Details

sample605.0ms

Algorithm

intervals

Results

307.0ms	57×	body	2560	valid
141.0ms	85×	body	1280	valid
52.0ms	66×	body	640	valid
18.0ms	28×	body	320	valid
4.0ms	14×	body	160	valid
4.0ms	6×	body	80	valid

simplify860.0ms

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.3b	(- x (tan x))
2.4b	(- x (sin x))

rewrite74.0ms

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:

29.0ms	(/ (- x (sin x)) (- x (tan x)))
11.0ms	(- x (tan x))
18.0ms	(- x (sin x))

series275.0ms

Counts

3 → 9

Calls

3 calls:

115.0ms	(/ (- x (sin x)) (- x (tan x)))
114.0ms	(- x (tan x))
46.0ms	(- x (sin x))

simplify1.9s

Counts

92 → 92

Iterations

Iter	Nodes
done	5017
3	3306
2	964
1	375
0	160

prune340.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* -27/2800 (* (* x x) (* x x)))
0.2b	(* x (* x 9/40))
0.2b	(* x 9/40)
13.8b	(+ (* -27/2800 (* (* x x) (* x x))) (+ -1/2 (* x (* x 9/40))))

rewrite271.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1` `add-cbrt-cube` `add-exp-log`
17×	`pow-prod-down` `prod-exp` `cbrt-unprod`
11×	`add-sqr-sqrt`
9×	`associate-l` `add-log-exp`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`associate-r`
4×	`insert-posit16`
3×	`sum-log` `*-commutative`
2×	`unswap-sqr`
1×	`+-commutative` `associate-+r+` `flip3-+` `flip-+`

Counts

4 → 81

Calls

4 calls:

98.0ms	(* -27/2800 (* (* x x) (* x x)))
23.0ms	(* x (* x 9/40))
6.0ms	(* x 9/40)
140.0ms	(+ (* -27/2800 (* (* x x) (* x x))) (+ -1/2 (* x (* x 9/40))))

series191.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* -27/2800 (* (* x x) (* x x)))
48.0ms	(* x (* x 9/40))
27.0ms	(* x 9/40)
64.0ms	(+ (* -27/2800 (* (* x x) (* x x))) (+ -1/2 (* x (* x 9/40))))

simplify2.2s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
2	2066
1	397
0	130

prune266.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.9b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
2.3b	(- x (tan x))
2.3b	(- x (tan x))

rewrite125.0ms

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:

17.0ms	(/ (sin x) (- x (tan x)))
94.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
5.0ms	(- x (tan x))
5.0ms	(- x (tan x))

series494.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (sin x) (- x (tan x)))
236.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
63.0ms	(- x (tan x))
81.0ms	(- x (tan x))

simplify2.4s

Counts

110 → 110

Iterations

Iter	Nodes
done	5183
3	4000
2	1111
1	392
0	180

prune371.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) x)
0.2b	(/ (/ (sin x) x) (cos x))
0.2b	(/ (/ (sin x) x) (cos x))
2.4b	(- (+ 1 (/ (/ (sin x) x) (cos x))) (+ (/ (sin x) x) (* (/ (sin x) x) (/ (/ (sin x) x) (cos x)))))

rewrite371.0ms

Algorithm

rewrite-expression-head

Rules

159×	`times-frac`
101×	`*-un-lft-identity`
98×	`add-sqr-sqrt`
96×	`add-cube-cbrt`
29×	`associate-/l*`
16×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
11×	`div-inv`
10×	`frac-sub`
9×	`associate-/r*`
7×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+`
6×	`frac-add`
4×	`pow1` `sum-log` `diff-log` `insert-posit16`
3×	`clear-num` `frac-2neg`
2×	`frac-times` `associate-l/` `associate-r/` `distribute-lft-out--` `associate-/l/`
1×	`sub-neg` `flip3--` `associate--l+` `flip--` `distribute-lft-out` `associate--r+` `difference-of-squares`

Counts

4 → 201

Calls

4 calls:

8.0ms	(/ (sin x) x)
15.0ms	(/ (/ (sin x) x) (cos x))
24.0ms	(/ (/ (sin x) x) (cos x))
314.0ms	(- (+ 1 (/ (/ (sin x) x) (cos x))) (+ (/ (sin x) x) (* (/ (sin x) x) (/ (/ (sin x) x) (cos x)))))

series400.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (sin x) x)
79.0ms	(/ (/ (sin x) x) (cos x))
90.0ms	(/ (/ (sin x) x) (cos x))
173.0ms	(- (+ 1 (/ (/ (sin x) x) (cos x))) (+ (/ (sin x) x) (* (/ (sin x) x) (/ (/ (sin x) x) (cos x)))))

simplify2.9s

Counts

213 → 213

Iterations

Iter	Nodes
done	5002
2	3296
1	843
0	300

prune1.2s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes35.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.6b

bsearch162.0ms

Steps

Iters	Range		Point
10	1.508099977930646e-06	2590629949647.022	2.4087276690935244
10	-26711381.42537418	-6.803810524357175e-07	-0.030161987993530287

simplify13.0ms

Iterations

Iter	Nodes
done	46
1	46
0	35

end0.0ms

sample13.3s

Algorithm

intervals

Results

5.8s	1608×	body	2560	valid
3.9s	2728×	body	1280	valid
2.2s	1901×	body	640	valid
579.0ms	933×	body	320	valid
521.0ms	469×	body	160	valid
61.0ms	361×	body	80	valid