Details

Time bar (total: 28.5s)

sample508.0ms

Algorithm
intervals
Results
174.0ms42×body5120valid
139.0ms75×body2560valid
106.0ms129×body1280valid
36.0ms70×body640valid
12.0ms78×body80valid
11.0ms30×body320valid
4.0ms19×body160valid

simplify28.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
04413
114913
286912
3500111

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ k t) 2.0)
1.0b
(* (pow t 3.0) (tan k))
19.5b
(/ (* 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)))

rewrite171.0ms

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)
15.0ms
(* (pow t 3.0) (tan k))
93.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
42.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series932.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(pow (/ k t) 2.0)
239.0ms
(* (pow t 3.0) (tan k))
380.0ms
(/ (* 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)))

simplify37.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
09912005
150011672

prune493.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 19.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.1b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
5.3b
(* (pow k 2.0) (pow t 1.0))
14.5b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite187.0ms

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:
17.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
17.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.0ms
(* (pow k 2.0) (pow t 1.0))
71.0ms
(* (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:
350.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
87.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
346.0ms
(* (pow k 2.0) (pow t 1.0))
660.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify146.0ms

Algorithm
egg-herbie
Counts
620 → 620
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
014397252
142967083
250037076

prune660.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 15.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.6b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.1b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
14.5b
(* (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)))

rewrite420.0ms

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:
4.0ms
(pow (sin k) 2)
45.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
17.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
135.0ms
(* (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)
342.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
93.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
664.0ms
(* (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)))

simplify265.0ms

Algorithm
egg-herbie
Counts
1480 → 1480
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
0199723615
1485419182
2500217933

prune590.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 11.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
3.2b
(* (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))))
5.1b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
10.5b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite1.6s

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:
18.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
190.0ms
(* (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))))
16.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
76.0ms
(* (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:
359.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
687.0ms
(* (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))))
96.0ms
(/ (* (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)))

simplify1.0s

Algorithm
egg-herbie
Counts
5782 → 5782
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
05001120203

prune1.9s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 9.6b

regimes538.0ms

Accuracy

37.3% (4.3b remaining)

Error of 15.7b against oracle of 11.4b and baseline of 18.2b

bsearch6.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06456
16456

end0.0ms

sample14.5s

Algorithm
intervals
Results
4.2s2222×body2560valid
4.1s965×body5120valid
3.4s4012×body1280valid
1.5s2487×body640valid
388.0ms1018×body320valid
247.0ms2002×body80valid
112.0ms449×body160valid