Details

sample529.0ms

Algorithm

intervals

Results

187.0ms	57×	body	1280	valid
67.0ms	39×	body	640	valid
59.0ms	155×	body	80	valid
53.0ms	55×	body	80	nan
26.0ms	22×	body	320	valid
6.0ms	6×	body	160	valid

simplify8.4s

Counts

1 → 1

Iterations

Iter	Nodes
7	8510
6	1843
5	606
4	239
3	124
2	80
1	46
0	20

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.8b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.2b	(/ (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F) (sin B))
0.3b	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
17.0b	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`add-exp-log`
19×	`add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`times-frac`
9×	`unpow-prod-down`
8×	`associate-l`
6×	`associate-/r*` `prod-exp`
5×	`pow1` `div-exp`
4×	`insert-posit16` `associate-/l*` `add-log-exp`
3×	`pow-to-exp` `cbrt-undiv` `pow-unpow` `associate-r` `pow-exp` `unswap-sqr` `sqr-pow`
2×	`clear-num` `frac-2neg` `cbrt-unprod` `div-inv` `distribute-lft-out`
1×	`pow-pow` `tan-quot` `associate-/r/` `*-commutative`

Counts

4 → 99

Calls

4 calls:

11.0ms	(/ x (tan B))
37.0ms	(/ (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F) (sin B))
113.0ms	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
40.0ms	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

series858.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(/ x (tan B))
236.0ms	(/ (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F) (sin B))
137.0ms	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
312.0ms	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

simplify2.0s

Counts

111 → 111

Iterations

Iter	Nodes
3	4607
2	1227
1	453
0	213

prune1.7s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.4b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.2b	(/ 1 (/ (sin B) (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)))
0.3b	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
17.0b	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

rewrite290.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log`
42×	`times-frac`
38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
33×	`add-cube-cbrt`
23×	`div-exp`
17×	`add-cbrt-cube`
12×	`prod-exp`
10×	`associate-/r*`
9×	`unpow-prod-down`
8×	`associate-l`
6×	`pow1` `cbrt-undiv` `div-inv` `associate-/l*`
5×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp`
4×	`insert-posit16` `add-log-exp`
3×	`pow-unpow` `associate-r` `unswap-sqr` `sqr-pow`
2×	`clear-num` `frac-2neg` `associate-/r/` `cbrt-unprod` `distribute-lft-out`
1×	`pow-pow` `tan-quot` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 138

Calls

4 calls:

10.0ms	(/ x (tan B))
87.0ms	(/ 1 (/ (sin B) (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)))
143.0ms	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
45.0ms	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

series716.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(/ x (tan B))
156.0ms	(/ 1 (/ (sin B) (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)))
132.0ms	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
260.0ms	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

simplify5.0s

Counts

150 → 150

Iterations

Iter	Nodes
3	8697
2	1810
1	616
0	279

prune2.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.4b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x (cos B)) (sin B))
0.2b	(/ 1 (/ (sin B) (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)))
0.3b	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
17.0b	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-exp-log`
36×	`times-frac`
32×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
27×	`add-cube-cbrt`
24×	`div-exp`
20×	`add-cbrt-cube`
13×	`prod-exp`
10×	`associate-/r*`
9×	`unpow-prod-down`
8×	`associate-l`
7×	`cbrt-undiv`
6×	`pow1` `div-inv`
5×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp`
4×	`insert-posit16` `associate-/l*` `add-log-exp`
3×	`pow-unpow` `associate-r` `cbrt-unprod` `unswap-sqr` `sqr-pow`
2×	`clear-num` `frac-2neg` `distribute-lft-out`
1×	`pow-pow` `associate-/r/` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 131

Calls

4 calls:

12.0ms	(/ (* x (cos B)) (sin B))
50.0ms	(/ 1 (/ (sin B) (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)))
118.0ms	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
40.0ms	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

series647.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ (* x (cos B)) (sin B))
135.0ms	(/ 1 (/ (sin B) (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)))
124.0ms	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
268.0ms	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

simplify5.8s

Counts

143 → 143

Iterations

Iter	Nodes
3	9641
2	1906
1	631
0	267

prune2.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.3b

localize93.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x (cos B)) (sin B))
0.2b	(* F (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)))
0.4b	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
17.0b	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

rewrite364.0ms

Algorithm

rewrite-expression-head

Rules

57×	`*-un-lft-identity`
54×	`times-frac`
51×	`add-sqr-sqrt`
41×	`add-cube-cbrt`
33×	`unpow-prod-down`
28×	`associate-r`
25×	`add-exp-log`
16×	`add-cbrt-cube`
9×	`associate-/l*` `sqr-pow`
8×	`div-exp` `distribute-lft-out`
7×	`pow1`
6×	`associate-/r*`
5×	`prod-exp`
4×	`cbrt-undiv` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `pow-unpow` `associate-l` `pow-exp` `cbrt-unprod` `div-inv`
2×	`clear-num` `frac-2neg`
1×	`pow-pow` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 143

Calls

4 calls:

24.0ms	(/ (* x (cos B)) (sin B))
143.0ms	(* F (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)))
131.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
63.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

series827.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (* x (cos B)) (sin B))
190.0ms	(* F (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)))
197.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
318.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

simplify3.0s

Counts

155 → 155

Iterations

Iter	Nodes
3	6392
2	1759
1	609
0	261

prune2.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes667.0ms

Accuracy

97.7% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 10.9b

bsearch653.0ms

Steps

Iters	Range		Point
10	19.9847175368848	353170825925.37476	641096.8187916952
8	-2.2521319192038365e+117	-7.272221204506035e+114	-7.352157093766344e+114

simplify24.0ms

Iterations

Iter	Nodes
2	47
1	47
0	37

end0.0ms

sample13.6s

Algorithm

intervals

Results

5.6s	1631×	body	1280	valid
3.0s	1441×	body	640	valid
2.2s	4780×	body	80	valid
1.0s	692×	body	320	valid
686.0ms	1673×	body	80	nan
640.0ms	327×	body	160	valid