Details

Time bar (total: 5.6s)

sample339.0ms

Algorithm
intervals
Results
41.0ms70×body1280valid
14.0ms159×body80valid
14.0ms40×body640valid
6.0ms23×body320valid
1.0ms8×body160valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0187
1336
2436
3546
4606
5626
6626

prune10.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
0.1b
(/ 1.0 (tan B))
0.2b
(/ 1.0 (sin B))
0.3b
(* x (/ 1.0 (tan B)))

rewrite45.0ms

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:
23.0ms
(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
2.0ms
(/ 1.0 (tan B))
2.0ms
(/ 1.0 (sin B))
12.0ms
(* x (/ 1.0 (tan B)))

series309.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
41.0ms
(/ 1.0 (tan B))
20.0ms
(/ 1.0 (sin B))
129.0ms
(* x (/ 1.0 (tan B)))

simplify51.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0438696
11724639
25002635

prune375.0ms

Filtered
129 candidates to 103 candidates (79.8%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite40.0ms

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:
31.0ms
(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
2.0ms
(/ 1.0 (sin B))
4.0ms
(/ (* x 1.0) (tan B))

series252.0ms

Counts
3 → 9
Calls
3 calls:
117.0ms
(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
24.0ms
(/ 1.0 (sin B))
111.0ms
(/ (* x 1.0) (tan B))

simplify39.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0350492
11353445
25002440

prune291.0ms

Filtered
100 candidates to 80 candidates (80.0%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
0.1b
(* x (cos B))
0.2b
(/ 1 (sin B))
0.2b
(/ (* x (cos B)) (sin B))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
126×times-frac
107×add-sqr-sqrt
105×*-un-lft-identity
98×add-cube-cbrt
91×prod-diff
28×div-inv
15×add-exp-log
13×fma-neg add-cbrt-cube
7×pow1
6×associate-/r* add-log-exp
4×expm1-log1p-u div-exp log1p-expm1-u associate-/l*
3×cbrt-undiv distribute-rgt-out-- associate-*r* associate-*l* difference-of-squares
2×frac-2neg prod-exp clear-num cbrt-unprod distribute-lft-out--
1×sub-neg rec-exp flip3-- pow-flip diff-log 1-exp pow-prod-down *-commutative frac-sub flip-- inv-pow sub-div unswap-sqr
Counts
4 → 204
Calls
4 calls:
25.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
3.0ms
(* x (cos B))
3.0ms
(/ 1 (sin B))
4.0ms
(/ (* x (cos B)) (sin B))

series250.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
42.0ms
(* x (cos B))
13.0ms
(/ 1 (sin B))
99.0ms
(/ (* x (cos B)) (sin B))

simplify76.0ms

Algorithm
egg-herbie
Counts
216 → 216
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05793808
121732513
250012510

prune354.0ms

Filtered
216 candidates to 96 candidates (44.4%)
Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (sin B))
0.2b
(/ 1.0 (sin B))
0.2b
(* (* x (/ 1.0 (sin B))) (cos B))
0.3b
(* x (/ 1.0 (sin B)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
29×add-cube-cbrt *-un-lft-identity
28×times-frac
22×add-exp-log add-cbrt-cube
16×associate-*r*
11×pow1
7×prod-exp cbrt-unprod
6×associate-/r* associate-/l*
4×cbrt-undiv expm1-log1p-u div-exp associate-*l* pow-prod-down log1p-expm1-u add-log-exp
3×div-inv
2×frac-2neg associate-*r/ clear-num *-commutative unswap-sqr
1×associate-*l/
Counts
4 → 115
Calls
4 calls:
2.0ms
(/ 1.0 (sin B))
2.0ms
(/ 1.0 (sin B))
13.0ms
(* (* x (/ 1.0 (sin B))) (cos B))
8.0ms
(* x (/ 1.0 (sin B)))

series208.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(/ 1.0 (sin B))
24.0ms
(/ 1.0 (sin B))
105.0ms
(* (* x (/ 1.0 (sin B))) (cos B))
60.0ms
(* x (/ 1.0 (sin B)))

simplify47.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0325672
11587587
25001587

prune309.0ms

Filtered
127 candidates to 92 candidates (72.4%)
Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes96.0ms

Accuracy

0% (0.2b 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
0158
1158

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.0s1663×body1280valid
532.0ms1424×body640valid
404.0ms4953×body80valid
173.0ms707×body320valid
74.0ms395×body160valid