Details

Time bar (total: 20.0s)

sample109.0ms

Algorithm
intervals
Results
28.0ms255×body80valid
20.0ms41×body640valid
12.0ms22×body1280valid
9.0ms25×body320valid
2.0ms10×body160valid

simplify957.0ms

Counts
1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.1b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
3.4b
(cos (/ (+ phi1 phi2) 2.0))
3.4b
(cos (/ (+ phi1 phi2) 2.0))
34.5b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite324.0ms

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:
129.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
13.0ms
(cos (/ (+ phi1 phi2) 2.0))
21.0ms
(cos (/ (+ phi1 phi2) 2.0))
144.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series838.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
32.0ms
(cos (/ (+ phi1 phi2) 2.0))
49.0ms
(cos (/ (+ phi1 phi2) 2.0))
629.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify709.0ms

Counts
147 → 147

prune750.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 24.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
3.4b
(cos (/ (+ phi1 phi2) 2.0))
3.4b
(cos (/ (+ phi1 phi2) 2.0))
34.5b
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite269.0ms

Algorithm
rewrite-expression-head
Rules
128×associate-*l/
96×flip3-- flip--
66×sqrt-div
64×frac-times frac-add
32×associate-*r/
9×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1
5×add-exp-log add-cbrt-cube
4×add-log-exp
3×unpow-prod-down pow-unpow cube-prod sqrt-prod
1×cube-mult pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 flip3-+ pow1/2 unpow3 pow-exp flip-+ rem-cube-cbrt sqr-pow
Counts
4 → 116
Calls
4 calls:
6.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
22.0ms
(cos (/ (+ phi1 phi2) 2.0))
22.0ms
(cos (/ (+ phi1 phi2) 2.0))
199.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series806.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
35.0ms
(cos (/ (+ phi1 phi2) 2.0))
34.0ms
(cos (/ (+ phi1 phi2) 2.0))
669.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify755.0ms

Counts
128 → 128

prune692.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 24.3b

localize37.0ms

Local error

Found 4 expressions with local error:

3.4b
(cos (/ (+ phi1 phi2) 2.0))
3.4b
(cos (/ (+ phi1 phi2) 2.0))
34.5b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
34.5b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite345.0ms

Algorithm
rewrite-expression-head
Rules
256×associate-*l/
192×flip3-- flip--
132×sqrt-div
128×frac-times frac-add
64×associate-*r/
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log add-cbrt-cube add-log-exp
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 172
Calls
4 calls:
22.0ms
(cos (/ (+ phi1 phi2) 2.0))
23.0ms
(cos (/ (+ phi1 phi2) 2.0))
139.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
136.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.4s

Counts
4 → 12
Calls
4 calls:
44.0ms
(cos (/ (+ phi1 phi2) 2.0))
32.0ms
(cos (/ (+ phi1 phi2) 2.0))
626.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
647.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify857.0ms

Counts
184 → 184

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 24.3b

localize47.0ms

Local error

Found 4 expressions with local error:

1.7b
(log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
3.4b
(cos (/ (+ phi1 phi2) 2.0))
3.4b
(cos (/ (+ phi1 phi2) 2.0))
34.5b
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite262.0ms

Algorithm
rewrite-expression-head
Rules
128×associate-*l/
96×flip3-- flip--
66×sqrt-div
64×frac-times frac-add
32×associate-*r/
13×log-pow
12×exp-prod
10×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
6×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×unpow-prod-down log-prod cube-prod sqrt-prod
1×cube-mult rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 unpow3 rem-log-exp flip-+ sqr-pow
Counts
4 → 117
Calls
4 calls:
16.0ms
(log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
21.0ms
(cos (/ (+ phi1 phi2) 2.0))
21.0ms
(cos (/ (+ phi1 phi2) 2.0))
177.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series851.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
36.0ms
(cos (/ (+ phi1 phi2) 2.0))
49.0ms
(cos (/ (+ phi1 phi2) 2.0))
694.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify750.0ms

Counts
129 → 129

prune856.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 24.3b

regimes725.0ms

Accuracy

72.1% (4.0b remaining)

Error of 29.3b against oracle of 25.4b and baseline of 39.6b

bsearch3.0ms

simplify1.0s

end0.0ms

sample5.3s

Algorithm
intervals
Results
2.0s8315×body80valid
1.2s1309×body640valid
803.0ms856×body1280valid
293.0ms718×body320valid
132.0ms387×body160valid