Details

Time bar (total: 12.9s)

sample281.0ms

Algorithm
intervals
Results
200.0ms142×body1280valid
49.0ms64×body640valid
10.0ms20×body320valid
3.0ms22×body80valid
2.0ms8×body160valid

simplify10.0ms

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: 11.7b

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)))
1.8b
(sin (- lambda1 lambda2))
1.9b
(cos (- lambda1 lambda2))

rewrite31.0ms

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:
5.0ms
(* (cos phi1) (sin phi2))
16.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms
(sin (- lambda1 lambda2))
4.0ms
(cos (- lambda1 lambda2))

series167.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (cos phi1) (sin phi2))
89.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms
(sin (- lambda1 lambda2))
17.0ms
(cos (- lambda1 lambda2))

simplify119.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0286430
11077367
24907367
35001367

prune320.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b
(* (cos phi1) (sin phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
1.9b
(cos (- lambda1 lambda2))

rewrite35.0ms

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 associate-*l/ *-commutative
2×cos-sum unswap-sqr
1×distribute-rgt-in sub-neg distribute-lft-in flip3-+ sin-cos-mult flip-+
Counts
4 → 69
Calls
4 calls:
15.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
4.0ms
(* (cos phi1) (sin phi2))
10.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms
(cos (- lambda1 lambda2))

series278.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
41.0ms
(* (cos phi1) (sin phi2))
87.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms
(cos (- lambda1 lambda2))

simplify48.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0387676
11684576
25002575

prune468.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

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))
4.0ms
(* (sin lambda1) (sin lambda2))
13.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
13.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series301.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (cos phi1) (sin phi2))
48.0ms
(* (sin lambda1) (sin lambda2))
99.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
112.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify60.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0420777
11833599
25001599

prune493.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
29×pow1 add-exp-log add-cbrt-cube
16×pow-prod-down prod-exp cbrt-unprod
13×add-sqr-sqrt
10×associate-*l*
9×add-cube-cbrt *-un-lft-identity
8×associate-*r*
4×*-commutative add-log-exp
3×associate-*r/ sin-mult
2×sin-cos-mult unswap-sqr
1×frac-times associate-*l/ cos-mult
Counts
4 → 84
Calls
4 calls:
4.0ms
(* (cos phi1) (sin phi2))
4.0ms
(* (sin lambda1) (sin lambda2))
13.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
18.0ms
(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series299.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (cos phi1) (sin phi2))
43.0ms
(* (sin lambda1) (sin lambda2))
97.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
113.0ms
(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify57.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0435735
11878572
25001572

prune452.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes336.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04449
14449

end0.0ms

sample8.9s

Algorithm
intervals
Results
6.6s4688×body1280valid
1.5s1909×body640valid
274.0ms534×body320valid
106.0ms656×body80valid
70.0ms213×body160valid