Details

sample384.0ms

Algorithm

intervals

Results

51.0ms	52×	body	1280	valid
33.0ms	52×	body	640	valid
21.0ms	142×	body	80	valid
8.0ms	18×	body	320	valid
5.0ms	17×	body	160	valid
5.0ms	45×	body	80	nan

simplify45.0ms

Algorithm

egg-herbie

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
6.0b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
18.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite125.0ms

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:

2.0ms	(/ 1.0 (tan B))
9.0ms	(* x (/ 1.0 (tan B)))
82.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
26.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series601.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ 1.0 (tan B))
112.0ms	(* x (/ 1.0 (tan B)))
293.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
157.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify83.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	784	1475
1	3245	1361
2	5001	1358

prune697.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin B))
0.6b	(cbrt (sin B))
2.5b	(* (/ F (cbrt (sin B))) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
18.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
42×	`times-frac`
37×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
22×	`associate-l`
18×	`add-exp-log` `cbrt-prod`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
9×	`unpow-prod-down` `unswap-sqr`
8×	`add-cbrt-cube`
7×	`associate-r`
6×	`prod-exp`
5×	`pow1` `sqr-pow`
4×	`expm1-log1p-u` `pow-neg` `log1p-expm1-u` `add-log-exp`
3×	`neg-sub0` `pow-to-exp` `div-exp` `pow-exp` `div-inv` `pow-sub`
2×	`frac-times` `pow1/3` `associate-*r/` `cbrt-unprod`
1×	`cbrt-undiv` `neg-mul-1` `pow-pow` `associate-l/` `un-div-inv` `-commutative`

Counts

4 → 136

Calls

4 calls:

1.0ms	(cbrt (sin B))
1.0ms	(cbrt (sin B))
83.0ms	(* (/ F (cbrt (sin B))) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
26.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series685.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(cbrt (sin B))
99.0ms	(cbrt (sin B))
338.0ms	(* (/ F (cbrt (sin B))) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
144.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify70.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	637	1522
1	2469	1427
2	5002	1415

prune704.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

2.5b	(* (/ F (cbrt (sin B))) (* (* (cbrt (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (cbrt (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))) (cbrt (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))))
18.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))
18.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))
18.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite604.0ms

Algorithm

rewrite-expression-head

Rules

108×	`cbrt-div`
90×	`pow-unpow`
82×	`frac-times`
72×	`times-frac`
65×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
57×	`neg-sub0` `pow-neg` `pow-sub`
42×	`associate-*r/`
39×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
29×	`associate-*l/`
28×	`add-exp-log`
22×	`associate-l`
16×	`pow1`
14×	`add-cbrt-cube`
12×	`prod-exp` `cbrt-unprod`
9×	`cbrt-prod` `unpow-prod-down`
7×	`div-inv`
6×	`pow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `neg-mul-1` `pow-pow` `div-exp` `pow-exp` `sqr-pow`
1×	`associate-r` `*-commutative`

Counts

4 → 245

Calls

4 calls:

520.0ms	(* (/ F (cbrt (sin B))) (* (* (cbrt (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (cbrt (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))) (cbrt (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))))
26.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))
23.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))
23.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series780.0ms

Counts

4 → 12

Calls

4 calls:

342.0ms	(* (/ F (cbrt (sin B))) (* (* (cbrt (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (cbrt (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))) (cbrt (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))))
147.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))
148.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))
143.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify85.0ms

Algorithm

egg-herbie

Counts

257 → 257

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	899	4307
1	2717	3442
2	5001	3113

prune1.3s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.1b	(/ F (sin B))
6.0b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
18.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite116.0ms

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:

3.0ms	(/ (* x 1.0) (tan B))
2.0ms	(/ F (sin B))
79.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
27.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series603.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (* x 1.0) (tan B))
47.0ms	(/ F (sin B))
296.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
144.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify73.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	733	1411
1	3020	1297
2	5001	1294

prune590.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes215.0ms

Accuracy

94% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 11.6b

bsearch210.0ms

Steps

Iters	Range		Point
11	5.8875643735727935e-36	6.729132434316701e-11	6.610898723777132e-11
2	-1.4642350205978134e+49	-1.2440326111864124e+49	-1.2715579123628376e+49

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	40
1	55	40
2	55	40

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.6s	1681×	body	1280	valid
920.0ms	1444×	body	640	valid
632.0ms	4719×	body	80	valid
303.0ms	709×	body	320	valid
168.0ms	1605×	body	80	nan
102.0ms	354×	body	160	valid