Details

Time bar (total: 25.2s)

sample443.0ms

Algorithm
intervals
Results
125.0ms33×body5120valid
125.0ms70×body2560valid
109.0ms134×body1280valid
43.0ms74×body640valid
12.0ms31×body320valid
7.0ms57×body80valid
2.0ms10×body160valid

simplify27.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (25.0ms)

IterNodesCost
04413
114713
285712
3500211

prune11.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.8b

localize18.0ms

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)))

rewrite90.0ms

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×associate-*r* 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 → 179
Calls
4 calls:
3.0ms
(pow (/ k t) 2.0)
7.0ms
(* (pow t 3.0) (tan k))
44.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
25.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series905.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(pow (/ k t) 2.0)
234.0ms
(* (pow t 3.0) (tan k))
370.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
241.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify137.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
09741954
149951620
250011620

prune451.0ms

Filtered
191 candidates to 88 candidates (46.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.5b

localize25.0ms

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×div-inv associate-/l* add-log-exp
3×unpow2
2×frac-2neg clear-num *-commutative
1×pow-flip associate-*r/ inv-pow
Counts
4 → 600
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))
8.0ms
(* (pow k 2.0) (pow t 1.0))
34.0ms
(* (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:
349.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
85.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
326.0ms
(* (pow k 2.0) (pow t 1.0))
671.0ms
(* (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
612 → 612
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
013167194
141627025
250027018

prune618.0ms

Filtered
612 candidates to 100 candidates (16.3%)
Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 15.0b

localize24.0ms

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)))

rewrite298.0ms

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×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 → 1460
Calls
4 calls:
1.0ms
(pow (sin k) 2)
24.0ms
(/ 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:
19.0ms
(pow (sin k) 2)
327.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
85.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
844.0ms
(* (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)))

simplify300.0ms

Algorithm
egg-herbie
Counts
1472 → 1472
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
0174223543
1457419111
2500217858

prune575.0ms

Filtered
1472 candidates to 85 candidates (5.8%)
Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.8b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite443.0ms

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 add-log-exp
3×associate-*r/ unpow2 unswap-sqr
2×frac-2neg clear-num *-commutative
Counts
4 → 1845
Calls
4 calls:
5.0ms
(/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0)))
79.0ms
(* (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))
34.0ms
(* (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:
347.0ms
(/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0)))
662.0ms
(* (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))))
88.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
651.0ms
(* (pow (/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify393.0ms

Algorithm
egg-herbie
Counts
1857 → 1857
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
0200640014
1500139675

prune756.0ms

Filtered
1857 candidates to 108 candidates (5.8%)
Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.5b

regimes510.0ms

Accuracy

-0.3% (3.1b remaining)

Error of 15.7b against oracle of 12.6b and baseline of 15.7b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05346
15346

end0.0ms

sample14.4s

Algorithm
intervals
Results
4.3s979×body5120valid
4.0s2137×body2560valid
3.6s4151×body1280valid
1.4s2495×body640valid
389.0ms1014×body320valid
263.0ms2066×body80valid
100.0ms399×body160valid