Details

Time bar (total: 30.5s)

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

sample505.0ms

Algorithm
intervals
Results
132.0ms30×body5120invalid
96.0ms36×body2560invalid
93.0ms111×body1280valid
46.0ms33×body2560valid
31.0ms56×body640valid
26.0ms7×body5120valid
24.0ms24×body1280invalid
10.0ms20×body640invalid
9.0ms24×body320valid
8.0ms19×body80valid
5.0ms14×body320invalid
3.0ms26×body80invalid
2.0ms6×body160valid
2.0ms7×body160invalid

simplify33.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
0500121

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: 37.8b

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)))))
5.8b
(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l))
8.1b
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
29.3b
(* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))

rewrite79.0ms

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:
17.0ms
(/ 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))
18.0ms
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
14.0ms
(* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))

series488.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0)))))
131.0ms
(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l))
169.0ms
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
74.0ms
(* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))

simplify57.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
051083531

prune265.0ms

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: 12.2b

Counts
182 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

2.9b
(* (/ (cos k) (pow (sin k) 2)) l)
5.4b
(* (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))
5.8b
(* 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 k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0))

rewrite120.0ms

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:
10.0ms
(* (/ (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))
31.0ms
(* 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))))
13.0ms
(* (pow (pow k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0))

series360.0ms

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

simplify107.0ms

Algorithm
egg-herbie
Counts
466 → 466
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
0548511044

prune639.0ms

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

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New45313466
Fresh639
Picked101
Done000
Total46016476

Merged error: 8.5b

Counts
476 → 16

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
2.9b
(* (/ (cos k) (pow (sin k) 2)) l)
5.4b
(* (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))
5.8b
(* 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))))

rewrite392.0ms

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)
17.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
32.0ms
(* (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))
82.0ms
(* 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))))

series290.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(pow (sin k) 2)
21.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
151.0ms
(* (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))
114.0ms
(* 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))))

simplify377.0ms

Algorithm
egg-herbie
Counts
1452 → 1452
Iterations

Useful iterations: 0 (142.0ms)

IterNodesCost
0590744704

prune479.0ms

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

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New144931452
Fresh31215
Picked101
Done000
Total1453151468

Merged error: 5.0b

Counts
1468 → 15

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
1.4b
(* (/ (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))
5.8b
(* 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))))))
7.9b
(* 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)))

rewrite355.0ms

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)
18.0ms
(* (/ (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))
99.0ms
(* 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))))))
19.0ms
(* 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)))

series317.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(pow (sin k) 2)
87.0ms
(* (/ (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))
113.0ms
(* 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)))

simplify308.0ms

Algorithm
egg-herbie
Counts
1147 → 1147
Iterations

Useful iterations: 0 (109.0ms)

IterNodesCost
0573641226

prune457.0ms

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

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New114161147
Fresh31114
Picked101
Done000
Total1145171162

Merged error: 4.7b

Counts
1162 → 17

regimes892.0ms

Accuracy

15.8% (2.3b remaining)

Error of 8.0b against oracle of 5.7b and baseline of 8.4b

bsearch3.7s

Steps
ItersRangePoint
8
2.2183660880134375e-14
2.916642576839703e-11
2.2473460020406468e-14
11
-1.7536077635074604e-121
-1.7846685013246022e-158
-1.1653754517657999e-138

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05994
15994

end0.0ms

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

sample14.9s

Algorithm
intervals
Results
3.6s728×body5120invalid
3.4s1276×body2560invalid
2.8s3276×body1280valid
1.4s948×body2560valid
1.1s2007×body640valid
656.0ms200×body5120valid
628.0ms744×body1280invalid
281.0ms547×body640invalid
268.0ms654×body320valid
133.0ms364×body320invalid
121.0ms919×body80invalid
90.0ms657×body80valid
69.0ms258×body160valid
45.0ms182×body160invalid

Profiling

Loading profile data...