Details

Time bar (total: 9.5s)

sample64.0ms

Algorithm
intervals
Results
16.0ms255×body80valid
11.0ms38×body640valid
9.0ms23×body1280valid
5.0ms27×body320valid
1.0ms11×body160valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03217
17117
224117
374717
4219617
5500117

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
2.5b
(cos (/ (+ phi1 phi2) 2.0))
2.5b
(cos (/ (+ phi1 phi2) 2.0))
34.7b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
130×associate-*l/
97×flip3-- flip--
66×sqrt-div
64×frac-times frac-add
32×associate-*r/
12×add-sqr-sqrt
9×*-un-lft-identity
7×pow1 add-cube-cbrt
6×add-exp-log add-cbrt-cube
5×associate-*l*
4×add-log-exp
3×associate-*r* sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 115
Calls
4 calls:
23.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
12.0ms
(cos (/ (+ phi1 phi2) 2.0))
10.0ms
(cos (/ (+ phi1 phi2) 2.0))
95.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series490.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
23.0ms
(cos (/ (+ phi1 phi2) 2.0))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
366.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify53.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
013123624
150023529

prune447.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.6b

localize25.0ms

Local error

Found 4 expressions with local error:

2.5b
(cos (/ (+ phi1 phi2) 2.0))
2.5b
(cos (/ (+ phi1 phi2) 2.0))
2.5b
(cos (/ (+ phi1 phi2) 2.0))
34.7b
(sqrt (+ (* (* (- lambda1 lambda2) (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))))

rewrite462.0ms

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))
10.0ms
(cos (/ (+ phi1 phi2) 2.0))
420.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (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))))

series431.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
22.0ms
(cos (/ (+ phi1 phi2) 2.0))
23.0ms
(cos (/ (+ phi1 phi2) 2.0))
359.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (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))))

simplify62.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012784428
150014345

prune559.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 24.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
2.5b
(cos (/ (+ phi1 phi2) 2.0))
2.5b
(cos (/ (+ phi1 phi2) 2.0))
34.7b
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite148.0ms

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:
3.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
10.0ms
(cos (/ (+ phi1 phi2) 2.0))
10.0ms
(cos (/ (+ phi1 phi2) 2.0))
114.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series467.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
23.0ms
(cos (/ (+ phi1 phi2) 2.0))
23.0ms
(cos (/ (+ phi1 phi2) 2.0))
375.0ms
(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
013493748
150013672

prune441.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 24.6b

localize26.0ms

Local error

Found 4 expressions with local error:

2.5b
(cos (/ (+ phi1 phi2) 2.0))
2.5b
(cos (/ (+ phi1 phi2) 2.0))
34.7b
(sqrt (+ (* (* (- lambda1 lambda2) (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))))
34.7b
(sqrt (+ (* (* (- lambda1 lambda2) (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))))

rewrite891.0ms

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:
11.0ms
(cos (/ (+ phi1 phi2) 2.0))
10.0ms
(cos (/ (+ phi1 phi2) 2.0))
425.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (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))))
425.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (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))))

series813.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(cos (/ (+ phi1 phi2) 2.0))
23.0ms
(cos (/ (+ phi1 phi2) 2.0))
384.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (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))))
382.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (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))))

simplify102.0ms

Algorithm
egg-herbie
Counts
184 → 184
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012788648
150018510

prune1.2s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 24.6b

regimes464.0ms

Accuracy

37% (8.7b remaining)

Error of 33.6b against oracle of 24.9b and baseline of 38.8b

bsearch96.0ms

Steps
ItersRangePoint
9
4.550363500027125e+48
6.711340266541749e+54
1.7815555754871838e+53
0
-2.1666926926305208e+135
-2.154318820904845e+135
-2.1605057567676828e+135

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04030
14030

end0.0ms

sample2.0s

Algorithm
intervals
Results
539.0ms8280×body80valid
359.0ms1269×body640valid
332.0ms808×body1280valid
158.0ms730×body320valid
50.0ms373×body160valid