Details

sample416.0ms

Algorithm

intervals

Results

146.0ms	51×	body	2560	valid
94.0ms	88×	body	1280	valid
67.0ms	53×	body	640	valid
16.0ms	34×	body	320	valid
4.0ms	13×	body	160	valid
3.0ms	17×	body	80	valid

simplify27.0ms

Counts: 1 → 1

prune44.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.3b

localize35.0ms

Local error

Found 3 expressions with local error:

1.1b	(- x (tan x))
1.1b	(- x (sin x))
0.0b	(/ (- x (sin x)) (- x (tan x)))

rewrite35.0ms

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:

Slowest

18.0ms	(/ (- x (sin x)) (- x (tan x)))
9.0ms	(- x (tan x))
5.0ms	(- x (sin x))

series615.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

480.0ms	(/ (- x (sin x)) (- x (tan x)))
86.0ms	(- x (tan x))
49.0ms	(- x (sin x))

simplify1.0s

Counts: 92 → 92

prune921.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

1.1b	(- x (tan x))
1.1b	(- x (sin x))
0.0b	(/ (- x (tan x)) (- x (sin x)))
0.0b	(/ 1 (/ (- x (tan x)) (- x (sin x))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
200×	`add-sqr-sqrt` `*-un-lft-identity`
92×	`add-cube-cbrt`
54×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/r/`
8×	`flip3--` `div-exp` `flip--` `associate-/l*` `add-log-exp`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv` `insert-posit16`
2×	`rec-exp` `clear-num` `sub-neg` `frac-2neg` `diff-log` `1-exp` `associate-/l/`
1×	`div-sub` `pow-flip` `inv-pow`

Counts

4 → 232

Calls

4 calls:

Slowest

31.0ms	(/ (- x (tan x)) (- x (sin x)))
31.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
10.0ms	(- x (sin x))
9.0ms	(- x (tan x))

series367.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

120.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
103.0ms	(- x (tan x))
92.0ms	(/ (- x (tan x)) (- x (sin x)))
52.0ms	(- x (sin x))

simplify1.2s

Counts: 244 → 244

prune2.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

1.1b	(- x (sin x))
1.1b	(- x (sin x))
1.1b	(- (/ x (- x (sin x))) (/ (tan x) (- x (sin x))))
0.2b	(/ (tan x) (- x (sin x)))

rewrite103.0ms

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` `tan-quot` `frac-sub` `sub-div` `associate-/l/`

Counts

4 → 99

Calls

4 calls:

Slowest

65.0ms	(- (/ x (- x (sin x))) (/ (tan x) (- x (sin x))))
16.0ms	(/ (tan x) (- x (sin x)))
10.0ms	(- x (sin x))
10.0ms	(- x (sin x))

series335.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

196.0ms	(- (/ x (- x (sin x))) (/ (tan x) (- x (sin x))))
54.0ms	(/ (tan x) (- x (sin x)))
47.0ms	(- x (sin x))
38.0ms	(- x (sin x))

simplify1.1s

Counts: 111 → 111

prune976.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

14.1b	(* (/ (/ (tan x) (+ x (sin x))) (- x (sin x))) (+ x (sin x)))
1.1b	(- x (sin x))
1.1b	(- x (sin x))
1.1b	(- (/ x (- x (sin x))) (* (/ (/ (tan x) (+ x (sin x))) (- x (sin x))) (+ x (sin x))))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

153×	`times-frac`
136×	`*-un-lft-identity`
113×	`add-sqr-sqrt`
96×	`associate-l`
64×	`add-cube-cbrt`
20×	`distribute-lft-out--` `difference-of-squares`
16×	`distribute-lft-out`
13×	`add-cbrt-cube` `add-exp-log` `associate-/r/`
10×	`flip-+` `add-log-exp`
9×	`flip3-+`
6×	`pow1` `div-inv`
5×	`associate-*r/` `frac-sub` `flip--`
4×	`frac-times` `flip3--` `associate-r` `insert-posit16`
3×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`distribute-rgt-in` `distribute-lft-in` `associate--r+` `sub-div`
1×	`distribute-rgt-out--` `pow-prod-down` `*-commutative`

Counts

4 → 179

Calls

4 calls:

Slowest

85.0ms	(* (/ (/ (tan x) (+ x (sin x))) (- x (sin x))) (+ x (sin x)))
54.0ms	(- (/ x (- x (sin x))) (* (/ (/ (tan x) (+ x (sin x))) (- x (sin x))) (+ x (sin x))))
7.0ms	(- x (sin x))
5.0ms	(- x (sin x))

series404.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

231.0ms	(- (/ x (- x (sin x))) (* (/ (/ (tan x) (+ x (sin x))) (- x (sin x))) (+ x (sin x))))
69.0ms	(* (/ (/ (tan x) (+ x (sin x))) (- x (sin x))) (+ x (sin x)))
61.0ms	(- x (sin x))
44.0ms	(- x (sin x))

simplify1.5s

Counts: 191 → 191

prune2.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes57.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.5b

bsearch160.0ms

end0.0ms

sample15.5s

Algorithm

intervals

Results

6.1s	1538×	body	2560	valid
5.7s	2794×	body	1280	valid
2.5s	1904×	body	640	valid
694.0ms	887×	body	320	valid
221.0ms	509×	body	160	valid
85.0ms	368×	body	80	valid