Details

Time bar (total: 27.0s)

sample202.0ms

Algorithm
intervals
Results
57.0ms37×body640valid
54.0ms254×body80valid
35.0ms28×body1280valid
20.0ms27×body320valid
5.0ms11×body160valid

simplify1.2s

Counts
1 → 1

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.3b

localize59.0ms

Local error

Found 4 expressions with local error:

4.0b
(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))

rewrite70.0ms

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
39.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
17.0ms
(cos (/ (+ phi2 phi1) 2))
13.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
628.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
554.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
151.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
40.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.3s

Counts
79 → 79

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.1b

localize44.0ms

Local error

Found 4 expressions with local error:

4.0b
(cos (/ (+ phi2 phi1) 2))
0.4b
(expm1 (cos (/ (+ phi2 phi1) 2)))
0.2b
(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))
0.2b
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))

rewrite30.0ms

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 insert-posit16 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
17.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
12.0ms
(cos (/ (+ phi2 phi1) 2))
0.0ms
(expm1 (cos (/ (+ phi2 phi1) 2)))
0.0ms
(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))

series341.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
146.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
98.0ms
(expm1 (cos (/ (+ phi2 phi1) 2)))
69.0ms
(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))
27.0ms
(cos (/ (+ phi2 phi1) 2))

simplify2.7s

Counts
71 → 71

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.1b

localize48.0ms

Local error

Found 4 expressions with local error:

4.0b
(cos (/ (+ phi2 phi1) 2))
0.4b
(expm1 (cos (/ (+ phi2 phi1) 2)))
0.2b
(log1p (log1p (expm1 (expm1 (cos (/ (+ phi2 phi1) 2))))))
0.2b
(expm1 (expm1 (cos (/ (+ phi2 phi1) 2))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
6×log1p-expm1-u
5×expm1-log1p-u
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 add-log-exp
2×expm1-log1p expm1-udef
1×log1p-udef log1p-expm1
Counts
4 → 46
Calls
4 calls:
Slowest
8.0ms
(cos (/ (+ phi2 phi1) 2))
0.0ms
(expm1 (cos (/ (+ phi2 phi1) 2)))
0.0ms
(log1p (log1p (expm1 (expm1 (cos (/ (+ phi2 phi1) 2))))))
0.0ms
(expm1 (expm1 (cos (/ (+ phi2 phi1) 2))))

series395.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
178.0ms
(expm1 (expm1 (cos (/ (+ phi2 phi1) 2))))
127.0ms
(log1p (log1p (expm1 (expm1 (cos (/ (+ phi2 phi1) 2))))))
61.0ms
(expm1 (cos (/ (+ phi2 phi1) 2)))
29.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.3s

Counts
58 → 58

prune1.2s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 4.1b

localize60.0ms

Local error

Found 4 expressions with local error:

4.0b
(cos (/ (+ phi2 phi1) 2))
0.7b
(exp (expm1 (expm1 (cos (/ (+ phi2 phi1) 2)))))
0.6b
(log (exp (expm1 (expm1 (cos (/ (+ phi2 phi1) 2))))))
0.4b
(expm1 (cos (/ (+ phi2 phi1) 2)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×exp-prod
5×pow1 log1p-expm1-u add-log-exp
4×expm1-log1p-u add-cbrt-cube add-exp-log log-pow insert-posit16
3×log-prod expm1-udef
2×exp-diff
1×log-div expm1-log1p rem-log-exp rem-exp-log
Counts
4 → 56
Calls
4 calls:
Slowest
9.0ms
(cos (/ (+ phi2 phi1) 2))
2.0ms
(log (exp (expm1 (expm1 (cos (/ (+ phi2 phi1) 2))))))
2.0ms
(exp (expm1 (expm1 (cos (/ (+ phi2 phi1) 2)))))
0.0ms
(expm1 (cos (/ (+ phi2 phi1) 2)))

series528.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
246.0ms
(exp (expm1 (expm1 (cos (/ (+ phi2 phi1) 2)))))
165.0ms
(log (exp (expm1 (expm1 (cos (/ (+ phi2 phi1) 2))))))
78.0ms
(expm1 (cos (/ (+ phi2 phi1) 2)))
39.0ms
(cos (/ (+ phi2 phi1) 2))

simplify3.8s

Counts
68 → 68

prune1.4s

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 4.1b

regimes1.7s

Accuracy

0% (0.2b remaining)

Error of 3.7b against oracle of 3.5b and baseline of 3.7b

bsearch7.0ms

end0.0ms

sample6.6s

Algorithm
intervals
Results
2.4s8403×body80valid
1.5s1280×body640valid
1.0s764×body1280valid
1.0s754×body320valid
143.0ms350×body160valid