Details

Time bar (total: 25.0s)

sample129.0ms

Algorithm
intervals
Results
40.0ms49×body1280valid
25.0ms25×body320valid
22.0ms37×body640valid
20.0ms137×body80valid
2.0ms8×body160valid

simplify3.0s

Counts
1 → 1
Iterations
IterNodes
done5038
54827
4843
3216
285
136
017

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.9b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ U (* (* 2 (cos (/ K 2))) J))
0.1b
(* (cos (/ K 2)) (* -2 J))
0.1b
(* (* 2 (cos (/ K 2))) J)
7.9b
(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (* (cos (/ K 2)) (* -2 J)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
32×add-cbrt-cube add-exp-log
23×pow1
15×prod-exp cbrt-unprod
12×pow-prod-down
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×associate-*l*
5×associate-*r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv times-frac div-exp *-commutative associate-/l*
1×clear-num associate-/r* frac-2neg div-inv
Counts
4 → 92
Calls
4 calls:
15.0ms
(/ U (* (* 2 (cos (/ K 2))) J))
15.0ms
(* (cos (/ K 2)) (* -2 J))
16.0ms
(* (* 2 (cos (/ K 2))) J)
39.0ms
(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (* (cos (/ K 2)) (* -2 J)))

series540.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(/ U (* (* 2 (cos (/ K 2))) J))
70.0ms
(* (cos (/ K 2)) (* -2 J))
61.0ms
(* (* 2 (cos (/ K 2))) J)
291.0ms
(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (* (cos (/ K 2)) (* -2 J)))

simplify1.6s

Counts
104 → 104
Iterations
IterNodes
done5001
21590
1418
0164

prune660.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2)))
0.1b
(/ U (* (* 2 (cos (/ K 2))) J))
0.1b
(* (* 2 (cos (/ K 2))) J)
7.9b
(* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2))) (* -2 J))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
32×add-cbrt-cube add-exp-log
23×pow1
15×prod-exp cbrt-unprod
12×pow-prod-down
11×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
7×associate-*r*
5×associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv times-frac div-exp *-commutative associate-/l*
1×clear-num associate-/r* frac-2neg div-inv unswap-sqr
Counts
4 → 93
Calls
4 calls:
7.0ms
(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2)))
16.0ms
(/ U (* (* 2 (cos (/ K 2))) J))
22.0ms
(* (* 2 (cos (/ K 2))) J)
26.0ms
(* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2))) (* -2 J))

series676.0ms

Counts
4 → 12
Calls
4 calls:
236.0ms
(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2)))
82.0ms
(/ U (* (* 2 (cos (/ K 2))) J))
60.0ms
(* (* 2 (cos (/ K 2))) J)
298.0ms
(* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2))) (* -2 J))

simplify2.1s

Counts
105 → 105
Iterations
IterNodes
done5002
21593
1419
0165

prune592.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.0b

localize76.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (* (cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))) (* (cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (cos (/ K 2)) (* -2 J))))
8.1b
(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
8.1b
(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
8.1b
(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
36×pow1 add-exp-log
24×pow-prod-down prod-exp cbrt-unprod
22×add-cbrt-cube
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×associate-*r* associate-*l* *-commutative
Counts
4 → 79
Calls
4 calls:
153.0ms
(* (* (cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))) (* (cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (cos (/ K 2)) (* -2 J))))
1.0ms
(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
1.0ms
(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
1.0ms
(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

series1.4s

Counts
4 → 12
Calls
4 calls:
375.0ms
(* (* (cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))) (* (cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (cos (/ K 2)) (* -2 J))))
369.0ms
(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
363.0ms
(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
312.0ms
(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

simplify4.1s

Counts
91 → 91
Iterations
IterNodes
done5005
34933
21107
1309
0124

prune601.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.0b

localize126.0ms

Local error

Found 4 expressions with local error:

8.1b
(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
8.1b
(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
8.1b
(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
8.1b
(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube pow1/3 add-exp-log insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 56
Calls
4 calls:
1.0ms
(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
9.0ms
(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
1.0ms
(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
1.0ms
(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

series1.5s

Counts
4 → 12
Calls
4 calls:
346.0ms
(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
385.0ms
(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
350.0ms
(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
405.0ms
(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

simplify1.9s

Counts
68 → 68
Iterations
IterNodes
done5012
41981
3528
2185
187
049

prune679.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.0b

regimes551.0ms

Accuracy

-9.1% (4.4b remaining)

Error of 8.2b against oracle of 3.8b and baseline of 7.9b

bsearch80.0ms

Steps
ItersRangePoint
5
-8.091786763451962e+243
-4.0158444704749664e+243
-6.5450850664377556e+243

simplify3.0ms

Iterations
IterNodes
done26
126
019

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.8s1477×body1280valid
1.2s4333×body80valid
792.0ms1252×body640valid
290.0ms629×body320valid
86.0ms310×body160valid