Details

Time bar (total: 4.5m)

sample903.0ms

Algorithm
intervals
Results
322.0ms79×body2560valid
200.0ms131×body1280valid
178.0ms29×body5120valid
121.0ms91×body640valid
21.0ms70×body80valid
20.0ms23×body320valid
4.0ms7×body160valid

simplify6.8s

Counts
1 → 1
Iterations
IterNodes
done5000
43734
3704
2144
144
019

prune42.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.9b

localize197.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 2.0 (pow (/ k t) 2.0))
6.5b
(/ (* l l) (* (sin k) (tan k)))
16.7b
(/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k))))
28.0b
(/ (/ 2.0 (pow (/ k t) 2.0)) (/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k)))))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
9211×times-frac
3212×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
2953×unpow-prod-down
656×div-inv
491×sqr-pow
467×add-exp-log
459×associate-/r/
401×tan-quot associate-*r/
331×div-exp
92×add-cbrt-cube
76×prod-exp
71×associate-/r*
66×associate-/l*
64×pow-exp
50×cbrt-undiv
47×pow-to-exp
16×cbrt-unprod
4×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
1×associate-/l/
Counts
4 → 2997
Calls
4 calls:
44.0ms
(/ 2.0 (pow (/ k t) 2.0))
72.0ms
(/ (* l l) (* (sin k) (tan k)))
112.0ms
(/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k))))
274.0ms
(/ (/ 2.0 (pow (/ k t) 2.0)) (/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k)))))

series3.5s

Counts
4 → 12
Calls
4 calls:
430.0ms
(/ 2.0 (pow (/ k t) 2.0))
312.0ms
(/ (* l l) (* (sin k) (tan k)))
795.0ms
(/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k))))
1.9s
(/ (/ 2.0 (pow (/ k t) 2.0)) (/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k)))))

simplify11.1s

Counts
3009 → 3009
Iterations
IterNodes
done5073
05073

prune58.1s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 12.6b

localize214.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (* (pow t 1.0) (pow k 2.0)))
6.5b
(* (pow t 1.0) (pow k 2.0))
6.5b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.7b
(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite711.0ms

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×*-un-lft-identity add-cube-cbrt
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 insert-posit16 log1p-expm1-u div-inv associate-/l* add-log-exp
3×unpow2
2×clear-num frac-2neg *-commutative
1×associate-*r/ pow-flip inv-pow
Counts
4 → 612
Calls
4 calls:
74.0ms
(/ 1 (* (pow t 1.0) (pow k 2.0)))
72.0ms
(* (pow t 1.0) (pow k 2.0))
81.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
256.0ms
(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series4.6s

Counts
4 → 12
Calls
4 calls:
1.2s
(/ 1 (* (pow t 1.0) (pow k 2.0)))
1.2s
(* (pow t 1.0) (pow k 2.0))
292.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1.9s
(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify9.4s

Counts
624 → 624
Iterations
IterNodes
done5013
23077
11169
0449

prune2.6s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 7.2b

localize213.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ l (sin k)) (/ l (sin k)))
0.7b
(/ 1 (pow k 2.0))
7.0b
(* (pow (/ 1 (pow t 1.0)) 1.0) (* (* (* (/ l (sin k)) (/ l (sin k))) (cos k)) (pow (/ 1 (pow k 2.0)) 1.0)))
13.8b
(* (* (* (/ l (sin k)) (/ l (sin k))) (cos k)) (pow (/ 1 (pow k 2.0)) 1.0))

rewrite2.9s

Algorithm
rewrite-expression-head
Rules
4662×add-exp-log
3220×prod-exp
1966×pow-exp
1540×div-exp
607×pow-to-exp
456×rec-exp 1-exp
103×times-frac
90×add-sqr-sqrt
80×unpow-prod-down
78×*-un-lft-identity add-cube-cbrt
76×add-cbrt-cube
43×associate-*r* associate-*l*
41×cbrt-unprod
15×associate-*l/
13×cbrt-undiv swap-sqr
12×sqr-pow
11×pow1
7×associate-/r* div-inv
6×associate-*r/
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×frac-times *-commutative associate-/l*
1×pow2 clear-num frac-2neg pow-plus pow-prod-down pow-sqr pow-prod-up pow-flip inv-pow
Counts
4 → 1175
Calls
4 calls:
92.0ms
(* (/ l (sin k)) (/ l (sin k)))
32.0ms
(/ 1 (pow k 2.0))
1.8s
(* (pow (/ 1 (pow t 1.0)) 1.0) (* (* (* (/ l (sin k)) (/ l (sin k))) (cos k)) (pow (/ 1 (pow k 2.0)) 1.0)))
564.0ms
(* (* (* (/ l (sin k)) (/ l (sin k))) (cos k)) (pow (/ 1 (pow k 2.0)) 1.0))

