Details

Time bar (total: 25.4s)

sample132.0ms

Algorithm
intervals
Results
46.0ms53×body1280valid
31.0ms58×body640valid
23.0ms205×body80valid
12.0ms32×body320valid
3.0ms11×body160valid

simplify29.0ms

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: 34.8b

localize26.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
5.1b
(* (/ (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))
21.3b
(/ (pow t 3.0) (* l l))

rewrite360.0ms

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))
299.0ms
(* (* (* (/ (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:
326.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
252.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
624.0ms
(* (* (* (/ (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

prune541.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.2b

localize32.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
2.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
9.3b
(/ (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))

rewrite524.0ms

Algorithm
rewrite-expression-head
Rules
277×add-exp-log
158×prod-exp
77×div-exp
70×add-cbrt-cube
64×times-frac
58×add-sqr-sqrt
54×associate-*l*
50×*-un-lft-identity
45×add-cube-cbrt
38×associate-*l/
37×cbrt-unprod
33×pow-exp
30×frac-times
27×unpow-prod-down
25×pow1
22×pow-to-exp
14×pow-prod-down
12×tan-quot cbrt-undiv associate-*r/
11×sqr-pow
10×cbrt-prod
9×associate-*r*
8×flip3-+ flip-+
5×associate-/l* unswap-sqr
4×add-log-exp
3×associate-/r* *-commutative div-inv distribute-lft-out
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num
Counts
4 → 238
Calls
4 calls:
26.0ms
(* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
21.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
459.0ms
(* (* (* (/ (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:
290.0ms
(* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
244.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
199.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
743.0ms
(* (* (* (/ (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))

simplify60.0ms

Algorithm
egg-herbie
Counts
250 → 250
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
014193731
150013292

prune1.2s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 8.7b

localize45.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 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)))
1.5b
(* (* (/ (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))
2.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
11.6b
(* (* (* (/ (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))

rewrite3.2s

Algorithm
rewrite-expression-head
Rules
5799×add-exp-log
3701×prod-exp
1809×div-exp
718×pow-exp
427×pow-to-exp
406×add-cbrt-cube
288×cbrt-unprod
179×frac-times
178×associate-*l/
112×cbrt-undiv
81×associate-*r/
56×tan-quot
47×associate-/r/
42×add-sqr-sqrt
40×pow1
37×times-frac
36×associate-*l*
34×*-un-lft-identity
32×flip3-+ flip-+
29×add-cube-cbrt
26×pow-prod-down
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 → 998
Calls
4 calls:
1.1s
(/ 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)))
298.0ms
(* (* (/ (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))
20.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.3s
(* (* (* (/ (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))

series2.0s

Counts
4 → 12
Calls
4 calls:
672.0ms
(/ 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)))
378.0ms
(* (* (/ (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))
236.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
721.0ms
(* (* (* (/ (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))

simplify305.0ms

Algorithm
egg-herbie
Counts
1010 → 1010
Iterations

Useful iterations: 1 (50.0ms)

IterNodesCost
0408732151
1500131215

prune2.1s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 6.5b

localize40.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 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)))
2.8b
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
2.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
11.6b
(* (* (/ (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))

rewrite2.4s

Algorithm
rewrite-expression-head
Rules
4315×add-exp-log
2746×prod-exp
1345×div-exp
502×pow-exp
340×add-cbrt-cube
299×pow-to-exp
235×cbrt-unprod
167×frac-times
154×associate-*l/
94×cbrt-undiv
85×associate-*r/
52×tan-quot
47×associate-/r/
42×add-sqr-sqrt
37×times-frac
36×associate-*l*
35×pow1
34×*-un-lft-identity
32×flip3-+ flip-+
29×add-cube-cbrt
22×pow-prod-down
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 → 785
Calls
4 calls:
1.0s
(/ 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)))
85.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
19.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.2s
(* (* (/ (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))

series2.0s

Counts
4 → 12
Calls
4 calls:
669.0ms
(/ 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)))
343.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
240.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
732.0ms
(* (* (/ (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))

simplify250.0ms

Algorithm
egg-herbie
Counts
797 → 797
Iterations

Useful iterations: 1 (50.0ms)

IterNodesCost
0397325808
1500124801

prune1.8s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 6.4b

regimes817.0ms

Accuracy

15.8% (5.1b remaining)

Error of 13.1b against oracle of 8.0b and baseline of 14.0b

bsearch398.0ms

Steps
ItersRangePoint
9
1.7275517273680223e-189
3.9795322733838714e-184
1.1821014357870538e-185
8
-4.409857096342441e-184
-4.445274812335677e-187
-5.142996245667799e-185

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08465
18465

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.9s2116×body1280valid
924.0ms1673×body640valid
689.0ms5928×body80valid
327.0ms864×body320valid
114.0ms448×body160valid