Details

Time bar (total: 4.5m)

sample6.1s

Algorithm
intervals
Results
5.4s1376×body10240exit
177.0ms85×body2560valid
170.0ms33×body5120valid
134.0ms130×body1280valid
60.0ms79×body640valid
16.0ms33×body320valid
12.0ms71×body80valid
5.0ms16×body160valid

simplify28.0ms

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: 42.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ k t) 2.0)
0.6b
(* (pow t 3.0) (tan k))
21.4b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
30.6b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite88.0ms

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:
3.0ms
(pow (/ k t) 2.0)
6.0ms
(* (pow t 3.0) (tan k))
46.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
21.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series886.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(pow (/ k t) 2.0)
228.0ms
(* (pow t 3.0) (tan k))
355.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
240.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify41.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
09912005
150011672

prune488.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 23.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.7b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
10.2b
(* (pow k 2.0) (pow t 1.0))
16.4b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite121.0ms

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:
8.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
6.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
11.0ms
(* (pow k 2.0) (pow t 1.0))
35.0ms
(* (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:
326.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
85.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
324.0ms
(* (pow k 2.0) (pow t 1.0))
633.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify150.0ms

Algorithm
egg-herbie
Counts
620 → 620
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
014397252
142967083
250037076

prune662.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 17.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.7b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.7b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.4b
(* (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)))

rewrite300.0ms

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:
1.0ms
(pow (sin k) 2)
20.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
6.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
62.0ms
(* (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)))

series1.3s

Counts
4 → 12
Calls
4 calls:
18.0ms
(pow (sin k) 2)
528.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
87.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
671.0ms
(* (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)))

simplify285.0ms

Algorithm
egg-herbie
Counts
1480 → 1480
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
0199723615
1485419182
2500217933

prune594.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
0.9b
(pow (cbrt (sin k)) 4)
1.2b
(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
16.4b
(* (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)))

rewrite3.1s

Algorithm
rewrite-expression-head
Rules
28004×times-frac
11423×add-sqr-sqrt
10970×add-cube-cbrt *-un-lft-identity
10470×add-exp-log
7729×unpow-prod-down
6478×div-exp
5244×prod-exp
4340×pow-exp
3843×cbrt-prod
3557×associate-*r*
2573×pow-to-exp
1342×sqr-pow
668×unpow2
620×rec-exp 1-exp
326×associate-/l*
303×div-inv
108×unswap-sqr
47×add-cbrt-cube
23×cbrt-undiv associate-/r/
12×associate-/r*
11×associate-*l*
8×cbrt-unprod
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow
2×pow-pow frac-2neg clear-num
1×pow-flip pow1/3 associate-*r/ *-commutative associate-/l/ inv-pow
Counts
4 → 9578
Calls
4 calls:
20.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
2.0ms
(pow (cbrt (sin k)) 4)
171.0ms
(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
1.4s
(* (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)))

series1.5s

Counts
4 → 12
Calls
4 calls:
327.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
120.0ms
(pow (cbrt (sin k)) 4)
84.0ms
(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
927.0ms
(* (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
9590 → 9590
Iterations

Useful iterations: 0 (105.0ms)

IterNodesCost
010779265700

prune55.6s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 5.2b

regimes1.1s

Accuracy

25.8% (4.8b remaining)

Error of 10.6b against oracle of 5.8b and baseline of 12.2b

bsearch18.7s

Steps
ItersRangePoint
9
1.7036844418110972e+193
2.7803876020353827e+199
9.375688098636269e+197
11
2.6674560874079103e+135
1.1854773946047583e+155
1.3529385316824283e+146
8
4.971444393542524e-202
2.713295064118725e-198
3.647319515079204e-200
8
-3.6175634999207456e-134
-2.5862744103785096e-137
-4.467607899251305e-137
10
-1.829086240692416e+154
-2.3805413543904345e+138
-3.2121767733629187e+153

simplify5.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0153199
1162199
2174199
3176199
4176199

end0.0ms

sample2.9m

Algorithm
intervals
Results
2.6m39586×body10240exit
4.9s2238×body2560valid
4.3s951×body5120valid
4.2s4002×body1280valid
1.8s2561×body640valid
491.0ms965×body320valid
339.0ms1969×body80valid
139.0ms437×body160valid