Details

Time bar (total: 24.4s)

sample371.0ms

Algorithm
intervals
Results
103.0ms34×body5120valid
93.0ms52×body2560valid
90.0ms126×body1280valid
43.0ms87×body640valid
11.0ms36×body320valid
7.0ms73×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: 39.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
0.6b
(* (pow t 3.0) (tan k))
20.8b
(/ (* 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)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
392×add-exp-log
265×prod-exp
74×div-exp add-cbrt-cube
61×pow-exp
41×pow-to-exp
40×cbrt-unprod
25×associate-*l*
21×add-sqr-sqrt
17×unpow-prod-down
16×add-cube-cbrt *-un-lft-identity
12×cbrt-undiv
10×times-frac
7×associate-*r/ associate-*r*
6×pow1
4×tan-quot expm1-log1p-u log1p-expm1-u add-log-exp
3×*-commutative unswap-sqr sqr-pow
2×associate-*l/ div-inv
1×frac-2neg pow-prod-down clear-num associate-/r* associate-/r/ associate-/l*
Counts
4 → 193
Calls
4 calls:
12.0ms
(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
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)))

series1.1s

Counts
4 → 12
Calls
4 calls:
267.0ms
(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
230.0ms
(* (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)))
244.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify130.0ms

Algorithm
egg-herbie
Counts
205 → 205
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
09252237
148051854
250011854

prune457.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 22.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.0b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
10.0b
(* (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
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))
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:
326.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
86.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
326.0ms
(* (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)))

simplify151.0ms

Algorithm
egg-herbie
Counts
620 → 620
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
014397252
142967083
250037076

prune665.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 17.8b

localize29.0ms

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))))
4.0b
(/ (* (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)))

rewrite269.0ms

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)
11.0ms
(/ 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))
35.0ms
(* (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:
18.0ms
(pow (sin k) 2)
324.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
84.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
836.0ms
(* (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 (88.0ms)

IterNodesCost
0199723615
1485419182
2500217933

prune588.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0)))
4.0b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
4.3b
(* (pow (/ (* (cbrt 1) (cbrt 1)) (pow k (/ 2.0 2))) 1.0) (* (pow (/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
12.2b
(* (pow (/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite402.0ms

Algorithm
rewrite-expression-head
Rules
9372×add-exp-log
6088×prod-exp
4663×pow-exp
3902×div-exp
2343×pow-to-exp
35×times-frac add-cbrt-cube
34×unpow-prod-down
29×associate-*l*
28×add-sqr-sqrt
23×add-cube-cbrt *-un-lft-identity
14×cbrt-unprod
13×associate-*r*
9×cbrt-prod associate-/r*
8×cbrt-undiv
7×associate-/l* sqr-pow
5×div-inv
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r/ unpow2 unswap-sqr
2×frac-2neg clear-num *-commutative
Counts
4 → 1853
Calls
4 calls:
7.0ms
(/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0)))
8.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
41.0ms
(* (pow (/ (* (cbrt 1) (cbrt 1)) (pow k (/ 2.0 2))) 1.0) (* (pow (/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
23.0ms
(* (pow (/ (cbrt 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
(/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0)))
87.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
639.0ms
(* (pow (/ (* (cbrt 1) (cbrt 1)) (pow k (/ 2.0 2))) 1.0) (* (pow (/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
633.0ms
(* (pow (/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify378.0ms

Algorithm
egg-herbie
Counts
1865 → 1865
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
0231040118
1500239788

prune792.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.0b

regimes320.0ms

Accuracy

32.6% (3.3b remaining)

Error of 16.7b against oracle of 13.5b and baseline of 18.3b

bsearch678.0ms

Steps
ItersRangePoint
4
9.790829469375981e+26
1.8099195021178418e+27
1.0301623366654742e+27
11
-3.364119594859113e-112
-1.3237712766476305e-147
-3.3044474230305537e-112

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05846
15846

end0.0ms

sample13.2s

Algorithm
intervals
Results
4.1s2165×body2560valid
4.0s963×body5120valid
2.9s4046×body1280valid
1.2s2500×body640valid
339.0ms1033×body320valid
242.0ms2061×body80valid
99.0ms460×body160valid