Details

sample479.0ms

Algorithm

intervals

Results

76.0ms	53×	body	1280	valid
28.0ms	44×	body	640	valid
23.0ms	156×	body	80	valid
14.0ms	30×	body	320	valid
5.0ms	46×	body	80	nan
3.0ms	11×	body	160	valid

simplify44.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	43	15
1	91	14
2	169	14
3	378	14
4	1100	14
5	5001	14
done	5001	14

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.2b	(* x (/ 1.0 (tan B)))
4.8b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
15.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
37×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
14×	`associate-r`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`add-exp-log`
11×	`add-cbrt-cube`
7×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`unpow-prod-down` `associate-l` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`tan-quot` `neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `associate-/r/` `-commutative` `fma-udef` `pow-sub` `sqr-pow`

Counts

4 → 122

Calls

4 calls:

5.0ms	(/ F (sin B))
17.0ms	(* x (/ 1.0 (tan B)))
0.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
59.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series558.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ F (sin B))
115.0ms	(* x (/ 1.0 (tan B)))
234.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
157.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify66.0ms

Counts

134 → 134

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	666	1019
1	2629	931
2	5001	928
done	5001	928

prune566.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(/ F (sin B))
4.8b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
15.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

11.0ms	(/ (* x 1.0) (tan B))
5.0ms	(/ F (sin B))
0.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
51.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series544.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (* x 1.0) (tan B))
54.0ms	(/ F (sin B))
229.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
147.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify55.0ms

Counts

123 → 123

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	616	964
1	2352	876
2	5001	873
done	5001	873

prune502.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ (* (cbrt 1.0) (cbrt 1.0)) 1)))
0.2b	(/ F (sin B))
4.8b	(fma (/ F (sin B)) (pow (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ (* (cbrt 1.0) (cbrt 1.0)) 1))) (/ (cbrt 1.0) 2.0)) (- (/ (* x 1.0) (tan B))))
15.1b	(pow (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ (* (cbrt 1.0) (cbrt 1.0)) 1))) (/ (cbrt 1.0) 2.0))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

40×	`pow-unpow`
33×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`unpow-prod-down`
9×	`add-exp-log` `cbrt-prod`
7×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
6×	`add-cbrt-cube`
5×	`pow1` `pow-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-to-exp` `associate-/r` `associate-/l` `sqr-pow`
2×	`pow-pow`
1×	`cbrt-undiv` `neg-sub0` `pow-neg` `neg-mul-1` `frac-2neg` `div-exp` `clear-num` `fma-udef` `pow-sub`

Counts

4 → 119

Calls

4 calls:

48.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ (* (cbrt 1.0) (cbrt 1.0)) 1)))
5.0ms	(/ F (sin B))
0.0ms	(fma (/ F (sin B)) (pow (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ (* (cbrt 1.0) (cbrt 1.0)) 1))) (/ (cbrt 1.0) 2.0)) (- (/ (* x 1.0) (tan B))))
84.0ms	(pow (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ (* (cbrt 1.0) (cbrt 1.0)) 1))) (/ (cbrt 1.0) 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

327.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ (* (cbrt 1.0) (cbrt 1.0)) 1)))
55.0ms	(/ F (sin B))
389.0ms	(fma (/ F (sin B)) (pow (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ (* (cbrt 1.0) (cbrt 1.0)) 1))) (/ (cbrt 1.0) 2.0)) (- (/ (* x 1.0) (tan B))))
328.0ms	(pow (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ (* (cbrt 1.0) (cbrt 1.0)) 1))) (/ (cbrt 1.0) 2.0))

simplify71.0ms

Counts

131 → 131

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	715	1712
1	2779	1598
2	5001	1580
done	5001	1580

prune641.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (sin B))
0.2b	(* (/ (* x 1.0) (sin B)) (cos B))
4.8b	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* (/ (* x 1.0) (sin B)) (cos B))))
15.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

11.0ms	(/ (* x 1.0) (sin B))
26.0ms	(* (/ (* x 1.0) (sin B)) (cos B))
0.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* (/ (* x 1.0) (sin B)) (cos B))))
49.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series548.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (* x 1.0) (sin B))
110.0ms	(* (/ (* x 1.0) (sin B)) (cos B))
229.0ms	(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* (/ (* x 1.0) (sin B)) (cos B))))
147.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify65.0ms

Counts

122 → 122

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	634	1064
1	2689	938
2	5002	935
done	5002	935

prune459.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes227.0ms

Accuracy

98.1% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 13.3b

bsearch279.0ms

Steps

Iters	Range		Point
9	5.807453888540714e+35	4.656082442494864e+40	5.8604197527249914e+35
9	-4906629045.550534	-392.4425927342909	-183851881.3296129

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	46
1	68	46
2	68	46
done	68	46

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.7s	1650×	body	1280	valid
902.0ms	1409×	body	640	valid
653.0ms	4747×	body	80	valid
320.0ms	728×	body	320	valid
169.0ms	1644×	body	80	nan
96.0ms	331×	body	160	valid