Details

sample519.0ms

Algorithm

intervals

Results

185.0ms	99×	body	1280	valid
126.0ms	38×	body	2560	valid
59.0ms	59×	body	640	valid
17.0ms	26×	body	320	valid
7.0ms	17×	body	160	valid
4.0ms	17×	body	80	valid

simplify42.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.3b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.0b	(- x (tan x))
2.0b	(- x (sin x))

rewrite36.0ms

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:

22.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
8.0ms	(- x (sin x))

series253.0ms

Counts

3 → 9

Calls

3 calls:

117.0ms	(/ (- x (sin x)) (- x (tan x)))
83.0ms	(- x (tan x))
53.0ms	(- x (sin x))

simplify932.0ms

Counts

92 → 92

Iterations

Iter	Nodes
3	2994
2	1005
1	375
0	160

prune873.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- x (tan x)))
2.0b	(- x (tan x))
2.0b	(- x (tan x))
2.0b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

rewrite97.0ms

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:

22.0ms	(/ (sin x) (- x (tan x)))
8.0ms	(- x (tan x))
5.0ms	(- x (tan x))
60.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

series494.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (sin x) (- x (tan x)))
53.0ms	(- x (tan x))
64.0ms	(- x (tan x))
276.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

simplify1.5s

Counts

110 → 110

Iterations

Iter	Nodes
3	3321
2	1111
1	392
0	180

prune944.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (/ 1 (- x (tan x))))
2.0b	(- x (tan x))
2.0b	(- x (tan x))
2.0b	(- (/ x (- x (tan x))) (* (sin x) (/ 1 (- x (tan x)))))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`associate-r`
17×	`times-frac`
14×	`add-cube-cbrt`
13×	`add-exp-log`
10×	`add-log-exp`
9×	`add-cbrt-cube`
6×	`pow1`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`flip3--` `prod-exp` `insert-posit16` `flip--`
3×	`sub-neg` `diff-log` `associate-l` `associate-*r/` `un-div-inv` `unswap-sqr`
2×	`div-exp` `associate-/r/` `frac-sub` `cbrt-unprod` `div-inv` `sub-div`
1×	`cbrt-undiv` `rec-exp` `distribute-rgt-out--` `1-exp` `pow-prod-down` `*-commutative`

Counts

4 → 93

Calls

4 calls:

20.0ms	(* (sin x) (/ 1 (- x (tan x))))
8.0ms	(- x (tan x))
9.0ms	(- x (tan x))
74.0ms	(- (/ x (- x (tan x))) (* (sin x) (/ 1 (- x (tan x)))))

series585.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (sin x) (/ 1 (- x (tan x))))
82.0ms	(- x (tan x))
96.0ms	(- x (tan x))
337.0ms	(- (/ x (- x (tan x))) (* (sin x) (/ 1 (- x (tan x)))))

simplify1.6s

Counts

105 → 105

Iterations

Iter	Nodes
3	4449
2	1345
1	462
0	187

prune933.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin x))
2.0b	(- x (tan x))
2.0b	(- x (tan x))
2.0b	(- (/ x (- x (tan x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (/ (- x (tan x)) (cbrt (sin x)))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
14×	`times-frac`
11×	`*-un-lft-identity`
10×	`add-log-exp` `difference-of-squares`
5×	`cbrt-prod` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`
1×	`pow1/3` `frac-sub`

Counts

4 → 65

Calls

4 calls:

1.0ms	(cbrt (sin x))
4.0ms	(- x (tan x))
4.0ms	(- x (tan x))
84.0ms	(- (/ x (- x (tan x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (/ (- x (tan x)) (cbrt (sin x)))))

series582.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(cbrt (sin x))
66.0ms	(- x (tan x))
71.0ms	(- x (tan x))
300.0ms	(- (/ x (- x (tan x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (/ (- x (tan x)) (cbrt (sin x)))))

simplify1.2s

Counts

77 → 77

Iterations

Iter	Nodes
3	3062
2	944
1	349
0	152

prune658.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes78.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.2b

bsearch148.0ms

Steps

Iters	Range		Point
8	0.00023203888932163942	0.10106394179147121	0.033370679126448435
7	-0.11981472621416538	-0.0008162261515098681	-0.033668191967710336

simplify6.0ms

Iterations

Iter	Nodes
2	33
1	33
0	28

end0.0ms

sample15.8s

Algorithm

intervals

Results

6.8s	1662×	body	2560	valid
5.9s	2702×	body	1280	valid
1.9s	1866×	body	640	valid
732.0ms	934×	body	320	valid
269.0ms	447×	body	160	valid
90.0ms	389×	body	80	valid