Details

sample452.0ms

Algorithm

intervals

Results

162.0ms	51×	body	1280	valid
57.0ms	41×	body	640	valid
50.0ms	162×	body	80	valid
22.0ms	21×	body	320	valid
12.0ms	51×	body	80	nan
5.0ms	9×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	20	27
1	42	27
2	83	26
3	152	26
4	362	26
5	1681	26
done	5000	26

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
6.4b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
20.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite407.0ms

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:

12.0ms	(/ 1.0 (tan B))
38.0ms	(* x (/ 1.0 (tan B)))
282.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
61.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series879.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ 1.0 (tan B))
152.0ms	(* x (/ 1.0 (tan B)))
400.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
278.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify2.5s

Counts

167 → 167

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	306	2742
1	867	2581
2	3839	2427
done	5000	2423

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.2b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.3b	(* x (/ 1.0 (tan B)))
20.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite399.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
25×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
22×	`times-frac`
21×	`associate-r`
16×	`add-cbrt-cube`
13×	`pow-unpow`
8×	`prod-exp`
7×	`pow1` `unpow-prod-down`
6×	`associate-l`
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` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `associate-/r/`

Counts

4 → 108

Calls

4 calls:

76.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
220.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
18.0ms	(* x (/ 1.0 (tan B)))
78.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

423.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
408.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
166.0ms	(* x (/ 1.0 (tan B)))
204.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify2.0s

Counts

120 → 120

Iterations

Useful iterations: 2 (732.0ms)

Iter	Nodes	Cost
0	265	2158
1	707	2049
2	3239	1861
done	5001	1861

prune629.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.2b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
20.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite396.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

18.0ms	(/ (* x 1.0) (tan B))
72.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
232.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
68.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (* x 1.0) (tan B))
894.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
362.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
213.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify2.0s

Counts

109 → 109

Iterations

Useful iterations: 2 (619.0ms)

Iter	Nodes	Cost
0	250	2060
1	658	1957
2	3206	1775
done	5001	1775

prune707.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sin B))
0.2b	(* (/ 1 (sin B)) (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.2b	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
20.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite561.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-sqr-sqrt`
86×	`times-frac`
61×	`*-un-lft-identity`
58×	`add-exp-log`
57×	`add-cube-cbrt`
27×	`unpow-prod-down`
25×	`div-exp` `associate-r`
20×	`add-cbrt-cube`
16×	`prod-exp`
13×	`pow-unpow` `associate-l`
12×	`unswap-sqr`
11×	`sqr-pow`
10×	`associate-/r*`
8×	`pow1`
6×	`cbrt-undiv` `pow-to-exp` `pow-exp` `associate-/l*`
5×	`rec-exp` `1-exp` `div-inv`
4×	`cbrt-unprod` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `pow-flip` `pow-pow` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 185

Calls

4 calls:

13.0ms	(/ 1 (sin B))
312.0ms	(* (/ 1 (sin B)) (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
126.0ms	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
93.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ 1 (sin B))
537.0ms	(* (/ 1 (sin B)) (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
369.0ms	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
181.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify651.0ms

Counts

197 → 197

Iterations

Useful iterations: done (641.0ms)

Iter	Nodes	Cost
0	313	4418
1	924	4180
done	5000	3778

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes370.0ms

Accuracy

97.6% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 10.3b

bsearch536.0ms

Steps

Iters	Range		Point
9	1.1468805456395365e+145	2.0635371984445258e+152	1.3810836897532057e+150
9	-1.1865512963685553e+161	-4.0372067733341917e+155	-4.0752787424031194e+155

simplify63.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	49	97
1	69	97
2	75	97
done	75	97

end0.0ms

sample10.3s

Algorithm

intervals

Results

4.0s	1657×	body	1280	valid
2.4s	1412×	body	640	valid
1.8s	4768×	body	80	valid
694.0ms	680×	body	320	valid
483.0ms	1514×	body	80	nan
237.0ms	362×	body	160	valid