Details

Time bar (total: 27.6s)

sample370.0ms

Algorithm
intervals
Results
103.0ms34×body5120valid
92.0ms52×body2560valid
90.0ms126×body1280valid
42.0ms87×body640valid
12.0ms36×body320valid
7.0ms73×body80valid
4.0ms18×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: 39.7b

localize19.0ms

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)))

rewrite63.0ms

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:
13.0ms
(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
6.0ms
(* (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:
269.0ms
(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
234.0ms
(* (pow t 3.0) (tan k))
374.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
249.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify133.0ms

Algorithm
egg-herbie
Counts
205 → 205
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
09252237
148051854
250011854

prune447.0ms

Filtered
205 candidates to 88 candidates (42.9%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 22.4b

localize26.0ms

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)))

rewrite106.0ms

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))
21.0ms
(* (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:
342.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
91.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
338.0ms
(* (pow k 2.0) (pow t 1.0))
658.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify147.0ms

Algorithm
egg-herbie
Counts
620 → 620
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
014397252
142967083
250037076

prune861.0ms

Filtered
620 candidates to 108 candidates (17.4%)
Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 17.8b

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))))
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)))

rewrite284.0ms

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)
17.0ms
(/ 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)))

series1.1s

Counts
4 → 12
Calls
4 calls:
19.0ms
(pow (sin k) 2)
338.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
91.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
643.0ms
(* (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)))

simplify304.0ms

Algorithm
egg-herbie
Counts
1480 → 1480
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
0199723615
1485419182
2500217933

prune594.0ms

Filtered
1480 candidates to 94 candidates (6.4%)
Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
25023×add-exp-log
19197×prod-exp
16899×pow-exp
11140×div-exp
7959×pow-to-exp
2990×rec-exp 1-exp
51×unpow-prod-down
43×times-frac
40×associate-*l*
37×add-cbrt-cube
36×add-sqr-sqrt
31×add-cube-cbrt *-un-lft-identity
14×cbrt-unprod
13×associate-*r*
9×associate-/r* sqr-pow
8×cbrt-undiv
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
3×associate-*r/ unpow2 unswap-sqr
2×frac-2neg clear-num *-commutative
1×pow-flip inv-pow
Counts
4 → 5770
Calls
4 calls:
7.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
19.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
93.0ms
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
25.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.8s

Counts
4 → 12
Calls
4 calls:
350.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
92.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
675.0ms
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
677.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.4s

Algorithm
egg-herbie
Counts
5782 → 5782
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
05001120203

prune1.9s

Filtered
5782 candidates to 279 candidates (4.8%)
Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 11.9b

regimes368.0ms

Accuracy

26.7% (4.8b remaining)

Error of 16.6b against oracle of 11.8b and baseline of 18.3b

bsearch740.0ms

Steps
ItersRangePoint
9
8.748475466890137e+114
2.505554558017924e+120
9.707773013878081e+119
5
5.384026678480704e-172
1.8015116876138906e-171
1.774015452417367e-171
9
-1.8005780183630275e-136
-6.981617379614258e-144
-3.0470406015640574e-139

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06682
16682

end0.0ms

sample13.1s

Algorithm
intervals
Results
4.1s2165×body2560valid
4.0s963×body5120valid
2.9s4046×body1280valid
1.2s2500×body640valid
335.0ms1033×body320valid
223.0ms2061×body80valid
106.0ms460×body160valid