Details

Time bar (total: 32.6s)

sample162.0ms

Algorithm
intervals
Results
63.0ms67×body1280valid
33.0ms52×body640valid
25.0ms187×body80valid
16.0ms36×body320valid
3.0ms11×body160valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 4 (348.0ms)

IterNodesCost
01925
14725
215625
379625
4409324
done500024

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.8b

localize31.0ms

Local error

Found 4 expressions with local error:

3.7b
(* (tan k) (/ (* (pow t 3.0) (sin k)) l))
4.9b
(/ (* (pow t 3.0) (sin k)) l)
6.3b
(* (/ 2.0 (* (* (tan k) (/ (* (pow t 3.0) (sin k)) l)) (fma 2 1.0 (pow (/ k t) 2.0)))) l)
12.8b
(* (* (tan k) (/ (* (pow t 3.0) (sin k)) l)) (fma 2 1.0 (pow (/ k t) 2.0)))

rewrite207.0ms

Algorithm
rewrite-expression-head
Rules
93×add-exp-log
59×add-cbrt-cube
47×prod-exp
27×cbrt-unprod
23×div-exp
17×add-sqr-sqrt
14×associate-*l*
13×pow1 cbrt-undiv add-cube-cbrt *-un-lft-identity associate-*r*
10×associate-*l/
9×times-frac
6×tan-quot
5×pow-prod-down
4×expm1-log1p-u pow-to-exp pow-exp log1p-expm1-u add-log-exp
3×frac-times associate-*r/ associate-/r* associate-/r/ *-commutative div-inv
2×fma-udef unswap-sqr
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/l*
Counts
4 → 129
Calls
4 calls:
16.0ms
(* (tan k) (/ (* (pow t 3.0) (sin k)) l))
6.0ms
(/ (* (pow t 3.0) (sin k)) l)
140.0ms
(* (/ 2.0 (* (* (tan k) (/ (* (pow t 3.0) (sin k)) l)) (fma 2 1.0 (pow (/ k t) 2.0)))) l)
37.0ms
(* (* (tan k) (/ (* (pow t 3.0) (sin k)) l)) (fma 2 1.0 (pow (/ k t) 2.0)))

series1.7s

Counts
4 → 12
Calls
4 calls:
249.0ms
(* (tan k) (/ (* (pow t 3.0) (sin k)) l))
231.0ms
(/ (* (pow t 3.0) (sin k)) l)
808.0ms
(* (/ 2.0 (* (* (tan k) (/ (* (pow t 3.0) (sin k)) l)) (fma 2 1.0 (pow (/ k t) 2.0)))) l)
440.0ms
(* (* (tan k) (/ (* (pow t 3.0) (sin k)) l)) (fma 2 1.0 (pow (/ k t) 2.0)))

simplify1.6s

Counts
141 → 141
Iterations

Useful iterations: 2 (340.0ms)

IterNodesCost
02833301
18263179
242152521
done50002521

prune579.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 25.8b

localize21.0ms

Local error

Found 4 expressions with local error:

3.7b
(* (tan k) (/ (pow t 3.0) (/ l (sin k))))
5.4b
(/ (pow t 3.0) (/ l (sin k)))
6.3b
(* (/ 2.0 (* (* (tan k) (/ (pow t 3.0) (/ l (sin k)))) (fma 2 1.0 (pow (/ k t) 2.0)))) l)
12.8b
(* (* (tan k) (/ (pow t 3.0) (/ l (sin k)))) (fma 2 1.0 (pow (/ k t) 2.0)))

rewrite278.0ms

Algorithm
rewrite-expression-head
Rules
329×times-frac
192×add-sqr-sqrt
169×add-cube-cbrt *-un-lft-identity
119×add-exp-log
102×associate-*r*
83×unpow-prod-down
59×add-cbrt-cube
47×prod-exp
45×div-exp
29×sqr-pow
23×cbrt-unprod
18×div-inv
17×cbrt-undiv
14×associate-*l*
13×pow1 associate-/r*
10×associate-*l/
8×pow-to-exp pow-exp unswap-sqr
7×associate-/l*
6×tan-quot
5×pow-prod-down associate-/r/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-times associate-*r/ *-commutative
2×fma-udef
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num
Counts
4 → 337
Calls
4 calls:
39.0ms
(* (tan k) (/ (pow t 3.0) (/ l (sin k))))
8.0ms
(/ (pow t 3.0) (/ l (sin k)))
164.0ms
(* (/ 2.0 (* (* (tan k) (/ (pow t 3.0) (/ l (sin k)))) (fma 2 1.0 (pow (/ k t) 2.0)))) l)
44.0ms
(* (* (tan k) (/ (pow t 3.0) (/ l (sin k)))) (fma 2 1.0 (pow (/ k t) 2.0)))

series1.9s

Counts
4 → 12
Calls
4 calls:
261.0ms
(* (tan k) (/ (pow t 3.0) (/ l (sin k))))
221.0ms
(/ (pow t 3.0) (/ l (sin k)))
971.0ms
(* (/ 2.0 (* (* (tan k) (/ (pow t 3.0) (/ l (sin k)))) (fma 2 1.0 (pow (/ k t) 2.0)))) l)
399.0ms
(* (* (tan k) (/ (pow t 3.0) (/ l (sin k)))) (fma 2 1.0 (pow (/ k t) 2.0)))

simplify920.0ms

Counts
349 → 349
Iterations

Useful iterations: done (906.0ms)

IterNodesCost
05817140
115416674
done50016621

prune1.6s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 22.3b

localize63.0ms

Local error

Found 4 expressions with local error:

