Details

sample744.0ms

Algorithm

intervals

Results

320.0ms	71×	body	2560	valid
243.0ms	78×	body	1280	valid
67.0ms	55×	body	640	valid
23.0ms	29×	body	320	valid
6.0ms	11×	body	160	valid
4.0ms	12×	body	80	valid

simplify28.0ms

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: 33.1b

localize19.0ms

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:

49.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series298.0ms

Counts

3 → 9

Calls

3 calls:

139.0ms	(/ (- x (sin x)) (- x (tan x)))
104.0ms	(- x (tan x))
55.0ms	(- x (sin x))

simplify2.1s

Counts

122 → 122

Iterations

Iter	Nodes
3	4455
2	1297
1	502
0	212

prune703.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize29.0ms

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))))
0.2b	(* 27/2800 (* x x))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 77

Calls

3 calls:

11.0ms	(- 9/40 (* 27/2800 (* x x)))
48.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
33.0ms	(* 27/2800 (* x x))

series323.0ms

Counts

3 → 9

Calls

3 calls:

114.0ms	(- 9/40 (* 27/2800 (* x x)))
163.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
45.0ms	(* 27/2800 (* x x))

simplify2.1s

Counts

86 → 86

Iterations

Iter	Nodes
3	3373
2	1049
1	342
0	113

prune489.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize84.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (sin x) x) (cos x))
0.2b	(* (cos x) (cos x))
2.0b	(- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))
32.1b	(fma (/ (sin x) (* (cos x) (cos x))) (/ (/ (sin x) x) x) (- (- (/ (/ (sin x) x) (cos x)) (/ (sin x) x)) (* (/ (/ (sin x) x) (cos x)) (/ (sin x) x))))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

1397×	`times-frac`
864×	`add-sqr-sqrt`
847×	`*-un-lft-identity`
841×	`add-cube-cbrt`
559×	`prod-diff`
104×	`div-inv`
43×	`fma-neg`
13×	`associate-/l*`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r` `swap-sqr` `div-exp` `associate-r` `associate-l*`
2×	`distribute-lft-out--`
1×	`pow2` `sqr-cos` `clear-num` `sub-neg` `frac-2neg` `pow-plus` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `frac-sub` `cbrt-unprod` `fma-udef` `flip--` `unswap-sqr` `associate-/l/`

Counts

4 → 740

Calls

4 calls:

11.0ms	(/ (/ (sin x) x) (cos x))
22.0ms	(* (cos x) (cos x))
64.0ms	(- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))
1.0ms	(fma (/ (sin x) (* (cos x) (cos x))) (/ (/ (sin x) x) x) (- (- (/ (/ (sin x) x) (cos x)) (/ (sin x) x)) (* (/ (/ (sin x) x) (cos x)) (/ (sin x) x))))

series705.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ (/ (sin x) x) (cos x))
20.0ms	(* (cos x) (cos x))
140.0ms	(- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))
479.0ms	(fma (/ (sin x) (* (cos x) (cos x))) (/ (/ (sin x) x) x) (- (- (/ (/ (sin x) x) (cos x)) (/ (sin x) x)) (* (/ (/ (sin x) x) (cos x)) (/ (sin x) x))))

simplify1.7s

Counts

752 → 752

Iterations

Iter	Nodes
1	2009
0	889

prune11.7s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes97.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.7b

bsearch154.0ms

Steps

Iters	Range		Point
10	0.002603609100038161	6235082944194588.0	0.02658761844916455
8	-145.89507053458865	-0.006947246361207331	-0.0328281005146998

simplify29.0ms

Iterations

Iter	Nodes
2	25
1	25
0	20

end0.0ms

sample17.0s

Algorithm

intervals

Results

7.1s	1657×	body	2560	valid
6.1s	2758×	body	1280	valid
2.4s	1857×	body	640	valid
739.0ms	921×	body	320	valid
258.0ms	441×	body	160	valid
99.0ms	366×	body	80	valid