Details

sample758.0ms

Algorithm

intervals

Results

358.0ms	96×	body	1280	valid
190.0ms	40×	body	2560	valid
76.0ms	63×	body	640	valid
24.0ms	24×	body	320	valid
15.0ms	19×	body	160	valid
4.0ms	14×	body	80	valid

simplify52.0ms

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: 26.1b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.8b	(- x (tan x))
1.9b	(- x (sin x))

rewrite44.0ms

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)))
5.0ms	(- x (tan x))
8.0ms	(- x (sin x))

series216.0ms

Counts

3 → 9

Calls

3 calls:

102.0ms	(/ (- x (sin x)) (- x (tan x)))
66.0ms	(- x (tan x))
48.0ms	(- x (sin x))

simplify1.6s

Counts

122 → 122

Iterations

Iter	Nodes
3	4396
2	1293
1	504
0	212

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (* x (cos x)))
0.3b	(* (cos x) (cos x))
0.6b	(- (/ (sin x) (* x (cos x))) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x)))
25.2b	(fma (/ (/ (sin x) x) x) (/ (sin x) (* (cos x) (cos x))) (- (/ (sin x) (* x (cos x))) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
25×	`add-cube-cbrt`
21×	`prod-diff`
15×	`times-frac`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
7×	`fma-neg`
6×	`add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`swap-sqr` `associate-r` `associate-l` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `fma-udef`
1×	`pow2` `sqr-cos` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `pow-plus` `flip3--` `diff-log` `pow-prod-down` `pow-sqr` `cos-mult` `-commutative` `pow-prod-up` `flip--` `associate--r+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 111

Calls

4 calls:

13.0ms	(/ (sin x) (* x (cos x)))
12.0ms	(* (cos x) (cos x))
39.0ms	(- (/ (sin x) (* x (cos x))) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x)))
0.0ms	(fma (/ (/ (sin x) x) x) (/ (sin x) (* (cos x) (cos x))) (- (/ (sin x) (* x (cos x))) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x))))

series789.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (sin x) (* x (cos x)))
18.0ms	(* (cos x) (cos x))
255.0ms	(- (/ (sin x) (* x (cos x))) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x)))
431.0ms	(fma (/ (/ (sin x) x) x) (/ (sin x) (* (cos x) (cos x))) (- (/ (sin x) (* x (cos x))) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x))))

simplify3.2s

Counts

123 → 123

Iterations

Iter	Nodes
3	6479
2	1337
1	458
0	199

prune1.7s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

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))

rewrite46.0ms

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:

5.0ms	(- 9/40 (* 27/2800 (* x x)))
25.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
14.0ms	(* 27/2800 (* x x))

series289.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(- 9/40 (* 27/2800 (* x x)))
153.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
44.0ms	(* 27/2800 (* x x))

simplify1.9s

Counts

86 → 86

Iterations

Iter	Nodes
3	3175
2	1030
1	343
0	113

prune621.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 3 expressions with local error:

0.5b	(/ (fma (sqrt x) (sqrt x) (- (sin x))) (- x (tan x)))
1.8b	(- x (tan x))
12.2b	(fma (sqrt x) (sqrt x) (- (sin x)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/r*` `add-cbrt-cube` `add-exp-log` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`expm1-log1p-u` `pow1` `fma-neg` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `fma-udef` `div-inv`

Counts

3 → 80

Calls

3 calls:

22.0ms	(/ (fma (sqrt x) (sqrt x) (- (sin x))) (- x (tan x)))
10.0ms	(- x (tan x))
1.0ms	(fma (sqrt x) (sqrt x) (- (sin x)))

series419.0ms

Counts

3 → 9

Calls

3 calls:

220.0ms	(/ (fma (sqrt x) (sqrt x) (- (sin x))) (- x (tan x)))
80.0ms	(- x (tan x))
119.0ms	(fma (sqrt x) (sqrt x) (- (sin x)))

simplify1.9s

Counts

89 → 89

Iterations

Iter	Nodes
3	4624
2	1209
1	432
0	186

prune879.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

regimes75.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.7b

bsearch168.0ms

Steps

Iters	Range		Point
9	0.08974485042074802	9369.000823706243	2.4331115039478592
8	-15521.296822102611	-0.2777104116290821	-2.4489045375766514

simplify7.0ms

Iterations

Iter	Nodes
2	38
1	38
0	29

end0.0ms

sample16.7s

Algorithm

intervals

Results

7.9s	1630×	body	2560	valid
5.5s	2747×	body	1280	valid
2.2s	1896×	body	640	valid
684.0ms	931×	body	320	valid
191.0ms	424×	body	160	valid
88.0ms	372×	body	80	valid