Details

sample427.0ms

Algorithm

intervals

Results

90.0ms	44×	body	1280	valid
88.0ms	59×	body	80	nan
66.0ms	51×	body	640	valid
46.0ms	140×	body	80	valid
32.0ms	35×	body	320	valid
9.0ms	14×	body	160	valid

simplify4.0s

Counts

1 → 1

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	20	27
1	42	27
2	83	26
3	151	26
4	345	26
5	876	26
6	3195	26
done	5000	26

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.3b	(* x (/ 1.0 (tan B)))
5.5b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
14.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite467.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
49×	`times-frac`
45×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
25×	`add-exp-log`
21×	`associate-r`
16×	`associate-l` `add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
8×	`unpow-prod-down` `prod-exp` `unswap-sqr`
7×	`pow1`
5×	`div-exp` `div-inv`
4×	`pow-neg` `cbrt-unprod` `add-log-exp` `sqr-pow`
3×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `associate-r/` `pow-exp` `associate-/r` `associate-/l*` `pow-sub`
2×	`frac-times` `*-commutative`
1×	`tan-quot` `neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `clear-num` `associate-/r/` `un-div-inv`

Counts

4 → 154

Calls

4 calls:

6.0ms	(/ F (sin B))
19.0ms	(* x (/ 1.0 (tan B)))
330.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
105.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series943.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/ F (sin B))
212.0ms	(* x (/ 1.0 (tan B)))
439.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
219.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify1.8s

Counts

166 → 166

Iterations

Useful iterations: 2 (745.0ms)

Iter	Nodes	Cost
0	303	2726
1	745	2555
2	2057	2401
done	5000	2401

prune959.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
0.3b	(* x (/ 1.0 (tan B)))
0.4b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
14.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite583.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
73×	`times-frac`
59×	`add-cube-cbrt` `*-un-lft-identity`
39×	`associate-r`
30×	`pow-unpow`
25×	`add-exp-log` `unpow-prod-down`
16×	`add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
9×	`pow1` `sqr-pow`
7×	`div-exp` `associate-/l*`
6×	`associate-l` `prod-exp` `unswap-sqr`
5×	`div-inv`
4×	`cbrt-unprod` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `pow-exp` `associate-/r*`
2×	`neg-sub0` `pow-neg` `associate-r/` `pow-prod-down` `-commutative` `associate-/l/` `pow-sub`
1×	`tan-quot` `neg-mul-1` `pow-pow` `frac-2neg` `clear-num` `associate-/r/`

Counts

4 → 174

Calls

4 calls:

287.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
30.0ms	(* x (/ 1.0 (tan B)))
174.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
78.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series1.4s

Counts

4 → 12

Calls

4 calls:

538.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
173.0ms	(* x (/ 1.0 (tan B)))
510.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
186.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify1.6s

Counts

186 → 186

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	341	3949
1	821	3760
2	2267	3533
done	5000	3527

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.2b	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
0.4b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
14.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite571.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
63×	`add-sqr-sqrt`
53×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
25×	`add-exp-log` `unpow-prod-down` `associate-r`
16×	`add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
9×	`sqr-pow`
8×	`div-exp` `associate-/l*`
7×	`pow1`
6×	`associate-/r*`
5×	`prod-exp` `div-inv`
4×	`cbrt-undiv` `add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `associate-l` `pow-exp` `cbrt-unprod`
2×	`neg-sub0` `pow-neg` `frac-2neg` `clear-num` `associate-/l/` `pow-sub`
1×	`tan-quot` `neg-mul-1` `pow-pow` `associate-r/` `pow-prod-down` `associate-/r/` `-commutative`

Counts

4 → 163

Calls

4 calls:

11.0ms	(/ (* x 1.0) (tan B))
260.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
223.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
68.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (* x 1.0) (tan B))
543.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
452.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
167.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify2.1s

Counts

175 → 175

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	326	3851
1	777	3672
2	2235	3445
done	5001	3439

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* F (/ (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B)))
0.4b	(/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.4b	(/ (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
14.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite672.0ms

Algorithm

rewrite-expression-head

Rules

340×	`times-frac`
203×	`add-sqr-sqrt`
182×	`*-un-lft-identity`
179×	`add-cube-cbrt`
80×	`unpow-prod-down`
79×	`associate-r`
66×	`add-exp-log`
38×	`div-exp`
28×	`associate-/l*` `sqr-pow`
20×	`add-cbrt-cube`
13×	`pow-unpow`
11×	`prod-exp` `div-inv`
10×	`pow-to-exp` `pow-exp` `associate-/r*`
9×	`rec-exp` `1-exp`
8×	`unswap-sqr`
7×	`pow1` `cbrt-undiv`
4×	`add-log-exp`
3×	`associate-l` `cbrt-unprod`
2×	`frac-2neg` `clear-num`
1×	`pow-flip` `pow-pow` `associate-r/` `pow-prod-down` `-commutative` `associate-/l/` `inv-pow`

Counts

4 → 320

Calls

4 calls:

257.0ms	(* F (/ (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B)))
101.0ms	(/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
211.0ms	(/ (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
80.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series2.2s

Counts

4 → 12

Calls

4 calls:

485.0ms	(* F (/ (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B)))
1.0s	(/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
491.0ms	(/ (/ 1 (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
230.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify2.1s

Counts

332 → 332

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	511	9401
1	1243	8559
2	2688	8092
done	5000	8062

prune1.4s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes389.0ms

Accuracy

95.6% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 10.4b

bsearch523.0ms

Steps

Iters	Range		Point
9	3.114035649502917e+72	1.0428382087987484e+80	3.3296852638566246e+72
9	-5.063582918003288e+31	-5.452804783141298e+22	-5.782687067962697e+22

simplify11.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	77
1	51	77
done	51	77

end0.0ms

sample10.0s

Algorithm

intervals

Results

4.2s	1688×	body	1280	valid
1.9s	4868×	body	80	valid
1.9s	1354×	body	640	valid
566.0ms	670×	body	320	valid
504.0ms	1632×	body	80	nan
254.0ms	346×	body	160	valid