Details

Time bar (total: 23.6s)

sample368.0ms

Algorithm
intervals
Results
105.0ms34×body5120valid
93.0ms52×body2560valid
88.0ms126×body1280valid
38.0ms87×body640valid
12.0ms36×body320valid
8.0ms73×body80valid
4.0ms18×body160valid

simplify27.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (25.0ms)

IterNodesCost
04413
114713
285712
3500211

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 39.7b

localize24.0ms

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)))

rewrite59.0ms

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 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 → 185
Calls
4 calls:
13.0ms
(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
5.0ms
(* (pow t 3.0) (tan k))
17.0ms
(/ (* 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:
268.0ms
(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
238.0ms
(* (pow t 3.0) (tan k))
364.0ms
(/ (* 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)))

simplify130.0ms

Algorithm
egg-herbie
Counts
197 → 197
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
09082174
147741790
250021790

prune411.0ms

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)))

rewrite113.0ms

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)))
8.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
10.0ms
(* (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:
331.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
80.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
328.0ms
(* (pow k 2.0) (pow t 1.0))
634.0ms
(* (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
612 → 612
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
013167194
141627025
250027018

prune609.0ms

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)))

rewrite283.0ms

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:
2.0ms
(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))
34.0ms
(* (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))))
89.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
646.0ms
(* (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)))

simplify286.0ms

Algorithm
egg-herbie
Counts
1472 → 1472
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
0174223543
1457419111
2500217858

prune558.0ms

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)))

rewrite622.0ms

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:
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:
331.0ms
(/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0)))
86.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
626.0ms
(* (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))))
620.0ms
(* (pow (/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify381.0ms

Algorithm
egg-herbie
Counts
1857 → 1857
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
0200640014
1500139675

prune732.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.7b

regimes304.0ms

Accuracy

0% (3.4b remaining)

Error of 16.2b against oracle of 12.8b and baseline of 16.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03426
13426

end0.0ms

sample13.2s

Algorithm
intervals
Results
4.1s2165×body2560valid
4.0s963×body5120valid
2.9s4046×body1280valid
1.1s2500×body640valid
342.0ms1033×body320valid
222.0ms2061×body80valid
98.0ms460×body160valid