Details

sample544.0ms

Algorithm

intervals

Results

222.0ms	51×	body	2560	valid
155.0ms	87×	body	1280	valid
70.0ms	36×	body	320	valid
35.0ms	52×	body	640	valid
4.0ms	16×	body	160	valid
2.0ms	14×	body	80	valid

simplify196.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.1b	(- x (tan x))
1.1b	(- x (sin x))

rewrite93.0ms

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` `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 → 110

Calls

3 calls:

43.0ms	(/ (- x (sin x)) (- x (tan x)))
10.0ms	(- x (tan x))
15.0ms	(- x (sin x))

series308.0ms

Counts

3 → 9

Calls

3 calls:

136.0ms	(/ (- x (sin x)) (- x (tan x)))
101.0ms	(- x (tan x))
71.0ms	(- x (sin x))

simplify2.7s

Counts

119 → 119

Iterations

Iter	Nodes
done	5000
3	4708
2	1277
1	501
0	209

prune526.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (/ (- x (sin x)) (- x (tan x)))))
0.0b	(/ (- x (sin x)) (- x (tan x)))
1.1b	(- x (tan x))
1.1b	(- x (sin x))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

0.0ms	(expm1 (log1p (/ (- x (sin x)) (- x (tan x)))))
31.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series448.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(expm1 (log1p (/ (- x (sin x)) (- x (tan x)))))
131.0ms	(/ (- x (sin x)) (- x (tan x)))
80.0ms	(- x (tan x))
47.0ms	(- x (sin x))

simplify3.4s

Counts

133 → 133

Iterations

Iter	Nodes
done	5000
3	4623
2	1285
1	515
0	220

prune747.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize92.0ms

Local error

Found 4 expressions with local error:

1.1b	(- x (tan x))
1.1b	(- x (sin x))
1.1b	(- x (sin x))
1.1b	(- x (sin x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`add-cube-cbrt`
12×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 112

Calls

4 calls:

5.0ms	(- x (tan x))
6.0ms	(- x (sin x))
6.0ms	(- x (sin x))
9.0ms	(- x (sin x))

series205.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- x (tan x))
39.0ms	(- x (sin x))
46.0ms	(- x (sin x))
43.0ms	(- x (sin x))

simplify3.3s

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
4	4582
3	1650
2	622
1	277
0	127

prune537.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

279×	`times-frac`
212×	`add-sqr-sqrt`
203×	`*-un-lft-identity`
201×	`add-cube-cbrt`
129×	`prod-diff`
43×	`fma-neg`
18×	`div-inv`
13×	`add-cbrt-cube` `add-exp-log`
11×	`pow1`
6×	`associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`cbrt-undiv` `swap-sqr` `div-exp` `associate-r` `associate-l` `difference-of-squares`
2×	`clear-num` `frac-2neg` `prod-exp` `cos-mult` `cbrt-unprod`
1×	`pow2` `sqr-cos` `quot-tan` `sub-neg` `pow-plus` `flip3--` `diff-log` `pow-prod-down` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `fma-udef` `flip--` `associate--r+` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 274

Calls

4 calls:

16.0ms	(/ (sin x) (cos x))
12.0ms	(/ (sin x) (* (cos x) (cos x)))
8.0ms	(* (cos x) (cos x))
75.0ms	(- (/ (/ (sin x) x) (cos x)) (fma (/ (sin x) (cos x)) (/ (/ (sin x) x) x) (/ (sin x) x)))

series357.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (sin x) (cos x))
50.0ms	(/ (sin x) (* (cos x) (cos x)))
34.0ms	(* (cos x) (cos x))
247.0ms	(- (/ (/ (sin x) x) (cos x)) (fma (/ (sin x) (cos x)) (/ (/ (sin x) x) x) (/ (sin x) x)))

simplify2.4s

Counts

286 → 286

Iterations

Iter	Nodes
done	5089
2	2958
1	949
0	408

prune2.5s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes131.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.2b

bsearch101.0ms

Steps

Iters	Range		Point
8	0.0004390994911134099	0.778402845272117	0.028579019903451953
9	-0.1501579911863904	-8.136897775944376e-09	-0.025546220888092473

simplify4.0ms

Iterations

Iter	Nodes
done	27
1	27
0	23

end0.0ms

sample13.2s

Algorithm

intervals

Results

6.5s	1561×	body	2560	valid
4.3s	2812×	body	1280	valid
1.4s	1804×	body	640	valid
453.0ms	952×	body	320	valid
191.0ms	500×	body	160	valid
64.0ms	371×	body	80	valid