Details

Time bar (total: 9.7s)

sample63.0ms

Algorithm
intervals
Results
18.0ms289×body80valid
11.0ms29×body1280valid
10.0ms36×body640valid
4.0ms18×body320valid
1.0ms9×body160valid

simplify54.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03217
17117
224117
374717
4219617
5500117

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
2.2b
(cos (/ (+ phi1 phi2) 2.0))
2.2b
(cos (/ (+ phi1 phi2) 2.0))
35.2b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite48.0ms

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:
8.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
19.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series545.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
407.0ms
(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
127 → 127
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
013123623
150023528

prune459.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 24.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
2.2b
(cos (/ (+ phi1 phi2) 2.0))
2.2b
(cos (/ (+ phi1 phi2) 2.0))
35.2b
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite49.0ms

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)
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
21.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series495.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
30.0ms
(cos (/ (+ phi1 phi2) 2.0))
25.0ms
(cos (/ (+ phi1 phi2) 2.0))
395.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify62.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
013493748
150013672

prune465.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 24.1b

localize25.0ms

Local error

Found 4 expressions with local error:

1.4b
(log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
2.2b
(cos (/ (+ phi1 phi2) 2.0))
2.2b
(cos (/ (+ phi1 phi2) 2.0))
35.2b
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite53.0ms

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:
5.0ms
(log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
27.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series504.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
25.0ms
(cos (/ (+ phi1 phi2) 2.0))
31.0ms
(cos (/ (+ phi1 phi2) 2.0))
401.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify64.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
013603931
150023837

prune557.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 24.1b

localize34.0ms

Local error

Found 4 expressions with local error:

2.2b
(cos (/ (+ phi1 phi2) 2.0))
2.2b
(cos (/ (+ phi1 phi2) 2.0))
2.2b
(cos (/ (+ phi1 phi2) 2.0))
35.2b
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (+ (* 2 (log (cbrt (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3))))) (log (cbrt (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3))))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
328×frac-times
308×associate-*l/
300×flip3-- flip--
210×sqrt-div
208×frac-add
144×cbrt-div
116×associate-*r/
73×flip3-+ flip-+
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 pow1/2
Counts
4 → 244
Calls
4 calls:
6.0ms
(cos (/ (+ phi1 phi2) 2.0))
6.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
35.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (+ (* 2 (log (cbrt (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3))))) (log (cbrt (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3))))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.5s

Counts
4 → 12
Calls
4 calls:
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
25.0ms
(cos (/ (+ phi1 phi2) 2.0))
1.4s
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (+ (* 2 (log (cbrt (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3))))) (log (cbrt (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3))))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify261.0ms

Algorithm
egg-herbie
Counts
256 → 256
Iterations

Useful iterations: 1 (70.0ms)

IterNodesCost
0394024544
1500324479

prune1.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 24.1b

regimes461.0ms

Accuracy

40.1% (8.7b remaining)

Error of 33.5b against oracle of 24.8b and baseline of 39.4b

bsearch93.0ms

Steps
ItersRangePoint
8
-1.7014204184464025e+74
-3.755291874649203e+71
-7.271065070706806e+71

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03321
13321

end0.0ms

sample1.8s

Algorithm
intervals
Results
536.0ms8364×body80valid
369.0ms1283×body640valid
319.0ms783×body1280valid
141.0ms696×body320valid
50.0ms361×body160valid