Details

sample418.0ms

Algorithm

intervals

Results

117.0ms	55×	body	1280	valid
77.0ms	59×	body	80	nan
67.0ms	50×	body	640	valid
43.0ms	144×	body	80	valid
23.0ms	24×	body	320	valid
7.0ms	11×	body	160	valid

simplify9.4s

Counts

1 → 1

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	20	27
1	64	26
2	202	24
3	1208	24
done	5001	24

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize47.0ms

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)))

rewrite480.0ms

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:

12.0ms	(/ 1.0 (tan B))
24.0ms	(* x (/ 1.0 (tan B)))
315.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
116.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series897.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ 1.0 (tan B))
183.0ms	(* x (/ 1.0 (tan B)))
448.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
221.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify521.0ms

Counts

175 → 175

Iterations

Useful iterations: done (513.0ms)

Iter	Nodes	Cost
0	314	2836
done	5001	2555

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize77.0ms

Local error

Found 4 expressions with local error:

0.3b	(* F (pow (sqrt (+ (fma F F 2.0) (* 2.0 x))) (- (/ 1.0 2.0))))
3.1b	(* (/ (* F (pow (sqrt (+ (fma F F 2.0) (* 2.0 x))) (- (/ 1.0 2.0)))) (sin B)) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (- (/ 1.0 2.0))))
16.6b	(sqrt (+ (fma F F 2.0) (* 2.0 x)))
16.6b	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))

rewrite449.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log`
31×	`add-sqr-sqrt`
27×	`prod-exp`
20×	`associate-r`
16×	`unpow-prod-down`
15×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
14×	`sqrt-prod`
12×	`div-exp`
10×	`associate-l`
9×	`pow-to-exp` `pow-exp`
8×	`unswap-sqr`
6×	`pow1`
5×	`pow-neg` `cbrt-unprod`
4×	`expm1-log1p-u` `sqrt-div` `associate-*r/` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`neg-sub0` `times-frac` `pow-sub`
2×	`cbrt-undiv` `frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `un-div-inv` `*-commutative` `flip-+`
1×	`associate-*l/` `div-inv`

Counts

4 → 123

Calls

4 calls:

53.0ms	(* F (pow (sqrt (+ (fma F F 2.0) (* 2.0 x))) (- (/ 1.0 2.0))))
318.0ms	(* (/ (* F (pow (sqrt (+ (fma F F 2.0) (* 2.0 x))) (- (/ 1.0 2.0)))) (sin B)) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (- (/ 1.0 2.0))))
6.0ms	(sqrt (+ (fma F F 2.0) (* 2.0 x)))
63.0ms	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))

series1.3s

Counts

4 → 12

Calls

4 calls:

367.0ms	(* F (pow (sqrt (+ (fma F F 2.0) (* 2.0 x))) (- (/ 1.0 2.0))))
754.0ms	(* (/ (* F (pow (sqrt (+ (fma F F 2.0) (* 2.0 x))) (- (/ 1.0 2.0)))) (sin B)) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (- (/ 1.0 2.0))))
100.0ms	(sqrt (+ (fma F F 2.0) (* 2.0 x)))
81.0ms	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))

simplify4.3s

Counts

135 → 135

Iterations

Useful iterations: done (4.3s)

Iter	Nodes	Cost
0	270	3848
1	2365	3039
done	5000	2608

prune999.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

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)))

rewrite365.0ms

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` `expm1-log1p-u` `pow-neg` `log1p-expm1-u` `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 → 151

Calls

4 calls:

6.0ms	(/ F (sin B))
12.0ms	(/ (* x 1.0) (tan B))
251.0ms	(* (/ 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)))

series943.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ F (sin B))
196.0ms	(/ (* x 1.0) (tan B))
421.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
246.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify604.0ms

Counts

163 → 163

Iterations

Useful iterations: done (597.0ms)

Iter	Nodes	Cost
0	296	2722
done	5001	2452

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite107.0ms

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` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `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 → 105

Calls

4 calls:

22.0ms	(/ (* x 1.0) (tan B))
29.0ms	(/ F (* (sin B) (pow (+ (fma F F 2.0) (* 2.0 x)) (/ 1.0 2.0))))
35.0ms	(* (sin B) (pow (+ (fma F F 2.0) (* 2.0 x)) (/ 1.0 2.0)))
16.0ms	(pow (+ (fma F F 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

170.0ms	(/ (* x 1.0) (tan B))
451.0ms	(/ F (* (sin B) (pow (+ (fma F F 2.0) (* 2.0 x)) (/ 1.0 2.0))))
408.0ms	(* (sin B) (pow (+ (fma F F 2.0) (* 2.0 x)) (/ 1.0 2.0)))
216.0ms	(pow (+ (fma F F 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify9.4s

Counts

117 → 117

Iterations

Useful iterations: done (9.4s)

Iter	Nodes	Cost
0	258	2074
1	4288	1963
done	5001	1707

prune759.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes295.0ms

Accuracy

98.3% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.6b

bsearch619.0ms

Steps

Iters	Range		Point
10	0.00013312118248051433	5162834274.222523	124116259.95074068
10	-5.567720691877046e+23	-6045414056204.408	-2.0391080431890348e+18

simplify11.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	78
1	58	78
2	65	78
done	65	78

end0.0ms

sample10.3s

Algorithm

intervals

Results

3.9s	1667×	body	1280	valid
2.4s	1344×	body	640	valid
2.2s	4897×	body	80	valid
717.0ms	711×	body	320	valid
366.0ms	1629×	body	80	nan
169.0ms	333×	body	160	valid