Details

Time bar (total: 14.9s)

sample64.0ms

Algorithm
intervals
Results
21.0ms290×body80valid
12.0ms41×body640valid
7.0ms18×body1280valid
4.0ms17×body320valid
1.0ms6×body160valid

simplify2.5s

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01732
13416
27616
319516
449116
5138616
6495016
done500016

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
3.4b
(cos (/ (+ phi1 phi2) 2.0))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×*-un-lft-identity
8×associate-*l*
7×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
6×associate-*r*
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod unswap-sqr
1×flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
3 → 53
Calls
3 calls:
3.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
11.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))

series580.0ms

Counts
3 → 9
Calls
3 calls:
462.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
90.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify1.5s

Counts
62 → 62
Iterations

Useful iterations: 3 (731.0ms)

IterNodesCost
0125990
1275983
2842835
33074824
done5000824

prune223.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
0.2b
(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
0.4b
(log1p (cos (/ (+ phi1 phi2) 2.0)))
3.4b
(cos (/ (+ phi1 phi2) 2.0))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity
6×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
5×expm1-log1p-u associate-*l*
4×log1p-expm1-u add-log-exp
3×associate-*r*
2×associate-*l/
1×log1p-udef expm1-log1p flip3-- log1p-expm1 pow-prod-down prod-exp *-commutative flip-- cbrt-unprod distribute-lft-out-- expm1-udef difference-of-squares unswap-sqr
Counts
4 → 55
Calls
4 calls:
10.0ms
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
0.0ms
(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
0.0ms
(log1p (cos (/ (+ phi1 phi2) 2.0)))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))

series252.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
57.0ms
(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
54.0ms
(log1p (cos (/ (+ phi1 phi2) 2.0)))
29.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify1.8s

Counts
67 → 67
Iterations

Useful iterations: 4 (915.0ms)

IterNodesCost
098808
1192718
2476622
31405619
43408616
done5001616

prune271.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
0.4b
(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
0.5b
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
3.4b
(cos (/ (+ phi1 phi2) 2.0))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
28×cbrt-prod
26×add-sqr-sqrt
17×*-un-lft-identity
15×add-cube-cbrt associate-*r*
10×unpow-prod-down cube-prod
7×pow1 add-exp-log
6×add-cbrt-cube
5×associate-*l* unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×cube-mult pow-unpow unpow3
2×associate-*l/
1×pow-to-exp flip3-- pow-pow pow1/3 pow-prod-down pow-exp prod-exp *-commutative flip-- rem-cbrt-cube cbrt-unprod distribute-lft-out-- rem-cube-cbrt difference-of-squares
Counts
4 → 97
Calls
4 calls:
19.0ms
(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
1.0ms
(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
1.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
5.0ms
(cos (/ (+ phi1 phi2) 2.0))

series191.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
26.0ms
(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
51.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
27.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify2.5s

Counts
109 → 109
Iterations

Useful iterations: 3 (960.0ms)

IterNodesCost
01311572
12751275
28881143
347981138
done50001138

prune360.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
3.4b
(cos (/ (+ phi1 phi2) 2.0))
3.4b
(cos (/ (+ phi1 phi2) 2.0))
3.4b
(cos (/ (+ phi1 phi2) 2.0))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-prod
1×pow1/3
Counts
4 → 40
Calls
4 calls:
1.0ms
(cbrt (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
7.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))

series219.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(cbrt (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify1.7s

Counts
52 → 52
Iterations

Useful iterations: 4 (168.0ms)

IterNodesCost
052537
193494
2165444
3319437
4816433
51925433
done5001433

prune275.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.1b

regimes388.0ms

Accuracy

0% (0.2b remaining)

Error of 3.5b against oracle of 3.4b and baseline of 3.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01618
11918
done1918

end0.0ms

sample1.8s

Algorithm
intervals
Results
555.0ms8373×body80valid
369.0ms1233×body640valid
330.0ms784×body1280valid
148.0ms718×body320valid
50.0ms359×body160valid