Details

Time bar (total: 7.7s)

sample187.0ms

Algorithm
intervals
Results
111.0ms123×body1280valid
42.0ms70×body640valid
10.0ms27×body320valid
3.0ms14×body160valid
2.0ms22×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12112
22112

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.7b

Counts
2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (sin (- lambda1 lambda2)))
0.4b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.5b
(cos (- lambda1 lambda2))
2.5b
(sin (- lambda1 lambda2))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity sin-sum add-cbrt-cube add-log-exp
4×sub-neg
3×distribute-rgt-in cos-diff distribute-lft-in associate-*r* associate-*l*
2×cos-sum associate-+r+
1×+-commutative flip3-+ pow-prod-down prod-exp sum-log sin-diff *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 55
Calls
4 calls:
6.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
4.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))
4.0ms
(sin (- lambda1 lambda2))

series45.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
23.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))
6.0ms
(sin (- lambda1 lambda2))

simplify69.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0249435
1795393
22920393
35001393

prune147.0ms

Filtered
49 candidates to 67 candidates (-36.7%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New561167
Fresh000
Picked101
Done000
Total571168

Merged error: 0.5b

Counts
68 → 11

localize29.0ms

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)))))
0.4b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.5b
(cos (- lambda1 lambda2))

rewrite18.0ms

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×distribute-rgt-in cos-diff sub-neg distribute-lft-in associate-*r* associate-*l*
2×cos-sum associate-+r+ associate-*r/
1×+-commutative flip3-- flip3-+ pow-prod-down prod-exp sum-log *-commutative flip-- cbrt-unprod flip-+ unswap-sqr
Counts
4 → 54
Calls
4 calls:
9.0ms
(* (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)))))
4.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))

series67.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
10.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
23.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))

simplify114.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0289748
11037658
24438658
35002658

prune129.0ms

Filtered
48 candidates to 66 candidates (-37.5%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New63366
Fresh3710
Picked101
Done000
Total671077

Merged error: 0.1b

Counts
77 → 10

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l* add-log-exp
3×distribute-rgt-in distribute-lft-in
2×sub-neg associate-+r+ associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative flip3-- flip3-+ sum-log flip-- flip-+ sin-mult
Counts
4 → 63
Calls
4 calls:
8.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos 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 phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
4.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series103.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
9.0ms
(* (sin lambda1) (sin lambda2))
13.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
51.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify43.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0345962
11380833
25001833

prune122.0ms

Filtered
52 candidates to 75 candidates (-44.2%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New75075
Fresh099
Picked011
Done000
Total751085

Merged error: 0.1b

Counts
85 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
0.5b
(log (exp (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
2.5b
(cos (- lambda1 lambda2))
2.5b
(sin (- lambda1 lambda2))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-log-exp
5×pow1
4×add-exp-log log-prod log-pow add-cbrt-cube
3×cos-diff exp-prod
2×sub-neg cos-sum associate-+r+ sin-sum
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ rem-log-exp exp-sum sum-log sin-diff flip-+
Counts
4 → 49
Calls
4 calls:
4.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(log (exp (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
4.0ms
(cos (- lambda1 lambda2))
4.0ms
(sin (- lambda1 lambda2))

series54.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
23.0ms
(log (exp (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
4.0ms
(cos (- lambda1 lambda2))
5.0ms
(sin (- lambda1 lambda2))

simplify124.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0221441
1580394
21497394
34376394
45002394

prune78.0ms

Filtered
46 candidates to 61 candidates (-32.6%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New58361
Fresh178
Picked101
Done011
Total601171

Merged error: 0.1b

Counts
71 → 11

regimes622.0ms

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
03022
13022

end0.0ms

sample5.6s

Algorithm
intervals
Results
3.4s3628×body1280valid
1.3s2322×body640valid
355.0ms958×body320valid
95.0ms407×body160valid
73.0ms685×body80valid

Profiling

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