Details

Time bar (total: 10.2s)

sample140.0ms

Algorithm
intervals
Results
55.0ms71×body1280valid
32.0ms53×body640valid
22.0ms179×body80valid
9.0ms22×body320valid
3.0ms13×body160valid

simplify23.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
0508625

prune14.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.3b

Counts
2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
2.9b
(* (/ (pow t 3.0) (* l l)) (sin k))
12.4b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
18.2b
(/ (pow t 3.0) (* l l))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
108×add-exp-log
58×prod-exp
52×add-cbrt-cube
26×cbrt-unprod
24×div-exp
21×add-sqr-sqrt
20×pow1
19×*-un-lft-identity
17×times-frac
16×associate-*l/
14×add-cube-cbrt
13×associate-*l*
11×associate-*r*
10×frac-times unpow-prod-down pow-prod-down
8×tan-quot cbrt-undiv pow-to-exp pow-exp
7×associate-/l*
6×associate-*r/
4×flip3-+ flip-+ add-log-exp unswap-sqr sqr-pow
3×*-commutative distribute-lft-out
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r*
Counts
4 → 144
Calls
4 calls:
11.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
9.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
26.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
6.0ms
(/ (pow t 3.0) (* l l))

series340.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
57.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
168.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
40.0ms
(/ (pow t 3.0) (* l l))

simplify67.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
049712558
149712558

prune291.0ms

Filtered
98 candidates to 156 candidates (-59.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1479156
Fresh011
Picked101
Done000
Total14810158

Merged error: 21.1b

Counts
158 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.3b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
9.0b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
12.4b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
304×add-exp-log
184×prod-exp
78×add-cbrt-cube
77×div-exp
50×add-sqr-sqrt
49×times-frac
44×associate-*l/ cbrt-unprod
42×*-un-lft-identity
37×add-cube-cbrt
36×associate-*l*
34×frac-times
33×pow-exp
29×pow1
24×unpow-prod-down
22×pow-to-exp
17×pow-prod-down
16×tan-quot
14×associate-*r/
12×cbrt-undiv
11×associate-*r*
10×cbrt-prod
8×flip3-+ flip-+ sqr-pow
5×associate-/l* unswap-sqr
4×add-log-exp
3×associate-/r* *-commutative distribute-lft-out
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num
Counts
4 → 229
Calls
4 calls:
17.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
11.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
34.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series368.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
54.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
45.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
186.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify94.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
049505585
149505585

prune516.0ms

Filtered
138 candidates to 241 candidates (-74.6%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New23110241
Fresh189
Picked101
Done000
Total23318251

Merged error: 15.3b

Counts
251 → 18

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 2.0 (* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
2.7b
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.3b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
12.4b
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite223.0ms

Algorithm
rewrite-expression-head
Rules
1254×add-exp-log
687×prod-exp
503×div-exp
187×add-cbrt-cube
145×pow-to-exp pow-exp
99×cbrt-unprod
78×associate-*l/
63×frac-times
49×cbrt-undiv
42×add-sqr-sqrt
37×times-frac
36×associate-*l*
34×*-un-lft-identity
29×pow1 add-cube-cbrt
28×tan-quot
25×associate-*r/
23×associate-/r/
20×unpow-prod-down
17×pow-prod-down
16×flip3-+ flip-+
11×associate-*r*
10×cbrt-prod
5×unswap-sqr
4×add-log-exp sqr-pow
3×*-commutative distribute-lft-out associate-/l*
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r*
Counts
4 → 397
Calls
4 calls:
64.0ms
(/ 2.0 (* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
43.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
11.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
61.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series495.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(/ 2.0 (* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
83.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
54.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
185.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify115.0ms

Algorithm
egg-herbie
Counts
409 → 409
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
055559772

prune617.0ms

Filtered
155 candidates to 409 candidates (-163.9%)
Pruning

21 alts after pruning (21 fresh and 0 done)

PrunedKeptTotal
New39811409
Fresh71017
Picked101
Done000
Total40621427

Merged error: 13.5b

Counts
427 → 21

localize31.0ms

Local error

Found 4 expressions with local error:

10.7b
(cbrt (* (/ (pow (cbrt t) 3.0) l) (sin k)))
10.7b
(cbrt (* (/ (pow (cbrt t) 3.0) l) (sin k)))
10.7b
(cbrt (* (/ (pow (cbrt t) 3.0) l) (sin k)))
12.4b
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (* (cbrt (* (/ (pow (cbrt t) 3.0) l) (sin k))) (cbrt (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (cbrt (* (/ (pow (cbrt t) 3.0) l) (sin k))))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
289×associate-*l/
246×add-exp-log
209×frac-times
159×prod-exp
147×cbrt-div
83×associate-*r/
63×div-exp
51×add-cbrt-cube
48×tan-quot
39×cbrt-unprod
32×flip3-+ flip-+
24×pow1
21×pow-to-exp pow-exp
15×pow-prod-down
10×*-un-lft-identity
9×cbrt-undiv
5×add-sqr-sqrt add-cube-cbrt associate-*r*
4×add-log-exp
3×cbrt-prod pow1/3 distribute-lft-out
1×distribute-rgt-in distribute-lft-in associate-*l* *-commutative
Counts
4 → 198
Calls
4 calls:
7.0ms
(cbrt (* (/ (pow (cbrt t) 3.0) l) (sin k)))
7.0ms
(cbrt (* (/ (pow (cbrt t) 3.0) l) (sin k)))
7.0ms
(cbrt (* (/ (pow (cbrt t) 3.0) l) (sin k)))
68.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (* (cbrt (* (/ (pow (cbrt t) 3.0) l) (sin k))) (cbrt (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (cbrt (* (/ (pow (cbrt t) 3.0) l) (sin k))))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series386.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(cbrt (* (/ (pow (cbrt t) 3.0) l) (sin k)))
65.0ms
(cbrt (* (/ (pow (cbrt t) 3.0) l) (sin k)))
66.0ms
(cbrt (* (/ (pow (cbrt t) 3.0) l) (sin k)))
188.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (* (cbrt (* (/ (pow (cbrt t) 3.0) l) (sin k))) (cbrt (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (cbrt (* (/ (pow (cbrt t) 3.0) l) (sin k))))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify94.0ms

Algorithm
egg-herbie
Counts
210 → 210
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
049848872
149848872

prune436.0ms

Filtered
100 candidates to 210 candidates (-110.0%)
Pruning

23 alts after pruning (22 fresh and 1 done)

PrunedKeptTotal
New2064210
Fresh21820
Picked011
Done000
Total20823231

Merged error: 11.7b

Counts
231 → 23

regimes775.0ms

Accuracy

28.5% (4.6b remaining)

Error of 16.5b against oracle of 11.9b and baseline of 18.3b

bsearch370.0ms

Steps
ItersRangePoint
9
9.618282249428914e+226
2.7215897305382794e+233
1.4558503343255128e+227
8
8.63801322205868e+166
5.968716258118037e+169
2.670986173632126e+169
11
7.605232119314455e-155
3.6476347041017933e-131
1.3337804818741451e-151
8
-1.334730375924918e-190
-2.6480832408403615e-194
-1.3078668923076751e-190

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
093219
193219

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.7s2056×body1280valid
1.1s1711×body640valid
744.0ms5908×body80valid
339.0ms870×body320valid
125.0ms465×body160valid

Profiling

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