Details

sample545.0ms

Algorithm

intervals

Results

200.0ms	63×	body	1280	valid
102.0ms	129×	body	80	valid
101.0ms	44×	body	640	valid
24.0ms	24×	body	320	valid
14.0ms	52×	body	80	nan
7.0ms	11×	body	160	valid

simplify4.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	20	27
1	43	26
2	91	24
3	169	24
4	366	24
5	915	24
6	3219	24
done	5001	24

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.7b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
8.4b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
18.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite455.0ms

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×	`expm1-log1p-u` `pow-neg` `cbrt-unprod` `log1p-expm1-u` `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 → 163

Calls

4 calls:

12.0ms	(/ 1.0 (tan B))
35.0ms	(* x (/ 1.0 (tan B)))
289.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
109.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series928.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ 1.0 (tan B))
169.0ms	(* x (/ 1.0 (tan B)))
463.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
225.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify1.7s

Counts

175 → 175

Iterations

Useful iterations: 2 (654.0ms)

Iter	Nodes	Cost
0	314	2836
1	764	2557
2	2104	2297
done	5000	2297

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ F (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)))
0.3b	(* x (/ 1.0 (tan B)))
0.3b	(* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B))
18.9b	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
25×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
22×	`times-frac`
17×	`associate-r`
16×	`add-cbrt-cube`
13×	`pow-unpow`
10×	`associate-l`
8×	`prod-exp`
7×	`pow1` `unpow-prod-down`
5×	`div-exp` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `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 → 116

Calls

4 calls:

20.0ms	(/ F (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)))
31.0ms	(* x (/ 1.0 (tan B)))
31.0ms	(* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B))
9.0ms	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

series2.7s

Counts

4 → 12

Calls

4 calls:

542.0ms	(/ F (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)))
173.0ms	(* x (/ 1.0 (tan B)))
1.4s	(* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B))
542.0ms	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

simplify1.7s

Counts

128 → 128

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	283	2182
1	692	2070
2	2048	1897
done	5000	1843

prune775.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.3b	(/ F (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)))
0.3b	(* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B))
18.9b	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

rewrite59.0ms

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-l` `prod-exp`
6×	`div-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`pow-to-exp` `associate-r` `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 → 105

Calls

4 calls:

18.0ms	(/ (* x 1.0) (tan B))
12.0ms	(/ F (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)))
18.0ms	(* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B))
5.0ms	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

series2.6s

Counts

4 → 12

Calls

4 calls:

160.0ms	(/ (* x 1.0) (tan B))
521.0ms	(/ F (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)))
1.5s	(* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B))
419.0ms	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

simplify1.7s

Counts

117 → 117

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	268	2084
1	649	1982
2	2018	1809
done	5001	1755

prune752.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)) F)
0.3b	(* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B))
0.4b	(/ 1 (/ (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)) F))
18.9b	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-exp-log`
45×	`times-frac`
38×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
26×	`div-exp`
20×	`add-cbrt-cube`
15×	`prod-exp`
13×	`pow-unpow`
10×	`associate-/r*`
7×	`cbrt-undiv` `unpow-prod-down` `associate-l` `div-inv`
6×	`pow1` `pow-to-exp` `pow-exp`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-r` `cbrt-unprod` `unswap-sqr` `sqr-pow`
2×	`frac-2neg` `clear-num`
1×	`pow-flip` `pow-pow` `associate-/r/` `*-commutative` `inv-pow`

Counts

4 → 145

Calls

4 calls:

15.0ms	(/ (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)) F)
39.0ms	(* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B))
16.0ms	(/ 1 (/ (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)) F))
4.0ms	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

series7.6s

Counts

4 → 12

Calls

4 calls:

3.6s	(/ (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)) F)
1.6s	(* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B))
1.9s	(/ 1 (/ (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)) F))
501.0ms	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

simplify1.5s

Counts

157 → 157

Iterations

Useful iterations: 2 (675.0ms)

Iter	Nodes	Cost
0	338	3722
1	843	3459
2	2553	3123
done	5001	3123

prune699.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes247.0ms

Accuracy

98.1% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.4b

bsearch410.0ms

Steps

Iters	Range		Point
9	0.04058914318552966	14449.683341850247	13711.082350685094
5	-115211.7032321185	-34401.421950388	-99469.45738864847

simplify12.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	77
1	55	77
2	64	77
done	64	77

end0.0ms

sample9.6s

Algorithm

intervals

Results

3.8s	1647×	body	1280	valid
2.4s	1420×	body	640	valid
1.3s	4721×	body	80	valid
744.0ms	1585×	body	80	nan
685.0ms	708×	body	320	valid
207.0ms	334×	body	160	valid