Details

Time bar (total: 8.0s)

sample366.0ms

Algorithm
intervals
Results
47.0ms57×body1280valid
22.0ms39×body640valid
18.0ms155×body80valid
11.0ms25×body320valid
3.0ms12×body160valid
3.0ms32×body80nan

simplify48.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
04315
19114
216914
337814
4110014
5500114

prune27.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 13.2b

Counts
2 → 2

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ F (sin B))
0.3b
(* x (/ 1.0 (tan B)))
6.8b
(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
15.9b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
4×div-inv
3×pow-unpow associate-*r/ clear-num
2×frac-2neg associate-*r*
1×tan-quot neg-sub0 distribute-lft-neg-in pow-to-exp pow-neg neg-mul-1 distribute-rgt-neg-in associate-/r/ un-div-inv *-commutative fma-udef pow-sub sqr-pow
Counts
4 → 18
Calls
4 calls:
2.0ms
(/ F (sin B))
3.0ms
(* x (/ 1.0 (tan B)))
1.0ms
(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
7.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series536.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ F (sin B))
106.0ms
(* x (/ 1.0 (tan B)))
222.0ms
(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
158.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify95.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 3 (91.0ms)

IterNodesCost
0235165
1792159
23537152
35001148

prune136.0ms

Filtered
30 candidates to 25 candidates (83.3%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New23730
Fresh101
Picked101
Done000
Total25732

Merged error: 0.1b

Counts
32 → 7

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* x 1.0) (tan B))
0.2b
(/ F (sin B))
6.8b
(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
15.9b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
4×div-inv
3×pow-unpow
2×frac-2neg clear-num associate-/l*
1×tan-quot neg-sub0 distribute-lft-neg-in pow-to-exp pow-neg neg-mul-1 distribute-rgt-neg-in associate-/r/ *-commutative fma-udef pow-sub sqr-pow
Counts
4 → 17
Calls
4 calls:
4.0ms
(/ (* x 1.0) (tan B))
2.0ms
(/ F (sin B))
1.0ms
(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
5.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series518.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(/ (* x 1.0) (tan B))
47.0ms
(/ F (sin B))
220.0ms
(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
139.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify73.0ms

Algorithm
egg-herbie
Counts
29 → 29
Iterations

Useful iterations: 3 (69.0ms)

IterNodesCost
0240174
1679168
22658161
35001160

prune127.0ms

Filtered
29 candidates to 24 candidates (82.8%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New25429
Fresh426
Picked101
Done000
Total30636

Merged error: 0.1b

Counts
36 → 6

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sin B) F)
0.2b
(/ 1 (/ (sin B) F))
6.8b
(fma (/ 1 (/ (sin B) F)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
15.9b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
5×div-inv
4×clear-num
3×pow-unpow frac-2neg associate-/r/
1×neg-sub0 distribute-lft-neg-in pow-to-exp pow-neg neg-mul-1 distribute-rgt-neg-in associate-/r* fma-udef remove-double-div inv-pow pow-sub sqr-pow
Counts
4 → 20
Calls
4 calls:
3.0ms
(/ (sin B) F)
3.0ms
(/ 1 (/ (sin B) F))
1.0ms
(fma (/ 1 (/ (sin B) F)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
5.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series533.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (sin B) F)
46.0ms
(/ 1 (/ (sin B) F))
315.0ms
(fma (/ 1 (/ (sin B) F)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
144.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify116.0ms

Algorithm
egg-herbie
Counts
32 → 32
Iterations

Useful iterations: 3 (112.0ms)

IterNodesCost
0253172
1792163
23829156
35002155

prune134.0ms

Filtered
32 candidates to 23 candidates (71.9%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New29332
Fresh055
Picked101
Done000
Total30838

Merged error: 0.1b

Counts
38 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* x 1.0) (tan B))
0.3b
(* (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)) F)
0.3b
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
15.9b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
6×associate-*l/
5×div-inv
4×associate-/l/ associate-/l*
3×neg-sub0 pow-neg pow-unpow frac-2neg clear-num pow-sub sqr-pow
2×*-commutative
1×tan-quot distribute-lft-neg-in pow-to-exp neg-mul-1 distribute-rgt-neg-in associate-*l* associate-/r/
Counts
4 → 27
Calls
4 calls:
4.0ms
(/ (* x 1.0) (tan B))
8.0ms
(* (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)) F)
7.0ms
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
5.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series922.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(/ (* x 1.0) (tan B))
350.0ms
(* (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)) F)
313.0ms
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
144.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify133.0ms

Algorithm
egg-herbie
Counts
39 → 39
Iterations

Useful iterations: 3 (128.0ms)

IterNodesCost
0298261
11002255
24700241
35001240

prune160.0ms

Filtered
39 candidates to 36 candidates (92.3%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New33639
Fresh437
Picked101
Done000
Total38947

Merged error: 0.0b

Counts
47 → 9

regimes161.0ms

Accuracy

98.1% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 11.1b

bsearch268.0ms

Steps
ItersRangePoint
9
2697524.489058797
7152780495357.076
175693108.13025206
9
-1.0189745070055278e+128
-2.2118801766293464e+120
-7.893249225787343e+120

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05641
16141
26141

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.4s1652×body1280valid
736.0ms1367×body640valid
564.0ms4790×body80valid
262.0ms711×body320valid
131.0ms1586×body80nan
93.0ms372×body160valid