Details

Time bar (total: 9.3s)

sample170.0ms

Algorithm
intervals
Results
108.0ms118×body1280valid
34.0ms70×body640valid
10.0ms31×body320valid
3.0ms15×body160valid
2.0ms22×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12112
22112

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.9b
(cos (- lambda1 lambda2))
5.1b
(sin (- lambda1 lambda2))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
6×add-log-exp
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×cos-diff
2×sub-neg cos-sum associate-+r+ sin-sum
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ sum-log sin-diff flip-+
Counts
4 → 40
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
3.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms
(cos (- lambda1 lambda2))
5.0ms
(sin (- lambda1 lambda2))

series153.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
104.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms
(cos (- lambda1 lambda2))
21.0ms
(sin (- lambda1 lambda2))

simplify125.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0205421
1508375
21327374
33685374
45002374

prune240.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.7b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos lambda1) (sin lambda2))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.9b
(cos (- lambda1 lambda2))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×cos-diff associate-*r* associate-*l*
2×cos-sum associate-+r+
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in flip3-+ pow-prod-down prod-exp sum-log *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 48
Calls
4 calls:
4.0ms
(* (cos lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
3.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms
(cos (- lambda1 lambda2))

series170.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (cos lambda1) (sin lambda2))
13.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
97.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
19.0ms
(cos (- lambda1 lambda2))

simplify59.0ms

Algorithm
egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0255532
1758467
22312466
35002466

prune301.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (* (sin lambda1) (sin lambda2)))
0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.4b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

rewrite17.0ms

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-*l* add-log-exp
4×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×*-commutative sin-mult
1×+-commutative flip3-+ associate-*r/ sum-log flip-+ unswap-sqr
Counts
4 → 56
Calls
4 calls:
8.0ms
(* (cos phi2) (* (sin lambda1) (sin lambda2)))
4.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
3.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series261.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(* (cos phi2) (* (sin lambda1) (sin lambda2)))
44.0ms
(* (sin lambda1) (sin lambda2))
18.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
122.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify37.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0283721
11122612
25001611

prune345.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))) (cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))
0.6b
(cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
0.6b
(cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
0.6b
(cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×flip3-+ pow1/3 flip-+
6×add-exp-log swap-sqr associate-*r* associate-*l*
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 → 87
Calls
4 calls:
16.0ms
(* (cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))) (cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))
2.0ms
(cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
2.0ms
(cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
2.0ms
(cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))

series843.0ms

Counts
4 → 12
Calls
4 calls:
229.0ms
(* (cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))) (cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))
201.0ms
(cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
203.0ms
(cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
210.0ms
(cbrt (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))

simplify44.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
02411791
110171625
250011557

prune487.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes541.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04435
14435

end0.0ms

sample5.3s

Algorithm
intervals
Results
3.2s3611×body1280valid
1.2s2273×body640valid
300.0ms919×body320valid
220.0ms741×body80valid
100.0ms456×body160valid