Details

Time bar (total: 18.2s)

sample133.0ms

Algorithm
intervals
Results
50.0ms58×body1280valid
31.0ms59×body640valid
20.0ms180×body80valid
13.0ms35×body320valid
3.0ms13×body160valid

simplify30.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04813
115813
290313
3500113

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize26.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (/ (pow t 3.0) (* l l)) (sin k))
3.2b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
13.0b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
16.0b
(/ (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:
15.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
34.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
290.0ms
(* (* (* (/ (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:
254.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
324.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
628.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
184.0ms
(/ (pow t 3.0) (* l l))

simplify121.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08011619
146461348
250021348

prune511.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.6b

localize33.0ms

Local error

Found 4 expressions with local error:

2.6b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.2b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
7.4b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
13.0b
(* (* (* (/ (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))

rewrite564.0ms

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:
18.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
78.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
448.0ms
(* (* (* (/ (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:
231.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
357.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
196.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
738.0ms
(* (* (* (/ (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))

simplify66.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013473795
150013312

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.8b
(pow (cbrt t) 3.0)
2.6b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
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))
13.0b
(* (* (* (/ (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))

rewrite735.0ms

Algorithm
rewrite-expression-head
Rules
1369×add-exp-log
791×prod-exp
489×div-exp
224×pow-exp
134×pow-to-exp
115×add-cbrt-cube
63×cbrt-unprod
44×associate-*l/
43×add-sqr-sqrt
36×associate-*l*
35×*-un-lft-identity
34×frac-times times-frac
30×pow1 add-cube-cbrt
26×unpow-prod-down
25×cbrt-undiv
17×pow-prod-down
16×tan-quot
14×associate-*r/
13×cbrt-prod
11×associate-*r*
8×flip3-+ flip-+
5×unswap-sqr sqr-pow
4×add-log-exp
3×pow-unpow *-commutative distribute-lft-out
2×pow-pow
1×distribute-rgt-in distribute-lft-in pow1/3 div-inv
Counts
4 → 378
Calls
4 calls:
2.0ms
(pow (cbrt t) 3.0)
18.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
108.0ms
(* (* (/ (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))
561.0ms
(* (* (* (/ (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))

series1.6s

Counts
4 → 12
Calls
4 calls:
304.0ms
(pow (cbrt t) 3.0)
231.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
359.0ms
(* (* (/ (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))
719.0ms
(* (* (* (/ (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))

simplify106.0ms

Algorithm
egg-herbie
Counts
390 → 390
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
018578767
150017915

prune955.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 7.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 2.0 (* (* (/ (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))))
0.8b
(pow (cbrt t) 3.0)
2.6b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
15.9b
(* (* (/ (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))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

rewrite650.0ms

Algorithm
rewrite-expression-head
Rules
2933×add-exp-log
1576×prod-exp
1188×div-exp
446×pow-exp
266×pow-to-exp
239×add-cbrt-cube
122×cbrt-unprod
70×cbrt-undiv
58×frac-times
51×associate-*l/
43×add-sqr-sqrt
38×associate-*r/
37×times-frac
35×associate-*l*
30×add-cube-cbrt *-un-lft-identity
28×pow1
26×unpow-prod-down
24×tan-quot
23×associate-/r/
16×flip3-+ pow-prod-down flip-+
13×cbrt-prod
5×unswap-sqr sqr-pow
4×distribute-rgt-in distribute-lft-in associate-*r* add-log-exp
3×pow-unpow associate-/l*
2×pow-pow *-commutative div-inv
1×frac-2neg pow1/3 clear-num associate-/r*
Counts
4 → 628
Calls
4 calls:
260.0ms
(/ 2.0 (* (* (/ (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))))
2.0ms
(pow (cbrt t) 3.0)
18.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
278.0ms
(* (* (/ (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)))

series1.9s

Counts
4 → 12
Calls
4 calls:
645.0ms
(/ 2.0 (* (* (/ (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))))
299.0ms
(pow (cbrt t) 3.0)
232.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
724.0ms
(* (* (/ (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)))

simplify182.0ms

Algorithm
egg-herbie
Counts
640 → 640
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0261017343
1500216530

prune1.1s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 6.9b

regimes603.0ms

Accuracy

15.7% (5.7b remaining)

Error of 13.4b against oracle of 7.8b and baseline of 14.5b

bsearch338.0ms

Steps
ItersRangePoint
7
2.309830911249617e-273
2.1610681829067e-271
2.1606191753491376e-272
8
-9.630385735190575e-163
-3.5037463057660106e-167
-7.04061596489922e-167

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08060
18060

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.7s2018×body1280valid
962.0ms1724×body640valid
670.0ms5947×body80valid
329.0ms853×body320valid
107.0ms428×body160valid