Details

sample571.0ms

Algorithm

intervals

Results

154.0ms	52×	body	640	valid
126.0ms	50×	body	1280	valid
62.0ms	148×	body	80	valid
40.0ms	13×	body	160	valid
31.0ms	23×	body	320	valid
23.0ms	64×	body	80	nan

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
6	2153
5	683
4	275
3	137
2	81
1	45
0	20

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.3b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.1b	(/ (sin B) F)
8.2b	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (/ (sin B) F))
20.6b	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

203×	`times-frac`
143×	`*-un-lft-identity`
113×	`add-sqr-sqrt` `add-cube-cbrt`
60×	`unpow-prod-down`
22×	`add-exp-log`
19×	`associate-/r*`
15×	`distribute-lft-out` `sqr-pow`
14×	`associate-/l*`
13×	`add-cbrt-cube`
12×	`div-inv`
11×	`div-exp`
5×	`pow1` `cbrt-undiv`
4×	`insert-posit16` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `clear-num` `frac-2neg` `pow-exp`
2×	`associate-/r/`
1×	`pow-pow` `tan-quot`

Counts

4 → 221

Calls

4 calls:

10.0ms	(/ x (tan B))
16.0ms	(/ (sin B) F)
127.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (/ (sin B) F))
56.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

series798.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ x (tan B))
37.0ms	(/ (sin B) F)
238.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (/ (sin B) F))
345.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

simplify1.7s

Counts

233 → 233

Iterations

Iter	Nodes
2	2537
1	920
0	396

prune2.9s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.2b	(* (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)) F)
0.3b	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
20.6b	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

rewrite366.0ms

Algorithm

rewrite-expression-head

Rules

63×	`*-un-lft-identity`
60×	`times-frac`
57×	`add-sqr-sqrt`
47×	`add-cube-cbrt`
33×	`unpow-prod-down`
28×	`associate-l`
22×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`associate-/l*`
9×	`sqr-pow`
8×	`distribute-lft-out`
7×	`pow1` `div-exp`
6×	`associate-/r*`
4×	`prod-exp` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `cbrt-undiv` `pow-unpow` `associate-r` `pow-exp` `div-inv`
2×	`clear-num` `frac-2neg` `cbrt-unprod`
1×	`pow-pow` `pow-prod-down` `associate-l/` `tan-quot` `associate-/r/` `-commutative`

Counts

4 → 150

Calls

4 calls:

5.0ms	(/ x (tan B))
155.0ms	(* (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)) F)
137.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
67.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

series903.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(/ x (tan B))
221.0ms	(* (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)) F)
200.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
302.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

simplify2.5s

Counts

162 → 162

Iterations

Iter	Nodes
3	4331
2	1430
1	573
0	264

prune1.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.2b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.2b	(* (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) F)
0.9b	(/ (* (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) F) (sin B))
20.6b	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

rewrite289.0ms

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:

5.0ms	(/ x (tan B))
178.0ms	(* (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) F)
49.0ms	(/ (* (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) F) (sin B))
55.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

series758.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ x (tan B))
143.0ms	(* (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) F)
220.0ms	(/ (* (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) F) (sin B))
255.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

simplify2.3s

Counts

111 → 111

Iterations

Iter	Nodes
3	5014
2	1232
1	453
0	213

prune1.5s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.3b	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
0.4b	(/ (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)) (/ 1 F))
20.6b	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

rewrite354.0ms

Algorithm

rewrite-expression-head

Rules

994×	`times-frac`
538×	`*-un-lft-identity`
444×	`add-sqr-sqrt` `add-cube-cbrt`
188×	`unpow-prod-down`
56×	`add-exp-log`
47×	`distribute-lft-out` `sqr-pow`
46×	`div-inv`
40×	`div-exp`
39×	`associate-/l*`
20×	`add-cbrt-cube`
19×	`associate-/r*`
10×	`cbrt-undiv`
6×	`pow-to-exp` `pow-exp`
5×	`pow1`
4×	`rec-exp` `1-exp` `insert-posit16` `add-log-exp`
3×	`pow-unpow` `clear-num` `frac-2neg`
2×	`associate-/r/`
1×	`pow-pow` `tan-quot` `associate-/l/`

Counts

4 → 536

Calls

4 calls:

10.0ms	(/ x (tan B))
124.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
133.0ms	(/ (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)) (/ 1 F))
61.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

series1.3s

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ x (tan B))
215.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
211.0ms	(/ (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)) (/ 1 F))
762.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

simplify3.8s

Counts

548 → 548

Iterations

Iter	Nodes
1	2382
0	828

prune5.9s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.2b

regimes509.0ms

Accuracy

0% (0.7b remaining)

Error of 10.7b against oracle of 10.0b and baseline of 10.7b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	26
1	26
0	21

end0.0ms

sample15.1s

Algorithm

intervals

Results

5.6s	1662×	body	1280	valid
4.4s	1427×	body	640	valid
2.4s	4726×	body	80	valid
1.1s	707×	body	320	valid
737.0ms	1624×	body	80	nan
375.0ms	344×	body	160	valid