Details

Time bar (total: 11.8s)

sample255.0ms

Algorithm
intervals
Results
190.0ms152×body1280valid
36.0ms52×body640valid
8.0ms19×body320valid
4.0ms28×body80valid
1.0ms5×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02715
14615
27115
37715
47715

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi1) (sin phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.8b
(sin (- lambda1 lambda2))
2.8b
(cos (- lambda1 lambda2))

rewrite20.0ms

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
1×distribute-rgt-in distribute-lft-in associate-*l/ sin-diff sin-cos-mult unswap-sqr
Counts
4 → 59
Calls
4 calls:
4.0ms
(* (cos phi1) (sin phi2))
6.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms
(sin (- lambda1 lambda2))
4.0ms
(cos (- lambda1 lambda2))

series175.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (cos phi1) (sin phi2))
89.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms
(sin (- lambda1 lambda2))
22.0ms
(cos (- lambda1 lambda2))

simplify111.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0286430
11077367
24907367
35001367

prune311.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos lambda1) (sin (- lambda2)))
0.2b
(* (cos phi1) (sin phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.8b
(cos (- lambda1 lambda2))

rewrite22.0ms

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*
5×pow-prod-down prod-exp cbrt-unprod
4×add-log-exp
3×cos-diff *-commutative
2×cos-sum unswap-sqr
1×distribute-rgt-in sub-neg distribute-lft-in associate-*l/ sin-neg distribute-rgt-neg-out sin-cos-mult
Counts
4 → 68
Calls
4 calls:
5.0ms
(* (cos lambda1) (sin (- lambda2)))
4.0ms
(* (cos phi1) (sin phi2))
6.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms
(cos (- lambda1 lambda2))

series202.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (cos lambda1) (sin (- lambda2)))
46.0ms
(* (cos phi1) (sin phi2))
89.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms
(cos (- lambda1 lambda2))

simplify41.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0338504
11347428
25001428

prune442.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
32×pow1 add-exp-log add-cbrt-cube
18×pow-prod-down prod-exp cbrt-unprod
12×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity associate-*r* associate-*l*
4×*-commutative sin-cos-mult add-log-exp
3×sin-mult
2×frac-times associate-*r/ associate-*l/ cos-mult unswap-sqr
Counts
4 → 87
Calls
4 calls:
4.0ms
(* (cos phi1) (sin phi2))
9.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
5.0ms
(* (sin lambda1) (sin lambda2))
9.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series299.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (cos phi1) (sin phi2))
109.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
47.0ms
(* (sin lambda1) (sin lambda2))
97.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify55.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0420777
11833599
25001599

prune488.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
28.6b
(cbrt (pow (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
30×pow1 add-exp-log add-cbrt-cube
17×pow-prod-down prod-exp cbrt-unprod
9×add-sqr-sqrt
8×cbrt-prod
7×add-cube-cbrt *-un-lft-identity
6×sin-cos-mult
5×associate-*r* associate-*l* sin-mult
4×add-log-exp
3×cube-div frac-times cbrt-div associate-*r/ associate-*l/ *-commutative
2×cos-mult
1×cube-mult unpow-prod-down pow1/3 unpow3 cube-prod rem-cbrt-cube unswap-sqr sqr-pow
Counts
4 → 89
Calls
4 calls:
8.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
8.0ms
(* (sin lambda1) (sin lambda2))
9.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
5.0ms
(cbrt (pow (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3))

series353.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
45.0ms
(* (sin lambda1) (sin lambda2))
98.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
99.0ms
(cbrt (pow (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3))

simplify62.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0415851
12038749
25001748

prune492.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes308.0ms

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 (1.0ms)

IterNodesCost
04543
14543

end0.0ms

sample8.0s

Algorithm
intervals
Results
5.9s4623×body1280valid
1.4s1919×body640valid
264.0ms577×body320valid
93.0ms657×body80valid
69.0ms224×body160valid