Details

Time bar (total: 24.9s)

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

sample555.0ms

Algorithm
intervals
Results
155.0ms48×body2560invalid
144.0ms26×body5120invalid
91.0ms106×body1280valid
34.0ms28×body2560valid
32.0ms56×body640valid
30.0ms10×body5120valid
19.0ms20×body1280invalid
9.0ms23×body320valid
7.0ms13×body640invalid
4.0ms29×body80invalid
4.0ms28×body80valid
3.0ms9×body320invalid
2.0ms7×body160invalid
1.0ms5×body160valid

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: 40.4b

Counts
2 → 2

localize23.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0)))))
6.8b
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
7.1b
(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l))
29.4b
(* (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)))))
16.0ms
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
18.0ms
(* l (* (/ 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))))

series486.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0)))))
167.0ms
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
132.0ms
(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l))
75.0ms
(* (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 (51.0ms)

IterNodesCost
049933531
149933531

prune278.0ms

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: 14.8b

Counts
182 → 12

localize26.0ms

Local error

Found 4 expressions with local error:

1.9b
(* (/ (cos k) (pow (sin k) 2)) l)
5.6b
(* (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))
7.1b
(* 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))))
7.5b
(* (pow (pow k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0))

rewrite113.0ms

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

series361.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
152.0ms
(* (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))
121.0ms
(* 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))))
66.0ms
(* (pow (pow k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0))

simplify124.0ms

Algorithm
egg-herbie
Counts
466 → 466
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
0526611040

prune647.0ms

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

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New45313466
Fresh6511
Picked101
Done000
Total46018478

Merged error: 10.0b

Counts
478 → 18

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
1.9b
(* (/ (cos k) (pow (sin k) 2)) l)
5.6b
(* (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))
7.1b
(* 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))))

rewrite363.0ms

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)
29.0ms
(* (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))
76.0ms
(* 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))))

series295.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(pow (sin k) 2)
23.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
152.0ms
(* (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))
115.0ms
(* 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))))

simplify419.0ms

Algorithm
egg-herbie
Counts
1452 → 1452
Iterations

Useful iterations: 0 (194.0ms)

IterNodesCost
0519844672

prune520.0ms

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

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New144571452
Fresh51217
Picked101
Done000
Total1451191470

Merged error: 6.8b

Counts
1470 → 19

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.7b
(* (/ (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))
6.7b
(* 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)))
7.1b
(* 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))))))

rewrite325.0ms

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:
3.0ms
(pow (sin k) 2)
17.0ms
(* (/ (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))
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)))
91.0ms
(* 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))))))

series321.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(pow (sin k) 2)
86.0ms
(* (/ (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))
110.0ms
(* 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)))
121.0ms
(* 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))))))

simplify398.0ms

Algorithm
egg-herbie
Counts
1147 → 1147
Iterations

Useful iterations: 0 (201.0ms)

IterNodesCost
0499041178
1499041178

prune497.0ms

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

21 alts after pruning (21 fresh and 0 done)

PrunedKeptTotal
New1136111147
Fresh81018
Picked101
Done000
Total1145211166

Merged error: 6.5b

Counts
1166 → 21

regimes1.1s

Accuracy

0% (2.5b remaining)

Error of 8.4b against oracle of 5.8b and baseline of 8.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05042
15042

end0.0ms

sample15.2s

Algorithm
intervals
Results
3.6s741×body5120invalid
3.1s1240×body2560invalid
2.9s3303×body1280valid
1.4s961×body2560valid
1.1s1960×body640valid
657.0ms201×body5120valid
656.0ms778×body1280invalid
347.0ms936×body80invalid
284.0ms667×body320valid
282.0ms542×body640invalid
139.0ms329×body320invalid
97.0ms657×body80valid
69.0ms251×body160valid
56.0ms202×body160invalid

Profiling

Loading profile data...