Details

Time bar (total: 10.1s)

sample170.0ms

Algorithm
intervals
Results
100.0ms117×body1280valid
42.0ms72×body640valid
9.0ms27×body320valid
3.0ms28×body80valid
2.0ms12×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12112
22112

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 1.0b

Counts
2 → 1

localize21.0ms

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))))
4.4b
(cos (- lambda1 lambda2))
4.6b
(sin (- lambda1 lambda2))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity
6×add-log-exp
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt add-cbrt-cube
3×cos-diff
2×sub-neg cos-sum associate-+r+ sin-sum distribute-lft-out
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ associate-*l* sum-log sin-diff flip-+
Counts
4 → 42
Calls
4 calls:
1.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
8.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))
4.0ms
(sin (- lambda1 lambda2))

series163.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
108.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms
(cos (- lambda1 lambda2))
23.0ms
(sin (- lambda1 lambda2))

simplify122.0ms

Algorithm
egg-herbie
Counts
54 → 54
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0199433
1483387
21249386
33510386
45002386

prune210.0ms

Filtered
54 candidates to 43 candidates (79.6%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New411354
Fresh000
Picked101
Done000
Total421355

Merged error: 0.7b

Counts
55 → 13

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (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))))
4.4b
(cos (- lambda1 lambda2))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
18×*-un-lft-identity
11×associate-*r*
8×associate-*l*
6×pow1 add-exp-log add-cube-cbrt add-cbrt-cube add-log-exp
5×unswap-sqr
4×distribute-lft-out-- difference-of-squares
3×distribute-rgt-in cos-diff sub-neg distribute-lft-in
2×cos-sum associate-+r+ associate-*r/ distribute-lft-out
1×+-commutative flip3-- flip3-+ pow-prod-down prod-exp sum-log *-commutative flip-- cbrt-unprod flip-+
Counts
4 → 64
Calls
4 calls:
24.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
1.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
8.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))

series296.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
13.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
113.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
19.0ms
(cos (- lambda1 lambda2))

simplify123.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0318812
11112723
24700722
35001722

prune323.0ms

Filtered
76 candidates to 53 candidates (69.7%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New71576
Fresh4812
Picked101
Done000
Total761389

Merged error: 0.1b

Counts
89 → 13

localize31.0ms

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

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×associate-*r*
16×*-un-lft-identity
12×associate-*l*
11×pow1 add-exp-log add-cbrt-cube
10×add-cube-cbrt
6×add-log-exp
5×unswap-sqr
4×pow-prod-down prod-exp cbrt-unprod
3×*-commutative distribute-lft-out
2×sin-mult
1×+-commutative flip3-+ associate-*r/ sum-log flip-+
Counts
4 → 72
Calls
4 calls:
10.0ms
(* (cos phi2) (* (sin lambda1) (sin lambda2)))
5.0ms
(* (sin lambda1) (sin lambda2))
1.0ms
(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)))))
11.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series274.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(* (cos phi2) (* (sin lambda1) (sin lambda2)))
51.0ms
(* (sin lambda1) (sin lambda2))
19.0ms
(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)))))
134.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify53.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0311830
11376721
25001720

prune371.0ms

Filtered
84 candidates to 62 candidates (73.8%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New77784
Fresh7512
Picked101
Done000
Total851297

Merged error: 0.1b

Counts
97 → 12

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (pow (cos phi1) 3) (pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))) (* (cos phi1) (cos phi1))))
0.4b
(pow (cos phi1) 3)
0.6b
(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
1.7b
(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
378×*-un-lft-identity
246×associate-*l*
144×distribute-lft-out
121×times-frac
97×unpow-prod-down
54×pow-unpow
52×add-sqr-sqrt
48×sum-cubes
36×add-cube-cbrt
13×add-exp-log add-cbrt-cube
11×pow1 associate-/r* associate-/l*
8×cos-mult
7×associate-/r/ unswap-sqr
6×associate-*r* add-log-exp
5×frac-add
4×pow-pow associate-*l/ pow-exp rem-cube-cbrt
3×flip3-- pow-prod-down prod-exp flip-- cbrt-unprod distribute-lft-out-- difference-of-squares
2×frac-times pow-to-exp flip3-+ unpow3 associate-*r/ *-commutative flip-+ associate-/l/ sqr-pow
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num div-inv
Counts
4 → 245
Calls
4 calls:
88.0ms
(/ (+ (pow (cos phi1) 3) (pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))) (* (cos phi1) (cos phi1))))
2.0ms
(pow (cos phi1) 3)
10.0ms
(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
17.0ms
(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

series1.1s

Counts
4 → 12
Calls
4 calls:
747.0ms
(/ (+ (pow (cos phi1) 3) (pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))) (* (cos phi1) (cos phi1))))
34.0ms
(pow (cos phi1) 3)
121.0ms
(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
148.0ms
(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

simplify200.0ms

Algorithm
egg-herbie
Counts
257 → 257
Iterations

Useful iterations: 2 (148.0ms)

IterNodesCost
09126973
146076671
250026667

prune729.0ms

Filtered
257 candidates to 98 candidates (38.1%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2525257
Fresh5611
Picked101
Done000
Total25811269

Merged error: 0.1b

Counts
269 → 11

regimes548.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04978
14978

end0.0ms

sample5.1s

Algorithm
intervals
Results
3.1s3535×body1280valid
1.2s2354×body640valid
311.0ms950×body320valid
100.0ms419×body160valid
88.0ms742×body80valid