Details

Time bar (total: 32.7s)

sample101.0ms

Algorithm
intervals
Results
29.0ms27×body1280valid
20.0ms236×body80valid
17.0ms45×body640valid
5.0ms18×body320valid
3.0ms12×body160valid

simplify3.9s

Counts
1 → 1
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
01732
13416
27616
325716
482616
5235516
done500016

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
0.1b
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
4.6b
(cos (/ (+ phi1 phi2) 2.0))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-exp-log add-cube-cbrt associate-*l* add-cbrt-cube
6×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod unswap-sqr
1×hypot-udef flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 63
Calls
4 calls:
0.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
8.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
39.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
14.0ms
(cos (/ (+ phi1 phi2) 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
538.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
779.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
152.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
38.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify2.6s

Counts
75 → 75
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01391279
13271271
29601077
331941060
done50001059

prune439.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
0.2b
(log1p (expm1 (cos (/ (+ phi1 phi2) 2.0))))
0.5b
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
4.6b
(cos (/ (+ phi1 phi2) 2.0))

rewrite48.0ms

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×associate-*l* log1p-expm1-u
4×expm1-log1p-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:
24.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
0.0ms
(log1p (expm1 (cos (/ (+ phi1 phi2) 2.0))))
0.0ms
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
21.0ms
(cos (/ (+ phi1 phi2) 2.0))

series399.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
85.0ms
(log1p (expm1 (cos (/ (+ phi1 phi2) 2.0))))
107.0ms
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
29.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify2.5s

Counts
67 → 67
Iterations

Useful iterations: done (2.5s)

IterNodesCost
0101813
1207719
2522627
31532622
done5000618

prune472.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ 1 (expm1 (cos (/ (+ phi1 phi2) 2.0))))
0.5b
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
0.5b
(log (+ 1 (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
4.6b
(cos (/ (+ phi1 phi2) 2.0))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
6×add-sqr-sqrt add-cube-cbrt add-log-exp
5×pow1 add-exp-log log1p-expm1-u
4×expm1-log1p-u log-prod add-cbrt-cube
3×fma-def
2×log-div flip3-+ flip-+ distribute-lft-out expm1-udef
1×+-commutative associate-+r- expm1-log1p log1p-def rem-log-exp sum-log log-pow
Counts
4 → 56
Calls
4 calls:
7.0ms
(+ 1 (expm1 (cos (/ (+ phi1 phi2) 2.0))))
0.0ms
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
5.0ms
(log (+ 1 (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
12.0ms
(cos (/ (+ phi1 phi2) 2.0))

series340.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(+ 1 (expm1 (cos (/ (+ phi1 phi2) 2.0))))
101.0ms
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
89.0ms
(log (+ 1 (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
58.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify8.0s

Counts
68 → 68
Iterations

Useful iterations: 4 (1.3s)

IterNodesCost
090819
1184664
2370611
3829603
42038598
54642598
done5000598

prune430.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ 1 (expm1 (cos (/ (+ phi1 phi2) 2.0))))
0.5b
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
0.5b
(log (* 1 (+ 1 (expm1 (cos (/ (+ phi1 phi2) 2.0))))))
4.6b
(cos (/ (+ phi1 phi2) 2.0))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
8×add-exp-log
7×pow1 *-un-lft-identity
6×add-log-exp
5×add-sqr-sqrt add-cube-cbrt log1p-expm1-u
4×expm1-log1p-u add-cbrt-cube
3×fma-def rem-log-exp
2×log-div flip3-+ associate-*r/ prod-exp log-pow flip-+ expm1-udef
1×+-commutative associate-+r- log-prod expm1-log1p 1-exp pow-prod-down sum-log distribute-lft-out
Counts
4 → 55
Calls
4 calls:
12.0ms
(+ 1 (expm1 (cos (/ (+ phi1 phi2) 2.0))))
1.0ms
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
20.0ms
(log (* 1 (+ 1 (expm1 (cos (/ (+ phi1 phi2) 2.0))))))
29.0ms
(cos (/ (+ phi1 phi2) 2.0))

series317.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(+ 1 (expm1 (cos (/ (+ phi1 phi2) 2.0))))
105.0ms
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
77.0ms
(log (* 1 (+ 1 (expm1 (cos (/ (+ phi1 phi2) 2.0))))))
48.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify5.1s

Counts
67 → 67
Iterations

Useful iterations: 4 (1.9s)

IterNodesCost
091794
1195618
2428572
3942564
42258559
done5000559

prune469.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.0b

regimes694.0ms

Accuracy

0% (0.2b remaining)

Error of 3.4b against oracle of 3.3b and baseline of 3.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01618
11918
done1918

end0.0ms

sample5.2s

Algorithm
intervals
Results
1.8s8440×body80valid
866.0ms1213×body640valid
798.0ms751×body1280valid
786.0ms734×body320valid
140.0ms379×body160valid