Details

Time bar (total: 4.6s)

sample60.0ms

Algorithm
intervals
Results
22.0ms55×body1280valid
12.0ms49×body640valid
10.0ms162×body80valid
3.0ms18×body320valid
1.0ms12×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0187
1336
2436
3546
4606
5626
6626

prune7.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
0.1b
(/ 1.0 (sin B))
0.1b
(/ 1.0 (tan B))
0.2b
(* x (/ 1.0 (tan B)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
31×*-un-lft-identity
29×add-cube-cbrt
28×times-frac
14×associate-*r*
13×add-exp-log add-cbrt-cube
8×add-log-exp
6×pow1 fma-def associate-/r* associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv div-exp associate-*l* div-inv
2×tan-quot frac-2neg associate-*r/ prod-exp clear-num sum-log associate-/r/ cbrt-unprod unswap-sqr
1×+-commutative neg-sub0 distribute-lft-neg-in associate-+l- neg-mul-1 distribute-rgt-neg-in flip3-+ pow-prod-down neg-log frac-add *-commutative flip-+ distribute-neg-frac distribute-lft-out
Counts
4 → 117
Calls
4 calls:
9.0ms
(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
3.0ms
(/ 1.0 (sin B))
8.0ms
(/ 1.0 (tan B))
7.0ms
(* x (/ 1.0 (tan B)))

series281.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
21.0ms
(/ 1.0 (sin B))
34.0ms
(/ 1.0 (tan B))
113.0ms
(* x (/ 1.0 (tan B)))

simplify48.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0438696
11724639
25002635

prune328.0ms

Filtered
129 candidates to 103 candidates (79.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
0.1b
(/ 1.0 (sin B))
0.1b
(/ (* x 1.0) (tan B))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
20×fma-def
18×add-sqr-sqrt add-cube-cbrt times-frac
10×add-exp-log add-cbrt-cube
9×distribute-rgt-neg-in
8×distribute-lft-neg-in
7×add-log-exp
6×associate-/r*
4×div-inv associate-/l*
3×tan-quot pow1 cbrt-undiv expm1-log1p-u div-exp associate-/r/ log1p-expm1-u
2×frac-2neg clear-num sum-log distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 flip3-+ neg-log frac-add prod-exp cbrt-unprod flip-+ distribute-neg-frac
Counts
3 → 91
Calls
3 calls:
17.0ms
(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
3.0ms
(/ 1.0 (sin B))
5.0ms
(/ (* x 1.0) (tan B))

series242.0ms

Counts
3 → 9
Calls
3 calls:
117.0ms
(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
18.0ms
(/ 1.0 (sin B))
106.0ms
(/ (* x 1.0) (tan B))

simplify39.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0350492
11353445
25002440

prune257.0ms

Filtered
100 candidates to 79 candidates (79.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
0.1b
(/ 1.0 (sin B))
0.1b
(/ (tan B) (* x 1.0))
0.3b
(/ 1 (/ (tan B) (* x 1.0)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
107×times-frac
68×*-un-lft-identity
59×add-sqr-sqrt add-cube-cbrt
56×fma-def
32×add-exp-log
29×distribute-rgt-neg-in
26×distribute-lft-neg-in
20×add-cbrt-cube
16×div-inv
15×div-exp
11×associate-/r*
9×associate-/l*
8×cbrt-undiv add-log-exp
5×pow1
4×expm1-log1p-u prod-exp log1p-expm1-u distribute-lft-out
3×rec-exp frac-2neg 1-exp clear-num associate-/r/
2×sum-log cbrt-unprod
1×tan-quot +-commutative neg-sub0 associate-+l- neg-mul-1 pow-flip flip3-+ neg-log frac-add flip-+ associate-/l/ distribute-neg-frac inv-pow
Counts
4 → 187
Calls
4 calls:
42.0ms
(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
3.0ms
(/ 1.0 (sin B))
5.0ms
(/ (tan B) (* x 1.0))
6.0ms
(/ 1 (/ (tan B) (* x 1.0)))

series271.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
21.0ms
(/ 1.0 (sin B))
48.0ms
(/ (tan B) (* x 1.0))
85.0ms
(/ 1 (/ (tan B) (* x 1.0)))

simplify57.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0549959
12347844
25001789

prune531.0ms

Filtered
199 candidates to 146 candidates (73.4%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma (/ x (tan B)) 1.0 (- (/ 1.0 (sin B))))
0.1b
(/ 1.0 (sin B))
0.1b
(/ x (tan B))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
7×add-exp-log add-cbrt-cube
6×associate-/r* associate-/l*
3×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×cbrt-undiv frac-2neg div-exp clear-num div-inv
1×tan-quot associate-/r/ fma-udef
Counts
3 → 69
Calls
3 calls:
1.0ms
(fma (/ x (tan B)) 1.0 (- (/ 1.0 (sin B))))
4.0ms
(/ 1.0 (sin B))
4.0ms
(/ x (tan B))

series238.0ms

Counts
3 → 9
Calls
3 calls:
118.0ms
(fma (/ x (tan B)) 1.0 (- (/ 1.0 (sin B))))
18.0ms
(/ 1.0 (sin B))
102.0ms
(/ x (tan B))

simplify54.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 3 (49.0ms)

IterNodesCost
0250412
1720379
22083379
35001375

prune220.0ms

Filtered
78 candidates to 64 candidates (82.1%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes57.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0147
1147

end0.0ms

sample1.8s

Algorithm
intervals
Results
710.0ms1741×body1280valid
375.0ms1397×body640valid
296.0ms4868×body80valid
136.0ms744×body320valid
46.0ms365×body160valid