Details

sample367.0ms

Algorithm

intervals

Results

45.0ms	55×	body	1280	valid
27.0ms	51×	body	640	valid
18.0ms	142×	body	80	valid
7.0ms	20×	body	320	valid
5.0ms	55×	body	80	nan
4.0ms	13×	body	160	valid

simplify44.0ms

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: 12.0b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))
5.9b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
15.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite82.0ms

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×	`tan-quot` `pow-prod-down` `associate-/r/` `*-commutative`
1×	`neg-mul-1` `pow-pow`

Counts

4 → 202

Calls

4 calls:

4.0ms	(/ 1.0 (tan B))
13.0ms	(* x (/ 1.0 (tan B)))
34.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
21.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series598.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1.0 (tan B))
111.0ms	(* x (/ 1.0 (tan B)))
294.0ms	(* (/ 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)))

simplify102.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	862	1761
1	3772	1671
2	5002	1671

prune719.0ms

Filtered

214 candidates to 147 candidates (68.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	200	14	214
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	201	14	215

Merged error: 0.0b

Counts

215 → 14

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.2b	(* x (/ 1.0 (tan B)))
0.3b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
15.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

163×	`*-un-lft-identity`
96×	`add-sqr-sqrt`
91×	`times-frac`
79×	`associate-r`
66×	`add-cube-cbrt`
60×	`distribute-lft-out`
59×	`unpow-prod-down`
48×	`associate-l`
27×	`associate-/r*`
25×	`add-exp-log`
17×	`unswap-sqr`
16×	`add-cbrt-cube`
13×	`pow-unpow`
11×	`sqr-pow`
9×	`pow1` `associate-*r/`
8×	`prod-exp`
7×	`associate-/l*`
6×	`*-commutative`
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` `pow-pow` `associate-/r/`

Counts

4 → 223

Calls

4 calls:

29.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
8.0ms	(* x (/ 1.0 (tan B)))
28.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
18.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series809.0ms

Counts

4 → 12

Calls

4 calls:

304.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
110.0ms	(* x (/ 1.0 (tan B)))
256.0ms	(* (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))

simplify108.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	884	2499
1	4041	2386
2	5001	2386

prune729.0ms

Filtered

235 candidates to 150 candidates (63.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	224	11	235
Fresh	11	2	13
Picked	1	0	1
Done	0	0	0
Total	236	13	249

Merged error: 0.0b

Counts

249 → 13

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sqrt 1.0) x) (/ (tan B) (sqrt 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)))
15.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

739×	`times-frac`
489×	`add-sqr-sqrt`
468×	`*-un-lft-identity`
372×	`add-cube-cbrt`
248×	`sqrt-prod`
183×	`associate-l`
134×	`associate-r`
61×	`unswap-sqr`
60×	`distribute-lft-out`
59×	`unpow-prod-down`
52×	`associate-/r*`
32×	`add-exp-log`
28×	`*-commutative`
23×	`add-cbrt-cube`
22×	`associate-/l*`
20×	`div-inv`
13×	`pow-unpow` `associate-/r/`
11×	`sqr-pow`
10×	`div-exp`
8×	`cbrt-undiv` `prod-exp`
7×	`pow1`
4×	`cbrt-unprod` `add-log-exp`
3×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num`
1×	`tan-quot` `pow-pow` `pow-prod-down` `associate-/l/`

Counts

4 → 601

Calls

4 calls:

21.0ms	(/ (* (sqrt 1.0) x) (/ (tan B) (sqrt 1.0)))
32.0ms	(/ 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)))
18.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series892.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(/ (* (sqrt 1.0) x) (/ (tan B) (sqrt 1.0)))
302.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
251.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
136.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify110.0ms

Algorithm

egg-herbie

Counts

613 → 613

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	2174	8221
1	5001	7945

prune1.8s

Filtered

613 candidates to 332 candidates (54.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	604	9	613
Fresh	9	3	12
Picked	1	0	1
Done	0	0	0
Total	614	12	626

Merged error: 0.0b

Counts

626 → 12

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) F)
0.2b	(/ 1 (/ (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) F))
0.3b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
15.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

597×	`times-frac`
592×	`*-un-lft-identity`
376×	`add-sqr-sqrt`
286×	`add-cube-cbrt`
234×	`associate-r`
190×	`distribute-lft-out`
189×	`unpow-prod-down`
150×	`associate-l`
82×	`associate-/r*`
58×	`add-exp-log`
54×	`unswap-sqr`
53×	`associate-/l*`
37×	`sqr-pow`
30×	`associate-/r/`
26×	`div-exp`
20×	`add-cbrt-cube`
18×	`*-commutative`
15×	`prod-exp`
13×	`pow-unpow`
8×	`pow1`
7×	`cbrt-undiv` `div-inv`
6×	`pow-to-exp` `pow-exp`
5×	`rec-exp` `1-exp`
4×	`clear-num` `add-log-exp`
3×	`frac-2neg` `cbrt-unprod` `remove-double-div`
1×	`pow-flip` `pow-pow` `pow-prod-down` `inv-pow`

Counts

4 → 550

Calls

4 calls:

34.0ms	(/ (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) F)
43.0ms	(/ 1 (/ (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) F))
29.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
18.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series950.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(/ (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) F)
362.0ms	(/ 1 (/ (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) F))
249.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
144.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify103.0ms

Algorithm

egg-herbie

Counts

562 → 562

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1585	8312
1	5001	7775

prune1.5s

Filtered

562 candidates to 280 candidates (49.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	561	1	562
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	562	12	574

Merged error: 0.0b

Counts

574 → 12

regimes223.0ms

Accuracy

97.1% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 10.8b

bsearch251.0ms

Steps

Iters	Range		Point
7	1.6295149932958335e+134	8.598898606995893e+135	9.148277637352841e+134
8	-1.0337377701230913e+162	-1.5028531132185973e+158	-1.5302707166292866e+158

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	57
1	69	57

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.3s	1612×	body	1280	valid
741.0ms	1390×	body	640	valid
564.0ms	4850×	body	80	valid
236.0ms	649×	body	320	valid
143.0ms	1629×	body	80	nan
84.0ms	348×	body	160	valid