Details

sample411.0ms

Algorithm

intervals

Results

56.0ms	54×	body	1280	valid
27.0ms	43×	body	640	valid
20.0ms	145×	body	80	valid
8.0ms	18×	body	320	valid
6.0ms	60×	body	80	nan
6.0ms	20×	body	160	valid

simplify47.0ms

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

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
7.5b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
19.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite137.0ms

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))
9.0ms	(* x (/ 1.0 (tan B)))
88.0ms	(* (/ 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)))

series608.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1.0 (tan B))
120.0ms	(* x (/ 1.0 (tan B)))
296.0ms	(* (/ 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 (68.0ms)

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

prune651.0ms

Filtered

167 candidates to 129 candidates (77.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

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	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.3b	(* x (/ 1.0 (tan B)))
19.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite131.0ms

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:

21.0ms	(/ 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)))
8.0ms	(* x (/ 1.0 (tan B)))
22.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series819.0ms

Counts

4 → 12

Calls

4 calls:

308.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
259.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
112.0ms	(* x (/ 1.0 (tan B)))
139.0ms	(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

prune442.0ms

Filtered

120 candidates to 89 candidates (74.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

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)))
19.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite124.0ms

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:

3.0ms	(/ (* x 1.0) (tan B))
21.0ms	(/ 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))

series800.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (* x 1.0) (tan B))
306.0ms	(/ 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)))
138.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify64.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (14.0ms)

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

prune412.0ms

Filtered

109 candidates to 83 candidates (76.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin B) (sqrt (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.3b	(* (* (sin B) (sqrt (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))) (sqrt (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
19.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))
19.5b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`add-cube-cbrt` `*-un-lft-identity`
26×	`pow-unpow`
20×	`associate-r`
18×	`times-frac`
17×	`sqrt-prod`
13×	`pow1` `add-exp-log` `unpow-prod-down`
11×	`add-cbrt-cube`
5×	`sqr-pow`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `pow-exp` `*-commutative` `div-inv`

Counts

4 → 107

Calls

4 calls:

75.0ms	(* (sin B) (sqrt (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
137.0ms	(* (* (sin B) (sqrt (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))) (sqrt (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))
22.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series777.0ms

Counts

4 → 12

Calls

4 calls:

248.0ms	(* (sin B) (sqrt (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
257.0ms	(* (* (sin B) (sqrt (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))) (sqrt (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))
133.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify65.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	500	1398
1	2023	1246
2	5001	1234

prune488.0ms

Filtered

119 candidates to 89 candidates (74.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

regimes261.0ms

Accuracy

98.1% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.9b

bsearch283.0ms

Steps

Iters	Range		Point
10	7.712829756242493e-08	8140883472.542182	406748.6327385026
7	-10079637148.511366	-110051303.36362042	-125465839.25710528

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	48
1	58	48

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.6s	1638×	body	1280	valid
971.0ms	1487×	body	640	valid
654.0ms	4687×	body	80	valid
315.0ms	703×	body	320	valid
173.0ms	1630×	body	80	nan
107.0ms	365×	body	160	valid