Details

sample580.0ms

Algorithm

intervals

Results

197.0ms	57×	body	1280	valid
84.0ms	147×	body	80	valid
75.0ms	47×	body	640	valid
23.0ms	21×	body	320	valid
15.0ms	54×	body	80	nan
4.0ms	7×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	20	27
1	42	27
2	83	26
3	152	26
4	362	26
5	1681	26
done	5000	26

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.3b	(* x (/ 1.0 (tan B)))
6.1b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
20.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite458.0ms

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×	`frac-times` `*-commutative`
1×	`tan-quot` `neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `clear-num` `associate-/r/` `un-div-inv`

Counts

4 → 154

Calls

4 calls:

6.0ms	(/ F (sin B))
38.0ms	(* x (/ 1.0 (tan B)))
303.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
105.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series902.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ F (sin B))
186.0ms	(* x (/ 1.0 (tan B)))
435.0ms	(* (/ F (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)))

simplify2.5s

Counts

166 → 166

Iterations

Useful iterations: 2 (952.0ms)

Iter	Nodes	Cost
0	303	2726
1	858	2563
2	3831	2411
done	5000	2411

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 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)))
0.3b	(* x (/ 1.0 (tan B)))
20.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite420.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
25×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
22×	`times-frac`
21×	`associate-r`
16×	`add-cbrt-cube`
13×	`pow-unpow`
8×	`prod-exp`
7×	`pow1` `unpow-prod-down`
6×	`associate-l`
5×	`div-exp` `unswap-sqr`
4×	`cbrt-unprod` `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 → 108

Calls

4 calls:

68.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
258.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
18.0ms	(* x (/ 1.0 (tan B)))
69.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

388.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
370.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
166.0ms	(* x (/ 1.0 (tan B)))
170.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify2.0s

Counts

120 → 120

Iterations

Useful iterations: 2 (755.0ms)

Iter	Nodes	Cost
0	265	2158
1	707	2049
2	3239	1861
done	5001	1861

prune735.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.2b	(/ 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)))
20.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite392.0ms

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:

11.0ms	(/ (* x 1.0) (tan B))
53.0ms	(/ 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)))
66.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (* x 1.0) (tan B))
464.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
367.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
180.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify1.9s

Counts

109 → 109

Iterations

Useful iterations: 2 (644.0ms)

Iter	Nodes	Cost
0	250	2060
1	658	1957
2	3206	1775
done	5001	1775

prune715.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 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)))
0.3b	(/ 1 (/ (tan B) (* x 1.0)))
20.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite431.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 131

Calls

4 calls:

65.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
277.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
15.0ms	(/ 1 (/ (tan B) (* x 1.0)))
70.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

404.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
368.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
143.0ms	(/ 1 (/ (tan B) (* x 1.0)))
174.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify2.1s

Counts

143 → 143

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	311	2599
1	821	2375
2	3773	2177
done	5000	2175

prune530.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes215.0ms

Accuracy

98.2% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.9b

bsearch638.0ms

Steps

Iters	Range		Point
8	13587.758917488305	15596962.563861683	1230529.5155546274
5	-1.1654524514486036e+19	-4.602935768153408e+18	-5.781402953055721e+18

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	73
1	44	73
done	44	73

end0.0ms

sample10.6s

Algorithm

intervals

Results

4.6s	1696×	body	1280	valid
2.2s	1381×	body	640	valid
1.9s	4838×	body	80	valid
660.0ms	675×	body	320	valid
402.0ms	1675×	body	80	nan
182.0ms	337×	body	160	valid