
0	101

prune213.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (/ 1 x) 1/2)
0.0b	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
0.3b	(* 1/12 x)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 47

Calls

3 calls:

10.0ms	(+ (/ 1 x) 1/2)
35.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
9.0ms	(* 1/12 x)

series60.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(+ (/ 1 x) 1/2)
21.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
16.0ms	(* 1/12 x)

simplify483.0ms

Counts

56 → 56

Iterations

Iter	Nodes
done	2004
2	723
1	210
0	76

prune171.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 1)
0.0b	(* (exp x) (exp x))
0.0b	(/ (exp x) (/ (- (exp (+ (+ x x) x)) 1) (+ (+ (exp x) 1) (* (exp x) (exp x)))))
3.2b	(- (exp (+ (+ x x) x)) 1)

rewrite511.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac`
140×	`add-sqr-sqrt`
127×	`*-un-lft-identity`
86×	`add-cube-cbrt`
27×	`associate-/r*`
26×	`difference-of-squares`
18×	`exp-prod`
13×	`difference-of-sqr-1` `distribute-lft-out--`
11×	`pow1` `add-cbrt-cube`
9×	`associate-/r/`
8×	`add-log-exp`
7×	`add-exp-log`
5×	`flip3-+` `flip-+` `div-inv`
4×	`pow-prod-down` `pow-sqr` `pow-prod-up` `insert-posit16`
3×	`cbrt-undiv` `swap-sqr` `div-exp` `associate-r` `associate-l` `associate-/l*`
1×	`pow2` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `pow-plus` `flip3--` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `distribute-lft-out` `unswap-sqr`

Counts

4 → 192

Calls

4 calls:

8.0ms	(+ (exp x) 1)
24.0ms	(* (exp x) (exp x))
264.0ms	(/ (exp x) (/ (- (exp (+ (+ x x) x)) 1) (+ (+ (exp x) 1) (* (exp x) (exp x)))))
211.0ms	(- (exp (+ (+ x x) x)) 1)

series128.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (exp x) 1)
17.0ms	(* (exp x) (exp x))
77.0ms	(/ (exp x) (/ (- (exp (+ (+ x x) x)) 1) (+ (+ (exp x) 1) (* (exp x) (exp x)))))
20.0ms	(- (exp (+ (+ x x) x)) 1)

simplify996.0ms

Counts

204 → 204

Iterations

Iter	Nodes
done	2000
1	901
0	328

prune922.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp x) (exp x))
0.0b	(* (exp (+ (+ x x) x)) (exp (+ (+ x x) x)))
0.0b	(/ (exp x) (/ (/ (- (* (exp (+ (+ x x) x)) (exp (+ (+ x x) x))) (* 1 1)) (+ (exp (+ (+ x x) x)) 1)) (+ (+ (exp x) 1) (* (exp x) (exp x)))))
3.1b	(- (* (exp (+ (+ x x) x)) (exp (+ (+ x x) x))) (* 1 1))

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

672×	`times-frac`
589×	`*-un-lft-identity`
373×	`add-sqr-sqrt`
315×	`add-cube-cbrt`
190×	`exp-prod`
150×	`distribute-lft-out`
72×	`associate-/r*`
66×	`distribute-lft1-in`
50×	`distribute-rgt-out`
49×	`difference-of-squares`
35×	`pow-prod-down` `pow-prod-up`
33×	`associate-/r/`
31×	`pow-sqr`
28×	`distribute-rgt1-in`
20×	`count-2`
18×	`pow1`
17×	`add-cbrt-cube` `div-inv`
16×	`flip3-+` `flip-+`
10×	`add-exp-log`
7×	`swap-sqr` `associate-r` `associate-l`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`exp-sum` `insert-posit16`
3×	`associate-/l*`
2×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `flip--`

Counts

4 → 473

Calls

4 calls:

29.0ms	(* (exp x) (exp x))
614.0ms	(* (exp (+ (+ x x) x)) (exp (+ (+ x x) x)))
1.1s	(/ (exp x) (/ (/ (- (* (exp (+ (+ x x) x)) (exp (+ (+ x x) x))) (* 1 1)) (+ (exp (+ (+ x x) x)) 1)) (+ (+ (exp x) 1) (* (exp x) (exp x)))))
432.0ms	(- (* (exp (+ (+ x x) x)) (exp (+ (+ x x) x))) (* 1 1))

series251.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (exp x) (exp x))
33.0ms	(* (exp (+ (+ x x) x)) (exp (+ (+ x x) x)))
154.0ms	(/ (exp x) (/ (/ (- (* (exp (+ (+ x x) x)) (exp (+ (+ x x) x))) (* 1 1)) (+ (exp (+ (+ x x) x)) 1)) (+ (+ (exp x) 1) (* (exp x) (exp x)))))
41.0ms	(- (* (exp (+ (+ x x) x)) (exp (+ (+ x x) x))) (* 1 1))

simplify1.5s

Counts

485 → 485

Iterations

Iter	Nodes
done	2001
0	756

prune2.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes36.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 20.9b

bsearch72.0ms

Steps

Iters	Range		Point
8	-0.0015977726548224043	-3.438608481379167e-06	-0.0015135317601704878

simplify13.0ms

Iterations

Iter	Nodes
done	39
1	39
0	30

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.6s	2604×	body	10240	exit
1.1s	2316×	body	1280	valid
504.0ms	1638×	body	640	valid
203.0ms	831×	body	320	valid
186.0ms	2782×	body	80	valid
57.0ms	435×	body	160	valid