Details

sample396.0ms

Algorithm

intervals

Results

48.0ms	45×	body	1280	valid
30.0ms	46×	body	640	valid
25.0ms	168×	body	80	valid
10.0ms	20×	body	320	valid
9.0ms	59×	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

prune25.0ms

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: 13.3b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
6.9b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
17.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite44.0ms

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)))
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)))

series594.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ 1.0 (tan B))
109.0ms	(* x (/ 1.0 (tan B)))
285.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
159.0ms	(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

prune635.0ms

Filtered

167 candidates to 129 candidates (77.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	153	14	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	154	14	168

Merged error: 0.0b

Counts

168 → 14

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
0.3b	(* x (/ 1.0 (tan B)))
0.3b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
17.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 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)) (- (/ 1.0 2.0))) (sin B)))
7.0ms	(* x (/ 1.0 (tan B)))
10.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series928.0ms

Counts

4 → 12

Calls

4 calls:

351.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
110.0ms	(* x (/ 1.0 (tan B)))
320.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
148.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify98.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	848	2078
1	3740	1960
2	5002	1960

prune636.0ms

Filtered

186 candidates to 143 candidates (76.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	184	2	186
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	187	13	200

Merged error: 0.0b

Counts

200 → 13

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.3b	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
0.3b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
17.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite44.0ms

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:

5.0ms	(/ (* x 1.0) (tan B))
14.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
10.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series910.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (* x 1.0) (tan B))
347.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
307.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
144.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify90.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	801	2023
1	3498	1905
2	5001	1905

prune606.0ms

Filtered

175 candidates to 137 candidates (78.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	174	1	175
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	175	13	188

Merged error: 0.0b

Counts

188 → 13

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (* x 1.0) (sin B)) (cos B))
0.3b	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
0.3b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
17.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 168

Calls

4 calls:

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

series921.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (/ (* x 1.0) (sin B)) (cos B))
353.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
319.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
145.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify95.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	852	2114
1	3722	1973
2	5001	1973

prune587.0ms

Filtered

180 candidates to 137 candidates (76.1%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	180	13	193

Merged error: 0.0b

Counts

193 → 13

regimes208.0ms

Accuracy

98% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 10.7b

bsearch267.0ms

Steps

Iters	Range		Point
6	3.4897325830764653e+115	3.2386625622476574e+116	3.740311987670497e+115
11	-18062256.86705318	-1.0508999232345835e-13	-7465709.542909528

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	38
1	50	38

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.4s	1651×	body	1280	valid
788.0ms	1366×	body	640	valid
616.0ms	4756×	body	80	valid
284.0ms	725×	body	320	valid
156.0ms	1630×	body	80	nan
90.0ms	342×	body	160	valid