Details

sample384.0ms

Algorithm

intervals

Results

59.0ms	64×	body	1280	valid
24.0ms	40×	body	640	valid
22.0ms	144×	body	80	valid
7.0ms	16×	body	320	valid
6.0ms	57×	body	80	nan
5.0ms	16×	body	160	valid

simplify45.0ms

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

prune27.0ms

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: 14.8b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
6.7b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
19.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite43.0ms

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))
7.0ms	(* x (/ 1.0 (tan B)))
13.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
12.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series589.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 1.0 (tan B))
108.0ms	(* 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 (70.0ms)

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

prune596.0ms

Filtered

167 candidates to 129 candidates (77.2%)

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: 0.0b

Counts

168 → 13

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.2b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
0.3b	(* x (/ 1.0 (tan B)))
19.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 135

Calls

4 calls:

4.0ms	(/ 1.0 (tan B))
11.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
7.0ms	(* x (/ 1.0 (tan B)))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series502.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ 1.0 (tan B))
207.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
107.0ms	(* x (/ 1.0 (tan B)))
146.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify72.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	636	1077
1	2630	1007
2	5002	1007

prune480.0ms

Filtered

147 candidates to 114 candidates (77.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	141	6	147
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	149	11	160

Merged error: 0.0b

Counts

160 → 11

localize22.0ms

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)) (- (/ 1.0 2.0)))) (sin B))
0.2b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
19.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite43.0ms

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

series796.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (* x 1.0) (tan B))
344.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
207.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
140.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify73.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	674	1245
1	2898	1127
2	5001	1127

prune412.0ms

Filtered

134 candidates to 102 candidates (76.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	130	4	134
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	136	9	145

Merged error: 0.0b

Counts

145 → 9

localize21.0ms

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)) (/ 1.0 2.0)))
0.2b	(/ (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
19.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

192×	`times-frac`
112×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
51×	`unpow-prod-down`
29×	`associate-/l*`
25×	`add-exp-log`
17×	`sqr-pow`
16×	`add-cbrt-cube`
13×	`pow-unpow` `associate-/r*`
12×	`div-exp`
8×	`div-inv`
6×	`cbrt-undiv`
5×	`pow1`
4×	`add-log-exp`
3×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num`
1×	`tan-quot` `pow-pow` `prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/`

Counts

4 → 214

Calls

4 calls:

5.0ms	(/ (* x 1.0) (tan B))
9.0ms	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
13.0ms	(/ (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
8.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series836.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (* x 1.0) (tan B))
236.0ms	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
359.0ms	(/ (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
133.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify106.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	990	3237
1	4176	3123
2	5001	3123

prune719.0ms

Filtered

226 candidates to 180 candidates (79.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	225	1	226
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	226	9	235

Merged error: 0.0b

Counts

235 → 9

regimes151.0ms

Accuracy

95.5% (0.5b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 10.5b

bsearch244.0ms

Steps

Iters	Range		Point
8	2.9224747477689166e+147	1.4472773819273594e+152	3.068134470845061e+147
8	-4.1653256596649633e+164	-1.0175704574175542e+162	-1.0328200120067305e+162

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	34
1	47	34

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.5s	1671×	body	1280	valid
814.0ms	1362×	body	640	valid
627.0ms	4763×	body	80	valid
291.0ms	692×	body	320	valid
159.0ms	1675×	body	80	nan
104.0ms	356×	body	160	valid

Details

sample384.0ms

simplify45.0ms

prune27.0ms

localize25.0ms

rewrite43.0ms

series589.0ms

simplify85.0ms

prune596.0ms

localize27.0ms

rewrite35.0ms

series502.0ms

simplify72.0ms

prune480.0ms

localize22.0ms

rewrite43.0ms

series796.0ms

simplify73.0ms

prune412.0ms

localize21.0ms

rewrite46.0ms

series836.0ms

simplify106.0ms

prune719.0ms

regimes151.0ms

bsearch244.0ms

simplify2.0ms

end0.0ms

sample3.8s

Profiling