Details

sample360.0ms

Algorithm

intervals

Results

39.0ms	48×	body	1280	valid
27.0ms	52×	body	640	valid
18.0ms	151×	body	80	valid
7.0ms	20×	body	320	valid
5.0ms	47×	body	80	nan
2.0ms	10×	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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.3b	(* x (/ 1.0 (tan B)))
6.7b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
17.6b	(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))))
12.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series600.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ F (sin B))
109.0ms	(* x (/ 1.0 (tan B)))
284.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
157.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify83.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (69.0ms)

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

prune640.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

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))))
0.3b	(* x (/ 1.0 (tan B)))
0.3b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
17.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite43.0ms

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:

11.0ms	(/ 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)))
11.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series772.0ms

Counts

4 → 12

Calls

4 calls:

294.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
106.0ms	(* x (/ 1.0 (tan B)))
243.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
129.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify72.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (15.0ms)

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

prune440.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

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)))
17.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite37.0ms

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))

series774.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (* x 1.0) (tan B))
295.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
238.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
133.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify63.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (14.0ms)

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

prune403.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (* x 1.0) (sin B)) (cos 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)))
17.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-exp-log`
27×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
15×	`times-frac`
13×	`pow-unpow`
10×	`associate-r` `associate-l` `prod-exp`
7×	`pow1` `unpow-prod-down`
6×	`div-exp` `cbrt-unprod`
4×	`cbrt-undiv` `add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `pow-exp` `div-inv` `associate-/l*` `sqr-pow`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `associate-/r`

Counts

4 → 102

Calls

4 calls:

7.0ms	(* (/ (* x 1.0) (sin B)) (cos B))
11.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
15.0ms	(* (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))

series776.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (/ (* x 1.0) (sin B)) (cos B))
294.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
247.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
128.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify73.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	659	1124
1	2920	989
2	5001	989

prune380.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes210.0ms

Accuracy

98.2% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.2b

bsearch243.0ms

Steps

Iters	Range		Point
6	24048332.968690775	157562194.2867214	25125956.155811463
10	-6.4583381063470516e+53	-1.8414219568180378e+42	-6.554700741605999e+42

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	42
1	68	42
2	68	42

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	1726×	body	1280	valid
756.0ms	1421×	body	640	valid
553.0ms	4727×	body	80	valid
254.0ms	671×	body	320	valid
137.0ms	1626×	body	80	nan
82.0ms	334×	body	160	valid