Details

sample712.0ms

Algorithm

intervals

Results

326.0ms	52×	body	2560	valid
176.0ms	77×	body	1280	valid
67.0ms	59×	body	640	valid
24.0ms	30×	body	320	valid
13.0ms	22×	body	160	valid
5.0ms	16×	body	80	valid

simplify31.0ms

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize76.0ms

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))

rewrite48.0ms

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:

19.0ms	(/ (- x (sin x)) (- x (tan x)))
10.0ms	(- x (tan x))
16.0ms	(- x (sin x))

series225.0ms

Counts

3 → 9

Calls

3 calls:

117.0ms	(/ (- x (sin x)) (- x (tan x)))
57.0ms	(- x (tan x))
51.0ms	(- x (sin x))

simplify2.0s

Counts

122 → 122

Iterations

Iter	Nodes
3	4455
2	1297
1	502
0	212

prune995.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- x (tan x)))
1.0b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.2b	(- x (tan x))
1.2b	(- x (tan x))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

713×	`*-un-lft-identity`
703×	`add-sqr-sqrt`
678×	`times-frac`
459×	`prod-diff`
417×	`add-cube-cbrt`
147×	`distribute-lft-out--`
141×	`difference-of-squares`
92×	`associate-/r/`
49×	`flip3--` `flip--`
46×	`div-inv`
27×	`fma-neg`
10×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`associate-/r*`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `associate-/l*`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub` `sub-div`

Counts

4 → 592

Calls

4 calls:

30.0ms	(/ (sin x) (- x (tan x)))
78.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
10.0ms	(- x (tan x))
9.0ms	(- x (tan x))

series554.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (sin x) (- x (tan x)))
289.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
65.0ms	(- x (tan x))
93.0ms	(- x (tan x))

simplify2.2s

Counts

604 → 604

Iterations

Iter	Nodes
2	3382
1	1401
0	620

prune7.3s

Pruning

4 alts after pruning (3 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))

rewrite59.0ms

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:

10.0ms	(- 9/40 (* 27/2800 (* x x)))
22.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
25.0ms	(* 27/2800 (* x x))

series311.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(- 9/40 (* 27/2800 (* x x)))
161.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
36.0ms	(* 27/2800 (* x x))

simplify2.2s

Counts

86 → 86

Iterations

Iter	Nodes
3	3373
2	1049
1	342
0	113

prune651.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (sin x) x) (cos x))
0.3b	(* (cos x) (cos x))
1.8b	(- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))
30.6b	(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))))

rewrite114.0ms

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:

12.0ms	(/ (/ (sin x) x) (cos x))
25.0ms	(* (cos x) (cos x))
54.0ms	(- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))
0.0ms	(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))))

series797.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (/ (sin x) x) (cos x))
19.0ms	(* (cos x) (cos x))
172.0ms	(- (/ (/ (sin x) x) (cos x)) (/ (sin x) x))
546.0ms	(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))))

simplify1.2s

Counts

752 → 752

Iterations

Iter	Nodes
1	2009
0	889

prune12.6s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes62.0ms

Accuracy

100% (0.0b remaining)

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

bsearch134.0ms

Steps

Iters	Range		Point
8	0.0042870261776910435	186.95626557948964	0.029500701526914974
9	-0.35383103211093586	-9.60334830165094e-09	-0.029021700279035747

simplify6.0ms

Iterations

Iter	Nodes
2	26
1	26
0	21

end0.0ms

sample16.5s

Algorithm

intervals

Results

7.2s	1626×	body	2560	valid
5.4s	2728×	body	1280	valid
2.3s	1903×	body	640	valid
1.1s	928×	body	320	valid
237.0ms	440×	body	160	valid
95.0ms	375×	body	80	valid