Details

sample57.0ms

Algorithm

intervals

Results

18.0ms	46×	body	1280	valid
14.0ms	55×	body	640	valid
9.0ms	151×	body	80	valid
4.0ms	23×	body	320	valid
2.0ms	12×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	18	7
1	31	6
2	39	6
3	50	6
4	53	6
5	53	6

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.2b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.1b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

99×	`frac-add` `distribute-neg-frac`
90×	`associate-*r/`
86×	`*-un-lft-identity`
79×	`associate-/l*`
75×	`add-sqr-sqrt`
70×	`add-cube-cbrt`
69×	`associate-/r*`
33×	`clear-num`
28×	`times-frac`
23×	`frac-2neg`
20×	`un-div-inv`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1`
4×	`associate-l`
3×	`cbrt-undiv` `div-exp` `div-inv` `distribute-lft-out`
2×	`tan-quot` `distribute-rgt-neg-in` `prod-exp` `sum-log` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `pow-prod-down` `neg-log` `*-commutative` `flip-+`

Counts

4 → 213

Calls

4 calls:

42.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
3.0ms	(/ 1.0 (sin B))
4.0ms	(/ 1.0 (tan B))
8.0ms	(* x (/ 1.0 (tan B)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
19.0ms	(/ 1.0 (sin B))
37.0ms	(/ 1.0 (tan B))
112.0ms	(* x (/ 1.0 (tan B)))

simplify54.0ms

Algorithm

egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1210	2296
1	5001	2112

prune376.0ms

Filtered

225 candidates to 142 candidates (36.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	215	10	225
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	216	10	226

Merged error: 0.0b

Counts

226 → 10

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (- (/ x (/ (tan B) 1.0))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.2b	(/ x (/ (tan B) 1.0))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

193×	`associate-/r*`
173×	`*-un-lft-identity`
171×	`frac-add` `distribute-neg-frac`
167×	`times-frac`
165×	`add-sqr-sqrt` `add-cube-cbrt`
93×	`associate-/l*`
31×	`frac-2neg` `clear-num`
15×	`div-inv`
10×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
7×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `distribute-lft-out`
2×	`distribute-rgt-neg-in` `sum-log`
1×	`tan-quot` `+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `neg-log` `flip-+` `associate-/l/`

Counts

3 → 293

Calls

3 calls:

73.0ms	(+ (- (/ x (/ (tan B) 1.0))) (/ 1.0 (sin B)))
3.0ms	(/ 1.0 (sin B))
7.0ms	(/ x (/ (tan B) 1.0))

series250.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(+ (- (/ x (/ (tan B) 1.0))) (/ 1.0 (sin B)))
22.0ms	(/ 1.0 (sin B))
112.0ms	(/ x (/ (tan B) 1.0))

simplify90.0ms

Algorithm

egg-herbie

Counts

302 → 302

Iterations

Useful iterations: 1 (47.0ms)

Iter	Nodes	Cost
0	2320	4347
1	5001	4245

prune610.0ms

Filtered

302 candidates to 214 candidates (29.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	297	5	302
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	304	8	312

Merged error: 0.0b

Counts

312 → 8

localize18.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ x (tan B))
0.2b	(/ (+ (* (- (/ x (tan B))) (/ (sin B) (sqrt 1.0))) (* (/ 1 1.0) (sqrt 1.0))) (/ (/ (sin B) 1.0) (sqrt 1.0)))
0.2b	(* (- (/ x (tan B))) (/ (sin B) (sqrt 1.0)))

rewrite606.0ms

Algorithm

rewrite-expression-head

Rules

3508×	`*-un-lft-identity`
3136×	`times-frac`
1929×	`add-sqr-sqrt`
1921×	`add-cube-cbrt`
1477×	`associate-/r*`
1269×	`associate-*l/`
1194×	`associate-l`
1190×	`associate-/l/`
1179×	`frac-add`
1170×	`distribute-neg-frac`
1125×	`associate-/l*`
1080×	`frac-times`
859×	`sqrt-prod`
830×	`distribute-lft-out`
375×	`clear-num`
365×	`frac-2neg`
353×	`div-inv`
346×	`distribute-rgt-neg-in`
120×	`associate-*r/`
34×	`associate-/r/`
22×	`associate-r`
20×	`un-div-inv`
19×	`add-exp-log` `add-cbrt-cube`
14×	`distribute-lft-neg-in`
8×	`cbrt-undiv` `div-exp`
5×	`pow1`
3×	`tan-quot` `add-log-exp` `unswap-sqr`
2×	`prod-exp` `cbrt-unprod`
1×	`distribute-lft-neg-out` `neg-mul-1` `flip3-+` `pow-prod-down` `*-commutative` `flip-+`

