Details

Time bar (total: 9.4s)

sample177.0ms

Algorithm
intervals
Results
107.0ms117×body1280valid
39.0ms67×body640valid
10.0ms28×body320valid
3.0ms14×body160valid
3.0ms30×body80valid

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: 0.9b

Counts
2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (sin (- lambda1 lambda2)))
0.7b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.0b
(sin (- lambda1 lambda2))
2.1b
(cos (- lambda1 lambda2))

rewrite21.0ms

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:
7.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
4.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(sin (- lambda1 lambda2))
4.0ms
(cos (- lambda1 lambda2))

series212.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
110.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
22.0ms
(sin (- lambda1 lambda2))
20.0ms
(cos (- lambda1 lambda2))

simplify76.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
0249435
1795394
22920393
35001393

prune284.0ms

Filtered
67 candidates to 49 candidates (73.1%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New531467
Fresh000
Picked101
Done000
Total541468

Merged error: 0.7b

Counts
68 → 14

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos lambda1) (sin lambda2))
0.2b
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.7b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.1b
(cos (- lambda1 lambda2))

rewrite23.0ms

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 cos-diff sub-neg distribute-lft-in
2×cos-sum associate-+r+ associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative flip3-- flip3-+ sum-log flip-- flip-+
Counts
4 → 65
Calls
4 calls:
5.0ms
(* (cos lambda1) (sin lambda2))
9.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
4.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))

series316.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (cos lambda1) (sin lambda2))
148.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
105.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
18.0ms
(cos (- lambda1 lambda2))

simplify42.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0343627
11275564
25002563

prune352.0ms

Filtered
77 candidates to 55 candidates (71.4%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New75277
Fresh31013
Picked101
Done000
Total791291

Merged error: 0.1b

Counts
91 → 12

localize32.0ms

Local error

Found 4 expressions with local error:

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)))))
0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.7b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

rewrite20.0ms

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
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative flip3-- flip3-+ sum-log flip-- flip-+ sin-mult
Counts
4 → 61
Calls
4 calls:
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)))))
5.0ms
(* (sin lambda1) (sin lambda2))
9.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
4.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series348.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(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)))))
47.0ms
(* (sin lambda1) (sin lambda2))
148.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
130.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify47.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0340888
11429774
25002773

prune329.0ms

Filtered
73 candidates to 52 candidates (71.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New71273
Fresh2911
Picked101
Done000
Total741185

Merged error: 0.1b

Counts
85 → 11

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b
(exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
0.7b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
0.8b
(log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity add-log-exp
7×pow1
6×add-exp-log exp-prod add-cbrt-cube
4×log-prod log-pow
3×associate-*r* associate-*l*
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/ exp-sum sum-log rem-exp-log
1×+-commutative flip3-- flip3-+ rem-log-exp pow-prod-down prod-exp *-commutative flip-- cbrt-unprod flip-+ unswap-sqr
Counts
4 → 64
Calls
4 calls:
8.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
5.0ms
(exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
4.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
5.0ms
(log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))

series580.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
174.0ms
(exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
128.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
133.0ms
(log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))

simplify43.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0304821
11268727
25002725

prune324.0ms

Filtered
76 candidates to 53 candidates (69.7%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New72476
Fresh1910
Picked101
Done000
Total741387

Merged error: 0.1b

Counts
87 → 13

regimes491.0ms

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
03833
13833

end0.0ms

sample5.5s

Algorithm
intervals
Results
3.4s3578×body1280valid
1.3s2321×body640valid
365.0ms952×body320valid
98.0ms415×body160valid
81.0ms734×body80valid