Details

sample362.0ms

Algorithm

intervals

Results

190.0ms	57×	body	2560	valid
70.0ms	85×	body	1280	valid
30.0ms	66×	body	640	valid
9.0ms	28×	body	320	valid
3.0ms	14×	body	160	valid
3.0ms	6×	body	80	valid

simplify75.0ms

Counts

1 → 1

Iterations

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

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.7b

localize51.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.3b	(- x (tan x))
2.4b	(- x (sin x))

rewrite74.0ms

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:

47.0ms	(/ (- x (sin x)) (- x (tan x)))
8.0ms	(- x (tan x))
12.0ms	(- x (sin x))

series351.0ms

Counts

3 → 9

Calls

3 calls:

128.0ms	(/ (- x (sin x)) (- x (tan x)))
155.0ms	(- x (tan x))
67.0ms	(- x (sin x))

simplify4.9s

Counts

92 → 92

Iterations

Iter	Nodes
done	5022
3	3361
2	965
1	375
0	160

prune748.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (* 9/40 x))
0.2b	(* 9/40 x)
0.2b	(* (* x x) 27/2800)
13.8b	(- (* x (* 9/40 x)) (+ (* (* x x) (* (* x x) 27/2800)) 1/2))

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

21.0ms	(* x (* 9/40 x))
19.0ms	(* 9/40 x)
41.0ms	(* (* x x) 27/2800)
176.0ms	(- (* x (* 9/40 x)) (+ (* (* x x) (* (* x x) 27/2800)) 1/2))

series213.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* x (* 9/40 x))
33.0ms	(* 9/40 x)
55.0ms	(* (* x x) 27/2800)
84.0ms	(- (* x (* 9/40 x)) (+ (* (* x x) (* (* x x) 27/2800)) 1/2))

simplify8.5s

Counts

85 → 85

Iterations

Iter	Nodes
done	5006
3	4361
2	1003
1	309
0	116

prune694.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize191.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin x))
2.4b	(- (/ (/ (* (sin x) (sin x)) (cos x)) (* x x)) 1)
2.7b	(- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))
17.4b	(/ (/ (* (sin x) (sin x)) (cos x)) (* x x))

rewrite322.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
33×	`times-frac`
27×	`add-cbrt-cube` `add-exp-log`
23×	`*-un-lft-identity`
12×	`add-cube-cbrt` `difference-of-squares`
11×	`pow1`
10×	`cbrt-undiv` `div-exp`
8×	`add-log-exp`
7×	`associate-/l*`
6×	`prod-exp` `cbrt-unprod`
4×	`div-sub` `insert-posit16`
3×	`difference-of-sqr-1` `swap-sqr` `associate-r` `associate-l` `sqr-sin` `div-inv` `distribute-lft-out--`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`associate--l-` `pow2` `clear-num` `associate-/r` `frac-2neg` `pow-plus` `pow-prod-down` `pow-sqr` `-commutative` `pow-prod-up` `frac-sub` `sin-mult` `unswap-sqr` `associate-/l/`

Counts

4 → 114

Calls

4 calls:

19.0ms	(* (sin x) (sin x))
83.0ms	(- (/ (/ (* (sin x) (sin x)) (cos x)) (* x x)) 1)
172.0ms	(- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))
39.0ms	(/ (/ (* (sin x) (sin x)) (cos x)) (* x x))

series615.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (sin x) (sin x))
235.0ms	(- (/ (/ (* (sin x) (sin x)) (cos x)) (* x x)) 1)
187.0ms	(- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))
138.0ms	(/ (/ (* (sin x) (sin x)) (cos x)) (* x x))

simplify4.0s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	2186
1	596
0	239

prune1.1s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes74.0ms

Accuracy

100% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 32.2b

bsearch174.0ms

Steps

Iters	Range		Point
10	1.508099977930646e-06	2590629949647.022	2.4087276690935244
10	-26711381.42537418	-6.803810524357175e-07	-2.4752504163968116

simplify13.0ms

Iterations

Iter	Nodes
done	41
1	41
0	30

end0.0ms

sample13.9s

Algorithm

intervals

Results

6.0s	1608×	body	2560	valid
5.0s	2728×	body	1280	valid
1.9s	1901×	body	640	valid
469.0ms	933×	body	320	valid
186.0ms	469×	body	160	valid
113.0ms	361×	body	80	valid