Counts

3 → 2619

Calls

3 calls:

4.0ms	(/ x (tan B))
238.0ms	(/ (+ (* (- (/ x (tan B))) (/ (sin B) (sqrt 1.0))) (* (/ 1 1.0) (sqrt 1.0))) (/ (/ (sin B) 1.0) (sqrt 1.0)))
26.0ms	(* (- (/ x (tan B))) (/ (sin B) (sqrt 1.0)))

series630.0ms

Counts

3 → 9

Calls

3 calls:

106.0ms	(/ x (tan B))
302.0ms	(/ (+ (* (- (/ x (tan B))) (/ (sin B) (sqrt 1.0))) (* (/ 1 1.0) (sqrt 1.0))) (/ (/ (sin B) 1.0) (sqrt 1.0)))
221.0ms	(* (- (/ x (tan B))) (/ (sin B) (sqrt 1.0)))

simplify441.0ms

Algorithm

egg-herbie

Counts

2628 → 2628

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5001	48638

prune5.3s

Filtered

2628 candidates to 1253 candidates (52.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	2622	6	2628
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	2630	6	2636

Merged error: 0b

Counts

2636 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (cos B))
0.2b	(/ (+ (* (- (/ (* x (cos B)) (sin B))) (/ (sin B) (sqrt 1.0))) (* (/ 1 1.0) (sqrt 1.0))) (/ (/ (sin B) 1.0) (sqrt 1.0)))
0.2b	(/ (* x (cos B)) (sin B))
0.2b	(* (- (/ (* x (cos B)) (sin B))) (/ (sin B) (sqrt 1.0)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

4723×	`*-un-lft-identity`
3597×	`times-frac`
3094×	`add-sqr-sqrt`
2926×	`associate-/l*`
2804×	`add-cube-cbrt`
2412×	`associate-*l/`
2368×	`associate-/r*`
2340×	`distribute-neg-frac`
2243×	`associate-/l/`
2232×	`frac-add`
2160×	`frac-times`
1918×	`associate-l`
1168×	`sqrt-prod`
913×	`distribute-lft-out`
582×	`clear-num`
572×	`frac-2neg`
455×	`distribute-rgt-neg-in`
445×	`associate-r`
360×	`div-inv`
144×	`unswap-sqr`
142×	`*-commutative`
120×	`associate-*r/`
40×	`distribute-lft-neg-in`
31×	`associate-/r/`
25×	`add-exp-log` `add-cbrt-cube`
20×	`un-div-inv`
9×	`cbrt-undiv` `div-exp`
8×	`pow1`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
2×	`pow-prod-down`
1×	`distribute-lft-neg-out` `neg-mul-1` `flip3-+` `flip-+`

Counts

4 → 3979

Calls

4 calls:

4.0ms	(* x (cos B))
595.0ms	(/ (+ (* (- (/ (* x (cos B)) (sin B))) (/ (sin B) (sqrt 1.0))) (* (/ 1 1.0) (sqrt 1.0))) (/ (/ (sin B) 1.0) (sqrt 1.0)))
8.0ms	(/ (* x (cos B)) (sin B))
50.0ms	(* (- (/ (* x (cos B)) (sin B))) (/ (sin B) (sqrt 1.0)))

series476.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* x (cos B))
213.0ms	(/ (+ (* (- (/ (* x (cos B)) (sin B))) (/ (sin B) (sqrt 1.0))) (* (/ 1 1.0) (sqrt 1.0))) (/ (/ (sin B) 1.0) (sqrt 1.0)))
97.0ms	(/ (* x (cos B)) (sin B))
124.0ms	(* (- (/ (* x (cos B)) (sin B))) (/ (sin B) (sqrt 1.0)))

simplify682.0ms

Algorithm

egg-herbie

Counts

3991 → 3991

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5001	72395

prune8.9s

Filtered

3991 candidates to 2116 candidates (47.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	3990	1	3991
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	3991	6	3997

Merged error: 0b

Counts

3997 → 6

regimes75.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	18
1	38	18
2	41	18
3	41	18

end0.0ms

sample1.7s

Algorithm

intervals

Results

666.0ms	1628×	body	1280	valid
388.0ms	1470×	body	640	valid
296.0ms	4957×	body	80	valid
134.0ms	739×	body	320	valid
45.0ms	354×	body	160	valid