Details

sample337.0ms

Algorithm

intervals

Results

99.0ms	69×	body	10240	exit
95.0ms	323×	body	80	valid
64.0ms	49×	body	1280	valid
35.0ms	42×	body	640	valid
12.0ms	22×	body	320	valid
2.0ms	6×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2021
5	2021
4	1521
3	381
2	122
1	48
0	19

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps))
0.0b	(/ (exp (* x (+ -1 eps))) eps)
0.0b	(/ (exp (* x (- -1 eps))) eps)
1.5b	(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
36×	`times-frac`
28×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
24×	`exp-sum`
18×	`add-log-exp`
12×	`distribute-rgt-in` `distribute-lft-in` `associate-/l*`
10×	`sub-neg`
8×	`add-cbrt-cube`
6×	`associate-/r*` `diff-log` `add-exp-log` `distribute-lft-out--`
4×	`pow1` `frac-sub` `insert-posit16`
3×	`sum-log` `flip3-+` `flip3--` `flip-+` `flip--` `distribute-lft-out`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv` `associate--r+`
1×	`+-commutative` `associate--l+` `associate--r-` `difference-of-squares`

Counts

4 → 122

Calls

4 calls:

11.0ms	(+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps))
9.0ms	(/ (exp (* x (+ -1 eps))) eps)
13.0ms	(/ (exp (* x (- -1 eps))) eps)
196.0ms	(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))

series310.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps))
41.0ms	(/ (exp (* x (+ -1 eps))) eps)
41.0ms	(/ (exp (* x (- -1 eps))) eps)
174.0ms	(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))

simplify1.5s

Counts

134 → 134

Iterations

Iter	Nodes
done	2003
3	2003
2	1853
1	553
0	237

prune1.9s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize37.0ms

Local error

Found 3 expressions with local error:

0.1b	(* x (* (* x x) 2/3))
0.2b	(* (* x x) 2/3)
6.8b	(+ (- 2 (* x x)) (* x (* (* x x) 2/3)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 58

Calls

3 calls:

77.0ms	(* x (* (* x x) 2/3))
29.0ms	(* (* x x) 2/3)
47.0ms	(+ (- 2 (* x x)) (* x (* (* x x) 2/3)))

series146.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(* x (* (* x x) 2/3))
45.0ms	(* (* x x) 2/3)
60.0ms	(+ (- 2 (* x x)) (* x (* (* x x) 2/3)))

simplify1.0s

Counts

67 → 67

Iterations

Iter	Nodes
done	2002
3	2002
2	804
1	244
0	91

prune620.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.5b

localize33.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* x x) x)
0.1b	(* 2/3 (* (* x x) x))
6.8b	(- (* 2/3 (* (* x x) x)) (* x x))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

31×	`pow1`
17×	`add-cbrt-cube` `add-exp-log`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt` `pow-plus` `pow-prod-up`
5×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`associate-r` `associate-l`
3×	`insert-posit16`
2×	`pow2` `pow-sqr` `*-commutative`
1×	`sub-neg` `flip3--` `diff-log` `pow3` `flip--` `unswap-sqr`

Counts

3 → 64

Calls

3 calls:

22.0ms	(* (* x x) x)
70.0ms	(* 2/3 (* (* x x) x))
40.0ms	(- (* 2/3 (* (* x x) x)) (* x x))

series249.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(* (* x x) x)
53.0ms	(* 2/3 (* (* x x) x))
147.0ms	(- (* 2/3 (* (* x x) x)) (* x x))

simplify1.2s

Counts

73 → 73

Iterations

Iter	Nodes
done	2000
3	2000
2	843
1	233
0	81

prune701.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.5b

localize64.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* (* x x) 2/3))
0.2b	(* (* x x) 2/3)
3.6b	(posit16->real (real->posit16 (+ (- 2 (* x x)) (* x (* (* x x) 2/3)))))
6.8b	(+ (- 2 (* x x)) (* x (* (* x x) 2/3)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

48.0ms	(* x (* (* x x) 2/3))
29.0ms	(* (* x x) 2/3)
0.0ms	(posit16->real (real->posit16 (+ (- 2 (* x x)) (* x (* (* x x) 2/3)))))
32.0ms	(+ (- 2 (* x x)) (* x (* (* x x) 2/3)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* x (* (* x x) 2/3))
50.0ms	(* (* x x) 2/3)
57.0ms	(posit16->real (real->posit16 (+ (- 2 (* x x)) (* x (* (* x x) 2/3)))))
43.0ms	(+ (- 2 (* x x)) (* x (* (* x x) 2/3)))

simplify1.1s

Counts

79 → 79

Iterations

Iter	Nodes
done	2001
3	2001
2	856
1	260
0	100

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.5b

regimes266.0ms

Accuracy

96.3% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.8b

bsearch345.0ms

Steps

Iters	Range		Point
10	0.0042870261776910435	159184409.05021107	100.79533204800275

simplify7.0ms

Iterations

Iter	Nodes
done	37
1	37
0	29

end0.0ms

sample11.8s

Algorithm

intervals

Results

3.8s	1964×	body	10240	exit
2.9s	1767×	body	1280	valid
2.7s	9993×	body	80	valid
1.1s	1282×	body	640	valid
495.0ms	282×	body	160	valid
362.0ms	636×	body	320	valid