Details

Time bar (total: 14.0s)

sample262.0ms

Algorithm
intervals
Results
187.0ms157×body1280valid
45.0ms58×body640valid
6.0ms15×body320valid
2.0ms20×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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.9b
(cos (- lambda1 lambda2))
4.9b
(sin (- lambda1 lambda2))

rewrite87.0ms

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:
28.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
31.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
15.0ms
(cos (- lambda1 lambda2))
11.0ms
(sin (- lambda1 lambda2))

series212.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
101.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms
(cos (- lambda1 lambda2))
23.0ms
(sin (- lambda1 lambda2))

simplify113.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0260456
11016389
24756389
35001389

prune328.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos lambda1) (sin lambda2))
0.2b
(* (sin lambda1) (cos lambda2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.9b
(cos (- lambda1 lambda2))

rewrite70.0ms

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 sin-cos-mult unswap-sqr
1×distribute-rgt-in sub-neg distribute-lft-in associate-*l/
Counts
4 → 68
Calls
4 calls:
12.0ms
(* (cos lambda1) (sin lambda2))
12.0ms
(* (sin lambda1) (cos lambda2))
34.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
11.0ms
(cos (- lambda1 lambda2))

series214.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (cos lambda1) (sin lambda2))
48.0ms
(* (sin lambda1) (cos lambda2))
98.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
22.0ms
(cos (- lambda1 lambda2))

simplify42.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0333481
11341409
25001409

prune437.0ms

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

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
15×pow1 add-exp-log add-cbrt-cube
12×associate-*r*
11×add-cube-cbrt *-un-lft-identity
10×associate-*l*
6×pow-prod-down prod-exp sin-cos-mult cbrt-unprod
5×sin-mult
4×frac-times associate-*r/ cos-mult *-commutative add-log-exp
3×unswap-sqr
2×distribute-rgt-in sub-neg flip3-- distribute-lft-in frac-sub flip-- sub-div
1×associate-*l/ sin-neg distribute-rgt-neg-out
Counts
4 → 88
Calls
4 calls:
12.0ms
(* (cos lambda1) (sin lambda2))
13.0ms
(* (sin lambda1) (cos lambda2))
92.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
16.0ms
(* (sin lambda1) (sin (- lambda2)))

series357.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (cos lambda1) (sin lambda2))
51.0ms
(* (sin lambda1) (cos lambda2))
202.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
57.0ms
(* (sin lambda1) (sin (- lambda2)))

simplify64.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
0500926
12214802
25001801

prune605.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite406.0ms

Algorithm
rewrite-expression-head
Rules
84×pow1
42×sin-mult
41×cos-mult
39×add-exp-log add-cbrt-cube
38×associate-*r/
35×pow-prod-down
34×frac-times
33×associate-/l/
23×associate-*l/
20×prod-exp cbrt-unprod
18×frac-sub
17×sin-cos-mult
10×add-sqr-sqrt sub-div
8×add-cube-cbrt *-un-lft-identity pow-sqr pow-prod-up
6×distribute-rgt-neg-out
5×associate-*r* associate-*l* sin-neg
4×pow-plus add-log-exp
3×cbrt-undiv times-frac div-exp associate-/r* associate-/r/ *-commutative
2×pow2 flip3-- swap-sqr flip--
1×distribute-lft-neg-out frac-2neg flip3-+ sqr-neg frac-add clear-num flip-+ div-inv associate-/l* unswap-sqr
Counts
4 → 156
Calls
4 calls:
16.0ms
(* (sin lambda1) (sin (- lambda2)))
59.0ms
(* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2))))
278.0ms
(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2)))))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
44.0ms
(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

series754.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (sin lambda1) (sin (- lambda2)))
66.0ms
(* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2))))
568.0ms
(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2)))))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
63.0ms
(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

simplify124.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (109.0ms)

IterNodesCost
07202149
141161653
250021644

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes433.0ms

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
04742
14742

end0.0ms

sample8.2s

Algorithm
intervals
Results
6.0s4633×body1280valid
1.4s1925×body640valid
252.0ms571×body320valid
83.0ms650×body80valid
63.0ms221×body160valid