Details

Time bar (total: 1.0m)

sample785.0ms

Algorithm
intervals
Results
257.0ms78×body2560valid
196.0ms119×body1280valid
189.0ms31×body5120valid
62.0ms76×body640valid
24.0ms40×body320valid
10.0ms55×body80valid
4.0ms10×body160valid

simplify945.0ms

Counts
1 → 1
Iterations

Useful iterations: done (944.0ms)

IterNodesCost
01925
14425
214825
384123
done500121

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (/ (pow t 3.0) (* l l)) (sin k))
0.8b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
16.8b
(/ (pow t 3.0) (* l l))
28.4b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite389.0ms

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:
54.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
134.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
12.0ms
(/ (pow t 3.0) (* l l))
157.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series1.9s

Counts
4 → 12
Calls
4 calls:
368.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
433.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
274.0ms
(/ (pow t 3.0) (* l l))
864.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify933.0ms

Counts
374 → 374
Iterations

Useful iterations: done (913.0ms)

IterNodesCost
067010352
117859880
done50019414

prune3.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 16.4b

localize80.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
7.1b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.3b
(* (pow k 2.0) (pow t 1.0))
14.5b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite293.0ms

Algorithm
rewrite-expression-head
Rules
1597×add-exp-log
1095×prod-exp
882×pow-exp
668×div-exp
492×pow-to-exp
130×rec-exp 1-exp
37×add-sqr-sqrt
32×unpow-prod-down
20×add-cube-cbrt *-un-lft-identity add-cbrt-cube
19×times-frac associate-*r*
18×associate-*l*
14×sqr-pow
12×unswap-sqr
8×associate-/r*
6×cbrt-unprod
5×pow1
4×cbrt-undiv expm1-log1p-u log1p-expm1-u unpow2 add-log-exp
3×pow-unpow div-inv
2×*-commutative
1×pow-pow frac-2neg associate-*r/ clear-num associate-/l*
Counts
4 → 575
Calls
4 calls:
8.0ms
(pow (sin k) 2)
36.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
35.0ms
(* (pow k 2.0) (pow t 1.0))
123.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.5s

Counts
4 → 12
Calls
4 calls:
25.0ms
(pow (sin k) 2)
114.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
454.0ms
(* (pow k 2.0) (pow t 1.0))
911.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify823.0ms

Counts
587 → 587
Iterations

Useful iterations: done (785.0ms)

IterNodesCost
044614510
1135512991
done500012210

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.4b

localize53.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
0.4b
(pow (sin k) 2)
7.1b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
14.5b
(* (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)))

rewrite670.0ms

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:
91.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
7.0ms
(pow (sin k) 2)
35.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
183.0ms
(* (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)))

series1.7s

Counts
4 → 12
Calls
4 calls:
527.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
33.0ms
(pow (sin k) 2)
160.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
989.0ms
(* (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)))

simplify1.2s

Counts
1480 → 1480
Iterations

Useful iterations: done (1.1s)

IterNodesCost
060550477
1205133540
done500031701

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.5b

localize64.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
3.2b
(* (pow (/ (* (cbrt 1) (cbrt 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))))
7.1b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
11.0b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
22078×add-exp-log
15966×prod-exp
12575×pow-exp
9172×div-exp
6095×pow-to-exp
1310×rec-exp 1-exp
37×add-cbrt-cube
31×unpow-prod-down
29×times-frac
26×associate-*l*
25×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
14×cbrt-unprod
13×associate-*r*
9×associate-/r*
8×cbrt-undiv
7×sqr-pow
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 → 4466
Calls
4 calls:
35.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
202.0ms
(* (pow (/ (* (cbrt 1) (cbrt 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))))
20.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
129.0ms
(* (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:
548.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
961.0ms
(* (pow (/ (* (cbrt 1) (cbrt 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))))
125.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
962.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify3.8s

Counts
4478 → 4478
Iterations

Useful iterations: done (3.5s)

IterNodesCost
01213193011
14701150848
done5000150291

prune2.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 10.1b

regimes1.1s

Accuracy

1.8% (6.9b remaining)

Error of 17.8b against oracle of 10.9b and baseline of 17.9b

bsearch1.8s

Steps
ItersRangePoint
9
-4.2137813279987533e-255
-6.519820153015127e-261
-4.1734607541863057e-255
10
-1.6447817576318978e-149
-4.499027040135842e-161
-4.565740119288729e-161
7
-3.2729874464247947e+146
-2.198617807245503e+144
-3.2165648286178957e+146

simplify15.0ms

Iterations

Useful iterations: done (14.0ms)

IterNodesCost
053168
166113
27182
37482
done7481

end0.0ms

sample31.7s

Algorithm
intervals
Results
9.4s4083×body1280valid
7.9s2239×body2560valid
7.3s936×body5120valid
4.9s2534×body640valid
727.0ms1056×body320valid
451.0ms2023×body80valid
190.0ms417×body160valid