Details

Time bar (total: 8.8s)

sample77.0ms

Algorithm
intervals
Results
21.0ms270×body80valid
14.0ms35×body1280valid
11.0ms38×body640valid
5.0ms27×body320valid
1.0ms8×body160valid

simplify57.0ms

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: 39.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
2.8b
(cos (/ (+ phi1 phi2) 2.0))
2.8b
(cos (/ (+ phi1 phi2) 2.0))
37.1b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite162.0ms

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:
25.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
11.0ms
(cos (/ (+ phi1 phi2) 2.0))
11.0ms
(cos (/ (+ phi1 phi2) 2.0))
103.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series626.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
28.0ms
(cos (/ (+ phi1 phi2) 2.0))
28.0ms
(cos (/ (+ phi1 phi2) 2.0))
471.0ms
(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 (28.0ms)

IterNodesCost
013123623
150023528

prune462.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 30.0b

localize29.0ms

Local error

Found 4 expressions with local error:

2.8b
(cos (/ (+ phi1 phi2) 2.0))
37.1b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
37.1b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
37.1b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite346.0ms

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:
11.0ms
(cos (/ (+ phi1 phi2) 2.0))
100.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
101.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
101.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.6s

Counts
4 → 12
Calls
4 calls:
31.0ms
(cos (/ (+ phi1 phi2) 2.0))
443.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
442.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
659.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify109.0ms

Algorithm
egg-herbie
Counts
256 → 256
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
0126610063
150019903

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 30.0b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b
(* R (- phi2 phi1))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
5×*-un-lft-identity associate-*r*
3×pow1 add-exp-log add-cube-cbrt associate-*l* add-cbrt-cube
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/
1×flip3-- pow-prod-down prod-exp *-commutative flip-- cbrt-unprod distribute-lft-out-- add-log-exp difference-of-squares unswap-sqr
Counts
1 → 26
Calls
1 calls:
21.0ms
(* R (- phi2 phi1))

series37.0ms

Counts
1 → 3
Calls
1 calls:
37.0ms
(* R (- phi2 phi1))

simplify50.0ms

Algorithm
egg-herbie
Counts
29 → 29
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
011298
146288
2188388
3500288

prune63.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 30.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (cbrt (- phi2 phi1)) (cbrt (- phi2 phi1)))
0.6b
(cbrt (- phi2 phi1))
0.6b
(cbrt (- phi2 phi1))
0.6b
(cbrt (- phi2 phi1))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
43×cbrt-prod
37×add-sqr-sqrt
35×*-un-lft-identity
18×cbrt-div
15×add-cube-cbrt
11×pow1
10×swap-sqr
9×flip3-- pow1/3 flip-- distribute-lft-out--
8×associate-*r* associate-*l*
7×difference-of-squares
6×add-exp-log
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 101
Calls
4 calls:
38.0ms
(* (cbrt (- phi2 phi1)) (cbrt (- phi2 phi1)))
4.0ms
(cbrt (- phi2 phi1))
4.0ms
(cbrt (- phi2 phi1))
7.0ms
(cbrt (- phi2 phi1))

series600.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(* (cbrt (- phi2 phi1)) (cbrt (- phi2 phi1)))
161.0ms
(cbrt (- phi2 phi1))
152.0ms
(cbrt (- phi2 phi1))
156.0ms
(cbrt (- phi2 phi1))

simplify159.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 3 (151.0ms)

IterNodesCost
0260760
1908723
24494670
35001661

prune289.0ms

Pruning

18 alts after pruning (15 fresh and 3 done)

Merged error: 29.8b

regimes809.0ms

Accuracy

70.3% (4.2b remaining)

Error of 29.1b against oracle of 25.0b and baseline of 39.0b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03353
13353

end0.0ms

sample2.0s

Algorithm
intervals
Results
546.0ms8234×body80valid
381.0ms1311×body640valid
321.0ms780×body1280valid
152.0ms739×body320valid
46.0ms339×body160valid