Details

Time bar (total: 24.6s)

analyze2.8s

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
0%99.9%0.1%8
0%99.9%0.1%9
0%99.9%0.1%10
0%99.5%0.5%11
0%99.1%0.9%12
0.4%97.3%2.3%13
0.7%95.8%3.5%14

sample444.0ms

Algorithm
intervals
Results
85.0ms105×body1280valid
83.0ms22×body5120invalid
77.0ms31×body2560invalid
52.0ms41×body2560valid
37.0ms9×body5120valid
34.0ms64×body640valid
25.0ms29×body1280invalid
10.0ms21×body640invalid
6.0ms16×body320valid
6.0ms17×body320invalid
3.0ms22×body80invalid
2.0ms8×body160valid
2.0ms8×body160invalid
2.0ms13×body80valid

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
0484221
1484221

prune14.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 41.0b

Counts
2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0)))))
5.3b
(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l))
7.1b
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
32.2b
(* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
356×add-exp-log
241×prod-exp
74×add-cbrt-cube
69×div-exp
48×pow-exp
40×cbrt-unprod
36×pow-to-exp
18×associate-*l*
14×add-sqr-sqrt
12×cbrt-undiv add-cube-cbrt *-un-lft-identity
11×pow1
7×associate-*r/
6×times-frac
5×associate-*r* associate-*l/
4×pow-prod-down add-log-exp
3×tan-quot unpow-prod-down *-commutative associate-/l*
2×associate-/r/ div-inv
1×frac-2neg clear-num associate-/r* unswap-sqr sqr-pow
Counts
4 → 168
Calls
4 calls:
13.0ms
(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0)))))
20.0ms
(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l))
16.0ms
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
12.0ms
(* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))

series467.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0)))))
126.0ms
(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l))
159.0ms
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
77.0ms
(* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))

simplify72.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
049933531
149933531

prune281.0ms

Filtered
82 candidates to 180 candidates (-119.5%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New16812180
Fresh011
Picked101
Done000
Total16913182

Merged error: 13.9b

Counts
182 → 13

localize27.0ms

Local error

Found 4 expressions with local error:

2.4b
(* (/ (cos k) (pow (sin k) 2)) l)
5.2b
(* (pow (* (pow (pow k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0) (* (/ (cos k) (pow (sin k) 2)) l))
5.3b
(* l (* 2.0 (* (pow (* (pow (pow k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0) (* (/ (cos k) (pow (sin k) 2)) l))))
9.2b
(* (pow (pow k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
1265×add-exp-log
1066×prod-exp
757×pow-exp
287×pow-to-exp
171×div-exp
71×unpow-prod-down
70×add-sqr-sqrt
47×associate-*l*
40×add-cbrt-cube
30×unswap-sqr
29×sqr-pow
28×add-cube-cbrt *-un-lft-identity times-frac
22×cbrt-unprod
16×associate-*r*
11×pow1
5×pow-prod-down
4×associate-*r/ *-commutative unpow2 add-log-exp
3×cbrt-undiv associate-*l/
1×div-inv
Counts
4 → 454
Calls
4 calls:
14.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
15.0ms
(* (pow (* (pow (pow k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0) (* (/ (cos k) (pow (sin k) 2)) l))
25.0ms
(* l (* 2.0 (* (pow (* (pow (pow k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0) (* (/ (cos k) (pow (sin k) 2)) l))))
11.0ms
(* (pow (pow k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0))

series346.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
145.0ms
(* (pow (* (pow (pow k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0) (* (/ (cos k) (pow (sin k) 2)) l))
111.0ms
(* l (* 2.0 (* (pow (* (pow (pow k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0) (* (/ (cos k) (pow (sin k) 2)) l))))
70.0ms
(* (pow (pow k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0))

simplify129.0ms

Algorithm
egg-herbie
Counts
466 → 466
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
0526611040

prune672.0ms

Filtered
135 candidates to 466 candidates (-245.2%)
Pruning

20 alts after pruning (19 fresh and 1 done)

PrunedKeptTotal
New45214466
Fresh7512
Picked011
Done000
Total45920479

Merged error: 8.2b

Counts
479 → 20

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin k) 2)
2.4b
(* (/ (cos k) (pow (sin k) 2)) l)
5.2b
(* (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (/ (neg 2.0) 2)) 1.0))) 1.0) (* (/ (cos k) (pow (sin k) 2)) l))
5.3b
(* l (* 2.0 (* (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (/ (neg 2.0) 2)) 1.0))) 1.0) (* (/ (cos k) (pow (sin k) 2)) l))))

