Details

Time bar (total: 19.3s)

sample132.0ms

Algorithm
intervals
Results
53.0ms66×body1280valid
30.0ms51×body640valid
23.0ms206×body80valid
7.0ms18×body320valid
2.0ms8×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

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize25.0ms

Local error

Found 4 expressions with local error:

3.2b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.9b
(* (/ (pow t 3.0) (* l l)) (sin k))
11.6b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
17.8b
(/ (pow t 3.0) (* l l))

rewrite351.0ms

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:
34.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
15.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
289.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
5.0ms
(/ (pow t 3.0) (* l l))

series1.4s

Counts
4 → 12
Calls
4 calls:
330.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
247.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
644.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
186.0ms
(/ (pow t 3.0) (* l l))

simplify118.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
08011619
146461348
250021348

prune492.0ms

Filtered
156 candidates to 93 candidates (59.6%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.2b

localize29.0ms

Local error

Found 4 expressions with local error:

3.2b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
3.9b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k))
6.7b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
11.6b
(* (* (* (* (/ (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))

rewrite744.0ms

Algorithm
rewrite-expression-head
Rules
346×add-exp-log
203×prod-exp
97×div-exp
82×add-cbrt-cube
55×associate-*l/
46×cbrt-unprod
41×pow-exp
35×frac-times
32×pow1
28×pow-to-exp
22×*-un-lft-identity
19×pow-prod-down
17×add-sqr-sqrt add-cube-cbrt
16×tan-quot
15×times-frac associate-*r/
13×cbrt-undiv
11×associate-*r*
8×flip3-+ flip-+
5×associate-/l*
4×unpow-prod-down add-log-exp sqr-pow
3×associate-*l* associate-/r* *-commutative distribute-lft-out
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num div-inv
Counts
4 → 204
Calls
4 calls:
110.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
31.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k))
3.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
584.0ms
(* (* (* (* (/ (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))

series1.6s

Counts
4 → 12
Calls
4 calls:
366.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
296.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k))
200.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
749.0ms
(* (* (* (* (/ (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))

simplify56.0ms

Algorithm
egg-herbie
Counts
216 → 216
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011793756
150013242

prune915.0ms

Filtered
216 candidates to 107 candidates (49.5%)
Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.8b
(pow (cbrt t) 3.0)
3.2b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
3.9b
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (/ (pow (cbrt t) 3.0) l)) (sin k))
11.6b
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
1587×add-exp-log
874×prod-exp
621×div-exp
280×pow-exp
172×pow-to-exp
119×add-cbrt-cube
64×cbrt-unprod
55×associate-*l/
35×frac-times
33×pow1
27×cbrt-undiv
19×pow-prod-down
16×tan-quot
15×*-un-lft-identity associate-*r/
11×associate-*r*
10×add-sqr-sqrt add-cube-cbrt
8×flip3-+ flip-+
6×unpow-prod-down
4×add-log-exp
3×cbrt-prod pow-unpow associate-*l* *-commutative distribute-lft-out
2×pow-pow
1×distribute-rgt-in distribute-lft-in pow1/3 sqr-pow
Counts
4 → 385
Calls
4 calls:
2.0ms
(pow (cbrt t) 3.0)
224.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
62.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (/ (pow (cbrt t) 3.0) l)) (sin k))
1.0s
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.7s

Counts
4 → 12
Calls
4 calls:
313.0ms
(pow (cbrt t) 3.0)
375.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
299.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (/ (pow (cbrt t) 3.0) l)) (sin k))
746.0ms
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify108.0ms

Algorithm
egg-herbie
Counts
397 → 397
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
016769431
150028480

prune758.0ms

Filtered
397 candidates to 104 candidates (26.2%)
Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.8b

localize36.0ms

Local error

Found 4 expressions with local error:

2.5b
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
6.4b
(/ (* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))))
7.2b
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (cbrt t) 3.0) l)) (sin k))
10.0b
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
906×add-exp-log
556×prod-exp
276×div-exp
136×pow-exp
107×add-cbrt-cube
84×pow-to-exp
56×cbrt-unprod
49×times-frac
30×*-un-lft-identity
28×associate-*l/
26×associate-*r/
25×add-sqr-sqrt add-cube-cbrt
23×cbrt-undiv
20×pow1
19×frac-times associate-/r*
14×tan-quot
11×associate-*r* associate-/l/
10×pow-prod-down
8×flip3-+ flip-+
6×unpow-prod-down sqr-pow
4×add-log-exp
3×associate-*l* *-commutative div-inv distribute-lft-out
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r/ associate-/l*
Counts
4 → 300
Calls
4 calls:
86.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
411.0ms
(/ (* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))))
25.0ms
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (cbrt t) 3.0) l)) (sin k))
473.0ms
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (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:
351.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
756.0ms
(/ (* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))))
249.0ms
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (cbrt t) 3.0) l)) (sin k))
852.0ms
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify93.0ms

Algorithm
egg-herbie
Counts
312 → 312
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
015607669
150016971

prune879.0ms

Filtered
312 candidates to 131 candidates (42.0%)
Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 6.2b

regimes724.0ms

Accuracy

35.1% (4.5b remaining)

Error of 12.1b against oracle of 7.6b and baseline of 14.5b

bsearch314.0ms

Steps
ItersRangePoint
8
1.8015029674677065e-123
4.857585983193909e-119
4.7860929615565165e-119
6
-1.3961247619941851e-122
-8.820801965383596e-124
-9.0564238570386e-124

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07561
17561

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.7s2041×body1280valid
958.0ms1728×body640valid
687.0ms5996×body80valid
332.0ms874×body320valid
108.0ms403×body160valid