Details

sample372.0ms

Algorithm

intervals

Results

44.0ms	49×	body	1280	valid
29.0ms	52×	body	640	valid
18.0ms	146×	body	80	valid
9.0ms	23×	body	320	valid
4.0ms	48×	body	80	nan
3.0ms	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	5001	14

prune26.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 11.6b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.2b	(* x (/ 1.0 (tan B)))
4.5b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
16.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

86×	`*-un-lft-identity`
71×	`add-sqr-sqrt`
53×	`add-cube-cbrt`
49×	`times-frac`
30×	`pow-unpow`
27×	`associate-r`
26×	`associate-l`
25×	`add-exp-log`
20×	`unpow-prod-down` `distribute-lft-out`
18×	`frac-times`
16×	`add-cbrt-cube` `associate-/l*`
15×	`associate-/r*`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`pow-neg`
11×	`neg-sub0` `associate-*r/` `pow-sub`
9×	`pow1` `associate-*l/`
8×	`prod-exp` `unswap-sqr`
6×	`clear-num`
5×	`frac-2neg` `div-exp` `div-inv`
4×	`cbrt-unprod` `add-log-exp` `sqr-pow`
3×	`cbrt-undiv` `pow-to-exp` `pow-exp` `un-div-inv`
2×	`pow-prod-down` `*-commutative`
1×	`tan-quot` `neg-mul-1` `pow-pow` `associate-/r/`

Counts

4 → 201

Calls

4 calls:

4.0ms	(/ F (sin B))
13.0ms	(* x (/ 1.0 (tan B)))
33.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
19.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series621.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ F (sin B))
113.0ms	(* x (/ 1.0 (tan B)))
295.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
161.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify105.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	855	1753
1	3857	1662
2	5001	1662

prune579.0ms

Filtered

213 candidates to 145 candidates (31.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	203	10	213
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	204	10	214

Merged error: 0.0b

Counts

214 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1.0 (tan B)))
0.2b	(/ (- 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)))
16.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

398×	`*-un-lft-identity`
329×	`times-frac`
254×	`add-sqr-sqrt`
189×	`add-cube-cbrt`
188×	`associate-l`
170×	`associate-r`
132×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
130×	`distribute-lft-out`
129×	`unpow-prod-down`
44×	`neg-mul-1`
38×	`unswap-sqr`
34×	`associate-/r*`
25×	`add-exp-log` `sqr-pow`
16×	`add-cbrt-cube`
14×	`associate-/l*`
13×	`pow-unpow` `*-commutative`
9×	`pow1` `associate-*r/`
8×	`prod-exp`
5×	`div-exp`
4×	`cbrt-unprod` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `pow-exp` `clear-num` `div-inv`
2×	`frac-2neg` `pow-prod-down` `un-div-inv`
1×	`tan-quot` `distribute-lft-neg-out` `neg-sub0` `pow-pow` `div-sub` `distribute-frac-neg` `associate-/r/`

Counts

4 → 485

Calls

4 calls:

8.0ms	(* x (/ 1.0 (tan B)))
36.0ms	(/ (- F) (* (- (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
28.0ms	(* (- (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
16.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series844.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* x (/ 1.0 (tan B)))
309.0ms	(/ (- F) (* (- (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
279.0ms	(* (- (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
139.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify101.0ms

Algorithm

egg-herbie

Counts

497 → 497

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1661	7358
1	5001	7243

prune1.3s

Filtered

497 candidates to 313 candidates (37.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	491	6	497
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	497	10	507

Merged error: 0.0b

Counts

507 → 10

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x (* (cbrt 1.0) (cbrt 1.0))) (/ (tan B) (cbrt 1.0)))
0.2b	(/ (- 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)))
16.9b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite283.0ms

