Details

sample396.0ms

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	42	15
1	83	14
2	151	14
3	356	14
4	1063	14
5	5002	14

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.1b

localize25.0ms

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)))

rewrite135.0ms

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:

2.0ms	(/ 1.0 (tan B))
9.0ms	(* x (/ 1.0 (tan B)))
89.0ms	(* (/ 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)))

series580.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1.0 (tan B))
110.0ms	(* x (/ 1.0 (tan B)))
281.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
154.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify81.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	767	1428
1	3183	1338
2	5001	1337

prune630.0ms

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)))

rewrite122.0ms

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×	`pow-neg` `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 → 128

Calls

4 calls:

1.0ms	(cbrt (sin B))
1.0ms	(cbrt (sin B))
89.0ms	(* (/ F (cbrt (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)))

series652.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(cbrt (sin B))
93.0ms	(cbrt (sin B))
322.0ms	(* (/ F (cbrt (sin B))) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
139.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify68.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	624	1474
1	2413	1403
2	5002	1397

prune624.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin B))
0.6b	(cbrt (* (cbrt (sin B)) (cbrt (sin B))))
2.5b	(* (/ F (* (cbrt (* (cbrt (sin B)) (cbrt (sin B)))) (cbrt (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)))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt` `pow-unpow`
29×	`add-exp-log`
25×	`add-cube-cbrt` `*-un-lft-identity`
21×	`times-frac`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`prod-exp`
11×	`add-cbrt-cube`
7×	`unpow-prod-down` `associate-r` `associate-l`
6×	`div-exp`
5×	`pow1`
4×	`cbrt-prod` `pow-to-exp` `pow-neg` `pow-exp` `cbrt-unprod` `add-log-exp`
3×	`neg-sub0` `div-inv` `pow-sub` `unswap-sqr` `sqr-pow`
2×	`cbrt-undiv` `frac-times` `pow1/3` `associate-*r/`
1×	`neg-mul-1` `pow-pow` `associate-l/` `un-div-inv` `-commutative`

Counts

4 → 109

Calls

4 calls:

1.0ms	(cbrt (sin B))
3.0ms	(cbrt (* (cbrt (sin B)) (cbrt (sin B))))
99.0ms	(* (/ F (* (cbrt (* (cbrt (sin B)) (cbrt (sin B)))) (cbrt (cbrt (sin B))))) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
24.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series652.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(cbrt (sin B))
107.0ms	(cbrt (* (cbrt (sin B)) (cbrt (sin B))))
317.0ms	(* (/ F (* (cbrt (* (cbrt (sin B)) (cbrt (sin B)))) (cbrt (cbrt (sin B))))) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
138.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify74.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	674	1590
1	2812	1442
2	5002	1434

prune577.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

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)))

rewrite122.0ms

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:

3.0ms	(/ (* x 1.0) (tan B))
2.0ms	(/ F (sin B))
85.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
25.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series564.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (* x 1.0) (tan B))
49.0ms	(/ F (sin B))
274.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
135.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify77.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	718	1363
1	2971	1274
2	5001	1273

prune524.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes188.0ms

Accuracy

94.1% (0.7b remaining)

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

bsearch196.0ms

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	43	37
1	43	37

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.7s	1681×	body	1280	valid
910.0ms	1444×	body	640	valid
647.0ms	4719×	body	80	valid
304.0ms	709×	body	320	valid
158.0ms	1605×	body	80	nan
104.0ms	354×	body	160	valid