Details

sample648.0ms

Algorithm

intervals

Results

233.0ms	55×	body	1280	valid
88.0ms	50×	body	640	valid
34.0ms	144×	body	80	valid
23.0ms	24×	body	320	valid
14.0ms	59×	body	80	nan
6.0ms	11×	body	160	valid

simplify8.2s

Counts

1 → 1

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	20	27
1	63	27
2	189	26
3	1168	26
done	5000	26

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
7.4b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
16.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite473.0ms

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))
39.0ms	(* x (/ 1.0 (tan B)))
319.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
90.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series931.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ 1.0 (tan B))
178.0ms	(* x (/ 1.0 (tan B)))
467.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
223.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify657.0ms

Counts

167 → 167

Iterations

Useful iterations: done (651.0ms)

Iter	Nodes	Cost
0	306	2742
done	5000	2571

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.2b	(/ (* x 1.0) (tan B))
7.4b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
16.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite395.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 143

Calls

4 calls:

6.0ms	(/ F (sin B))
18.0ms	(/ (* x 1.0) (tan B))
276.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
89.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series834.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ F (sin B))
166.0ms	(/ (* x 1.0) (tan B))
408.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
191.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify574.0ms

Counts

155 → 155

Iterations

Useful iterations: done (569.0ms)

Iter	Nodes	Cost
0	288	2628
done	5000	2467

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.3b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.3b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
16.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite463.0ms

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:

23.0ms	(/ (* x 1.0) (tan B))
99.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
260.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
74.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

167.0ms	(/ (* x 1.0) (tan B))
498.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
478.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
201.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify9.6s

Counts

109 → 109

Iterations

Useful iterations: done (9.6s)

Iter	Nodes	Cost
0	250	2060
1	4314	1947
done	5000	1777

prune631.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin B) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0)))
0.3b	(* (* (sin B) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0))) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0)))
16.6b	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))
16.6b	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))

rewrite928.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
24×	`prod-exp`
22×	`add-sqr-sqrt`
20×	`associate-r`
14×	`unpow-prod-down`
13×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
11×	`add-cbrt-cube`
8×	`pow-to-exp` `pow-exp`
6×	`pow1`
4×	`sqrt-div` `associate-l` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`sqr-pow`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `*-commutative` `flip-+`

Counts

4 → 92

Calls

4 calls:

279.0ms	(* (sin B) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0)))
550.0ms	(* (* (sin B) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0))) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0)))
47.0ms	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))
49.0ms	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))

series950.0ms

Counts

4 → 12

Calls

4 calls:

436.0ms	(* (sin B) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0)))
356.0ms	(* (* (sin B) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0))) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0)))
82.0ms	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))
76.0ms	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))

simplify1.6s

Counts

104 → 104

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	187	2749
1	1153	2228
done	5001	1990

prune548.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes341.0ms

Accuracy

98.3% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.7b

bsearch664.0ms

Steps

Iters	Range		Point
10	0.00013312118248051433	5162834274.222523	13740.113416283992
10	-5.567720691877046e+23	-6045414056204.408	-6436982318645.525

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	34	73
1	41	73
done	41	73

end0.0ms

sample9.5s

Algorithm

intervals

Results

3.5s	1667×	body	1280	valid
2.1s	1344×	body	640	valid
1.6s	4897×	body	80	valid
1.0s	711×	body	320	valid
425.0ms	1629×	body	80	nan
247.0ms	333×	body	160	valid