Details

sample745.0ms

Algorithm

intervals

Results

326.0ms	55×	body	2560	valid
181.0ms	89×	body	1280	valid
72.0ms	56×	body	640	valid
48.0ms	7×	body	160	valid
37.0ms	43×	body	320	valid
2.0ms	6×	body	80	valid

simplify30.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.7b	(- x (tan x))
1.7b	(- x (sin x))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`fma-neg`
5×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 113

Calls

3 calls:

23.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
32.0ms	(- x (sin x))

series299.0ms

Counts

3 → 9

Calls

3 calls:

138.0ms	(/ (- x (sin x)) (- x (tan x)))
106.0ms	(- x (tan x))
55.0ms	(- x (sin x))

simplify2.1s

Counts

122 → 122

Iterations

Iter	Nodes
3	4455
2	1297
1	502
0	212

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
0.2b	(* 27/2800 (* x x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `prod-diff` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate-r` `associate-l`
2×	`expm1-log1p-u` `sub-neg` `associate-r/` `-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
1×	`flip3--` `flip--`

Counts

2 → 56

Calls

2 calls:

37.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
13.0ms	(* 27/2800 (* x x))

series201.0ms

Counts

2 → 6

Calls

2 calls:

147.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
54.0ms	(* 27/2800 (* x x))

simplify2.5s

Counts

62 → 62

Iterations

Iter	Nodes
3	3341
2	908
1	309
0	102

prune469.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
1.7b	(- x (sin x))
2.5b	(/ (- x (sin x)) (+ (- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x)) (* (tan x) 0)))
18.4b	(- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x))

rewrite282.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt` `*-un-lft-identity`
23×	`add-cube-cbrt`
15×	`times-frac`
12×	`prod-diff`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `pow1` `flip3--` `fma-neg` `associate-/r/` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`cbrt-prod` `associate-/r*`
2×	`sub-neg` `diff-log` `associate-*l/` `frac-add` `tan-quot` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `pow1/3` `div-sub` `div-exp` `flip-+` `div-inv`

Counts

4 → 107

Calls

4 calls:

1.0ms	(cbrt x)
8.0ms	(- x (sin x))
218.0ms	(/ (- x (sin x)) (+ (- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x)) (* (tan x) 0)))
53.0ms	(- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x))

series637.0ms

Counts

4 → 12

Calls

4 calls:

297.0ms	(cbrt x)
56.0ms	(- x (sin x))
149.0ms	(/ (- x (sin x)) (+ (- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x)) (* (tan x) 0)))
135.0ms	(- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x))

simplify3.0s

Counts

119 → 119

Iterations

Iter	Nodes
3	4715
2	1508
1	585
0	242

prune1.0s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

2.4b	(sqrt (+ (- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x)) (* (tan x) 0)))
2.4b	(sqrt (+ (- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x)) (* (tan x) 0)))
18.4b	(- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x))
18.4b	(- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x))

rewrite369.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `sqrt-div` `add-cube-cbrt` `add-log-exp`
6×	`pow1` `prod-diff` `sqrt-prod`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `associate-*l/` `frac-add` `tan-quot` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `flip-+`

Counts

4 → 78

Calls

4 calls:

122.0ms	(sqrt (+ (- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x)) (* (tan x) 0)))
160.0ms	(sqrt (+ (- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x)) (* (tan x) 0)))
41.0ms	(- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x))
45.0ms	(- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x))

series416.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(sqrt (+ (- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x)) (* (tan x) 0)))
79.0ms	(sqrt (+ (- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x)) (* (tan x) 0)))
116.0ms	(- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x))
126.0ms	(- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x))

simplify1.2s

Counts

90 → 90

Iterations

Iter	Nodes
3	2723
2	872
1	350
0	145

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes102.0ms

Accuracy

100% (0.0b remaining)

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

bsearch162.0ms

Steps

Iters	Range		Point
10	1.4996160052323843e-06	45385424.466692075	0.03204447297348137
6	-0.09702975014721212	-0.00744726966661137	-0.025688062190600255

simplify8.0ms

Iterations

Iter	Nodes
2	25
1	25
0	20

end0.0ms

sample16.6s

Algorithm

intervals

Results

6.9s	1602×	body	2560	valid
5.7s	2775×	body	1280	valid
2.6s	1927×	body	640	valid
862.0ms	918×	body	320	valid
200.0ms	446×	body	160	valid
128.0ms	332×	body	80	valid