Details

Time bar (total: 41.1s)

sample219.0ms

Algorithm
intervals
Results
61.0ms133×body80valid
59.0ms53×body640valid
55.0ms40×body1280valid
13.0ms16×body320valid
8.0ms14×body160valid

simplify1000.0ms

Counts
1 → 1
Iterations
IterNodes
52067
4616
3185
279
134
017

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.6b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* J 2) (cos (/ K 2)))
0.2b
(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
7.4b
(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
11.1b
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

rewrite740.0ms

Algorithm
rewrite-expression-head
Rules
98×add-cbrt-cube add-exp-log
49×prod-exp cbrt-unprod
26×pow1
24×cbrt-undiv div-exp
19×add-sqr-sqrt
16×*-un-lft-identity add-cube-cbrt
14×associate-*l*
12×times-frac
11×associate-*r*
10×pow-prod-down
7×swap-sqr
6×sqrt-prod
4×sqrt-div insert-posit16 div-inv add-log-exp
3×associate-*l/ *-commutative
2×flip3-+ flip-+
1×pow2 frac-times rem-sqrt-square sqrt-pow1 pow-plus pow1/2 associate-*r/ pow-sqr pow-prod-up unswap-sqr
Counts
4 → 133
Calls
4 calls:
16.0ms
(* (* J 2) (cos (/ K 2)))
143.0ms
(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
365.0ms
(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
211.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series662.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(* (* J 2) (cos (/ K 2)))
148.0ms
(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
253.0ms
(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
182.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify1.5s

Counts
145 → 145
Iterations
IterNodes
23067
1664
0231

prune2.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* J 2) (cos (/ K 2)))
0.2b
(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
7.4b
(* (* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (cos (/ K 2))) (* -2 J))
11.1b
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

rewrite652.0ms

Algorithm
rewrite-expression-head
Rules
101×add-cbrt-cube add-exp-log
51×prod-exp cbrt-unprod
29×pow1
24×cbrt-undiv div-exp
17×add-sqr-sqrt
14×*-un-lft-identity add-cube-cbrt
12×times-frac pow-prod-down
11×associate-*r*
9×associate-*l*
7×swap-sqr
5×associate-*l/
4×sqrt-div insert-posit16 div-inv add-log-exp
3×*-commutative sqrt-prod
2×flip3-+ flip-+
1×pow2 frac-times rem-sqrt-square sqrt-pow1 pow-plus pow1/2 associate-*r/ pow-sqr pow-prod-up unswap-sqr
Counts
4 → 131
Calls
4 calls:
23.0ms
(* (* J 2) (cos (/ K 2)))
101.0ms
(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
334.0ms
(* (* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (cos (/ K 2))) (* -2 J))
191.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series595.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* (* J 2) (cos (/ K 2)))
137.0ms
(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
245.0ms
(* (* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (cos (/ K 2))) (* -2 J))
147.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify1.4s

Counts
143 → 143
Iterations
IterNodes
23038
1664
0231

prune2.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.0b

localize65.0ms

Local error

Found 4 expressions with local error:

10.2b
(sqrt (* (cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))))
17.0b
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
17.0b
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
17.0b
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

rewrite478.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
12×pow1
9×cbrt-prod sqrt-pow1 flip3-+ pow1/3 flip-+
8×sqrt-div
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×frac-times add-cbrt-cube add-exp-log insert-posit16 add-log-exp
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 rem-sqrt-square pow-plus pow1/2 sqrt-prod
Counts
4 → 70
Calls
4 calls:
196.0ms
(sqrt (* (cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))))
112.0ms
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
95.0ms
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
73.0ms
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series1.0s

Counts
4 → 12
Calls
4 calls:
273.0ms
(sqrt (* (cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))))
264.0ms
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
230.0ms
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
252.0ms
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify16.0s

Counts
82 → 82
Iterations
IterNodes
415585
31886
2444
1203
0115

prune1.6s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 9.0b

localize91.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ U J) (/ U J))
0.2b
(* (cos (* K 1/2)) (cos (* K 1/2)))
7.4b
(* (sqrt (+ (/ (* (* (/ U J) (/ U J)) 1/4) (* (cos (* K 1/2)) (cos (* K 1/2)))) 1)) (* (cos (/ K 2)) (* -2 J)))
11.1b
(sqrt (+ (/ (* (* (/ U J) (/ U J)) 1/4) (* (cos (* K 1/2)) (cos (* K 1/2)))) 1))

rewrite571.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
43×*-un-lft-identity
40×times-frac
39×add-cube-cbrt
28×pow1
27×add-cbrt-cube add-exp-log
23×associate-*l*
17×associate-*r*
16×swap-sqr
11×prod-exp cbrt-unprod
8×pow-prod-down sqrt-prod
5×unswap-sqr
4×cbrt-undiv sqrt-div div-exp insert-posit16 div-inv add-log-exp
3×associate-*l/ *-commutative
2×pow2 flip3-+ pow-plus pow-sqr pow-prod-up flip-+ distribute-lft-out
1×frac-times rem-sqrt-square sqr-cos sqrt-pow1 pow1/2 associate-*r/ cos-mult
Counts
4 → 141
Calls
4 calls:
13.0ms
(* (/ U J) (/ U J))
29.0ms
(* (cos (* K 1/2)) (cos (* K 1/2)))
369.0ms
(* (sqrt (+ (/ (* (* (/ U J) (/ U J)) 1/4) (* (cos (* K 1/2)) (cos (* K 1/2)))) 1)) (* (cos (/ K 2)) (* -2 J)))
158.0ms
(sqrt (+ (/ (* (* (/ U J) (/ U J)) 1/4) (* (cos (* K 1/2)) (cos (* K 1/2)))) 1))

series510.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (/ U J) (/ U J))
22.0ms
(* (cos (* K 1/2)) (cos (* K 1/2)))
270.0ms
(* (sqrt (+ (/ (* (* (/ U J) (/ U J)) 1/4) (* (cos (* K 1/2)) (cos (* K 1/2)))) 1)) (* (cos (/ K 2)) (* -2 J)))
173.0ms
(sqrt (+ (/ (* (* (/ U J) (/ U J)) 1/4) (* (cos (* K 1/2)) (cos (* K 1/2)))) 1))

simplify850.0ms

Counts
153 → 153
Iterations
IterNodes
22414
1714
0243

prune2.3s

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 9.0b

regimes523.0ms

Accuracy

13.1% (7.7b remaining)

Error of 16.3b against oracle of 8.6b and baseline of 17.5b

bsearch350.0ms

Steps
ItersRangePoint
7
1.5808418332513636e-257
2.759767119684114e-255
1.2100371248519592e-256
9
-4.351189563635498e-165
-2.8493599587798838e-173
-1.7365939269127396e-172

simplify5.0ms

Iterations
IterNodes
233
133
024

end0.0ms

sample5.8s

Algorithm
intervals
Results
2.0s1482×body1280valid
1.5s4273×body80valid
1.4s1300×body640valid
455.0ms628×body320valid
141.0ms320×body160valid