Details

sample443.0ms

Algorithm

intervals

Results

49.0ms	42×	body	640	valid
47.0ms	51×	body	1280	valid
25.0ms	168×	body	80	valid
6.0ms	58×	body	80	nan
6.0ms	14×	body	320	valid
4.0ms	13×	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

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: 15.1b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
9.2b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
17.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite55.0ms

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:

12.0ms	(/ 1.0 (tan B))
8.0ms	(* x (/ 1.0 (tan B)))
14.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
13.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series614.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1.0 (tan B))
114.0ms	(* x (/ 1.0 (tan B)))
303.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
161.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify86.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	767	1426
1	3176	1335
2	5001	1334

prune607.0ms

Filtered

167 candidates to 128 candidates (76.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	154	13	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	155	13	168

Merged error: 0.1b

Counts

168 → 13

localize25.0ms

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)))
0.3b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
17.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 133

Calls

4 calls:

11.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
8.0ms	(* x (/ 1.0 (tan B)))
11.0ms	(* F (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)))

series843.0ms

Counts

4 → 12

Calls

4 calls:

364.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
110.0ms	(* x (/ 1.0 (tan B)))
216.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
152.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify86.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	721	1298
1	3136	1178
2	5001	1178

prune469.0ms

Filtered

145 candidates to 109 candidates (75.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	139	6	145
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	146	12	158

Merged error: 0.0b

Counts

158 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
0.3b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
17.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 122

Calls

4 calls:

5.0ms	(/ (* x 1.0) (tan B))
15.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
11.0ms	(* F (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)))

series836.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (* x 1.0) (tan B))
360.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
218.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
148.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify75.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	674	1243
1	2891	1123
2	5002	1123

prune427.0ms

Filtered

134 candidates to 101 candidates (75.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	130	4	134
Fresh	6	5	11
Picked	0	1	1
Done	0	0	0
Total	136	10	146

Merged error: 0.0b

Counts

146 → 10

localize26.0ms

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	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
0.3b	(/ 1 (/ (tan B) (* x 1.0)))
17.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 156

Calls

4 calls:

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

series821.0ms

Counts

4 → 12

Calls

4 calls:

361.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
216.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
88.0ms	(/ 1 (/ (tan B) (* x 1.0)))
156.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify97.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	817	1524
1	3804	1367
2	5002	1325

prune434.0ms

Filtered

168 candidates to 109 candidates (64.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	167	11	178

Merged error: 0.0b

Counts

178 → 11

Details

sample443.0ms

simplify48.0ms

prune12.0ms

localize27.0ms

rewrite55.0ms

series614.0ms

simplify86.0ms

prune607.0ms

localize25.0ms

rewrite46.0ms

series843.0ms

simplify86.0ms

prune469.0ms

localize24.0ms

rewrite45.0ms

series836.0ms

simplify75.0ms

prune427.0ms

localize26.0ms

rewrite44.0ms

series821.0ms

simplify97.0ms

prune434.0ms

regimes178.0ms

bsearch6.0ms

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