Details

sample594.0ms

Algorithm

intervals

Results

240.0ms	49×	body	2560	valid
127.0ms	79×	body	1280	valid
118.0ms	72×	body	640	valid
20.0ms	30×	body	320	valid
6.0ms	13×	body	160	valid
3.0ms	13×	body	80	valid

simplify22.0ms

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.9b	(- x (tan x))
0.9b	(- x (sin x))

rewrite60.0ms

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:

19.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
34.0ms	(- x (sin x))

series287.0ms

Counts

3 → 9

Calls

3 calls:

143.0ms	(/ (- x (sin x)) (- x (tan x)))
89.0ms	(- x (tan x))
55.0ms	(- x (sin x))

simplify1.8s

Counts

92 → 92

Iterations

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

prune364.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
0.4b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.9b	(- x (tan x))
0.9b	(- x (tan x))

rewrite123.0ms

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:

14.0ms	(/ (sin x) (- x (tan x)))
81.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
17.0ms	(- x (tan x))
9.0ms	(- x (tan x))

series476.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (sin x) (- x (tan x)))
247.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
65.0ms	(- x (tan x))
60.0ms	(- x (tan x))

simplify2.4s

Counts

110 → 110

Iterations

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

prune411.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (sin x) (cos x)) x)
0.2b	(/ (/ (sin x) x) (cos x))
0.2b	(/ (/ (sin x) x) (cos x))
0.9b	(- (+ 1 (/ (/ (sin x) x) (cos x))) (+ (/ (sin x) x) (* (/ (sin x) x) (/ (/ (sin x) x) (cos x)))))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

225×	`times-frac`
135×	`*-un-lft-identity`
132×	`add-sqr-sqrt`
130×	`add-cube-cbrt`
39×	`associate-/l*`
19×	`add-cbrt-cube` `add-exp-log`
16×	`add-log-exp`
15×	`div-inv`
10×	`frac-sub`
9×	`cbrt-undiv` `associate-/r*` `div-exp`
7×	`flip3-+` `flip-+`
6×	`frac-add`
4×	`pow1` `sum-log` `diff-log` `insert-posit16`
3×	`clear-num` `frac-2neg` `associate-/l/`
2×	`frac-times` `associate-l/` `associate-r/` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `associate--l+` `flip--` `distribute-lft-out` `associate--r+` `difference-of-squares`

Counts

4 → 244

Calls

4 calls:

23.0ms	(/ (/ (sin x) (cos x)) x)
23.0ms	(/ (/ (sin x) x) (cos x))
23.0ms	(/ (/ (sin x) x) (cos x))
134.0ms	(- (+ 1 (/ (/ (sin x) x) (cos x))) (+ (/ (sin x) x) (* (/ (sin x) x) (/ (/ (sin x) x) (cos x)))))

series376.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (/ (sin x) (cos x)) x)
64.0ms	(/ (/ (sin x) x) (cos x))
60.0ms	(/ (/ (sin x) x) (cos x))
190.0ms	(- (+ 1 (/ (/ (sin x) x) (cos x))) (+ (/ (sin x) x) (* (/ (sin x) x) (/ (/ (sin x) x) (cos x)))))

simplify3.3s

Counts

256 → 256

Iterations

Iter	Nodes
done	5005
2	4008
1	1090
0	399

prune1.5s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
0.9b	(- x (tan x))
0.9b	(- x (tan x))
2.8b	(log (exp (/ (sin x) (- x (tan x)))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`times-frac`
24×	`add-cube-cbrt`
22×	`log-pow`
21×	`exp-prod`
9×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/r*`
4×	`flip3--` `associate-/r/` `insert-posit16` `flip--`
3×	`log-prod` `associate-/l*`
2×	`sub-neg` `diff-log` `div-inv`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `rem-log-exp`

Counts

4 → 102

Calls

4 calls:

15.0ms	(/ (sin x) (- x (tan x)))
4.0ms	(- x (tan x))
4.0ms	(- x (tan x))
16.0ms	(log (exp (/ (sin x) (- x (tan x)))))

series364.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (sin x) (- x (tan x)))
85.0ms	(- x (tan x))
86.0ms	(- x (tan x))
93.0ms	(log (exp (/ (sin x) (- x (tan x)))))

simplify1.8s

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
3	2405
2	842
1	305
0	169

prune528.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes43.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.4b

bsearch193.0ms

Steps

Iters	Range		Point
10	2.618543036730298e-08	12461.173664998358	0.06331538098159631
9	-101227.54480913779	-5.532094628653386e-05	-0.0654189940460499

simplify5.0ms

Iterations

Iter	Nodes
done	33
1	33
0	25

end0.0ms

sample16.1s

Algorithm

intervals

Results

6.8s	1612×	body	2560	valid
4.8s	2679×	body	1280	valid
2.7s	1843×	body	640	valid
861.0ms	985×	body	320	valid
310.0ms	503×	body	160	valid
90.0ms	378×	body	80	valid