Details

Time bar (total: 24.7s)

sample504.0ms

Algorithm
intervals
Results
190.0ms47×body5120valid
124.0ms71×body2560valid
113.0ms148×body1280valid
39.0ms77×body640valid
7.0ms59×body80valid
7.0ms19×body320valid
3.0ms13×body160valid

simplify28.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
04413
114913
286912
3500111

prune11.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 37.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ k t) 2.0)
0.3b
(* (pow t 3.0) (tan k))
19.5b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
29.4b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite87.0ms

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))
45.0ms
(/ (* 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)))

series901.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(pow (/ k t) 2.0)
232.0ms
(* (pow t 3.0) (tan k))
362.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
242.0ms
(* (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

prune480.0ms

Filtered
199 candidates to 96 candidates (48.2%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
6.4b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.6b
(* (pow k 2.0) (pow t 1.0))
13.4b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite117.0ms

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)))
6.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
11.0ms
(* (pow k 2.0) (pow t 1.0))
33.0ms
(* (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:
321.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
85.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
321.0ms
(* (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)))

simplify155.0ms

Algorithm
egg-herbie
Counts
620 → 620
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
014397252
142967083
250037076

prune645.0ms

Filtered
620 candidates to 108 candidates (17.4%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.4b

localize30.0ms

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))))
6.4b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
13.4b
(* (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)))

rewrite286.0ms

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)
21.0ms
(/ 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))
61.0ms
(* (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:
25.0ms
(pow (sin k) 2)
327.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
86.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
857.0ms
(* (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)))

simplify286.0ms

Algorithm
egg-herbie
Counts
1480 → 1480
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
0199723615
1485419182
2500217933

prune607.0ms

Filtered
1480 candidates to 95 candidates (6.4%)
Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (cos k) (sin k))
0.9b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
2.4b
(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
13.4b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

rewrite241.0ms

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:
3.0ms
(/ (cos k) (sin k))
24.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
28.0ms
(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
64.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

series1.1s

Counts
4 → 12
Calls
4 calls:
20.0ms
(/ (cos k) (sin k))
337.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
89.0ms
(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
650.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

simplify164.0ms

Algorithm
egg-herbie
Counts
951 → 951
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
0240215175
1500112337

prune784.0ms

Filtered
951 candidates to 143 candidates (15.0%)
Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.7b

regimes351.0ms

Accuracy

44.9% (4.4b remaining)

Error of 13.0b against oracle of 8.6b and baseline of 16.6b

bsearch1.0s

Steps
ItersRangePoint
5
8.355688030489222e+136
1.7536374092389934e+137
1.61120490404906e+137
5
2.9722462368625467e-105
6.3520433824112605e-105
3.0026811713127095e-105
8
-1.270413291935828e-147
-1.547725440753949e-151
-5.710806469245302e-150

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06970
16970

end0.0ms

sample14.1s

Algorithm
intervals
Results
4.2s2223×body2560valid
4.1s965×body5120valid
3.3s4023×body1280valid
1.3s2496×body640valid
381.0ms1039×body320valid
268.0ms2136×body80valid
102.0ms428×body160valid