Details

Time bar (total: 6.0s)

sample309.0ms

Algorithm
intervals
Results
22.0ms51×body1280valid
14.0ms51×body640valid
12.0ms162×body80valid
3.0ms16×body320valid
1.0ms9×body160valid

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0187
1336
2436
3546
4606
5626
6626

prune8.0ms

Filtered
1 candidates to 1 candidates (100.0%)
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)))

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:
22.0ms
(+ (- (* 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)))

series308.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
23.0ms
(/ 1.0 (sin B))
37.0ms
(/ 1.0 (tan B))
128.0ms
(* x (/ 1.0 (tan B)))

simplify51.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0438696
11724639
25002635

prune380.0ms

Filtered
129 candidates to 104 candidates (80.6%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt *-un-lft-identity
17×add-cube-cbrt
13×add-exp-log add-cbrt-cube
12×times-frac
8×add-log-exp
6×pow1 fma-def associate-/r*
4×expm1-log1p-u log1p-expm1-u associate-/l*
3×cbrt-undiv div-exp associate-*r* associate-*l* div-inv
2×distribute-rgt-neg-in frac-2neg prod-exp clear-num sum-log cbrt-unprod distribute-lft-out
1×+-commutative neg-sub0 distribute-lft-neg-in associate-+l- neg-mul-1 flip3-+ associate-*r/ pow-prod-down neg-log frac-add *-commutative flip-+ distribute-neg-frac unswap-sqr
Counts
4 → 96
Calls
4 calls:
9.0ms
(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
4.0ms
(/ 1.0 (sin B))
4.0ms
(* x (cos B))
5.0ms
(/ (* x (cos B)) (sin B))

series268.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
22.0ms
(/ 1.0 (sin B))
38.0ms
(* x (cos B))
100.0ms
(/ (* x (cos B)) (sin B))

simplify47.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0375642
11519573
25001568

prune306.0ms

Filtered
108 candidates to 83 candidates (76.9%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
93×times-frac
65×*-un-lft-identity
63×add-sqr-sqrt add-cube-cbrt
19×associate-/r*
13×add-exp-log add-cbrt-cube
9×associate-/l*
8×div-inv add-log-exp
6×fma-def
5×cbrt-undiv div-exp
4×pow1 expm1-log1p-u log1p-expm1-u
3×frac-2neg clear-num
2×distribute-rgt-neg-in sum-log distribute-lft-out
1×+-commutative neg-sub0 distribute-lft-neg-in associate-+l- neg-mul-1 quot-tan flip3-+ associate-*r/ neg-log frac-add associate-/r/ flip-+ distribute-neg-frac
Counts
4 → 155
Calls
4 calls:
12.0ms
(+ (- (* 1.0 (/ x (/ (sin B) (cos B))))) (/ 1.0 (sin B)))
4.0ms
(/ 1.0 (sin B))
6.0ms
(/ x (/ (sin B) (cos B)))
5.0ms
(/ (sin B) (cos B))

series252.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(+ (- (* 1.0 (/ x (/ (sin B) (cos B))))) (/ 1.0 (sin B)))
19.0ms
(/ 1.0 (sin B))
101.0ms
(/ x (/ (sin B) (cos B)))
20.0ms
(/ (sin B) (cos B))

simplify69.0ms

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05921292
124081214
250021209

prune509.0ms

Filtered
167 candidates to 138 candidates (82.6%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (- (* 1.0 (/ x (/ (sin B) (cos B)))))) (cbrt (- (* 1.0 (/ x (/ (sin B) (cos B)))))))
0.6b
(cbrt (- (* 1.0 (/ x (/ (sin B) (cos B))))))
0.6b
(cbrt (- (* 1.0 (/ x (/ (sin B) (cos B))))))
0.6b
(cbrt (- (* 1.0 (/ x (/ (sin B) (cos B))))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
46×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3 swap-sqr associate-*r* associate-*l*
8×associate-*r/
7×distribute-lft-neg-in neg-mul-1 cbrt-div distribute-rgt-neg-in distribute-neg-frac
6×add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times pow-plus associate-*l/ prod-exp *-commutative cbrt-unprod
Counts
4 → 105
Calls
4 calls:
12.0ms
(* (cbrt (- (* 1.0 (/ x (/ (sin B) (cos B)))))) (cbrt (- (* 1.0 (/ x (/ (sin B) (cos B)))))))
2.0ms
(cbrt (- (* 1.0 (/ x (/ (sin B) (cos B))))))
2.0ms
(cbrt (- (* 1.0 (/ x (/ (sin B) (cos B))))))
2.0ms
(cbrt (- (* 1.0 (/ x (/ (sin B) (cos B))))))

series893.0ms

Counts
4 → 12
Calls
4 calls:
265.0ms
(* (cbrt (- (* 1.0 (/ x (/ (sin B) (cos B)))))) (cbrt (- (* 1.0 (/ x (/ (sin B) (cos B)))))))
208.0ms
(cbrt (- (* 1.0 (/ x (/ (sin B) (cos B))))))
210.0ms
(cbrt (- (* 1.0 (/ x (/ (sin B) (cos B))))))
209.0ms
(cbrt (- (* 1.0 (/ x (/ (sin B) (cos B))))))

simplify41.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
02701549
19571442
250011321

prune445.0ms

Filtered
117 candidates to 95 candidates (81.2%)
Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes59.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0179
1219
2219

end0.0ms

sample1.8s

Algorithm
intervals
Results
740.0ms1707×body1280valid
393.0ms1431×body640valid
312.0ms4924×body80valid
135.0ms680×body320valid
54.0ms373×body160valid