series3.0s

Counts
4 → 12
Calls
4 calls:
173.0ms
(* (/ l (sin k)) (/ l (sin k)))
733.0ms
(/ 1 (pow k 2.0))
1.4s
(* (pow (/ 1 (pow t 1.0)) 1.0) (* (* (* (/ l (sin k)) (/ l (sin k))) (cos k)) (pow (/ 1 (pow k 2.0)) 1.0)))
708.0ms
(* (* (* (/ l (sin k)) (/ l (sin k))) (cos k)) (pow (/ 1 (pow k 2.0)) 1.0))

simplify5.9s

Counts
1187 → 1187
Iterations
IterNodes
done5000
12503
0907

prune4.0s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 4.8b

localize319.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ l (sin k)) (/ l (sin k)))
2.1b
(* (* (* (* (/ l (sin k)) (/ l (sin k))) (cos k)) (pow (/ 1 (pow k (/ 2.0 2))) 1.0)) (pow (/ 1 (pow k (/ 2.0 2))) 1.0))
6.4b
(* (* (* (/ l (sin k)) (/ l (sin k))) (cos k)) (pow (/ 1 (pow k (/ 2.0 2))) 1.0))
7.0b
(* (pow (/ 1 (pow t 1.0)) 1.0) (* (* (* (* (/ l (sin k)) (/ l (sin k))) (cos k)) (pow (/ 1 (pow k (/ 2.0 2))) 1.0)) (pow (/ 1 (pow k (/ 2.0 2))) 1.0)))

rewrite16.6s

Algorithm
rewrite-expression-head
Rules
66428×add-exp-log
50176×prod-exp
35984×pow-exp
24148×div-exp
11072×pow-to-exp
8304×rec-exp 1-exp
116×add-cbrt-cube
103×times-frac
102×unpow-prod-down
89×add-sqr-sqrt
77×*-un-lft-identity add-cube-cbrt
72×associate-*r*
71×cbrt-unprod
44×associate-*l*
28×associate-*l/
16×cbrt-undiv
13×swap-sqr
12×sqr-pow
11×pow1
7×associate-*r/ div-inv
4×expm1-log1p-u frac-times *-commutative insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
1×pow2 pow-plus pow-prod-down pow-sqr pow-prod-up
Counts
4 → 11695
Calls
4 calls:
60.0ms
(* (/ l (sin k)) (/ l (sin k)))
2.3s
(* (* (* (* (/ l (sin k)) (/ l (sin k))) (cos k)) (pow (/ 1 (pow k (/ 2.0 2))) 1.0)) (pow (/ 1 (pow k (/ 2.0 2))) 1.0))
638.0ms
(* (* (* (/ l (sin k)) (/ l (sin k))) (cos k)) (pow (/ 1 (pow k (/ 2.0 2))) 1.0))
6.7s
(* (pow (/ 1 (pow t 1.0)) 1.0) (* (* (* (* (/ l (sin k)) (/ l (sin k))) (cos k)) (pow (/ 1 (pow k (/ 2.0 2))) 1.0)) (pow (/ 1 (pow k (/ 2.0 2))) 1.0)))

series3.0s

Counts
4 → 12
Calls
4 calls:
183.0ms
(* (/ l (sin k)) (/ l (sin k)))
722.0ms
(* (* (* (* (/ l (sin k)) (/ l (sin k))) (cos k)) (pow (/ 1 (pow k (/ 2.0 2))) 1.0)) (pow (/ 1 (pow k (/ 2.0 2))) 1.0))
697.0ms
(* (* (* (/ l (sin k)) (/ l (sin k))) (cos k)) (pow (/ 1 (pow k (/ 2.0 2))) 1.0))
1.4s
(* (pow (/ 1 (pow t 1.0)) 1.0) (* (* (* (* (/ l (sin k)) (/ l (sin k))) (cos k)) (pow (/ 1 (pow k (/ 2.0 2))) 1.0)) (pow (/ 1 (pow k (/ 2.0 2))) 1.0)))

simplify15.5s

Counts
11707 → 11707
Iterations
IterNodes
done5000
04084

prune1.3m

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 3.9b

regimes3.1s

Accuracy

38.5% (6.2b remaining)

Error of 10.7b against oracle of 4.5b and baseline of 14.6b

bsearch1.4s

Steps
ItersRangePoint
6
3.302865865338161e+140
2.346698867006384e+141
2.3132826167896824e+141
9
-2.0274263258127503e+155
-3.7852266759278375e+149
-7.701141167434097e+153

simplify37.0ms

Iterations
IterNodes
done56
156
045

end0.0ms

sample33.0s

Algorithm
intervals
Results
9.9s4087×body1280valid
8.8s2214×body2560valid
7.4s923×body5120valid
4.2s2494×body640valid
956.0ms974×body320valid
656.0ms2015×body80valid
342.0ms488×body160valid