Details

sample837.0ms

Algorithm

intervals

Results

252.0ms	54×	body	2560	valid
160.0ms	82×	body	1280	valid
119.0ms	67×	body	640	valid
27.0ms	29×	body	320	valid
6.0ms	13×	body	160	valid
3.0ms	11×	body	80	valid

simplify15.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	19
3	19
2	17
1	13
0	6

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize36.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.9b	(- x (tan x))
1.9b	(- x (sin x))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 83

Calls

3 calls:

34.0ms	(/ (- x (sin x)) (- x (tan x)))
11.0ms	(- x (tan x))
13.0ms	(- x (sin x))

series237.0ms

Counts

3 → 9

Calls

3 calls:

95.0ms	(/ (- x (sin x)) (- x (tan x)))
75.0ms	(- x (tan x))
67.0ms	(- x (sin x))

simplify908.0ms

Counts

92 → 92

Iterations

Iter	Nodes
done	2010
3	2010
2	964
1	375
0	160

prune771.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- x (tan x)))
1.8b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.9b	(- x (tan x))
1.9b	(- x (tan x))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
33×	`times-frac`
18×	`distribute-lft-out--`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`flip3--` `add-cbrt-cube` `add-exp-log` `associate-/r/` `flip--`
5×	`associate-/r*`
4×	`pow1` `insert-posit16`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub` `sub-div`

Counts

4 → 98

Calls

4 calls:

12.0ms	(/ (sin x) (- x (tan x)))
79.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
8.0ms	(- x (tan x))
9.0ms	(- x (tan x))

series570.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (sin x) (- x (tan x)))
299.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
95.0ms	(- x (tan x))
93.0ms	(- x (tan x))

simplify1.2s

Counts

110 → 110

Iterations

Iter	Nodes
done	2000
3	2000
2	1111
1	392
0	180

prune949.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) (* x x))
0.1b	(* (* (* x x) (* x x)) 27/2800)
0.4b	(* (* x x) 9/40)
17.1b	(- (- (* (* x x) 9/40) 1/2) (* (* (* x x) (* x x)) 27/2800))

rewrite396.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 130

Calls

4 calls:

44.0ms	(* (* x x) (* x x))
109.0ms	(* (* (* x x) (* x x)) 27/2800)
30.0ms	(* (* x x) 9/40)
209.0ms	(- (- (* (* x x) 9/40) 1/2) (* (* (* x x) (* x x)) 27/2800))

series218.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (* x x) (* x x))
65.0ms	(* (* (* x x) (* x x)) 27/2800)
34.0ms	(* (* x x) 9/40)
64.0ms	(- (- (* (* x x) 9/40) 1/2) (* (* (* x x) (* x x)) 27/2800))

simplify1.5s

Counts

142 → 142

Iterations

Iter	Nodes
done	2003
3	2003
2	1110
1	379
0	135

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize79.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/6 (* x (* x x)))
1.9b	(- x (tan x))
19.1b	(/ (+ (+ (* 1/6 (* x (* x x))) (* (pow x 7) 1/5040)) (* (pow x 5) -1/120)) (- x (tan x)))
24.7b	(+ (+ (* 1/6 (* x (* x x))) (* (pow x 7) 1/5040)) (* (pow x 5) -1/120))

rewrite864.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
13×	`pow1`
11×	`add-log-exp`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`insert-posit16`
3×	`sum-log` `associate-l` `associate-/l*`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l+` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `associate-r` `*-commutative` `div-inv`

Counts

4 → 91

Calls

4 calls:

50.0ms	(* 1/6 (* x (* x x)))
4.0ms	(- x (tan x))
548.0ms	(/ (+ (+ (* 1/6 (* x (* x x))) (* (pow x 7) 1/5040)) (* (pow x 5) -1/120)) (- x (tan x)))
260.0ms	(+ (+ (* 1/6 (* x (* x x))) (* (pow x 7) 1/5040)) (* (pow x 5) -1/120))

series383.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* 1/6 (* x (* x x)))
70.0ms	(- x (tan x))
139.0ms	(/ (+ (+ (* 1/6 (* x (* x x))) (* (pow x 7) 1/5040)) (* (pow x 5) -1/120)) (- x (tan x)))
97.0ms	(+ (+ (* 1/6 (* x (* x x))) (* (pow x 7) 1/5040)) (* (pow x 5) -1/120))

simplify1.3s

Counts

103 → 103

Iterations

Iter	Nodes
done	2013
3	2013
2	1678
1	478
0	196

prune717.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes71.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.8b

bsearch164.0ms

Steps

Iters	Range		Point
10	1.8230705747381016e-09	4364471.442644652	0.03210649578243009
9	-0.030639508246526274	-1.9696345359431407e-07	-0.025621427997812182

simplify5.0ms

Iterations

Iter	Nodes
done	27
1	27
0	22

end0.0ms

sample15.5s

Algorithm

intervals

Results

7.4s	1537×	body	2560	valid
4.7s	2771×	body	1280	valid
2.1s	1907×	body	640	valid
773.0ms	955×	body	320	valid
197.0ms	447×	body	160	valid
89.0ms	383×	body	80	valid