2.8b
(* (tan k) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt (/ l (sin k))) (cbrt (/ l (sin k))))))
6.3b
(* (/ 2.0 (* (* (* (tan k) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt (/ l (sin k))) (cbrt (/ l (sin k)))))) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k))))) (fma 2 1.0 (pow (/ k t) 2.0)))) l)
10.8b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt (/ l (sin k))) (cbrt (/ l (sin k)))))
12.8b
(* (* (* (tan k) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt (/ l (sin k))) (cbrt (/ l (sin k)))))) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k))))) (fma 2 1.0 (pow (/ k t) 2.0)))

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
593×add-exp-log
346×prod-exp
182×div-exp
105×add-cbrt-cube
66×cbrt-unprod
60×pow-exp
40×pow-to-exp
30×cbrt-undiv
28×associate-*l/
21×add-sqr-sqrt
18×associate-*r* associate-*l*
17×pow1
16×times-frac
13×frac-times add-cube-cbrt *-un-lft-identity associate-/r/
10×tan-quot
9×associate-*r/
8×cbrt-div pow-prod-down
5×associate-/l* unswap-sqr
4×expm1-log1p-u unpow-prod-down log1p-expm1-u add-log-exp sqr-pow
3×*-commutative div-inv
2×fma-udef
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r*
Counts
4 → 241
Calls
4 calls:
50.0ms
(* (tan k) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt (/ l (sin k))) (cbrt (/ l (sin k))))))
1.5s
(* (/ 2.0 (* (* (* (tan k) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt (/ l (sin k))) (cbrt (/ l (sin k)))))) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k))))) (fma 2 1.0 (pow (/ k t) 2.0)))) l)
9.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt (/ l (sin k))) (cbrt (/ l (sin k)))))
432.0ms
(* (* (* (tan k) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt (/ l (sin k))) (cbrt (/ l (sin k)))))) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k))))) (fma 2 1.0 (pow (/ k t) 2.0)))

series2.1s

Counts
4 → 12
Calls
4 calls:
332.0ms
(* (tan k) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt (/ l (sin k))) (cbrt (/ l (sin k))))))
1.1s
(* (/ 2.0 (* (* (* (tan k) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt (/ l (sin k))) (cbrt (/ l (sin k)))))) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k))))) (fma 2 1.0 (pow (/ k t) 2.0)))) l)
284.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt (/ l (sin k))) (cbrt (/ l (sin k)))))
470.0ms
(* (* (* (tan k) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt (/ l (sin k))) (cbrt (/ l (sin k)))))) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k))))) (fma 2 1.0 (pow (/ k t) 2.0)))

simplify610.0ms

Counts
253 → 253
Iterations

Useful iterations: done (599.0ms)

IterNodesCost
049211557
1157710795
done500010645

prune1.0s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 20.5b

localize32.0ms

Local error

Found 4 expressions with local error:

2.5b
(cbrt (/ l (sin k)))
2.5b
(cbrt (/ l (sin k)))
6.3b
(* (/ 2.0 (* (* (* (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k))))) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k))))) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k))))) (fma 2 1.0 (pow (/ k t) 2.0)))) l)
12.8b
(* (* (* (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k))))) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k))))) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k))))) (fma 2 1.0 (pow (/ k t) 2.0)))

rewrite6.8s

Algorithm
rewrite-expression-head
Rules
1203×add-exp-log
713×prod-exp
428×div-exp
167×add-cbrt-cube
115×cbrt-unprod
114×pow-to-exp pow-exp
65×associate-*l/
50×cbrt-undiv
34×frac-times
26×cbrt-prod
24×add-sqr-sqrt
23×associate-*l*
22×add-cube-cbrt *-un-lft-identity
21×times-frac
20×pow1
16×tan-quot
15×associate-/r/
14×associate-*r/
11×pow-prod-down
6×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×div-inv
2×cbrt-div pow1/3 *-commutative fma-udef
1×distribute-rgt-in distribute-lft-in unswap-sqr
Counts
4 → 325
Calls
4 calls:
2.0ms
(cbrt (/ l (sin k)))
2.0ms
(cbrt (/ l (sin k)))
5.6s
(* (/ 2.0 (* (* (* (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k))))) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k))))) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k))))) (fma 2 1.0 (pow (/ k t) 2.0)))) l)
1.2s
(* (* (* (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k))))) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k))))) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k))))) (fma 2 1.0 (pow (/ k t) 2.0)))

series1.8s

Counts
4 → 12
Calls
4 calls:
158.0ms
(cbrt (/ l (sin k)))
164.0ms
(cbrt (/ l (sin k)))
951.0ms
(* (/ 2.0 (* (* (* (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k))))) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k))))) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k))))) (fma 2 1.0 (pow (/ k t) 2.0)))) l)
486.0ms
(* (* (* (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k))))) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k))))) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k))))) (fma 2 1.0 (pow (/ k t) 2.0)))

simplify940.0ms

Counts
337 → 337
Iterations

Useful iterations: done (919.0ms)

IterNodesCost
055717013
1187515692
done500114774

prune1.1s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 18.3b

regimes996.0ms

Accuracy

30.7% (2.4b remaining)

Error of 18.7b against oracle of 16.3b and baseline of 19.8b

bsearch278.0ms

Steps
ItersRangePoint
4
8.153705944602147e-176
1.200976953367537e-175
8.274207931760685e-176
7
-4.087386172615961e-89
-2.4342644268904678e-91
-2.484142728377253e-91

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
043156
157156
done57156

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.8s2039×body1280valid
943.0ms1636×body640valid
727.0ms6034×body80valid
340.0ms853×body320valid
116.0ms435×body160valid