Details

Time bar (total: 14.0s)

sample275.0ms

Algorithm
intervals
Results
203.0ms162×body1280valid
38.0ms56×body640valid
14.0ms18×body320valid
2.0ms14×body80valid
2.0ms6×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02715
14615
27115
37715
47715

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (cos phi2))
0.3b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.4b
(cos (- lambda1 lambda2))
3.6b
(sin (- lambda1 lambda2))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×associate-*r*
4×associate-*l* pow-prod-down prod-exp cbrt-unprod add-log-exp
3×cos-diff
2×sub-neg cos-sum sin-sum *-commutative sin-cos-mult
1×distribute-rgt-in distribute-lft-in associate-*l/ sin-diff unswap-sqr
Counts
4 → 60
Calls
4 calls:
5.0ms
(* (sin phi1) (cos phi2))
16.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms
(cos (- lambda1 lambda2))
4.0ms
(sin (- lambda1 lambda2))

series177.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (sin phi1) (cos phi2))
91.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms
(cos (- lambda1 lambda2))
21.0ms
(sin (- lambda1 lambda2))

simplify107.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0254435
11026372
24856372
35001372

prune508.0ms

Filtered
72 candidates to 51 candidates (70.8%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.6b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (cos phi2))
0.2b
(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
0.3b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.4b
(cos (- lambda1 lambda2))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×associate-*r* add-log-exp
4×associate-*l* pow-prod-down prod-exp cbrt-unprod
3×cos-diff
2×sub-neg cos-sum *-commutative sin-cos-mult
1×distribute-rgt-in flip3-- distribute-lft-in diff-log associate-*l/ flip-- unswap-sqr
Counts
4 → 62
Calls
4 calls:
4.0ms
(* (sin phi1) (cos phi2))
7.0ms
(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
10.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms
(cos (- lambda1 lambda2))

series239.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (sin phi1) (cos phi2))
91.0ms
(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
88.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms
(cos (- lambda1 lambda2))

simplify39.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0316541
11291468
25002468

prune415.0ms

Filtered
74 candidates to 51 candidates (68.9%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (cos phi2))
0.2b
(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
0.2b
(* (sin lambda1) (sin (- lambda2)))
0.3b
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1 add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity associate-*r*
7×associate-*l*
6×sin-cos-mult add-log-exp
5×pow-prod-down prod-exp cbrt-unprod sin-mult
4×frac-times associate-*r/ cos-mult
3×sub-neg flip3-- *-commutative flip--
2×distribute-rgt-in distribute-lft-in frac-sub sub-div unswap-sqr
1×diff-log associate-*l/ sin-neg distribute-rgt-neg-out
Counts
4 → 82
Calls
4 calls:
4.0ms
(* (sin phi1) (cos phi2))
5.0ms
(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
6.0ms
(* (sin lambda1) (sin (- lambda2)))
25.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series383.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (sin phi1) (cos phi2))
99.0ms
(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
52.0ms
(* (sin lambda1) (sin (- lambda2)))
188.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify66.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
0486986
12225863
25001861

prune602.0ms

Filtered
94 candidates to 69 candidates (73.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (* (sin phi1) (cos phi2)) (- (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin (- lambda2))) 3))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (+ (* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2)))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
0.3b
(pow (* (sin lambda1) (sin (- lambda2))) 3)
0.4b
(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
0.5b
(pow (* (cos lambda1) (cos lambda2)) 3)

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
71×cos-mult
60×frac-add
59×sin-mult
49×pow1
35×associate-/r/
34×frac-times associate-*r/
31×add-exp-log associate-*l/ add-cbrt-cube
19×pow-prod-down
13×prod-exp cbrt-unprod
10×cube-div
9×associate-/l/
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow-unpow
5×sin-cos-mult
4×pow-pow flip3-+ pow-exp pow-sqr pow-prod-up flip-+ add-log-exp rem-cube-cbrt
3×cbrt-undiv times-frac div-exp associate-/r*
2×cube-mult pow-to-exp unpow-prod-down flip3-- pow-plus unpow3 cube-prod frac-sub flip-- sub-div sqr-pow
1×pow2 frac-2neg swap-sqr associate-*r* associate-*l* cube-neg sin-neg clear-num *-commutative distribute-rgt-neg-out div-inv associate-/l*
Counts
4 → 151
Calls
4 calls:
121.0ms
(/ (* (* (sin phi1) (cos phi2)) (- (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin (- lambda2))) 3))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (+ (* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2)))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
3.0ms
(pow (* (sin lambda1) (sin (- lambda2))) 3)
13.0ms
(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
3.0ms
(pow (* (cos lambda1) (cos lambda2)) 3)

series974.0ms

Counts
4 → 12
Calls
4 calls:
778.0ms
(/ (* (* (sin phi1) (cos phi2)) (- (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin (- lambda2))) 3))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (+ (* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2)))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
77.0ms
(pow (* (sin lambda1) (sin (- lambda2))) 3)
54.0ms
(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
65.0ms
(pow (* (cos lambda1) (cos lambda2)) 3)

simplify60.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013014271
150024008

prune1.0s

Filtered
163 candidates to 95 candidates (58.3%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes397.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04884
14884

end0.0ms

sample8.3s

Algorithm
intervals
Results
6.1s4608×body1280valid
1.4s1931×body640valid
277.0ms606×body320valid
99.0ms659×body80valid
56.0ms196×body160valid