Details

Time bar (total: 24.4s)

sample142.0ms

Algorithm
intervals
Results
45.0ms273×body80valid
24.0ms31×body1280valid
24.0ms40×body640valid
13.0ms30×body320valid
3.0ms12×body160valid

simplify3.0s

Counts
1 → 1
Iterations
IterNodes
done5003
51878
4761
3231
272
134
017

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.6b

localize22.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
2.6b
(cos (/ (+ phi2 phi1) 2.0))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×*-un-lft-identity
8×associate-*l*
7×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
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:
6.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
29.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
23.0ms
(cos (/ (+ phi2 phi1) 2.0))

series1.2s

Counts
3 → 9
Calls
3 calls:
1.0s
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
131.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
44.0ms
(cos (/ (+ phi2 phi1) 2.0))

simplify2.4s

Counts
62 → 62
Iterations
IterNodes
done5006
33706
2913
1306
0127

prune564.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.4b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2.0)))))
0.3b
(log1p (expm1 (cos (/ (+ phi2 phi1) 2.0))))
0.5b
(expm1 (cos (/ (+ phi2 phi1) 2.0)))
2.6b
(cos (/ (+ phi2 phi1) 2.0))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity
6×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
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-- pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod flip-- distribute-lft-out-- expm1-udef difference-of-squares unswap-sqr
Counts
4 → 55
Calls
4 calls:
17.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2.0)))))
0.0ms
(log1p (expm1 (cos (/ (+ phi2 phi1) 2.0))))
0.0ms
(expm1 (cos (/ (+ phi2 phi1) 2.0)))
10.0ms
(cos (/ (+ phi2 phi1) 2.0))

series394.0ms

Counts
4 → 12
Calls
4 calls:
190.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2.0)))))
76.0ms
(log1p (expm1 (cos (/ (+ phi2 phi1) 2.0))))
92.0ms
(expm1 (cos (/ (+ phi2 phi1) 2.0)))
37.0ms
(cos (/ (+ phi2 phi1) 2.0))

simplify2.0s

Counts
67 → 67
Iterations
IterNodes
done5006
31638
2525
1219
0100

prune652.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.4b

localize47.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (* (cos (/ (+ phi1 phi2) 2.0)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))))
2.6b
(cos (/ (+ phi1 phi2) 2.0))
2.6b
(cos (/ (+ phi1 phi2) 2.0))
2.6b
(cos (/ (+ phi1 phi2) 2.0))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt log1p-expm1-u add-log-exp
1×cbrt-prod cbrt-div pow1/3 cube-unmult associate-*r/ cos-mult rem-cbrt-cube
Counts
4 → 40
Calls
4 calls:
15.0ms
(cbrt (* (cos (/ (+ phi1 phi2) 2.0)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))))
13.0ms
(cos (/ (+ phi1 phi2) 2.0))
13.0ms
(cos (/ (+ phi1 phi2) 2.0))
9.0ms
(cos (/ (+ phi1 phi2) 2.0))

series145.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(cbrt (* (cos (/ (+ phi1 phi2) 2.0)) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))))
31.0ms
(cos (/ (+ phi1 phi2) 2.0))
39.0ms
(cos (/ (+ phi1 phi2) 2.0))
39.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify3.4s

Counts
52 → 52
Iterations
IterNodes
done5016
52806
4988
3392
2154
187
048

prune670.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (cos (/ (+ phi2 phi1) 2.0)))
0.2b
(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi2 phi1) 2.0)))))
0.5b
(log (exp (cos (/ (+ phi2 phi1) 2.0))))
2.6b
(cos (/ (+ phi2 phi1) 2.0))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×*-un-lft-identity
12×add-cube-cbrt
9×log-prod exp-prod
8×pow1 log-pow
7×associate-*r*
6×add-cbrt-cube add-exp-log
5×associate-*l* add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×distribute-rgt-in distribute-lft-in
2×associate-*l/
1×flip3-- rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod flip-- distribute-lft-out-- difference-of-squares unswap-sqr rem-exp-log
Counts
4 → 73
Calls
4 calls:
11.0ms
(exp (cos (/ (+ phi2 phi1) 2.0)))
41.0ms
(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi2 phi1) 2.0)))))
29.0ms
(log (exp (cos (/ (+ phi2 phi1) 2.0))))
9.0ms
(cos (/ (+ phi2 phi1) 2.0))

series275.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(exp (cos (/ (+ phi2 phi1) 2.0)))
141.0ms
(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi2 phi1) 2.0)))))
29.0ms
(log (exp (cos (/ (+ phi2 phi1) 2.0))))
41.0ms
(cos (/ (+ phi2 phi1) 2.0))

simplify2.3s

Counts
85 → 85
Iterations
IterNodes
done5003
31990
2600
1245
0119

prune849.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.4b

regimes1.1s

Accuracy

0% (0.2b remaining)

Error of 4.0b against oracle of 3.7b and baseline of 4.0b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done19
119
016

end0.0ms

sample5.0s

Algorithm
intervals
Results
1.8s8291×body80valid
1.2s797×body1280valid
846.0ms1305×body640valid
519.0ms771×body320valid
90.0ms357×body160valid