Details

sample477.0ms

Algorithm

intervals

Results

72.0ms	52×	body	1280	valid
32.0ms	51×	body	640	valid
23.0ms	149×	body	80	valid
12.0ms	26×	body	320	valid
5.0ms	45×	body	80	nan
3.0ms	9×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Useful iterations: 2 (19.0ms)

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))
6.9b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
18.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite260.0ms

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:

6.0ms	(/ 1.0 (tan B))
18.0ms	(* x (/ 1.0 (tan B)))
172.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
56.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series629.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 1.0 (tan B))
119.0ms	(* x (/ 1.0 (tan B)))
308.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
163.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify1.1s

Counts

175 → 175

Iterations

Useful iterations: 2 (396.0ms)

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

prune730.0ms

Pruning

13 alts after pruning (13 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	(/ (* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F) (sin B))
0.3b	(* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F)
18.2b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
31×	`times-frac`
30×	`pow-unpow`
25×	`add-exp-log`
17×	`associate-r`
16×	`add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
10×	`associate-l`
8×	`prod-exp`
7×	`pow1` `unpow-prod-down`
5×	`div-exp` `unswap-sqr`
4×	`expm1-log1p-u` `associate-*l/` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `pow-neg` `pow-exp` `associate-/r*` `pow-sub` `sqr-pow`
2×	`*-commutative` `associate-/l/`
1×	`tan-quot` `neg-mul-1` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `associate-/r/` `associate-/l`

Counts

4 → 139

Calls

4 calls:

17.0ms	(* x (/ 1.0 (tan B)))
15.0ms	(/ (* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F) (sin B))
12.0ms	(* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F)
7.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.9s

Counts

4 → 12

Calls

4 calls:

119.0ms	(* x (/ 1.0 (tan B)))
819.0ms	(/ (* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F) (sin B))
664.0ms	(* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F)
341.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify1.2s

Counts

151 → 151

Iterations

Useful iterations: 2 (455.0ms)

Iter	Nodes	Cost
0	341	2633
1	855	2482
2	2574	2306
done	5000	2306

prune623.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(/ (* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F) (sin B))
0.3b	(* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F)
18.2b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`pow-unpow`
27×	`add-cube-cbrt` `*-un-lft-identity`
25×	`add-exp-log`
24×	`times-frac`
16×	`add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
7×	`unpow-prod-down` `associate-l` `prod-exp`
6×	`div-exp` `associate-/r*`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`neg-sub0` `pow-to-exp` `pow-neg` `associate-r` `pow-exp` `cbrt-unprod` `pow-sub` `unswap-sqr` `sqr-pow`
2×	`frac-2neg` `clear-num` `associate-/l/` `associate-/l*`
1×	`tan-quot` `neg-mul-1` `pow-pow` `associate-/r/` `*-commutative`

Counts

4 → 128

Calls

4 calls:

13.0ms	(/ (* x 1.0) (tan B))
12.0ms	(/ (* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F) (sin B))
12.0ms	(* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F)
7.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.9s

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ (* x 1.0) (tan B))
817.0ms	(/ (* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F) (sin B))
656.0ms	(* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F)
339.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify1.3s

Counts

140 → 140

Iterations

Useful iterations: 2 (418.0ms)

Iter	Nodes	Cost
0	326	2535
1	811	2394
2	2538	2218
done	5000	2218

prune558.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(/ F (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
0.2b	(/ (/ F (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))) (sin B))
18.2b	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

192×	`times-frac`
112×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
51×	`unpow-prod-down`
29×	`associate-/l*`
25×	`add-exp-log`
17×	`sqr-pow`
16×	`add-cbrt-cube`
13×	`pow-unpow` `associate-/r*`
12×	`div-exp`
8×	`div-inv`
6×	`cbrt-undiv`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num`
1×	`tan-quot` `pow-pow` `prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/`

Counts

4 → 222

Calls

4 calls:

12.0ms	(/ (* x 1.0) (tan B))
7.0ms	(/ F (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
19.0ms	(/ (/ F (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))) (sin B))
4.0ms	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (* x 1.0) (tan B))
246.0ms	(/ F (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
385.0ms	(/ (/ F (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))) (sin B))
322.0ms	(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

simplify1.3s

Counts

234 → 234

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	437	5816
1	1001	5583
2	2687	5386
done	5000	5363

prune903.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes163.0ms

Accuracy

97.3% (0.3b remaining)

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

bsearch276.0ms

Steps

Iters	Range		Point
8	1.4733657795017903	1363.812291646281	1344.0953273231628
10	-2.7762754645039914e+173	-4.0077794084511924e+158	-4.0606577341876937e+158

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	68
1	42	68
2	48	68
done	48	68

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.7s	1676×	body	1280	valid
871.0ms	1376×	body	640	valid
683.0ms	4828×	body	80	valid
318.0ms	717×	body	320	valid
187.0ms	1680×	body	80	nan
91.0ms	312×	body	160	valid