Details

Time bar (total: 10.9s)

sample64.0ms

Algorithm
intervals
Results
16.0ms258×body80valid
12.0ms43×body640valid
10.0ms25×body1280valid
4.0ms20×body320valid
1.0ms10×body160valid

simplify51.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03217
17117
224117
374717
4219617
5500117

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
3.5b
(cos (/ (+ phi1 phi2) 2.0))
3.5b
(cos (/ (+ phi1 phi2) 2.0))
38.8b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite190.0ms

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:
64.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
10.0ms
(cos (/ (+ phi1 phi2) 2.0))
11.0ms
(cos (/ (+ phi1 phi2) 2.0))
93.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series503.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
28.0ms
(cos (/ (+ phi1 phi2) 2.0))
22.0ms
(cos (/ (+ phi1 phi2) 2.0))
365.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify60.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
013733924
150013756

prune449.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 26.1b

localize21.0ms

Local error

Found 4 expressions with local error:

3.5b
(cos (/ (+ phi1 phi2) 2.0))
3.5b
(cos (/ (+ phi1 phi2) 2.0))
3.5b
(cos (/ (+ phi1 phi2) 2.0))
38.8b
(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))))

rewrite534.0ms

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:
10.0ms
(cos (/ (+ phi1 phi2) 2.0))
10.0ms
(cos (/ (+ phi1 phi2) 2.0))
11.0ms
(cos (/ (+ phi1 phi2) 2.0))
493.0ms
(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))))

series449.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(cos (/ (+ phi1 phi2) 2.0))
29.0ms
(cos (/ (+ phi1 phi2) 2.0))
23.0ms
(cos (/ (+ phi1 phi2) 2.0))
373.0ms
(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))))

simplify61.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012784428
150014345

prune563.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 26.1b

localize27.0ms

Local error

Found 4 expressions with local error:

3.5b
(cos (/ (+ phi1 phi2) 2.0))
3.5b
(cos (/ (+ phi1 phi2) 2.0))
3.5b
(cos (/ (+ phi1 phi2) 2.0))
38.8b
(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite873.0ms

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:
10.0ms
(cos (/ (+ phi1 phi2) 2.0))
11.0ms
(cos (/ (+ phi1 phi2) 2.0))
10.0ms
(cos (/ (+ phi1 phi2) 2.0))
832.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series462.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(cos (/ (+ phi1 phi2) 2.0))
30.0ms
(cos (/ (+ phi1 phi2) 2.0))
24.0ms
(cos (/ (+ phi1 phi2) 2.0))
385.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify66.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
012755363
150015269

prune445.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 26.1b

localize32.0ms

Local error

Found 4 expressions with local error:

3.5b
(cos (/ (+ phi1 phi2) 2.0))
3.5b
(cos (/ (+ phi1 phi2) 2.0))
38.8b
(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
38.8b
(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite1.7s

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:
10.0ms
(cos (/ (+ phi1 phi2) 2.0))
10.0ms
(cos (/ (+ phi1 phi2) 2.0))
834.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
837.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series808.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(cos (/ (+ phi1 phi2) 2.0))
23.0ms
(cos (/ (+ phi1 phi2) 2.0))
375.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
379.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify110.0ms

Algorithm
egg-herbie
Counts
184 → 184
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
0127510518
1500110358

prune878.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 26.1b

regimes620.0ms

Accuracy

74% (3.7b remaining)

Error of 29.4b against oracle of 25.7b and baseline of 39.8b

bsearch4.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02734
12734

end0.0ms

sample1.9s

Algorithm
intervals
Results
520.0ms8339×body80valid
370.0ms1318×body640valid
334.0ms804×body1280valid
144.0ms727×body320valid
48.0ms367×body160valid