Details

Time bar (total: 1.1m)

sample807.0ms

Algorithm
intervals
Results
220.0ms134×body1280valid
213.0ms73×body2560valid
213.0ms29×body5120valid
85.0ms79×body640valid
23.0ms35×body320valid
13.0ms64×body80valid
4.0ms10×body160valid

simplify2.8s

Counts
1 → 1
Iterations

Useful iterations: 4 (1.5s)

IterNodesCost
01925
14425
214825
381623
4462521
done500021

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.5b

localize24.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (/ (pow t 3.0) (* l l)) (sin k))
1.0b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
16.9b
(/ (pow t 3.0) (* l l))
26.1b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite329.0ms

Algorithm
rewrite-expression-head
Rules
340×times-frac
272×add-exp-log
153×unpow-prod-down
144×add-sqr-sqrt
137×add-cube-cbrt *-un-lft-identity
128×div-exp
103×prod-exp
59×add-cbrt-cube
58×associate-*l/
54×associate-/r/
38×tan-quot
34×pow-exp
32×div-inv
24×pow-to-exp
21×cbrt-unprod
19×cbrt-undiv frac-times associate-*r/
18×associate-/r*
17×associate-/l*
15×sqr-pow
12×associate-*l*
11×pow1
6×associate-*r*
4×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp unswap-sqr
2×frac-2neg clear-num *-commutative
1×associate-/l/
Counts
4 → 362
Calls
4 calls:
41.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
90.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
20.0ms
(/ (pow t 3.0) (* l l))
147.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
360.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
436.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
274.0ms
(/ (pow t 3.0) (* l l))
769.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify989.0ms

Counts
374 → 374
Iterations

Useful iterations: done (970.0ms)

IterNodesCost
067010352
115169848
done50009342

prune2.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.0b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.0b
(* (pow k 2.0) (pow t 1.0))
15.9b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite323.0ms

Algorithm
rewrite-expression-head
Rules
1645×add-exp-log
1122×prod-exp
899×pow-exp
688×div-exp
509×pow-to-exp
140×rec-exp 1-exp
37×add-sqr-sqrt
29×unpow-prod-down
25×add-cbrt-cube
22×times-frac
20×add-cube-cbrt *-un-lft-identity
19×associate-*r*
18×associate-*l*
13×sqr-pow
12×unswap-sqr
9×associate-/r*
7×cbrt-unprod
6×cbrt-undiv
5×pow1
4×expm1-log1p-u log1p-expm1-u div-inv associate-/l* add-log-exp
3×unpow2
2×frac-2neg clear-num *-commutative
1×pow-flip associate-*r/ inv-pow
Counts
4 → 608
Calls
4 calls:
39.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
39.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
25.0ms
(* (pow k 2.0) (pow t 1.0))
118.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.3s

Counts
4 → 12
Calls
4 calls:
547.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
142.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
534.0ms
(* (pow k 2.0) (pow t 1.0))
1.0s
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify2.0s

Counts
620 → 620
Iterations

Useful iterations: done (1.9s)

IterNodesCost
049115125
1122012973
2298412703
done500012259

prune992.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin k) 2)
0.7b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.0b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
15.9b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite732.0ms

Algorithm
rewrite-expression-head
Rules
5603×add-exp-log
4515×prod-exp
3078×pow-exp
2032×div-exp
1869×pow-to-exp
434×rec-exp 1-exp
27×add-cbrt-cube
23×add-sqr-sqrt
22×times-frac
20×unpow-prod-down
18×add-cube-cbrt *-un-lft-identity
12×associate-*r*
11×associate-*l*
9×associate-/r*
8×cbrt-unprod
7×cbrt-undiv
6×pow1 sqr-pow
4×expm1-log1p-u log1p-expm1-u div-inv associate-/l* unpow2 add-log-exp
3×pow-unpow unswap-sqr
2×frac-2neg clear-num
1×pow-flip pow-pow associate-*r/ *-commutative inv-pow
Counts
4 → 1468
Calls
4 calls:
8.0ms
(pow (sin k) 2)
91.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
19.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
298.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.0s

Counts
4 → 12
Calls
4 calls:
32.0ms
(pow (sin k) 2)
558.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
104.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1.3s
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify2.1s

Counts
1480 → 1480
Iterations

Useful iterations: done (2.0s)

IterNodesCost
060550477
1152531964
2321231674
done500130411

prune1.0s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 8.2b

localize55.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
3.6b
(* (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
5.0b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
12.2b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
13973×add-exp-log
10155×prod-exp
8251×pow-exp
5914×div-exp
4231×pow-to-exp
920×rec-exp 1-exp
81×unpow-prod-down
64×times-frac
61×associate-*l*
49×add-sqr-sqrt
44×add-cube-cbrt *-un-lft-identity
37×add-cbrt-cube
21×sqrt-prod
14×cbrt-unprod
13×associate-*r*
12×sqr-pow
9×associate-/r*
8×cbrt-undiv
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
3×associate-*r/ unpow2 unswap-sqr
2×frac-2neg clear-num *-commutative
1×pow-flip inv-pow
Counts
4 → 3211
Calls
4 calls:
39.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
261.0ms
(* (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
21.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
122.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.6s

Counts
4 → 12
Calls
4 calls:
494.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
933.0ms
(* (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
138.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
994.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify3.2s

Counts
3223 → 3223
Iterations

Useful iterations: done (2.9s)

IterNodesCost
01021126601
12425106350
24569103275
done500095088

prune1.5s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 7.8b

regimes866.0ms

Accuracy

50.9% (4.6b remaining)

Error of 13.5b against oracle of 8.9b and baseline of 18.3b

bsearch3.0s

Steps
ItersRangePoint
9
4.61796087672408e+142
4.211818690154182e+148
4.1624864010972877e+148
9
3.52171888948357e-128
1.4516394228846858e-122
1.0269445451976019e-127
3
-7.892754447676382e-163
-5.427098322068537e-163
-7.730538530348133e-163
10
-6.354265220965125e+156
-1.7344183351890289e+146
-7.341974747858959e+153

simplify24.0ms

Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
079205
1100204
done100204

end0.0ms

sample33.5s

Algorithm
intervals
Results
10.1s4188×body1280valid
9.2s2235×body2560valid
7.6s950×body5120valid
4.0s2468×body640valid
1.1s1065×body320valid
535.0ms2058×body80valid
235.0ms489×body160valid