Details

sample486.0ms

Algorithm

intervals

Results

228.0ms	48×	body	2560	valid
99.0ms	82×	body	1280	valid
38.0ms	54×	body	640	valid
18.0ms	42×	body	320	valid
6.0ms	11×	body	160	valid
4.0ms	19×	body	80	valid

simplify30.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	6	9
1	13	9
2	17	9
3	19	9
done	19	9

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize24.0ms

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))

rewrite134.0ms

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×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 110

Calls

3 calls:

49.0ms	(/ (- x (sin x)) (- x (tan x)))
20.0ms	(- x (tan x))
59.0ms	(- x (sin x))

series276.0ms

Counts

3 → 9

Calls

3 calls:

127.0ms	(/ (- x (sin x)) (- x (tan x)))
80.0ms	(- x (tan x))
68.0ms	(- x (sin x))

simplify1.6s

Counts

119 → 119

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	209	1823
1	501	1569
2	2266	1386
done	5002	1362

prune400.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.9b	(- x (sin x))
1.3b	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
27.7b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

1.0ms	(cbrt x)
8.0ms	(- x (sin x))
38.0ms	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
1.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

series1.8s

Counts

4 → 12

Calls

4 calls:

305.0ms	(cbrt x)
50.0ms	(- x (sin x))
928.0ms	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
490.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

simplify1.3s

Counts

103 → 103

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	168	1778
1	363	1645
2	1443	1195
done	5001	950

prune384.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (cos x))
0.8b	(- (/ x (- x (/ (sin x) (cos x)))) (/ (sin x) (- x (/ (sin x) (cos x)))))
0.9b	(- x (/ (sin x) (cos x)))
0.9b	(- x (/ (sin x) (cos x)))

rewrite449.0ms

Algorithm

rewrite-expression-head

Rules

1341×	`add-sqr-sqrt`
1116×	`times-frac`
900×	`*-un-lft-identity`
654×	`prod-diff`
574×	`add-cube-cbrt`
306×	`difference-of-squares`
162×	`distribute-lft-out--`
102×	`associate-/r/`
58×	`div-inv`
54×	`flip3--` `flip--`
30×	`fma-neg`
10×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `associate-/r` `associate-/l`
1×	`cbrt-undiv` `quot-tan` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 780

Calls

4 calls:

12.0ms	(/ (sin x) (cos x))
282.0ms	(- (/ x (- x (/ (sin x) (cos x)))) (/ (sin x) (- x (/ (sin x) (cos x)))))
24.0ms	(- x (/ (sin x) (cos x)))
16.0ms	(- x (/ (sin x) (cos x)))

series494.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (sin x) (cos x))
290.0ms	(- (/ x (- x (/ (sin x) (cos x)))) (/ (sin x) (- x (/ (sin x) (cos x)))))
79.0ms	(- x (/ (sin x) (cos x)))
102.0ms	(- x (/ (sin x) (cos x)))

simplify1.1s

Counts

792 → 792

Iterations

Useful iterations: done (1000.0ms)

Iter	Nodes	Cost
0	836	63656
1	1909	58451
done	5001	46801

prune3.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma 27/2800 (pow x 4) 1/2)
0.3b	(* 9/40 (pow x 2))
14.3b	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
8×	`add-exp-log` `associate-r`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube` `add-log-exp`
4×	`unpow-prod-down` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `associate-l` `prod-diff` `prod-exp` `log1p-expm1-u`
2×	`fma-udef` `unpow2` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `fma-neg` `diff-log` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `associate--r+`

Counts

3 → 58

Calls

3 calls:

0.0ms	(fma 27/2800 (pow x 4) 1/2)
12.0ms	(* 9/40 (pow x 2))
16.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

series308.0ms

Counts

3 → 9

Calls

3 calls:

161.0ms	(fma 27/2800 (pow x 4) 1/2)
54.0ms	(* 9/40 (pow x 2))
93.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

simplify1.9s

Counts

67 → 67

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	106	845
1	250	714
2	1251	624
done	5001	581

prune189.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes40.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.8b

bsearch125.0ms

Steps

Iters	Range		Point
9	5.2366538615162886e-09	1.4124627081995123	0.030777233034415038
8	-0.03117879455470207	-1.716801800522696e-06	-0.029879180996958295

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	24	60
1	28	41
done	28	41

end0.0ms

sample14.0s

Algorithm

intervals

Results

7.3s	1621×	body	2560	valid
4.0s	2728×	body	1280	valid
1.6s	1861×	body	640	valid
579.0ms	943×	body	320	valid
205.0ms	473×	body	160	valid
66.0ms	374×	body	80	valid