Details

Time bar (total: 23.8s)

sample416.0ms

Algorithm
intervals
Results
121.0ms71×body2560valid
111.0ms25×body5120valid
95.0ms118×body1280valid
43.0ms83×body640valid
11.0ms30×body320valid
10.0ms61×body80valid
3.0ms14×body160valid

simplify29.0ms

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: 39.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ k t) 2.0)
1.3b
(* (pow t 3.0) (tan k))
20.0b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
26.6b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite86.0ms

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:
6.0ms
(pow (/ k t) 2.0)
6.0ms
(* (pow t 3.0) (tan k))
42.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
22.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series910.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(pow (/ k t) 2.0)
241.0ms
(* (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)))
240.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify41.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
09912005
150011672

prune520.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 20.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.6b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
5.9b
(* (pow k 2.0) (pow t 1.0))
16.4b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite118.0ms

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))
33.0ms
(* (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:
332.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
86.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
321.0ms
(* (pow k 2.0) (pow t 1.0))
638.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify154.0ms

Algorithm
egg-herbie
Counts
620 → 620
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
014397252
142967083
250037076

prune679.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 16.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.4b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
4.6b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.4b
(* (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)))

rewrite297.0ms

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:
6.0ms
(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))
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)))

series1.1s

Counts
4 → 12
Calls
4 calls:
18.0ms
(pow (sin k) 2)
329.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
87.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
645.0ms
(* (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)))

simplify301.0ms

Algorithm
egg-herbie
Counts
1480 → 1480
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
0199723615
1485419182
2500217933

prune596.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cos k) (fabs (sin k)))
0.4b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
2.0b
(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l)))
16.4b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l))))

rewrite233.0ms

Algorithm
rewrite-expression-head
Rules
3841×add-exp-log
2622×prod-exp
1370×div-exp
1330×pow-exp
679×pow-to-exp
248×rec-exp 1-exp
99×times-frac
80×add-sqr-sqrt
65×add-cbrt-cube
59×add-cube-cbrt *-un-lft-identity
45×associate-*r*
24×associate-*l*
22×cbrt-undiv cbrt-unprod
8×div-inv
7×pow1 unpow-prod-down
6×associate-/l* unswap-sqr
5×associate-*r/
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
2×frac-times frac-2neg associate-*l/ clear-num *-commutative
1×pow-flip pow-prod-down associate-/r/ inv-pow sqr-pow
Counts
4 → 939
Calls
4 calls:
3.0ms
(/ (cos k) (fabs (sin k)))
21.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
30.0ms
(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l)))
63.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l))))

series1.2s

Counts
4 → 12
Calls
4 calls:
17.0ms
(/ (cos k) (fabs (sin k)))
325.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
70.0ms
(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l)))
799.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l))))

simplify165.0ms

Algorithm
egg-herbie
Counts
951 → 951
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0240516881
1500113989

prune818.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.1b

regimes349.0ms

Accuracy

44.3% (3.9b remaining)

Error of 12.7b against oracle of 8.7b and baseline of 15.8b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06664
16664

end0.0ms

sample14.3s

Algorithm
intervals
Results
4.3s2249×body2560valid
4.0s951×body5120valid
3.5s4085×body1280valid
1.3s2482×body640valid
354.0ms958×body320valid
256.0ms2069×body80valid
123.0ms484×body160valid