Details

sample381.0ms

Algorithm

intervals

Results

53.0ms	51×	body	1280	valid
28.0ms	43×	body	640	valid
22.0ms	157×	body	80	valid
9.0ms	20×	body	320	valid
6.0ms	54×	body	80	nan
3.0ms	11×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	20	27
1	43	26
2	88	24
3	164	24
4	341	24
5	852	24
6	2805	24
done	5001	24

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize27.0ms

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×	`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:

2.0ms	(/ 1.0 (tan B))
10.0ms	(* x (/ 1.0 (tan B)))
84.0ms	(* (/ 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)))

series595.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1.0 (tan B))
110.0ms	(* x (/ 1.0 (tan B)))
291.0ms	(* (/ 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)))

simplify859.0ms

Counts

175 → 175

Iterations

Useful iterations: 2 (349.0ms)

Iter	Nodes	Cost
0	314	2836
1	785	2557
2	2118	2297
done	5000	2297

prune751.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 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))
18.6b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite37.0ms

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×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `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 → 182

Calls

4 calls:

13.0ms	(* F (/ (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (sin B)))
8.0ms	(* x (/ 1.0 (tan B)))
4.0ms	(/ (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)))

series1.5s

Counts

4 → 12

Calls

4 calls:

379.0ms	(* F (/ (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (sin B)))
118.0ms	(* x (/ 1.0 (tan B)))
713.0ms	(/ (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (sin B))
329.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify840.0ms

Counts

194 → 194

Iterations

Useful iterations: 2 (399.0ms)

Iter	Nodes	Cost
0	384	3815
1	935	3630
2	2566	3423
done	5000	3423

prune832.0ms

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	(/ (* x 1.0) (tan B))
0.2b	(* 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))
18.6b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite34.0ms

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` `expm1-log1p-u` `log1p-expm1-u` `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 → 171

Calls

4 calls:

6.0ms	(/ (* x 1.0) (tan B))
13.0ms	(* 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))) (sin B))
4.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.5s

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (* x 1.0) (tan B))
378.0ms	(* F (/ (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (sin B)))
727.0ms	(/ (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (sin B))
327.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify824.0ms

Counts

183 → 183

Iterations

Useful iterations: 2 (397.0ms)

Iter	Nodes	Cost
0	369	3717
1	888	3542
2	2532	3335
done	5000	3335

prune757.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.2b	(* F (* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ 1 (sin B))))
0.4b	(* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ 1 (sin B)))
18.6b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-exp-log`
50×	`add-sqr-sqrt`
38×	`prod-exp`
36×	`times-frac`
35×	`*-un-lft-identity`
32×	`add-cube-cbrt`
30×	`pow-unpow`
23×	`add-cbrt-cube`
14×	`div-exp` `associate-r`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
10×	`associate-l`
9×	`pow-to-exp` `unpow-prod-down` `pow-exp` `unswap-sqr`
8×	`associate-*r/` `cbrt-unprod`
7×	`pow1`
6×	`rec-exp` `1-exp`
5×	`neg-sub0` `pow-neg` `pow-sub` `sqr-pow`
4×	`cbrt-undiv` `expm1-log1p-u` `frac-times` `associate-*l/` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-/r*`
2×	`un-div-inv` `*-commutative`
1×	`tan-quot` `neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r/` `associate-/l*`

Counts

4 → 168

Calls

4 calls:

3.0ms	(/ (* x 1.0) (tan B))
15.0ms	(* F (* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ 1 (sin B))))
15.0ms	(* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ 1 (sin B)))
4.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.5s

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (* x 1.0) (tan B))
372.0ms	(* F (* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ 1 (sin B))))
727.0ms	(* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ 1 (sin B)))
335.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify1.1s

Counts

180 → 180

Iterations

Useful iterations: 2 (495.0ms)

Iter	Nodes	Cost
0	369	3551
1	945	3143
2	2679	2869
done	5000	2869

prune606.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes172.0ms

Accuracy

97.4% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 10.8b

bsearch258.0ms

Steps

Iters	Range		Point
8	9.896777056605239e+26	2.3418024522712145e+30	1.0576703886591284e+27
8	-3.0830650772848447e+72	-1.4756167269512789e+69	-1.5313961451328438e+69

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	38	74
1	53	74
2	61	74
done	61	74

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.7s	1645×	body	1280	valid
890.0ms	1337×	body	640	valid
678.0ms	4855×	body	80	valid
323.0ms	683×	body	320	valid
168.0ms	1499×	body	80	nan
102.0ms	337×	body	160	valid