Details

sample3.8s

Algorithm

intervals

Results

2.2s	42×	body	2560	valid
473.0ms	86×	body	1280	valid
324.0ms	64×	body	640	valid
45.0ms	35×	body	320	valid
39.0ms	18×	body	160	valid
3.0ms	11×	body	80	valid

simplify653.0ms

Counts

1 → 1

Iterations

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

prune94.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.8b

localize1.3s

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.3b	(- x (tan x))
1.3b	(- x (sin x))

rewrite375.0ms

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×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

62.0ms	(/ (- x (sin x)) (- x (tan x)))
29.0ms	(- x (tan x))
220.0ms	(- x (sin x))

series2.2s

Counts

3 → 9

Calls

3 calls:

346.0ms	(/ (- x (sin x)) (- x (tan x)))
302.0ms	(- x (tan x))
1.5s	(- x (sin x))

simplify10.2s

Counts

89 → 89

Iterations

Iter	Nodes
done	5004
3	3277
2	954
1	371
0	157

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize303.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (sin x) x) (cos x))
0.2b	(/ (/ (sin x) x) (cos x))
0.2b	(/ (/ (sin x) x) (cos x))
0.2b	(* (/ (/ (sin x) x) (cos x)) (/ (/ (sin x) x) (cos x)))

rewrite602.0ms

Algorithm

rewrite-expression-head

Rules

507×	`times-frac`
306×	`add-sqr-sqrt`
270×	`add-cube-cbrt` `*-un-lft-identity`
55×	`add-exp-log` `add-cbrt-cube`
43×	`swap-sqr` `associate-r` `associate-l`
39×	`associate-/l*`
31×	`div-inv`
27×	`cbrt-undiv` `div-exp`
11×	`pow1`
9×	`prod-exp` `associate-/r*` `cbrt-unprod` `unswap-sqr`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num` `associate-/l/`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 382

Calls

4 calls:

36.0ms	(/ (/ (sin x) x) (cos x))
30.0ms	(/ (/ (sin x) x) (cos x))
43.0ms	(/ (/ (sin x) x) (cos x))
408.0ms	(* (/ (/ (sin x) x) (cos x)) (/ (/ (sin x) x) (cos x)))

series814.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(/ (/ (sin x) x) (cos x))
81.0ms	(/ (/ (sin x) x) (cos x))
101.0ms	(/ (/ (sin x) x) (cos x))
412.0ms	(* (/ (/ (sin x) x) (cos x)) (/ (/ (sin x) x) (cos x)))

simplify7.0s

Counts

394 → 394

Iterations

Iter	Nodes
done	5001
1	1334
0	362

prune7.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize369.0ms

Local error

Found 4 expressions with local error:

1.3b	(- x (tan x))
1.3b	(- x (sin x))
1.3b	(- x (sin x))
1.3b	(- x (sin x))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

13.0ms	(- x (tan x))
13.0ms	(- x (sin x))
14.0ms	(- x (sin x))
16.0ms	(- x (sin x))

series423.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- x (tan x))
109.0ms	(- x (sin x))
69.0ms	(- x (sin x))
141.0ms	(- x (sin x))

simplify18.1s

Counts

68 → 68

Iterations

Iter	Nodes
done	5000
5	4997
4	1740
3	750
2	355
1	153
0	76

prune1.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize255.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* 9/40 x))
0.1b	(* (* x x) (* x x))
0.1b	(* 9/40 x)
14.3b	(+ (* x (* 9/40 x)) (- (* (* (* x x) (* x x)) -27/2800) 1/2))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

122×	`pow1`
36×	`pow-prod-up`
27×	`pow-prod-down`
23×	`add-exp-log` `add-cbrt-cube`
22×	`pow-sqr`
18×	`pow-plus`
13×	`pow2`
12×	`prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
5×	`associate-r`
3×	`*-commutative`
2×	`associate-+r+` `sum-log` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3-+` `diff-log` `swap-sqr` `flip-+`

Counts

4 → 114

Calls

4 calls:

40.0ms	(* x (* 9/40 x))
58.0ms	(* (* x x) (* x x))
15.0ms	(* 9/40 x)
964.0ms	(+ (* x (* 9/40 x)) (- (* (* (* x x) (* x x)) -27/2800) 1/2))

series386.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* x (* 9/40 x))
62.0ms	(* (* x x) (* x x))
169.0ms	(* 9/40 x)
106.0ms	(+ (* x (* 9/40 x)) (- (* (* (* x x) (* x x)) -27/2800) 1/2))

simplify6.8s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	1105
1	345
0	118

prune1.2s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes307.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.4b

bsearch548.0ms

Steps

Iters	Range		Point
9	2.490703692944805e-05	37.746059492850215	2.4532506186394216
10	-75476531921.81544	-1.440408271564231	-2.4478149728366576

simplify673.0ms

Iterations

Iter	Nodes
done	41
1	41
0	29

end1.0ms

sample1.1m

Algorithm

intervals

Results

27.7s	2719×	body	1280	valid
24.2s	1611×	body	2560	valid
12.3s	1852×	body	640	valid
2.9s	950×	body	320	valid
433.0ms	486×	body	160	valid
95.0ms	382×	body	80	valid