Details

Time bar (total: 26.7s)

analyze2.6s

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

sample456.0ms

Algorithm
intervals
Results
117.0ms42×body2560invalid
92.0ms106×body1280valid
64.0ms18×body5120invalid
63.0ms43×body2560valid
32.0ms56×body640valid
19.0ms7×body5120valid
13.0ms15×body1280invalid
12.0ms18×body320valid
8.0ms16×body640invalid
7.0ms9×body320invalid
4.0ms28×body80invalid
3.0ms9×body160valid
2.0ms17×body80valid
1.0ms5×body160invalid

simplify38.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (36.0ms)

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: 38.7b

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)))))
4.4b
(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l))
8.0b
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
32.0b
(* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))

rewrite75.0ms

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)))))
22.0ms
(* 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)
13.0ms
(* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))

series492.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0)))))
133.0ms
(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l))
167.0ms
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
79.0ms
(* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))

simplify73.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
049933531
149933531

prune290.0ms

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

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New16911180
Fresh011
Picked101
Done000
Total17012182

Merged error: 12.0b

Counts
182 → 12

localize27.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (/ (cos k) (pow (sin k) 2)) l)
4.4b
(* 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))))
6.2b
(* (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))
7.4b
(* (pow (pow k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0))

rewrite110.0ms

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)
28.0ms
(* 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))))
16.0ms
(* (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))
12.0ms
(* (pow (pow k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0))

series368.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
117.0ms
(* 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))))
154.0ms
(* (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))
76.0ms
(* (pow (pow k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0))

simplify132.0ms

Algorithm
egg-herbie
Counts
466 → 466
Iterations

Useful iterations: 0 (72.0ms)

IterNodesCost
0526611040

prune699.0ms

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

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New45313466
Fresh5611
Picked101
Done000
Total45919478

Merged error: 5.7b

Counts
478 → 19

localize30.0ms

Local error

Found 4 expressions with local error:

0.9b
(* l (* (/ (cos k) (pow (sin k) 2)) (pow (pow (pow t (neg 1.0)) 1.0) 1.0)))
1.4b
(* (/ (cos k) (pow (sin k) 2)) (pow (pow (pow t (neg 1.0)) 1.0) 1.0))
4.4b
(* l (* 2.0 (* (pow (pow (pow k (neg 2.0)) 1.0) 1.0) (* l (* (/ (cos k) (pow (sin k) 2)) (pow (pow (pow t (neg 1.0)) 1.0) 1.0))))))
7.5b
(* (pow (pow (pow k (neg 2.0)) 1.0) 1.0) (* l (* (/ (cos k) (pow (sin k) 2)) (pow (pow (pow t (neg 1.0)) 1.0) 1.0))))

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
2061×add-exp-log
1726×prod-exp
1228×pow-exp
484×pow-to-exp
336×div-exp
103×unpow-prod-down
98×add-sqr-sqrt
59×add-cbrt-cube
52×times-frac
49×associate-*l*
36×cbrt-unprod
35×unswap-sqr
31×sqr-pow
29×add-cube-cbrt *-un-lft-identity
18×associate-*r*
11×pow1
10×unpow2
7×associate-*r/
4×cbrt-undiv pow-prod-down associate-*l/ *-commutative add-log-exp
1×div-inv
Counts
4 → 635
Calls
4 calls:
15.0ms
(* l (* (/ (cos k) (pow (sin k) 2)) (pow (pow (pow t (neg 1.0)) 1.0) 1.0)))
21.0ms
(* (/ (cos k) (pow (sin k) 2)) (pow (pow (pow t (neg 1.0)) 1.0) 1.0))
46.0ms
(* l (* 2.0 (* (pow (pow (pow k (neg 2.0)) 1.0) 1.0) (* l (* (/ (cos k) (pow (sin k) 2)) (pow (pow (pow t (neg 1.0)) 1.0) 1.0))))))
26.0ms
(* (pow (pow (pow k (neg 2.0)) 1.0) 1.0) (* l (* (/ (cos k) (pow (sin k) 2)) (pow (pow (pow t (neg 1.0)) 1.0) 1.0))))

series369.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(* l (* (/ (cos k) (pow (sin k) 2)) (pow (pow (pow t (neg 1.0)) 1.0) 1.0)))
51.0ms
(* (/ (cos k) (pow (sin k) 2)) (pow (pow (pow t (neg 1.0)) 1.0) 1.0))
117.0ms
(* l (* 2.0 (* (pow (pow (pow k (neg 2.0)) 1.0) 1.0) (* l (* (/ (cos k) (pow (sin k) 2)) (pow (pow (pow t (neg 1.0)) 1.0) 1.0))))))
131.0ms
(* (pow (pow (pow k (neg 2.0)) 1.0) 1.0) (* l (* (/ (cos k) (pow (sin k) 2)) (pow (pow (pow t (neg 1.0)) 1.0) 1.0))))

simplify165.0ms

Algorithm
egg-herbie
Counts
647 → 647
Iterations

Useful iterations: 0 (79.0ms)

IterNodesCost
0513417849

prune689.0ms

Filtered
133 candidates to 647 candidates (-386.5%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New63611647
Fresh9918
Picked101
Done000
Total64620666

