Details

Time bar (total: 26.9s)

sample155.0ms

Algorithm
intervals
Results
50.0ms45×body640valid
32.0ms248×body80valid
20.0ms25×body1280valid
11.0ms28×body320valid
3.0ms12×body160valid

simplify1.0s

Counts
1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.6b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
4.6b
(cos (/ (+ phi1 phi2) 2.0))
4.6b
(cos (/ (+ phi1 phi2) 2.0))
35.1b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite367.0ms

Algorithm
rewrite-expression-head
Rules
142×associate-*l/
102×flip3-- flip--
68×frac-times
66×sqrt-div
64×frac-add
44×pow1
34×associate-*r/
17×pow-prod-down
16×add-exp-log add-cbrt-cube
8×prod-exp cbrt-unprod
6×add-sqr-sqrt
5×add-cube-cbrt *-un-lft-identity
4×pow-sqr pow-prod-up add-log-exp
3×sqrt-prod
2×pow-plus
1×pow2 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 swap-sqr associate-*r* associate-*l* *-commutative flip-+
Counts
4 → 135
Calls
4 calls:
141.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
11.0ms
(cos (/ (+ phi1 phi2) 2.0))
12.0ms
(cos (/ (+ phi1 phi2) 2.0))
173.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series867.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
40.0ms
(cos (/ (+ phi1 phi2) 2.0))
38.0ms
(cos (/ (+ phi1 phi2) 2.0))
644.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify738.0ms

Counts
147 → 147

prune727.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 26.9b

localize48.0ms

Local error

Found 4 expressions with local error:

4.6b
(cos (/ (+ phi1 phi2) 2.0))
4.6b
(cos (/ (+ phi1 phi2) 2.0))
4.6b
(cos (/ (+ phi1 phi2) 2.0))
35.1b
(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite920.0ms

Algorithm
rewrite-expression-head
Rules
128×associate-*l/
96×flip3-- flip--
66×sqrt-div
64×frac-times frac-add
32×associate-*r/
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 100
Calls
4 calls:
22.0ms
(cos (/ (+ phi1 phi2) 2.0))
24.0ms
(cos (/ (+ phi1 phi2) 2.0))
23.0ms
(cos (/ (+ phi1 phi2) 2.0))
831.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series745.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(cos (/ (+ phi1 phi2) 2.0))
39.0ms
(cos (/ (+ phi1 phi2) 2.0))
31.0ms
(cos (/ (+ phi1 phi2) 2.0))
645.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify759.0ms

Counts
112 → 112

prune856.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 26.9b

localize49.0ms

Local error

Found 4 expressions with local error:

4.6b
(cos (/ (+ phi1 phi2) 2.0))
4.6b
(cos (/ (+ phi1 phi2) 2.0))
6.0b
(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
35.1b
(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
256×associate-*l/
192×flip3-- flip--
132×sqrt-div
128×frac-times frac-add
66×log-div exp-diff
64×associate-*r/
9×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
7×pow1
6×log-prod exp-prod exp-sum sqrt-prod
4×add-exp-log add-cbrt-cube add-log-exp
3×log-pow
2×sqrt-pow1 flip3-+ pow1/2 flip-+
1×rem-sqrt-square rem-exp-log
Counts
4 → 179
Calls
4 calls:
18.0ms
(cos (/ (+ phi1 phi2) 2.0))
12.0ms
(cos (/ (+ phi1 phi2) 2.0))
517.0ms
(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
804.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.4s

Counts
4 → 12
Calls
4 calls:
35.0ms
(cos (/ (+ phi1 phi2) 2.0))
35.0ms
(cos (/ (+ phi1 phi2) 2.0))
655.0ms
(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
673.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify949.0ms

Counts
191 → 191

prune1.6s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 26.9b

localize74.0ms

Local error

Found 4 expressions with local error:

4.6b
(cos (/ (+ phi1 phi2) 2.0))
4.6b
(cos (/ (+ phi1 phi2) 2.0))
6.4b
(pow E (log (sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
35.1b
(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
256×associate-*l/
192×flip3-- flip--
132×sqrt-div
128×frac-times frac-add
66×log-div pow-sub
64×associate-*r/
10×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
8×pow1
6×unpow-prod-up pow-unpow log-prod sqrt-prod
5×add-exp-log
4×add-cbrt-cube add-log-exp
3×unpow-prod-down log-pow
2×sqrt-pow1 flip3-+ pow1/2 pow-exp flip-+
1×pow-to-exp rem-sqrt-square e-exp-1 pow-pow sqr-pow
Counts
4 → 186
Calls
4 calls:
18.0ms
(cos (/ (+ phi1 phi2) 2.0))
13.0ms
(cos (/ (+ phi1 phi2) 2.0))
550.0ms
(pow E (log (sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
804.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.6s

Counts
4 → 12
Calls
4 calls:
45.0ms
(cos (/ (+ phi1 phi2) 2.0))
33.0ms
(cos (/ (+ phi1 phi2) 2.0))
891.0ms
(pow E (log (sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
634.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.1s

Counts
198 → 198

prune1.9s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 20.2b

regimes1.8s

Accuracy

52.2% (8.7b remaining)

Error of 29.1b against oracle of 20.4b and baseline of 38.5b

bsearch6.0ms

simplify946.0ms

end0.0ms

sample5.4s

Algorithm
intervals
Results
1.4s8351×body80valid
1.2s1268×body640valid
914.0ms798×body1280valid
852.0ms719×body320valid
93.0ms365×body160valid