Details

Time bar (total: 38.1s)

sample465.0ms

Algorithm
intervals
Results
141.0ms72×body2560valid
125.0ms30×body5120valid
99.0ms125×body1280valid
47.0ms80×body640valid
10.0ms31×body320valid
9.0ms83×body80valid
6.0ms25×body160valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 4 (381.0ms)

IterNodesCost
01925
14425
214325
371023
4377821
done500021

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 37.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (pow (/ k t) 2.0) (tan k))
6.7b
(* (* (/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k))) l) l)
7.3b
(* (/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k))) l)
26.8b
(/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k)))

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
379×add-exp-log
182×prod-exp
145×div-exp
94×add-cbrt-cube
44×pow-exp
38×cbrt-unprod
35×times-frac
32×add-sqr-sqrt
31×pow-to-exp
30×cbrt-undiv associate-*l*
22×add-cube-cbrt *-un-lft-identity
15×unpow-prod-down
11×pow1
9×associate-*r*
8×associate-/l*
6×div-inv
5×unswap-sqr
4×tan-quot associate-*r/ pow-prod-down add-log-exp
3×associate-*l/ associate-/r/ *-commutative
2×sqr-pow
1×frac-2neg clear-num associate-/r* associate-/l/
Counts
4 → 203
Calls
4 calls:
16.0ms
(* (pow (/ k t) 2.0) (tan k))
102.0ms
(* (* (/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k))) l) l)
35.0ms
(* (/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k))) l)
13.0ms
(/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k)))

series1.7s

Counts
4 → 12
Calls
4 calls:
212.0ms
(* (pow (/ k t) 2.0) (tan k))
683.0ms
(* (* (/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k))) l) l)
505.0ms
(* (/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k))) l)
306.0ms
(/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k)))

simplify974.0ms

Counts
215 → 215
Iterations

Useful iterations: 2 (405.0ms)

IterNodesCost
03355196
19264753
233433891
done50003891

prune507.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.9b

localize22.0ms

Local error

Found 4 expressions with local error:

2.5b
(/ (* (cos k) l) (pow (sin k) 2))
5.4b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))
6.7b
(* (* 2.0 (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))) l)
7.1b
(* (pow k 2.0) (pow t 1.0))

rewrite237.0ms

Algorithm
rewrite-expression-head
Rules
2134×add-exp-log
1515×prod-exp
826×pow-exp
682×div-exp
406×pow-to-exp
140×rec-exp 1-exp
40×add-cbrt-cube
36×add-sqr-sqrt
29×unpow-prod-down
22×associate-*r*
19×add-cube-cbrt *-un-lft-identity times-frac associate-*l* cbrt-unprod
13×sqr-pow
12×unswap-sqr
9×pow1
8×associate-/r*
6×cbrt-undiv
4×add-log-exp
3×associate-*r/ pow-prod-down *-commutative div-inv unpow2
1×frac-2neg associate-*l/ clear-num associate-/l*
Counts
4 → 598
Calls
4 calls:
5.0ms
(/ (* (cos k) l) (pow (sin k) 2))
30.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))
125.0ms
(* (* 2.0 (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))) l)
8.0ms
(* (pow k 2.0) (pow t 1.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ (* (cos k) l) (pow (sin k) 2))
468.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))
907.0ms
(* (* 2.0 (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))) l)
319.0ms
(* (pow k 2.0) (pow t 1.0))

simplify1.3s

Counts
610 → 610
Iterations

Useful iterations: 2 (706.0ms)

IterNodesCost
059716175
1172114076
2403613392
done500113392

prune593.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin k) 2)
2.5b
(/ (* (cos k) l) (pow (sin k) 2))
5.4b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))
6.7b
(* (* 2.0 (* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))) l)

rewrite487.0ms

Algorithm
rewrite-expression-head
Rules
7037×add-exp-log
5664×prod-exp
2879×pow-exp
2026×div-exp
1577×pow-to-exp
434×rec-exp 1-exp
38×add-cbrt-cube
22×add-sqr-sqrt
20×unpow-prod-down
19×times-frac
18×cbrt-unprod
17×add-cube-cbrt *-un-lft-identity
15×associate-*r*
12×associate-*l*
10×pow1
8×associate-/r*
6×cbrt-undiv sqr-pow
4×unpow2 add-log-exp
3×pow-unpow associate-*r/ pow-prod-down div-inv unswap-sqr
2×*-commutative
1×pow-pow frac-2neg associate-*l/ clear-num associate-/l*
Counts
4 → 1457
Calls
4 calls:
1.0ms
(pow (sin k) 2)
6.0ms
(/ (* (cos k) l) (pow (sin k) 2))
56.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))
194.0ms
(* (* 2.0 (* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))) l)

series1.3s

Counts
4 → 12
Calls
4 calls:
18.0ms
(pow (sin k) 2)
91.0ms
(/ (* (cos k) l) (pow (sin k) 2))
478.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))
700.0ms
(* (* 2.0 (* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))) l)

simplify1.6s

Counts
1469 → 1469
Iterations

Useful iterations: 2 (982.0ms)

IterNodesCost
084253180
1265834769
2455233657
done500033657

prune543.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
2.5b
(/ (* (cos k) l) (pow (sin k) 2))
3.8b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))
6.7b
(* (* 2.0 (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2))))) l)

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
18850×add-exp-log
15132×prod-exp
8353×pow-exp
5812×div-exp
3535×pow-to-exp
1616×rec-exp 1-exp
50×add-cbrt-cube
25×cbrt-unprod
22×add-sqr-sqrt times-frac
17×add-cube-cbrt unpow-prod-down *-un-lft-identity
15×associate-*r*
12×associate-*l*
10×pow1
9×associate-/r*
8×cbrt-undiv
5×sqr-pow
4×associate-*r/ div-inv associate-/l* add-log-exp
3×pow-prod-down unpow2 unswap-sqr
2×frac-2neg clear-num *-commutative
1×pow-flip associate-*l/ inv-pow
Counts
4 → 3162
Calls
4 calls:
8.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
5.0ms
(/ (* (cos k) l) (pow (sin k) 2))
33.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))
602.0ms
(* (* 2.0 (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2))))) l)

series1.6s

Counts
4 → 12
Calls
4 calls:
337.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
82.0ms
(/ (* (cos k) l) (pow (sin k) 2))
480.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))
677.0ms
(* (* 2.0 (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2))))) l)

simplify1.2s

Counts
3174 → 3174
Iterations

Useful iterations: 0 (600.0ms)

IterNodesCost
02509133043
done5001133043

prune6.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.4b

regimes331.0ms

Accuracy

9.3% (3.6b remaining)

Error of 8.0b against oracle of 4.4b and baseline of 8.4b

bsearch248.0ms

Steps
ItersRangePoint
4
-5.282251310708395e+180
-2.9663123383915125e+180
-3.0209864353103622e+180

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03582
14882
done4882

end0.0ms

sample13.9s

Algorithm
intervals
Results
4.0s970×body5120valid
4.0s2154×body2560valid
3.4s4083×body1280valid
1.3s2474×body640valid
374.0ms1021×body320valid
243.0ms2010×body80valid
105.0ms445×body160valid