rewrite352.0ms

Algorithm
rewrite-expression-head
Rules
6626×add-exp-log
6281×prod-exp
4618×pow-exp
1798×pow-to-exp
801×div-exp
38×add-cbrt-cube
36×add-sqr-sqrt associate-*l*
28×times-frac
24×add-cube-cbrt *-un-lft-identity
21×cbrt-unprod
14×unpow-prod-down
12×pow1
6×sqr-pow
5×associate-*r* unpow2 unswap-sqr
4×associate-*r/ pow-prod-down add-log-exp
3×cbrt-undiv pow-unpow associate-*l/ *-commutative
1×pow-pow div-inv
Counts
4 → 1440
Calls
4 calls:
2.0ms
(pow (sin k) 2)
9.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
28.0ms
(* (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (/ (neg 2.0) 2)) 1.0))) 1.0) (* (/ (cos k) (pow (sin k) 2)) l))
73.0ms
(* l (* 2.0 (* (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (/ (neg 2.0) 2)) 1.0))) 1.0) (* (/ (cos k) (pow (sin k) 2)) l))))

series283.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(pow (sin k) 2)
20.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
143.0ms
(* (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (/ (neg 2.0) 2)) 1.0))) 1.0) (* (/ (cos k) (pow (sin k) 2)) l))
116.0ms
(* l (* 2.0 (* (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (/ (neg 2.0) 2)) 1.0))) 1.0) (* (/ (cos k) (pow (sin k) 2)) l))))

simplify436.0ms

Algorithm
egg-herbie
Counts
1452 → 1452
Iterations

Useful iterations: 0 (197.0ms)

IterNodesCost
0519844672

prune502.0ms

Filtered
91 candidates to 1452 candidates (-1495.6%)
Pruning

19 alts after pruning (18 fresh and 1 done)

PrunedKeptTotal
New144661452
Fresh61218
Picked101
Done011
Total1453191472

Merged error: 4.5b

Counts
1472 → 19

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin k) 2)
1.0b
(* (/ (cos k) (pow (sin k) 2)) (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0))
4.6b
(* l (* (/ (cos k) (pow (sin k) 2)) (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0)))
5.3b
(* l (* 2.0 (* (pow (pow (pow k (/ (neg 2.0) 2)) 1.0) 1.0) (* l (* (/ (cos k) (pow (sin k) 2)) (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0))))))

rewrite324.0ms

Algorithm
rewrite-expression-head
Rules
5645×add-exp-log
5209×prod-exp
3655×pow-exp
1351×pow-to-exp
756×div-exp
45×add-cbrt-cube
43×add-sqr-sqrt
34×associate-*l*
32×times-frac
27×cbrt-unprod
24×add-cube-cbrt *-un-lft-identity
15×unpow-prod-down
12×pow1 sqr-pow
10×unswap-sqr
7×associate-*r*
6×unpow2
5×associate-*r/
4×pow-prod-down add-log-exp
3×cbrt-undiv pow-unpow associate-*l/ *-commutative
1×pow-pow div-inv
Counts
4 → 1135
Calls
4 calls:
2.0ms
(pow (sin k) 2)
16.0ms
(* (/ (cos k) (pow (sin k) 2)) (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0))
17.0ms
(* l (* (/ (cos k) (pow (sin k) 2)) (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0)))
86.0ms
(* l (* 2.0 (* (pow (pow (pow k (/ (neg 2.0) 2)) 1.0) 1.0) (* l (* (/ (cos k) (pow (sin k) 2)) (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0))))))

series299.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(pow (sin k) 2)
83.0ms
(* (/ (cos k) (pow (sin k) 2)) (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0))
102.0ms
(* l (* (/ (cos k) (pow (sin k) 2)) (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0)))
110.0ms
(* l (* 2.0 (* (pow (pow (pow k (/ (neg 2.0) 2)) 1.0) 1.0) (* l (* (/ (cos k) (pow (sin k) 2)) (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0))))))

simplify403.0ms

Algorithm
egg-herbie
Counts
1147 → 1147
Iterations

Useful iterations: 0 (201.0ms)

IterNodesCost
0499041178
1499041178

prune461.0ms

Filtered
91 candidates to 1147 candidates (-1160.4%)
Pruning

21 alts after pruning (20 fresh and 1 done)

PrunedKeptTotal
New114071147
Fresh41317
Picked101
Done011
Total1145211166

Merged error: 4.5b

Counts
1166 → 21

regimes1.0s

Accuracy

0% (2.6b remaining)

Error of 8.2b against oracle of 5.6b and baseline of 8.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05042
15042

end0.0ms

sample14.9s

Algorithm
intervals
Results
3.4s1236×body2560invalid
3.4s748×body5120invalid
2.7s3260×body1280valid
1.4s960×body2560valid
1.1s2024×body640valid
744.0ms211×body5120valid
694.0ms797×body1280invalid
269.0ms666×body320valid
261.0ms515×body640invalid
140.0ms354×body320invalid
133.0ms994×body80invalid
88.0ms617×body80valid
69.0ms262×body160valid
44.0ms178×body160invalid

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