Details

Time bar (total: 27.5s)

sample399.0ms

Algorithm
intervals
Results
123.0ms70×body2560valid
107.0ms33×body5120valid
97.0ms134×body1280valid
33.0ms74×body640valid
10.0ms32×body320valid
7.0ms58×body80valid
2.0ms8×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: 40.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ k t) 2.0)
1.9b
(* (pow t 3.0) (tan k))
19.2b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
32.6b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite52.0ms

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)
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)))

series893.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(pow (/ k t) 2.0)
237.0ms
(* (pow t 3.0) (tan k))
356.0ms
(/ (* 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)))

simplify44.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
09912005
150011672

prune499.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.5b

localize23.0ms

Local error

Found 4 expressions with local error:

1.1b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.9b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.4b
(* (pow k 2.0) (pow t 1.0))
13.7b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite115.0ms

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)))
9.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
11.0ms
(* (pow k 2.0) (pow t 1.0))
22.0ms
(* (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:
330.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
87.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
332.0ms
(* (pow k 2.0) (pow t 1.0))
637.0ms
(* (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
620 → 620
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
014397252
142967083
250037076

prune670.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 15.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
1.1b
(/ 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))
13.7b
(* (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:
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))
38.0ms
(* (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)
336.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
88.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
643.0ms
(* (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)))

simplify281.0ms

Algorithm
egg-herbie
Counts
1480 → 1480
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
0199723615
1485419182
2500217933

prune619.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
3.3b
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
4.9b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
10.2b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
25023×add-exp-log
19197×prod-exp
16899×pow-exp
11140×div-exp
7959×pow-to-exp
2990×rec-exp 1-exp
51×unpow-prod-down
43×times-frac
40×associate-*l*
37×add-cbrt-cube
36×add-sqr-sqrt
31×add-cube-cbrt *-un-lft-identity
14×cbrt-unprod
13×associate-*r*
9×associate-/r* sqr-pow
8×cbrt-undiv
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
3×associate-*r/ unpow2 unswap-sqr
2×frac-2neg clear-num *-commutative
1×pow-flip inv-pow
Counts
4 → 5770
Calls
4 calls:
19.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
99.0ms
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
8.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
26.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.7s

Counts
4 → 12
Calls
4 calls:
333.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
650.0ms
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
88.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
640.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.1s

Algorithm
egg-herbie
Counts
5782 → 5782
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
05001120203

prune2.2s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 9.7b

regimes545.0ms

Accuracy

28.6% (4.2b remaining)

Error of 15.9b against oracle of 11.8b and baseline of 17.6b

bsearch535.0ms

Steps
ItersRangePoint
8
4.502120548238565e-176
1.5644592057666205e-171
1.5339611689415887e-171
9
-1.479226403545783e-97
-5.0491939268701e-104
-1.2094829756305392e-97

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06562
16562

end0.0ms

sample13.4s

Algorithm
intervals
Results
4.2s979×body5120valid
4.0s2137×body2560valid
3.0s4148×body1280valid
1.2s2496×body640valid
344.0ms1015×body320valid
236.0ms2066×body80valid
85.0ms400×body160valid