Details

sample382.0ms

Algorithm

intervals

Results

53.0ms	51×	body	1280	valid
27.0ms	43×	body	640	valid
21.0ms	157×	body	80	valid
8.0ms	20×	body	320	valid
6.0ms	54×	body	80	nan
3.0ms	11×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	20	27
1	42	27
2	80	26
3	146	26
4	317	26
5	811	26
6	2761	26
done	5000	26

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
7.8b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
18.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite129.0ms

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×	`tan-quot` `frac-times` `associate-/r/` `*-commutative`
1×	`neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `clear-num` `un-div-inv`

Counts

4 → 155

Calls

4 calls:

2.0ms	(/ 1.0 (tan B))
8.0ms	(* x (/ 1.0 (tan B)))
83.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
26.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series581.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1.0 (tan B))
108.0ms	(* x (/ 1.0 (tan B)))
285.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
152.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify841.0ms

Counts

167 → 167

Iterations

Useful iterations: 2 (330.0ms)

Iter	Nodes	Cost
0	306	2742
1	768	2573
2	2065	2415
done	5001	2415

prune636.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
0.3b	(* x (/ 1.0 (tan B)))
0.3b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
18.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite181.0ms

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:

82.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
8.0ms	(* x (/ 1.0 (tan B)))
61.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
24.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series914.0ms

Counts

4 → 12

Calls

4 calls:

350.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
110.0ms	(* x (/ 1.0 (tan B)))
308.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
146.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify773.0ms

Counts

186 → 186

Iterations

Useful iterations: 2 (365.0ms)

Iter	Nodes	Cost
0	341	3949
1	849	3760
2	2306	3533
done	5000	3533

prune706.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

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)))
0.3b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
18.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite176.0ms

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:

3.0ms	(/ (* x 1.0) (tan B))
81.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
61.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
24.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series917.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (* x 1.0) (tan B))
345.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
310.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
151.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify785.0ms

Counts

175 → 175

Iterations

Useful iterations: 2 (357.0ms)

Iter	Nodes	Cost
0	326	3851
1	802	3672
2	2271	3445
done	5000	3445

prune665.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x (cos B)) (sin B))
0.2b	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
0.3b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
18.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite171.0ms

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×	`neg-mul-1` `pow-pow` `associate-r/` `pow-prod-down` `-commutative`

Counts

4 → 162

Calls

4 calls:

4.0ms	(/ (* x (cos B)) (sin B))
79.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
59.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
23.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series885.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (* x (cos B)) (sin B))
343.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
311.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
138.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify718.0ms

Counts

174 → 174

Iterations

Useful iterations: 2 (318.0ms)

Iter	Nodes	Cost
0	312	3866
1	777	3687
2	2219	3454
done	5000	3454

prune758.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes162.0ms

Accuracy

98% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 10.9b

bsearch249.0ms

Steps

Iters	Range		Point
7	5.286434132095145e+107	4.224606621740393e+109	7.167014820044611e+107
9	-9.509086209243448e+25	-5.276190702543451e+18	-1.5429963473208183e+19

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	77
1	57	77
done	57	77

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.6s	1645×	body	1280	valid
853.0ms	1337×	body	640	valid
683.0ms	4855×	body	80	valid
301.0ms	683×	body	320	valid
150.0ms	1499×	body	80	nan
100.0ms	337×	body	160	valid