Details

Time bar (total: 6.1s)

sample310.0ms

Algorithm
intervals
Results
21.0ms51×body1280valid
13.0ms51×body640valid
11.0ms162×body80valid
3.0ms16×body320valid
1.0ms9×body160valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0187
1336
2436
3546
4606
5626
6626

prune7.0ms

Pruning

1 alts after pruning (1 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 (sin B))
0.2b
(/ 1.0 (tan B))
0.2b
(* x (/ 1.0 (tan B)))

rewrite37.0ms

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:
8.0ms
(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
3.0ms
(/ 1.0 (sin B))
4.0ms
(/ 1.0 (tan B))
9.0ms
(* x (/ 1.0 (tan B)))

series292.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
22.0ms
(/ 1.0 (sin B))
35.0ms
(/ 1.0 (tan B))
122.0ms
(* x (/ 1.0 (tan B)))

simplify52.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0438696
11724639
25002635

prune349.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

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:
13.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
4.0ms
(/ 1 (sin B))
4.0ms
(* x (cos B))
5.0ms
(/ (* x (cos B)) (sin B))

series238.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
13.0ms
(/ 1 (sin B))
39.0ms
(* x (cos B))
95.0ms
(/ (* x (cos B)) (sin B))

simplify77.0ms

Algorithm
egg-herbie
Counts
216 → 216
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05793808
121732513
250012510

prune326.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
1373×times-frac
862×add-sqr-sqrt
842×*-un-lft-identity
832×add-cube-cbrt
572×prod-diff
105×div-inv
19×associate-/r*
15×add-exp-log
14×associate-/r/
13×fma-neg add-cbrt-cube
9×associate-/l* difference-of-squares
6×div-exp add-log-exp
5×pow1 cbrt-undiv
4×expm1-log1p-u log1p-expm1-u
3×frac-2neg clear-num distribute-lft-out--
1×sub-neg rec-exp quot-tan flip3-- pow-flip diff-log 1-exp frac-sub flip-- inv-pow
Counts
4 → 747
Calls
4 calls:
44.0ms
(- (/ 1 (sin B)) (/ x (/ (sin B) (cos B))))
4.0ms
(/ 1 (sin B))
6.0ms
(/ x (/ (sin B) (cos B)))
4.0ms
(/ (sin B) (cos B))

series220.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(- (/ 1 (sin B)) (/ x (/ (sin B) (cos B))))
13.0ms
(/ 1 (sin B))
91.0ms
(/ x (/ (sin B) (cos B)))
26.0ms
(/ (sin B) (cos B))

simplify207.0ms

Algorithm
egg-herbie
Counts
759 → 759
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
0219929556
1500222297

prune918.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (cbrt (/ (sin B) (cos B))) (cbrt (/ (sin B) (cos B))))
0.6b
(cbrt (/ (sin B) (cos B)))
0.6b
(cbrt (/ (sin B) (cos B)))
0.6b
(cbrt (/ (sin B) (cos B)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
103×cbrt-prod
81×add-sqr-sqrt
69×times-frac
57×add-cube-cbrt *-un-lft-identity
16×swap-sqr associate-*r* associate-*l*
11×pow1
9×pow1/3 unswap-sqr
7×cbrt-div div-inv
6×add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times pow-plus associate-*r/ associate-*l/ prod-exp *-commutative cbrt-unprod
Counts
4 → 152
Calls
4 calls:
13.0ms
(* (cbrt (/ (sin B) (cos B))) (cbrt (/ (sin B) (cos B))))
3.0ms
(cbrt (/ (sin B) (cos B)))
3.0ms
(cbrt (/ (sin B) (cos B)))
3.0ms
(cbrt (/ (sin B) (cos B)))

series490.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(* (cbrt (/ (sin B) (cos B))) (cbrt (/ (sin B) (cos B))))
111.0ms
(cbrt (/ (sin B) (cos B)))
112.0ms
(cbrt (/ (sin B) (cos B)))
118.0ms
(cbrt (/ (sin B) (cos B)))

simplify46.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
02791733
110471628
250021577

prune542.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes56.0ms

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
0148
1148

end0.0ms

sample1.7s

Algorithm
intervals
Results
694.0ms1707×body1280valid
380.0ms1431×body640valid
288.0ms4924×body80valid
120.0ms680×body320valid
46.0ms373×body160valid