Details

Time bar (total: 24.7s)

sample224.0ms

Algorithm
intervals
Results
81.0ms266×body80valid
46.0ms39×body640valid
40.0ms27×body1280valid
17.0ms24×body320valid
6.0ms11×body160valid

simplify1.1s

Counts
1 → 1

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize34.0ms

Local error

Found 4 expressions with local error:

2.7b
(cos (/ (+ phi2 phi1) 2))
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
0.1b
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.0b
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt
6×associate-*r*
4×expm1-log1p-u insert-posit16 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 → 67
Calls
4 calls:
Slowest
19.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
8.0ms
(cos (/ (+ phi2 phi1) 2))
6.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
638.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
529.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
136.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
31.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.2s

Counts
79 → 79

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.6b

localize57.0ms

Local error

Found 4 expressions with local error:

2.7b
(cos (/ (+ phi2 phi1) 2))
0.4b
(log1p (cos (/ (+ phi2 phi1) 2)))
0.2b
(expm1 (log1p (cos (/ (+ phi2 phi1) 2))))
0.2b
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi2 phi1) 2)))))

rewrite32.0ms

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×expm1-log1p-u associate-*l*
4×insert-posit16 log1p-expm1-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 → 59
Calls
4 calls:
Slowest
20.0ms
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi2 phi1) 2)))))
10.0ms
(cos (/ (+ phi2 phi1) 2))
1.0ms
(log1p (cos (/ (+ phi2 phi1) 2)))
0.0ms
(expm1 (log1p (cos (/ (+ phi2 phi1) 2))))

series664.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
404.0ms
(log1p (cos (/ (+ phi2 phi1) 2)))
168.0ms
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi2 phi1) 2)))))
69.0ms
(expm1 (log1p (cos (/ (+ phi2 phi1) 2))))
24.0ms
(cos (/ (+ phi2 phi1) 2))

simplify2.4s

Counts
71 → 71

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.6b

localize52.0ms

Local error

Found 4 expressions with local error:

2.7b
(cos (/ (+ phi2 phi1) 2))
0.5b
(log (exp (cos (/ (+ phi2 phi1) 2))))
0.4b
(log1p (log (exp (cos (/ (+ phi2 phi1) 2)))))
0.2b
(expm1 (log1p (log (exp (cos (/ (+ phi2 phi1) 2))))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×expm1-log1p-u pow1
4×add-cbrt-cube add-exp-log log-pow insert-posit16 log1p-expm1-u add-log-exp
3×log-prod exp-prod
1×log1p-udef expm1-log1p rem-log-exp log1p-expm1 expm1-udef
Counts
4 → 52
Calls
4 calls:
Slowest
27.0ms
(log (exp (cos (/ (+ phi2 phi1) 2))))
12.0ms
(cos (/ (+ phi2 phi1) 2))
0.0ms
(log1p (log (exp (cos (/ (+ phi2 phi1) 2)))))
0.0ms
(expm1 (log1p (log (exp (cos (/ (+ phi2 phi1) 2))))))

series176.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
63.0ms
(expm1 (log1p (log (exp (cos (/ (+ phi2 phi1) 2))))))
59.0ms
(log1p (log (exp (cos (/ (+ phi2 phi1) 2)))))
29.0ms
(log (exp (cos (/ (+ phi2 phi1) 2))))
24.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.9s

Counts
64 → 64

prune1.4s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.6b

localize74.0ms

Local error

Found 4 expressions with local error:

2.7b
(cos (/ (+ phi2 phi1) 2))
2.7b
(cos (/ (+ phi2 phi1) 2))
2.7b
(cos (/ (+ phi2 phi1) 2))
0.7b
(cbrt (* (* (log1p (cos (/ (+ phi2 phi1) 2))) (log1p (cos (/ (+ phi2 phi1) 2)))) (log1p (cos (/ (+ phi2 phi1) 2)))))

rewrite41.0ms

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 insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Counts
4 → 43
Calls
4 calls:
Slowest
14.0ms
(cos (/ (+ phi2 phi1) 2))
11.0ms
(cbrt (* (* (log1p (cos (/ (+ phi2 phi1) 2))) (log1p (cos (/ (+ phi2 phi1) 2)))) (log1p (cos (/ (+ phi2 phi1) 2)))))
8.0ms
(cos (/ (+ phi2 phi1) 2))
8.0ms
(cos (/ (+ phi2 phi1) 2))

series149.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
61.0ms
(cbrt (* (* (log1p (cos (/ (+ phi2 phi1) 2))) (log1p (cos (/ (+ phi2 phi1) 2)))) (log1p (cos (/ (+ phi2 phi1) 2)))))
33.0ms
(cos (/ (+ phi2 phi1) 2))
31.0ms
(cos (/ (+ phi2 phi1) 2))
24.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.9s

Counts
55 → 55

prune1.3s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.6b

regimes1.2s

Accuracy

0% (0.2b remaining)

Error of 3.6b against oracle of 3.3b and baseline of 3.6b

bsearch4.0ms

end0.0ms

sample6.7s

Algorithm
intervals
Results
2.0s8377×body80valid
1.6s1260×body640valid
1.5s775×body1280valid
938.0ms694×body320valid
142.0ms331×body160valid