Details

Time bar (total: 1.7m)

sample516.0ms

Algorithm
intervals
Results
170.0ms36×body5120valid
136.0ms73×body2560valid
120.0ms146×body1280valid
37.0ms73×body640valid
14.0ms70×body80valid
11.0ms31×body320valid
2.0ms9×body160valid

simplify27.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
04413
114913
286912
3500111

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ k t) 2.0)
1.5b
(* (pow t 3.0) (tan k))
22.4b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
26.5b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite173.0ms

Algorithm
rewrite-expression-head
Rules
337×add-exp-log
220×prod-exp
71×div-exp
65×add-cbrt-cube
51×pow-exp
34×pow-to-exp cbrt-unprod
30×unpow-prod-down
28×add-sqr-sqrt
24×associate-*l*
23×add-cube-cbrt *-un-lft-identity
19×times-frac
12×cbrt-undiv
5×pow1 associate-*r/
4×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp sqr-pow
3×tan-quot pow-unpow div-inv unswap-sqr
2×*-commutative
1×pow-pow frac-2neg associate-*l/ clear-num associate-/r* associate-/r/ associate-/l*
Counts
4 → 187
Calls
4 calls:
6.0ms
(pow (/ k t) 2.0)
15.0ms
(* (pow t 3.0) (tan k))
95.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
43.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series854.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(pow (/ k t) 2.0)
218.0ms
(* (pow t 3.0) (tan k))
345.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
228.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify40.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
09912005
150011672

prune525.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 24.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
7.5b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.1b
(* (pow k 2.0) (pow t 1.0))
17.2b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
1645×add-exp-log
1122×prod-exp
899×pow-exp
688×div-exp
509×pow-to-exp
140×rec-exp 1-exp
37×add-sqr-sqrt
29×unpow-prod-down
25×add-cbrt-cube
22×times-frac
20×add-cube-cbrt *-un-lft-identity
19×associate-*r*
18×associate-*l*
13×sqr-pow
12×unswap-sqr
9×associate-/r*
7×cbrt-unprod
6×cbrt-undiv
5×pow1
4×expm1-log1p-u log1p-expm1-u div-inv associate-/l* add-log-exp
3×unpow2
2×frac-2neg clear-num *-commutative
1×pow-flip associate-*r/ inv-pow
Counts
4 → 608
Calls
4 calls:
18.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
16.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.0ms
(* (pow k 2.0) (pow t 1.0))
72.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.4s

Counts
4 → 12
Calls
4 calls:
323.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
83.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
329.0ms
(* (pow k 2.0) (pow t 1.0))
618.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify158.0ms

Algorithm
egg-herbie
Counts
620 → 620
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
014397252
142967083
250037076

prune682.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 19.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.9b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
7.5b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.2b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite411.0ms

Algorithm
rewrite-expression-head
Rules
5603×add-exp-log
4515×prod-exp
3078×pow-exp
2032×div-exp
1869×pow-to-exp
434×rec-exp 1-exp
27×add-cbrt-cube
23×add-sqr-sqrt
22×times-frac
20×unpow-prod-down
18×add-cube-cbrt *-un-lft-identity
12×associate-*r*
11×associate-*l*
9×associate-/r*
8×cbrt-unprod
7×cbrt-undiv
6×pow1 sqr-pow
4×expm1-log1p-u log1p-expm1-u div-inv associate-/l* unpow2 add-log-exp
3×pow-unpow unswap-sqr
2×frac-2neg clear-num
1×pow-flip pow-pow associate-*r/ *-commutative inv-pow
Counts
4 → 1468
Calls
4 calls:
4.0ms
(pow (sin k) 2)
47.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
16.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
139.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.1s

Counts
4 → 12
Calls
4 calls:
18.0ms
(pow (sin k) 2)
339.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
83.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
620.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify284.0ms

Algorithm
egg-herbie
Counts
1480 → 1480
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
0199723615
1485419182
2500217933

prune637.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 15.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
1.0b
(/ (pow (cbrt (sin k)) 4) l)
2.1b
(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
17.2b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))

rewrite3.5s

Algorithm
rewrite-expression-head
Rules
28034×times-frac
11443×add-sqr-sqrt
10990×add-cube-cbrt *-un-lft-identity
10474×add-exp-log
7747×unpow-prod-down
6481×div-exp
5244×prod-exp
4340×pow-exp
3852×cbrt-prod
3557×associate-*r*
2573×pow-to-exp
1345×sqr-pow
668×unpow2
620×rec-exp 1-exp
336×associate-/l*
304×div-inv
108×unswap-sqr
49×add-cbrt-cube
24×cbrt-undiv
23×associate-/r/
15×associate-/r*
11×associate-*l*
8×cbrt-unprod
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
1×pow-flip associate-*r/ *-commutative associate-/l/ inv-pow
Counts
4 → 9614
Calls
4 calls:
46.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
20.0ms
(/ (pow (cbrt (sin k)) 4) l)
183.0ms
(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
1.7s
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))

series1.4s

Counts
4 → 12
Calls
4 calls:
325.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
110.0ms
(/ (pow (cbrt (sin k)) 4) l)
84.0ms
(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
922.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))

simplify2.3s

Algorithm
egg-herbie
Counts
9626 → 9626
Iterations

Useful iterations: 0 (123.0ms)

IterNodesCost
010784270016

prune1.2m

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 9.2b

regimes908.0ms

Accuracy

31.5% (4.0b remaining)

Error of 11.1b against oracle of 7.1b and baseline of 12.9b

bsearch1.5s

Steps
ItersRangePoint
9
8.033366954270567e+141
2.4640937426249722e+148
5.502176481489901e+146
5
9.661391276069124e-188
2.1962009731399517e-187
2.174121878485279e-187
9
-1.3717348311758257e-224
-6.118841445143518e-230
-1.7201755034038933e-227
8
-1.0492990687338703e+133
-6.188138656270848e+129
-9.188359687395319e+130

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0103173
1103173

end0.0ms

sample14.6s

Algorithm
intervals
Results
4.4s986×body5120valid
4.0s2126×body2560valid
3.5s4180×body1280valid
1.4s2467×body640valid
379.0ms1021×body320valid
250.0ms2131×body80valid
117.0ms463×body160valid