Details

sample379.0ms

Algorithm

intervals

Results

40.0ms	49×	body	1280	valid
27.0ms	46×	body	640	valid
18.0ms	159×	body	80	valid
7.0ms	20×	body	320	valid
5.0ms	57×	body	80	nan
2.0ms	10×	body	160	valid

simplify48.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	42	15
1	83	14
2	151	14
3	356	14
4	1063	14
5	5002	14

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.3b	(* x (/ 1.0 (tan B)))
8.5b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
17.2b	(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×	`frac-times` `*-commutative`
1×	`tan-quot` `neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `clear-num` `associate-/r/` `un-div-inv`

Counts

4 → 154

Calls

4 calls:

4.0ms	(/ F (sin 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)))

series613.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ F (sin B))
111.0ms	(* x (/ 1.0 (tan B)))
292.0ms	(* (/ 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)))

simplify86.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	765	1418
1	3213	1329
2	5001	1328

prune624.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

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))))
0.3b	(* x (/ 1.0 (tan B)))
0.3b	(* (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))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
25×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
22×	`times-frac`
21×	`associate-r`
16×	`add-cbrt-cube`
13×	`pow-unpow`
8×	`prod-exp`
7×	`pow1` `unpow-prod-down`
6×	`associate-l`
5×	`div-exp` `unswap-sqr`
4×	`cbrt-unprod` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `pow-exp` `div-inv` `associate-/l*` `sqr-pow`
2×	`*-commutative`
1×	`tan-quot` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `associate-/r/`

Counts

4 → 108

Calls

4 calls:

10.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
7.0ms	(* x (/ 1.0 (tan B)))
11.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
9.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series796.0ms

Counts

4 → 12

Calls

4 calls:

299.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
113.0ms	(* x (/ 1.0 (tan B)))
249.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
135.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify73.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	654	1088
1	2850	977
2	5002	977

prune419.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 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)))
17.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-cbrt-cube`
15×	`times-frac`
13×	`pow-unpow`
7×	`unpow-prod-down` `associate-r` `prod-exp`
6×	`div-exp`
5×	`pow1`
4×	`cbrt-undiv` `associate-/r` `associate-/l` `add-log-exp`
3×	`pow-to-exp` `associate-l` `pow-exp` `cbrt-unprod` `div-inv` `unswap-sqr` `sqr-pow`
2×	`frac-2neg` `clear-num`
1×	`tan-quot` `pow-pow` `associate-/r/` `*-commutative`

Counts

4 → 97

Calls

4 calls:

5.0ms	(/ (* x 1.0) (tan B))
10.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
11.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
9.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series782.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (* x 1.0) (tan B))
293.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
246.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
132.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify65.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	608	1033
1	2584	922
2	5001	922

prune387.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sin B))
0.2b	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.4b	(* (/ 1 (sin B)) (/ F (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))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-sqr-sqrt`
86×	`times-frac`
61×	`*-un-lft-identity`
58×	`add-exp-log`
57×	`add-cube-cbrt`
27×	`unpow-prod-down`
25×	`div-exp` `associate-r`
20×	`add-cbrt-cube`
16×	`prod-exp`
13×	`pow-unpow` `associate-l`
12×	`unswap-sqr`
11×	`sqr-pow`
10×	`associate-/r*`
8×	`pow1`
6×	`cbrt-undiv` `pow-to-exp` `pow-exp` `associate-/l*`
5×	`rec-exp` `1-exp` `div-inv`
4×	`cbrt-unprod` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `pow-flip` `pow-pow` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 185

Calls

4 calls:

4.0ms	(/ 1 (sin B))
9.0ms	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
19.0ms	(* (/ 1 (sin B)) (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
9.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series748.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ 1 (sin B))
239.0ms	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
356.0ms	(* (/ 1 (sin B)) (/ F (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))

simplify95.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	824	2210
1	3935	2034
2	5001	2014

prune596.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes156.0ms

Accuracy

97.7% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 10.8b

bsearch243.0ms

Steps

Iters	Range		Point
9	1.5006309519768893e-05	21.660028671588154	21.34148422173504
7	-4.105717082425732e+23	-5.651135004763443e+21	-5.764800031457758e+21

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	37
1	54	37

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	1684×	body	1280	valid
763.0ms	1406×	body	640	valid
557.0ms	4751×	body	80	valid
254.0ms	675×	body	320	valid
142.0ms	1546×	body	80	nan
88.0ms	356×	body	160	valid