Details

sample372.0ms

Algorithm

intervals

Results

49.0ms	59×	body	1280	valid
21.0ms	167×	body	80	valid
18.0ms	34×	body	640	valid
5.0ms	13×	body	320	valid
4.0ms	52×	body	80	nan
3.0ms	12×	body	160	valid

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.3b	(* x (/ 1.0 (tan B)))
7.7b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
18.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite44.0ms

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:

3.0ms	(/ F (sin B))
7.0ms	(* x (/ 1.0 (tan B)))
14.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
13.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series607.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ F (sin B))
110.0ms	(* x (/ 1.0 (tan B)))
286.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
160.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify83.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	765	1418
1	3213	1329
2	5001	1328

prune614.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt F)
0.5b	(* (cbrt F) (cbrt F))
2.5b	(* (/ (cbrt F) (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
18.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-sqr-sqrt`
44×	`add-cube-cbrt` `*-un-lft-identity`
42×	`times-frac`
31×	`cbrt-prod`
30×	`pow-unpow`
28×	`associate-l`
20×	`add-exp-log`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-r` `unswap-sqr`
12×	`pow1`
9×	`unpow-prod-down`
8×	`add-cbrt-cube`
7×	`pow1/3` `prod-exp`
6×	`swap-sqr`
5×	`sqr-pow`
4×	`pow-neg` `add-log-exp`
3×	`neg-sub0` `pow-to-exp` `div-exp` `pow-exp` `cbrt-unprod` `div-inv` `pow-sub`
2×	`frac-times` `associate-r/` `pow-prod-down` `pow-sqr` `-commutative` `pow-prod-up`
1×	`cbrt-undiv` `pow2` `neg-mul-1` `pow-pow` `pow-plus` `associate-*l/` `un-div-inv`

Counts

4 → 157

Calls

4 calls:

1.0ms	(cbrt F)
6.0ms	(* (cbrt F) (cbrt F))
16.0ms	(* (/ (cbrt F) (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
11.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series849.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(cbrt F)
192.0ms	(* (cbrt F) (cbrt F))
340.0ms	(* (/ (cbrt 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)))

simplify81.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	727	1573
1	2990	1489
2	5001	1472

prune740.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(/ F (sin B))
7.7b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
18.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite40.0ms

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:

5.0ms	(/ (* x 1.0) (tan B))
3.0ms	(/ F (sin B))
14.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series585.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (* x 1.0) (tan B))
52.0ms	(/ F (sin B))
284.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
142.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify77.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (59.0ms)

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

prune568.0ms

Pruning

10 alts after pruning (9 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))
0.2b	(/ F (sin B))
7.6b	(/ (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
18.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

184×	`times-frac`
106×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
45×	`unpow-prod-down`
25×	`add-exp-log`
17×	`associate-/l*`
16×	`add-cbrt-cube`
15×	`sqr-pow`
13×	`pow-unpow` `associate-/r*`
12×	`div-exp` `div-inv`
6×	`cbrt-undiv`
5×	`pow1`
4×	`add-log-exp`
3×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num`
1×	`tan-quot` `pow-pow` `prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/`

Counts

4 → 206

Calls

4 calls:

5.0ms	(/ (* x 1.0) (tan B))
4.0ms	(/ F (sin B))
13.0ms	(/ (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
9.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series591.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (* x 1.0) (tan B))
48.0ms	(/ F (sin B))
301.0ms	(/ (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
133.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify102.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	939	3042
1	4072	2953
2	5001	2952

prune775.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes153.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 12.0b

bsearch281.0ms

Steps

Iters	Range		Point
8	8844.837273169236	536699583.1073491	1584339.738457524
10	-1.2046105318349406e+27	-20837379028.642044	-25045099127.8392

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	39
1	47	39

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	1729×	body	1280	valid
735.0ms	1375×	body	640	valid
567.0ms	4819×	body	80	valid
239.0ms	634×	body	320	valid
141.0ms	1627×	body	80	nan
92.0ms	360×	body	160	valid