Details

Time bar (total: 5.0s)

sample307.0ms

Algorithm
intervals
Results
22.0ms55×body1280valid
12.0ms49×body640valid
11.0ms162×body80valid
3.0ms18×body320valid
1.0ms12×body160valid

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0187
1336
2436
3546
4606
5626
6626

prune9.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

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)))

rewrite42.0ms

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:
21.0ms
(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
3.0ms
(/ 1.0 (sin B))
4.0ms
(/ 1.0 (tan B))
10.0ms
(* x (/ 1.0 (tan B)))

series304.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
22.0ms
(/ 1.0 (sin B))
35.0ms
(/ 1.0 (tan B))
127.0ms
(* x (/ 1.0 (tan B)))

simplify52.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0438696
11724639
25002635

prune352.0ms

Filtered
129 candidates to 103 candidates (79.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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))

rewrite27.0ms

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:
16.0ms
(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
3.0ms
(/ 1.0 (sin B))
5.0ms
(/ (* x 1.0) (tan B))

series250.0ms

Counts
3 → 9
Calls
3 calls:
119.0ms
(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
20.0ms
(/ 1.0 (sin B))
111.0ms
(/ (* x 1.0) (tan B))

simplify37.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0350492
11353445
25002440

prune265.0ms

Filtered
100 candidates to 79 candidates (79.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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)))

rewrite61.0ms

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:
39.0ms
(+ (- (/ 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)))

series284.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
21.0ms
(/ 1.0 (sin B))
50.0ms
(/ (tan B) (* x 1.0))
88.0ms
(/ 1 (/ (tan B) (* x 1.0)))

simplify59.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0549959
12347844
25001789

prune490.0ms

Filtered
199 candidates to 146 candidates (73.4%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log add-sqr-sqrt *-un-lft-identity add-cbrt-cube
18×add-cube-cbrt
15×times-frac
8×add-log-exp
7×associate-*l*
6×pow1 fma-def associate-/r*
5×cbrt-undiv div-exp prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u associate-/l*
3×associate-*r* div-inv
2×frac-2neg associate-*l/ clear-num sum-log
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 unswap-sqr
Counts
4 → 104
Calls
4 calls:
8.0ms
(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
3.0ms
(/ 1.0 (sin B))
5.0ms
(/ (* x 1.0) (sin B))
7.0ms
(* (/ (* x 1.0) (sin B)) (cos B))

series295.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
19.0ms
(/ 1.0 (sin B))
61.0ms
(/ (* x 1.0) (sin B))
108.0ms
(* (/ (* x 1.0) (sin B)) (cos B))

simplify57.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0440756
12045660
25001655

prune283.0ms

Filtered
116 candidates to 88 candidates (75.9%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes57.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01816
12416
22416

end0.0ms

sample1.7s

Algorithm
intervals
Results
711.0ms1741×body1280valid
351.0ms1397×body640valid
284.0ms4868×body80valid
141.0ms744×body320valid
45.0ms365×body160valid