Details

sample384.0ms

Algorithm

intervals

Results

53.0ms	55×	body	1280	valid
24.0ms	38×	body	640	valid
23.0ms	139×	body	80	valid
10.0ms	22×	body	320	valid
5.0ms	18×	body	160	valid
5.0ms	43×	body	80	nan

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	42	15
1	83	14
2	151	14
3	356	14
4	1063	14
5	5002	14

prune12.0ms

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: 13.5b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))
5.9b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
17.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite45.0ms

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×	`tan-quot` `frac-times` `associate-/r/` `*-commutative`
1×	`neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `clear-num` `un-div-inv`

Counts

4 → 155

Calls

4 calls:

4.0ms	(/ 1.0 (tan B))
8.0ms	(* 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)))

series603.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1.0 (tan B))
125.0ms	(* x (/ 1.0 (tan B)))
285.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
158.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify85.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	767	1428
1	3183	1338
2	5001	1337

prune588.0ms

Filtered

167 candidates to 129 candidates (77.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	156	11	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	157	11	168

Merged error: 0.0b

Counts

168 → 11

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1.0 (tan B)))
0.3b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.3b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
17.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite41.0ms

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:

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

series775.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* x (/ 1.0 (tan B)))
292.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
245.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
129.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify73.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	654	1088
1	2850	977
2	5002	977

prune372.0ms

Filtered

120 candidates to 88 candidates (73.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	115	5	120
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	120	11	131

Merged error: 0.0b

Counts

131 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.3b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.3b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
17.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

5.0ms	(/ (* x 1.0) (tan B))
10.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
11.0ms	(* (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))

series767.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (* x 1.0) (tan B))
292.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
238.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
132.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify67.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	608	1033
1	2584	922
2	5001	922

prune327.0ms

Filtered

109 candidates to 82 candidates (75.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	110	10	120

Merged error: 0.0b

Counts

120 → 10

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (tan B) (* x 1.0)))
0.3b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.3b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
17.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
41×	`add-exp-log`
38×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-cbrt-cube`
16×	`div-exp`
13×	`pow-unpow`
9×	`prod-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `unpow-prod-down` `associate-r` `div-inv`
6×	`pow1` `associate-/l*`
4×	`add-log-exp`
3×	`pow-to-exp` `rec-exp` `1-exp` `associate-l` `pow-exp` `cbrt-unprod` `unswap-sqr` `sqr-pow`
2×	`frac-2neg` `clear-num`
1×	`pow-flip` `pow-pow` `associate-/r/` `*-commutative` `inv-pow`

Counts

4 → 131

Calls

4 calls:

6.0ms	(/ 1 (/ (tan B) (* x 1.0)))
10.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
11.0ms	(* (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))

series754.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ 1 (/ (tan B) (* x 1.0)))
300.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
242.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
130.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify90.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	751	1316
1	3538	1168
2	5003	1129

prune356.0ms

Filtered

143 candidates to 91 candidates (63.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	143	10	153

Merged error: 0.0b

Counts

153 → 10

regimes170.0ms

Accuracy

97.7% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 10.5b

bsearch299.0ms

Steps

Iters	Range		Point
9	6.639887946216544e-07	6.398614580632226	6.307961579786368
9	-1.2184884793536382e+160	-5.281823845977543e+154	-5.328341862942584e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	37
1	47	37

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.6s	1713×	body	1280	valid
858.0ms	1368×	body	640	valid
667.0ms	4676×	body	80	valid
319.0ms	697×	body	320	valid
170.0ms	1652×	body	80	nan
103.0ms	354×	body	160	valid