Algorithm

rewrite-expression-head

Rules

2097×	`times-frac`
1770×	`add-sqr-sqrt`
1228×	`*-un-lft-identity`
1020×	`add-cube-cbrt`
915×	`associate-r`
914×	`cbrt-prod`
427×	`unswap-sqr`
392×	`associate-l`
184×	`swap-sqr`
132×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
130×	`distribute-lft-out`
129×	`unpow-prod-down`
81×	`*-commutative`
68×	`add-cbrt-cube`
59×	`associate-/r*`
57×	`associate-/l*`
48×	`div-inv`
44×	`neg-mul-1`
41×	`add-exp-log`
32×	`cbrt-undiv`
29×	`cbrt-unprod`
25×	`sqr-pow`
13×	`pow-unpow` `div-exp` `associate-/r/`
12×	`prod-exp`
7×	`pow1`
4×	`add-log-exp`
3×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num`
1×	`tan-quot` `distribute-lft-neg-out` `neg-sub0` `pow-pow` `div-sub` `distribute-frac-neg` `pow-prod-down` `associate-/l/`

Counts

4 → 1523

Calls

4 calls:

49.0ms	(/ (* x (* (cbrt 1.0) (cbrt 1.0))) (/ (tan B) (cbrt 1.0)))
39.0ms	(/ (- F) (* (- (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
25.0ms	(* (- (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
16.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series915.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(/ (* x (* (cbrt 1.0) (cbrt 1.0))) (/ (tan B) (cbrt 1.0)))
307.0ms	(/ (- F) (* (- (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
277.0ms	(* (- (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
147.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify263.0ms

Algorithm

egg-herbie

Counts

1535 → 1535

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5001	26714

prune5.6s

Filtered

1535 candidates to 1028 candidates (33.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	1530	5	1535
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	1536	9	1545

Merged error: 0.0b

Counts

1545 → 9

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (- 1) (* (- (sin B)) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0)))) (/ F (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0))))
0.4b	(/ F (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0)))
16.9b	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))
16.9b	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))

rewrite568.0ms

Algorithm

rewrite-expression-head

Rules

2120×	`*-un-lft-identity`
1605×	`associate-/r*`
1156×	`unpow-prod-down`
1139×	`associate-l`
1056×	`frac-times`
1014×	`add-sqr-sqrt`
910×	`distribute-lft-out`
863×	`sqrt-prod`
663×	`add-cube-cbrt`
580×	`associate-r`
495×	`times-frac`
381×	`associate-/l*`
273×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
182×	`unswap-sqr`
133×	`sqr-pow`
91×	`neg-mul-1`
83×	`add-exp-log`
74×	`clear-num`
73×	`frac-2neg`
48×	`associate-*l/`
34×	`div-exp` `*-commutative`
32×	`prod-exp`
27×	`add-cbrt-cube`
22×	`associate-*r/`
10×	`pow-to-exp` `pow-exp`
8×	`pow1` `cbrt-undiv` `cbrt-unprod`
4×	`sqrt-div` `add-log-exp`
3×	`div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `un-div-inv` `flip-+`
1×	`distribute-lft-neg-out` `distribute-frac-neg` `pow-prod-down`

Counts

4 → 1723

Calls

4 calls:

309.0ms	(* (/ (- 1) (* (- (sin B)) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0)))) (/ F (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0))))
21.0ms	(/ F (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0)))
18.0ms	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))
14.0ms	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))

series767.0ms

Counts

4 → 12

Calls

4 calls:

382.0ms	(* (/ (- 1) (* (- (sin B)) (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0)))) (/ F (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0))))
271.0ms	(/ F (pow (sqrt (+ (+ (* F F) 2.0) (* 2.0 x))) (/ 1.0 2.0)))
60.0ms	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))
55.0ms	(sqrt (+ (+ (* F F) 2.0) (* 2.0 x)))

simplify399.0ms

Algorithm

egg-herbie

Counts

1735 → 1735

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5001	42082

prune5.0s

Filtered

1735 candidates to 772 candidates (55.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	1735	0	1735
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	1735	9	1744

Merged error: 0.0b

Counts

1744 → 9

regimes170.0ms

Accuracy

98.1% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 10.4b

bsearch248.0ms

Steps

Iters	Range		Point
7	3.934319081849634e+93	9.936034952497785e+95	3.9992969853246413e+93
7	-5154421704.732712	-46881322.55292306	-99771073.77480982

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	67
1	77	67
2	92	67
3	94	67
4	94	67

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	1678×	body	1280	valid
781.0ms	1460×	body	640	valid
556.0ms	4623×	body	80	valid
259.0ms	701×	body	320	valid
131.0ms	1550×	body	80	nan
87.0ms	357×	body	160	valid