Details

Time bar (total: 25.4s)

sample454.0ms

Algorithm
intervals
Results
142.0ms34×body5120valid
125.0ms135×body1280valid
96.0ms54×body2560valid
42.0ms78×body640valid
15.0ms36×body320valid
8.0ms62×body80valid
4.0ms18×body160valid

simplify28.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (27.0ms)

IterNodesCost
04413
114913
286912
3500111

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 37.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ k t) 2.0)
1.3b
(* (pow t 3.0) (tan k))
20.7b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
25.8b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite54.0ms

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:
5.0ms
(pow (/ k t) 2.0)
5.0ms
(* (pow t 3.0) (tan k))
21.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
11.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series899.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(pow (/ k t) 2.0)
231.0ms
(* (pow t 3.0) (tan k))
357.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
247.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify41.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09912005
150011672

prune495.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
3.5b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
5.7b
(* (pow k 2.0) (pow t 1.0))
16.8b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite107.0ms

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:
7.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
8.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.0ms
(* (pow k 2.0) (pow t 1.0))
21.0ms
(* (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:
333.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
87.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
322.0ms
(* (pow k 2.0) (pow t 1.0))
639.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify155.0ms

Algorithm
egg-herbie
Counts
620 → 620
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
014397252
142967083
250037076

prune660.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 17.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.8b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
3.5b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.8b
(* (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)))

rewrite279.0ms

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:
3.0ms
(pow (sin k) 2)
12.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
8.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
39.0ms
(* (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)
335.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
81.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
652.0ms
(* (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)))

simplify287.0ms

Algorithm
egg-herbie
Counts
1480 → 1480
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
0199723615
1485419182
2500217933

prune594.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.7b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cos k) (fabs (sin k)))
0.8b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
1.8b
(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l)))
16.8b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l))))

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
3841×add-exp-log
2622×prod-exp
1370×div-exp
1330×pow-exp
679×pow-to-exp
248×rec-exp 1-exp
99×times-frac
80×add-sqr-sqrt
65×add-cbrt-cube
59×add-cube-cbrt *-un-lft-identity
45×associate-*r*
24×associate-*l*
22×cbrt-undiv cbrt-unprod
8×div-inv
7×pow1 unpow-prod-down
6×associate-/l* unswap-sqr
5×associate-*r/
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
2×frac-times frac-2neg associate-*l/ clear-num *-commutative
1×pow-flip pow-prod-down associate-/r/ inv-pow sqr-pow
Counts
4 → 939
Calls
4 calls:
4.0ms
(/ (cos k) (fabs (sin k)))
12.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
20.0ms
(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l)))
30.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l))))

series1.2s

Counts
4 → 12
Calls
4 calls:
12.0ms
(/ (cos k) (fabs (sin k)))
537.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
75.0ms
(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l)))
622.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l))))

simplify173.0ms

Algorithm
egg-herbie
Counts
951 → 951
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0240516881
1500113989

prune819.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 9.5b

regimes409.0ms

Accuracy

51.1% (3.4b remaining)

Error of 11.9b against oracle of 8.5b and baseline of 15.4b

bsearch1.1s

Steps
ItersRangePoint
8
1.4340110496867217e+151
1.1272970871767278e+155
3.912578152959539e+153
7
8.316703124824052e-161
8.630576680100012e-159
3.062784656086729e-159
6
-1.4773917663625897e-168
-1.770571560429151e-169
-1.2495359247218516e-168
7
-4.0387374422910434e+145
-2.3578160794753884e+144
-4.3481340441220306e+144

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
070100
173100
276100
376100

end0.0ms

sample14.8s

Algorithm
intervals
Results
4.3s2239×body2560valid
4.3s987×body5120valid
3.6s4056×body1280valid
1.4s2484×body640valid
389.0ms983×body320valid
253.0ms1990×body80valid
121.0ms447×body160valid