Details

sample445.0ms

Algorithm

intervals

Results

68.0ms	53×	body	1280	valid
35.0ms	52×	body	640	valid
20.0ms	144×	body	80	valid
8.0ms	19×	body	320	valid
6.0ms	57×	body	80	nan
2.0ms	9×	body	160	valid

simplify48.0ms

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

prune11.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 13.0b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.3b	(* x (/ 1.0 (tan B)))
6.5b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
16.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite51.0ms

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:

12.0ms	(/ F (sin B))
8.0ms	(* x (/ 1.0 (tan B)))
13.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
12.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series598.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ F (sin B))
109.0ms	(* x (/ 1.0 (tan B)))
293.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
150.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify90.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	765	1416
1	3206	1325
2	5002	1324

prune558.0ms

Filtered

166 candidates to 126 candidates (75.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	156	10	166
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	157	10	167

Merged error: 0.0b

Counts

167 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B)))
0.3b	(* x (/ 1.0 (tan B)))
0.4b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B))
16.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
73×	`times-frac`
59×	`add-cube-cbrt` `*-un-lft-identity`
39×	`associate-r`
30×	`pow-unpow`
25×	`add-exp-log` `unpow-prod-down`
16×	`add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
9×	`pow1` `sqr-pow`
7×	`div-exp` `associate-/l*`
6×	`associate-l` `prod-exp` `unswap-sqr`
5×	`div-inv`
4×	`cbrt-unprod` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `pow-exp` `associate-/r*`
2×	`neg-sub0` `pow-neg` `associate-r/` `pow-prod-down` `-commutative` `associate-/l/` `pow-sub`
1×	`tan-quot` `neg-mul-1` `pow-pow` `frac-2neg` `clear-num` `associate-/r/`

Counts

4 → 174

Calls

4 calls:

14.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B)))
7.0ms	(* x (/ 1.0 (tan B)))
10.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series919.0ms

Counts

4 → 12

Calls

4 calls:

348.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B)))
112.0ms	(* x (/ 1.0 (tan B)))
312.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B))
146.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify97.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	848	2076
1	3733	1956
2	5001	1956

prune585.0ms

Filtered

186 candidates to 142 candidates (76.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	182	4	186
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	185	11	196

Merged error: 0.0b

Counts

196 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.2b	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B)))
0.4b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B))
16.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
63×	`add-sqr-sqrt`
53×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
25×	`add-exp-log` `unpow-prod-down` `associate-r`
16×	`add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
9×	`sqr-pow`
8×	`div-exp` `associate-/l*`
7×	`pow1`
6×	`associate-/r*`
5×	`prod-exp` `div-inv`
4×	`cbrt-undiv` `add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `associate-l` `pow-exp` `cbrt-unprod`
2×	`neg-sub0` `pow-neg` `frac-2neg` `clear-num` `associate-/l/` `pow-sub`
1×	`tan-quot` `neg-mul-1` `pow-pow` `associate-r/` `pow-prod-down` `associate-/r/` `-commutative`

Counts

4 → 163

Calls

4 calls:

8.0ms	(/ (* x 1.0) (tan B))
13.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B)))
10.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series907.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (* x 1.0) (tan B))
345.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B)))
315.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B))
140.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify95.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	801	2021
1	3491	1901
2	5002	1901

prune550.0ms

Filtered

175 candidates to 136 candidates (77.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	172	3	175
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	175	11	186

Merged error: 0.0b

Counts

186 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.2b	(/ (* x (cos B)) (sin B))
6.5b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
16.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 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×	`neg-mul-1` `pow-pow` `associate-l/` `un-div-inv` `-commutative`

Counts

4 → 142

Calls

4 calls:

3.0ms	(/ F (sin B))
5.0ms	(/ (* x (cos B)) (sin B))
17.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
9.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series572.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ F (sin B))
95.0ms	(/ (* x (cos B)) (sin B))
289.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
140.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify79.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	693	1382
1	2893	1285
2	5001	1284

prune465.0ms

Filtered

154 candidates to 116 candidates (75.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	154	11	165

Merged error: 0.0b

Counts

165 → 11

regimes167.0ms

Accuracy

98.2% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.8b

bsearch237.0ms

Steps

Iters	Range		Point
6	6.170726729532675e+63	3.8430166095794773e+64	6.2371804121605565e+63
9	-16048011.320361046	-4.445721189598084	-2446487.4979457934

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	39
1	58	39

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.5s	1694×	body	1280	valid
817.0ms	1369×	body	640	valid
634.0ms	4765×	body	80	valid
288.0ms	687×	body	320	valid
158.0ms	1606×	body	80	nan
101.0ms	345×	body	160	valid

Details

sample445.0ms

simplify48.0ms

prune11.0ms

localize25.0ms

rewrite51.0ms

series598.0ms

simplify90.0ms

prune558.0ms

localize27.0ms

rewrite48.0ms

series919.0ms

simplify97.0ms

prune585.0ms

localize22.0ms

rewrite47.0ms

series907.0ms

simplify95.0ms

prune550.0ms

localize23.0ms

rewrite40.0ms

series572.0ms

simplify79.0ms

prune465.0ms

regimes167.0ms

bsearch237.0ms

simplify2.0ms

end0.0ms

sample3.8s

Profiling