Details

sample394.0ms

Algorithm

intervals

Results

49.0ms	56×	body	1280	valid
26.0ms	43×	body	640	valid
21.0ms	155×	body	80	valid
10.0ms	18×	body	320	valid
6.0ms	58×	body	80	nan
4.0ms	13×	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

prune15.0ms

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: 11.1b

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)))
4.8b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
15.4b	(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×	`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:

3.0ms	(/ 1.0 (tan B))
6.0ms	(* 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)))

series573.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ 1.0 (tan B))
107.0ms	(* x (/ 1.0 (tan B)))
276.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
157.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify81.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (65.0ms)

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

prune827.0ms

Filtered

167 candidates to 128 candidates (76.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	155	12	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	156	12	168

Merged error: 0.0b

Counts

168 → 12

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))
15.4b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite47.0ms

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:

15.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B)))
6.0ms	(* x (/ 1.0 (tan B)))
10.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B))
9.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series888.0ms

Counts

4 → 12

Calls

4 calls:

340.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B)))
104.0ms	(* x (/ 1.0 (tan B)))
307.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B))
137.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify101.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	848	2076
1	3733	1956
2	5001	1956

prune869.0ms

Filtered

186 candidates to 142 candidates (76.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	185	1	186
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	187	11	198

Merged error: 0.0b

Counts

198 → 11

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.2b	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B)))
0.4b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B))
15.4b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite42.0ms

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:

4.0ms	(/ (* x 1.0) (tan B))
13.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B)))
9.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B))
9.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series892.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (* x 1.0) (tan B))
341.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B)))
303.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B))
144.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify87.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	801	2021
1	3491	1901
2	5002	1901

prune827.0ms

Filtered

175 candidates to 136 candidates (77.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	172	3	175
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	176	10	186

Merged error: 0.0b

Counts

186 → 10

localize29.0ms

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	(/ 1 (/ (tan B) (* x 1.0)))
0.4b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B))
15.4b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 197

Calls

4 calls:

13.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B)))
6.0ms	(/ 1 (/ (tan B) (* x 1.0)))
9.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B))
9.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series882.0ms

Counts

4 → 12

Calls

4 calls:

348.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B)))
83.0ms	(/ 1 (/ (tan B) (* x 1.0)))
306.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))) (sin B))
144.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify104.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	944	2302
1	4402	2145
2	5002	2106

prune845.0ms

Filtered

209 candidates to 143 candidates (68.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	208	1	209
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	208	11	219

Merged error: 0.0b

Counts

219 → 11

regimes310.0ms

Accuracy

97.7% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 10.8b

bsearch246.0ms

Steps

Iters	Range		Point
6	1.9994114391144223e+41	8.975909569126579e+41	2.028544699977216e+41
9	-15209204325134504.0	-94168834.41758807	-143528529.51788655

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	39
1	61	39

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.4s	1631×	body	1280	valid
804.0ms	1371×	body	640	valid
629.0ms	4852×	body	80	valid
281.0ms	710×	body	320	valid
154.0ms	1644×	body	80	nan
92.0ms	345×	body	160	valid

Details

sample394.0ms

simplify45.0ms

prune15.0ms

localize25.0ms

rewrite41.0ms

series573.0ms

simplify81.0ms

prune827.0ms

localize22.0ms

rewrite47.0ms

series888.0ms

simplify101.0ms

prune869.0ms

localize25.0ms

rewrite42.0ms

series892.0ms

simplify87.0ms

prune827.0ms

localize29.0ms

rewrite45.0ms

series882.0ms

simplify104.0ms

prune845.0ms

regimes310.0ms

bsearch246.0ms

simplify2.0ms

end0.0ms

sample3.8s

Profiling