Details

sample338.0ms

Algorithm

intervals

Results

97.0ms	166×	body	80	valid
77.0ms	51×	body	1280	valid
43.0ms	41×	body	640	valid
13.0ms	20×	body	320	valid
12.0ms	55×	body	80	nan
2.0ms	6×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	20	27
1	42	27
2	83	26
3	152	26
4	362	26
5	1702	26
done	5000	26

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
7.2b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
16.8b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite284.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
49×	`times-frac`
45×	`*-un-lft-identity` `add-cube-cbrt`
30×	`pow-unpow`
25×	`add-exp-log`
21×	`associate-r`
16×	`add-cbrt-cube` `associate-l`
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×	`neg-sub0` `pow-to-exp` `cbrt-undiv` `associate-/r` `pow-exp` `associate-r/` `associate-/l*` `pow-sub`
2×	`frac-times` `tan-quot` `associate-/r/` `*-commutative`
1×	`clear-num` `neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `un-div-inv`

Counts

4 → 155

Calls

4 calls:

9.0ms	(/ 1.0 (tan B))
16.0ms	(* x (/ 1.0 (tan B)))
191.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
57.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series973.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ 1.0 (tan B))
177.0ms	(* x (/ 1.0 (tan B)))
461.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
268.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify2.0s

Counts

167 → 167

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	306	2742
1	867	2581
2	3845	2427
done	5000	2423

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize98.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt F)
0.5b	(* (cbrt F) (cbrt F))
2.8b	(* (/ (cbrt F) (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
16.8b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite294.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-sqr-sqrt`
44×	`*-un-lft-identity` `add-cube-cbrt`
42×	`times-frac`
31×	`cbrt-prod`
30×	`pow-unpow`
28×	`associate-l`
20×	`add-exp-log`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-r` `unswap-sqr`
12×	`pow1`
9×	`unpow-prod-down`
8×	`add-cbrt-cube`
7×	`pow1/3` `prod-exp`
6×	`swap-sqr`
5×	`sqr-pow`
4×	`pow-neg` `add-log-exp`
3×	`neg-sub0` `pow-to-exp` `div-exp` `pow-exp` `cbrt-unprod` `div-inv` `pow-sub`
2×	`frac-times` `pow-prod-down` `associate-r/` `pow-sqr` `-commutative` `pow-prod-up`
1×	`pow2` `cbrt-undiv` `neg-mul-1` `pow-pow` `pow-plus` `associate-*l/` `un-div-inv`

Counts

4 → 157

Calls

4 calls:

2.0ms	(cbrt F)
17.0ms	(* (cbrt F) (cbrt F))
196.0ms	(* (/ (cbrt F) (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
67.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series1.5s

Counts

4 → 12

Calls

4 calls:

312.0ms	(cbrt F)
348.0ms	(* (cbrt F) (cbrt F))
592.0ms	(* (/ (cbrt F) (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
241.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify3.0s

Counts

169 → 169

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	288	2961
1	825	2729
2	4013	2605
done	5000	2603

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.1b	(/ F (sin B))
7.2b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
16.8b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 143

Calls

4 calls:

17.0ms	(/ (* x 1.0) (tan B))
8.0ms	(/ F (sin B))
171.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
41.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series941.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(/ (* x 1.0) (tan B))
73.0ms	(/ F (sin B))
458.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
241.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify1.9s

Counts

155 → 155

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	288	2628
1	807	2471
2	3788	2325
done	5000	2323

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize72.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.1b	(/ F (sin B))
7.1b	(/ (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
16.8b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

184×	`times-frac`
106×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
45×	`unpow-prod-down`
25×	`add-exp-log`
17×	`associate-/l*`
16×	`add-cbrt-cube`
15×	`sqr-pow`
13×	`pow-unpow` `associate-/r*`
12×	`div-exp` `div-inv`
6×	`cbrt-undiv`
5×	`pow1`
4×	`add-log-exp`
3×	`pow-to-exp` `clear-num` `frac-2neg` `pow-exp`
1×	`pow-pow` `prod-exp` `tan-quot` `associate-/r/` `cbrt-unprod` `associate-/l/`

Counts

4 → 206

Calls

4 calls:

8.0ms	(/ (* x 1.0) (tan B))
7.0ms	(/ F (sin B))
132.0ms	(/ (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
79.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series914.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ (* x 1.0) (tan B))
60.0ms	(/ F (sin B))
468.0ms	(/ (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
220.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify1.9s

Counts

218 → 218

Iterations

Useful iterations: 2 (836.0ms)

Iter	Nodes	Cost
0	408	5817
1	1020	5584
2	4921	5434
done	5002	5434

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes311.0ms

Accuracy

94.5% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 13.8b

bsearch630.0ms

Steps

Iters	Range		Point
11	1.583250720483607e-07	2710528402378101.5	18380437.495112307
9	-1.9763734922418815e+126	-2.615624459402513e+121	-2.648293288116179e+121

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	73
1	44	73
done	44	73

end0.0ms

sample10.5s

Algorithm

intervals

Results

3.6s	1691×	body	1280	valid
2.6s	4849×	body	80	valid
2.0s	1344×	body	640	valid
1.0s	707×	body	320	valid
449.0ms	1604×	body	80	nan
189.0ms	338×	body	160	valid