Merged error: 3.4b

Counts
666 → 20

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (pow (pow (pow k (/ (neg 2.0) 2)) 1.0) 1.0) (* l (* (* (pow (pow (pow t (neg 1.0)) 1.0) 1.0) (/ (cos k) (pow (sin k) 2))) (pow (pow (pow k (/ (neg 2.0) 2)) 1.0) 1.0))))
1.4b
(* (pow (pow (pow t (neg 1.0)) 1.0) 1.0) (/ (cos k) (pow (sin k) 2)))
4.4b
(* l (* 2.0 (* (pow (pow (pow k (/ (neg 2.0) 2)) 1.0) 1.0) (* l (* (* (pow (pow (pow t (neg 1.0)) 1.0) 1.0) (/ (cos k) (pow (sin k) 2))) (pow (pow (pow k (/ (neg 2.0) 2)) 1.0) 1.0))))))
5.3b
(* l (* (* (pow (pow (pow t (neg 1.0)) 1.0) 1.0) (/ (cos k) (pow (sin k) 2))) (pow (pow (pow k (/ (neg 2.0) 2)) 1.0) 1.0)))

rewrite859.0ms

Algorithm
rewrite-expression-head
Rules
15601×add-exp-log
14816×prod-exp
12163×pow-exp
4549×pow-to-exp
2226×div-exp
103×unpow-prod-down
98×add-sqr-sqrt
78×add-cbrt-cube
52×times-frac cbrt-unprod
36×associate-*l*
35×unswap-sqr
31×associate-*r* sqr-pow
29×add-cube-cbrt *-un-lft-identity
11×pow1 associate-*r/
10×unpow2
4×cbrt-undiv pow-prod-down *-commutative add-log-exp
3×associate-*l/
1×div-inv
Counts
4 → 3263
Calls
4 calls:
64.0ms
(* (pow (pow (pow k (/ (neg 2.0) 2)) 1.0) 1.0) (* l (* (* (pow (pow (pow t (neg 1.0)) 1.0) 1.0) (/ (cos k) (pow (sin k) 2))) (pow (pow (pow k (/ (neg 2.0) 2)) 1.0) 1.0))))
29.0ms
(* (pow (pow (pow t (neg 1.0)) 1.0) 1.0) (/ (cos k) (pow (sin k) 2)))
154.0ms
(* l (* 2.0 (* (pow (pow (pow k (/ (neg 2.0) 2)) 1.0) 1.0) (* l (* (* (pow (pow (pow t (neg 1.0)) 1.0) 1.0) (/ (cos k) (pow (sin k) 2))) (pow (pow (pow k (/ (neg 2.0) 2)) 1.0) 1.0))))))
31.0ms
(* l (* (* (pow (pow (pow t (neg 1.0)) 1.0) 1.0) (/ (cos k) (pow (sin k) 2))) (pow (pow (pow k (/ (neg 2.0) 2)) 1.0) 1.0)))

series421.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(* (pow (pow (pow k (/ (neg 2.0) 2)) 1.0) 1.0) (* l (* (* (pow (pow (pow t (neg 1.0)) 1.0) 1.0) (/ (cos k) (pow (sin k) 2))) (pow (pow (pow k (/ (neg 2.0) 2)) 1.0) 1.0))))
55.0ms
(* (pow (pow (pow t (neg 1.0)) 1.0) 1.0) (/ (cos k) (pow (sin k) 2)))
113.0ms
(* l (* 2.0 (* (pow (pow (pow k (/ (neg 2.0) 2)) 1.0) 1.0) (* l (* (* (pow (pow (pow t (neg 1.0)) 1.0) 1.0) (/ (cos k) (pow (sin k) 2))) (pow (pow (pow k (/ (neg 2.0) 2)) 1.0) 1.0))))))
129.0ms
(* l (* (* (pow (pow (pow t (neg 1.0)) 1.0) 1.0) (/ (cos k) (pow (sin k) 2))) (pow (pow (pow k (/ (neg 2.0) 2)) 1.0) 1.0)))

simplify833.0ms

Algorithm
egg-herbie
Counts
3275 → 3275
Iterations

Useful iterations: 0 (250.0ms)

IterNodesCost
05094109051

prune780.0ms

Filtered
130 candidates to 3275 candidates (-2419.2%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New326693275
Fresh61319
Picked101
Done000
Total3273223295

Merged error: 3.1b

Counts
3295 → 22

regimes1.4s

Accuracy

21.6% (3.4b remaining)

Error of 7.5b against oracle of 4.1b and baseline of 8.4b

bsearch471.0ms

Steps
ItersRangePoint
11
4.169163728222193e-121
9.72489931579868e-97
7.410408846849746e-103
6
-1.3422964099146297e-50
-1.2523677182311417e-51
-1.2700187514190925e-51

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
012191
112191

end0.0ms

sample15.0s

Algorithm
intervals
Results
3.5s760×body5120invalid
3.2s1264×body2560invalid
2.8s3203×body1280valid
1.5s998×body2560valid
1.2s2052×body640valid
639.0ms755×body1280invalid
614.0ms194×body5120valid
297.0ms567×body640invalid
282.0ms664×body320valid
148.0ms372×body320invalid
125.0ms914×body80invalid
87.0ms633×body80valid
70.0ms256×body160valid
48.0ms171×body160invalid

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