Details

sample380.0ms

Algorithm

intervals

Results

55.0ms	56×	body	1280	valid
33.0ms	49×	body	640	valid
20.0ms	148×	body	80	valid
7.0ms	15×	body	320	valid
5.0ms	47×	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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))
6.0b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
17.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite126.0ms

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:

2.0ms	(/ 1.0 (tan B))
8.0ms	(* x (/ 1.0 (tan B)))
83.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
26.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series586.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1.0 (tan B))
112.0ms	(* x (/ 1.0 (tan B)))
283.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
156.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify82.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	767	1428
1	3183	1338
2	5001	1337

prune635.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.2b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.2b	(* x (/ 1.0 (tan B)))
17.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite130.0ms

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:

74.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
21.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
8.0ms	(* x (/ 1.0 (tan B)))
23.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series788.0ms

Counts

4 → 12

Calls

4 calls:

251.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
295.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
112.0ms	(* x (/ 1.0 (tan B)))
129.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify75.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (16.0ms)

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

prune430.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.2b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.3b	(* x (/ 1.0 (sin B)))
17.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
25×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
22×	`times-frac`
20×	`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×	`pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `associate-/r`

Counts

4 → 107

Calls

4 calls:

73.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
21.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
7.0ms	(* x (/ 1.0 (sin B)))
24.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series721.0ms

Counts

4 → 12

Calls

4 calls:

244.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
290.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
57.0ms	(* x (/ 1.0 (sin B)))
129.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify72.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	636	1081
1	2849	970
2	5002	970

prune447.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 1 (* 1.0 (/ x (sin B)))) (cos B))
0.2b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.2b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
17.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-exp-log`
25×	`add-cbrt-cube`
23×	`add-sqr-sqrt` `prod-exp`
18×	`add-cube-cbrt` `*-un-lft-identity`
14×	`pow1`
13×	`pow-unpow`
12×	`times-frac`
11×	`cbrt-unprod`
10×	`associate-r`
7×	`unpow-prod-down`
6×	`div-exp` `pow-prod-down`
4×	`associate-l` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `1-exp` `pow-exp` `associate-/l*` `unswap-sqr` `sqr-pow`
2×	`associate-r/` `-commutative` `div-inv`
1×	`pow-pow` `frac-2neg` `associate-l/` `clear-num` `associate-/r`

Counts

4 → 102

Calls

4 calls:

34.0ms	(* (* 1 (* 1.0 (/ x (sin B)))) (cos B))
73.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
20.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
24.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series776.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (* 1 (* 1.0 (/ x (sin B)))) (cos B))
245.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
293.0ms	(/ F (* (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))

simplify77.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	713	1146
1	3145	991
2	5002	991

prune367.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes185.0ms

Accuracy

97.1% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 10.6b

bsearch343.0ms

Steps

Iters	Range		Point
11	0.004380743253548005	3.322019708152893e+19	348481.0471608294
10	-1.0520778951349131e+66	-1.6792489016483447e+56	-2.986262569812043e+56

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	43
1	62	43
2	62	43

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.6s	1662×	body	1280	valid
930.0ms	1482×	body	640	valid
645.0ms	4707×	body	80	valid
297.0ms	683×	body	320	valid
169.0ms	1660×	body	80	nan
99.0ms	353×	body	160	valid