Details

Time bar (total: 25.2s)

sample453.0ms

Algorithm
intervals
Results
154.0ms84×body2560valid
119.0ms29×body5120valid
92.0ms109×body1280valid
44.0ms81×body640valid
11.0ms33×body320valid
9.0ms78×body80valid
3.0ms12×body160valid

simplify29.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (27.0ms)

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: 40.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ k t) 2.0)
1.0b
(* (pow t 3.0) (tan k))
21.6b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
30.7b
(* (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:
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)))
26.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series911.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(pow (/ k t) 2.0)
239.0ms
(* (pow t 3.0) (tan k))
365.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
246.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify48.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09912005
150011672

prune488.0ms

Filtered
199 candidates to 96 candidates (48.2%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 22.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.8b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.7b
(* (pow k 2.0) (pow t 1.0))
16.3b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite123.0ms

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:
8.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
6.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.0ms
(* (pow k 2.0) (pow t 1.0))
38.0ms
(* (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:
338.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
88.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
335.0ms
(* (pow k 2.0) (pow t 1.0))
654.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify157.0ms

Algorithm
egg-herbie
Counts
620 → 620
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
014397260
144217083
250027083

prune652.0ms

Filtered
620 candidates to 109 candidates (17.6%)
Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 17.7b

localize24.0ms

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))))
5.8b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.3b
(* (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)))

rewrite311.0ms

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))
62.0ms
(* (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:
20.0ms
(pow (sin k) 2)
347.0ms
(/ 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))
656.0ms
(* (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)))

simplify291.0ms

Algorithm
egg-herbie
Counts
1480 → 1480
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
0199723615
1485419182
2500217933

prune609.0ms

Filtered
1480 candidates to 95 candidates (6.4%)
Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0)))
3.8b
(* (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))))
5.8b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
11.2b
(* (pow (/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite447.0ms

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:
6.0ms
(/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0)))
77.0ms
(* (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))))
6.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
36.0ms
(* (pow (/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.9s

Counts
4 → 12
Calls
4 calls:
340.0ms
(/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0)))
645.0ms
(* (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))))
86.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
862.0ms
(* (pow (/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify396.0ms

Algorithm
egg-herbie
Counts
1865 → 1865
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0231040118
1500239788

prune775.0ms

Filtered
1865 candidates to 117 candidates (6.3%)
Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.5b

regimes590.0ms

Accuracy

39.5% (2.6b remaining)

Error of 16.4b against oracle of 13.7b and baseline of 18.1b

bsearch482.0ms

Steps
ItersRangePoint
7
6.741420631845205e-121
1.9029214291354354e-119
6.1373319556558765e-120
7
-4.01235141168889e-148
-3.25787386598788e-150
-1.1260466702701772e-149

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06768
16768

end0.0ms

sample13.8s

Algorithm
intervals
Results
4.2s2289×body2560valid
3.8s906×body5120valid
3.4s4061×body1280valid
1.3s2535×body640valid
331.0ms950×body320valid
238.0ms2014×body80valid
118.0ms487×body160valid