Details

Time bar (total: 24.8s)

analyze2.7s

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

sample411.0ms

Algorithm
intervals
Results
93.0ms110×body1280valid
87.0ms18×body5120invalid
77.0ms38×body2560invalid
39.0ms26×body2560valid
39.0ms71×body640valid
18.0ms5×body5120valid
13.0ms15×body1280invalid
8.0ms15×body640invalid
6.0ms15×body320valid
3.0ms24×body80valid
3.0ms25×body80invalid
3.0ms9×body320invalid
2.0ms9×body160invalid
1.0ms5×body160valid

simplify36.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
0484221
1484221

prune13.0ms

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: 37.9b

Counts
2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0)))))
7.4b
(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l))
8.4b
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
26.7b
(* (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)))))
19.0ms
(* 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))))

series489.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0)))))
134.0ms
(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l))
165.0ms
(* (/ 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))))

simplify71.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049933531
149933531

prune256.0ms

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

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1719180
Fresh011
Picked101
Done000
Total17210182

Merged error: 14.1b

Counts
182 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (/ (cos k) (pow (sin k) 2)) l)
5.1b
(* (pow (pow k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0))
6.3b
(* (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))
7.4b
(* 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))))

rewrite112.0ms

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:
9.0ms
(* (/ (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))
14.0ms
(* (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))
29.0ms
(* 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))))

series364.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
69.0ms
(* (pow (pow k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0))
153.0ms
(* (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))
120.0ms
(* 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))))

simplify127.0ms

Algorithm
egg-herbie
Counts
466 → 466
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
0526611040

prune663.0ms

Filtered
134 candidates to 466 candidates (-247.8%)
Pruning

19 alts after pruning (18 fresh and 1 done)

PrunedKeptTotal
New45412466
Fresh369
Picked011
Done000
Total45719476

Merged error: 9.8b

Counts
476 → 19

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
1.7b
(* (/ (cos k) (pow (sin k) 2)) l)
6.3b
(* (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))
7.4b
(* 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))))

rewrite370.0ms

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:
3.0ms
(pow (sin k) 2)
16.0ms
(* (/ (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))
75.0ms
(* 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))))

series287.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(pow (sin k) 2)
21.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
150.0ms
(* (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))
113.0ms
(* 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))))

simplify425.0ms

Algorithm
egg-herbie
Counts
1452 → 1452
Iterations

Useful iterations: 0 (198.0ms)

IterNodesCost
0519844672

prune468.0ms

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

18 alts after pruning (17 fresh and 1 done)

PrunedKeptTotal
New144841452
Fresh41317
Picked101
Done011
Total1453181471

Merged error: 7.0b

Counts
1471 → 18

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.4b
(* (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))))
7.4b
(* 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))))))
7.8b
(* 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)))

rewrite475.0ms

Algorithm
rewrite-expression-head
Rules
8682×add-exp-log
8070×prod-exp
6433×pow-exp
2365×pow-to-exp
1260×div-exp
54×add-cbrt-cube
34×cbrt-unprod
24×unpow-prod-down
21×associate-*l*
12×pow1 add-sqr-sqrt add-cube-cbrt *-un-lft-identity
7×associate-*r/
4×pow-prod-down add-log-exp sqr-pow
3×cbrt-undiv pow-unpow associate-*r* associate-*l/ *-commutative
1×pow-pow unpow2
Counts
4 → 1796
Calls
4 calls:
3.0ms
(pow (sin k) 2)
43.0ms
(* (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))))
87.0ms
(* 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))))))
18.0ms
(* 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)))

series350.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(pow (sin k) 2)
122.0ms
(* (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))))
111.0ms
(* 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))))))
113.0ms
(* 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)))

simplify468.0ms

Algorithm
egg-herbie
Counts
1808 → 1808
Iterations

Useful iterations: 0 (141.0ms)

IterNodesCost
0498070678
1498070678

prune387.0ms

Filtered
72 candidates to 1808 candidates (-2411.1%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New180081808
Fresh7916
Picked101
Done101
Total1809171826

Merged error: 6.3b

Counts
1826 → 17

regimes866.0ms

Accuracy

0% (2.2b remaining)

Error of 8.1b against oracle of 5.9b and baseline of 8.1b

bsearch0.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05042
15042

end0.0ms

sample15.3s

Algorithm
intervals
Results
3.8s767×body5120invalid
3.4s1276×body2560invalid
2.8s3307×body1280valid
1.4s956×body2560valid
1.1s1970×body640valid
651.0ms215×body5120valid
648.0ms780×body1280invalid
310.0ms567×body640invalid
272.0ms661×body320valid
126.0ms912×body80invalid
123.0ms332×body320invalid
99.0ms653×body80valid
72.0ms238×body160valid
45.0ms179×body160invalid

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