Details

sample378.0ms

Algorithm

intervals

Results

46.0ms	46×	body	1280	valid
26.0ms	42×	body	640	valid
24.0ms	175×	body	80	valid
10.0ms	19×	body	320	valid
6.0ms	58×	body	80	nan
2.0ms	8×	body	160	valid

simplify47.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	43	15
1	91	14
2	169	14
3	378	14
4	1100	14
5	5001	14

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.2b	(* x (/ 1.0 (tan B)))
9.1b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
18.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite130.0ms

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×	`expm1-log1p-u` `pow-neg` `cbrt-unprod` `log1p-expm1-u` `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 → 162

Calls

4 calls:

2.0ms	(/ F (sin B))
8.0ms	(* x (/ 1.0 (tan B)))
86.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
27.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series603.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ F (sin B))
109.0ms	(* x (/ 1.0 (tan B)))
287.0ms	(* (/ 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)))

simplify86.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	780	1466
1	3262	1352
2	5001	1349

prune680.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

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))))
0.2b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
18.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite133.0ms

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×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `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 → 116

Calls

4 calls:

8.0ms	(* x (/ 1.0 (tan B)))
23.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
76.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
22.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series786.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* x (/ 1.0 (tan B)))
298.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
243.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
131.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify76.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	671	1143
1	2919	1016
2	5001	1009

prune489.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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))))
0.2b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
18.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite128.0ms

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` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `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 → 105

Calls

4 calls:

4.0ms	(/ (* x 1.0) (tan B))
21.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
77.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
22.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series781.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (* x 1.0) (tan B))
292.0ms	(/ 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)))
135.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify72.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	625	1088
1	2653	961
2	5001	954

prune442.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.2b	(* (/ 1 (sin B)) (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
18.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

85×	`add-sqr-sqrt`
80×	`times-frac`
59×	`add-exp-log`
55×	`*-un-lft-identity`
51×	`add-cube-cbrt`
27×	`unpow-prod-down`
25×	`div-exp` `associate-r`
23×	`add-cbrt-cube`
17×	`prod-exp`
13×	`pow-unpow` `associate-l`
12×	`unswap-sqr`
11×	`sqr-pow`
10×	`associate-/r*`
7×	`pow1` `cbrt-undiv`
6×	`pow-to-exp` `pow-exp`
5×	`cbrt-unprod` `div-inv`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`tan-quot` `frac-times` `pow-pow` `associate-r/` `pow-prod-down` `associate-l/` `associate-/r/` `*-commutative`

Counts

4 → 184

Calls

4 calls:

3.0ms	(/ (* x 1.0) (tan B))
35.0ms	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
88.0ms	(* (/ 1 (sin B)) (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
25.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series828.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (* x 1.0) (tan B))
236.0ms	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
350.0ms	(* (/ 1 (sin B)) (/ F (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))

simplify106.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	931	2249
1	4399	2057
2	5003	2044

prune682.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes204.0ms

Accuracy

94.7% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 10.8b

bsearch233.0ms

Steps

Iters	Range		Point
7	1836.721956390875	43768.65998072103	19373.444776583467
7	-2.652094989992387e+127	-1.49008099530695e+125	-1.514749380973243e+125

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	44
1	68	44
2	68	44

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.7s	1704×	body	1280	valid
907.0ms	1389×	body	640	valid
646.0ms	4677×	body	80	valid
307.0ms	687×	body	320	valid
166.0ms	1625×	body	80	nan
109.0ms	362×	body	160	valid