Details

Time bar (total: 20.0s)

sample119.0ms

Algorithm
intervals
Results
50.0ms69×body1280valid
19.0ms42×body640valid
19.0ms188×body80valid
9.0ms29×body320valid
4.0ms17×body160valid

simplify29.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04813
115813
290313
3500113

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.0b

Counts
2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

2.3b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
4.1b
(* (/ (pow t 3.0) (* l l)) (sin k))
13.7b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
14.0b
(/ (pow t 3.0) (* l l))

rewrite64.0ms

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:
15.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
10.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
25.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
7.0ms
(/ (pow t 3.0) (* l l))

series1.4s

Counts
4 → 12
Calls
4 calls:
322.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
241.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
629.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
181.0ms
(/ (pow t 3.0) (* l l))

simplify116.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08011619
146461348
250021348

prune506.0ms

Filtered
156 candidates to 93 candidates (59.6%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1479156
Fresh000
Picked101
Done000
Total1489157

Merged error: 15.1b

Counts
157 → 9

localize30.0ms

Local error

Found 4 expressions with local error:

2.3b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
8.8b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
13.7b
(* (* (* (/ (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))

rewrite90.0ms

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:
19.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
12.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
35.0ms
(* (* (* (/ (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))

series1.5s

Counts
4 → 12
Calls
4 calls:
355.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
238.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
197.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
730.0ms
(* (* (* (/ (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))

simplify68.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
013473795
150013312

prune1.0s

Filtered
241 candidates to 150 candidates (62.2%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New2347241
Fresh088
Picked101
Done000
Total23515250

Merged error: 10.5b

Counts
250 → 15

localize45.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ 2.0 (* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
2.3b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
13.7b
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite385.0ms

Algorithm
rewrite-expression-head
Rules
5733×add-exp-log
3663×prod-exp
1790×div-exp
709×pow-exp
424×pow-to-exp
412×add-cbrt-cube
291×cbrt-unprod
206×associate-*l/
179×frac-times
109×cbrt-undiv
56×tan-quot
53×associate-*r/
49×pow1
47×associate-/r/
42×add-sqr-sqrt
37×times-frac
36×associate-*l*
34×*-un-lft-identity
33×pow-prod-down
32×flip3-+ flip-+
29×add-cube-cbrt
20×unpow-prod-down
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 → 988
Calls
4 calls:
81.0ms
(/ 2.0 (* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
42.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
13.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
72.0ms
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.2s

Counts
4 → 12
Calls
4 calls:
642.0ms
(/ 2.0 (* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
585.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
241.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
729.0ms
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify306.0ms

Algorithm
egg-herbie
Counts
1000 → 1000
Iterations

Useful iterations: 1 (59.0ms)

IterNodesCost
0411831583
1500128649

prune2.0s

Filtered
1000 candidates to 247 candidates (24.7%)
Pruning

23 alts after pruning (23 fresh and 0 done)

PrunedKeptTotal
New986141000
Fresh5914
Picked101
Done000
Total992231015

Merged error: 9.5b

Counts
1015 → 23

localize44.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ (sqrt 2.0) (/ (* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (sqrt 2.0)))
2.3b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
13.7b
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite405.0ms

Algorithm
rewrite-expression-head
Rules
5968×add-exp-log
3663×prod-exp
2024×div-exp
709×pow-exp
438×add-cbrt-cube
424×pow-to-exp
291×cbrt-unprod
136×times-frac
134×cbrt-undiv
116×associate-*l/
98×frac-times
83×add-sqr-sqrt
75×*-un-lft-identity
70×add-cube-cbrt
54×sqrt-prod
49×pow1
36×associate-*l*
33×pow-prod-down
32×tan-quot
30×associate-*r/
20×unpow-prod-down
16×flip3-+ flip-+
11×associate-*r*
10×cbrt-prod associate-/r*
9×div-inv
6×associate-/l*
5×unswap-sqr
4×add-log-exp sqr-pow
3×*-commutative distribute-lft-out
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r/
Counts
4 → 1013
Calls
4 calls:
89.0ms
(/ (sqrt 2.0) (/ (* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (sqrt 2.0)))
43.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
13.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
74.0ms
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.2s

Counts
4 → 12
Calls
4 calls:
893.0ms
(/ (sqrt 2.0) (/ (* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (sqrt 2.0)))
367.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
237.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
711.0ms
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify327.0ms

Algorithm
egg-herbie
Counts
1025 → 1025
Iterations

Useful iterations: 1 (58.0ms)

IterNodesCost
0470534470
1500131459

prune2.5s

Filtered
1025 candidates to 287 candidates (28.0%)
Pruning

26 alts after pruning (26 fresh and 0 done)

PrunedKeptTotal
New1014111025
Fresh71522
Picked101
Done000
Total1022261048

Merged error: 9.5b

Counts
1048 → 26

regimes846.0ms

Accuracy

7.6% (6.9b remaining)

Error of 17.4b against oracle of 10.4b and baseline of 17.9b

bsearch285.0ms

Steps
ItersRangePoint
9
2.2008713026740717e-11
0.0008024596835574527
3.991291502179229e-11
4
-6.557124365143935e-147
-3.451179428073472e-147
-3.52399151005714e-147

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0103124
1103124

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.4s2035×body1280valid
814.0ms1745×body640valid
613.0ms5959×body80valid
300.0ms903×body320valid
94.0ms404×body160valid