Details

Time bar (total: 24.2s)

sample456.0ms

Algorithm
intervals
Results
154.0ms32×body5120valid
125.0ms65×body2560valid
99.0ms130×body1280valid
38.0ms84×body640valid
8.0ms25×body320valid
8.0ms71×body80valid
3.0ms13×body160valid

simplify28.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
04413
114713
285712
3500211

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 37.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ k t) 2.0)
1.0b
(* (pow t 3.0) (tan k))
20.3b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
28.8b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite51.0ms

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×associate-*r* 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 → 179
Calls
4 calls:
4.0ms
(pow (/ k t) 2.0)
6.0ms
(* (pow t 3.0) (tan k))
18.0ms
(/ (* 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)))

series928.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(pow (/ k t) 2.0)
243.0ms
(* (pow t 3.0) (tan k))
375.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
250.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify133.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
09741954
149951620
250011620

prune446.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.9b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.6b
(* (pow k 2.0) (pow t 1.0))
15.3b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite109.0ms

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×div-inv associate-/l* add-log-exp
3×unpow2
2×frac-2neg clear-num *-commutative
1×pow-flip associate-*r/ inv-pow
Counts
4 → 600
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))
25.0ms
(* (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:
334.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
89.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
335.0ms
(* (pow k 2.0) (pow t 1.0))
643.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify156.0ms

Algorithm
egg-herbie
Counts
612 → 612
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
013167194
141627025
250027018

prune603.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.5b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
4.9b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
15.3b
(* (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)))

rewrite266.0ms

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×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 → 1460
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))
37.0ms
(* (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:
19.0ms
(pow (sin k) 2)
349.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
89.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
654.0ms
(* (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)))

simplify294.0ms

Algorithm
egg-herbie
Counts
1472 → 1472
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
0174223543
1457419111
2500217858

prune574.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 14.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (cos k) (fabs (sin k)))
0.5b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
2.3b
(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l)))
15.3b
(* (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))))

rewrite197.0ms

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×associate-/r* 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 → 931
Calls
4 calls:
4.0ms
(/ (cos k) (fabs (sin k)))
16.0ms
(/ 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)))
31.0ms
(* (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))))

series1.3s

Counts
4 → 12
Calls
4 calls:
12.0ms
(/ (cos k) (fabs (sin k)))
334.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
72.0ms
(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l)))
840.0ms
(* (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
943 → 943
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0215016793
1500113902

prune761.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.2b

regimes234.0ms

Accuracy

37.9% (4.3b remaining)

Error of 13.0b against oracle of 8.7b and baseline of 15.7b

bsearch1.4s

Steps
ItersRangePoint
11
1.0214325673685319e-168
4.5400010301605304e-147
3.0824926484891765e-154
6
-3.920045823384307e-128
-7.646965138302796e-129
-1.937285085663093e-128
5
-1.470191470976475e+156
-4.544732995620792e+155
-4.655619290883968e+155

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07276
17276

end0.0ms

sample13.5s

Algorithm
intervals
Results
4.2s2242×body2560valid
4.0s936×body5120valid
3.0s4095×body1280valid
1.2s2531×body640valid
336.0ms986×body320valid
227.0ms2005×body80valid
107.0ms469×body160valid