Details

Time bar (total: 10.4s)

sample173.0ms

Algorithm
intervals
Results
105.0ms120×body1280valid
38.0ms73×body640valid
10.0ms18×body320valid
3.0ms32×body80valid
3.0ms13×body160valid

simplify5.0ms

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: 1.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (sin (- lambda1 lambda2)))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.7b
(sin (- lambda1 lambda2))
2.7b
(cos (- lambda1 lambda2))

rewrite24.0ms

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:
11.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
3.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(sin (- lambda1 lambda2))
4.0ms
(cos (- lambda1 lambda2))

series193.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
96.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms
(sin (- lambda1 lambda2))
22.0ms
(cos (- lambda1 lambda2))

simplify73.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0249435
1795394
22920393
35001393

prune274.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.2b
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.7b
(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 add-cbrt-cube add-log-exp
3×cos-diff associate-*r* associate-*l*
2×distribute-rgt-in cos-sum associate-+r+ distribute-lft-in flip3-+ associate-*r/ flip-+
1×+-commutative sub-neg pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
Counts
4 → 52
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
12.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
3.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms
(cos (- lambda1 lambda2))

series267.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
140.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
97.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms
(cos (- lambda1 lambda2))

simplify41.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0330767
11333672
25001671

prune359.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

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 associate-+r+ distribute-lft-in flip3-+ associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
1×+-commutative sum-log sin-mult
Counts
4 → 61
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
12.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
4.0ms
(* (sin lambda1) (sin lambda2))
3.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series418.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
138.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
48.0ms
(* (sin lambda1) (sin lambda2))
212.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify50.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0387981
11680847
25001846

prune388.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3))
0.4b
(pow (cos phi1) 3)
0.6b
(pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)
0.8b
(- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt add-cbrt-cube add-log-exp
6×pow-unpow
4×unpow-prod-down cube-prod
3×cube-div pow-pow associate-*r/ pow-exp rem-cube-cbrt
2×cube-mult pow-to-exp flip3-+ unpow3 associate--l+ flip-+ sqr-pow
1×+-commutative distribute-rgt-in sub-neg flip3-- distribute-lft-in diff-log pow-prod-down frac-add prod-exp sum-log cos-mult sum-cubes flip-- cbrt-unprod sin-mult distribute-lft-out
Counts
4 → 75
Calls
4 calls:
11.0ms
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3))
1.0ms
(pow (cos phi1) 3)
7.0ms
(pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)
10.0ms
(- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

series1.6s

Counts
4 → 12
Calls
4 calls:
1.2s
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3))
28.0ms
(pow (cos phi1) 3)
183.0ms
(pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)
210.0ms
(- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

simplify98.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
06001046
12959929
25001929

prune514.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes490.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04965
14965

end0.0ms

sample5.2s

Algorithm
intervals
Results
3.3s3554×body1280valid
1.2s2311×body640valid
327.0ms948×body320valid
102.0ms440×body160valid
78.0ms746×body80valid
1.0ms1×body2560valid