Details

sample572.0ms

Algorithm

intervals

Results

171.0ms	57×	body	640	valid
145.0ms	49×	body	1280	valid
87.0ms	162×	body	80	valid
19.0ms	17×	body	320	valid
17.0ms	59×	body	80	nan
12.0ms	10×	body	160	valid

simplify4.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5030
6	2759
5	813
4	310
3	144
2	82
1	42
0	20

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize105.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* (/ 1.0 (tan B)) x)
8.1b	(* (pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ (- 1.0) 2.0)) (/ F (sin B)))
19.4b	(pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ (- 1.0) 2.0))

rewrite508.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 158

Calls

4 calls:

12.0ms	(/ 1.0 (tan B))
42.0ms	(* (/ 1.0 (tan B)) x)
317.0ms	(* (pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ (- 1.0) 2.0)) (/ F (sin B)))
123.0ms	(pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ (- 1.0) 2.0))

series3.6s

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ 1.0 (tan B))
176.0ms	(* (/ 1.0 (tan B)) x)
2.7s	(* (pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ (- 1.0) 2.0)) (/ F (sin B)))
614.0ms	(pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ (- 1.0) 2.0))

simplify4.7s

Counts

170 → 170

Iterations

Iter	Nodes
done	5000
2	3185
1	1045
0	370

prune2.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.6b

localize89.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (* (pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0)) (sin B)))
0.2b	(* (pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0)) (sin B))
0.3b	(* (/ 1.0 (tan B)) x)
19.4b	(pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0))

rewrite486.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
25×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
22×	`times-frac`
21×	`associate-l`
16×	`add-cbrt-cube`
13×	`pow-unpow`
8×	`prod-exp`
7×	`pow1` `unpow-prod-down`
6×	`associate-r`
5×	`div-exp` `unswap-sqr`
4×	`cbrt-unprod` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `pow-exp` `div-inv` `associate-/l*` `sqr-pow`
2×	`*-commutative`
1×	`tan-quot` `pow-pow` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `associate-/r/`

Counts

4 → 108

Calls

4 calls:

87.0ms	(/ F (* (pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0)) (sin B)))
276.0ms	(* (pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0)) (sin B))
43.0ms	(* (/ 1.0 (tan B)) x)
71.0ms	(pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0))

series3.3s

Counts

4 → 12

Calls

4 calls:

727.0ms	(/ F (* (pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0)) (sin B)))
1.8s	(* (pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0)) (sin B))
165.0ms	(* (/ 1.0 (tan B)) x)
607.0ms	(pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0))

simplify4.0s

Counts

120 → 120

Iterations

Iter	Nodes
done	5002
2	2146
1	708
0	277

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.2b	(/ F (* (pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0)) (sin B)))
0.2b	(* (pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0)) (sin B))
19.4b	(pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0))

rewrite455.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
25×	`add-cube-cbrt` `*-un-lft-identity`
22×	`add-exp-log`
21×	`times-frac`
13×	`pow-unpow` `add-cbrt-cube`
7×	`unpow-prod-down` `associate-l`
6×	`prod-exp` `associate-/l*`
5×	`pow1` `div-exp`
4×	`associate-/r*` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `associate-r` `pow-exp` `div-inv` `unswap-sqr` `sqr-pow`
2×	`frac-2neg` `clear-num` `cbrt-unprod`
1×	`tan-quot` `pow-pow` `associate-/r/` `*-commutative`

Counts

4 → 103

Calls

4 calls:

11.0ms	(/ x (tan B))
87.0ms	(/ F (* (pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0)) (sin B)))
272.0ms	(* (pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0)) (sin B))
79.0ms	(pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0))

series3.5s

Counts

4 → 12

Calls

4 calls:

201.0ms	(/ x (tan B))
809.0ms	(/ F (* (pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0)) (sin B)))
1.9s	(* (pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0)) (sin B))
640.0ms	(pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0))

simplify3.6s

Counts

115 → 115

Iterations

Iter	Nodes
done	5000
2	1876
1	637
0	260

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0)) (sin B))
0.2b	(/ 1 (* (pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0)) (sin B)))
0.2b	(* F (/ 1 (* (pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0)) (sin B))))
19.4b	(pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0))

rewrite970.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-exp-log`
34×	`prod-exp`
27×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
16×	`div-exp`
15×	`times-frac`
13×	`pow-unpow`
10×	`associate-r` `associate-l`
8×	`pow1` `pow-to-exp` `rec-exp` `1-exp` `pow-exp`
7×	`unpow-prod-down`
6×	`cbrt-unprod`
4×	`cbrt-undiv` `add-log-exp` `unswap-sqr`
3×	`div-inv` `associate-/l*` `sqr-pow`
2×	`*-commutative`
1×	`pow-flip` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `un-div-inv` `inv-pow`

Counts

4 → 123

Calls

4 calls:

278.0ms	(* (pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0)) (sin B))
170.0ms	(/ 1 (* (pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0)) (sin B)))
450.0ms	(* F (/ 1 (* (pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0)) (sin B))))
62.0ms	(pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0))

series5.5s

Counts

4 → 12

Calls

4 calls:

1.8s	(* (pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0)) (sin B))
2.3s	(/ 1 (* (pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0)) (sin B)))
756.0ms	(* F (/ 1 (* (pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0)) (sin B))))
620.0ms	(pow (+ (* 2.0 x) (+ (* F F) 2.0)) (/ 1.0 2.0))

simplify3.9s

Counts

135 → 135

Iterations

Iter	Nodes
done	5000
2	2334
1	786
0	289

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes527.0ms

Accuracy

97.8% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 10.6b

bsearch627.0ms

Steps

Iters	Range		Point
10	6.402043939282351e-10	87.84726908649233	86.69108830173802
6	-5.870687798111552	-1.440408271564231	-5.807335808175188

simplify19.0ms

Iterations

Iter	Nodes
done	48
1	48
0	38

end0.0ms

sample13.6s

Algorithm

intervals

Results

4.6s	1667×	body	1280	valid
3.6s	1408×	body	640	valid
2.9s	4750×	body	80	valid
830.0ms	666×	body	320	valid
729.0ms	1640×	body	80	nan
312.0ms	341×	body	160	valid