Details

Time bar (total: 9.2s)

sample193.0ms

Algorithm
intervals
Results
123.0ms125×body1280valid
37.0ms69×body640valid
12.0ms31×body320valid
3.0ms13×body160valid
3.0ms18×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12112
22112

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.7b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.5b
(sin (- lambda1 lambda2))
3.5b
(cos (- lambda1 lambda2))

rewrite20.0ms

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)))))
9.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms
(sin (- lambda1 lambda2))
5.0ms
(cos (- lambda1 lambda2))

series144.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
97.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms
(sin (- lambda1 lambda2))
17.0ms
(cos (- lambda1 lambda2))

simplify118.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0205421
1508375
21327374
33684374
45001374

prune231.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.6b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
3.5b
(sin (- 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×associate-*r* associate-*l*
2×sin-sum
1×+-commutative sub-neg flip3-+ pow-prod-down prod-exp sum-log sin-diff *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 47
Calls
4 calls:
4.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 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)))
5.0ms
(sin (- lambda1 lambda2))

series201.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sin lambda1) (sin lambda2))
14.0ms
(atan2 (* (cos phi2) (sin (- lambda1 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)))
20.0ms
(sin (- lambda1 lambda2))

simplify99.0ms

Algorithm
egg-herbie
Counts
59 → 59
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0260561
1912490
23390489
35001489

prune315.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
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 lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.6b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

rewrite25.0ms

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:
4.0ms
(* (sin lambda1) (sin lambda2))
16.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos 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)))

series323.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (sin lambda1) (sin lambda2))
134.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
17.0ms
(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)))))
124.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify48.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0340888
11429774
25002773

prune381.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
7.2b
(cbrt (* (sin lambda1) (sin lambda2)))
7.2b
(cbrt (* (sin lambda1) (sin lambda2)))
7.2b
(cbrt (* (sin lambda1) (sin lambda2)))

rewrite9.0ms

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×cbrt-prod cbrt-div pow1/3 sin-mult
1×+-commutative flip3-+ sum-log flip-+
Counts
4 → 41
Calls
4 calls:
3.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
2.0ms
(cbrt (* (sin lambda1) (sin lambda2)))
2.0ms
(cbrt (* (sin lambda1) (sin lambda2)))
2.0ms
(cbrt (* (sin lambda1) (sin lambda2)))

series397.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
92.0ms
(cbrt (* (sin lambda1) (sin lambda2)))
91.0ms
(cbrt (* (sin lambda1) (sin lambda2)))
92.0ms
(cbrt (* (sin lambda1) (sin lambda2)))

simplify87.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0191432
1690390
22737371
35001371

prune302.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes459.0ms

Accuracy

0% (0.2b 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
04655
14655

end0.0ms

sample5.7s

Algorithm
intervals
Results
3.4s3565×body1280valid
1.4s2381×body640valid
370.0ms935×body320valid
107.0ms715×body80valid
105.0ms403×body160valid
1.0ms1×body2560valid