Details

sample452.0ms

Algorithm

intervals

Results

55.0ms	58×	body	1280	valid
50.0ms	40×	body	640	valid
22.0ms	156×	body	80	valid
7.0ms	18×	body	320	valid
4.0ms	38×	body	80	nan
2.0ms	8×	body	160	valid

simplify42.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	42	15
1	83	14
2	151	14
3	356	14
4	1063	14
5	5002	14
done	5002	14

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.2b	(* x (/ 1.0 (tan B)))
7.7b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
17.8b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite252.0ms

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:

5.0ms	(/ F (sin B))
17.0ms	(* x (/ 1.0 (tan B)))
166.0ms	(* (/ 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)))

series627.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ F (sin B))
116.0ms	(* x (/ 1.0 (tan B)))
297.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
160.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify80.0ms

Counts

166 → 166

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	765	1418
1	3213	1329
2	5001	1328
done	5001	1328

prune630.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

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))
17.8b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite350.0ms

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:

17.0ms	(* x (/ 1.0 (tan B)))
154.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
122.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
50.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series949.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(* x (/ 1.0 (tan B)))
354.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
329.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
147.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify92.0ms

Counts

186 → 186

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	848	2078
1	3740	1960
2	5002	1960
done	5002	1960

prune704.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 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))
17.8b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite338.0ms

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:

10.0ms	(/ (* x 1.0) (tan B))
153.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
122.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
47.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series946.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (* x 1.0) (tan B))
362.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
321.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
149.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify88.0ms

Counts

175 → 175

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	801	2023
1	3498	1905
2	5001	1905
done	5001	1905

prune676.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sin B) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (- (/ 1.0 2.0))))
0.4b	(/ (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (- (/ 1.0 2.0))) (/ (sin B) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (- (/ 1.0 2.0)))))
17.7b	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))
17.7b	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))

rewrite379.0ms

Algorithm

rewrite-expression-head

Rules

720×	`times-frac`
444×	`unpow-prod-down`
362×	`add-sqr-sqrt`
360×	`add-cube-cbrt` `*-un-lft-identity`
228×	`sqrt-prod`
74×	`sqr-pow`
46×	`associate-/r*`
35×	`add-exp-log`
25×	`associate-/r/`
24×	`div-exp`
13×	`neg-sub0` `pow-neg` `div-inv` `associate-/l*` `pow-sub`
11×	`add-cbrt-cube`
8×	`pow-to-exp` `pow-exp`
6×	`pow1`
4×	`cbrt-undiv` `sqrt-div` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `clear-num` `flip-+` `associate-/l/`

Counts

4 → 522

Calls

4 calls:

78.0ms	(/ (sin B) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (- (/ 1.0 2.0))))
190.0ms	(/ (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (- (/ 1.0 2.0))) (/ (sin B) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (- (/ 1.0 2.0)))))
33.0ms	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))
37.0ms	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))

series726.0ms

Counts

4 → 12

Calls

4 calls:

256.0ms	(/ (sin B) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (- (/ 1.0 2.0))))
356.0ms	(/ (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (- (/ 1.0 2.0))) (/ (sin B) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (- (/ 1.0 2.0)))))
59.0ms	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))
55.0ms	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))

simplify151.0ms

Counts

534 → 534

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1566	17816
1	5001	17072
done	5001	17072

prune1.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes145.0ms

Accuracy

97.5% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 10.3b

bsearch266.0ms

Steps

Iters	Range		Point
8	51.26549425761527	36428.8834987219	29425.178765531156
8	-1.3862397102148612e+48	-1.294252092905928e+45	-2.0888318481520247e+45

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	40
1	65	40
2	65	40
done	65	40

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.7s	1746×	body	1280	valid
845.0ms	1383×	body	640	valid
622.0ms	4697×	body	80	valid
266.0ms	660×	body	320	valid
164.0ms	1675×	body	80	nan
96.0ms	352×	body	160	valid