Details

sample57.0ms

Algorithm

intervals

Results

21.0ms	56×	body	1280	valid
11.0ms	38×	body	640	valid
8.0ms	131×	body	80	valid
4.0ms	20×	body	320	valid
1.0ms	11×	body	160	valid

simplify12.8s

Counts

1 → 1

Iterations

Iter	Nodes
9	9892
8	1985
7	571
6	236
5	102
4	50
3	29
2	22
1	18
0	9

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1 (exp (* -2 x)))
0.0b	(/ 2 (+ 1 (exp (* -2 x))))
3.0b	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
15×	`times-frac`
12×	`add-cube-cbrt`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out`
4×	`associate-/r*` `difference-of-squares`
3×	`pow1` `insert-posit16` `associate-/l*`
2×	`flip3-+` `difference-of-sqr-1` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `div-inv` `flip--` `distribute-lft-out--`

Counts

3 → 67

Calls

3 calls:

5.0ms	(+ 1 (exp (* -2 x)))
11.0ms	(/ 2 (+ 1 (exp (* -2 x))))
53.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

series128.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(+ 1 (exp (* -2 x)))
39.0ms	(/ 2 (+ 1 (exp (* -2 x))))
74.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

simplify2.8s

Counts

76 → 76

Iterations

Iter	Nodes
4	3911
3	1437
2	615
1	266
0	120

prune731.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp (* -2 x)) 1)
0.0b	(/ 2 (+ (exp (* -2 x)) 1))
3.0b	(- (/ 2 (+ (exp (* -2 x)) 1)) 1)

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
15×	`times-frac`
12×	`add-cube-cbrt`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out`
4×	`associate-/r*` `difference-of-squares`
3×	`pow1` `insert-posit16` `associate-/l*`
2×	`flip3-+` `difference-of-sqr-1` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `div-inv` `flip--` `distribute-lft-out--`

Counts

3 → 67

Calls

3 calls:

14.0ms	(+ (exp (* -2 x)) 1)
20.0ms	(/ 2 (+ (exp (* -2 x)) 1))
78.0ms	(- (/ 2 (+ (exp (* -2 x)) 1)) 1)

series136.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(+ (exp (* -2 x)) 1)
32.0ms	(/ 2 (+ (exp (* -2 x)) 1))
87.0ms	(- (/ 2 (+ (exp (* -2 x)) 1)) 1)

simplify3.2s

Counts

76 → 76

Iterations

Iter	Nodes
4	4276
3	1395
2	565
1	257
0	117

prune581.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (pow x 5) 2/15)
0.1b	(* (* x -1/3) (* x x))
0.4b	(* x -1/3)
20.3b	(+ (+ (* (pow x 5) 2/15) x) (* (* x -1/3) (* x x)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
20×	`add-cbrt-cube`
18×	`pow1`
16×	`add-sqr-sqrt`
12×	`prod-exp`
11×	`associate-l`
10×	`cbrt-unprod`
9×	`*-un-lft-identity` `pow-prod-down` `add-cube-cbrt` `add-log-exp`
7×	`associate-r`
4×	`unpow-prod-down` `insert-posit16` `unswap-sqr`
3×	`sum-log` `*-commutative`
2×	`sqr-pow`
1×	`pow-to-exp` `+-commutative` `associate-+l+` `flip3-+` `pow-exp` `flip-+`

Counts

4 → 82

Calls

4 calls:

9.0ms	(* (pow x 5) 2/15)
35.0ms	(* (* x -1/3) (* x x))
5.0ms	(* x -1/3)
42.0ms	(+ (+ (* (pow x 5) 2/15) x) (* (* x -1/3) (* x x)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (pow x 5) 2/15)
50.0ms	(* (* x -1/3) (* x x))
17.0ms	(* x -1/3)
70.0ms	(+ (+ (* (pow x 5) 2/15) x) (* (* x -1/3) (* x x)))

simplify1.9s

Counts

94 → 94

Iterations

Iter	Nodes
3	4962
2	1061
1	321
0	132

prune767.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* (* x x) 1/3))
0.1b	(* (* x x) (* x x))
0.2b	(* (* x x) 1/3)
20.2b	(- (* 2/15 (* x (* (* x x) (* x x)))) (* x (* (* x x) 1/3)))

rewrite320.0ms

Algorithm

rewrite-expression-head

Rules

129×	`pow1`
36×	`pow-prod-up`
32×	`pow-prod-down`
30×	`add-cbrt-cube` `add-exp-log`
22×	`pow-sqr`
18×	`pow-plus`
17×	`prod-exp` `cbrt-unprod`
13×	`pow2`
7×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
5×	`associate-r` `associate-l`
4×	`insert-posit16`
3×	`*-commutative`
2×	`unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `swap-sqr` `flip--`

Counts

4 → 119

Calls

4 calls:

55.0ms	(* x (* (* x x) 1/3))
31.0ms	(* (* x x) (* x x))
16.0ms	(* (* x x) 1/3)
215.0ms	(- (* 2/15 (* x (* (* x x) (* x x)))) (* x (* (* x x) 1/3)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* x (* (* x x) 1/3))
57.0ms	(* (* x x) (* x x))
43.0ms	(* (* x x) 1/3)
195.0ms	(- (* 2/15 (* x (* (* x x) (* x x)))) (* x (* (* x x) 1/3)))

simplify1.7s

Counts

131 → 131

Iterations

Iter	Nodes
3	3638
2	902
1	338
0	121

prune1.0s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes100.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.0b

bsearch135.0ms

Steps

Iters	Range		Point
10	0.0027002530800994988	446233850.42817044	0.00654275487662059
8	-0.5883935043627003	-0.00125944232679287	-0.007463572132942926

simplify5.0ms

Iterations

Iter	Nodes
2	37
1	37
0	25

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.4s	1696×	body	1280	valid
513.0ms	1210×	body	640	valid
340.0ms	4139×	body	80	valid
203.0ms	634×	body	320	valid
55.0ms	321×	body	160	valid