Details

Time bar (total: 8.8s)

sample64.0ms

Algorithm
intervals
Results
18.0ms269×body80valid
12.0ms29×body1280valid
9.0ms29×body640valid
6.0ms27×body320valid
2.0ms12×body160valid

simplify51.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03217
17117
224117
374717
4219617
5500117

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
3.3b
(cos (/ (+ phi1 phi2) 2.0))
3.3b
(cos (/ (+ phi1 phi2) 2.0))
38.4b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite96.0ms

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:
29.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
45.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series546.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))
29.0ms
(cos (/ (+ phi1 phi2) 2.0))
396.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify62.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013733924
150013756

prune460.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 26.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
3.3b
(cos (/ (+ phi1 phi2) 2.0))
3.3b
(cos (/ (+ phi1 phi2) 2.0))
38.4b
(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
128×associate-*l/
96×flip3-- flip--
66×sqrt-div
64×frac-times frac-add
32×associate-*r/
8×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×pow1
4×add-exp-log log-pow add-cbrt-cube add-log-exp
3×log-prod exp-prod sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 rem-log-exp flip-+
Counts
4 → 108
Calls
4 calls:
10.0ms
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
7.0ms
(cos (/ (+ phi1 phi2) 2.0))
49.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series479.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
30.0ms
(cos (/ (+ phi1 phi2) 2.0))
397.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify59.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012963713
150013633

prune452.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 26.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
3.3b
(cos (/ (+ phi1 phi2) 2.0))
3.3b
(cos (/ (+ phi1 phi2) 2.0))
38.4b
(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
128×associate-*l/
96×flip3-- flip--
66×sqrt-div
64×frac-times frac-add
32×associate-*r/
8×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×pow1
4×add-exp-log log-pow add-cbrt-cube add-log-exp
3×log-prod exp-prod sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 rem-log-exp flip-+
Counts
4 → 108
Calls
4 calls:
10.0ms
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
55.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series492.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
408.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify58.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012923884
150013802

prune474.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 26.0b

localize29.0ms

Local error

Found 4 expressions with local error:

3.3b
(cos (/ (+ phi1 phi2) 2.0))
38.4b
(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
38.4b
(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
38.4b
(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
384×associate-*l/
288×flip3-- flip--
198×sqrt-div
192×frac-times frac-add
96×associate-*r/
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 244
Calls
4 calls:
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
53.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
55.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
55.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series1.3s

Counts
4 → 12
Calls
4 calls:
32.0ms
(cos (/ (+ phi1 phi2) 2.0))
405.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
416.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
413.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify119.0ms

Algorithm
egg-herbie
Counts
256 → 256
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
0126811083
1500110911

prune1.2s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 26.0b

regimes493.0ms

Accuracy

75.4% (3.5b remaining)

Error of 29.4b against oracle of 25.9b and baseline of 40.0b

bsearch2.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02734
12734

end0.0ms

sample1.9s

Algorithm
intervals
Results
563.0ms8354×body80valid
383.0ms1239×body640valid
338.0ms784×body1280valid
174.0ms784×body320valid
50.0ms353×body160valid