Details

Time bar (total: 26.4s)

sample102.0ms

Algorithm
intervals
Results
31.0ms50×body1280valid
18.0ms38×body640valid
16.0ms138×body80valid
7.0ms18×body320valid
3.0ms12×body160valid

simplify3.0s

Counts
1 → 1
Iterations
IterNodes
done5042
72651
6720
5277
4165
3112
268
134
017

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos (/ K 2.0)) J)
0.2b
(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
9.0b
(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
9.1b
(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

rewrite403.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
17×pow1
16×*-un-lft-identity
15×add-sqr-sqrt add-cbrt-cube
12×add-cube-cbrt
10×associate-*l* prod-exp
8×sqrt-prod
7×unpow-prod-down pow-prod-down cbrt-unprod
4×sqrt-div associate-*r* pow-exp add-log-exp
3×pow-unpow times-frac div-exp
2×flip3-+ associate-*l/ *-commutative flip-+ distribute-lft-out
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv unswap-sqr sqr-pow
Counts
4 → 85
Calls
4 calls:
12.0ms
(* (cos (/ K 2.0)) J)
21.0ms
(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
289.0ms
(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
76.0ms
(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

series900.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(* (cos (/ K 2.0)) J)
225.0ms
(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
361.0ms
(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
242.0ms
(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

simplify1.9s

Counts
97 → 97
Iterations
IterNodes
done5000
21523
1515
0203

prune783.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos (* 0.5 K)) J)
0.2b
(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
9.0b
(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (* 0.5 K)) J) -2.0))
9.1b
(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

rewrite446.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
17×pow1
16×*-un-lft-identity
15×add-sqr-sqrt add-cbrt-cube
12×add-cube-cbrt
10×associate-*l* prod-exp
8×sqrt-prod
7×unpow-prod-down pow-prod-down cbrt-unprod
4×sqrt-div associate-*r* pow-exp add-log-exp
3×pow-unpow times-frac div-exp
2×flip3-+ associate-*l/ *-commutative flip-+ distribute-lft-out
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv unswap-sqr sqr-pow
Counts
4 → 85
Calls
4 calls:
12.0ms
(* (cos (* 0.5 K)) J)
18.0ms
(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
317.0ms
(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (* 0.5 K)) J) -2.0))
96.0ms
(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

series1.3s

Counts
4 → 12
Calls
4 calls:
90.0ms
(* (cos (* 0.5 K)) J)
613.0ms
(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
365.0ms
(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (* 0.5 K)) J) -2.0))
187.0ms
(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

simplify2.2s

Counts
97 → 97
Iterations
IterNodes
done5001
21538
1521
0206

prune708.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos (/ K 2.0)))
0.3b
(cbrt (cos (/ K 2.0)))
9.0b
(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))) (* (cbrt (cos (/ K 2.0))) J)) -2.0))
9.1b
(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

rewrite632.0ms

Algorithm
rewrite-expression-head
Rules
30×pow1
29×add-exp-log
23×add-cbrt-cube
19×pow-prod-down prod-exp cbrt-unprod
13×*-un-lft-identity
10×add-sqr-sqrt
9×add-cube-cbrt
8×sqrt-prod
7×associate-*l*
6×cbrt-prod
4×sqrt-div add-log-exp
2×flip3-+ pow1/3 associate-*l/ flip-+ distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* *-commutative
Counts
4 → 74
Calls
4 calls:
1.0ms
(cbrt (cos (/ K 2.0)))
1.0ms
(cbrt (cos (/ K 2.0)))
523.0ms
(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))) (* (cbrt (cos (/ K 2.0))) J)) -2.0))
104.0ms
(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

series992.0ms

Counts
4 → 12
Calls
4 calls:
243.0ms
(cbrt (cos (/ K 2.0)))
211.0ms
(cbrt (cos (/ K 2.0)))
347.0ms
(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))) (* (cbrt (cos (/ K 2.0))) J)) -2.0))
191.0ms
(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

simplify2.5s

Counts
86 → 86
Iterations
IterNodes
done5004
21529
1412
0153

prune685.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 10.0b

localize94.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt J)
0.6b
(cbrt J)
9.0b
(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (* (cos (/ K 2.0)) (* (cbrt J) (cbrt J))) (cbrt J)) -2.0))
9.1b
(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
25×pow1
24×add-exp-log
19×add-cbrt-cube
15×pow-prod-down prod-exp cbrt-unprod
13×*-un-lft-identity
10×add-sqr-sqrt
9×add-cube-cbrt
8×sqrt-prod
7×associate-*l*
6×cbrt-prod
4×sqrt-div add-log-exp
2×flip3-+ pow1/3 associate-*l/ flip-+ distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* *-commutative
Counts
4 → 71
Calls
4 calls:
2.0ms
(cbrt J)
1.0ms
(cbrt J)
975.0ms
(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (* (cos (/ K 2.0)) (* (cbrt J) (cbrt J))) (cbrt J)) -2.0))
118.0ms
(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

series1.2s

Counts
4 → 12
Calls
4 calls:
284.0ms
(cbrt J)
309.0ms
(cbrt J)
349.0ms
(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (* (cos (/ K 2.0)) (* (cbrt J) (cbrt J))) (cbrt J)) -2.0))
214.0ms
(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

simplify2.3s

Counts
83 → 83
Iterations
IterNodes
done5001
21394
1399
0148

prune547.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 10.0b

regimes828.0ms

Accuracy

16.2% (7.9b remaining)

Error of 16.3b against oracle of 8.4b and baseline of 17.8b

bsearch186.0ms

Steps
ItersRangePoint
8
1.1230878641706415e-202
1.1274284215203474e-198
1.4278873675692663e-201
6
-4.323701454343753e-196
-5.442375696279729e-197
-8.069925597012032e-197

simplify8.0ms

Iterations
IterNodes
done42
142
030

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.2s1545×body1280valid
1.0s4249×body80valid
666.0ms1229×body640valid
246.0ms663×body320valid
107.0ms317×body160valid