Details

sample4.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 14.648438%

Guaranteed chance to sample good point: 44.300629%

Results

50.0ms	53×	body	1280	valid
38.0ms	56×	body	640	valid
15.0ms	111×	body	80	valid
11.0ms	26×	body	320	valid
4.0ms	29×	body	80	invalid
3.0ms	10×	body	160	valid
1.0ms	5×	body	80	nan

simplify399.0ms

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

prune14.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 10.9b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.3b	(* x (/ 1.0 (tan B)))
5.0b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
14.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite41.0ms

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)))
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)))

series134.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ F (sin B))
27.0ms	(* x (/ 1.0 (tan B)))
56.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
40.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify83.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	813	1470
1	3354	1381
2	5001	1380

prune378.0ms

Filtered

126 candidates to 166 candidates (-31.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	151	15	166
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	152	15	167

Merged error: 0.8b

Counts

167 → 15

localize22.0ms

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))
14.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite49.0ms

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)))

series148.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B)))
24.0ms	(* x (/ 1.0 (tan B)))
47.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B))
22.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify99.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	892	2150
1	3830	2033
2	5001	2033

prune449.0ms

Filtered

142 candidates to 186 candidates (-31.0%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	183	3	186
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	186	15	201

Merged error: 0.8b

Counts

201 → 15

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))))
0.3b	(* x (/ 1.0 (tan B)))
0.3b	(/ (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
14.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

214×	`times-frac`
133×	`add-sqr-sqrt`
128×	`add-cube-cbrt` `*-un-lft-identity`
51×	`unpow-prod-down`
37×	`add-exp-log`
34×	`associate-/r*`
30×	`pow-unpow`
21×	`div-exp`
17×	`sqr-pow`
16×	`add-cbrt-cube`
14×	`associate-r`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`associate-/r/`
9×	`div-inv`
8×	`pow1`
6×	`neg-sub0` `pow-neg` `associate-/l*` `pow-sub`
5×	`cbrt-undiv` `pow-to-exp` `pow-exp`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`associate-l`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `unswap-sqr`
1×	`tan-quot` `neg-mul-1` `pow-flip` `pow-pow` `associate-r/` `pow-prod-down` `-commutative` `inv-pow`

Counts

4 → 264

Calls

4 calls:

14.0ms	(/ 1 (/ (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))))
7.0ms	(* x (/ 1.0 (tan B)))
10.0ms	(/ (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series172.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ 1 (/ (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))))
25.0ms	(* x (/ 1.0 (tan B)))
48.0ms	(/ (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
22.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify63.0ms

Algorithm

egg-herbie

Counts

276 → 276

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1166	4020
1	5001	3771

prune637.0ms

Filtered

183 candidates to 276 candidates (-50.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	274	2	276
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	275	16	291

Merged error: 0.8b

Counts

291 → 16

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.3b	(* x (/ 1.0 (tan B)))
0.4b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
13.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
25×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
22×	`times-frac`
21×	`associate-r`
16×	`add-cbrt-cube`
13×	`pow-unpow`
8×	`prod-exp`
7×	`pow1` `unpow-prod-down`
6×	`associate-l`
5×	`div-exp` `unswap-sqr`
4×	`cbrt-unprod` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `pow-exp` `div-inv` `associate-/l*` `sqr-pow`
2×	`*-commutative`
1×	`tan-quot` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `associate-/r/`

Counts

4 → 108

Calls

4 calls:

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

series199.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
24.0ms	(* x (/ 1.0 (tan B)))
57.0ms	(* (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))

simplify75.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	703	1170
1	3086	1048
2	5001	1048

prune205.0ms

Filtered

90 candidates to 120 candidates (-33.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	116	4	120
Fresh	4	10	14
Picked	1	0	1
Done	0	1	1
Total	121	15	136

Merged error: 0.8b

Counts

136 → 15

regimes368.0ms

Accuracy

97.5% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 10.2b

bsearch120.0ms

Steps

Iters	Range		Point
3	1.8123114175646434e+145	2.263645252707503e+145	2.235436888011074e+145
9	-1.9392463033970455e+160	-5.182736594717531e+151	-1.3370382420413004e+154

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	69
1	78	69

end0.0ms

sample8.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 14.648438%

Guaranteed chance to sample good point: 44.300629%

Results

1.7s	1674×	body	1280	valid
806.0ms	1376×	body	640	valid
536.0ms	3931×	body	80	valid
285.0ms	665×	body	320	valid
129.0ms	913×	body	80	invalid
96.0ms	354×	body	160	valid
10.0ms	97×	body	80	nan

Details

sample4.7s

simplify399.0ms

prune14.0ms

localize24.0ms

rewrite41.0ms

series134.0ms

simplify83.0ms

prune378.0ms

localize22.0ms

rewrite49.0ms

series148.0ms

simplify99.0ms

prune449.0ms

localize24.0ms

rewrite54.0ms

series172.0ms

simplify63.0ms

prune637.0ms

localize21.0ms

rewrite39.0ms

series199.0ms

simplify75.0ms

prune205.0ms

regimes368.0ms

bsearch120.0ms

simplify3.0ms

end0.0ms

sample8.2s

Profiling