Details

sample632.0ms

Algorithm

intervals

Results

208.0ms	52×	body	2560	valid
124.0ms	98×	body	1280	valid
78.0ms	53×	body	640	valid
15.0ms	26×	body	320	valid
7.0ms	15×	body	160	valid
2.0ms	12×	body	80	valid

simplify52.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	19
3	19
2	17
1	13
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.2b	(- x (tan x))
1.2b	(- x (sin x))

rewrite69.0ms

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:

25.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series669.0ms

Counts

3 → 9

Calls

3 calls:

371.0ms	(/ (- x (sin x)) (- x (tan x)))
127.0ms	(- x (tan x))
170.0ms	(- x (sin x))

simplify967.0ms

Counts

92 → 92

Iterations

Iter	Nodes
3	2994
2	1005
1	375
0	160

prune781.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 3 expressions with local error:

0.0b	(- 9/40 (* 27/2800 (* x x)))
0.1b	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
0.4b	(* 27/2800 (* x x))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-cbrt-cube` `add-exp-log`
7×	`add-sqr-sqrt`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`associate-r` `associate-l`
3×	`sub-neg` `insert-posit16`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `associate-r/` `-commutative` `flip--` `unswap-sqr`
1×	`diff-log`

Counts

3 → 59

Calls

3 calls:

10.0ms	(- 9/40 (* 27/2800 (* x x)))
41.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
25.0ms	(* 27/2800 (* x x))

series328.0ms

Counts

3 → 9

Calls

3 calls:

111.0ms	(- 9/40 (* 27/2800 (* x x)))
161.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
56.0ms	(* 27/2800 (* x x))

simplify1.4s

Counts

68 → 68

Iterations

Iter	Nodes
3	2384
2	737
1	264
0	89

prune521.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.0b	(log (exp (/ (- x (sin x)) (- x (tan x)))))
1.2b	(- x (tan x))
1.2b	(- x (sin x))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt` `*-un-lft-identity`
50×	`times-frac`
32×	`log-pow`
31×	`exp-prod`
28×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/r` `flip3--` `flip--` `associate-/l`
4×	`associate-/r/` `insert-posit16`
3×	`log-prod`
2×	`sub-neg` `diff-log` `div-sub` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `exp-diff` `div-exp` `rem-log-exp`

Counts

4 → 128

Calls

4 calls:

27.0ms	(/ (- x (sin x)) (- x (tan x)))
23.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
4.0ms	(- x (tan x))
5.0ms	(- x (sin x))

series358.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (- x (sin x)) (- x (tan x)))
125.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
77.0ms	(- x (tan x))
41.0ms	(- x (sin x))

simplify946.0ms

Counts

140 → 140

Iterations

Iter	Nodes
3	2927
2	1052
1	444
0	223

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ (- x (tan x)) (- x (sin x))))
0.0b	(/ (- x (tan x)) (- x (sin x)))
1.2b	(- x (tan x))
1.2b	(- x (sin x))

rewrite69.0ms

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:

30.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
23.0ms	(/ (- x (tan x)) (- x (sin x)))
7.0ms	(- x (tan x))
5.0ms	(- x (sin x))

series360.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
127.0ms	(/ (- x (tan x)) (- x (sin x)))
71.0ms	(- x (tan x))
39.0ms	(- x (sin x))

simplify783.0ms

Counts

244 → 244

Iterations

Iter	Nodes
2	2469
1	827
0	324

prune2.0s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes73.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.3b

bsearch176.0ms

Steps

Iters	Range		Point
10	3.724243043503383e-05	335086.0623706297	0.028004662405730834
9	-1352.1675980196485	-0.00125944232679287	-0.02581010450665607

simplify5.0ms

Iterations

Iter	Nodes
2	28
1	28
0	22

end0.0ms

sample17.3s

Algorithm

intervals

Results

8.3s	1622×	body	2560	valid
5.1s	2697×	body	1280	valid
2.5s	1901×	body	640	valid
763.0ms	948×	body	320	valid
310.0ms	479×	body	160	valid
91.0ms	353×	body	80	valid