Details

Time bar (total: 7.7s)

sample66.0ms

Algorithm
intervals
Results
18.0ms266×body80valid
14.0ms46×body640valid
9.0ms20×body1280valid
6.0ms29×body320valid
2.0ms12×body160valid

simplify50.0ms

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: 41.3b

localize21.0ms

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))
37.5b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite103.0ms

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:
31.0ms
(* (* (- 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))
49.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series543.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
30.0ms
(cos (/ (+ phi1 phi2) 2.0))
393.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify63.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013733924
150013756

prune504.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 28.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
3.5b
(cos (/ (+ phi1 phi2) 2.0))
3.5b
(cos (/ (+ phi1 phi2) 2.0))
37.5b
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite87.0ms

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:
1.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
64.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series513.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
25.0ms
(cos (/ (+ phi1 phi2) 2.0))
25.0ms
(cos (/ (+ phi1 phi2) 2.0))
413.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify56.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
013493745
150023672

prune518.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 28.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
3.5b
(cos (/ (+ phi1 phi2) 2.0))
3.5b
(cos (/ (+ phi1 phi2) 2.0))
37.5b
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (cbrt (pow (pow (cos (/ (+ phi1 phi2) 2.0)) 3) 3)))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite125.0ms

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:
1.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
6.0ms
(cos (/ (+ phi1 phi2) 2.0))
8.0ms
(cos (/ (+ phi1 phi2) 2.0))
99.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (cbrt (pow (pow (cos (/ (+ phi1 phi2) 2.0)) 3) 3)))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series512.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
25.0ms
(cos (/ (+ phi1 phi2) 2.0))
29.0ms
(cos (/ (+ phi1 phi2) 2.0))
411.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (cbrt (pow (pow (cos (/ (+ phi1 phi2) 2.0)) 3) 3)))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify63.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
013543911
150013840

prune527.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 28.2b

localize31.0ms

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))
37.5b
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (cbrt (pow (pow (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) 3) 3)))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite120.0ms

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:
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
92.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (cbrt (pow (pow (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) 3) 3)))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series489.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(cos (/ (+ phi1 phi2) 2.0))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
407.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (cbrt (pow (pow (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) 3) 3)))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify70.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
012894768
150024681

prune571.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 28.2b

regimes664.0ms

Accuracy

72.1% (3.8b remaining)

Error of 29.2b against oracle of 25.3b and baseline of 39.1b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03838
13838

end0.0ms

sample2.0s

Algorithm
intervals
Results
586.0ms8283×body80valid
433.0ms1372×body640valid
344.0ms767×body1280valid
168.0ms701×body320valid
53.0ms357×body160valid