Details

Time bar (total: 37.3s)

sample386.0ms

Algorithm
intervals
Results
107.0ms25×body5120valid
92.0ms116×body1280valid
91.0ms60×body2560valid
53.0ms93×body640valid
11.0ms32×body320valid
8.0ms69×body80valid
3.0ms13×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: 41.9b

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))
21.7b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
29.5b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite92.0ms

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:
4.0ms
(pow (/ k t) 2.0)
6.0ms
(* (pow t 3.0) (tan k))
49.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
22.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series901.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(pow (/ k t) 2.0)
233.0ms
(* (pow t 3.0) (tan k))
358.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
245.0ms
(* (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

prune477.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 23.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
5.4b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.8b
(* (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)))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
1597×add-exp-log
1095×prod-exp
882×pow-exp
668×div-exp
492×pow-to-exp
130×rec-exp 1-exp
37×add-sqr-sqrt
32×unpow-prod-down
20×add-cube-cbrt *-un-lft-identity add-cbrt-cube
19×times-frac associate-*r*
18×associate-*l*
14×sqr-pow
12×unswap-sqr
8×associate-/r*
6×cbrt-unprod
5×pow1
4×cbrt-undiv expm1-log1p-u log1p-expm1-u unpow2 add-log-exp
3×pow-unpow div-inv
2×*-commutative
1×pow-pow frac-2neg associate-*r/ clear-num associate-/l*
Counts
4 → 575
Calls
4 calls:
1.0ms
(pow (sin k) 2)
6.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
9.0ms
(* (pow k 2.0) (pow t 1.0))
36.0ms
(* (pow (/ 1 (* (pow k 2.0) (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)
86.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
323.0ms
(* (pow k 2.0) (pow t 1.0))
638.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify144.0ms

Algorithm
egg-herbie
Counts
587 → 587
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
013046971
138736815
250036814

prune638.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 18.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
0.4b
(pow (sin k) 2)
5.4b
(/ (* (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)))

rewrite303.0ms

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:
22.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
1.0ms
(pow (sin k) 2)
6.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
65.0ms
(* (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:
339.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
18.0ms
(pow (sin k) 2)
87.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
867.0ms
(* (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 (89.0ms)

IterNodesCost
0199723615
1485419182
2500217933

prune616.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (cos k) (/ (/ (sin k) l) l))
0.3b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
2.9b
(/ (/ (cos k) (/ (/ (sin k) l) l)) (pow (sin k) (/ 2 2)))
16.8b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (sin k) l) l)) (pow (sin k) (/ 2 2))))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
7270×times-frac
6775×add-exp-log
3784×div-exp
3642×prod-exp
3110×add-sqr-sqrt
2967×add-cube-cbrt *-un-lft-identity
2786×pow-exp
1577×pow-to-exp
942×associate-*r*
839×unpow-prod-down
434×rec-exp 1-exp
295×sqr-pow
216×div-inv
140×associate-/l*
56×add-cbrt-cube
51×associate-/r*
39×unswap-sqr
29×cbrt-undiv
16×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 → 3675
Calls
4 calls:
14.0ms
(/ (cos k) (/ (/ (sin k) l) l))
22.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
62.0ms
(/ (/ (cos k) (/ (/ (sin k) l) l)) (pow (sin k) (/ 2 2)))
448.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (sin k) l) l)) (pow (sin k) (/ 2 2))))

series1.2s

Counts
4 → 12
Calls
4 calls:
75.0ms
(/ (cos k) (/ (/ (sin k) l) l))
333.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
91.0ms
(/ (/ (cos k) (/ (/ (sin k) l) l)) (pow (sin k) (/ 2 2)))
662.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (sin k) l) l)) (pow (sin k) (/ 2 2))))

simplify718.0ms

Algorithm
egg-herbie
Counts
3687 → 3687
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
0500183055

prune13.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.0b

regimes312.0ms

Accuracy

13.8% (2.9b remaining)

Error of 10.8b against oracle of 7.9b and baseline of 11.2b

bsearch660.0ms

Steps
ItersRangePoint
10
-1.1549747614155664e-91
-4.809581082357105e-102
-1.856992087426494e-100
7
-5.136766128027413e+148
-1.1919610862734025e+147
-6.290931522942836e+147

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06461
16461

end0.0ms

sample13.8s

Algorithm
intervals
Results
4.1s2195×body2560valid
3.8s911×body5120valid
3.3s4022×body1280valid
1.4s2518×body640valid
379.0ms1054×body320valid
246.0ms2002×body80valid
112.0ms443×body160valid