Details

sample729.0ms

Algorithm

intervals

Results

158.0ms	50×	body	640	valid
134.0ms	59×	body	80	nan
119.0ms	55×	body	1280	valid
50.0ms	144×	body	80	valid
33.0ms	24×	body	320	valid
7.0ms	11×	body	160	valid

simplify4.0s

Counts

1 → 1

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	20	27
1	42	27
2	83	26
3	151	26
4	345	26
5	876	26
6	3195	26
done	5000	26

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize40.0ms

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)))

rewrite871.0ms

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:

13.0ms	(/ 1.0 (tan B))
38.0ms	(* x (/ 1.0 (tan B)))
721.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
86.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series961.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ 1.0 (tan B))
176.0ms	(* x (/ 1.0 (tan B)))
469.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
260.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify1.7s

Counts

167 → 167

Iterations

Useful iterations: 2 (600.0ms)

Iter	Nodes	Cost
0	306	2742
1	747	2573
2	2039	2415
done	5000	2415

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

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)))

rewrite464.0ms

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:

13.0ms	(/ F (sin B))
25.0ms	(/ (* x 1.0) (tan B))
356.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
59.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series986.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ F (sin B))
173.0ms	(/ (* x 1.0) (tan B))
494.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
242.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify1.7s

Counts

155 → 155

Iterations

Useful iterations: 2 (681.0ms)

Iter	Nodes	Cost
0	288	2628
1	701	2467
2	2025	2313
done	5000	2313

prune1.1s

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))
0.3b	(/ 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))

rewrite475.0ms

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:

14.0ms	(/ (* x 1.0) (tan B))
72.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
308.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
78.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

156.0ms	(/ (* x 1.0) (tan B))
532.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
423.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
228.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify1.8s

Counts

109 → 109

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	250	2060
1	601	1951
2	1936	1765
done	5000	1753

prune666.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite903.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`add-cube-cbrt` `*-un-lft-identity`
26×	`pow-unpow`
20×	`associate-r`
18×	`times-frac`
17×	`sqrt-prod`
13×	`pow1` `add-exp-log` `unpow-prod-down`
11×	`add-cbrt-cube`
5×	`sqr-pow`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `pow-exp` `*-commutative` `div-inv`

Counts

4 → 107

Calls

4 calls:

259.0ms	(* (sin B) (sqrt (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
502.0ms	(* (* (sin B) (sqrt (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))) (sqrt (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
64.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))
75.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

438.0ms	(* (sin B) (sqrt (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
395.0ms	(* (* (sin B) (sqrt (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))) (sqrt (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
186.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))
214.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify3.8s

Counts

119 → 119

Iterations

Useful iterations: 3 (1.9s)

Iter	Nodes	Cost
0	204	2948
1	494	2494
2	1469	2290
3	4350	2266
done	5000	2266

prune854.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes303.0ms

Accuracy

98.3% (0.2b remaining)

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

bsearch602.0ms

Steps

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

simplify36.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	76
1	50	76
2	56	76
done	56	76

end0.0ms

sample9.9s

Algorithm

intervals

Results

3.5s	1667×	body	1280	valid
2.3s	4897×	body	80	valid
2.0s	1344×	body	640	valid
927.0ms	711×	body	320	valid
365.0ms	1629×	body	80	nan
217.0ms	333×	body	160	valid