Details

sample383.0ms

Algorithm

intervals

Results

51.0ms	58×	body	1280	valid
29.0ms	49×	body	640	valid
17.0ms	139×	body	80	valid
8.0ms	22×	body	320	valid
5.0ms	54×	body	80	nan
1.0ms	6×	body	160	valid

simplify44.0ms

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

prune24.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (+ (* F F) 2.0) (* 2.0 x))
0.3b	(* x (/ 1.0 (tan B)))
7.9b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
18.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
40×	`times-frac`
37×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
23×	`add-exp-log`
21×	`associate-r`
16×	`associate-l`
14×	`add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
9×	`add-log-exp`
8×	`unpow-prod-down` `prod-exp` `unswap-sqr`
7×	`pow1`
4×	`pow-neg` `div-exp` `cbrt-unprod` `div-inv` `sqr-pow`
3×	`neg-sub0` `pow-to-exp` `associate-*r/` `pow-exp` `sum-log` `pow-sub`
2×	`cbrt-undiv` `frac-times` `*-commutative`
1×	`tan-quot` `+-commutative` `neg-mul-1` `associate-+l+` `pow-pow` `flip3-+` `pow-prod-down` `associate-*l/` `associate-/r/` `un-div-inv` `flip-+`

Counts

4 → 140

Calls

4 calls:

6.0ms	(+ (+ (* F F) 2.0) (* 2.0 x))
7.0ms	(* x (/ 1.0 (tan B)))
13.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
12.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series590.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (+ (* F F) 2.0) (* 2.0 x))
110.0ms	(* x (/ 1.0 (tan B)))
290.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
161.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify92.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	813	1382
1	3495	1293
2	5001	1292

prune572.0ms

Filtered

152 candidates to 115 candidates (75.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (+ (* F F) 2.0) (* 2.0 x))
0.2b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
0.3b	(* x (/ 1.0 (tan B)))
18.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
31×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
28×	`times-frac`
21×	`associate-r`
15×	`add-exp-log`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
11×	`add-cbrt-cube`
9×	`add-log-exp`
7×	`pow1` `unpow-prod-down`
6×	`associate-l`
5×	`prod-exp` `unswap-sqr`
3×	`pow-neg` `associate-*r/` `sum-log` `cbrt-unprod` `div-inv` `sqr-pow`
2×	`neg-sub0` `pow-to-exp` `pow-exp` `*-commutative` `pow-sub`
1×	`tan-quot` `cbrt-undiv` `+-commutative` `neg-mul-1` `associate-+l+` `pow-pow` `flip3-+` `div-exp` `pow-prod-down` `associate-/r/` `un-div-inv` `flip-+`

Counts

4 → 120

Calls

4 calls:

6.0ms	(+ (+ (* F F) 2.0) (* 2.0 x))
11.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
7.0ms	(* x (/ 1.0 (tan B)))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (+ (* F F) 2.0) (* 2.0 x))
206.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
107.0ms	(* x (/ 1.0 (tan B)))
145.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify74.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	681	1031
1	2938	962
2	5001	962

prune483.0ms

Filtered

132 candidates to 100 candidates (75.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
0.2b	(+ (+ (* F F) 2.0) (* 2.0 x))
0.2b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
18.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt` `pow-unpow`
25×	`add-cube-cbrt` `*-un-lft-identity`
21×	`times-frac`
20×	`add-exp-log`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
11×	`add-cbrt-cube`
9×	`add-log-exp`
7×	`unpow-prod-down` `associate-r`
6×	`prod-exp`
5×	`pow1` `pow-neg`
4×	`associate-*r/` `div-exp`
3×	`neg-sub0` `pow-to-exp` `associate-l` `pow-exp` `associate-/r*` `sum-log` `div-inv` `associate-/l/` `pow-sub` `unswap-sqr` `sqr-pow`
2×	`cbrt-undiv` `un-div-inv` `cbrt-unprod`
1×	`+-commutative` `neg-mul-1` `associate-+l+` `pow-pow` `frac-2neg` `flip3-+` `clear-num` `-commutative` `flip-+` `associate-/l`

Counts

4 → 113

Calls

4 calls:

11.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
6.0ms	(+ (+ (* F F) 2.0) (* 2.0 x))
10.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
12.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series703.0ms

Counts

4 → 12

Calls

4 calls:

336.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
24.0ms	(+ (+ (* F F) 2.0) (* 2.0 x))
201.0ms	(* F (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)))

simplify69.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	629	1222
1	2712	1116
2	5001	1116

prune439.0ms

Filtered

125 candidates to 95 candidates (76.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
0.2b	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.2b	(+ (+ (* F F) 2.0) (* 2.0 x))
18.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

189×	`times-frac`
110×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
51×	`unpow-prod-down`
28×	`associate-/l*`
20×	`add-exp-log`
17×	`sqr-pow`
13×	`pow-unpow`
11×	`add-cbrt-cube`
10×	`div-exp` `associate-/r*`
9×	`add-log-exp`
7×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv`
3×	`pow-to-exp` `pow-exp` `sum-log`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l+` `pow-pow` `flip3-+` `flip-+` `associate-/l/`

Counts

4 → 205

Calls

4 calls:

13.0ms	(/ (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
9.0ms	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
6.0ms	(+ (+ (* F F) 2.0) (* 2.0 x))
8.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series733.0ms

Counts

4 → 12

Calls

4 calls:

350.0ms	(/ (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
228.0ms	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
24.0ms	(+ (+ (* F F) 2.0) (* 2.0 x))
132.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify102.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	945	3214
1	3994	3112
2	5002	3112

prune788.0ms

Filtered

217 candidates to 171 candidates (78.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes163.0ms

Accuracy

96.9% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 10.7b

bsearch294.0ms

Steps

Iters	Range		Point
11	4.1748304064482475	1.504765998962328e+20	152227.76471163236
8	-5.852158442175802e+75	-3.1094155269257426e+71	-3.661057205446993e+71

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	44
1	68	44

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.4s	1657×	body	1280	valid
786.0ms	1443×	body	640	valid
575.0ms	4747×	body	80	valid
263.0ms	685×	body	320	valid
147.0ms	1678×	body	80	nan
87.0ms	353×	body	160	valid